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Risk-sensitive control as inference with Rényi divergence	Accept (poster)	Summary: This paper explores the core research question, "What kind of control problem is solved by control-as-inference (CaI) with Renyi divergence?" The authors characterize the CaI objective that results from replacing Kullback-Leibler (KL) divergence with the more general Renyi divergence. They show that the Renyi order parameter $\alpha$ controls risk-sensitivity of the learned policy and refer to the result as risk-sensitive CaI (RCaI). The paper also proposes a policy gradient method for optimizing the resulting objective via variational inference. An experiment is provided in the Pendulum-v1 environment from OpenAI Gymnasium. Strengths: The paper is relatively well-written, easy-to-read, and the ideas discussed are interesting and appear novel. Risk-sensitive RL / control is an important problem area, and contributions made are likely to have impact. Weaknesses: While the work is interesting the paper lacks a strong motivation. The research question of "what kind of problem is solved by CaI with Renyi divergence?" is interesting enough, but the authors propose no hypothesis or motivation for why one would want to consider Renyi divergence. What is wrong with the existing formulation in terms of KL divergence? I believe that there is a straightforward answer to this question, but the current manuscript does not address it. The resulting RSAC algorithm is somewhat more complicated than the SAC counterpart, and so a strong justification for what is gained by considering RSAC in lieu of SAC, or indeed any of the other risk-sensitive RL approaches, would be necessary. One way to justify the proposed method over existing ones is to empirically demonstrate some advantage. However, the authors do not provide such empirical comparison. There is no comparison of the proposed method(s) to baselines from the literature. The authors only consider a single environment (Pendulum-v1). Moreover, the notion of "risk" is not clear in the chosen environment. Overall the experimental validation needs to be more convincing to recommend publication. The authors should consider more environments, particularly where there is a precise notion of "risk", and compare to baseline methods such as SAC, MBPO, MPO, VMBPO, Mismatched no More, etc. Detailed comments * L284-286 : It is unclear what the authors intend to demonstrate to show that the proposed method "works." It would be helpful to be more specific. What are you showing? * Eq. (23) : The existence of the exponential function in the gradient suggests that learning may be numerically unstable. The authors should address numerical stability of their approach beyond noting it in the conclusion. * L147-151 : These are known results and references should be provided for them Technical Quality: 3 Clarity: 3 Questions for Authors: See "Weaknesses" section Confidence: 5 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: The authors explicitly note some limitations of the work in the Conclusions section. Flag For Ethics Review: ['No ethics review needed.'] Rating: 3 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you very much for your thoughtful comments. > While the work is interesting the paper lacks a strong motivation. . . . risk-sensitive RL approaches, would be necessary. We apologize for the unclear presentation, which misled the reviewer thinking that our motivation was to improve SAC. Our main motivation is to extend the framework of CaI and to provide new theoretical perspectives on CaI. As mentioned in the literature review, there has been an attempt to use a divergence other than the KL divergence for CaI, and it was shown that model predictive control based on the Tsallis divergence outperforms the KL divergence in some situations. Despite this advantage found experimentally, no theoretical properties of CaI with divergences other than the KL divergence were known. In this work, we have discovered that the Renyi divergence is a natural choice for the extension of CaI in the sense that the resulting policy solves the well-known risk-sensitive control problem with exponential utility. In addition to this theoretical discovery, thanks to the proposed unifying framework, we have revealed several equivalences between RCaI, MaxEnt control, the optimal posterior for CaI, and linearly-solvable control. In summary, our main contribution is to establish a unifying framework of CaI based on the Renyi divergence, which improves our theoretical understanding on CaI. Furthermore, the fact that the theoretically established our framework (RCaI) gives risk-sensitive extension of the well-known SAC also strengthens our contribution. Additionally, we would like to emphasize that the derived RSAC algorithm requires only a minor modification to the standard SAC. Indeed, by letting $ \eta = 0 $ in the gradients (34)-(36), we recover SAC. This is an advantage of RSAC because techniques for stabilizing SAC, e.g., reparameterization, target networks, double Q-network, can be directly used for RSAC. We will specify the above in the revised version. > One way to justify the proposed method . . . MPO, VMBPO, Mismatched no More, etc. We sincerely apologize for the lack of explanation. The notion of risk of the risk-sensitive control with exponential utility can be described by minimax robust control, and through the experiment, we aim to show the robustness of policies learned by RSAC for risk-averse cases $ \eta > 0 $. Indeed, for the unregularized case, it is known that risk-sensitive control with $ \eta > 0 $ equivalently solves the following minimax control problem (Petersen, James, Dupuis, (IEEE TAC, 2000)): $$ \\min_{\\{u_t\\}} \max_{\\nu \\in B_d (\\mu)} \\mathbb{E}\_{\\nu} [ c_T(x_T) + \\sum_{t=0}^{T-1} c_t(x_t,u_t) ] ,$$ where $ \mu $ is the reference distribution of the trajectory $ \\{x\_t\\}\_{t=0}^{T} $, $ \\nu $ is the perturbed distribution of $ \\{x\_t\\}\_{t=0}^{T} $, and $ B_d (\\mu) := \\{ \\nu : D_{\\rm KL} (\\nu \\\| \\mu) \\le d \\} $ defines the set of all admissible perturbed distributions $ \\nu $. The radius $ d $ is related to the sensitivity parameter $ \\eta $. This minimax problem optimizes the control considering the worst-case perturbation of the state distributions, which means that the risk-sensitive control with $ \eta > 0 $ is robust against the perturbation of system parameters and the noise. Therefore, RSAC is expected to learn robust policies. However, we have not yet revealed the equivalence between the "regularized" risk-sensitive control and minimax control. The role of the experiment in this paper is to verify the robustness of RSAC, which has not yet been ensured theoretically in this work. Consequently, we have observed the robustness as expected. To make the robustness clearer, we have plotted the empirical distribution of the cost for different $ \\eta $ in Fig. 1 of the attached PDF. Please see the PDF for the discussion of this additional evaluation. It should be noted that the experiment shows RSAC with $ \\eta > 0 $ is more robust than the standard SAC ($ \\eta = 0 $). We believe that the experiment together with this additional evaluation plays a sufficient role in complementing the theoretical contribution of this work. Even though it would be preferable to compare RSAC with methods other than SAC to show its advantages besides the robustness, it is beyond the scope of this work because the focus of this work is on a theoretically established unifying framework of CaI, not on RSAC. We plan to study the properties of RSAC including its numerical issue in a forthcoming paper; please see also the response to the comment on the numerical instability. We will specify the above in the revised manuscript. > L284-286 : It is unclear what the authors intend . . . What are you showing? We apologize for the unclear explanation. As explained above, the experiment is conducted to verify the robustness of policies learned by RSAC. > The existence of the exponential function . . . beyond noting it in the conclusion. First, we would like to emphasize that in the experiment, even for $ \\eta = 0.02 $, where the numerical instability is not problematic, the robustness of the learned policy is improved. Hence, although it is desirable to resolve the numerical instability for large $ \|\\eta\| $, we consider RSAC to be useful enough at the moment to improve the robustness of the policies. It may be possible to alleviate this numerical issue by considering a dual problem associated with the regularized risk-sensitive control as done for resolving the numerical instability of the Sinkhorn algorithm used for solving entropic optimal transport problems. We would like to try this approach in a forthcoming paper, where we aim to reveal the properties of RSAC. Lastly, we would like to emphasize that this issue is not specific to our algorithms, but occurs in general risk-sensitive RL with exponential utility. > L147-151 : These are known results . . . provided for them We would like to cite (Whittle, (John Wiley & Sons, 1990)) for them. --- Rebuttal Comment 1.1: Title: Thanks for the responses Comment: Thank you for the thorough responses. I reviewed my and your comments, as well as re-read the paper and in retrospect feel my score of 2 was a bit harsh. I will upgrade my score to a 3. That said, I think this paper presents nice preliminary work but has some fundamental issues. First, lack of experimental validation. I appreciate the authors' position that this is intended to be a theoretical work, but fundamentally you propose an algorithm and then fail to demonstrate that it is effective in any reasonable settings other than one very limited experiment. All other reviewers call out this weakness and, surprisingly in my opinion, seem to overlook it in their scoring. I would urge other reviewers to reconsider the suitability of this paper for NeurIPS with the present state of experimental validation or lack thereof. The work would have much higher impact if the resulting algorithm were more extensively validated. The second fundamental weakness is that this paper is poorly motivated. The authors give no motivation as to why one would consider Renyi divergence in place of KL divergence beyond citing a few papers that have looked into this. The authors imply that derivation of the exponential risk measure is a contribution, but the equivalence of CaI (or equivalently RL-as-inference) and the exponential utility is well-known. Here are a few papers that show this relationship: * Equation (8) : O'Donoghue, Brendan. "Variational bayesian reinforcement learning with regret bounds." Advances in Neural Information Processing Systems 34 (2021): 28208-28221. * Appendix A.1 : Eysenbach, Benjamin, et al. "Mismatched no more: Joint model-policy optimization for model-based rl." Advances in Neural Information Processing Systems 35 (2022): 23230-23243. * Noorani, Erfaun, Christos Mavridis, and John Baras. "Risk-sensitive reinforcement learning with exponential criteria." arXiv preprint arXiv:2212.09010 (2022). --- Reply to Comment 1.1.1: Title: Thank you for your additional comments Comment: Thank you for introducing the papers. Nevertheless, they do not provide the equivalence between CaI and risk-sensitive control with exponential utility in a satisfactory manner. Detailed explanations are as follows. > Equation (8) : O'Donoghue, Brendan. "Variational bayesian reinforcement learning with regret bounds." Advances in Neural Information Processing Systems 34 (2021): 28208-28221. Equation (8) of the above paper is a well-known result that for a given function $ K_l^t $, the optimal value of the entropy-regularized optimization problem takes the form of the exponential utility. However, the fact that the optimal value is given by the exponential utility does not imply the equivalence between the MaxEnt control (CaI using the KL divergence) and the risk-sensitive control. Although the exponential utility function is utilized in this paper, the risk-sensitive control problem is not addressed, and thus, the relationship between CaI and the risk-sensitive control is not revealed at all. > Appendix A.1 : Eysenbach, Benjamin, et al. "Mismatched no more: Joint model-policy optimization for model-based rl." Advances in Neural Information Processing Systems 35 (2022): 23230-23243. As mentioned in Appendix B.1 (A.1 may be incorrect) of the above paper, VMBPO solves a risk-seeking control problem with exponential utility. For the variational inference of the distribution of the state and control input trajectory, VMBPO uses the variational distribution whose transition distribution is not fixed. This setting essentially results in the risk-seeking (optimistic) policies as known in (S. Levine, arXiv:1805.00909, 2018). However, we would like to emphasize that from this setting, we cannot derive the equivalence between CaI and risk-averse control problems. Our result does not have this restriction, which implies that for connecting the risk-sensitive control and probabilistic inference, CaI using the Renyi divergence is a more appropriate framework. > Noorani, Erfaun, Christos Mavridis, and John Baras. "Risk-sensitive reinforcement learning with exponential criteria." arXiv preprint arXiv:2212.09010 (2022). In the above paper, the equivalence between a risk-sensitive control problem and a maxmini control problem with KL regularization is shown (Corollary 1). Although this result is interesting, it is not related to the equivalence between CaI and the risk-sensitive control. Additionally, in Remark 1, it is mentioned that by making "heuristic assumptions" on the measure $P_\mu$, the MaxEnt control objective can be reconstructed by the risk-sensitive control objective. However, these heuristic assumptions suppose that the distribution of the optimal trajectory of the state and the action is uniform, which is not satisfied in general. Our equivalence result does not require such unrealistic assumptions. This fact also clarifies that for connecting the risk-sensitive control and probabilistic inference, CaI using the Renyi divergence is a more appropriate framework. We also would like to emphasize that the above paper does not show the relationship between the risk-sensitive control and probabilistic inference. We would like to add the above explanations to the revised version. If there are any other papers we should comment on, we would be grateful if you could share them with us. If you understand our equivalence results (please see Fig. 1), you will also understand their importance, and the above responses further clarify our theoretical contributions of extending CaI to RCaI. Our approach using the Renyi divergence enables the risk-sensitive extension of CaI, which cannot be attained by the previous approaches as explained above. If you still think our motivation is weak even considering the above responses, we do not know what motivation is needed beyond the following facts: - Using a divergence other than the KL divergence in model predictive control as inference gives good experimental results (Wang, So, Gibson, et. al., in Robotics: Science and Systems, 2021). - Variational inference using divergences other than the KL divergence has been well studied in the machine learning community. > The work would have much higher impact if the resulting algorithm were more extensively validated. We agree with this, and we are sorry that we were not able to conduct additional experiments. However, we would like to emphasize again that the proposal of the RL algorithms is a byproduct of RCaI. Experiments are not essential to demonstrate the correctness and the significance of the theoretical results. Even though there is room for additional evaluations of the algorithms, we believe our theoretical contributions are enough to be considered for publication in NeurIPS, which publishes many theoretical papers. --- Rebuttal 2: Title: Thanks for the responses Comment: Thanks for taking the time to respond to my concerns. Due to my reviewer load I do not have time to respond to all of your comments, but will respond to the high-priority items. > "This setting essentially results in the risk-seeking (optimistic) policies...we cannot derive the equivalence between CaI and risk-averse control problems." The authors show the (well-known) equivalence to the entropic risk objective. Equivalence to the entropic risk objective is sufficient to show, both, risk-seeking and risk-averse control. Note that the entropic risk objective is the cumulant generating function and thus (by Taylor series) is equivalent to (in your notation and as shown on L148-149): $$\frac{1}{\eta} \log \mathbb{E}[\exp(\Phi(\tau))] = \mathbb{E}[\Phi(\tau)] + \frac{\eta}{2} Var[\Phi(\tau)] + O(\eta^2)$$ From this equivalence it is clear that positive $\eta$ biases towards policies that have higher return variance (i.e. risk-seeking) and negative $\eta$ biases towards policies with lower return variance (i.e. risk-averse). Discussion in the CaI (and RL-as-inference) literature is centered on risk-seeking policies because they are more problematic, but risk-averse policies are easily obtainable from the formulation. > "We agree with this, and we are sorry that we were not able to conduct additional experiments." The present state of experimental validation is far below the standard set by NeurIPS, despite this being a theoretically oriented paper. This opinion is shared by all reviewers, but we differ in how we consider the impact of this in our scoring. I appreciate the nature of tight deadlines but, at the end of the day, the experimental validation is simply below standard in my opinion and I cannot argue for acceptance in good conscience. That said, I do think this line of work has merit and should be further developed. --- Rebuttal Comment 2.1: Title: Thank you again for your response Comment: Thank you for your response despite your reviewer load. > Equivalence to the entropic risk objective is sufficient to show, both, risk-seeking and risk-averse control. We would like to explain that this comment is incorrect and that the difference between the previous work and ours is significant, which means RCaI is the appropriate risk-sensitive extension of CaI. VMBPO maximizes the entropic risk objective $ \frac{1}{\eta} \log \mathbb{E} [\exp(\eta \Phi(\tau))] $. However, we would like to emphasize that the equivalence for VMBPO holds only for positive $\eta$ resulting in risk-seeking policies. Tricks such as the change of variables do not work to obtain risk-averse policies by VMBPO. Risk-averse policies ($\eta < 0$) cannot be obtained by their approach inherently. The risk-seeking property of the policies obtained by CaI whose variational distribution does not fix its transition distribution, is intrinsic. This is why we mentioned that we cannot derive the equivalence between CaI and risk-averse control problems from VMBPO. To derive the equivalence between CaI and risk-sensitive control for both risk-seeking and risk-averse cases, we need a fundamentally different approach from the previous work, and the solution we discovered is CaI using the Renyi divergence. Our equivalence can deal with both risk-seeking ($\eta > 0$) and risk-averse ($\eta < 0$) policies. This is a significant difference between the previous work and our result. This difference is crucial because the robustness of risk-averse policies is important for applications. For reference, we would like to note that in Appendix B.1 of the following suggested paper, the risk-sensitivity parameter $ \eta $ is restricted to be positive (risk-seeking). This is not for simplicity, but negative sensitivity (risk-averse) parameters cannot be dealt with in the framework used by VMBPO. > Eysenbach, Benjamin, et al. "Mismatched no more: Joint model-policy optimization for model-based rl." Advances in Neural Information Processing Systems 35 (2022): 23230-23243.	Summary: The paper generalizes the control as inference framework to the risk-sensitive setting using Renyi divergence variational inference. This yields a cost function with an exponential utility and log-probability regularization, weighted by the Renyi divergence parameter $\eta$. From the Taylor expansion of the cost, we can see that $\eta$ controls the level to which we are risk-averse or risk-seeking. And when $\eta$ goes to zero, we recover the traditional MaxEnt control problem. Next, the authors show that the risk-sensitive optimal policy can be obtained by solving the soft Bellman equation, which relates it to many existing methods. They also show that for deterministic dynamics, their framework, RCaI, and MaxEnt give the same optimal policy. The authors then develop RCaI versions of the policy gradient and soft actor-critic algorithms. They also show that using Renyi entropy regularization in place of the standard KL divergence in maximum entropy control yields an optimal policy with the same structure. Finally, they provide a proof-of-concept experiment on the classical Pendulum benchmark using their risk-sensitive SAC algorithm. They show that the choice of risk-sensitivity parameter can improve robustness to dynamics mismatch. Strengths: - RCaI is a novel formulation of risk-sensitive control using the control-as-inference framework with a unique choice of divergence metric. They derive two RL algorithms from this framework, a policy gradient and soft actor-critic algorithm, which are easily swapped in for their risk-neutral equivalents. - The authors show that RCaI actually generalizes the MaxEnt formulation to incorporate risk sensitivity. They also show many interesting properties of the optimal policy and how it relates to existing approaches. - They show experimentally that RCaI may yield improvements in robustness by introducing the risk-sensitivity term. - The paper is well organized and overall written well. It provides a thorough related work section and does a good job explaining the novelty and results. Weaknesses: - The experimental evaluation is sparse, with only one simple task and no baselines other than RSAC with $\eta=0$. They also do not evaluate the policy gradient method and contrast it with RSAC. Technical Quality: 3 Clarity: 4 Questions for Authors: - How does the risk-sensitive policy gradient method compare to RSAC and REINFORCE? Confidence: 4 Soundness: 3 Presentation: 4 Contribution: 3 Limitations: The authors discuss limitations of their method in the conclusions. Specifically, they discuss the numerical instability of their method for large $\eta$ cases. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you very much for your thoughtful comments. > The experimental evaluation is sparse, with only one simple task and no baselines other than RSAC with $ \eta = 0 $. They also do not evaluate the policy gradient method and contrast it with RSAC. We sincerely apologize for the lack of explanation. First, we would like to clarify the purpose of the experiment in this work. The notion of risk of the risk-sensitive control with exponential utility can be described by minimax robust control, and through the experiment, we aim to show the robustness of policies learned by RSAC for risk-averse cases $ \\eta > 0 $. Indeed, for the unregularized case, it is known that risk-sensitive control with $ \\eta > 0 $ equivalently solves the following minimax control problem [R1]: $$ \\min_{\\{u_t\\}} \\max_{\nu \\in B_d (\\mu)} \\mathbb{E}\_{\\nu} [ c_T(x_T) + \\sum_{t=0}^{T-1} c_t(x_t,u_t) ], $$ where $ \\mu $ is the reference distribution of the trajectory $ \\{x_t\\}\_{t=0}^{T} $, $ \nu $ is the perturbed distribution of $ \\{x_t\\}\_{t=0}^{T} $, and $ B_d (\\mu) := \\{ \\nu : D_{\\rm KL} (\\nu \\\| \\mu) \\le d \\} $ defines the set of all admissible perturbed distributions $ \\nu $. The radius $ d $ is related to the sensitivity parameter $ \\eta $. This minimax problem optimizes the control considering the worst-case perturbation of the state distributions, which means that the risk-sensitive control with $ \\eta > 0 $ is robust against the perturbation of system parameters and the noise. Therefore, RSAC is expected to learn robust policies. However, we have not yet revealed the equivalence between the "regularized" risk-sensitive control and minimax control. The role of the experiment in this paper is to verify the robustness of RSAC, which has not yet been ensured theoretically in this work. Consequently, we have observed the robustness as expected. As an additional evaluation, we have plotted the empirical distributions of the cost under RSAC for different $ \\eta $ in Fig. 1 of the attached PDF. As can be seen, only the distribution for $ \\eta = 0.02 $ does not change so much under the system perturbations. The distribution for SAC ($ \\eta = 0 $) with $ l = 1.5 $ deviates from the original one ($ l = 1.0 $), and another peak of the distribution appears in the high-cost area. This means that there is a high probability of incurring a high cost, which clarifies the advantage of RSAC. On the other hand, the more risk-seeking the policy becomes, the less robust against the system perturbation it becomes. However, at the expense of the robustness, for $ l = 1.25 $, the policy with $ \\eta = -0.02 $ yields a high probability in the low-cost area (from cost $ =20 $ to $ {\rm cost} = 80 $). We believe that the experiment together with this additional evaluation plays a sufficient role in complementing the theoretical contribution of this work. Even though it would be preferable to compare RSAC with any other methods to show its advantages besides the robustness, it is beyond the scope of this work because our main motivation is to extend the framework of CaI and to provide new theoretical perspectives on CaI. We plan to study the properties of RSAC in a forthcoming paper. [R1] I. R. Petersen, M. R. James, and P. Dupuis, "Minimax optimal control of stochastic uncertain systems with relative entropy constraints," IEEE Transactions on Automatic Control, vol. 45, no. 3, 2000. > How does the risk-sensitive policy gradient method compare to RSAC and REINFORCE? We are very sorry that we were not able to conduct the additional experiment of the derived risk-sensitive REINFORCE in time for the rebuttal. However, we would like to mention that REINFORCE suffers from high variance, delayed updates, and less sample efficiency, and SAC generally outperforms REINFORCE in a wide range of environments. Hence, it is expected that RSAC also outperforms the derived risk-sensitive REINFORCE. For the comparison between the risk-sensitive REINFORCE and the standard REINFORCE, the previous work [20] showed that by using an appropriate sensitivity parameter $ \\eta $, the risk-sensitive REINFORCE learns faster and has lower variance than the standard REINFORCE for the unregularized case. The regularized risk-sensitive REINFORCE derived in this paper will have similar properties to the unregularized risk-sensitive REINFORCE because the only difference between the regularized and unregularized REINFORCE methods is the presence of the log-probability term in the policy gradient. [20] E. Noorani and J. S. Baras, "Risk-sensitive REINFORCE: A Monte Carlo policy gradient algorithm for exponential performance criteria," in 2021 60th IEEE Conference on Decision and Control (CDC), pp. 1522-1527, 2021.	Summary: This paper considers the control as inference framework of RL. Instead of minimizing the KL which is commonly done in control as inference (and has been shown to be equivalent to MaxEnt RL), they consider minimizing the Rényi divergence. They prove that this minimization is equivalent to minimizing a functional similar to the entropic risk measure, and show that the order of the Rényi divergence controls the risk behaviour of the policy obtained (averse/neutral/seeking). They then show that this minimization over policies is equivalent to solving a soft Bellman equation. They then take another route of generalizing maximum entropy control, by replacing the standard entropy with Rényi entropy, which they prove is also optimized by the same soft Bellman equation. They then show how this can be transformed into an implementable algorithm, by introducing a variant of policy gradient and soft actor-critic for their formulation. They round out their work with an experiment section to illustrate properties of their algorithm at varying levels of risk sensitivity. Strengths: I find this paper to be clearly written, and guides the reader through their contributions. The theoretical results and their proof also flow nicely and are clearly presented. I think that taking the two paths to generalize MaxEnt RL (replacing the minimization of the KL with Rényi and replacing the entropy regularization with Rényi entropy regularization) is a very nice approach and makes a strong case for why this is a natural generalization. Overall I think this is an interesting theoretical work and extension to the MaxEnt RL framework, and I think it can inspire future work. Weaknesses: I believe that the major weakness of this work is the experiment section. I understand the goal of this work is mainly theoretical, however, I believe the current experiments are unmotivated, and do not complement the theoretical results. In particular, there is currently only a single experiment, which I believe to be unfit for the following reasons: - the experiment measures the generalization across environments of the algorithm at different levels of $\eta$. I am quite surprised by this, as none of the theoretical results discuss generalization across environments. - the theoretical results prove that the algorithm optimizes a quantity that does not solely depend on the expectation of the cost function, but the plot shows the average cost obtained by the algorithm. - touching on the previous point, I think that what the experiment section can be quite helpful for, which it currently lacks, is provide the reader with a more intuitive understanding of the level of risk sensitivity as a function of $\eta$. For example, perhaps one could plot the empirical distributions of returns obtained for different $\eta$ (so that one can visualize the difference between risk-seeking/neutral/averse, and how continuous this behaviour is wrt $\eta$). - there is only a single environment used (Pendulum-v1), with no justification as to why this was chosen. I believe that if the experiment section can be improved in the ways I highlighted above, the paper has the potential to be more interpretable and impactful, and I would be happy to update my score to reflect this. Technical Quality: 4 Clarity: 3 Questions for Authors: - It is written that for large $\|\eta\|$ the algorithm is unstable. In the experiments, the largest $\|\eta\|$ used is .02. Is the algorithm unstable for $\eta$ larger than this? A better understanding of what range $\eta$ can safely take would be helpful. - There have been a number of risk-senstive soft actor critic algorithms proposed in recent years, none of which are referenced in this paper. Is there a reason why you haven't mentioned them, and compared/contrasted your proposed algorithm to them? Confidence: 4 Soundness: 4 Presentation: 3 Contribution: 3 Limitations: The authors adequately discuss the limitations, and list them as items for future work (such as numerical instability for large $\|\eta\|$). Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you very much for your thoughtful comments. > the experiment measures the generalization . . . discuss generalization across environments. We apologize for the lack of explanation. Through the experiment, we aim to show the robustness of policies learned by the risk-sensitive soft actor-critic (RSAC) for risk-averse cases $ \\eta > 0 $. Indeed, for the unregularized case, it is known that risk-sensitive control with exponential utility solves a robust control problem (Petersen, James, Dupuis, (IEEE TAC, 2000)). Specifically, risk-sensitive control with $ \\eta > 0 $ equivalently solves the following minimax control problem: $$ \\min_{\\{u_t\\}} \\max_{\\nu \\in B_d (\\mu)} \mathbb{E}\_{\\nu} [ c_T(x_T) + \\sum_{t=0}^{T-1} c_t(x_t,u_t) ], $$ where $ \\mu $ is the reference distribution of the trajectory $ \\{x_t\\}\_{t=0}^{T} $, $ \\nu $ is the perturbed distribution of $ \\{x_t\\}\_{t=0}^{T} $, and $ B_d (\mu) := \\{ \\nu : D_{\\rm KL} (\\nu \\\| \\mu) \\le d \\} $ defines the set of all admissible perturbed distributions $ \\nu $. The radius $ d $ is related to the sensitivity parameter $ \\eta $. This minimax problem optimizes the control considering the worst-case perturbation of the state distributions, which means that the risk-sensitive control with $ \\eta > 0 $ is robust against the perturbation of system parameters and the noise. Therefore, RSAC is expected to learn robust policies, which generalize well across environments. However, we have not yet revealed the equivalence between the "regularized" risk-sensitive control and minimax control. The role of the experiment in this paper is to verify the robustness of RSAC, which has not yet been ensured theoretically in this work. Consequently, we have observed the robustness as expected. We will add the above explanation to the revised manuscript. > the theoretical results prove that . . . one could plot the empirical distributions of returns obtained for different $ \eta $ Following your suggestion, we have plotted the empirical distributions of costs for different $ \eta $ in Fig. 1 of the attached PDF. As can be seen, only the distribution for $ \eta = 0.02 $ does not change so much under the system perturbations. The distribution for SAC ($ \eta = 0 $) with $ l = 1.5 $ deviates from the original one ($ l = 1.0 $), and another peak of the distribution appears in the high-cost area. This means that there is a high probability of incurring a high cost, which clarifies the advantage of RSAC. On the other hand, the more risk-seeking the policy becomes, the less robust against the system perturbation it becomes. However, at the expense of the robustness, for $ l = 1.25 $, the policy with $ \eta = -0.02 $ yields a high probability in the low-cost area (from cost $ =20 $ to $ {\rm cost} = 80 $). We will add the evaluation of the empirical distributions to the revised manuscript. We appreciate your suggestion. > there is only a single environment used (Pendulum-v1), with no justification as to why this was chosen. We are very sorry that we were not able to conduct an additional experiment on a different environment in time for the rebuttal. As mentioned above, the purpose of the experiment is to verify the robustness of RSAC, which has not been proved theoretically in this paper. Although it would be preferable to use several environments, we believe that the experiment together with the additional evaluation of the empirical distributions plays a sufficient role in complementing the theoretical contribution of this work. > I believe that if the experiment section can be improved in the ways I highlighted above, the paper has the potential to be more interpretable and impactful, and I would be happy to update my score to reflect this. We hope the additional evaluation and the responses have made our work more interpretable and impactful. > It is written that for large $ \|\eta\| $ the algorithm is unstable. . . . A better understanding of what range $ \eta $ can safely take would be helpful. Since $ \eta $ appears, for example, as $ \exp(\eta Q^{(\phi)}(x_t,u_t)) $ in the gradients (34)-(36), the magnitude of $ \eta $ that does not cause the numerical instability depends on the scale of the reward (cost). Therefore, we need to choose $ \eta $ depending on environments. In the experiment using Pendulum-v1, $ \|\eta\| $ that is larger than $ 0.03 $ results in the failure of learning due to the numerical instability. We would like to emphasize that this issue is not specific to our algorithms, but occurs in general risk-sensitive reinforcement learning with exponential utility. Thank you for your suggestion. We will add the above explanation to the revised version. > There have been a number of risk-sensitive soft actor critic algorithms . . . Is there a reason why you haven't mentioned them, and compared/contrasted your proposed algorithm to them? This is because in this paper, we focus on the risk sensitivity induced by the exponential performance criteria. To the best of our knowledge, the only work that proposes a risk-sensitive soft actor-critic type algorithm for the exponential utility is (Enders, Harrison, Schiffer, (arXiv:2402.09992, 2024)) mentioned in the manuscript. If you know of any other references and could share them with us, we sincerely appreciate it. If we should mention another type of risk-sensitive soft actor-critic, we would like to add the references (Duan, Guan, Li, Ren, Sun, Cheng, (IEEE TNNLS, 2021), (Choi, Dance, Kim, Hwang, Park, (ICRA, 2021)), which consider risk by distributional RL, to the manuscript. An advantage of RSAC over other risk-sensitive approaches including the distributional RL is that we only need minor modifications to the standard SAC. Thanks to this, techniques for stabilizing SAC, e.g., reparameterization, minibatch sampling with a replay buffer, target networks, double Q-network, can be directly used for RSAC.	Summary: In this paper, the authors consider a risk-sensitive control problem with Renyi divergence. The contributions are primarily theoretical with some rudimentary experiments. The contributions include connection to risk-sensitive control under exponential cost formulation, with Renyi divergence leading to an additional regularization term. Extensions to a RL setting with a policy gradient theorem and an actor-critic version are proposed. An alternative risk-senstive control problem with Renyi entropy is discussed. Strengths: - Tackles an important risk-sensitive control problem and makes advances by employing a general divergence measure - Connections to exponential utility formulation Weaknesses: - Some bits of RL extension are unclear to me (see questions below). Technical Quality: 3 Clarity: 3 Questions for Authors: 1. The policy gradient theorem in Prop 7 has an expectation over trajectories. Does this mean for one update to the policy parameter, an entire trajectory needs to be simulated? In other words, is there a REINFORCE variant that updates after every sample transition? 2. The soft-actor critic extension is unclear to me. Does the proposed soft actor critic algorithm with gradient estimates in (34)-(36)? If yes, can you characterize the limiting policy wrt risk-sensitivity? What about compatibility issues that one usually sees with actor-critic algorithms that employ function approximation? 3. While this may be outside the scope of this work, can you comment on extensions to a long-run average cost formulation, with Renyi divergence? Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: None Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you very much for your thoughtful comments. We sincerely appreciate your positive evaluation. > The policy gradient theorem in Prop 7 has an expectation over trajectories. Does this mean for one update to the policy parameter, an entire trajectory needs to be simulated? In other words, is there a REINFORCE variant that updates after every sample transition? We are not entirely certain whether the derived risk-sensitive REINFORCE can be extended to the one that updates the policy parameter after every sample transition because we do not know of the specific literature that the reviewer has in mind. Nevertheless, we expect that such extension is possible because the policy gradient (23) for the regularized risk-sensitive control is structurally the same as the standard policy gradient for the risk-neutral control. That is, by replacing the exponential of the accumulated cost $ \\exp(\\eta c_T(x_T) + \\eta \\sum_{s=t}^{T-1} (c_s(x_s,u_s) + \\log \\pi^{(\\theta)} (u_s \| x_s))) $ in (23) by $ c_T(x_T) + \\sum_{s=t}^{T-1} (c_s(x_s,u_s) + \\log \\pi^{(\\theta)} (u_s \| x_s)) $, we recover the standard REINFORCE with regularization. > The soft-actor critic extension is unclear to me. Does the proposed soft actor critic algorithm with gradient estimates in (34)-(36)? If yes, can you characterize the limiting policy wrt risk-sensitivity? Yes, the proposed soft actor-critic estimates the gradient by the sample approximation of (34)-(36). For example, the gradient estimate of $ \\nabla_\\phi \mathcal{J}\_Q(\\phi) $ is given by $ (\\nabla_\\phi Q^{(\\phi)}(x_t,u_t)) \\exp(\\eta Q^{(\\phi)}(x_t,u_t) - \\eta c(x_t,u_t)) \\{ T_\\eta (Q^{(\\phi)}(x_t,u_t) - c(x_t,u_t)) - T_\\eta( V^{(\\psi)}(x_{t+1}) ) \\} $, where $ x_t $, $ u_t $, and $ x_{t+1} $ are samples. Although we do not yet know how to analyze the limiting policy learned by the proposed soft actor-critic algorithm, it is interesting to investigate the relationship between the risk-sensitivity parameter $ \eta $ and the robustness of the limiting policy. We appreciate your insightful comment, and we would like to study it in future work. > What about compatibility issues that one usually sees with actor-critic algorithms that employ function approximation? The compatible function approximation theorem can be extended to the proposed soft actor-critic algorithm. For the standard actor-critic algorithm, the compatibility of a function approximator $ Q^{(\\phi)} $ is defined by the condition $ \\nabla_\\phi Q^{(\\phi)} (x,u) = \\nabla_\\theta \\log \\pi^{(\\theta)} (u_t\|x_t) $ [R1]. For the proposed risk-sensitive soft actor-critic (RSAC), the compatibility condition is modified as $ \\nabla_\\phi Q^{(\\phi)} (x,u) \\exp(\\eta Q^{(\\phi)} (x,u) - \\eta c(x,u)) = \\nabla_\\theta \\log \\pi^{(\\theta)} (u_t\|x_t) $, where $ \\eta $ is the risk-sensitivity parameter. By letting $ \\eta = 0 $, we recover the standard compatibility condition. We would like to omit the detail of the compatible function approximation theorem for RSAC because we plan to study the properties of RSAC in a forthcoming paper. [R1] R. S. Sutton, D. McAllester, S. Singh, and Y. Mansour, "Policy gradient methods for reinforcement learning with function approximation," Advances in Neural Information Processing Systems, vol. 12, pp. 1057-1063, 1999. > While this may be outside the scope of this work, can you comment on extensions to a long-run average cost formulation, with Renyi divergence? There will be several technical difficulties in dealing with the regularized risk-sensitive control (reinforcement learning) for the long-run average cost by the same reason as for the unregularized case [29, R2]. Even so, we expect that similar results to ours will hold for the long-run average problems, that is, the regularized risk-sensitive control problem with long-run average cost will boil down to solving a soft Bellman equation, and this leads to risk-sensitive soft actor-critic for long-run average cost. We would like to tackle this important and challenging extension in future work. [29] V. S. Borkar, "Q-learning for risk-sensitive control," Mathematics of Operations Research, vol. 27, no. 2, pp. 294-311, 2002. [R2] A. Biswas and V. S. Borkar, "Ergodic risk-sensitive control--a survey," Annual Reviews in Control, vol. 55, pp. 118-141, 2023.	Rebuttal 1: Rebuttal: We have attached a PDF file with the experimental results of the empirical distributions of cost under the derived risk-sensitive soft actor-critic. Pdf: /pdf/147a3077ad9b5938c5b3f3aa018803a0c9a6a86e.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
On provable privacy vulnerabilities of graph representations	Accept (poster)	Summary: This paper investigates the ability of the similarity-based edge reconstruction attack (SERA) on attacking both sparse and dense networks, under various configurations of graph neural network (GNN) structures. The authors demonstrate, through both theoretical analysis and experimental results, that SERA performs well on sparse networks but poorly on dense networks. Additionally, they demonstrate the effectiveness of the noisy aggregation (NAG) technique on the resilience of SERA. Strengths: This is a initial work to take a step towards a principled theoretical understanding of the effectiveness of SERA over sparse/dense features and different configurations of linear GNN. The theoretical results are presented in a clear and sound way. The proof is rigorous and clearly demonstrated. The explainations following each theorem give good supplements to the theory. Weaknesses: 1. Writing Quality: The writing in this paper needs improvement. The authors have used many unnecessarily complex words and sentences, making the paper harder to read and understand. Additionally, there are numerous typos and grammatical errors that need to be corrected. 2. Theoretical Analysis Limitation: The theoretical analysis focuses on linear GNNs rather than non-linear GNNs. While the authors have shown experimentally that results for linear GNNs can serve as proxies for those of non-linear GNNs, the guarantee of this is unclear to me. 3. Rationale for Studying SERA: In section 2.1, the authors mention that there are attacks more powerful than SERA. This raises the question of why they chose to study SERA in the first place. 4. Accuracy of Statistic in experiment: In Table 1, the authors measure the similarity between feature similarity and edge presence using a statistic $\mathcal{H}$, which only evaluates the similarity of features between nodes with an edge. It does not consider nodes without an edge, leading me to question the accuracy of the statistic to measure similarity and thus the results analysis. In my opinion, it should also capture the dissimilarity of features between nodes without an edge. Technical Quality: 3 Clarity: 2 Questions for Authors: (1) In line 286, it is stated, "Yet the behaviors in small d regimes appear to be less predictable, a phenomenon we hypothesize may be attributable to an inadequate concentration of inner products in instances where the feature dimension is relatively small." Can the authors explain in detail what this means? Confidence: 3 Soundness: 3 Presentation: 2 Contribution: 2 Limitations: None Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your valuable comments, we will integrate your suggestions into revised versions of our paper. Below we address some specific points: ## Q1: About the writing style Thank you for the advice and we will polish our writing to improve clarity and conciseness. ## Q2: On the limitations of study linear GNNs Please kindly refer to the first point in our global response. Firstly, it is quite challenging to directly analyze the performance of nonlinear GNNs, especially when the underlying GNNs are with more than 1 layers and the dependence on network depth is a critical factor of the study. Secondly, linear GNNs such as SGC constitute an important type of GNN architecture in practice. By characterizing the provable privacy vulneratbilities of such kind of GNNs, we reveal the threats that can potentially break the privacy of linear graph representations. Lastly, it remains to investigate that whether the inclusion of nonlinearity can mitigate the threat. While answering this question is hard in theory, we conducted extensive experiments demonstrating that nonlinear GNNs are often more vulnerable than linear GNNs. ## Q3: Rationale of studying SERA We chose SERA as the object of our analysis because of it is training-free, and requires a moderate level of adversary knowledge (node embeddings). There exists attacks with higher empirical attacking performance than SERA that utilizes additional knowledge (i.e., a certain part of input graph has already been compromised [1]) and a more sophisticated attacking procedure (i.e., training a shadow model [1]). In this paper, we take a first step toward establishing the vulnerabilities of graph representations in a theoretically principled way by studying the performance of SERA. For those attacks that are more sophisticated than SERA, it is an interesting question to study the improvement of attacking performance by quantitatively characterize the advantage of side information or auxiliary training, which is beyond the scope of our paper and we leave them for future explorations. ## Q4: Accuracy of experiment We agree with you that the definition of feature homophily is not suitable as a proper metric for describing the correlation between edge existence and node feature similarity. We include this metric primarily because this one is defined in previous works [2] and we list it mainly for completeness. The metric that indeed reflect the correlation is the $\widehat{A}^{\text{FS}}$ in table 1, which stands for tha AUC score between feature similarity and edge existence, that takes both edges and non-edges into account. We base most of our empirical findings regarding table 1 on the $\widehat{A}^{\text{FS}}$ metric. Please kindly refer to the experimental observations in section 7.1 ## Q5: Explaination of the statement in line 286 We appologize for making the statement too difficult to parse, and we shall restate the claim in revisions of our paper. By this statement, we want to express the following: - When $d$ is small (so that the assumptions in theorem 4.1 no longer holds), the claims in theorem 4.1 no longer holds empirically, as the attacking performances are limited (i.e., AUC score $\le 80\\%$). - We further explain why the phenomenon of limited attacking performance in small $d$ regime stems from: In our analysis, one primary mathematical tool is the concentration of inner products of two Gaussian vectors, which is highly dependent on the dimension of the two vectors (i.e., the feature dimension). When the concentration is insufficient (a consequence of small $d$), our analysis would then be no longer correct and this partly explains why the attacking performance is limited in small $d$ regimes. [1] He, Xinlei, et al. "Stealing links from graph neural networks." 30th USENIX security symposium (USENIX security 21). 2021. [2] Luan, Sitao, et al. "When do graph neural networks help with node classification? investigating the homophily principle on node distinguishability." Advances in Neural Information Processing Systems 36 (2023).	Summary: The paper studies the performance of similarity-based edge reconstruction attacks (SERA) for graph representations, considering two particular similarity measures (cosine and correlation). The main contributions are presented in Theorem 4.1 and Theorem 5.1, which analyze the performance of SERA on graph representations (without privacy-preservation techniques applied), and in Theorem 6.1, which considers noise aggregation (NAG) for privacy-preservation. Strengths: See my comments in Weaknesses Weaknesses: My concerns are as follows: While I appreciate the efforts in deriving generalization bounds for this specific attack model, the implications of this paper remain insignificant to me. The results in Theorem 4.1 and Theorem 5.1 seem too straightforward, as they can be immediately inferred from the perspective of detection theory. For instance, focusing on the linear graph neural network in Equation (1), Theorem 4.1 essentially states that the accuracy of correlation detection grows with increasing samples. There are certainly existing works that have already characterized the statistical performance of link prediction in more general and profound ways, rather than fixing the detection method and linear aggregation as assumed in Theorems 4.1 and 5.1. Please refer to the papers "Revisiting Link Prediction: A Data Perspective" and "Statistical Guarantees for Link Prediction using Graph Neural Networks." Theorem 5.1 also appears trivial. For example, the paper "GAP: Differentially Private Graph Neural Networks with Aggregation Perturbation" had already characterized the level of differential privacy for edge prediction. There is extensive literature connecting detection accuracy with differential privacy. For example, you can derive mutual information and then obtain the detection error bound by applying Fano's inequality (assuming the prior distribution of the graph representations, as stated in your paper). My question is, what is the new observation from Theorem 6.1? Technical Quality: 2 Clarity: 2 Questions for Authors: Lines 109-118: The description of the two-party attack model is confusing. I had to read the model description in the Appendix to understand it. Please keep the writing concise and precise to improve readability. Lines 31-36: Can you explain how "feature similarity may serve as a confounding factor, potentially impacting the efficacy of similarity-based attacks"? This statement contradicts the previous sentence. Line 156: $\Theta$ is not defined. Confidence: 4 Soundness: 2 Presentation: 2 Contribution: 2 Limitations: The authors adequately addressed the limitations in the Appendix. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your valuable comments. We appreciate your mentioning the two related works and we will include them in the related works of our paper with careful discusssions. As both of them focus on link prediction, we would like to make the following clarification first: ## In theory, link prediction is related to, but different from edge reconstruction Theoretically speaking, the problem of link prediction is formulated as the design of some algorithm $\mathcal{A}$ that takes input a known graph topology $A$ and some auxiliary features $X$ and output a predictor that is able to infer either missing edges in the training graph or generalizes to unseen graphs. Speaking in the context of statistical learning, the goal of link prediction is generalization. However, edge reconstruction is understood as an inverse problem[6] that is formulated as the design of some algorithm $\mathcal{A}$ that takes input a graph embedding with some knowledge on its generation process, and outputs an estimated topology that most possibly yields the graph embedding. The goal of edge reconstruction is not generalization as it recovers input graph in an instance-wise fashion (therefore, we think you probably misunderstood the type of our analysis by refering to it as generalization bounds). The difference here is somewhat reminiscent of that between the study of regression and compressive sensing: The techniques required in the analysis may have overlaps, but the two problems are different and require different types of analysis. Next we address your questions in detail: ## Q1: Are theorem 4.1 and 5.1 trivial, based on recent developments on link prediction? Now that we have explained the difference between link prediction and edge reconstruction, we state here why the theoretical developments in the two related works do not imply our establishments: - In [1], the authors focused on dataset properties that may influence the performance of link prediction. The analysis therein is conducted on certain types of random graphs, but the guarantees do not involve any specific algorithms or performance measures. Therefore we do not see any implications of [1] regarding our theoretical interest. - In [2], the authors derived generalization bounds of linear GNN under a moderately sparse graphon model, i.e., the edge density is of the order $\Omega(\log n / n)$. As we have previously mentioned, the generalization bounds of link prediciton is very different from edge recovery error bounds which is basically an inverse problem. Meanwhile, theorem 4.1 applies to graphs that are potentially much more sparse than those considered in [2] (please refer to assumption (i) in theorem 4.1. Besides, analyzing graphon models in sparse regimes as in our paper, i.e., $p_{uv} = o(\log n / n)$ is highly nontrivial [5]). Therefore, both the analytical setup and goal are different between [2] and our paper. Regarding your comment that theorem 4.1 "essentially states that the accuracy of correlation detection grows with increasing samples", it is worth mentioning that in most of the theory developments in machine learning we need some sort of complexity that decreases with sample size and this should not be considered as essential implications of theory. Indeed, an important message of theorem 4.1 and 5.1 is that sparsity plays a key role of edge recovery and we are not aware of any previous works that noticed this factor. ## Q2: On theorem 6.1 and experiments Theorem 6.1 is mainly used as a statement that ascertains the protection guarantee of NAG against a wide range of adversaries, it slightly improves previous results [3] by allowing a more flexible choice of victim GNNs. ([3] only considers parameter-free GNN with summation pooling). Theorem 6.1 is indeed much easier to prove than theorem 4.1 and 5.1, and we do not consider theorem 6.1 to be our main theoretical contribution. However, we are interested in whether SERA can be utilized as a privacy auditing tool that empirically elicits the privacy level of NAG which are guaranteed by theorem 6.1------Such kind of empirical investigation is often considered as important research problems: For example, there has been considerable effort in designing MIA to audit DPSGD[4], and in such kind of study, we would need a theoretical privacy guarantee in the first place, which is what theorem 6.1 does.(We will include a more detailed discussion on privacy auditing in our revisions) According to our empirical findings, there are cases when SERA is ineffective but the theoretical privacy level according to theorem 6.1 is vacuous, thereby implying the limitations of SERA as a privacy auditing tool. In section 6, theorem 6.1 also serves as the motivation of our experiments. Hopefully we have addressed your theoretical concerns, and we would like to have an in-depth discussion with you. Please kindly let us know if you still have any questions regarding our theoretical contributions. [1] Mao, Haitao, et al. "Revisiting link prediction: A data perspective." arXiv preprint arXiv:2310.00793 (2023). [2] Chung, Alan, Amin Saberi, and Morgane Austern. "Statistical Guarantees for Link Prediction using Graph Neural Networks." arXiv preprint arXiv:2402.02692 (2024). [3] Sajadmanesh, Sina, et al. "{GAP}: Differentially Private Graph Neural Networks with Aggregation Perturbation." 32nd USENIX Security Symposium (USENIX Security 23). 2023. [4] Nasr, Milad, et al. "Adversary instantiation: Lower bounds for differentially private machine learning." 2021 IEEE Symposium on security and privacy (SP). IEEE, 2021. [5] Xu, Jiaming. "Rates of convergence of spectral methods for graphon estimation." International Conference on Machine Learning. PMLR, 2018. [6] Pasdeloup, Bastien, et al. "Graph reconstruction from the observation of diffused signals." 2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton). IEEE, 2015. --- Rebuttal Comment 1.1: Title: Please let us know if you have further concerns Comment: Thank you for taking the time to review our paper. We genuinely appreciate your comments and believe they will help enhance our work. As the discussion period is drawing to a close, we would still like to engage with you further about our theoretical contributions. Please let us know if you have any additional concerns or questions.	Summary: The paper studies to which degree graph representations are vulnerable to similarity-based edge reconstruction attacks (SERA). SERAs encompass a variety of attacks used to recover the structure of a graph, where a SERA guesses that an edge exists between pairs of nodes that have similar embeddings. The paper considers linear GNNs and highlights how SERAs are particularly successful in reconstructing large and sparse graphs. On the other hand, the authors show that edge recovery is less successful when considering graphs generated from a stochastic block model. Additionally, the paper presents an analysis and discussion of noisy aggregation as a mitigation technique against SERAs. Strengths: The paper presents an interesting overview of the strengths and limitations of edge reconstruction attacks based on similarity. The motivation is clear and the paper is generally well structured. The results on the theoretical performance of SERAs on both sparse and dense synthetic graphs are accompanied by an empirical evaluation. Weaknesses: Assumptions The assumptions in Theorem 4.1 require further discussion. While the authors mention in Remark 4.2 that the assumptions may not "consistently align with practical scenarios", it is unclear in which cases they may align at all with a practical scenario. In section 7.1, you state that the linear model you analyse theoretically can be used as a proxy for a non-linear counterpart. I therefore wonder: to which degree do the assumptions in Theorem 4.1 hold on real datasets? Empirical evaluation The readability of the he empirical results in Section 7 could be improved. Specifically, the plots in Figure 1 and Figure 2 are very small, and the labels too tiny. $\hat{A}^\text{SERA}$ in Table 1 is not defined, and so is the expression "trained" and "non-trained", in this context. With respect to the results themselves, in Section 7.1 you claim that "SERA is able to achieve near-perfect reconstruction of all edges only in the 'large $d$, small $L$' regime". Figure 1a, however, seems to show that for large $d$ the attack AUROC is high for all depths $L$. These results would benefit from further comments and a better visualization of the results, as it is at the moment not easy to infer numerical values form the colour gradients in Figure 1. Language clarity The language is at times excessively verbose and difficult to parse. For instance, in the description of the threat model in line 116, the "objectives ascribed to the adversary" are described as "decidedly audacious", as they aim at the "potential elucidation of the entire suite of edges" of an attacked graph. These sentences are not only difficult to read, but also vague. I would strongly recommend a more dry writing style which is better suited to convey technical content as, despite the good general organization of the paper, the current style hinders ease of read and is the main motivation for my low presentation score. Other comments * The brackets used for citations should, generally, not be interpreted as part of the sentence. So, e.g., in line 68, "proposed by [10]" -> "proposed by Duddu et al. [10]". * Line 80, "don't" -> "do not". * Line 152. "be a universal" -> "be universal". * "related works" -> "related work". * References to theorems, sections, etc., are inconsistently reported with both lower-case or upper-case initials. * Several equations, particularly in the appendix, should be better typeset to help readability. Specifically, several parenthesis are not adjusted for the size of the expressions they contain. Technical Quality: 3 Clarity: 1 Questions for Authors: * In Remark 4.2 you state that the requirement of plolylogarithmic growth of the feature dimension is a byproduct of your proof. Can then this requirement be removed? How? * In your theoretical investigation you do not use homophily to derive your results. While this is an interesting perspective as you bound the attack performance if homophily is not an assumption, what can you say when homophily _is_ an assumption? Confidence: 3 Soundness: 3 Presentation: 1 Contribution: 3 Limitations: The paper discusses limitations in the appendix. It would preferable to expand the discussion of limitations in the main body of the paper. The discussion of future work is completely deferred to the appendix, and would benefit as well from a dedicated paragraph in the main body of the paper. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your valuable comments and advices, we will integrate your suggestions into revised versions of our paper. Below we address some specific points: ## Q1: Practicality of assumptions in theorem 4.1 According to our understanding, the primary concern is to what extent the assumption $d = \Omega(\text{polylog}(n))$ holds in practice. In our real-world experiments, the Cora and Citeseer datasets could be loosely regarded to satisty the assumption (Cora: $n=2708, d=1433$, Citeseer: $n=3327, d=3703$). Yet satisfiability of this polylog dimension relation seems not to be a necessary condition for SERA to succeed (at least empirically): For example, the Amazon Products and Reddit dataset are much larger in scale with much fewer features, yet the performance of SERA are fairly strong even for $L=5$. Regarding your question about whether the polylog factor can be removed, we think that the lower bound on $d$ can be improved to have a smaller exponent over $\log n$ (regarding the $6L+2$ in our paper) via a better handling of probabilistic arguments. But currently we do not know how to avoid the $(\log n)^{O(L)}$ dependence, which is an exciting future direction. ## Q2: Clarifications of empirical evaluations We will revise our graphical presentation in figure 1 in revised versions of the paper by adding visible score marks for a better illustration. Regarding your concern about the correctness of our claim in "Large $d$, small $L$" regimes, please kindly refer to our attached pdf file which shows the numerical values of SERA on Erdos Renyi graph with feature dimensions $d \in \\{512, 1024, 2048\\}$. The results demonstrates that the performance peaks at $L=3$ and reduces significantly for $L \ge 8$ across all the setups. It is true that the attack AUROC may still be as large as $95\\%$ when $n$ is large, but the performance drop is also statistically significant as opposed to near $100\\%$ AUROC for $L=3$. Therefore the empircal observations align with our theory findings. Regarding the missing defnitions in table 1, please kindly refer to our global response for an overview of the design of this table. Specifically, $\widehat{A}^{\text{SERA}}$ denotes the reconstruction is based on SERA over graph representations (we will change it to SERA for clarity in revisions), and the term trained and non-trained are used to indicate how the weight of the underlying victim GNN is obtained, either via random initialization or well-trained. ## Q3: Possiblity of incorporating homophily into our theory This is a very interesting question. In the setup of theorem 4.1 in our paper, we allow the edge generation probability $p_{uv}$ to depend on features $x_u$ and $x_v$ in an arbitrary fashion, which naturally includes the case of homophily. According to our understanding of your question, you might be suggesting the exploration of shaper reconstruction bounds that quantitatively incorporate a homophily measure into the bound that drastically change the complexity. This is a rather challenging task as a good quantitative characterization of homophily in this setup is non-trivial in the first place. While this question is beyond the scope of our paper, it warrants a careful study in the future. --- Rebuttal Comment 1.1: Comment: I thank you very much for your detailed answers and the additional experimental results. I think my current rating, considering the revision work necessary to improve readability, is appropriate for your submission and I will thus keep it as is. While the impact of a contribution has, of course, a degree of subjectivity, I nevertheless want to say that, differently to what reviewer VCKp points out, I find your analysis of the success/failure modes SERA and their link to sparsity to be valuable. I thus encourage further investigation in similar directions, to which I am looking forward! --- Reply to Comment 1.1.1: Title: Response by the authors Comment: Thank you very much for the valuable responses. We really appreciate your insightful comments!	null	null	Rebuttal 1: Rebuttal: We thank the reviewers for their thought-provoking comments. We believe these valuable comments will lead to improvements of our paper. As we noticed some common concerns among the reviews, we provide some clarifications below: ## About our analysis on linear GNN In appendix F.3 of our paper, we acknowledge that our analysis under linear GNN is a limitation of our work. The mathematical challenge in extending our analysis to nonlinear GNN stems from the relationships between node representations $h_v^{(L)}$'s and node features $x_v$'s. Under nonlinear GNNs, it becomes prohibitively hard to compute the non-trivial upper or lower bounds for the correlations between $h_u^{(L)}$ and $h_v^{(L)}$ for either $u \neq v$ or $u = v$. Additionally, so far as we have noticed, many previous non-asymptotic theoretical developments on multi-layer GNNs are based on the linear GNN model [1, 2]. While theoretically analyzing nonlinear GNNs is challenging, we provide empirical evidences in section 7 (and more specifically in Appendix E.2) that systematically compare the performances of linear GNN and 4 prevailing nonlinear GNNs (GCN, SAGE, GAT and GIN) over 8 benchmark datasets with varying homophily level (See table 3 for a detailed report). The attack performances exhibit strong correlation between linear GNN and nonlinear GNNs across datasets. Besides, we observe from experimental results that linear GNN often exhibits slightly weaker attack performance than nonlinear GNNs. As we have shown that edge information is provably vulnerable even under linear GNN, we believe an analogue with nonlinear GNNs should hold and we left these developments to future explorations. ## Some clarifications of tables and figures We thank the reviewers for pointing out illustration issues in figure 1 and table 1 of the paper. We provide some clarifications below: 1. [Figure 1] We present a detailed list of attack performance numbers in the attached pdf for $d \in \\{512, 1024, 2048\\}$ (corresponding to figure 1(a)). We will include a number-marked grid in revisions of the paper for improved illustrations. 2. [Table 1] The rationale behind the design of table 1 is that we want to verify the effectiveness as well as the robustness of SERA against varying dataset characteristics as well as training dynamics. To measure dataset characteristics (regarding homophily level), we use the feature homophily metric as well as the AUROC of feature similarity against edge existence, which we denote as $\widehat{A}^\text{FS}$. To systematically investigate the impact of traning dynamics, we conduct two set of experiments where the GNN weights are obtained either via random initializations (non-trained in table 1 and table 3), or via a standard training procedure (trained in table 1 and table 3) which we detail in appendix E.2 of the paper. ## About the writing style We thank the reviewers for advices on our writing style and we will carefully polish our writing by enhancing clairty and conciseness. [1] Wu, Xinyi, et al. "A Non-Asymptotic Analysis of Oversmoothing in Graph Neural Networks." The Eleventh International Conference on Learning Representations. [2] Chung, Alan, Amin Saberi, and Morgane Austern. "Statistical Guarantees for Link Prediction using Graph Neural Networks." arXiv preprint arXiv:2402.02692 (2024). Pdf: /pdf/07304d2b02c173459573173c4e0f601e2434e07a.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Neural decoding from stereotactic EEG: accounting for electrode variability across subjects	Accept (poster)	Summary: The work proposes a transformer architecture for decoding behavior using sEEG neural recording which can account for inter-subject variability that exist due to different placements of sEEG electrodes, different SNRs, inherent biological differences etc. The ability of the proposed transformer architecture to deal with inter-subject variability allows the transformer architecture to leverage a much larger multi-subject dataset as compare to existing works which rely on subject-specific models. The proposed architecture consists of six main components: (i) a CNN temporal tokenizer; (ii) A temporal attention mechanism; (iii) A hand-designed RBF-based spatial encoding of different electrode locations; (iv) A spatial attention mechanism; (iv) a feed-forward MLP to extract small dimension neural representations; and (iv) a multi-head regression layer to deal with inherent patient-to-patient variability. The authors test their proposed architecture on a dataset collected from 21 subjects performing a visual color-change task, and show that their proposed architecture significantly boosts its decoding performance when using multi-subject datasets as compared to single-subject dataset. Strengths: - The paper is well-written and easy to follow. - The paper addresses an important issue of data heterogeneity in sEEG recordings among participants which makes constructing large dataset challenging as data from multiple participants cannot be easily pooled together. This particularly affects the applicability of deep learning models as they typically rely on large datasets to get low generalization error. - The proposed architecture is clearly defined and uses a multi-head regression layer with a shared trunk (similar to some multi-task architecture) to model inter-patient variability. The authors also employ spatial and temporal attention layers to model temporal dependence in the neural activity and the spatial dependence between different electrodes, respectively. and - The experimental details are clearly provided and the results shown in the work clearly show that training transformers on multi-subject dataset significantly boosts their decoding performance. - The ablation study is insightful and provides important insights into the functioning of different components of the proposed architecture. Weaknesses: 1. A main weakness of this paper is the spatial encoding (which is framed as a main contribution of the work) only seems to marginally improve the performance of the transformer architecture. The results shown in Section 4.5 only show that average decrease of 0.02 in $R^2$ coefficient across the subjects which is well within the standard error of 0.05 (line 279) reported by authors for the average $R^2$ coefficient with the transformer model incorporating spatial encoding. I am surprised why the authors do not use this result to conclude that the proposed spatial encoding does not have a significant effect on model's accuracy and, consequently, the heterogeneity in the actual positions of sEEG electrode does not seem to impede the training of multi-subject models. Looking at authors' result of ablation study in A.3.1, it seems more plausible that attention mechanism for space (without which the $R^2$ coefficient decreases by a more significant amount of ~0.1, figure 6) is the main mechanism by which the proposed architecture deals with electrode heterogeneity. 2. Furthermore, the ablation study detailed in A.3.1 seems to suggest that it is the multi-head regression component of the proposed architecture is the main component enabling the better performance of multi-subject model. I am surprised as to why this observation is not mentioned in the main manuscript. 3. Due to the marginal performance boost offered by positional encoding, the argument that heterogeneity of electrode placement needs to be explicitly accounted for by tokenizing space and time separately seems weak (lines 161-164). Consequently, the separation of time and space attention mechanism does not seem to be adequately justified. I think comparison against 2-D attention mechanism will benefit the study. 4. Comparison against other methodology is limited. Authors only compare their architecture on single-subject dataset with multi-subject dataset and show a significant increase in the performance of their transformer architecture when training with the larger multi-subject data. Naively training transformer architecture without heavy regularization on small single subject dataset seems to provide poor performance as already discussed in Ye & Pandarinath'21. Hence, the gains of using multi-subject dataset reported in this study might be artificially larger than the ones obtained with proper regularization (such as dropout, $L_2,$ and $L_1$ regularization) of the transformer architecture. Furthermore, authors should also use some classical decoding models such as (PCA with linear regression, Unscented Kalman Filters, see Xu et al. JNE'22) to give a sense of how much gain is obtained in the first place by using the more complicated transformers architecture and provide a baseline accuracy for comparison. Authors should also compare against existing techniques such as SEEG-Net (Wang et al. Computers in Biology and Medicine'22) which used domain generalization techniques for dealing with heterogeneous sEEG data distribution among different subjects. As a side note, I think the work would benefit from a discussion on multi-task literature, as the multi-head regression structure is quite similar to many multi-task architecture proposed earlier (shared trunk architecture, see the review Crawshaw'20 on arvix). Minor: - Line 210: "long-range dependency" might be more appropriate than "long-term dependency" as the authors are talking about variables representing space. - Please provide the test/train/validation splits used in this work. It would facilitate in understanding the reported test $R^2$ coefficient. Technical Quality: 2 Clarity: 4 Questions for Authors: 1. Line 230: What is C? Should it be E? 2. Section 3.2.2: Spatial Positional Encoding: A couple of questions: - I am assuming that an MRI for each subject in the study was available, from which the MNI coordinates of the sEEG electrodes were calculated. In the spirit of being fully data-driven, why not use the whole MRI (with the sEEG shanks) for encoding the spatial latents? A simple CNN or Graph Convolutional Net could be used to directly encode the spatial information into a latent which can be used instead of the hand-designed coordinate-based spatial feature used in this work. A minor issue might be that the spatial latents might also contain information about the electrodes discarded in the preprocessing but that can possibly be remedied by appropriate masking or removing the sEEG coordinated from the MRI while pre-processing (whichever is easier). A possible advantage of directly using the MRI data would be that it would also account for differences in the brain structure along with the difference in sEEG probe placement. - I do not understand the point of using $m$-different 1-D RBFs for modeling the positional encoding. Is the goal to model positional encodings at different spatial scales. Why is information at different spatial scales relevant? How are the different $\sigma_j$ chosen (are they learnt from the data or chosen as hyperparameters)? The choice seems somewhat arbitrary, especially since the gain in the model's performance by using the spatial encoding is marginal (a 0.02 increase in R$^2$) as reported by the authors in Section 4.3. - Is the rationale for using 1-D RBFs, i.e., the RBF for each coordinate (eq (4)) instead of using 3-D RBFs (e.g., something like $C\exp(-D((x-\mu_x)^2+(y-\mu_y)^2+(z-\mu_z)^2$)) is to also incorporate the information of the direction of the coordinate. - Lines 205-207: The authors state that the projected positional encodings are added to the latents. I am having trouble fully understanding what does this operation entail? Does this mean that the projected positional encodings, denoted by $p\in\mathbb{R}^K$, and the latents, denoted as $z_{int}^{3} = z_{int}[i,j,:]$ (using the pythonic notation) for some $0 \leq i \leq E-1$ and $0 \leq j \leq T-1$, are added to produce the output $o\in\mathbb{R}^{E\times T\times K}$ of the operation in the following manner: $o^{3}=z_{int}^3+p$ followed by appropriate stacking. If that is the case, then what are the relative magnitudes of $z_{int}^{3}$ and $p$? Since $p$ is calculated using the 1-D RBFs, depending upon the magnitude of $\sigma_j$'s, the corresponding projected $p$ could be really numerically small, and the corresponding output $o^3=z_{int}^3+p$ might be dominated by the term $z_{int}^3$. I think checking the relative magnitude of $z_{int}^3$ and $p$, and ensuring that they roughly have comparable magnitudes is important to ensure that the positional encoding impact the final outcome. 3. Why is Huber loss used for training multi-subject model whereas MSE loss used for training single-subject loss? Ideally both multi-subject and single-subject models should have been trained using both losses and for each model, the Huber or MSE loss should have been chosen based on validation error. The choice is surprising as I would have expected to use the more robust Huber loss on the single-subject model (which would be more noisy and prone to effects of outliers) and MSE on the multi-subject data where the much larger size of the dataset can regularize the training process. 4. Another point of potential unfair comparison is that single-subject models are trained for much smaller number of total (gradient) descent steps compared to multi-subject models. On average, the multi-subject models have 21x larger dataset compared to a single-subject model. Hence, a single epoch while training multi-subject models will go through 21 x more gradient descent steps compared to an epoch of a single-subject model. So, multi-subject model trains for 21x longer than the single-subject model. I think authors should provide a justification for this large discrepancy in the training periods of multi-subject and single-subject models. For example, try training the multi-subject model for 1000/20 = 50 epochs and see its $R^2$ coefficient or try training a couple of best-performing single-subject model and train them for 21000 epochs and see their performance. Edit: This comment is no longer applicable. I missed the part about different batch-sizes. Confidence: 3 Soundness: 2 Presentation: 4 Contribution: 3 Limitations: Yes, the authors provide a discussion on some limitations in the discussion section. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for a very detailed review. Here, we provide our response to your questions. Due to space constraints, for each question we provide only the beginning of your prompt. We apologize for the inconvenience. _Throughout this rebuttal we refer to single-subject as SS and multi-subject as MS._ ## Weaknesses > 1. A main weakness of this paper is the spatial encoding... Thanks for the constructive criticism. Indeed, our proposed PE only marginally boosts decoding performance, suggesting the attention mechanism in space is the main mechanism by which our model deals with electrode heterogeneity. We will highlight this in our revised manuscript. > 2. Furthermore, the ablation study detailed in A.3.1... This is a valid point. We will highlight this in revisions. > 3. Due to the marginal performance boost offered by positional encoding... Thanks for suggesting this. We compared the performance of our architecture against a variant where 2D attention is performed over time & space. We include the results of this analysis in Table 4 of our General Response (see also Figure 1E of the pdf). The results suggest that our proposed architecture outperforms its 2D attention variant by $\Delta R^{2} = 0.06$. > 4. Comparison against other methodology is limited... Thanks for the constructive criticism. To address this, we compared our model with classic and SOTA SS models. The results, shown in Table 1 of our General Response, indicate that our architecture outperforms all baselines across the board. Unfortunately, UKF and SEEG-Net are missing from those baselines. We have been unable to get good results using UKF, likely due to the nature of our data, since the trial response times (included in UKF's state) are not stationary, making state estimation unreliable. We also looked into sEEG-Net, but the code is not public and the method requires substantial modification before use, since it operates on the electrode level while our problems requires operation on the subject level. We are still trying to make those models work and hope to include them as baselines in revisions. Thank you for suggesting we discuss multi-task literature in revisions. We plan to do so, including Crawshaw (2020), in the related work section of our manuscript. ## Minor > * Line 210: "long-range dependency" might be more appropriate... We will amend this in revisions. > * Please provide the test/train/validation splits... The training/validation/test split is 70/15/15. We will include this in revisions. ## Questions > 1. Line 230: What is C? Should it be E? Yes. We will fix the typo in revisions. > * I am assuming that an MRI for each subject in the study was available... This is a great idea. Unfortunately, for this dataset we only have the MNI coordinates of electrodes and not whole MRIs or other imaging data. Therefore, we are unable to test this out. We look forward to exploring this option in the future. > * I do not understand the point of using m-different 1-D RBFs for modeling the positional encoding... Your intuition is correct; we used RBFs with different variances to encode position at different spatial scales. This is relevant because studies (Meunier (2009)) show that the brain has a hierarchical modular structure. Therefore, encoding both short and long electrode connections could be useful. The scales $\sigma_{j}$ for each RBF were hyperparameters with values: [1, 2, 4, ..., 64]. > * Is the rationale for using 1-D RBFs, i.e., the RBF for each coordinate... We used 1D RBFs instead of 3D because 1D RBFs: (1) inform the model with direction (as you correctly identified) and (2) introduce less parameters to the model compared to 3D RBFs. Specifically, assuming that sampling an interval in 1D requires m points, sampling a 3D interval, separately in each dimension, at the same scale requires 3m points. Sampling the same 3D interval in 3 dimensions combined requires m$^{3}$ points. > * Lines 205-207: The authors state that the projected positional encodings are added to the latents... Thank you for this insightful suggestion. Your description of the operation correct. To ensure that $z^{3}$ & $p$ have comparable magnitudes, we computed $\|\|z^{3}\|\|$ and $\|\|p\|\|$ for 512 random samples from our test set. The norms were $\|\|z^{3}\|\| = 0.790 \pm 0.53$ & $\|\|p\|\| = 0.013 \pm 0.01$ (mean + sdev), suggesting that $\|\|z^{3}\|\|$ is greater than $\|\|p\|\|$ but not to the extent that the model's output would be unaffected by this operation. > 3. Why is Huber loss used for training multi-subject model whereas MSE loss used for training single-subject... We optimized SS models using MSE Loss because $R^{2}$ is directly proportional to the MSE Loss. Following your suggestion we trained both SS & MS models using both MSE & Huber Loss. The results show that training with Huber Loss boosts performance for all models. We have update the SS model results to reflect this. _Table 5. Comparison of model performance trained with Huber vs MSE Loss_ Model \| MSE \| Huber --- \| --- \| --- SS \| 0.28 $\pm$ 0.05 \| 0.30 $\pm$ 0.05 MS \| 0.35 $\pm$ 0.05 \| 0.39 $\pm$ 0.05 > 4. Another point of potential unfair comparison... Thank you for this thoughtful concern. Your intuition is correct. However, the MS and SS models were trained with batch size 1024 and 64, respectively (see line 599 of manuscript). Our dataset contains 3685 trials (175 trials per subject). Therefore, during 1K training epochs MS and SS models underwent 4K and 3K gradient descent steps (GDS), respectively. To ensure that this did not artificially inflate the performance difference between the MS and SS models, we retrained all SS models for 1.5K epochs (4.5K GDS). The average per-subject test set R$^2$ of the SS models was 0.29 $\pm$ 0.05 (mean $\pm$ sem). The MS model still outperformed those by $\Delta R^{2} = 0.10$. In practice, we used 1K epochs because we observed that they were enough for the training objective of all model to converge. --- Rebuttal Comment 1.1: Comment: I have read the author rebuttal and increased my overall score to 5. - I still think the biggest weakness of the work is comparison with existing baselines. Authors do not compare against any existing state of the art method, e.g., Ye & Pandarinath'21 or SEEG-NET. - Authors should also not claim that "This work is the first to train a unified, multi-session, multi-subject models for neural decoding based on sEEG", when SEEG-Net (Wang et al. Computers in Biology and Medicine'22) has done it two years earlier. - I think it is a bit of a stretch to claim that $\\\|p\\\|$ (which is $\sim$50 times smaller than the standard deviation in $\\\|z^3\\\|$) is affecting the output $o$. - I do not agree with the authors' assertion that 3-D RBFs require much more parameters. The common RBF kernel is of the form $\exp(-\\\|x-x_0\\\|^2/\sigma^2)$ which only requires a single parameter $\sigma$, which would result in exactly the same number of parameters. You could potentially increase the numbers of parameters by using the Mahalanobis distance instead of the standard distance but even in that case the number of parameters for each RBF kernel is $6$ instead of $1$ (overall parameters 6x9 = 54), which compared to the number of parameters in the transformer architecture are negligible. Also I do not understand how 1-D RBFs are able to sample a 3-D space using $3m$ points. Note that if I am discretizing each dimensions using $m$ bins, then I have discretized the 3-D space into $m^3$. Consider the example where I discretize each dimension into two bins {0,1}, then I access 8 different bins in 3-D space as {0,0,0}, {0,0,1}, {0,1,0}, {0,1,1}, {1,0,0}, {1,0,1}, {1,1,0}, and {1,1,1}. --- Reply to Comment 1.1.1: Comment: Thank you for your response and for updating your score! We are very happy that our responses and new experiments addressed at least some of your concerns. Please find our answers to your new comments below: > * I still think the biggest weakness of the work is comparison with existing baselines. Authors do not compare against any existing state of the art method, e.g., Ye & Pandarinath'21 or SEEG-NET. Based on your initial feedback, we put a lot of effort into comparing our models with baselines. However, you would like us to compare against: 1. Ye and Pandarinath (2021): The NDT model is designed to "transform sequences of binned spiking activity into inferred firing rates" (this is directly quoted from the paper: line 1 of section 2). NDT operates on _single-unit electrophysiology datasets, which can only be recorded with microelectrode arrays_. In this work, we use an sEEG dataset and it is impossible to resolve single units from sEEG recordings. Given the nature of our dataset, it is unclear how we could use NDT on our data. 2. Wang et al. (2022): sEEG-Net is a model designed for pathological activity detection for drug-resistant epilepsy. It accepts univariate timeseries of neural activity from _single_ sEEG electrodes and classifies them as: physiologic, pathological, or artifact (it maps $R^{T} \rightarrow R^{3}$). In contrast, in this work we are dealing with a problem where multi-variate timeseries of neural activity from _multiple_ sEEG electrodes need to be mapped to a response time (map $R^{E \times T} \rightarrow R^{1}$). Therefore, without extensive modificaton, sEEG-Net cannot work on our data. Adding to this, _the code for sEEG-Net is not public, hampering our efforts to reproduce the model._ We hope you understand that we have been unable to provide those comparisons for solid reasons. > Authors should also not claim that "This work is the first to train a unified, multi-session, multi-subject models for neural decoding based on sEEG", when SEEG-Net (Wang et al. Computers in Biology and Medicine'22) has done it two years earlier. We respectfully disagree. We believe our claim is justified because: 1. sEEG-Net is not a neural decoding model, rather a pathological activity detection model. Neural decoding and pathological activity detection are two very different tasks. 2. sEEG-Net operates on single-electrodes (univariate timeseries of single sEEG electrodes) while our models operate on single-subjects (multivariate timeseries of many sEEG electrodes). > * I think it is a bit of a stretch to claim that $\|\|p\|\|$ (which is 50 times smaller than the standard deviation in $\|\|z\|\|^{3}$) is affecting the output $o$. We echo that the contribution of $\|\|p\|\|$ is very small. We will make sure to discuss this limitation in our revised manuscript and emphasize the need to identify better spatial positional encoding schemes, such as encoding whole brain MRI scans or using atlases other than MNI, as you and reviewer o6UF suggested. > * I do not agree with the authors' assertion that 3-D RBFs require much more parameters. The common RBF kernel is of the form $exp(-\|\|x-x_{0}^{2} / \sigma^{2})$ which only requires a single parameter $\sigma$, which would result in exactly the same number of parameters. You could potentially increase the numbers of parameters by using the Mahalanobis distance instead of the standard distance but even in that case the number of parameters for each RBF kernel is 6 instead of 1 (overall parameters 6x9 = 54), which compared to the number of parameters in the transformer architecture are negligible. Also I do not understand how 1-D RBFs are able to sample a 3-D space using $3m$ points. Note that if I am discretizing each dimensions using $m$ bins, then I have discretized the 3-D space into $m^{3}$. Consider the example where I discretize each dimension into two bins {0,1}, then I access 8 different bins in 3-D space as {0,0,0}, {0,0,1}, {0,1,0}, {0,1,1}, {1,0,0}, {1,0,1}, {1,1,0}, and {1,1,1}. We agree that the number of parameters saved by using a 1D RBFs instead of a 3D RBFs is negligible compared to the number of parameters of the transformer. The main benefit of 1D RBFs is the encoding of directionality. In terms of how 1-D RBFs are able to sample 3D space using $3m$ points, we would like to clarify that this statement in our previous response was poorly written. Our previous statement intended to convey that to center 1-D RBFs (separately in the x, y, and z direction) to the $m^{3}$ points of a 3D space, you only need to compute $3 m$ distinct 1-D RBFs. All $m^{3}$ RBFs required to map the 3D space can be computed by appropriately multiplying those $3 m $ RBFs. We apologize for the confusion. Thanks again for your feedback and for the insightful discussion, which we believe has substantially improved the quality of our work.	Summary: The authors propose a novel training framework and architecture to predict response time for a color change behavior task from stereotactic electroencephalography (sEEG) data, focusing on integrating data across multiple subjects despite the variability in electrode placement and count. The model tokenizes neural activity within electrodes using convolutions, extracts temporal dependencies with self-attention, incorporates electrode location with a positional encoding scheme followed by another spatial self-attention layer, and a subject-specific prediction layer. The model is trained on data from 21 subjects, using different procedures: single-subject training (baseline), multi-subject training, and multi-subject training plus single-subject finetuning. The proposed method demonstrates an improved ability to decode trial-wise response times compared to the baseline, and transferability of learned representations to new subjects. Strengths: * Innovative Framework: The proposed framework effectively addresses the heterogeneity across subjects, a significant challenge in sEEG data processing, by using electrode placement and subject-specific prediction layers. The ability to pretrain the model on a larger multi-subject dataset and fine-tune it for new subjects with minimal training is a valuable feature, enhancing the model's practicality and applicability. * Comprehensive Evaluation: The model's performance is validated using a substantial dataset (21 subjects), showing consistent improvement in performance for most subjects. An ablation study is also performed. Weaknesses: The paper discusses the impact of the positional decoding in the ablation study, but this is the least impactful structure compared to other layers (Fig 6). It would be beneficial to explore other position decoding mechanisms besides using MNI locations for future work, perhaps based on different brain atlases. Technical Quality: 4 Clarity: 3 Questions for Authors: 1. With the number of electrodes differing across subjects, how did you handle the different input sizes? 2. Instead of plotting all the sEEG channels, it would be helpful to show the selected channels actually used in training. 3. What is the (relative) root mean square error for the prediction? Confidence: 4 Soundness: 4 Presentation: 3 Contribution: 3 Limitations: The method could provide valuable insights for various BCI studies if the authors can demonstrate its performance on more complex tasks. In the Discussion, the authors mention that developing a multi-task model is planned for future work. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your thoughtful feedback and question. We were really excited to read that "The proposed framework effectively addresses the heterogeneity across subjects, a significant challenge in sEEG data processing". Here, we provide our response to your questions and the results from new experiments that we ran to address your concerns. If you would like any further clarifications, please let us know. ## Weaknesses > The paper discusses the impact of the positional decoding in the ablation study, but this is the least impactful structure compared to other layers (Fig 6). It would be beneficial to explore other position decoding mechanisms besides using MNI locations for future work, perhaps based on different brain atlases. Thank you for the insightful suggestion! We echo your observation that our proposed spatial positional encoding only improves decoding performance slightly and agree that future work should identify better ways to encode the location of sEEG electrodes in the brain. Using different brain atlases is a great suggestion that we will definitely look into. Unfortunately, for this dataset, we only have the MNI coordinates of the sEEG electrodes and therefore we are not able to test whether encoding position with some other atlases would achieve better decoding results. However, we certainly look forward to exploring such ideas in the future. The best we could do to adress your feedback was to compare our spatial positional encoding approach against other positional encoding approaches. The results are summarized in Table 2 of our General Response and suggest that our proposed positional encoding, works as well as, or better than other approaches. However, as you pointed out, the explored positional encoding schemes are far from comprehensive, indicating that there is still a lot of margin for improving spatial positional encoding mechanisms. We will make sure to discuss the idea of encoding electrode location using other brain atlases in section 4.5 of our revised manuscript. ## Questions > 1. With the number of electrodes differing across subjects, how did you handle the different input sizes? This is a great question. Our models is capable of handling different input sizes due to the ability of convolutional neural networks and transformers to accept inputs of varying lengths. Prior to procesing the latents with our architecture's MLP, we pad the latents of all subjects to a fixed length. For the mathematical details, we refer you to section 3.2 of our manuscript. Here, we try to provide a more intuitive explanation of why our network is capable of handling inputs of different sizes. The input to our network, $X \in R^{E \times T}$, is a 2D array of electrodes $\times$ timepoints, where $E$ refers to the electrode dimension and $T$ to the time dimension. The tokenizer performs $K$ 1-D convolutions on the input along the time dimension $T$, while parallelizing the computation across the $E$ dimension (electrodes). This operation returns a latent $z \in R^{E \times T \times K}$, where $K$ refers to the number of convolutional kernels. Then, self-attention is performed on $z$ along the time dimension, while computation is parallelized across the $E$ dimension. Self-attention can accept sequences of arbitrary lengths and therefore no matter the number of timepoints of the latent $z$, this operation can be performed successfully. The output of the self-attention has the same size as the input, returning a latent of the form $z \in R^{E \times T \times K}$. Then positional encodings are added to the latents, which does not alter the shape of $z$. Another self-attention operation is performed, this time along the $E$ dimension of $z$, parallelized across the $T$ dimension (timepoints), which again preserves the size of the latent $z \in R^{E \times T \times K}$. At this point, the latents are unrolled to get a latent of the form $z \in R^{E \cdot T \cdot K}$. $T$ and $K$ have the same dimensionality across subjects; $E$ however (the number of electrodes) does not. Therefore, each subject is going to have a latent $z \in R^{E \cdot T \cdot K}$ that has a unique dimensionality. This latent will be projected to a lower dimensional space through a multi-layer perceptron, which requires a fixed input length. Therefore, at this stage the latents $z \in R^{E \cdot T \cdot K}$ are padded with zeros to obtain a fixed length $E_{max} \cdot T \cdot K$ that is common to all subjects. For convenience, $E_{max}$ is set to the maximum number of electrodes that a subject has in our cohort. The MLP projects the latent to $z \in R^{F}$, where $F$ represents a small number of features that will then be projected through the subject-specific MLPs to a single number corresponding to the response time of a subject for a given trial. We hope that this explanation answers your question. > 2. Instead of plotting all the sEEG channels, it would be helpful to show the selected channels actually used in training. This is a great suggestion. Please take a look at Figure 2 of the pdf we submitted with our General Response and let us know if you have any further suggestions. We will appreciate your input on this. > 3. What is the (relative) root mean square error for the prediction? For the multi-subject model, the root mean square error for all predicted response times in the test set, across subjects is RMSE = 0.082 $\pm$ 0.002 (mean $\pm$ sem) sec. For reference, the mean response time in the test set across subjects is $0.41$ $\pm$ 0.005 sec (mean $\pm$ sem). We will make sure to include this in section 4.3 of our revised manuscript. --- Rebuttal Comment 1.1: Comment: Thanks for the detailed response and additional analysis. The new experiments substantially enhance the quality of the work. --- Reply to Comment 1.1.1: Comment: Thank you for your response. We are happy to read that our new experiments substantially enhanced the quality of the work.	Summary: This paper presents a framework and architecture for decoding behavior across subjects using stereotactic electroencephalography (sEEG) data, addressing the challenge of electrode variability. By tokenizing neural activity with convolutions and employing self-attention mechanisms along with a positional encoding scheme based on MNI coordinates, the model extracts effective spatiotemporal neural representations. The study demonstrates successful decoding of behavioral response times from 21 subjects' data and shows that the pretrained neural representations can be transferred to new subjects with minimal training data. This work offers a scalable approach for integrating and decoding sEEG data across multiple subjects. Strengths: 1. Multi-Subject Generalization: The framework's ability to generalize across subjects by combining data from multiple individuals and training a unified model is a substantial step forward compared to traditional single-subject approaches. 2. Methodology: The detailed methodology, including signal preprocessing, and bootstrap randomization test for identifying significant electrodes, ensures the robustness of the proposed approach. 3. Clarity: The paper is well-organized and clearly written, making it accessible to readers from both neuroscience and machine learning backgrounds Weaknesses: Plz go and check questions. Technical Quality: 2 Clarity: 3 Questions for Authors: 1. Scale and diversity of the dataset: The paper mentions using data from 21 subjects, totaling 3600 behavioral trials and 100 hours of sEEG recordings. Is this amount of data sufficient to represent the neural activity patterns of all subjects? Could the diversity of the dataset be insufficient to support the model's generalization capabilities? 2. Effectiveness of spatial positional encoding: The paper proposes a spatial positional encoding method based on MNI coordinates to handle electrode placement variability across subjects. Has the effectiveness of this method been thoroughly validated? Are there comparative experiments showing that this encoding method is superior to other possible encoding methods? 3. Individualized decoder heads: The paper mentions that each subject has a personalized task head for downstream decoding tasks. How effective is this approach when dealing with new subjects? Are there detailed experimental results demonstrating the performance of this method on new subjects? 4. Computational complexity and scalability: The paper outlines a complex model architecture involving convolutional tokenization, self-attention in both time and electrode dimensions, and individualized regression heads. What are the computational requirements for training and running this model? Is the approach scalable to larger datasets or real-time applications? Confidence: 4 Soundness: 2 Presentation: 3 Contribution: 2 Limitations: Plz go and check questions. Flag For Ethics Review: ['Ethics review needed: Research involving human subjects'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your though provoking feedback. We appreciate reading that "combining data from multiple individuals and training a unified model is a substantial step forward compared to traditional single-subject approaches"! Here, we provide our response to your questions and the results from new experiments that we ran to address your concerns. We are available to provide further clarification, if needed. > 1. Scale and diversity of the dataset: The paper mentions using data from 21 subjects, totaling 3600 behavioral trials and 100 hours of sEEG recordings. Is this amount of data sufficient to represent the neural activity patterns of all subjects? Could the diversity of the dataset be insufficient to support the model's generalization capabilities? This is a very thoughtful concern. It is likely that the amount of data in our dataset is insufficient to represent the neural activity patterns of all humans in a global sense. However, our dataset is larger than that of other recent sEEG datasets (Angrick (2021), Petrosyan (2022), Meng (2021), Wu (2022), Wu (2024) have data from 12 subjects or less), suggesting that it is more likely to represent general neural activity patterns compared to most other sEEG datasets. In terms of our dataset's diversity: (1) our cohort is composed of 13 females and 8 males, (2) subjects' age ranges from 16 to 57 years old, and (3) electrode number & placement for each subject is unique (solely based on clinical needs). Across subjects electrodes span white and grey matter; cortical, subcortical, and deep structures; and every major structural region of the brain (see Figure 2 of our General Response pdf). Our dataset is very diverse, suggesting that our model, trained on the combined data of all subjects, is likely to generalize. Thanks for the food for thought, we will include this discussion in our revised manuscript. > 2. Effectiveness of spatial positional encoding: The paper proposes a spatial positional encoding method based on MNI coordinates to handle electrode placement variability across subjects. Has the effectiveness of this method been thoroughly validated? Are there comparative experiments showing that this encoding method is superior to other possible encoding methods? Thanks for pointing out this limitation. In response to this concern, we validated our spatial positional encoding against other positional encodings. The results are summarized in Table 2 of our General Response and suggest that our proposed positional encoding, based on MNI coordinates, works as well as or better than other approaches. We believe it is also important to note that the MNI-Fourier and MNI-RBF positional encoding schemes outperform other approaches, indicating that informing models with sEEG electrode location boosts their performance. However, the performance gains are small, indicating that there is still a lot of margin for improving spatial positional encoding mechanisms. We will make sure to discuss these findings in section 4.5 of our revised manuscript. > 3. Individualized decoder heads: The paper mentions that each subject has a personalized task head for downstream decoding tasks. How effective is this approach when dealing with new subjects? Are there detailed experimental results demonstrating the performance of this method on new subjects? This is a great question. We echo that the ability of dealing with new subjects is very important to support our model's generalization capabilities. In section 4.4 of our submitted manuscript we demonstrate that our approach is effective when dealing with new subjects. Specifically, in that section, we take a leave-one-out cross validation approach in which we train 21 models (one for each subject in our cohort) each of which is trained on the combined data of all subjects except one. Then, we use the weights of the pre-trained models as a basis of finetune, upon which we train a new single-subject model with the data of the left-out subject. Across subjects, the models trained on other subjects and finetuned to a new one achieved an average test set $R^{2}$ score of $0.37 \pm 0.06$ (mean $\pm$ sem). Importantly, the performance of those models is superior to that of models trained from scratch and outperforms all baseline models (see Table 1 of our General Response) by $\Delta R^{2} >= 0.10$. > 4. Computational complexity and scalability: The paper outlines a complex model architecture involving convolutional tokenization, self-attention in both time and electrode dimensions, and individualized regression heads. What are the computational requirements for training and running this model? Is the approach scalable to larger datasets or real-time applications? The computational resources used to train our model are provided in lines 617-619 of our submitted manuscript. Single- and multi-subject models train within 5 mins and 1 hour, respectively, on a machine with an AMD EPYC 7502P Processor and one Nvidia A40 GPU, which is well within the resources of most computational research labs. The memory requirement to train the multi-subject model with a batch size of 1024 is $\sim$ 8 GiB, making model training tractable using less powerful GPUs as well. In terms of scalability, assuming that the batch size remains fixed, irrespective of the dataset size, the aforementioned computational resources should be enough to train the model. Naturally, the time requirement for training would scale linearly with the number available trials. However, even a dataset of $\sim$ 80K trials would train in roughly 24 hrs, which is very manageable considering the dataset size. To investigate whether our model can be used in real time, we measured the model's inference time on a sever and a laptop (see Table 3 of our General Response). All inference times are on the order of a few msec, which easily allows for integrating our model with real-time systems. We will make sure to add this result to our revised manuscript. --- Rebuttal Comment 1.1: Title: To authors Comment: Thank you for the authors' efforts and detailed responses. However, I still have concerns regarding the scale of the dataset. While the authors mention that recent sEEG datasets contain fewer than 12 subjects, this does not sufficiently justify that 23 subjects are adequate. In related fields, datasets often include 50, 100, or even more subjects to ensure robustness and generalizability. I have raised my rating to 4. --- Rebuttal 2: Comment: Thank you for your response and for updating your score! We are very happy that our responses and new experiments addressed at least some of your concerns. Please find our answers to your new comments below: > Thank you for the authors' efforts and detailed responses. However, I still have concerns regarding the scale of the dataset. While the authors mention that recent sEEG datasets contain fewer than 12 subjects, this does not sufficiently justify that 23 subjects are adequate. In related fields, datasets often include 50, 100, or even more subjects to ensure robustness and generalizability. We echo that a larger dataset (50-100 subjects) would provide stronger evidence for the model's generalization capabilities. However, as reviewer o6UF mentioned "gathering this 50-100 sEEG subjects could take years, if not decades, not to mention the additional difficulty of recruiting them for behavioral studies". Importantly, if the scientific community found value in studies containing 12 subjects or less, it is likely that it will find value in our 21-subject study as well. > I acknowledge the challenges of data collection from a medical perspective. However, there are still larger, publicly available sEEG datasets. This is very insightful. _If you could point us towards those datasets, by specifying either the publication with which they are associated or the link to the dataset repository, we would be very thankful_ and we look forward to working with those datasets in the future. > If collecting sEEG data in epilepsy is too difficult, it might be worth considering using other types of brain signals, which could be more suitable for applying machine learning techniques. Thank you for your suggestion. While there are certainly many different types of brain signals that can be analyzed using machine learning techniques, possibly with larger datasets, we believe that there is a lot of value in applying machine learning techniques to sEEG datasets because: 1. sEEG is currently the gold standard invasive neural recording modality used in humans. Therefore, improving neural decoding based on sEEG bring it closer to clinical translation compared to other neural recording modalities which might provide a lot of data from animal models but have very rarely been used in humans due to safety or other concerns (such as microelectrode array recordings for example). Edit: We would also like to emphasize that _even if another neural recording modality was used, the only clinical population approved for collecting intracranial neural recordings would be epilepsy patients_. Therefore, the challenges associated with collecting a large dataset would carry over to any other modality as well. 2. there is a lot of scientific value in showing that machine learning tools can be used on smaller datasets, as in numerous fields (healthcare & medicine, astronomy, environmental science, to name a few) collecting large datasets can be extremely costly and time-consuming. Our work is especially valuable in that sense, since we show that combining many small datasets, despite data heterogeneity, can lead to better machine learning models, compared to training on the smaller datasets individually. Thanks for engaging in the discussion! We very much appreaciate your insights and truly believe that our work has become stonger based on your feedback and suggestions.	Summary: The paper presents a novel approach to sEEG decoding. Authors highlight the benefit of using data from various subjects for training. However, due to the nature of the sEEG technique, collection of such data is difficult. Authors provide a new deep learning based decoding approach which utilizes spatial positional encoding (to provide a model with information on electrodes’ locations), temporal and spatial attention, MLP and subject-specific regression heads. Then, authors train their model in multiple frameworks and highlight the efficacy of multi-subject training. Strengths: The paper highlights a novel approach to sEEG decoding which enables training of their model on multiple subjects. Generalization across subjects is overall a very important and difficult task to achieve in many modalities and applications of neuroimaging. Authors present a method which has a value in itself and provides ideas for future research in this direction. A paper clearly presents the ideas and performed experiments. Visualizations help to understand both the data collection process and the deep learning architecture. Weaknesses: 1. No comparison with other methods during within-subject training was done. Authors only provide the results for their own architecture for within-subject experiments. Therefore, they only show that their multi-subject trained model is stronger compared to their single-subject model. However, it might be possible that some of the other existing single-subject State-of-the-Art models will be more effective than authors’ multi-subject model on authors’ data. The importance of these comparisons are magnified by the fact that authors’ dataset will stay private (therefore only the authors of this paper can provide metrics for other models applied to this dataset); and by the reasonably large size of authors’ model (it might be too big to be efficiently trained on a single person data, while other models, which were developed for single-subject tasks, might be lighter and train better on small datasets). 2. Decoding performance with and without spatial positional encoding seems very similar. For such a difference it is interesting to see if it has a statistical significance. Technical Quality: 3 Clarity: 3 Questions for Authors: 1. How many trainable and frozen parameters there were during training and finetuning of the model? 2. How large is the variance in the response time within each subject? 3. Are all K convolution kernels in Convolution tokenizer the same for all electrodes? 4. How much recording hours of data was used overall and on average per subject (only the electrode-hours are provided)? 5. What is the statistical significance of the metrics increase while using positional encoding compared to not using it? Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 1 Limitations: Yes, authors provide a good description of the limitations and address potential topics for future research (larger datasets, self-supervised pre-training). Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your thoughtful feedback and suggestions. We are excited to read that our "method has a value in itself and provides ideas for future research"! Here, we provide our response to your comments/questions and the results from new experiments that we ran to address your concerns. We hope that our answers will clear any lingering concerns. We are also available to provide further clarification, if needed. ## Weaknesses > 1. No comparison with other methods during within-subject training was done. Authors only provide the results for their own architecture for within-subject experiments. Therefore, they only show that their multi-subject trained model is stronger compared to their single-subject model. However, it might be possible that some of the other existing single-subject State-of-the-Art models will be more effective than authors’ multi-subject model on authors’ data. The importance of these comparisons are magnified by the fact that authors’ dataset will stay private (therefore only the authors of this paper can provide metrics for other models applied to this dataset); and by the reasonably large size of authors’ model (it might be too big to be efficiently trained on a single person data, while other models, which were developed for single-subject tasks, might be lighter and train better on small datasets). We thank the reviewer for this constructive criticism. To address this, we trained classic and state-of-the-art single-subject models to compare against our model. The results are summarized in Table 1 of our General Response (see also Figure 1 of the attached pdf) and suggest that our architecture outperforms the baselines when trained on either single-subject or multi-subject data. Specifically, our single-subject models outperformed all baselines by $\Delta R^{2} >= 0.03$, while our multi-subject models outperformed all baseline by $\Delta R^{2} >= 0.12$. Importantly, our transfer learned single-subject models also beat the baselines by $\Delta R^{2} >= 0.10$. We hope that these comparisons are sufficient to address your concerns. We plan to include this analysis in section 4 of our revised manuscript. > 2. Decoding performance with and without spatial positional encoding seems very similar. For such a difference it is interesting to see if it has a statistical significance. To identify whether the difference in the decoding performance with and without spatial positional encoding is statistically significant, we performed a Wilcoxon rank-sum test between the groups: (1) $R^{2}$ of all subjects obtained by training the multi-subject model with spatial positional encoding, and (2) $R^{2}$ of all subjects obtained by training the multi-subject model without spatial positional encoding. The test returned a test-statistic = 0.34 and a p-value = 0.73, indicating that there is no significant difference between the performance of the model with and without spatial positional encoding. We plan to include this result in section 4.5 of our revised manuscript. ## Questions > 1. How many trainable and frozen parameters there were during training and finetuning of the model? The total number of trainable parameters for the multi-subject model is 797,095. From those parameters 753,394 are shared across subjects and the rest 43,701 parameters are subject-specific (2,081 parameters per subject). When training single-subject models (section 4.2) and multi-session, multi-subject models (section 4.3), all parameters of the model (shared + subject specific) were trained. When transferring the pretrained, multi-subject models to new subjects (section 4.4), for the first 400 epochs the shared parameters were kept frozen (753,394 parameters) while the subject-specific parameters were being trained (2,081 parameters per subject). For the remaining 600 epochs, all parameters were unfrozen and trained. We plan to include those numbers in section A.2 of our revised manuscript. > 2. How large is the variance in the response time within each subject? For convenience, the mean of the variance of the response times across all 21 subjects of our dataset is $\sigma^{2} = 0.011 \pm 0.0017$ (mean $\pm$ sem) sec$^{2}$. The variance of the response times for each subject is: (18, 9, 5, 6, 7, 3, 4, 5, 17, 25, 4, 9, 9, 13, 21, 19, 8, 31, 4, 11, 5) $\times 10^{-3}$ sec$^{2}$. > 3. Are all K convolution kernels in Convolution tokenizer the same for all electrodes? Yes. The K convolutional kernels that our tokenizer uses are the same for all electrodes of all subjects. This design choice increases the effective number of training samples available to the tokenizer, making it less prone to overfitting and increasing the model's robustness. We will make sure to ephasize this in section 3.2.1 of our revised manuscript. > 4. How much recording hours of data was used overall and on average per subject (only the electrode-hours are provided)? The total recording hours of data used during model training were 1.54 hrs. The average per-subject recording time that was used for model training was 4.39 $\pm$ 0.39 (mean $\pm$ sem) mins. We will make sure to add those is section A.2 of our manuscript. > 5. What is the statistical significance of the metrics increase while using positional encoding compared to not using it? The increase in the performance due to spatial positional encoding compared to not using it is not statistically significant. Please refer to our response to your comment under _Weaknesses (bullet point No. 2)_ for a detailed description of how we obtained this result.	Rebuttal 1: Rebuttal: We thank the reviewers for their thoughtful feedback. The reviewers pointed out that our unified multi-session, multi-subject modeling approach "is a substantial step forward compared to traditional single-subject approaches" (pdN2) that "provides ideas for future research" (VKBz). Some highlights from the reviewers: * Method: "the paper highlights a novel approach to sEEG decoding which enables training of their model on multiple subjects" (VKBz), " The detailed methodology [...] ensures the robustness of the proposed approach" (pdN2), "The ability to pretrain the model on a larger multi-subject dataset and fine-tune it for new subjects with minimal training is a valuable feature, enhancing the model's practicality and applicability" (o6UF) * Impact: "Authors present a method which has a value in itself and provides ideas for future research in this direction" (VKBz), "The paper addresses an important issue of data heterogeneity in sEEG recordings among participants which makes constructing large dataset challenging" (j3GS), "The proposed framework effectively addresses the heterogeneity across subjects, a significant challenge in sEEG data processing" (o6UF), "Generalization across subjects is overall a very important and difficult task to achieve" (VKBz) * Experiments \& Evaluation: "The model's performance is validated using a substantial dataset (21 subjects), showing consistent improvement in performance for most subjects" (o6UF), "The experimental details are clearly provided" (j3GS), "The ablation study is insightful" (j3GS) * Writing \& Presentation: "The paper is well-organized and clearly written, making it accessible to readers from both neuroscience and machine learning backgrounds" (pdN2), "well-written and easy to follow" (j3GS),"paper clearly presents the ideas and performed experiments" (VKBz) Based upon reviewer comments, we ran a number of new experiments, and are currently working on the following revisions to our manuscript: * _Comparisons with single-subject baselines_. As suggested by reviewers j3GS & VKBz, we compared the performance of our model against other traditional and state of-the-art models (see Table 1). The results indicate that our model outperforms other approaches across the board. When trained on single-subjects, our model outperforms the baselines by $\Delta R^{2} >= 0.03$, while when trained on mutli-subject data, our model beats the baselines by $\Delta R^{2} >= 0.12$. Importantly, the single-subject models obtained by finetuning multi-subject models to new subjects also beat the baselines by $\Delta R^{2} >= 0.10$. Those results demonstrate the power of multi-subject approaches compared to single-subject ones. _Table 1. Comparison of our model's performance against baselines. Results report mean $\pm$ sem._ Model \| $R^{2}$ --- \| --- PCA + Wiener Filter \| 0.13 $\pm$ 0.18 PCA + L$_{2}$-Regression \| 0.17 $\pm$ 0.14 PCA + XGBoost \| 0.17 $\pm$ 0.06 MLP \| 0.23 $\pm$ 0.06 CNN + MLP \| 0.27 $\pm$ 0.07 PCA + L$_{1}$-Regression \| 0.27 $\pm$ 0.04 Ours (Single-Subject) \| 0.30 $\pm$ 0.05 Ours (Multi-Subject) \| 0.39 $\pm$ 0.05 Ours (Multi-Subject + Finetune) \| 0.41 $\pm$ 0.05 Ours (Single-Subject + Finetune) \| 0.37 $\pm$ 0.06 * _Comparison of other positional encodings (PEs) against ours_: All reviewers pointed out that model performance only benefits slightly by our spatial PE. To address this, we trained variants of our architecture using different PEs and compared them against ours (see Table 2). The results suggest that our proposed PE performs as well as, or better than other approaches. However, we echo the reviewers' concern that the gains are modest. Therefore, we plan to include these results along with a discussion of other possible PEs, based on whole brain MRIs (j3GS) or based on atlases other than MNI (o6UF), in our revised manuscript. _Table 2. Comparison of different PE schemes. Results report the mean $\pm$ sem._ PE Type \| $R^{2}$ --- \| --- Vaswani (2017) \| 0.16 $\pm$ 0.04 MNI-Fourier \| 0.39 $\pm$ 0.05 No PE \| 0.37 $\pm$ 0.05 MNI-RBF (ours) \| 0.39 $\pm$ 0.05 * _Real-Time applicability_. Reviewer pdN2 suggested we check whether our model can be used in real time. To test this, we measured our model's inference time on two machines (see Table 3). The results show that our model can be used in real time, since its inference time is on the order of msec, while real time systems run on the order of 100 msec. _Table 3. Inference time on different hardware._ Machine \| CPU \| GPU \| Units -- \| -- \| -- \| -- AMD EPYC 7502P + Nvidia A40 \| 9.1 \| 5.1 \| msec Inter Core i9 + Nvidia A2000 \| 4.0 \| 7.9 \| msec * _Separate attention in space & time vs 2-D attention over space & time_. Reviewer j3GS suggested we check whether our model's decoding performance would benefit by employing one 2-D self-attention mechanism over the time & space dimensions of our data, instead of two separate self-attention mechanisms over the aforementioned dimensions. We identified that our method outperforms the 2-D attention variant by $\Delta R^{2} = 0.06$ (see Table 4). Our proposed architecture trains faster, too. _Table 4. Comparison of our approach vs the 2-D attention variant. Results report the mean $\pm$ sem._ Model Variant \| $R^{2}$ score \| Training Time --- \| --- \| --- Combined attn in time & space \| 0.33 $\pm$ 0.05 \| 141.6 $\pm$ 3.23 mins Separate attn in time & space (Ours) \| 0.39 $\pm$ 0.05 \| 25.7 $\pm$ 0.03 mins Impact of this work: This work is the first to train a unified, multi-session, multi-subject models for neural decoding based on sEEG. We demonstrate our approach on a very diverse dataset, with data from 21 subjects whose electrodes are heterogenously placed in brain locations that are unique to each subject. We show that pretrained multi-subject model can be transferred to new subjects, demonstrating their practicality and applicability. This work highlights the power of multi-subject approaches for neural decoding based on sEEG. Pdf: /pdf/4546383f24a523959e81e0b0a2653ad95168622d.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Mind the Graph When Balancing Data for Fairness or Robustness	Accept (poster)	Summary: This paper theoretically studies the applicability of data balancing in achieving fairness or robustness. The paper shows that data balancing may fail depending on the data generation mechanism. The paper introduces conditions for data balancing to produce invariant and optimal models. The paper also shows that data balancing can negatively impact fairness or robustness when combined with regularization strategies. Strengths: Originality The paper extends the previous results on data balancing as mitigation for invariant models by considering different failure models and proposes strategies to distinguish between them. Qualify The paper offers some valuable insights into data balancing techniques, especially the failure modes of data balancing. Weaknesses: This theoretical work on data balancing for fairness and robustness in machine learning presents some valuable insights, but falls short in several key areas. The paper's main contribution lies in demonstrating cases where data balancing techniques fail to achieve fairness. However, it does not effectively synthesize these findings into clear principles or rules, lacking a clear, overarching takeaway message. A more effective approach might have been to distill the various cases and propositions into a set of guiding principles or a unified framework for approaching fairness using data balancing. The authors present several propositions in Section 4, summarizing some of their results. While these propositions offer a formal structure to the paper, the conclusions they provide are relatively intuitive and do not significantly advance the field's understanding of data balancing. Another limitation of the paper is its focus on negative results. The authors primarily demonstrate scenarios where data balancing techniques are ineffective ("CANNOT results"), without offering constructive solutions to these identified problems. This approach, while valuable for highlighting potential pitfalls, reduces the paper's overall significance and applicability. Technical Quality: 3 Clarity: 3 Questions for Authors: In Assumption 2.3, does “a function of X” mean “a subset of X”? Can the proposed method be applied to other types of distribution shift, like prior shift or concept shift? Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: N/A Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for their comment and evaluation of our work. We respond to each comment below and provide a new table and figure in the general rebuttal. We hope that these changes provide a more balanced and guiding framing of data balancing for fairness and robustness and that you will consider revising your score if they do. W1: lack of guidance Based on this comment and on the suggestion from Reviewer YT39, we now provide a table including each graph, whether data balancing provides an invariant and optimal model, whether regularization does (and which type), and next steps if they don’t. We note that section 4 provides conditions that are not dependent on the causal graph of the application and that Proposition 5.1 also holds irrespective of the graph. W2: intuitive results We partially agree with the reviewer that some results might seem intuitive to researchers familiar with the field. We would however argue that most practitioners are not aware of the limitations of data balancing, and that Proposition 5.1 and its consequences on the interaction between data balancing and other mitigation strategies are novel. To better highlight interesting cases, we slightly modify Figure 1(b) to refer to a purely spurious dependence between $Y$ and $Z$ in the causal case. While it might be intuitive for purely spurious cases to be addressed with joint data balancing, we show that for a causal case this is not a valid assumption. We also add experiments with Amazon reviews to illustrate this result. Section 3: Causal task: helpfulness of reviews with Amazon reviews (Ni et al., 2019). Inspired by Veitch et al. (2021), we refer to the causal task of predicting the helpfulness rating of an Amazon review (thumbs up or down, $Y$) from its text ($X$). We add a synthetic factor of variation $Z$ such that words like ‘the' or ‘my' are replaced by ‘thexxxx' and ‘myxxxx' ($Z=0$) or ‘theyyyy' and ‘myyyyy' ($Z=1$). We train a BERT (Devlin et al., 2019) model on a class-balanced version of the data for reference (due to high class imbalance), and compare to a model trained on jointly balanced data, both evaluated on their training distribution and on a distribution $P^0$ with no association. In this case, jointly balancing improves fairness and risk-invariance, with the model's performance on the training distribution (acc.: $0.574\pm0.016$) being similar to that on $P^0$ (Table 1). This however comes at a high performance cost when compared to the class balanced model's performance on $P$ (acc: $0.658\pm0.015$). Therefore, data balancing might not lead to optimality for this causal task.” Section 5: We add the following empirical analysis to the discussion on the causal task of Figure 1(b). Please see the pdf added to the main rebuttal for the figure and table. “We illustrate this result on the Amazon reviews dataset from Section 3 by imposing a marginal MMD regularization $f(X) \perp Z$ during training and evaluating risk-invariance across multiple $P' \in \mathcal{P}$. When training on $P$, we observe that the regularization allows to 'flatten' the curve, such that from medium to high values of MMD regularization, the model is risk-invariant (Figure 4). On the jointly balanced data, medium values of the regularization degrade risk-invariance (see green curves on Figure 4(b)). Overall, model performance is also lower for the models trained on $Q$ compared to models trained on $P$ across test sets from $P' \in \mathcal{P}$, at similar levels of regularization (see Figure 4(c) for MMD=16). This result displays that $X^\perp_Z$ is not a sufficient statistic for $Y$ in $Q$.” W3: focus on negative results Our work does provide success cases, including conditions for these. We also discuss cases in which balancing helps without leading to an invariant model. We hope that with the addition of the guidance table (answer to W1) and the results from Amazon reviews showing that the model is invariant but not optimal, the reviewer will agree that we provide a nuanced and helpful analysis of data balancing for fairness and robustness. Q1 A function of $X$ can be a subset of $X$ but can also express a latent variable that does not directly select features, e.g. in an image. We will clarify. Q2 In this work, we discuss risk-invariance, optimality and multiple fairness criteria. We select these criteria as they are best suited to capture the effects of undesired dependencies between $Y$ and $Z$ on the model’s outputs. In particular, risk-invariance to correlation shift corresponds to the settings of “spurious correlations” discussed in the field of robustness (e.g. Sagawa et al., 2020). Using a similar framework, one could define conditions for other risk-invariance criteria. This is mentioned in our discussion (line 372). It is however unlikely that joint data balancing on $Y$ and $Z$ would provide invariant models if there is a covariate shift as the balancing does not affect $X$ directly. For concept or prior shifts, the same methodology could be applied, although having a canonical causal graph would help. We will add this comment to the discussion.	Summary: The paper analyses training risk invariant models using data balancing. The authors consider the cases in which data balancing might help obtain risk-invariant models and the cases in which data balancing does not achieve the desired effect. The paper also considers the effect of regularization for robust model training, and how that compares to data balancing. Strengths: The results presented are sound, and the problem considered in the paper is of practical relevance. I liked that the authors tried to analyse the problem on a simple semi-synthetic setup first, before moving onto the real-world data. This provides a nice test-bed to test and motivate the methodology presented. Weaknesses: 1. The paper only considers risk invariance w.r.t. correlation shift. Can this be generalised to other forms of distribution shifts? 2. The paper only considers the question of joint balancing of Y, Z. As the authors show in Proposition 5.1, joint balancing will not effectively remove the undesirable paths in G in all cases. Can the conditions be generalised to other forms of balancing? 3. Obtaining a DAG for a real-world setup involves the decomposition of $X$ (and positing causal relationships between these components). This seems like a non-trivial task in general. The authors don't touch upon the practical aspects of obtaining the DAG in the real world. 4. The paper does not provide a systematic methodology for determining whether data balancing is a good idea for a given real-world dataset. The experiment seems to be using a trial-and-error method to establish the failure modes, but this seems highly impractical. 5. Overall, I think the presentation can be improved. Certain parts of the paper are a bit vague. (See the questions below for more details.) Technical Quality: 3 Clarity: 2 Questions for Authors: 1. In line 161, does "performance" correspond to model accuracy? If so, how is the performance on $P^0$ lower than that on P? (where the latter has an overall accuracy of 0.717) 2. How do you try to decode $Z$ from the representation $\phi(X)$? This is an important piece of information that seems to be missing? 3. In Table 1, what is the test distribution on which the accuracy is measured? What is P(Z=1) for example, and is the test distribution of (X, Y, Z) fixed across the different tasks in Table 1? It seems that these test distributions differ across the different tasks. If so, the comparison of accuracy does not seem to be fair. 4. There is no motivation behind the choice of the 4 cases in Figure 1. These seem somewhat arbitrary. Why were these chosen specifically? Is there a systematic way of considering the different cases? 5. Does the model f need to be a neural network necessarily? If so, this should be made clear. 6. What do "penulatimate representation" and "intermediate representation" mean? Are these referring to the hidden layers of the model? 7. I found the paragraph starting on line 270 to be quite vague. For example, the authors talk about "regularization" without explicitly defining the regularization term. > "If we consider both the purely spurious correlation and the entangled case, we see that regularization and data balancing would have the same effects of blocking any dependence..." I am not sure I completely understand this statement either. The regularization is a methodology which would potentially modify the distribution of f(X), but the distribution of data (X, Y, Z) would still remain unchanged, so how does regularization change the DAG of data? In figure 3 and table 2, the accuracy on the original data distribution P should also be logged. In fact, in real-world settings, the practitioners would care about the accuracy on the original data distribution (not Q or P^0). Confidence: 3 Soundness: 3 Presentation: 2 Contribution: 2 Limitations: The authors have addressed the limitations of their work in the final section. Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for their comments and questions. We reply to each below, although the format of the rebuttal doesn’t allow us to provide the proposed text amendments. We prioritized answering all comments but would be happy to provide these suggested changes during the discussion. We hope that this alleviates your concerns and would appreciate a revision of our score if it does. W1: risk-invariance In this work, we discuss risk-invariance, optimality and multiple fairness criteria. We select these criteria as they are best suited to capture the effects of undesired dependencies between $Y$ and $Z$ on the model’s outputs. In particular, risk-invariance to correlation shift corresponds to the settings of “spurious correlations” discussed in the field of robustness (e.g. Sagawa et al., 2020). Using a similar framework, one could define conditions for other risk-invariance criteria. This is mentioned in our discussion (line 372). It is however unlikely that joint data balancing on $Y$ and $Z$ would provide invariant models if there is a covariate shift as the balancing does not affect $X$ directly. We will add this comment to the discussion. W2: other balancing schemes Our work focuses on joint balancing as it is commonly used to address undesired dependencies between $Y$ and $Z$. We briefly discuss class and group balancing in the Appendix, but they do not lead to an independence between $Y$ and $Z$ and are not included in further analyses. It is unlikely that unique conditions can be derived across multiple balancing schemes, especially as these balancing schemes are typically defined based on specific causal graphs (e.g. Kaur et al., 2023, Sun et al., 2023). For instance, Kaur et al. (2023) show that no unique regularization strategy or set of independences can be imposed to obtain an invariant model in an anti-causal case with multiple attributes. We will amend line 383 which discusses this. W3: decomposition of $X$ In Veitch et al. (2021), the authors display a causal and an anti-causal graph that decomposes $X$ into its subcomponents. They show that, under certain assumptions, this decomposition always exists. Therefore, when a causal graph of the application exists, the decomposition of $X$ can be performed based on the definitions of the subcomponents of $X$. Similarly, the relationships between these components can be defined by an upper-bound, i.e. only assuming the independences based on the definitions. In our work, we assume specific (in)dependencies between the subcomponents of $X$ to provide an upper-bound on the effectiveness of data balancing. We will add text under Assumption 2.3 to clarify this. We however agree that the decomposition increases complexity when the number of variables increases. In this case, grouping variables can ease the task, as in Kaur et al., 2023. W4: application in real-world In section 6, we posit that we have a partial causal graph, i.e. we make the assumption of an anti-causal task. While we hope to be in the case of Figure 1(a), our results suggest that the graph is more complex. To understand which graph might represent our data generative process, we consider how regularization interplays with potential failures and use these analyses to highlight which graph is most likely. This process does not perform “trial-error” but rather tests specific hypotheses and aims at identifying the most suitable mitigation strategy when the graph is not fully specified. We will make this clearer and reframe Section 6. Q1, Q3 All results in Table 1 are assessed on $P^0$. Performance on $P$ is mentioned in the text. We will clarify in the text and table caption. $P^0$ is the same for Figures 1(a) and (d), but includes $V$ for 1(c) as otherwise it would be out-of-distribution due to the absence of $X_V$. We note that we do not compare results with each other, but rather assess whether each case leads to an invariant and optimal model. Q2 To assess encoding, we perform transfer learning by fixing the representation $\phi$ and training a new linear layer $h$ that predicts the factor of variation $Z$. All experimental details are in Appendix D, including metrics and their operationalization (D.2). We will make this clear and move materials if possible. Q4 These graphs were selected as they represent different cases studied in the literature, albeit sometimes simplified to provide the upper bound for data balancing. This will be added. Beyond the illustration of our results, the specific selection of these graphs does not affect our results as we aim to be graph-independent (e.g. section 4, Proposition 5.1). Q5 The model does not require to be a neural network, although the regularization scheme might differ for different architectures. Q6 Yes, this will be clarified. We will also add that this condition should be respected by any architecture, although we only formalize it for a specific form of $f(X)$. Please see our response to W1 from Reviewer YT39 for the full rewrite. Q7 We will explicitly relate the recommended “independence between f(X) and Z conditioned on Y” to a regularization term (implemented in experiments with MMD). Q8 The regularization does not affect the DAG but would approximate a distribution generated from a DAG in which these paths are blocked. We will clarify in the text. Q9 We add the performance on $P$ in tables (see pdf). We note that practitioners who desire fairness and/or robustness criteria evaluate their model on multiple distributions, and that $P^0$ or $Q$ might be more suitable choices as discussed in Dutta et al., 2020.	Summary: The paper focuses on the topic of data balancing for fairness and robustness and uses a causal graph as a tool to analyze the effects of data balancing. In the paper, the paper tries to show both the positive impacts and potential pitfalls of data balancing. For the fairness aspect, the paper focuses on the independence between groups and labels in the data. For the robustness aspect, the paper focuses on the lowest risk across a family of target distributions. The paper uses several synthetic and benchmark datasets to support their theoretical analyses on data balancing. Strengths: * S1. The paper empirically shows both the positive and negative impacts of data balancing, which possibly provides some insights into both the fairness and robustness field. * S2. The paper also suggests some causal graph-based analyses to understand the effects of data balancing. Weaknesses: * W1. This paper examines both fairness and robustness, yet the relationship between these two aspects or the reason the paper focuses on these two remains somewhat obscure. The paper could benefit from giving a more in-depth discussion or intuition on why fairness and robustness are susceptible to similar issues. Potential discussions may include 1) how similar analysis can apply to these two different objectives and 2) why the paper focuses on fairness and robustness among various safety criteria. * W2. While the paper employs synthetic and benchmark datasets to illustrate various failure cases, a more concrete real-world motivating examples would further highlight the importance of addressing these failure cases in both fair and robust training. * Minor suggestion: It would be better to use full name of CBN in Figure 1. Technical Quality: 3 Clarity: 3 Questions for Authors: The questions are included in the weakness section. Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: The paper has reasonable limitation, future work, and impact section. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for their comments and suggestions. We respond to each point below: W1: fairness and robustness. Our work focuses on undesired dependencies between $Y$ and $Z$ and on the use of data balancing to mitigate any bias that might result from these dependencies. This focus directly maps to fairness criteria, as well as to robustness to distribution shift in which the additional factor of variation represents the environment. In fact, fairness and robustness criteria can be equivalent in certain cases, as described in [Makar and D’Amour, 2023](http://arxiv.org/abs/2209.09423). Amongst fairness and robustness, we consider multiple, widely used criteria. To the best of our knowledge, other safety criteria do not clearly map to this framing of undesired dependencies (e.g. privacy, accountability, recourse, interpretability, alignment) and do not refer to data balancing. We however note that some terms defined in the Ethics community can be evaluated with fairness and robustness metrics, such as representational harms (equivalent to demographic parity) or stereotypes (e.g. robustness to correlation shifts or equalized odds). We provide further discussion on the selection of fairness and robustness criteria in the preliminaries: Section 2.1.: Due to undesired independencies, a model may be optimal on $P$ but perform poorly on another distribution of interest $P’(X, Y, Z)$ (e.g. in deployment), and/or might display disparities across subsets of the data (e.g. $P(X, Y \|Z = 0)$). To identify such behavior, various safety criteria have been proposed, with criteria in the fields of fairness* and robustness to domain shift being specifically designed to capture changes in model outputs across distributions. W2: real-world motivating example.* In this work, we focus on simple cases to identify the successes and pitfalls of data balancing. We feel that our synthetic setup illustrates those best, due to their simplicity and the availability of the ground truth causal graph. To further illustrate failure modes in simple cases, we are adding a semi-synthetic version of Amazon reviews, which represents a causal case similar to that of Figure 1(b). Using this dataset, we show that data balancing overall improves fairness and robustness metrics, but does not lead to an optimal model. We further show that performing data balancing hinders the effectiveness of regularization as it leads to models with lower performance across multiple distributions, and introduces variance in the risk for higher values of the regularizing hyper-parameter. Section 3: Causal task: helpfulness of reviews with Amazon reviews (Ni et al., 2019). Inspired by Veitch et al. (2021), we refer to the causal task of predicting the helpfulness rating of an Amazon review (thumbs up or down, $Y$) from its text ($X$). We add a synthetic factor of variation $Z$ such that words like 'the' or 'my' are replaced by 'thexxxx' and 'myxxxx' ($Z=0$) or 'theyyyy' and 'myyyyy' ($Z=1$). We train a BERT (Devlin et al., 2019) model on a class-balanced version of the data for reference (due to high class imbalance), and compare to a model trained on jointly balanced data, both evaluated on their training distribution and on a distribution $P^0$ with no association. In this case, jointly balancing improves fairness and risk-invariance, with the model's performance on the training distribution (acc.: $0.574\pm0.016$) being similar to that on $P^0$ (Table 1). This however comes at a high performance cost when compared to the class balanced model's performance on $P$ (acc: $0.658\pm0.015$). Therefore, data balancing might not lead to optimality for this causal task. Section 5: We add the following empirical analysis to the discussion on the causal task of Figure 1(b). Please see the pdf added to the main rebuttal for the figure and table. “We illustrate this result on the Amazon reviews dataset from Section 3 by imposing a marginal MMD regularization $f(X) \perp Z$ during training and evaluating risk-invariance across multiple $P' \in \mathcal{P}$. When training on $P$, we observe that the regularization allows to 'flatten' the curve, such that from medium to high values of MMD regularization, the model is risk-invariant (Figure 4). On the jointly balanced data, medium values of the regularization degrade risk-invariance (see green curves on Figure 4(b)). Overall, model performance is also lower for the models trained on $Q$ compared to models trained on $P$ across test sets from $P' \in \mathcal{P}$, at similar levels of regularization (see Figure 4(c) for MMD=16). This result displays that $X^\perp_Z$ is not a sufficient statistic for $Y$ in $Q$. Minor comment Thank you, we will not use the acronym in the Figure (see table in pdf).	Summary: The paper studies the role of data balancing e.g. on sensitive attributes or class labels on obtaining fair or robust models. It identifies various causal graphs and corresponding independence conditions under which data balancing is expected to succeed (or may fail) to provide recommendations on when to use (or not to rely on) it. The main contributions are in deriving sufficient conditions for data balancing to yield invariance under correlation shifts and relating the conditions to observations made in prior work through extensive experiments. Strengths: 1. Data balancing is a simple pre-processing method that one may occasionally resort to in practice to achieve fairness or robustness. Explaining when it may not work or when it works is significant. 2. Presentation and visualizations are clear, gives the required background, and explains the results in context of prior work. Jointly treating robustness and fairness in the exposition is a good way to generalize the results across the two problems. I like the organization of the results in successive sections 3-6 which are natural questions one may ask on data balancing. 3. The work discusses the implications when causal graph is not completely specified, features are learned, and tests the hypotheses on real, high-dimensional data (in contrast to causal ML work which typically only tests on tabular data). Experiments are carefully constructed. Weaknesses: 1. The writing can be clarified in places. For instance, I did not find a result which gives both necessary and sufficient condition contrary to the claim in Section 4 - please correct me if wrong. 2. (minor) Results can be summarized more concisely in a figure/table that shows the causal graphs or dependence structures where data balancing is fine and recommendations (e.g. on regularizers) for the other scenarios. 3. (minor) Some more recent works could be discussed. See comments below. Technical Quality: 3 Clarity: 3 Questions for Authors: Please clarify which results are necessary, sufficient, and both. Minor comments which do not require a response from the authors: Although not necessary, please consider citing the original works for risk invariance under correlation shift for the claim in line 194, e.g. from Rojas-Carulla 2018 Invariant Models for Causal Transfer Learning https://arxiv.org/abs/1507.05333 or Peters et al. 2016 Causal inference using invariant prediction: identification and confidence intervals https://arxiv.org/abs/1501.01332. Consider relating the findings to more recent work such as Kaur et al. 2023 Modeling the Data-Generating Process is Necessary for Out-of-Distribution Generalization https://arxiv.org/abs/2206.07837. Please specify whether it is feasible and how to check if the sufficient conditions hold. Consider commenting on data augmentation that might achieve the same conditions as data balancing in some scenarios. I would suggest adding a footnote that the term sufficient statistic differs slightly from its traditional definition e.g. in line 198 it is more appropriate to say that E[Y\|X_Z^\perp] is a sufficient statistic for the outcome risk function E[Y\|X], not for Y. --- After the response Thanks for responding to the my concerns. I do not have any more questions and feel that the work is significant in that it presents a better understanding of data balancing (a commonly-used method in fairness or robustness problems). I have raised my score to 7 as a result. Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: Limitations are acknowledged in good amount of detail. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for their positive comments on our work. We respond to the comments below: 1. Necessary and sufficient conditions: Thank you for this comment. Our results show that Propositions 4.2 and 4.3 are sufficient, while Proposition 4.4 is necessary. Based on the comment from Reviewer AEL7, we redefine Proposition 4.4 to make it more general, and rework the proof to highlight its necessity. We also rephrase Section 4 to avoid any confusion. Section 4: “In this section, we introduce a sufficient condition on the data generative process and a necessary condition on the model representation that, taken together, lead to a risk-invariant and optimal prediction model after training on $Q$.” Line 218: “We hence see that when a causal graph of the application is available, Corollary 4.3 can provide indicators on when data balancing might succeed or fail, with the caveat that Corollary 4.3 is not a necessary condition.” Line 220: “While Proposition 4.2 and its corollary provide conditions on the data generating process, prior work has demonstrated that the learning strategy also influences the model's fairness and robustness characteristics. In Proposition 4.2, we assume that the optimal risk-minimizer $f(X):=E_Q [ Y \mid X]=E_Q [ Y \mid X^{\perp}_Z]$ can be found during training a machine learning model $\hat f(X)$. Therefore, $\hat f(X)$ should be of a function class that can represent $E_Q [ Y \mid X^{\perp}_Z]$. Let's consider the special case where $\hat f(X)$ has the form $h(\phi(X))$, in which $h$ is a ``simple'' function of $\phi(X)$. This case would correspond to e.g. the last layers of a neural network or when learning a model based on a representation $\phi(X)$ (e.g. embeddings, transfer learning). We have the following necessary conditions on $h(\phi(X))$: Proposition 4.4. For $\hat f(X) = h(\phi(X))$ to be optimal and risk-invariant w.r.t. $\mathcal{P}$, we require that (i) $h(\phi(X))$ is able to represent $E_{Q}[Y \mid X_Z^\perp]$, and (ii) $h(\phi(X)) = E_Q[Y \mid X_Z^\perp]$ such that $h(\phi(X))$ is only a function of $X_Z^\perp$. In Proposition 4.4, we require that (i) $h(\phi(X))$ preserves all the information about the expectation of $Y$ that is in $X_Z^\perp$, and that $h(\phi(X))$ only changes with $X_Z^\perp$ and not with $X_Y^\perp$ or $X_{Y \wedge Z}$. Given our assumptions on $h$ and $\phi$, $\phi(X)$ must be disentangled in the sense that the simple function $h$ eliminates any dependence on $X_Y^\perp$ or $X_{Y \wedge Z}$. For example, if $h$ is a linear function, it must be possible to linearly project out all dependence on $X_Y^\perp$ and $X _{Y \wedge Z}$. We note that such a representation can be obtained even if the data is entangled, e.g. by dropping modes of variation during training. [...]” Appendix B.1. Proof: Remember that we assume that $\hat f(X)$ takes the form $h(\phi(X))$. If $h(\phi(X))$ cannot represent $E_{Q}[Y \mid X_Z^\perp]$, it is straightforward that $\hat f(X)$ cannot be optimal. Similarly, for $\hat f(X)$ to be risk-invariant w.r.t. $\mathcal{P}$, we need that $h(\phi(X)) = E_Q[Y \| X] = E_Q[Y \| X_Z^\perp]$ (sufficient statistics). As the right hand side varies only with $X_Z^\perp$, $h(\phi(X))$ can only vary with $X_Z^\perp$ and cannot depend on $X_Y^\perp$ or $X_{Y \wedge Z}$. 2. Summary of results: Thank you for this suggestion. Based on this comment and those of other reviewers, we now provide such a table, depicted in the attached pdf. 3. Recent work: Thank you for the additional references and other minor suggestions. We have incorporated them in our revision. With regards to Kaur et al., 2023, we note that our Figure 1(c) is a realization of the canonical graph presented in their Figure 2(a). We will add this work to our related works section and include it in possible mitigation strategies when considering multiple attributes. We however note that this work focuses on an anti-causal graph in which $X_c$ (unobserved) is the only cause of $Y$ (hence a sufficient statistics) and studies multiple mitigation strategies. On the other hand, we focus on data balancing and attempt to consider multiple data generative processes. We hope these clarifications alleviate your concerns and that you will consider amending your score to support the publication of this work. --- Rebuttal Comment 1.1: Title: Thanks for the response Comment: The response adequately addresses all of my concerns. I particularly appreciate the table summarizing the work and updates to the text on sufficient and necessary conditions. I feel that the work is significant in that it presents a better understanding of data balancing (a commonly-used method in fairness or robustness problems). I have raised my score to 7 as a result.	Rebuttal 1: Rebuttal: We thank the reviewers for their constructive comments and suggestions. We have answered each point in detail, but wanted to highlight some of the important changes here for visibility: - We reframed our findings in a comprehensive table to guide the reader for next steps (see pdf). - We have added a semi-synthetic dataset based on Amazon reviews to highlight how causal cases can behave unexpectedly (see pdf). - We have clarified the language throughout the paper and reworked Proposition 4.4 to highlight its necessity, as well as its framing in the context of neural networks. Our work provides a framework to investigate a popular formulation of data balancing, leading to the detection of failure cases as well as success cases. We discuss both the positive and negative aspects, and aim for generality rather than focusing on a single graph. We complement our theoretical insights with experiments on 3 datasets, in text and vision applications, using multiple architectures. We hope these changes and our response address most comments and are looking forward to further discussions during the next week. Pdf: /pdf/0d8d4fbb31861c8495a969c3fc21e1cb80db8b7e.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
How Molecules Impact Cells: Unlocking Contrastive PhenoMolecular Retrieval	Accept (poster)	Summary: The paper introduces MolPhenix for tackling the contrastive phenomolecular retrieval problem. MolPhenix employs a uni-modal pretrained phenomics model, an inter-sample similarity-aware loss function, and conditions on the representation of molecular concentration. This approach effectively addresses challenges such as experimental batch effects, inactive molecule perturbations, and encoding perturbation concentration. Experimental results demonstrate the model's effectiveness in the retrieval task. Strengths: - The paper is well-written and the motivation is clear. - The identified challenges are highly relevant and significant in the biological context, and the proposed methods are logical and well-conceived. - The experimental results indicate substantial improvements over baselines across various settings in the retrieval task. Weaknesses: - In Table 2 and Table 4, there is a significant performance increase for DCL, CWCL, SigLip, and S2L compared to other baselines. The source of these improvements is unclear. Conducting an ablation study for each of the three components of the method, corresponding to the three challenges, would provide more insights. - The paper primarily compares MolPhenix with CLOOME and a few other general domain objectives. However, numerous related studies specifically within the molecular-phenotype contrastive learning domain [1-6] are not discussed or compared. - The paper emphasizes the retrieval task, with experimental results showing only the top 1% recall accuracy. This limits the overall impact of the findings. Considering broader application scenarios based on the proposed method could enhance the paper's significance. [1] Cross-modal graph contrastive learning with cellular images. bioRxiv 2022. [2] Contrastive learning of image- and structure-based representations in drug discovery. ICLR MLDD 2022. [3] Molecule-Morphology Contrastive Pretraining for Transferable Molecular Representation. ICML CompBio 2023. [4] MMCL-CDR: enhancing cancer drug response prediction with multi-omics and morphology images contrastive representation learning. Bioinformatics 2023. [5] Removing Biases from Molecular Representations via Information Maximization. ICLR 2024. [6] Learning Molecular Representation in a Cell. arXiv 2024. Technical Quality: 3 Clarity: 3 Questions for Authors: - The retrieval accuracy results in the paper are reported as top 1% accuracy. However, this metric may be less informative when the retrieval set is very large, as the top 1% can still include a substantial number of molecules. Could the authors also provide results for top N accuracy, where N = 1, 10, and 100? Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: The authors have noted several limitations in their methods and experiments. Additional limitations are listed in the Weaknesses and Questions sections. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for providing detailed feedback for our paper. Below, we aim to address your concerns point-by-point Concern #1: In Table 2 and Table 4, there is a significant performance increase for DCL, CWCL, SigLip, and S2L compared to other baselines. The source of these improvements is unclear. We assess the effectiveness of S2L, SigLip, and DCL losses by analyzing the gradient flow of the InfoNCE and DCL formulations. In particular, we analyze the cases where inactive molecules cause the gradient to vanish, inhibiting training using InfoNCE and variants thereof. Decoupled contrastive learning (DCL) loss is an effective alternative to the InfoNCE loss due to the modification by removing the positive term from the denominator: $$ \mathcal{L}\_{\text{DCL}} = - \frac{1}{N}\sum\_{i=1}^N \left[ \log \frac{ \exp(\langle \mathbf{z}\_{x\_i}, \mathbf{z}\_{m\_i} \rangle / \tau) }{ \sum\_{k = 1, k \neq i}^{N} \exp(\langle \mathbf{z}\_{x\_i}, \mathbf{z}\_{m\_k} \rangle / \tau) + \cancel{\exp(\langle \mathbf{z}\_{x\_i}, \mathbf{z}\_{m\_i} \rangle / \tau)} } \right]. $$ The authors show that when computing the gradient of InfoNCE, the term $q_{B,i}$ which they name the negative-positive coupling (NPC) term modulates the gradient of each sample and in cases where the term becomes small gradient flow is inhibited: $$ q\_{B,i} = 1 - \frac{ \exp(\langle \mathbf{z}\_{x\_i}, \mathbf{z}\_{m\_i} \rangle / \tau) }{ \sum\_{k = 1, k \neq i}^{N} \exp(\langle \mathbf{z}\_{x\_i}, \mathbf{z}\_{m\_k} \rangle / \tau) + \exp(\langle \mathbf{z}\_{x\_i}, \mathbf{z}\_{m\_i} \rangle / \tau) }. $$ NPC can be small when the positive samples are too close to one another, when there is a small number of negative samples, or when the negative samples are too simple to discriminate versus the positive pair. By removing $\exp(\langle \mathbf{z}\_{x\_i}, \mathbf{z}\_{m\_i} \rangle / \tau)$ from the denominator, DCL simplifies the training thus removing the NPC term from the gradient calculation. We hypothesize that in our case inactive molecules tend to be simple negatives, thus inhibiting the gradient flow that would otherwise be helpful to the model training. Training the model with a loss that separates the positive gradient term (attracting samples from two modalities) from the negative (repelling negative pairs) achieves higher overall performance. Similarly to DCL, SigLIP and S2L losses are computed for each pair of samples independently, thus separating the positive and negative loss terms. Thus the gradient calculation for informative samples is unaffected by the NPC term, resulting in higher overall performance. Concern #2: The paper primarily compares MolPhenix with CLOOME and a few other general domain objectives… numerous related studies specifically within the molecular-phenotype contrastive learning domain. We thank the reviewer for an in depth exploration of relevant works. We note that the second paper linked is an early presentation of CLOOME (2023) to which we extensively compare (2nd referenced paper in reviewer suggested list). In addition we utilized a number of strong baselines from the Image-Text multi-modality literature such as CWCL (2023), SigLIP (2023), and DCL (2021). We agree with the reviewer that we can strengthen the pheno-molecular multi-modal related works section. We focussed our assessment on works that innovate on the methodological components but agree it is important to capture a broader perspective. We note that these additional works support the importance of MolPhenix as it demonstrates the importance of learning an effective joint embedding of phenomic experiments and molecular structures. MolPhenix contributions can be used in further improvement of utilizing phenomics and cell-profiliing experiments for cancer cell line drug response prediction (4th referenced paper in reviewer suggested list) and gene knockout predictions (6th referenced paper in reviewer suggested list). As the authors of “Cross-modal graph contrastive learning with cellular images” conclude in their paper: “There are still some challenges that need to be addressed, such as inherent data noise and batch effect. These could be resolved by designing specific encoders for cellular images, optimizing cross-modal fusion mechanisms, and introducing heterogeneous cross-modal data”. Our work aims to introduce general methods for extracting additional information from phenomic data such as k-patch averaging, S2L inter-sample similarity aware loss, and concentration encoding. We have updated our related Molecular-Phenomic Contrastive Learning section to reference and discuss the listed works. Concern #3: Could the authors also provide results for top N accuracy, where N = 1, 10, and 100? In the Image-Text domain it is common to provide N=1,10,100 0-shot class retrieval results. Since the number of classes between studies for a given dataset is consistent, top-K results always correspond to a semantically meaningful metric. However, in our case we believe these statistics might be misleading since different works evaluate on datasets of different sizes, thus making the N=1 recall task of varying difficulty in a dataset of 100 molecules VS 100,000. Other published works resort to a similar strategy, for example “Cross-modal graph contrastive learning with cellular images” in Table 1 report Hit@1, 5, 10 which actually correspond to percentages due to the subsampling of the overall data to 100 data points. Similarly, “Molecule-Morphology Contrastive Pretraining for Transferable Molecular Representation” report top 1, 5, and 10% retrieval in Figure 2. We note that in the external dataset - held out dose evaluation setting, the dataset consists of 1639 molecules making the top1% include just 16 molecules total. We thank you for a detailed and thorough assessment of this work. Please let us know if there are any additional points we can discuss, to improve your assessment of our work. --- Rebuttal Comment 1.1: Title: Reply to rebuttal Comment: I want to thank the authors for their detailed responses to my questions. --- Reply to Comment 1.1.1: Comment: Please let us know if there are any additional clarifications that we can provide that could increase your support for the acceptance of the paper	Summary: The paper makes a significant step forward in the task of phenotype-molecular retrieval–the task to find the molecule applied to perturb a set of cells given a microscopy readout. This problem can be modeled using multi-modal contrastive learning. The proposed MolPhenix method leverages pre-trained foundation models to encode the microscopy images and molecular structures. Then a novel contrastive loss is used which takes into account domain specific issues like batch effect and different concentrations of the applied molecules. Through thorough evaluations and ablations the authors show increased performance over a baseline. Strengths: - The paper tackles a task relevant for drug discovery and shows a significant step forward in predictive performance - The paper is very well written - The authors perform extensive experiments on held out molecules, phenotypes and dataset - The CLOOME baseline is tuned convincingly - The proposed guidelines for the task are supported by ablation studies - The paper combines and improves upon SOTA methods in multi-modal contrastive learning - The authors show domain knowledge by incorporating reasonable data processing and training strategies (batch effect removal + undersampling of inactive molecules) Weaknesses: - The authors focus on retrieval instead of evaluation of the latent space. Given the expressiveness of the leveraged foundation models, generating phenotypes or molecules should be possible. It would be great if the authors could comment on this or other explorations of the phenotypic space. - The authors train on a private dataset which makes the paper almost not reproducible. However, due to detailed model descriptions, the guidelines could be evaluated on other datasets. Technical Quality: 4 Clarity: 4 Questions for Authors: - Please elaborate on generative or mechanistic opportunities of the model - You argue MolPhenix cannot be applied to images. Please elaborate since instead of ph-1 a simple non domain-specific image feature extractor could be used. Have you studied the results? - Please comment on which model weights of ph-1, Mol-1, and MolPhenix are publicly available or you will be releasing Confidence: 3 Soundness: 4 Presentation: 4 Contribution: 3 Limitations: - Limited reproducibility due to private datasets and the model weights likely not being released Flag For Ethics Review: ['No ethics review needed.'] Rating: 8 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for the positive, insightful comments and the detailed feedback. We believe your perspective will help shape this into a stronger work. Below, we aim to discuss each of the suggestions and discussion points individually. Discussion point #1: “Generating phenotypes or molecules should be possible” We agree with the reviewer that this is a really exciting future direction for the work. As a first step in establishing pheno-molecular multi-modal learning, we decided to focus on the retrieval task due to its straight forward quantitative evaluation advantage. Our goal in this work was to establish a set of design decisions and guidelines that we can quantitatively investigate for effective latent space stratification. High pheno-molecular retrieval rates would indicate to us, that the model learns effective stratification of the latent space, opening up the door for future experiments with molecular and phenomics generation. This is a critical research direction with applications in drug-discovery such as identifying phenotypically similar molecular analogs with applications to generic molecule research. There is a unique set of challenges in evaluating high quality, diverse molecule designs. The state of the art for assessing molecule quality are still biological experiments, which we are excited to explore in future works. Discussion #2: The authors focus on retrieval instead of evaluation of the latent space. We certainly agree with the reviewer that MolPhenix embeddings should be able to provide additional interesting assessments as to the quality of the model latent space. To that end we have multiple experiments described in Appendixes E1 and E2 which we could not include in the main text due to space constraints. In addition, we conduct experiments assessing the quality of the learned molecular representation by experimenting on 35 downstream tasks, discussed in more detail in the general response (Table 4 attached PDF). Some brief details on appendix experiments: We were interested in assessing whether our molecular encoder captures pheno-activity throughout training. We found that by specifying only the molecular structure and the corresponding concentration, we are able to predict molecular activity levels with an ROC-AUC of 0.9. Visualization of the model latent space can be found in supplementary Figure 7. These results open up the door for in-silico activity screening that have previously been infeasible. In addition, these can be used as in-silico dose-response curve evaluations, finding an activity - dosage trade-off for a previously unscreened molecule. In appendix E2 we evaluate MolPhenix’s ability to identify previously known concordant perturbations between small molecules and genetic knockouts. From a database of known relationships, we encode the molecular perturbation with the MolPhenix molecular encoder and assess whether it is able to match them with a corresponding embedding of a genetic knockout. To create an embedding of a genetic perturbation, we embed results from a phenomic experiment of cell lines with a corresponding gene knocked out. We find that this in-silico perturbation concordance experiment is able to provide strong results relative to a fully experimental baseline. We believe these findings are important initial experiments demonstrating downstream utility applications of MolPhenix learned embeddings. Concern #3: The authors train on a private dataset which makes the paper almost not reproducible. However, due to detailed model descriptions, the guidelines could be evaluated on other datasets. We are unfortunately unable to release the training dataset for MolPhenix but aim to disseminate generalizable findings that can be helpful to other scientists working in this domain. To that end we provide pseudo-code and algorithmic descriptions for S2L loss. Additionally, our algorithm implementation is kept in PyTorch-like syntax for easier reproducibility. In addition, we evaluate our models on a large openly accessible dependent RxRx3 dataset which can be used for evaluation of other models and benchmarking other design choices by the community. Concern #4: Please elaborate on generative or mechanistic opportunities of the model This is an important point that we hope that we’ve addressed in sufficient detail in discussion points 1 and 2. Concern #5: You argue MolPhenix cannot be applied to images. Please elaborate since instead of ph-1 a simple non domain-specific image feature extractor could be used. We thank the reviewer for bringing up this important point, and would like to clarify that any sufficiently expressive image feature encoder can be used. In the general reviewer response, for example, we demonstrate that we can use an alternative encoder that is trained in a supervised fashion to predict identity of genetic perturbations (as an alternative to θPh-1). We hope that these experiments in addition to use of an ensemble of publicly accessible fingerprints provide sufficient evidence that the guidelines are generalizable across a number of public and private encoders. We have updated Table 1 caption to be a more clear description of our training pipeline: “We note that MolPhenix’s main components such as S2L and embeddings averaging relies on having a pre-trained uni-modal phenomics model.” Concern #6: Please comment on which model weights of ph-1, Mol-1 and MolPhenix are publicly available or you will be releasing? We note that the code and training data for Mol-1 are available, which we will provide references to in the final version of the paper. In addition, a public version of θph-1 will be available for inference. Thank you for your positive review and your interest in our work. We will be happy to further discuss and answer any additional points of interest. --- Rebuttal Comment 1.1: Comment: Thank you for your comprehensive response. I have increased my score.	Summary: The paper introduces MolPhenix, a framework for contrastive phenomolecular retrieval that integrates phenomic data and molecular structures into a joint embedding space. Key contributions include combining phenomic and molecular data for improved retrieval accuracy, proposing effective training guidelines, and addressing cumulative concentrations and label noise. The framework demonstrates significant performance improvements over existing methods, particularly in zero-shot settings, and is supported by comprehensive experiments and ablation studies. Strengths: The paper is well-structured and comprehensive, showcasing rigorous experimentation through extensive ablation studies, comparisons with baseline methods, and evaluations. Its strength lies in the detailed and methodical approach to validating the MolPhenix framework, providing strong evidence for its effectiveness and potential applications. The experimental design is robust, demonstrating the framework's superiority in various scenarios and contributing valuable insights to the field. Additionally, the integration of molecular and phenomic data into a joint multi-modal embedding offers a fresh perspective, enhancing the overall impact and originality of the work. Weaknesses: 1. The clarity of this work could be significantly improved. The task and background are not well stated, and the related work is not adequately introduced. Many biological terminologies are mentioned, creating a large gap between the introduction and the real dataset. 2. The paper could benefit from including comparisons with a broader range of state-of-the-art methods, particularly those from adjacent fields such as multi-modal representation learning in genomics and proteomics. This would highlight the specific innovations of MolPhenix more distinctly. 3. The significance of the work could be more explicitly articulated and demonstrated. Although terms like drug discovery are mentioned, the real-world impact is not clear for readers. Technical Quality: 3 Clarity: 2 Questions for Authors: 1. For molecular representations, did you consider combining GNNs and fingerprints? In other tasks, such as property prediction, their combination often surpasses the performance of each method individually. 2. Did you consider to report and compare metrics for top-5 and top-10 recall? Confidence: 3 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: The authors have adequately addressed the limitations. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for providing detailed feedback on our paper. We aim to address the feedback point by point below: Concern #1: The clarity of this work could be significantly improved We thank the reviewer for this constructive feedback, we believe this work is best assessed with the required context of molecular biology, so we aim to enhance the accessibility of our paper by adding a biological terms explanation in the appendix. In particular, we will define the following terms: phenomics, cell morphology, cell line (ARPE-19), molecular concentration, phenomolecular retrieval, cell staining, molecular perturbations, inactive molecule perturbations, batch effects, molecular fingerprints, initial cell state assumption. While we agree the clarity of the paper can always be further improved, we note that the presentation of our paper was a highlight for other reviewers: YXwu “The paper is well-structured and clearly written”, ELHC “The paper is very well written”, Vz3t “The paper is well-written, and the motivation is clear.” Getting high ratings in soundness (3, 3, 4, 3) and presentation (3, 3, 4, 3). Additional information on related works can be found in section 2, and we have expanded the “Related Work” section on molecular-phenomic approaches. Please let us know if this clarifies the accessibility of the paper, or if there is any additional terminology that we can add to the glossary. Concern #2: Comparisons with a broader range of state-of-the-art methods in … multi-modal representation learning in genomics and proteomics We’ve restricted the scope of this paper to studying phenomics and molecular modalities. While expanding to other biological modalities such as genomics or proteomics would undoubtedly be very interesting, it requires a significant commitment to curating the data and innovation in biological sequence model space. This is a direction we leave for future exploration. The reviewer could be interested in a 0-shot evaluation that we perform to investigate MolPhenix’s ability to generalize to genetic knock-out perturbations (Appendix D2). We assess the model’s 0-shot generalization capabilities that are known to have similar molecular effects to learned molecular perturbations. The evaluation demonstrates that MolPhenix learns the landscape of genetic perturbations, allowing the model to recover known biological pairs. On the methodological front, we compare to SOTA in the Image-Text multi-modal training consisting of DCL(2021), CWCL (2023), and SigLip (2023) - recent methods that have demonstrated significant success. In addition, we conduct thorough evaluations benchmarking recently published CLOOME (November 2023) model. Concern #3: Significance of the work could be more explicitly articulated and demonstrated Although the main text of our paper is mostly focused on pheno-molecular retrieval, we have some initial experiments in the appendix assessing the model’s ability to perform other biologically relevant tasks. We perform pheno-activity experiments, demonstrating that the learned embedding is predictive of molecule - concentration tuple morphology impact (Appendix E1). This opens the door to potential in-silico activity pre-sceening and in-silico dose-response curve construction. In addition, we perform 0-shot biological activity experiments mentioned earlier in Appendix D2. In the general reviewer response, we include new experiments showcasing the effectiveness of the learned latent space by conducting a KNN evaluation of the MolPhenix latent space. We assess the learned embedding on 35 molecular property prediction tasks across the Polaris and TDC datasets (see Table 4 in the attached PDF). Our findings indicate that MolPhenix, when trained with Fingerprint embeddings, consistently outperforms standalone input fingerprints, effectively clustering molecules according to their molecular properties. Concern #4: “Combining GNNs and fingerprints” This is a valuable evaluation for the completeness of our work. Please find the results for these experiments in the general reviewer response (Table 2 and 3 in the attached PDF). We find that combining pre-trained GNN and molecular fingerprints further enhances retrieval performance. Concern #5: “Report and compare metrics for top-5 and top-10 recall” We also report top-5% accuracy metrics in supplementary tables 8, 9, 10 and 11. We choose to report hits in top-K% since we have variable sized test sets. Top K metrics do not control for the difficulty of this task unless artificially subsampled to a pre-determined size. This is proportionally equivalent to Top-K% evaluation metrics, but has the downside of being stochastic contingent on composition of the batch. Kindly consider adjusting our overall score if our response addressed your primary concerns. We would be happy to answer any additional questions you may have in order for you to support acceptance of our work.	Summary: This paper introduces MolPhenix, a model designed to learn a joint latent space between molecular structures and microscopy phenomic experiments, addressing the challenge of contrastive phenomolecular retrieval. The authors point out three key challenges in this domain: limited paired data & batch effects, inactive molecular perturbations, and variable concentrations. To address these issues, they propose a set of guidelines: 1) leveraging a pre-trained phenomics foundation model (ph-1), 2) mitigating the impact of inactive molecules through undersampling and a novel soft-weighted sigmoid locked loss (S2L), and 3) encoding molecular concentration both implicitly (within the S2L loss) and explicitly (by parsing dosage concentration). The primary experiments focus on the task of phenomolecular retrieval. For active molecules, MolPhenix achieves up to 77.33% top-1% retrieval accuracy, representing an 8.1-fold improvement over the baseline. The paper includes necessary ablation studies and evaluations across multiple datasets, demonstrating the effectiveness of their approach in both cumulative and held-out concentration settings. Strengths: 1. Novel approach: The paper introduces MolPhenix, a comprehensive framework that addresses several key challenges in contrastive phenomolecular retrieval by combining multiple innovative techniques. This new framework demonstrates notably strong performance. 2. Concentration encoding: The study explores both implicit and explicit methods for encoding molecular concentration, enhancing the model's ability to capture dose-dependent effects and generalize across concentrations. The explicit concentration module and inactive molecule undersampling techniques may inspire future multi-molecule research. 3. Detailed ablation: The paper provides an in-depth analysis of results, including the impact of various components (e.g., loss functions, concentration encoding methods) on model performance, presented in both the main body and appendix. Weaknesses: The following are just some minor concerns, listed in descending order of importance: 1. Insufficient justification for S2L loss: While the paper introduces the S2L loss as a key contribution, it lacks a thorough theoretical analysis explaining why this loss function is suitable for the phenomolecular retrieval task. A more rigorous mathematical analysis of S2L would strengthen the paper's contribution. 2. Inadequate ablation of pretrained components: As a phenomolecular retrieval "framework", the study should include ablation studies using different molecular and phenomic encoders. However, it appears that experiments were conducted only with fixed molecular GNN and phenomic models. 3. Oversimplified treatment of batch effects: The paper claims to address batch effects through embedding averaging, but this approach may be too simplistic. A more detailed explanation of why simple averaging can alleviate batch effects, or some minor adjustments to this batch effect removal procedure, would be beneficial. Technical Quality: 3 Clarity: 3 Questions for Authors: Regarding the equality of involved datasets: 1. How would the model's performance vary if only the open-source RxRx3 data or only the private novel data were used? 2. Given that many components of MolPhenix are publicly pretrained models, is it feasible to construct a comparable model using solely open-source resources? Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The authors have properly adressed the limitations in their paper. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for providing detailed feedback on the paper. Concern #1: Additional justification for the S2L loss In this section we provide some additional intuition for the S2L loss and further relate it to previous works. We first assess the conceptual similarities between InfoNCE and CWCL loss and justify a similar extrapolation for the relationship between S2L and SigLIP losses. InfoNCE can be considered a special case of the CWCL loss, where $w_{ij}$ is set to 0 for all pairs of $i$ and $j$ unless $i=j$. Conceptually, this is equivalent to stating that all the negative pairs are equally distant from the reference sample. We will consider a uni directional loss CWCL, for identifying $\mathcal{X}$ from $\mathcal{M}$: $$ \mathcal{L}\_{\text{CWCL}, \: \mathcal{M} \rightarrow \mathcal{X}} = - \frac{1}{N}\sum\_{i=1}^N \left[ \frac{1}{\sum\_{j=1}^{N} \mathbf{w}^{\mathcal{X}}\_{i,j}} \sum\_{j=1}^{N} \mathbf{w}^{\mathcal{X}}\_{i,j} \log \frac{ \exp{\left( \langle \mathbf{z}\_{x\_i},\mathbf{z}\_{m\_j} \rangle / \tau \right) }} { \sum\_{k=1}^{N} \exp{ \left( \langle \mathbf{z}\_{x\_j}, \mathbf{z}\_{m\_k} \rangle / \tau \right) }} \right]. $$ If we set $w_{ij} = 0$ when $i \neq j$ and $1$ otherwise then the term $\Sigma_{j=1}^{N} w_{i,j}^\mathcal{X}$ evaluates to 1 and the above expression simplifies to: $$ \mathcal{L}\_{\text{InfoNCE}} = - \frac{1}{N}\sum\_{i=1}^N \left[ \log \frac{ \exp(\langle \mathbf{z}\_{x\_i}, \mathbf{z}\_{m\_i} \rangle / \tau) }{ \sum\_{k = 1}^{N} \exp(\langle \mathbf{z}\_{x\_i}, \mathbf{z}\_{m\_k} \rangle / \tau) } \right]. $$ In the case of CWCL, a non 0 $w_{i,j}$ determined by a within modality similarity function informed by a pre-trained model Similarly SigLip can be considered a special case of S2L when $w_{i,j}^{\mathcal{X}} = 0$ when $i \neq j$ and $w_{i,j}^{\mathcal{X}} = 1$ in the case $i=j$. This is the formulation of S2L $$ \mathcal{L}\_{\text{S2L}} = - \frac{1}{N} \sum\_{i=1}^N \sum\_{j=1}^N \log \left[ \frac{\mathbf{w}^{\mathcal{X}}\_{i,j}} {1 + \exp \left( -\alpha \mathbf{z}\_{\mathbf{x}\_{i}}.\mathbf{z}\_{\mathbf{m}\_{j}} + b \right) } + \frac{(1 - \mathbf{w}^{\mathcal{X}}\_{i,j})} {1 + \exp \left( \alpha \mathbf{z}\_{\mathbf{x}\_{i}}.\mathbf{z}\_{\mathbf{m}\_{j}} + b \right) } \right]. $$ It can be simplified to SigLIP by setting $w_{i,j}^{\mathcal{X}}$ to $1$ when $y_{i,j} = 1$ thus setting the term $\frac{(1 - \mathbf{w}^{\mathcal{X}}\_{i,j})}{1 + \exp \left( \alpha \mathbf{z}\_{\mathbf{x}\_{i}} \cdot \mathbf{z}\_{\mathbf{m}\_{j}} + b \right)}$, corresponding to $i \neq j$, we set $w_{i,j}^{\mathcal{X}}$ to $0$ thus negating the first part of the $\mathcal{L}_{S2L}$ loss, evaluating to: $$ \mathcal{L}\_{\text{SigLIP}} = - \frac{1}{N} \sum\_{i=1}^N \sum\_{j=1}^N \left[ \log \frac{1}{1 + \exp{ \left( \mathbf{y}\_{i,j}(-\alpha \: \langle \mathbf{z}\_{\mathbf{x}\_{i}}, \mathbf{z}\_{\mathbf{m}\_{j}} \rangle + b) \right) }} \right]. $$ Having a $0 \leq w_{i,j}^{\mathcal{X}} \leq 1$ allows us to inform the training by going between discrete negative labels to continuous informed by some prior information. This information is given by a pre-trained encoder $\theta_{Phi}$, in our case but can be informed by any pre-trained model. Concern #2: “Inadequate ablation of pre-trained components” To investigate the impact of pre-trained encoders, we perform additional experiments evaluating a supervised phenomic image encoder and highlight the ablation study of molecular fingerprints described in Figure 5. Instead of Ph1, we trained Molphenix framework using AdaBN, a CNN-based supervised phenomic encoder, with an analogous implementation discussed in [1]. We find that the general trends between Ph-1 and AdaBN are consistent with a slight decrease in overall performance. These findings provide additional support to the generality of the proposed guidelines. In addition, we leveraged from Mol1, which is a MPNN based GNN model with 1B parameters - an expressive capable molecular encoder [2, 3]. We note that combining Mol-1 embeddings with ECFP, MACCS, and Morgan fingerprints can provide Molphenix with richer information and yields overall higher MolPhenix performance (Table 2 and 3 of PDF in general response). We also performed an ablation study over publicly available fingerprint encoding methods, which are an effective baseline for molecular representations. We demonstrate that MolPhenix demonstrates strong retrieval performance with the use of fingerprints as an alternative to pre-trained GNN (Figure 5). Concern #3: “Oversimplified treatment of batch effects” The reviewer is accurate in noting that batch effect area is a smaller portion of the overall paper contributions as it is a rich area of research, especially in the biological sciences. Our intention was to highlight the ability of averaging phenomic encoder embeddings which is infeasible when working with samples directly in the image space. We perform an ablation, studying the effects of taking a random number of embeddings when performing averaging and find a small improvement in retrieval performance (Figure 5). Concern #4, Q1 & Q2: Training data employed is comprised of 1.3M pairs of perturbations, however, RXRX3 is composed of 1,674 known chemical entities at 8 concentrations each and is primarily used as a validation dataset. JUMP-CP [4] is a promising open source dataset which is being released in increments is a promising future phenomic data resource. With the availability of JUMP-CP it will be possible to train a fully open source analog of Molphenix. A beta version of Ph-1 is publicly available and will be linked in the updated paper. In our ablations demonstrated in Figure 5 we show that molecular fingerprinting methods are a strong baseline and are comparable with Mol-1 performance. Kindly let us know if our response above addressed your concerns. We will be happy to further discuss and answer any questions you may have.	Rebuttal 1: Rebuttal: We thank all the reviewers for providing detailed feedback on the paper. We are appreciative of the general support regarding the thoroughness and value of our scientific work: - “experimental design is robust, demonstrating the framework's superiority in various scenarios and contributing valuable insights to the field” - kfG5 - “significant step forward in the task of phenotype-molecular retrieval” - ELHC - “The experimentation of this work is comprehensive and detailed to justify the proposed method.” - YXwu - “comprehensive framework that addresses several key challenges.. demonstrates notably strong performance” - r9h5 - “the proposed methods are logical and well-conceived” - Vz3t We also appreciate the comments on the clarity of delivery, which is crucial for interdisciplinary works: - “The paper is well-structured and clearly written with clear explanations of the methodologies.” - YXwu - “The paper is well-structured and comprehensive” - kfG5 - “The paper is very well written” - ELHC - “The paper is well-written and the motivation is clear.” - Vz3t The reviewer feedback has been extremely useful in improving the work in terms of clarity and additional evidence. In our rebuttal, (1) broaden the scope of our work beyond pheno-molecular retrieval by highlighting and performing additional experiments, (2) we demonstrate additional encoders to support the generalizability of our guidelines, (3) enhance the overall clarity and scientific background. We expanded our evaluation with additional experiments supporting the utility of MolPhenix beyond retrieval. We conducted experiments evaluating the learned latent space, pheno-activity prediction, and zero-shot biological perturbation matching. In the attached PDF document, reviewers will find a KNN evaluation of the MolPhenix latent space, assessing the learned embedding on 35 molecular property prediction tasks across the Polaris and TDC datasets (Table 4 attached PDF). We find that MolPhenix trained with Fingerprint embeddings consistently outperforms standalone input fingerprints, demonstrating that the MolPhenix latent space effectively clusters molecules according to their molecular properties. We observed an interesting effect where prediction quality is positively correlated with implied dosage, indicating that MolPhenix learns dosage-specific effects. Furthermore, we aim to expand on this analysis in the appendix of the full paper. Additionally, we point reviewers to pheno-activity experiments demonstrating that MolPhenix can predict dosage-dependent molecular activity, opening opportunities for in-silico prediction of previously unseen molecular structures and dosages. Furthermore, we performed zero-shot biological perturbation predictions, by pairing known biological relationships between molecular structures and gene knockout phenotypes. This analysis provides preliminary evidence that MolPhenix learns underlying biological signals. These experiments are described in appendices E1 and E2, highlighting the utility of the learned latent space for biological challenges beyond identifying pheno-similar molecules (Supplementary Figure 7, 8). Several reviewers (YXwu, r9h5, ELHC) recommended expanding our evaluation to include additional encoders to demonstrate a broader capability of pheno-molecular recall guidelines. To that end, we conducted an additional study evaluating a supervised pre-trained vision encoder trained to predict the identity of a perturbation. The results are available in the included one-page document. In brief, we demonstrate the proposed guidelines generalize to a supervised CNN encoder used as a phenomolecular backbone. Additionally, we highlight our ablation study (Figure 5) where we investigate the impact of publicly available molecular fingerprinting methods as molecular encoders. Finally, we received valuable feedback on clarifying background terminology, adding pheno-molecular prior works, and improving the clarity of our table legends. We aim for this work to be accessible to scientists across disciplines, and have added a glossary of terms to the appendix and expanded the related works. We also provide additional justification and intuition for the S2L inter-sample similarity-aware loss in individual response to reviewer r9h5. We thank the reviewers for a careful reading of our paper and their broadly positive feedback. We believe that our changes, guided by your suggestions, strengthen the paper in terms of clarity and contribution for which we are grateful. We hope this work will be of interest to the broader community. References for all the responses: - [1] Sypetkowski, Maciej, et al. "Rxrx1: A dataset for evaluating experimental batch correction methods." Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2023. - [2] Masters, Dominic, et al. "Gps++: An optimised hybrid mpnn/transformer for molecular property prediction." arXiv preprint arXiv:2212.02229 (2022). - [3] Sypetkowski, Maciej, et al. "On the Scalability of GNNs for Molecular Graphs." arXiv preprint arXiv:2404.11568 (2024). - [4] Chandrasekaran, Srinivas Niranj, et al. "JUMP Cell Painting dataset: morphological impact of 136,000 chemical and genetic perturbations." BioRxiv (2023): 2023-03. Pdf: /pdf/ea4d1e55a8aa430bc33426d7832280ab3771cc4a.pdf	NeurIPS_2024_submissions_huggingface	2,024	Summary: This work focuses on predicting the molecular impact on cellular functions and investigates the problem of contrastive phenomolecular retrieval. It introduces MolPhenix, a model that leverages a joint latent space between molecular structures and microscopy-based phenomic experiments using contrastive learning. The main contributions include the use of a pre-trained phenomics model, a novel inter-sample similarity-aware loss (S2L), and molecular concentration conditioning, leading to a significant improvement over the previous state-of-the-art in zero-shot molecular retrieval of active molecules. Strengths: The introduction of the MolPhenix model, which utilizes a pre-trained phenomics model, a novel inter-sample similarity-aware loss (S2L), and molecular concentration conditioning, is original and demonstrates improvements over existing methodologies. The experimentation of this work is comprehensive and detailed to justify the proposed method. The paper is well-structured and clearly written with clear explanations of the methodologies. The problem investigated is important in the field of drug discovery and has a growing interest. Weaknesses: For the captions of Table 2~5, it is better to mention the experimental setting (cumulative concentration & held-out concentrations). The current captions are nearly the same (Table 2 vs. Table 4, and Table 3 vs. Table 5), which is kind of confusing. Technical Quality: 3 Clarity: 3 Questions for Authors: For the pretrained GNN, are there any specific advantages to choosing the current one, given that there are many other pretrained GNNs that can be used to extract molecular representations? Are there any discussions regarding the results of different concentration encoding choices? In a cumulative concentration setting, one-hot performs the best, while in a held-out concentration setting, not using any explicit concentration is the best choice overall. Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The authors have adequately addressed the limitations. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for a thorough and rigorous examination of our paper. Below we aim to address the questions and clarifications to further improve the work. Concern #1: For the captions of Table 2~5, it is better to mention the experimental setting. Thank you for your feedback. We changed the captions to clarify and simplify the experimental setting and explanation of results in Tables 2, 3, 4 and 5. For example, following is the updated caption for Table 2 “ Evaluation on cumulative concentrations: Top-1\% recall accuracy with use of the proposed MolPhenix guidelines evaluating impact of training loss on retrieval. We omit explicit concentration from this experiment.”. Concern #2: “Specific advantages to choosing the current [GNN].” Molphenix architecture is flexible, allowing that the proposed components be replaced by other phenomic or molecular pretrained models. However, we leveraged from Mol-1, which is a MPNN based GNN model with 1B parameters which allows us to maximize architecture expressivity while minimizing the risk of overfitting [2, 3]. We also note that combining Mol-1 molecular embeddings with ECFP, MACCS, and Morgan fingerprints can provide Molphenix with richer molecular information and yields overall higher performance of MolPhenix in both cumulative and held-out concentration scenarios. Results for active and all molecules retrieval of Molphenix trained on the discussed combinational molecular embeddings are available in table 2 and 3 of our global response (attached pdf). To evaluate the impact of GNN encoder we also perform a fingerprint ablation assessing the impact of fingerprint expressivity on retrieval indicated in Figure 5 of the paper. Concern #3: “discussions regarding the results of different concentration encoding choices” We note in the last sentence of section 5.2 in the paper that one-hot encoding shows significant improvements in a cumulative concentration setting, however it is limited to unseen dosage. In evaluation on held-out concentration, the model isn’t required to discriminate between molecules with different concentrations, thus explicitly providing dosage isn’t directly useful. In this experiment, sigmoid embedding can be thought of as a continuous way of separating “high” and “low” concentrations, showing effectiveness in this setting. We believe that the best encoding choice is dependable on the type of in-silico application. For example, if the objective is to identify unseen molecules with same morphological impacts or if the objective to simulate the impact of a molecule for un-tested dosage. We thank the reviewer for providing this feedback and we will add this additional discussion to the final version of the paper. Thank you for your positive feedback, and we will be happy to further discuss and answer any questions you may have.	null	null	null	null	null	null
Near-Optimal Dynamic Regret for Adversarial Linear Mixture MDPs	Accept (poster)	Summary: This paper studies the adversarial MDPs, which assume unknown (but stochastic) transition models and adversarial rewards. This paper adopts the linear mixture MDP setting, and they aim to study the dynamic regret, where the comparison policy are allowed to be changed along $K$ steps. The algorithm this paper proposed is a combination of policy optimization with exponential weights and online mirror descent. In the meantime, the mirror descent constraint set is updated according to the value target regression framework. This algorithm adopts the merits of both policy optimization and online linear optimization, and achieves optimal rate of regret. Strengths: This paper is well written. The algorithm, propositions and theorems are presented clearly. From technical side, the algorithm is computationally efficient and very simple. The regret of the algorithm matches the lower bound as well. Weaknesses: All techniques used in this paper are existed in previous works. Apart from this, I don't see significant drawbacks in this paper. Technical Quality: 4 Clarity: 4 Questions for Authors: I have the following questions for the authors: 1. Does the algorithm apply to other type of non-stationary measures, e.g. switching cost, etc? 2. The lower bound presented in this paper is a constructive lower bound. Can you obtain instance dependent lower bound (given any the transition model, to obtain a lower bound adapts to the transition model)? Confidence: 3 Soundness: 4 Presentation: 4 Contribution: 3 Limitations: Yes. The authors addressed all the limitations listed in the guidelines. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thanks for your appreciation of our work! We will address your questions below. --- Q1: "Does the algorithm apply to other types of non-stationary measures, e.g. switching cost, etc?" A1: Thanks for your helpful question. Our algorithm can also be adapted to other types of non-stationary measures, such as the generalized path-length described by Hall & Willett (2013). This measure is defined as $P_K^\prime = \sum_{k=2}^K \sum_{h=1}^H \\| q_{k,h}^c - \Phi_{k,h}(q_{k-1,h}^c) \\|$, where $\Phi_{k,h}(\cdot)$ is a known dynamic model. When $\Phi_{k,h}(\cdot)$ is an identity function, this measure reduces to the path-length we used. The advantage of this generalized path-length measure is that it allows us to incorporate prior knowledge of the environment's non-stationarity into the dynamic model. If the dynamic model can predict the environment perfectly, (e.g., $q_{k,h}^c = \Phi_{k,h}(q_{k-1,h}^c)$), the generalized path-length $P_K^\prime$ will be zero, much smaller than the traditional path-length $P_K$. This capability can significantly enhance the performance of our algorithm in environments where the non-stationarity can be accurately modeled. As we focus on the basic setting to present our main results more clearly, we did not include this extension in the current version. We will include a discussion of this extension in the revised version to highlight the flexibility and applicability of our algorithm to various non-stationary measures. --- Q2: "Can you obtain instance dependent lower bound?" A2: Thank you for your insightful questions. Obtaining an instance-dependent lower bound is indeed an interesting and challenging problem. To the best of our knowledge, there is no existing instance-dependent lower bound that directly depends on the transition kernel, even for static regret. The main difficulty lies in identifying a suitable quantity (such as max/min value, rank, etc.) of the transition kernel that accurately characterizes the problem's hardness. There are other types of instance-dependent lower bounds in the literature, such as those that depend on the optimal value function. However, obtaining such a lower bound is more difficult than deriving a worst-case lower bound, which is already a challenging and open problem. We believe that achieving an instance-optimal dynamic regret is an exciting direction for future research, and our work represents a significant step toward this goal. --- Q3: "All techniques used in this paper exist in previous works." A3: Indeed, the high-level algorithmic ideas in our work exist in previous works. However, previous efforts failed to achieve optimal dynamic regret due to the inherent limitations of two methodologies in dynamic regret analysis, as highlighted in Sec 3.1 and 3.2. It was only after realizing that the two methodologies could complement each other, as we demonstrate, that optimal dynamic regret could be achieved. One of our technical contributions lies in revealing this crucial yet underexplored connection between the two most popular methods. We believe this optimal result is interesting and important for the community. Moreover, our technique for exploring the connection of two methodologies could be useful for broader problems in RL theory. --- We hope our responses address your concerns. We are happy to provide further clarification if needed. Thanks! --- References: [1] Hall, E. C., & Willett, R. M., Dynamical models and tracking regret in online convex programming. In ICML'13. --- Rebuttal Comment 1.1: Comment: Thank you very much for your response. I do not have further questions.	Summary: The paper explores reinforcement learning in linear mixture Markov Decision Processes (MDPs) with adversarial rewards and unknown transitions. It analyzes policy-based and occupancy-measure-based methods, identifying their strengths and weaknesses. The paper introduced an algorithm that merges both approaches to achieve near-optimal dynamic regret, which is the first work that achieves this. Strengths: 1. The paper proposes a novel algorithm that combines the strengths of policy-based and occupancy-measure-based methods 2. According to the authors, the paper achieves near-optimal dynamic regret for adversarial linear mixture MDPs, and is the first work that does this. 3. The paper is presented nicely and compared to previous approaches Weaknesses: The paper lacks experimental validation, but could be reasonable given it is a theoretical paper. Intuitively it would not scale to complex high dimensional environments empirically if it were implemented into a practical algorithm. Technical Quality: 3 Clarity: 3 Questions for Authors: None. Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The authors discussed limitations of the work. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your positive feedback. We take this opportunity to highlight the key contributions of our work. --- Q1: "The paper lacks experimental validation, but could be reasonable given it is a theoretical paper..." A1: The primary goal of this work is to advance the theoretical understanding of adversarial linear mixture MDPs. The optimal dynamic regret of adversarial linear mixture MDPs is a fundamental and open question in RL theory. We design an algorithm that achieves the optimal dynamic regret for the first time, along with a matching lower bound. This accomplishment is made possible by revealing a crucial yet underexplored connection between two popular methodologies. We believe that our work represents a significant step forward in this area and provides valuable insights for the community. Further experimental validation and implementation into practical algorithms is an interesting and important direction for future work, although it is beyond the scope of this paper. --- We are happy to provide clarification if you have any further questions. Thanks! --- Rebuttal Comment 1.1: Comment: I appreciate the authors' response, which is reasonable. I will keep my score unchanged.	Summary: This work studies adversarial Linear Mixture MDPs, where the reward function can vary across different episodes, and aims to analyze the dynamic regret, where the baseline policy can also change across different episodes with respect to the dynamic environment. The authors propose a novel algorithm with a theoretical guarantee of the dynamic regret. In addition, the authors provide a hard-to-learn instance, which suggests that the regret guarantee cannot be improved by any algorithm. Strengths: 1. This work provide a algorithm with theoretically guarantee for the dynamic regret with adversarial environment, which is strictly stronger guarantee than the previous static regret analysis. 2. The authors provide a hard-to-learn instance, which suggests that the proposed algorithm has already achieved a near-optimal regret guarantee. 3. This paper is well-written and easy to follow. Weaknesses: 1. The proposed algorithm is computationally inefficient. Firstly, calculating the feature $\phi{k,h}$ requires evaluating the value function over all possible next states. Secondly, the performance of the occupancy-measure-based method relies on solving a global optimization problem over all state-action pairs. For methods with linear function approximation, such state/action spaces are usually huge and require high computational costs in the previous two steps. Though this is a common issue in the analysis of linear mixture MDPs and occupancy-measure-based methods, it will still affect the impact of the proposed algorithm. 2. There is a similar setting that also considers the dynamic regret guarantee (e.g., [1]) in a non-stationary environment. This non-stationary MDP setting measures the environment's dynamics by the difference between adjacent reward/transition functions. In contrast, this work measures the dynamics by the difference between adjacent policy/occupancy. It is better to make a comparison with this setting and previous results. Otherwise, it is challenging to compare fairly with previous work or evaluate the bound of the dynamic regret in this study. [1] Nonstationary Reinforcement Learning with Linear Function Approximation Technical Quality: 3 Clarity: 3 Questions for Authors: 1.For the regret guarantee, why does there exist a $\sqrt{HK \cdot H}$ term? It is directly dominated by the first term $d\sqrt{H^3K}$. 2. The baseline policy $\pi_k^c$ should be chosen with knowledge of the online reward function before episode $k$, , or it can depend on the future reward function until the end of episode $K$. Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: N/A Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your constructive review. We will address your questions below. --- Q1: "Why does there exist a $\sqrt{HK \cdot H}$ term in the regret bound? It is directly dominated by the first term $d\sqrt{H^3K}$" A1: Thanks for your careful observation. It is indeed directly dominated by the first term $d\sqrt{H^3K}$. We present the regret bound in this form to highlight the key three terms for this problem: the first term $d\sqrt{H^3K}$ represents the regret incurred from dealing with the unknown transition kernel, the second term $\sqrt{HK \cdot H}$ corresponds to the static regret when the environment is stationary, and the third term $\sqrt{HK \cdot P_K}$ captures the regret due to the non-stationarity of the environment. We will provide more intuition in the revised version. --- Q2: "The chosen of policy $\pi_k^c$ ..." A2: Yes, we can choose $\pi_k^c$ arbitrarily, allowing it to depend on the future reward function until the end of episode $K$. Our algorithm does not require the knowledge of the compared policy $\pi_k^c$ and our results hold universally for any sequence of compared policies. This flexibility enables our measure to adapt automatically to the non-stationary environment. --- Q3: "The proposed algorithm is computationally inefficient..." A3: We note that no prior work has achieved optimal dynamic regret, even for computationally inefficient algorithms. Therefore, the most central problem in this area is determining the optimal statistical complexity and how to achieve it. We design an algorithm with optimal dynamic regret for the first time, along with a matching lower bound. This is achieved by revealing a crucial yet underexplored connection between the two most popular methodologies, which is crucial for our results and could be useful for broader problems in RL theory. As the reviewer noted, computational complexity is a common issue for algorithms in this area and thus beyond the scope of this work. Achieving both computational efficiency and statistical optimality is an important and challenging future work. Nevertheless, our work has already made a significant step in this direction. --- Q4: "There is a similar setting that also considers the dynamic regret guarantee (e.g., [1]) in a non-stationary environment." A4: Thanks for pointing out this work, which also addresses the non-stationarity issue in MDPs and is thus related to our research. We will make sure to add a discussion on the connection between our work and [1] in the next version. However, it's crucial to highlight that the setting and results of [1] is fundamentally different from ours: - They study non-stationary stochastic MDPs, where the reward is assumed to be stochastically generated by parametric models with parameters continuously drifting. For example, the reward function is $r_k(s, a) = \theta_k^* \phi(s, a)$, where $\theta_k^$ is drifting over time. - In contrast, we study non-stationary adversarial* MDPs, allowing rewards adversarially chosen and do not make any stochastic assumption over the rewards. The objective is to be competitive with a sequence of time-varying compared policies. The algorithmic approaches to handle non-stationarity are also significantly different. For stochastic MDPs, methods such as sliding windows, restarts, and weighting are used. For adversarial MDPs, we employ two-layer structures. The optimal dynamic regret results also differ: $O(B^{1/3} K^{2/3})$ for stochastic MDPs and $O(P_K^{1/2} K^{1/2})$ for adversarial MDPs. An illustrative example highlighting the difference is when the difference between adjacent rewards scales linearly with time (i.e., $B=\Theta(K)$) but the optimal policy remains the same ($P_K = 0$). In this case, [1] suffers linear dynamic regret, while our dynamic regret remains sublinear. To summarize, the two settings and respective algorithms/results are incomparable. They can be viewed as two distinct models for non-stationary online MDPs. --- We hope our responses address your concerns. If your concerns have been addressed, we appreciate it if you could consider re-evaluating our work. --- Rebuttal Comment 1.1: Title: Thanks for the review! Have we properly addressed your concerns? Comment: We sincerely appreciate your constructive feedback and are especially grateful for bringing the paper [1] to our attention. We will revise the paper to cite [1] and incorporate the above discussions in the next version. Given that the author-reviewer discussion period is soon coming to an end, please let us know if our response has properly addressed the concerns. We will be happy to provide clarification if you have any further questions. Thanks! Best, Authors	Summary: Disclaimer: This specific area falls outside my expertise, as indicated by my confidence score. Nevertheless, I have carefully reviewed this paper and the relevant literature to offer the most informed feedback possible. This paper studies the dynamic regret for adversarial linear mixture MDPs, with unknown transitions and full-information feedback. It introduces a hybrid algorithm that combines a policy-based variance-aware value target regression method [Zhou 2021] with the occupancy-measure based method [Li et. al. 2024a]. The authors provide the dynamic regret analysis of this hybrid algorithm, demonstrating its near-optimality up to logarithmic factors by showing both upper and lower bound. In particular, it removes dependence on the state number S from the prior result in Li et. al 2024a. Strengths: It establishes a near-optimal dynamic regret for the first-time in its setting, improving over the results presented in [Li et al. 2024a], Weaknesses: 1. I feel that the contributions of this paper could be highlighted better, given that the proposed algorithm involves various components from the literature. I’m not sure if I fully understand, but it seems that the main contribution lies more in the regret analysis rather than the algorithm itself. The proposed algorithm seems to be a combination of existing components from prior works [Li et. al 2024a and Zhou et al. 2021]. In particular, would it be fair to describe the proposed algorithm as Algorithm 1 in Li et. al 2024a, leveraging the techniques from UCRL-VTR+ [Zhou et. al 2021] to compute the confidence set, in place of the EstimateTransition routine in Algorithm 4 of Li et. al 2024a? 2. The organization and the clarity of Section 3 can be improved to help with better understanding. Although Section 3.1 and 3.2 seem to aim to outline the pros and cons to motivate the proposed hybrid approach in Section 3.3, a more concise presentation could improve readability. Additionally, reordering 3.2 and 3.1 may better align with the flow in Sec. 3.3. 3. The limitation of the work should explicitly mention the assumptions on access to the oracle in Algorithm 2. It’s a strong assumption and seems crucial in the ability to remove the dependence on the number of states S in the upper bound. Minor: typos noted below Line 243: The formula for KL-divergence Line 326: “Combinin” Technical Quality: 3 Clarity: 2 Questions for Authors: In the weakness section, I noted my interpretation of the proposed algorithm. Could you elaborate if any new techniques are developed in this work? It will help me better understand the contributions of the work. Can you comment on the intuition of why it is possible to remove the dependence on S in the upper bound? Confidence: 1 Soundness: 3 Presentation: 2 Contribution: 2 Limitations: The introduction acknowledges the limitation of lower computational efficiency due to the occupancy measure based component. But I think that the additional assumptions regarding access to the oracle, introduced by algorithm 2, should be explicitly stated as a limitation. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thanks for your helpful comments. We will address your questions below. --- Q1: "It seems that the main contribution lies more in the regret analysis rather than the algorithm itself. Could you elaborate if any new techniques are developed in this work?" A1: Thanks for your question. Both the algorithm and the regret analysis are new and non-trivial. Even though one may feel the high-level algorithmic ideas are similar to previous works, previous efforts failed to achieve optimal dynamic regret due to the inherent limitations of two methodologies in dynamic regret analysis, as highlighted in Sec 3.1 and 3.2. Our primary technical contribution lies in revealing a crucial yet underexplored connection between the two most popular methods: the occupancy-measure-based approach and the policy-based approach. These two methods are widely used in the literature, but they are typically considered separately. So It was only after realizing that the two methodologies could complement each other, as we demonstrate, that the new algorithm and optimal dynamic regret could be achieved. We believe this optimal result is interesting and important for the community. Moreover, our technique for exploring the connection of two methodologies is novel and could be useful for broader problems in RL theory. We will emphasize this point more clearly in the revised version. --- Q2: "Can you comment on the intuition of why it is possible to remove the dependence on $S$ in the upper bound?" A2: The key insight is that Li et al. (2024a) focus on the difference in occupancy measures (state-action distributions) between two policies, whereas we concentrate on the difference in their value functions (expected rewards). The value function difference can be much smaller than the difference between state-action distributions (e.g., when the rewards are all zeros, the value function differences are zero while the difference between state-action distributions can be arbitrary). This approach allows us to remove the dependence on $S$ in the upper bound. We will provide more intuition in the revised version. --- Q3: "Would it be fair to describe the proposed algorithm as .." A3: The main component of our algorithm is the occupancy-measure-based global optimization (Algorithm 1 in Li et. al 2024a) and the policy-based value-targeted regression (UCRL-VTR+ [Zhou et. al 2021]). However, the key insight is to combine these two methodologies in a novel way to achieve optimal dynamic regret. We connect the two methodologies by using the occupancy measure to policy conversion in Section 3.3.2, which is non-trivial and requires careful analysis. --- Q4: "The organization and the clarity of Section 3 can be improved to help with better understanding." A4: Thanks for the suggestion. We will reorder 3.2 and 3.1 to better align with the flow in Sec. 3.3 and present Section 3 more concisely. --- Q5: "The limitation of the work should explicitly mention the assumptions on access to the oracle in Algorithm 2 ..." A5: We appreciate your observation. This assumption is not the reason for removing the dependence on $S$ in the upper bound. In fact, this is a standard assumption in the literature and has been used in all existing works on linear mixture MDPs (e.g., Zhou et al., 2021, He et al., 2022, Li et al., 2023). This assumption is just used to compute the $Q$-function by backward induction. The Oracle can be estimated by Monte Carlo methods in practice. We will clarify this point in the revised version. --- We hope our responses clarify the technical contributions and address your concerns. If your concerns have been addressed, we appreciate it if you could consider re-evaluating our work. References: [1] Zhou, D., Gu, Q., & Szepesvari, C., Nearly Minimax Optimal Reinforcement Learning for Linear Mixture Markov Decision Processes. In COLT'21. [2] He J., Zhou D., & Gu Q., Near-optimal Policy Optimization Algorithms for Learning Adversarial Linear Mixture MDPs. In AISTATS'22. [3] Li, L. F., Zhao, P., & Zhou, Z. H., Dynamic Regret of Adversarial Linear Mixture MDPs. In NeurIPS'23. --- Rebuttal Comment 1.1: Comment: Thank you for providing the clarifications. I have increased the score accordingly. --- Reply to Comment 1.1.1: Title: Thank you! Comment: Thank you for your re-evaluation and the revised score. We are happy to discuss work with you.	null	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Visual Pinwheel Centers Act as Geometric Saliency Detectors	Accept (poster)	Summary: This work aims to explain the origin and functional benefits of pinwheel structures in V1 compared to salt-and-pepper configurations. They use a two-dimensional self-evolving spiking neural network (SESNN) model with Hebbian-like plasticity and empirical morphological data to simulate the evolution from salt-and-pepper clusters to pinwheel structures. Their findings reveal that neurons at pinwheel centers exhibit heightened sensitivity and quicker responses to complex spatial textures in natural images, acting as primary processors for intricate contours, while adjacent iso-orientation domains refine edge representations. Strengths: - The question is of high interest: Pinwheel structures amazed experimentalist and theorist alike for decades. This is one of the main hallmarks of difference in sensory processing in primates vs rodents. - Bioplausibility of the model: use of bioplausible modeling (spiking neurons and learning rules) - Through citations to previous works Weaknesses: - More analyses to support the main claim in needed (see limitations) - The use of different learning rules for E>E vs E>I is justified computationally (for stability) but not discussed in terms of bio-plausibility. Technical Quality: 3 Clarity: 3 Questions for Authors: - In Related works line 228, when referring to ANN models explaining pinwheels, the lack of temporal processing in these models were mentioned but their ability in connecting these maps to the overall functionality of the network is not discussed. Since the main claim of this paper is about functionality of PCs, I wonder what authors think about the functional role previous work attributed to PCs. Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: - In the setup, It seems that the difference between receptive filed sizes of monkeys, cats and mice was ignored. In mice receptive fields for V1 are generally much larger than monkeys (>20x, see ref below for example). - The claim about functionality of pinwheels requires more support: the question whether the differences in responses of PCs and IODs in terms of response latency, etc have a functional role could be verified by using SESNN as a frontend for a simple DNN performing object recognition, motion detection, etc. At this point, it remains a different in response properties. - Code is not shared at this version. Van den Bergh G, Zhang B, Arckens L, Chino YM. Receptive-field properties of V1 and V2 neurons in mice and macaque monkeys. J Comp Neurol. 2010 Jun 1;518(11):2051-70. doi: 10.1002/cne.22321. PMID: 20394058; PMCID: PMC2881339. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your detailed review and insightful comments on our manuscript. ## Points Raised: ### 1. Bioplausibility of Learning Rules for E>E vs E>I Connections: Response: We recognize the importance of bioplausibility in modeling neuronal networks. In the context of our SESNN model, biological plausibility in learning rules for E>E and E>I connections is essential for simulating realistic neural behavior. We integrate principles of Hebbian-like plasticity, similar to biological brains, where synaptic connections between neurons strengthen based on their co-activation. E>E connections, according to [1], is set to be weaker than E>I connections. By incorporating these bioplausible learning rules, SESNN models can better balance excitation and inhibition that is crucial for maintaining stable neural activity levels and emulate the complex processing capabilities observed in biological neural networks. 1. Hofer, S. B., Ko, H., Pichler, B., Vogelstein, J., Ros, H., Zeng, H., … & Mrsic-Flogel, T. D. (2011). Differential connectivity and response dynamics of excitatory and inhibitory neurons in visual cortex. Nature Neuroscience, 14(8), 1045-1052. ### 2. Functional Role of Pinwheel Centers in Previous Work: Response: The three cited works provide significant insights into the functional roles attributed to pinwheel centers (PCs) in the visual cortex from different perspectives. One study explores how the retino-cortical mapping ratio influences the organization of visual cortical maps, including columnar structures and salt-and-pepper patterns[1]. Another research[2] investigates how orthogonal tiling projections from the retina to the visual cortex contribute to the formation of visual maps, including the arrangement of pinwheel centers. Also, a study[3] presents a network model that explains the emergence of simple and complex cells in the visual cortex, with PCs playing a pivotal role in this development. Though they haven't consider PCs latency as salieny detector, the three cited works collectively highlighted the multifaceted roles of pinwheel centers in visual processing. 1. Jaeson Jang, Min Song, and Se-Bum Paik. Retino-Cortical Mapping Ratio Predicts Columnar and Salt-and-Pepper Organization in Mammalian Visual Cortex. Cell Reports, 30(10), 3270-3279.e3, March 2020. 2. Min Song, Jaeson Jang, Gwangsu Kim, and Se-Bum Paik. Projection of Orthogonal Tiling from the Retina to the Visual Cortex. Cell Reports, 34(1), January 2021. 3. Louis Tao, Michael Shelley, David McLaughlin, and Robert Shapley. An egalitarian network model for the emergence of simple and complex cells in visual cortex. Proceedings of the National Academy of Sciences, 101(1), 366-371, January 2004. ### 3. Receptive Field Sizes Across Species: Response: In our study, we acknowledge the differences in receptive field sizes across species such as monkeys, cats, and mice. The focus of our research is primarily on the overlap and interaction within orientation maps, where we have normalized receptive fields for comparative analysis. The size of receptive field in v1 is more about resolution than orientation map formation, for example theres more than ten times change in the rf size from fovea to peripheral in macaque v1 while very little change in the properties of the corresponding orientation map[1,2]. Therefore we expect little effects from receptive field shift sizes across species as long as the overlap is constant. However, if time permits, we can further verify this in our model during the discussion period. 1. Bosking, W. H., Zhang, Y., Schofield, B., & Fitzpatrick, D. (1997). Orientation selectivity and the arrangement of horizontal connections in tree shrew striate cortex. The Journal of Neuroscience, 17(6), 2112-2127. 2. Horton, J. C., & Hocking, D. R. (1996). Intrinsic variability of ocular dominance column periodicity in normal macaque monkeys. Journal of Neuroscience, 16(22), 7228-7339. ### 4. Verification of Functional Claims with Simple DNN: Response: We designed a Spiking Neural Network (SNN) for classifying the Fashion MNIST (FMNIST) dataset. The images were first processed by the SESNN network, generating a 20ms spike train. This spike train was then fed into a convolutional SNN. The final layers consisted of a flattened layer, followed by two linear layers, leading to the classification output. The network was trained using surrogate gradient methods. For comparison, we also evaluated a version of the SESNN where the neuronal activity was resampled based on firing rates to generate Poisson spike trains, effectively removing latency. The classification accuracy of the SNN with and without latency across different classes of the FMNIST dataset is summarized in the tables below: \|Dataset Class\| Accuracy(%) of Model With Latency\| Accuracy(%) of Model Without Latency\| \|-\|-\|-\| \| T-shirt / top\| 86.80 \| 85.40\| \|Trouser\| 97.30\|96.40\| \|Pullover\| 83.40\| 83.80\| \|Dress\| 91.10\| 90.30\| \|Coat\| 83.60\| 81.60\| \|Sandal\|96.20\|96.80\| \|Shirt\|73.20\|67.80\| \|Sneaker\| 95.40\| 95.40\| \|Bag\| 97.80\| 97.00\| \|Ankle boot\|96.10\|94.20\| \|Overall\|90.09\|88.87\| This experiment elucidates the functional significance of differences in response latency between pinwheel centers and iso-orientation domains (IODs). We also did decoding and reconstruction part with results addressed in Fig.S(b) of Supplemental PDF File. ### 5. Sharing of Code: Response: The code is shared at https://github.com/HenryGithub1?tab=following. ## Conclusion: Your feedback has been invaluable in identifying areas for enhancement. We appreciate the opportunity to improve our paper and are committed to delivering a revised version that meets the standards of thorough evaluation and clarity. Thus, we kindly urge you to reconsider the score in light of our clarifications. We remain available to provide further explanations if there are any additional questions. Thank you once again for your thorough review and constructive input. --- Rebuttal Comment 1.1: Comment: Thank you for clarifications. I raised the score. --- Reply to Comment 1.1.1: Comment: Thank you for your interest in our work. We appreciate you taking the time to review it.	Summary: This paper introduced a novel spiking neural network (SNN) to investigate the functional roles of pinwheel structures in the primary visual cortex of higher mammals and primates. By adjusting a visual RF overlapping parameter, their model can produce the salt-and-pepper and pinwheel organizations observed in lower (rodent) and higher (macaque and cat) mammals. Their results suggest neurons in pinwheel centers are more responsive towards complex geometry and spatial textures than those in the iso-orientation domains. Strengths: - This paper investigates the important problem of salt-and-pepper vs pinwheel structure observed in the mammalian visual cortex. Their model shows that visual overlap can influence the topological organization in V1 is interesting, and that the resulting orientation preference maps match experiential data obtained from rodents, macaques, and cats. - The paper is very well-written. Moreover, analysis of the spatial-temporal response pattern and response time with respect to the complexity of the visual scene is novel and interesting. Weaknesses: - The paper lacks a comparison with previous work or verification with experimental data. For instance, only one metric from the baseline model is reported in Table 1. Please see points 2 and 3 in “Questions”. - The SESNN model shows a rippling effect/pattern (Figure 2) and a heightened response with high contour complexity (Figure 3) in pinwheel centers, it is unclear whether or not this is indeed the case in the visual cortex without validation/comparison with experimental data. Technical Quality: 3 Clarity: 4 Questions for Authors: - One of the main claims is the differences in neuronal response time with respect to the complexity of the visual scene between salt-and-pepper and pinwheel organizations. Based on Figure 3c, other than the initial time point (1 ms), the two structures seem to have similar response ranges and a downward trend as latency increases. Can the author comment on that? - In Table 1, the authors compare a baseline model and the SESNN model against the experimental data obtained from macaques. Can the authors clarify why the NNPD and hypercolumn size are “N/A” for the baseline model? Without a proper baseline, it is difficult to evaluate how well the proposed model is performing in this specific task. - Moreover, can the authors clarify why the pinwheel density is omitted as a metric in Section 2.1, though it is included in Table 1? - Finally, I believe a brief description of the baseline model, and how it differs from SESNN, should be added to the main text. - I believe the analysis would be more complete if the authors could add the pinwheel data from rodents and cats in Table 1 to compare the performance of the proposed model against the baseline. Confidence: 3 Soundness: 3 Presentation: 4 Contribution: 3 Limitations: I strongly suggest the authors discuss the limitations of this work and potential future research direction in the paper. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: # Rebuttal for Reviewer FA4k Thank you for your thorough review and valuable feedback on our paper. We appreciate your recognition of the strengths of our model and its presentation. ## Points Raised: ### 1. Neuronal Response Time to Complexity of Visual Scene: Response: Based on our findings, pinwheel centers (PCs) exhibits quicker and stronger neuronal responses to complex spatial textures in natural visual scenes. This contrasts with neurons organized in salt-and-pepper configurations, which generally exhibit slower responses to such stimuli. Though the downward trends look similar in both structures the slope is higher for pinwheels and demonstrate a clear preference for more complex inputs by responding quicker. ### 2. Comparison with Previous Model: Question1: I believe a brief description of the baseline model, and how it differs from SESNN, should be added to the main text. Response: We investigated previous model and found that the "baseline" model's performance in generating a complete pinwheel structure, crucial for validation by our metrics, did not meet our criteria, leaving NNPD and hypercolumn size not available for calculation. Therefore, "N/A" was appropriately indicated in Table 1. However we may have misused the word "baseline", "a previous model" is more appropriate. Specificaly, the mentioned model[1] is a spiking neural network model simulating the formation of orientation and ocular dominance maps in the visual cortex. In contrast, the SESNN model in the current study not only forms orientation and ocular dominance maps but also involve both salt-and-pepper clusters and pinwheel structures. SESNN overtakes the baseline model in generation of Pinwheel structures, and shows that Pinwheel centers act as first-order processors with heightened sensitivity and reduced latency to intricate contours. This advancement underscores the SESNN model’s ability to better mimic the functional advantages observed in the visual cortex of higher mammals, providing a significant improvement over previous approaches. 1. Srinivasa, N., & Jiang, Q. (2013). Stable learning of functional maps in self-organizing spiking neural networks with continuous synaptic plasticity. Frontiers in Computational Neuroscience, 7, 10. Question2: Can the authors clarify why the pinwheel density is omitted as a metric in Section 2.1, though included in Table 1? Response: In a paper published in 2010[1], it was established that pinwheel density is approximately 3.14, which is considered a reliable metric for assessing the quality of pinwheel structures. Our model also measured pinwheel density, consistently finding it around three, aligning well with experimental evidence. In Figure 2, we varied the overlap size, and given our earlier analysis, the density remains around three in our model with reasonable change in overlap (as long as it does not cause a transition to salt-and-pepper structure). Therefore, it wasn't necessary to use pinwheel density to measure the impact of overlap. However, we included pinwheel density in Table 1 because it is a crucial benchmark for comparing the quality of pinwheel structures across different models, including our baseline model and real animal data. 1. Kaschube, M., Schnabel, M., Löwel, S., Coppola, D. M., White, L. E., & Wolf, F. (2010). Universality in the Evolution of Orientation Columns in the Visual Cortex. Science, 330(6007), 1113-1116. doi:10.1126/science.1194869 ### 3. Include Experimental Data to Compare: Response: We acknowledge the importance of experimental data and did extra investigation on the experimental data from rodents and cats[1-3] and will add into the revised manuscript. This addition will provide a broader comparative analysis and strengthen the validation of our model across different mammalian species. Yet we didn't identify existing research that can explicitly address our conclusion. However, this is the novelty point of our work from the perspective of computational models, we'll try to launch behavioral experiment evidence soon by cooperating with experimentalists. 1. Stryker, M. P., Sherk, H., Leventhal, A. G., & Hirsch, H. V. Physiological consequences for the cat's visual cortex of effectively restricting early visual experience with oriented contours. Journal of Neurophysiology 1978, 41(4), 896-909. 2. Tanaka, S., Miyashita, M., Wakabayashi, N., O’Hashi, K., Tani, T., & Ribot, J. (2020). Development and reorganization of orientation representation in the cat visual cortex: Experience-dependent synaptic rewiring in early life. Frontiers in Neuroinformatics, 14, Article 41. 3. Vita, D. J., Orsi, F. S., Stanko, N. G., et al. Development and organization of the retinal orientation selectivity map. Nat Commun 2024, 15, 4829. ### 4. Discussion of Limitations and Future Work Response: We recognize the need to discuss the limitations of our work more comprehensively and outline potential future research directions in the paper. This will ensure transparency and guide further advancements in this area of study. Several limitations should be considered, including potential oversimplification of biological neural networks, and the exclusive focus on functions of spatial aspects of the saliency map. Future research could focus on empirically validating these findings using neurophysiological techniques in biological models, developing dynamic computational models that can address more apects of saliency comprehensively to broaden our understanding of neural network functionality and advance applications in neuroscience and artificial intelligence. ## Conclusion: Your feedback has been instrumental. By enhancing our comparisons with previous work, providing further validation with experimental data, and addressing the noted limitations, we aim to strengthen the impact and robustness of our study. Thank you once again for your valuable feedback and for the opportunity to improve our paper. --- Rebuttal Comment 1.1: Title: Response to rebuttal Comment: I thank the authors for their thorough responses and they have addressed most of my main concerns. I have therefore updated the score. As to "Neuronal Response Time to Complexity of Visual Scene”, it is not visually obvious that the response time downward trend is stronger in the pinwheel structure. I suggest the authors quantify the downward trends in Figure 3c between pinwheels vs salt-and-pepper, and show their statistical significance at all time points. --- Rebuttal 2: Comment: Thank you for acknowledging our effort. As for quantifying the difference between downward trends in pinwheels and salt-and-pepper, we consider statistical significance between every other 2 ms for both pinwheel and salt-and-pepper structures to show the downward trend is only significant among pinwheels. (Since recorded neurons are not guaranteed to be in the same pinwheel, the statistical significance of a direct comparison of slopes is unavailable.): \| Latency-Gap(ms) \| p for Pinwheel \| p for Salt & Pepper\| \|-------------\|---\|---\| \|1-3 \|0.00002\|0.25352\| \|3-5 \|0.01208\|0.73593\| \|5-6 \|0.64746\|0.16130\| \|7-9 \|0.95521\|0.99757\| The statistical significance of pinwheels vs salt-and-pepper at all time points: \| Latency(ms) \| 1 \| 2 \| 3 \| 4 \| 5 \| 6\| 7\| 8\| 9\| 10\| \|-------------\|---\|---\|---\|---\|---\|---\|---\|--\|--\|---\| \| p (Pinwheel vs Salt & Pepper) \|0.0001\|0.0180\|0.0034\|0.0173\|0.2146\|0.1233\|0.0490\|0.0004\|0.0274\|0.5049\|	Summary: The authors present a comprehensive model of the primary visual cortex adapted for various mammalian species, demonstrating its ability to reproduce orientation maps and compatibility with experimental data across different factors such as neuron density or RF overlap. Importantly, they provide evidence in their model that pinwheel centers act as saliency detectors. Strengths: While the result put forward by the paper may seem intuitive, as a PC contains in a close neighborhood cells selective to different orientations, and thus may be a good candidate for a saliency detector, yet this model gives some interesting quantitative predictions. Weaknesses: Given the link with neuroscience, more links with behavioural data would be beneficial: are animals without PCs less efficient in detecting saliency? Is the density of PCs compatible with the "resolution" of the saliency map? In general, this feature of PCs as detecting features containing multiple orientations should be more broadly tested, for instance by using existing results on textures with different orientation bandwidths. such work could help better undertand the underlying principles which give rise to that particular feature. (The link to https://github.com/HenryGithub1?tab=following (and to its followers) may reveal the authorship, which may be a problem for NeurIPS. Use anonymous links instead. There is a strong overlap with submission 16614, most certainly from the same authors.) Technical Quality: 3 Clarity: 3 Questions for Authors: In the computation of entropy, why use luminance values instead of that of the (whitened) images used during the training? Also the numbers used in the paper and synthesized in table 2 are given following previous papers, bt it is not said at what eccentricity they are computed. Could you please provide this information? How do you justify that the emergence is uniform while retinotopic space is not (certainly thanks to the fact that RF size is function of eccentricity, as well as the RF density, but this is not discussed in the paper as far as I could read)? Confidence: 5 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: The main result is figure 3, and to better the mechanisms leading to this result, an ablation study would be an asset to the paper. Minor: in Figure 4c, your error bar escapes the imit of valid values (normalized entropy higher than 1). Use quantile regression to estimate the 95% confidence interval? Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: # Rebuttal for Reviewer Boae Thank you for your insightful feedback and constructive comments on our paper. ## Points Raised: ### 1. Behavioral Data and Saliency Detection: Question1: Are animals without PCs less efficient in detecting saliency?" Response: We acknowledge the importance of behavioral data, yet we didn't identify existing research that can explicitly prove with behavioral data that animals lacking well-defined pinwheel centers (PCs) in their visual cortex may indeed be less efficient in detecting saliency compared to species with distinct pinwheel organizations. However, we do expect so as PCs are critical for integrating information from surrounding iso-orientation domains (IODs), allowing for enhanced sensitivity to complex visual features like edges and textures[1]. Since most related experiments didn‘t focus on this address, which is the novelty point of our work from the perspective of computational models, we'll try to launch behavioral experiment evidence soon by cooperating with experimentalists. Question2: Is the density of PCs compatible with the 'resolution' of the saliency map? Response: If we understand correctly, the 'resolution' of the saliency map should be referring to resolution of image. Then, the density of PCs within the cortex correlates with the resolution of the saliency map, where higher densities typically enable finer discrimination of visual stimuli. In general, comparative neuroanatomy studies across species have shown that variations in PC density and organization impact visual processing capabilities, influencing the ability to detect and respond to salient visual cues[2]. 1. Bosking, W. H., Zhang, Y., Schofield, B., & Fitzpatrick, D. (1997). Orientation selectivity and the arrangement of horizontal connections in tree shrew striate cortex. The Journal of Neuroscience, 17(6), 2112-2127. 2. Angelucci, A., & Rosa, M. G. (2015). Resolving the organization of the third tier visual cortex in primates: A hypothesis-based approach. Visual Neuroscience, 32(E010). ### 2. Testing on Textures with Different Orientation Bandwidths: Response: We agree that such work could help better undertand the underlying principles which give rise to that particular feature and will incorporate results from textures with different orientation bandwidths to validate our model further. This will help clarify the underlying principles governing the observed features in PCs. ### 3. Computation of Entropy using luminance values: Response: With our definition of saliency, we want to control other saliency components like contrast, and use binarized luminance value to isolate the effect of geometric complexity. ### 4. Uniform Emergence and Retinotopic Space: Question1: "The numbers used in the paper and synthesized in table 2 are given following previous papers, but it is not said at what eccentricity they are computed. Could you please provide this information?" Response: For mouse[1] and cat[2], the receptive field eccentricity ranged from 0 to 90°, and the corresponding level used here is around 0°. For macaque[3], the eccentricity ranges from 0 to 15°. Here we all used data corresponding to lowest eccenctricity level at 0°. 1. van Beest, E.H., Mukherjee, S., Kirchberger, L. et al. Mouse visual cortex contains a region of enhanced spatial resolution. Nat Commun 12, 4029 (2021). 2. Wilson, J. R., & Sherman, S. M. (1976). Receptive-field characteristics of neurons in cat striate cortex: changes with visual field eccentricity. Journal of neurophysiology, 39(3), 512-533. 3. Tehovnik, E. J., & Slocum, W. M. (2007). Phosphene induction by microstimulation of macaque V1. Brain Research Reviews, 53(2), 337–343. Question2: How do you justify that the emergence is uniform while retinotopic space is not? Response: The uniform emergence of orientation maps in the visual cortex, despite non-uniform retinotopic space, underscores the sophisticated self-organizing principles governing neural development, and is primarily facilitated by receptive field (RF) size with eccentricity and the density of RFs across the visual field[1]. Neurons in the visual cortex adaptively adjust their RF sizes according to their distance from the fovea, ensuring optimal sensitivity to visual features at different spatial resolutions[2]. Additionally, the density of RFs compensates for variations in retinal input, with higher eccentricity regions exhibiting smaller, densely packed RFs[3]. ### 5. Limitations: Question1: Ablation study. Response: We ablate the local connectivity of trained pinwheel orientation map while keeping other properties. This result indicate the structured connectivity from pinwheel may be the underlying mechanism for its better saliency. Due to time limit we're not able to conduct more detailed ablation studies, however we thank your suggestions and will furnish our word with more ablation studies soon. Question2: Minor correction in Figure 4c. Response: Thanks for the suggestion, to address this question we now use boxplot to show the trend and statistical features as provided in supplemental PDF file. ### 6. Anonymous Links and Overlap with Submission: Response: We will replace the GitHub link with anonymous references and clearly distinguish any shared content with submission 16614 through proper citation and differentiation. ## Conclusion: Your feedback has been invaluable in identifying areas for enhancement. Thank you once again for your thorough review and constructive suggestions. We are committed to refining our work to contribute effectively to the field of visual processing and the role of pinwheel centers. --- Rebuttal Comment 1.1: Comment: We are currently awaiting feedback on our rebuttal from Reviewer Boae. We have thoroughly addressed all the concerns and eagerly anticipate their insights, which would significantly contribute to enhancing our work. --- Rebuttal 2: Comment: We are now providing this additional information to ensure a comprehensive understanding of our study and to address your valuable feedback more thoroughly. About behavioral data: Linking our model with behavioral data could further strengthen our findings. Currently, no studies show that animals (like rodents) without PCs are less efficient in detecting saliency. However, electrophysiological studies suggest that PCs have delayed response latency, indicative of higher-order processing [citations 6, 7, 21 in our paper]. This arises from using drifting grating stimuli that activate IODs more readily. Koch et al. [citation 6 in our paper] note that IODs exhibit cross-orientation suppression under complex stimuli, narrowing their tuning, unlike PCs. This study, however, omits temporal neural data within pinwheel structures. The SESNN model aligns with physiological findings, showing that IODs and PCs favor single and complex orientation stimuli, respectively. About the textures with different orientation bandwidths: Understanding the tuning of PCs in V1 to various edges, corners, and junctions is crucial. In Fig. 4e of our paper, we show that PCs exhibit broader orientation tuning curves than iso-orientation domains, which may allow them to detect T-junctions and corners, as demonstrated by Ming Li et al. (2019, Science Advances) and Erin Koch et al. (2016, Nature Communications). Your insightful comment prompted us to further examine the distribution of PCs' tuning curves. We have analyzed the acute angles formed by the primary and secondary peaks in the orientation tuning curve (Table 1). Table 1 shows that PCs are more frequently associated with larger acute angles (closer to orthogonal, 90°), indicating a preference for orthogonal junctions. However, this result does not distinguish between "L" and "T" junctions beyond their angle. We suggest deferring such high-order feature extraction to higher visual cortices like V2 and V4, which are involved in texture detection, as discussed by Tianye Wang et al. (2024, Nature Communications) and Anna W. Roe et al. (2012, Neuron). Table 1: Probability distribution of preferred adjusted acute angles in pinwheel centers. (Corresponding figure is available in anonymous GitHub repository) \| Adjusted acute angle range (degrees) \| Probability (%) \| \|-----------------------\|-----------------\| \| 0 - 9 \| 0 \| \| 9 - 18 \| 0 \| \| 18 - 27 \| 1.30 \| \| 27 - 36 \| 0 \| \| 36 - 45 \| 3.90 \| \| 45 - 54 \| 6.49 \| \| 54 - 63 \| 5.19 \| \| 63 - 72 \| 14.29 \| \| 72 - 81 \| 22.08 \| \| 81 - 90 \| 46.75 \| Ablation study: In our paper (Fig. 4e), we present a mechanism of multiple orientation tuning that is crucial for processing complexity. Our experiment (Table 1) on PCs' preferred acute angles suggests that their broad tuning enables detection of complex junctions like T- and L-junctions, likely due to differences in local connectivity within and between iso-orientation domains. We appreciate the reviewer's feedback and conducted an ablation study by disrupting local connectivity and shuffling the spatial positions of orientation-tuning receptive fields in the pinwheel orientation map, while keeping other properties constant (Table 2). This supports the conclusion that structured connectivity, as shown in Fig. 4e, underlies the enhanced saliency detection by pinwheels. Table 2: Ablation study on local connectivity and orientation-tuning receptive fields (available in anonymous Github). The table shows normalized entropy values (mean ± std). \| Latency (ms) \| 1\| 2\| 3\| 4\| 5\| 6\| 7\| \|-\|-\|-\|-\|-\|-\|-\|-\| \|Pinwheels (control group) \| 0.915 ± 0.049 \| 0.950 ± 0.170 \| 0.899 ± 0.259 \| 0.468 ± 0.214 \| 0.462 ± 0.202 \| 0.491 ± 0.173 \| 0.491 ± 0.235 \| \| Interchange feedforward connection (FF)\| 0.948 ± 0.070 \| 0.897 ± 0.222 \| 0.889 ± 0.226 \| 0.558 ± 0.208 \| 0.503 ± 0.159 \| 0.486 ± 0.158 \| 0.464 ± 0.253 \| \|Shuffle lateral connections\| 0.959 ± 0.288 \| 0.916 ± 0.208 \| 0.909 ± 0.262 \| 0.500 ± 0.205 \| 0.947 ± 0.270 \| 0.874 ± 0.194 \| 0.501 ± 0.264 \| \|Interchange FF, shuffle lateral connections\| 0.866 ± 0.221 \| 0.904 ± 0.186 \| 0.524 ± 0.181 \| 0.907 ± 0.200 \| 0.626 ± 0.229 \| 0.492 ± 0.184 \| 0.738 ± 0.268 \| \|Shuffle all FF\| 0.893 ± 0.073 \| 0.937 ± 0.193 \| 0.816 ± 0.093 \| 0.783 ± 0.151 \| 0.820 ± 0.029 \| 0.905 ± 0.126 \| 0.837 ± 0.184 \| \|Shuffle all connections\| 0.849 ± 0.101 \| 0.875 ± 0.100 \| 0.888 ± 0.136 \| 0.821 ± 0.125 \| 0.818 ± 0.119 \| 0.699 ± 0.140 \| 0.767 ± 0.098 \| --- Rebuttal Comment 2.1: Comment: Please note that you should not do this, as was explicitly pointed out by the instructions sent out yesterday: > The deadline for submitting the rebuttal has now passed. The reviewers will now read the rebuttals you posted. When relevant, they will ask for clarification questions. The discussion phase is meant to clarify these questions, rather than to provide further comments regarding the reviews. I will leave it to the reviewers to decide whether they want to take this comment into account or not. --- Reply to Comment 2.1.1: Comment: Thank you for the clarification. I apologize for any misunderstanding regarding the submission guidelines. Our intention was to help the reviewers better understand our work.	Summary: This paper uses a self-evolving spiking neural network model to investigate why some visual systems develop pinwheel structures while others have salt-and-pepper organization of orientation tuning. The simulation shows that the organization depends on the amount of receptive field overlap between neighbouring neurons. Experiments on the trained network show that pinwheel centers respond more efficiently to complex edge structure in images than salt-and-pepper neurons. Strengths: +The findings relating orientation tuning organization to receptive field overlap are quite interesting and seem novel. +The modelling approach seems well-designed and has a lot of potential to investigate the evolutionary advantages of different types of organization for different images/tasks. Weaknesses: - The experiments seem to use binary edge map images only, if I’ve understood them correctly. No visual system evolved to process these kinds of binary images, so it’s unclear what conclusions we should draw from these experiments. It would be much more useful to show experimental results for real images. - Entropy in a local region of the edge map is used as a proxy for geometric complexity, but this just measures the proportion of pixels in a local part of the edge map which are white vs. black. A little patch of random noise (50% white and 50% black pixels) would have maximum entropy but no geometric information. From the experiments, it’s hard to tell what aspect of the high-entropy regions the pinwheel centers are more responsive to – would they respond highly to random noise? Or are they responding to edge intersections? Corners? Textures? Given that the input to the model is a binary edge map, there are many ways the edges could be characterized to better understand the tuning. Technical Quality: 2 Clarity: 2 Questions for Authors: Do the pinwheel centers show faster responses to regions of the image that are ground-truth boundary vs. other regions of the image? (If a BSDS image is input to the model, do the pinwheel centers respond differently to the pixels which are 1 in the edge map than those which are 0?) This might show an advantage for these cells in boundary detection or figure-ground analysis. Are pinwheel centers tuned for particular types of edge structure (for example, giving a different response for T-junctions than other types of junctions)? Confidence: 4 Soundness: 2 Presentation: 2 Contribution: 2 Limitations: Not applicable Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: # Rebuttal for Reviewer TFr2 Thank you for your detailed feedback on our paper. We appreciate your recognition of the novelty in our approach and the potential of our modeling technique. ## Points Raised: ### 1. Use of Binary Edge Maps: Response: We indeed used whitened natural images to train the model and tested with binary image map. We used binary edge maps as an initial test to isolate the geometric complexity of natural images while eliminating the influence of luminance and contrast variations. By using binary images, we ensure that the model focuses on detecting complex features inherent in natural scenes, rather than being influenced by luminance differences and thus explicitly demonstrate that pinwheel centers respond more efficiently to complex edge/contour structures. Luminance and contrast are important elements for saliency, complementing complexity saliency. In this case, we will further consider natural images to validate our model's performance in more realistic scenarios. Future experiments will involve testing with real-world images to validate our model's performance in more realistic scenarios, particularly in boundary detection and figure-ground separation. As addressed in Fig.S1(a) in supplemental PDF, we indeed observe PC's significantly shorter latency in response to edges than other regions of the BSDS500 natural images. ### 2. Entropy as a Proxy for Geometric Complexity: Response: The concept of using entropy in a local region of the edge map as a proxy for geometric complexity can be encapsulated by the following equation which is derived from the idea of Shannon's mutual information[1]:$$H = H_{Geometric\ Complexity} + H_{Noise}$$ This equation suggests that the entropy of an image region is composed of both geometric information and noise. In our current approach, we hypothesize that the noise level in the edge maps (artificial star-like binary images and BSDS 500 groundtruth in Figs. 3 and 4) is negligible, allowing us to consider entropy as a direct measure of geometric complexity. By assuming that noise is zero, we can simplify our analysis and use entropy to reflect the structural information within the image accurately. However, we acknowledge the potential influence of noise on entropy measurements. To address this, we plan to include a noise term in our study soon, which will help us differentiate between random noise and true geometric complexity, ensuring a more robust and accurate assessment of image structure. 1. Shannon, C. E. (1948). “A Mathematical Theory of Communication.” Bell System Technical Journal, 27(3), 379-423. ### 3. Pinwheel Centers' Response to Ground-Truth Boundaries and Specific Edge Structures: Question1: Do the pinwheel centers show faster responses to regions of the image that are ground-truth boundary vs. other regions of the image? Response: Our model demonstrates that pinwheel centers respond faster to binarized boundaries, indicating their role as saliency detectors without the influence of other elements. We consider additional tests using diverse datasets to provide a comprehensive evaluation of our model's functionality toward edge detection in non-binarized original images, and indeed observed statically significant speed advantage of PC in detection of edges (>5 ms) than other regions (~10ms) as illustrated in Fig.S1(a), Supplemental PDF file. Question2: Are pinwheel centers tuned for particular types of edge structure? Response: Understanding the tuning of pinwheel centers to various edge junctions and textures is crucial. Pinwheel centers have the broadest orientation tuning curves, as verified by Fig. 4e. They significantly contribute to detecting T-junctions and corners, as shown by citation 7 in our paper[1]. Additionally, textures are detected in V4, as demonstrated by Tianye Wang et al. in their 2024 Nature Communications article. Due to time limitations, we will provide the new results during our discussion period. Thank you for understanding. 1.Wang, T., Lee, T.S., Yao, H. et al. Large-scale calcium imaging reveals a systematic V4 map for encoding natural scenes. Nat Commun 15, 6401 (2024). ## Conclusion: While we acknowledge the limitations highlighted in the review, we believe that our initial findings provide a strong foundation for future research. We appreciate the opportunity to improve our work and are confident that these enhancements will demonstrate the robustness and applicability of our model in understanding visual processing. We have made every effort to address the Reviewer TFr2's concerns and kindly urge you to reconsider the score in light of our clarifications. We remain available to provide further explanations if there are any additional questions. Thank you for your valuable feedback. --- Rebuttal Comment 1.1: Title: Response to rebuttal Comment: I understand how the entropy measure is calculated, but it doesn't seem to distinguish between increasing geometric complexity (e.g., more highly-branching junctions) and increasing texture (e.g., more jagged-looking edges). The measure only cares about how many of the pixels in the window are white. The entropy of a straight line and a corner are the same according to this measure, even though the corner is (I assume?) more geometrically complex. It seems like in most cases, the highest-entropy parts of the image would be textured natural background structures like trees or mountains, while the more important foreground objects (like a person) may have lower entropy because they have smoother boundaries. I also don't really understand what we can take away from the model's response to binary edge maps, given that the cells were trained on natural images. The analysis in Fig.S1(a) looks promising. What is the pattern for salt-and-pepper? Also, just out of curiousity, why are the images filtered as shown in the supplemental? It looks like they have been bandpass filtered to remove low spatial frequency information. --- Reply to Comment 1.1.1: Comment: We are still awaiting feedback on our rebuttal from Reviewer TFr2. We have carefully addressed all the concerns and sincerely hope to receive their insights soon, as it would greatly assist us in improving our work. If our clarifications address your concerns satisfactorily, we would greatly appreciate it if you could consider raising the score. --- Rebuttal 2: Comment: Thank you for your insightful comments regarding the distinction between geometric complexity and texture complexity. We appreciate the opportunity to clarify our approach and address your concerns: How to distinguish geometric complexity and texture: 1. Local pixel entropy with sliding windows (LPESW): Global pixel entropy, indeed, does not measure geometric complexity within a window. Instead, we used MATLAB's `entropyfilt` function, which calculates local entropy for each pixel's neighborhood using sliding windows. This LPESW method evaluates the variation and complexity of pixel spatial distributions. While it doesn’t directly measure geometric shapes, it reflects their complexity through local intensity variations. By sliding a small window across the binary images, the local entropy measure captures the spatial distribution of entropy within these windows. This spatial distribution inherently includes geometric information, allowing it to detect local changes in intensity that characterize edges, corners, and other complex patterns. 2. Verification with additional experiments by LPESW: To verify our paper's approach, we conducted new experiments using various shapes, including lines, angles, L-, T-, and X-junctions (geometric complexity), as well as jagged edges (texture). The maximum entropy values obtained were 0.52 (lines), 0.72 (angles), 0.73 (junctions), and 0.94 bits (jagged edges), respectively. These results confirm that our LPESW method is sensitive to the complexity of geometric structures. (Available in the previously mentioned anonymous GitHub repository.) 3. Comparison with geometrical entropy (GE): To further validate LPESW, we first approximate the contours of the shape using the Ramer-Douglas-Peucker algorithm, which simplifies the contour by reducing the number of vertices while preserving the general shape. The resulting vertices form a polygon, which serves as the basis for calculating the distribution of edge lengths and angles. GE is then defined as the sum of entropy values from these two distributions. We have tested the same shapes (as mentioned in point 2) using the GE measure. The results showed a strong correlation with in max values with LPESW (table 1) when calcuated with siliding windows, confirming the validity of LPESW for our experiments. (Also available in the previously mentioned anonymous GitHub repository.) 4. Recognition of white noise: While the global GE for the pattern returns a NaN directly for white noise without structures, we understand that pixel entropy cannot differentiate noise from geometric shapes with max values as the reviewer suggested. However, since white noise will lead to consistently large pixel entropy in all sliding windows, geometrical structures would exhibit much variable distribution of pixel entropy across windows. Thus, we can also differentiate with standard deviation ($\sigma$) of local pixel entropy when performing LPESW as in table 2. Table 1: Relationship between maximum values of local pixel entropy (both normalized to [0,1]) and local geometrical entropy ($r^{2} = 0.85$) for various shapes (lines, angles, L-, T-, X- junctions, and jagged edges). \|Various shapes \|Max local pixel entropy \| Max local geometrical entropy \| \|-------------------\|----------------------------\|------------------------------------\| \|line 1 \|0.56 \| 0.43 \| \|line 2 \|0.56 \| 0.43 \| \|angle 1 \|0.81 \| 0.87 \| \|angle 2 \|0.79 \| 0.86 \| \|angle 3 \|0.77 \| 0.87 \| \| L-junction \|0.78 \| 0.74 \| \| T-junction \|0.78 \| 0.64 \| \| X-junction \|0.78 \| 0.84 \| \| jagged edges \|1.00 \| 1.00 \| (please see the next official comment) Title: Response to Official Comment 1 --- Rebuttal 3: Comment: Table 2: Standard deviation values of local pixel entropy and directly calculated global GE can both identify noise from various shapes (lines, angles, L-, T-, X- junctions, and jagged edges). \|Various shapes \|$\sigma$ of local pixel entropy \| Global geometrical entropy (bits) \| \|------------------\|----------------------------\|------------------------------------\| \|White Noise \|4.34e-04 \|NaN \| \|line 1 \|0.13 \| 0 \| \|line 2 \|0.13 \| 0 \| \|angle 1 \|0.17 \| 1 \| \|angle 2 \|0.16 \| 1 \| \|angle 3 \|0.17 \| 1 \| \| L-junction \|0.13 \| 1 \| \| T-junction \|0.14 \| 2.37 \| \| X-junction \|0.16 \| 2.73 \| \| jagged edges \|0.21 \| 4.65 \| We appreciate the reviewer's careful and instructive comments and plan to incorporate GE in revisions and future work. This will enhance the robustness of our analysis and clarify how pinwheel centers can sensitively respond to the complexity of natural images. Model's response to binary edge maps: We used binary edge maps to isolate geometric complexity by eliminating luminance and contrast. This allowed us to focus on detecting complex features inherent in natural scenes. When images are binarized, texture complexity often results in variations in local geometric edges and shapes. These variations can be captured by the measure of local pixel entropy with sliding window, which reflects the local intensity distribution's complexity. The natural images response pattern for salt-and-peppers: Due to the restrictions on uploading figures, we have instead provided the data in a tabular format (table 3). The latency for salt-and-pepper neurons on boundaries is significantly lower than that for neurons in other areas (P < 0.0001) (Corresponding figure is available in anonymous GitHub repository). Table 3: Latency for salt-and-pepper neurons on boundaries and neurons in other areas. \| Salt-and-peppers' neuron type \| Mean latency (ms) \| Standard deviation (ms) \| \|--------------------------------\|---------------------\|--------------------------------\| \| Neurons on boundaries \| 2.832 \| 2.998 \| \| Neurons in other areas \| 5.137 \| 4.626 \| Filtered images: The BSDS 500 images we used are whitened, aligning with our model's training process (Olshausen and Field, 1996, Nature) (citation 36 in our paper). Whitening reduces nearby pixel correlation by down-weighting low-frequency content, which typically dominates and causes correlations. This process also enhances important image features, such as edges and contours, to preserve structural details. Additionally, whitening attenuates high frequencies, which often correspond to noise, thereby reducing noise from being introduced into the image. PCs tuning for particular types of edge structure: Figure 4e in our paper shows that PCs have broader orientation tuning curves than iso-orientation domains, which may enable them to detect T-junctions and corners, as demonstrated by Ming Li et al. (2019, Sci.Adv.) and Erin Koch et al. (2016,Nat. Commun.). We analyzed the acute angles formed by the primary and secondary peaks in the tuning curves (Table 4), revealing that PCs prefer larger acute angles, closer to orthogonal (90°), indicating a preference for orthogonal junctions. While this result doesn't distinguish between "L" and "T" junctions beyond their angle, we suggest that higher visual cortices like V2 and V4 handle such distinctions, as shown by Tianye Wang et al. (2024, Nat. Commun.) and Anna W. Roe et al. (2012, Neuron). Table 4: Probability distribution of preferred adjusted acute angles in pinwheel centers. (Available in anonymous GitHub) \| Adjusted acute angle range (degrees) \| Probability (%) \| \|-----------------------\|-----------------\| \| 0 - 9 \| 0 \| \| 9 - 18 \| 0 \| \| 18 - 27 \| 1.30 \| \| 27 - 36 \| 0 \| \| 36 - 45 \| 3.90 \| \| 45 - 54 \| 6.49 \| \| 54 - 63 \| 5.19 \| \| 63 - 72 \| 14.29 \| \| 72 - 81 \| 22.08 \| \| 81 - 90 \| 46.75 \| We would like to express our sincere gratitude for your time and effort in reviewing our paper. Title: Response to Official Comment 2	Rebuttal 1: Rebuttal: We greatly thank the reviewers for their valuable advice and comments, which are very helpful for us to further improve this work. We are especially encouraged by the recognition from the reviewers: 1. The findings are quite interesting and novel. The modeling approach seems well-designed. 2. This work can be a good candidate for a saliency detector and gives some interesting quantitative predictions. 3. Their model is interesting and matches experiential data across species. The paper is very well-written and their analysis is novel and interesting. The paper solves an interesting problem combined with biophysics and neuroscience. 4. The question is of high interest. The paper is good for a thorough investigation of previous works and good bio-plausibility of the model. There were some unclear points in the paper that may have caused confusion. To address these unclear points, we have made thorough revisions. The significant changes are summarized as follows: 1. We have validated the efficiency of PCs in response to edges again by testing with real image data, in accordance with the suggestions of Reviewer TFr2. 2. We have investigated more into the relationship between our model and biological ground truth, following the suggestions of Reviewer Boae. 3. We have verified with experimental data and compared it with previous models to validate our model, as suggested by Reviewer FA4k. 4. We have accomplished a DNN implementation to our model SESNN performing object recognition to elucidate the functional significance of differences in response latency between pinwheel centers and iso-orientation domains (IODs), based on the recommendations of Reviewer indp. Pdf: /pdf/87b760754781ad7e1f696172af92a85527d72713.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
MAC Advice for facility location mechanism design	Accept (poster)	Summary: This paper studied facility location games with mostly approximately correct (MAC) predictions. In this setting, there are n agents in a metric space, and k facilities to be located in that space. The cost of each agent is defined as the minimum distance from the facilities to their location. Each agent location is private, and the mechanism designer can predict the agent locations. In a MAC prediction, there are two parts of data: some (more than half) are approximately correct up to an additive error, and the others are arbitrary. The goal is to approximately minimize the total cost of all agents while eliciting truthfulness, given the predictions. -For a 2-facility location on a line space, they designed a randomized mechanism that guarantees an expected approximation ratio of 3.6+, which is better than the result which is derived from the no-prediction setting. -For single-facility location in a more general metric space, they designed a deterministic mechanism which is better than the result which is derived from the no-prediction setting when the part of arbitrary prediction is small. -They also studied k-facility location in a general metric space where at least a fraction of the agents must be assigned to each of the k-facilities. A truthful mechanism with a constant approximation ratio is presented. Strengths: Overall, this is an interesting and new topic with a few papers having studied facility location with prediction. The leverage of the prediction helps to improve the approximation ratio when we deal with multiple facilities and multi-dimensional space. Weaknesses: One concern is that I am not sure whether the MAC model is natural enough in this problem. I find the mechanisms designed in this paper are not very interesting in the sense that the predictions are exploited in a very heavy way. For most of the mechanisms, they go like this: if some conditions are satisfied, the mechanism uses the predictions with the agents’ reports completely ignored; otherwise, the predictions are ignored and traditional facility location mechanisms are used. This makes me feel that the mechanisms are artificial, and I also feel like the conceptual contribution of this paper is incremental due to this. Moreover, the structure of the paper can be improved. The model proposed is quite general while many special cases are studied. For example, there are many settings such as single/2/k facilities, deterministic/randomized mechanisms, and line/general spaces. It would be better to give a table to tell which combinations are addressed and which are not. Technical Quality: 4 Clarity: 2 Questions for Authors: No question. Confidence: 3 Soundness: 4 Presentation: 2 Contribution: 2 Limitations: N.A. Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your feedback. We respond to your comments and questions below. If our response is satisfactory, we would greatly appreciate it if you would consider raising your score. * Concern: “One concern is that I am not sure whether the MAC model is natural enough in this problem.” Reply: We would like to try and demonstrate that the MAC model is quite natural as a way to capture predictions for facility location mechanism design problems. For example, in such problems, historical data can give predicted locations for each of the agents, which we can then use (along with agent reports) to get better mechanisms. Another “real life” motivational example is the following: * Example: A large tech company (such as Google or Apple) wants to set up a facility (such as a physical store or data center) as close as possible to its users' home location in some city. They can predict home locations of people via a learning algorithm, trained on features such as GPS data, which WiFi hotspots they are connected to, which stores they often buy at (via wallet application data), and more. When a prediction is correct, it might be close to correct (approximately correct), e.g., due to GPS location not being accurate so the neighboring house location might be predicted rather than the real one. Also, it might be the case that a prediction is far from being correct (such as faulty GPS data, or a place of work being identified as a place of living). For most people, the features contain enough information to approximately predict their home location. Please also see the discussion in the introduction section (lines 41-80) for why this kind of model is needed to support handling the important issue of outliers, and the discussion in appendix B laying out more potential sources for such MAC predictions. * Concern: “I find the mechanisms designed in this paper are not very interesting in the sense that the predictions are exploited in a very heavy way. For most of the mechanisms, they go like this: if some conditions are satisfied, the mechanism uses the predictions with the agents’ reports completely ignored; otherwise, the predictions are ignored and traditional facility location mechanisms are used. This makes me feel that the mechanisms are artificial, and I also feel like the conceptual contribution of this paper is incremental due to this.” Reply: The mechanisms that only use predictions (and ignore the agent reports) are the ones in the “warm up” Section 6.1: these results are to develop our tools and build towards the main results. The main technical core of the paper is in Section 6.2, which incorporates both the predictions and the input (agent-reported locations) in quite a non-trivial way. Indeed, we strongly believe it goes beyond the common approach of interpolating between the best “no predictions” algorithm and the approach of completely trusting the predictions: * The first stage for choosing the first facility via Big-Cluster-Center using the robust statistics results we developed in Appendices F and H, has different guarantees for balanced and unbalanced instances. * The second stage chooses the second facility using both the predictions (by using the first facility) and the input (reported locations). * Finally, it is only the characterization we develop for balanced vs unbalanced optimal clustering cases that allows us to show that the two stages together return a good solution, as in the proof of Theorem 9 (Appendix J). This is why we believe the resulting mechanism is interesting and non-trivial. We hope you will agree with us! * Concern: “Moreover, the structure of the paper can be improved. The model proposed is quite general while many special cases are studied. For example, there are many settings such as single/2/k facilities, deterministic/randomized mechanisms, and line/general spaces. It would be better to give a table to tell which combinations are addressed and which are not.” Reply: One contribution of the paper is to introduce the new model which is general, and to show how it can be used to achieve beyond worst-case analysis in several examples (of facility location mechanism design). We thank the reviewer for suggesting a table for the results and we completely agree it will make things clearer. We intend to add it to the next version.	Summary: The authors study variants of the facility location problem from a mechanism design perspective, in which the mechanism receives predictions on the agents' locations. A percentage of the predictions may have an unbounded error, whilst the remainder of the predictions can be incorrect up to a certain bound. This is in contrast to most existing work on facility location with predictions, in which the designer is given predictions for the optimal facility placements. Specifically, the paper looks at the single facility location problem in multiple dimensions, and the 2-facility location problem on a line, designing strategyproof mechanisms with bounded approximation ratios. Strengths: The paper is written and structured very well, and I had almost no issues with understanding the paper. I found very few typos or grammatical errors (see Minor comments). The setting is novel, well-motivated, and is applicable to a wide range of researchers (as the paper is relevant to the fields of both machine learning and computational social choice/mechanism design). I did not find any errors in the proofs, which were technically sound. The approximation ratios achieved by the algorithms improve on existing results under reasonable conditions (though this is achieved with the help of predictions). The use of the Big-Cluster-Center mechanism and its analysis is quite interesting. Weaknesses: My main concern is on the omission of the epsilon term throughout the paper and slightly vague discussion in the appendix, which is a bit suspicious. This could be improved by being more precise with the effect of epsilon on the results. (see the first question) Minor comments: Question 1: “despite large” -> “despite a large” Line 74: add a comma -> “using agent reports, it is…” Line 299: add a comma after the approximation ratio expression Line 358: “sine”-> “since” The references in lines 55-57, 84-86, 194 should be \citep instead of \citet Theorem 9 begins with “For a for a” Definition 13 could be written slightly more formally: instead of “the goal is”, the authors could write something like “the objective is” Technical Quality: 3 Clarity: 3 Questions for Authors: Could the authors give some precise examples on how the algorithms’ approximation ratios would change for both small and large epsilon>0? If my understanding is correct, would each approximation ratio have an additive epsilon*n term for small epsilon, and be unbounded for large epsilon? Would “winner-imposing mechanisms” such as from the paper “Winner-Imposing Strategyproof Mechanisms for Multiple Facility Location Games” by Fotakis and Tzamos (2013) be applicable in this setting? If so, could this concept be used to extend the “second-proportional mechanism” to multiple facilities? Regarding the phrase “While we have not optimized the constants,…” on line 129, specifically which constants are being referred to here? And can the authors comment on how much room there is for improvement? Are the existing deterministic mechanisms for the 2-facility location problem with predictions (in the paper by Xu and Lu (2022)) immediately applicable in this setting? Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: N.A. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for their feedback! We are glad that the reviewer appreciated many aspects of our work. In what follows, we attempt to address the remaining concern and questions. * Concern: “My main concern is on the omission of the epsilon term throughout the paper and slightly vague discussion in the appendix, which is a bit suspicious. This could be improved by being more precise with the effect of epsilon on the results. (see the first question)” Reply: In the reply to the first question later in this rebuttal, we explain the mixed-additive-and-multiplicative nature of the cost that we get by introducing epsilon, showing why it is in fact reasonable to not include it in the calculation. We note that while we considered dropping epsilon from this work (and calling it Mostly Correct Predictions), we ultimately decided to keep it for the following reasons: 1. We wanted to present a general/flexible model that would be useful for problems beyond those considered here. To the best of our knowledge, mechanism design subject to our definition of MAC predictions has not been studied even for the epsilon=0 case, so we could not revert to existing notions from the literature. Moreover, we anticipate that the case of non-zero epsilon may be interesting in other settings, and we wanted to present a comprehensive model to the community. 2. We think that in many instances of facility location it might be unrealistic to expect perfect predictions (𝜖=0), but is realistic to expect a small 𝜖. This notion emphasizes that this is not a problem, and is handled just as well by the model. * Regarding the minor comments: Thank you, we will fix all these. * Question: “Could the authors give some precise examples on how the algorithms’ approximation ratios would change for both small and large epsilon>0? If my understanding is correct, would each approximation ratio have an additive epsilonn term for small epsilon, and be unbounded for large epsilon?” Reply: Since the cost increases additively by at most 𝜖n for all values, we would get a mixed-additive-and-multiplicative result in this setting. Hence, as 𝜖 gets large compared to OPT/n (i.e., large compared to the average optimal cost for each client), our approximation would indeed be unbounded. In this case, one can say that the predictions are not worth using, since the noise (the additive error in the predictions) is more than the signal (the average cost for clients). * For instance, consider the (degenerate) single facility location problem with n input agents, all located on the real line at x=0, and all MAC predictions are x=𝜖. Our mechanism would return x=𝜖 as the location for the facility. The mechanism’s cost is 𝜖n while the optimal cost is 0, resulting in an unbounded approximation ratio. While each agent only pays an 𝜖 more, the (purely multiplicative) approximation ratio does not capture the fact that this is still a good solution for a small 𝜖. This kind of example can be extended to k facilities. We are happy to add this discussion to the next version. Question: “Would “winner-imposing mechanisms” such as from the paper “Winner-Imposing Strategyproof Mechanisms for Multiple Facility Location Games” by Fotakis and Tzamos (2013) be applicable in this setting? If so, could this concept be used to extend the “second-proportional mechanism” to multiple facilities?” Reply: This is a very interesting question. As Fotakis and Tzamos (2013) point out, giving the mechanism power to force agents to only use a single facility does indeed improve the approximation ratio to a k-dependent constant. Without this additional power, the problem is harder: for $k=3$ they get a linear $(n-1)$ approximation ratio. We focused on the problem without this additional power, but we believe it likely that utilizing this additional power can yield better approximation ratios with MAC predictions as well. One promising strategy could be to use the matching between predictions and agent-reported values (as we mention in lines 383-385). This way, it might be possible to force an agent to only use a facility near its predicted value if the reported value is close to the predicted value. This will be a great future direction! * Question: “Regarding the phrase “While we have not optimized the constants,…” on line 129, specifically which constants are being referred to here? And can the authors comment on how much room there is for improvement?” Reply We refer mostly to the constants in Theorems 4 and Theorem 13. It is tight asymptotically in terms of the balancedness constant b: given a constant $k$, the approximation ratio of our mechanism is $1 + \Omega(1/b)$ (we have such an example for $k=2$ which we omitted from the paper). There is room for improvement here for large values of $k$, specifically in extending the theorem to larger values of $\delta$. * Question: “Are the existing deterministic mechanisms for the 2-facility location problem with predictions (in the paper by Xu and Lu (2022)) immediately applicable in this setting?” Reply: Indeed, we can use the optimal solution for the predicted points as the predicted centers, and then use the mechanism of Xu and Lu (2022). However, the instance from Example 1 shows that even a single outlier can cause the predicted solution’s optimum to be very bad and thus their mechanism will also perform poorly given this prediction. --- Rebuttal Comment 1.1: Comment: Thank you very much for the detailed reply. I have no further questions.	Summary: This work considers facility location mechanism design in the presence of (pretty good) advice on locations. In this setting, agents report their locations to impact the places facilities are installed or built. In this model, the designer has access to advice that is Mostly and Approximately Correct, a notion introduced by this work whereby at least $1-\delta$ of the advice is approximately correct with additive error at most $\epsilon$. The authors show that they can use that advice to beat the theoretical results without advice. In particular, for 2 facility location on a line, they can achieve approximation ratio of $3.6 + O (\delta)$, a significant improvement over the best known without advice. The algorithm for merging the advice and reports is a simple combination of the two: first, use the advice to place the first facility, then use the agent reports to place the second facility. The analysis is quite related to some analysis from Lu et al 2010 for facility location in metric spaces without advice, but they are able to improve the analysis since they are on the line. Strengths: This work presents a general model, MAC, for advice that would seem to be useful in many other situations. In particular the model includes a small chance of arbitrarily bad advice. The presented algorithm details how to use that advice in order to improve on the classic 2-facility location on a line problem. Weaknesses: While the MAC notion is a clean one that would seem to be a good vehicle for exploring advice, the additive error here plays a minimal role - the authors immediately drop the $\epsilon$ everywhere... "we drop the $\epsilon$ from the calculations to avoid "dragging" the additive $\epsilon$-dependent term along each result". As a result of that... is it really better to include it in the first place if you're going to ignore it? Or better to say that the advice is mostly correct and then describe how behavior scales with the additive error? It feels overall like a simpler notion from literature could have been used for advice if the additive error wasn't going to play any sort of role in the analysis. The underlying approach - while beneficial that it is simple, is a little dependent on the fact that it is somewhat easy to split this problem into two: the first facility location, and the second facility location. The approach and analysis for the second facility location draws very heavily on prior work from Lu et al (2010), and is able to improve on that primarily because of the restriction to real line rather than metric. Relative to prior work, this work assumes a prediction for each agent. This helps quite a bit in minimizing error, as the use of medians and clustering can mitigate the risk of some outliers. As a result, I wouldn't say that the impact is an improvement on an existing result, but more of a change in the type of error and prediction. Technical Quality: 3 Clarity: 3 Questions for Authors: Relative to the work without predictions, there is the requirement that the number of agents assigned to each facility is at least a minimum value. How sensitive is this? Can this be dropped or is there a tight upper bound? Confidence: 2 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: N/a Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for their feedback! We are glad that the reviewer appreciated some aspects of our work like its usefulness in many situations. We respond to your comments and questions below. If our response is satisfactory, we would greatly appreciate it if you would consider raising your score. * Concern: “While the MAC notion is a clean one that would seem to be a good vehicle for exploring advice, the additive error here plays a minimal role - the authors immediately drop the 𝜖 everywhere... "we drop the 𝜖 from the calculations to avoid "dragging" the additive 𝜖-dependent term along each result". As a result of that... is it really better to include it in the first place if you're going to ignore it? Or better to say that the advice is mostly correct and then describe how behavior scales with the additive error? It feels overall like a simpler notion from literature could have been used for advice if the additive error wasn't going to play any sort of role in the analysis.” Reply: We agree it is an option to drop 𝜖 for much of this work (and call it Mostly Correct Predictions), but we see the following advantages in keeping it: 1. We wanted to present a general/flexible model that would be useful for problems beyond those considered here. To the best of our knowledge, mechanism design subject to our definition of MAC predictions has not been studied even for the 𝜖=0 case, so we could not revert to existing notions from the literature. Moreover, we anticipate that the case of non-zero 𝜖 may be interesting in other settings, and we wanted to present a comprehensive model to the community. 2. We think that in many instances of facility location it might be unrealistic to expect perfect predictions (𝜖=0), but is realistic to expect a small 𝜖. This notion emphasizes that this is not a problem, and is handled just as well by the model. * Concern: “while beneficial that it is simple, is a little dependent on the fact that it is somewhat easy to split this problem into two: the first facility location, and the second facility location”. Reply: While our Robust Half technique approach does proceed in two stages, the stages delicately complement each other, rather than being independent. The first stage for choosing the first facility via Big-Cluster-Center using the robust statistics results we developed in Appendices F and H, has different guarantees for balanced and unbalanced instances. The second stage chooses the second facility using both the predictions (by using the first facility) and the input (reported locations). Finally, it is only the characterization we develop for balanced vs unbalanced optimal clustering cases that allows us to show that the two stages together return a good solution, as in the proof of Theorem 9 (Appendix J). * Concern: “The approach and analysis for the second facility location draws very heavily on prior work from Lu et al (2010), and is able to improve on that primarily because of the restriction to real line rather than metric.” Reply: The approximation ratio of 4 for the algorithm of Lu et al. is in fact tight for the line metric space (see Section 4.3 of their paper showing a lower bound of 4 for the performance of their algorithm for points on the line). So the access to the MAC advice is crucial for improving the approximation (to $3.6 + O(\delta)$) for this tight case. Thus our result separates between what can currently be done with/without advice! Our results show that MAC predictions are useful for other problems too (like the single facility, and the balanced k-facilities), and we hope they will be useful for other settings --- including the approximation for two-facility location on more general metrics --- in the near future. * Concern: “Relative to prior work, this work assumes a prediction for each agent. This helps quite a bit in minimizing error, as the use of medians and clustering can mitigate the risk of some outliers. As a result, I wouldn't say that the impact is an improvement on an existing result, but more of a change in the type of error and prediction.” Reply: We completely agree: we get an improvement over the “no predictions” setting, but in relation to the previous models, the MAC model is incomparable. That said, it presents a different and useful (and also important, we believe) perspective: by allowing a delta fraction of the predictions to be arbitrarily bad, it is robust to outliers, and gives a finer-grained control over the kinds of errors that may arise in applications. * Question: “Relative to the work without predictions, there is the requirement that the number of agents assigned to each facility is at least a minimum value. How sensitive is this? Can this be dropped or is there a tight upper bound?” Reply: To avoid any possible misunderstanding, let us emphasize that our main results do not require that the number of agents assigned to each facility is at least a minimum value. The only results with this requirement are Theorem 4/Theorem 13 on the balanced k-facility location (for k>1) with predictions. About the sensitivity: The bounds we know on the sensitivity are in Theorem 13 (line 898, Appendix G). At a high level, this says that our approximations improve as we consider more balanced solutions. Moreover, we cannot remove the balancedness assumption for this type of mechanism as Example 1 (lines 63-68) shows. We do not have a bound in the general case. Finally, we note that the balanced setting is closely related to the capacitated variant of the problem — studied without predictions by Aziz et al. (2020) who showed a linear (O(n)) approximation ratio for k=2. For k=2 the minimum cluster size setting implies a maximum size (capacitated) and vice versa; therefore, Theorem 13 can be viewed as an improvement of the capacitated variant via MAC predictions to a constant approximation ratio.	Summary: This paper studies a learning-augmented version of the facilitation location mechanism design problem. In particular, the authors consider a model for predictions they call “mostly approximately correct” in which most points have an estimate close to the true value and a small fraction can be arbitrarily wrong. In the paper, they first recap that the standard statistics are indeed robust with respect to distance and approximation. Then, they apply these results to solve 1-facility location in $\mathbb{R}^d$ and 2-facility location on a line. The latter they do by breaking the problem down into picking the location of the second facility conditioned on the first one being fixed (which is solved by Lu et al. 2020) and separately estimating a good location for the first one. Strengths: - defines MAC predictions in a sensible way - uses results from robust statistics to show that MAC predictions can be used for the original problem - provides results for a handful of relevant versions of the problem - they claim results show that the problem strictly benefits from having this kind of MAC advice, demonstrating a separation between what can be done without the advice and what can be done with it. If this is true, this is a great strength of the paper. Weaknesses: I am unsure if I quite believe the claim that the problem strictly benefits from having this kind of MAC advice for the following reason. It seems in line 331-2 that the better approximation factor comes from analyzing the algorithm in a more restricted metric space, not from having access to the MAC advice. Technical Quality: 4 Clarity: 4 Questions for Authors: - Why have definitions 9 and 10 been defined in generality for a pair of location estimators $f, \hat{f}$ that might be the same? It seems like they are only used in the case where \hat{f} = f, so why not just define them that way to begin with (which is perhaps more familiar to the audience anyway)? - In Theorem 2, is $med_1(X)$ the cost for the optimizer of the 1-median cost function? - Theorem 4, looks like $\delta < 1/k^2$ (up to constants) is necessary. Is this a limitation? - I would have found it clearer to define a third set $\tilde{X}$ (which may be dependent on time if the mechanism is iterative) that represents the reported locations of the agents. Then, strategyproofness is just saying that $\tilde{X} = X.$ That way, it is clear the algorithm gets the _reported_ locations (which confused me at first), but the strategyproof property of the mechanism means agents have no reason to deviate from the truth. - It would be helpful to have a short explanation of why the coordinatewise median gets $\sqrt{d}$ approximation factor. - In lines 294-295, what is the randomness over? Is it randomness over the state of the world? So with probability, e.g., 1/n^2, all of the points could be bad? - Generally, it would be helpful as a reader to receive some prose descriptions of the algorithms, why they work, and the results as they are presented in technical detail. - it would be helpful to have a summary table of the problem with different values of k, d and with/without randomization, with/without MAC advice (your results) for at-a-glance parsing the strengths of your paper. - Relatedly, are there computational hardness results? - Can you please briefly comment on other abstractions people have used for learned auxiliary inputs to an algorithm? And how MAC is similar / different to them? The nature of the prediction in [Agrawal 2022] is quite different. Small things: - I believe lines 222-224 need to be moved to before Definition 6 - Please add a definition of “strategyproof” - line 332, I believe the citation year should be 2020 Confidence: 3 Soundness: 4 Presentation: 4 Contribution: 3 Limitations: theorem statements detail the settings in which they apply, so the scope of the theoretical results are well-addressed. Flag For Ethics Review: ['No ethics review needed.'] Rating: 8 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for their detailed and helpful feedback! We are glad that the reviewer appreciated many aspects of our work. We respond to your comments and questions below. If our response to the suspected concern is satisfactory, we would greatly appreciate it if you would consider raising your score. 1. Concerns: * Concern: “It seems in line 331-2 that the better approximation factor comes from analyzing the algorithm in a more restricted metric space, not from having access to the MAC advice.” Reply: The approximation ratio of $4$ for the algorithm of Lu et al. (2010) [1] is in fact tight for the line metric space. (See Section 4.3 of their paper showing a lower bound of 4 for the performance of their algorithm for points on the line.) So the access to the MAC advice is indeed crucial for improving the approximation (to $3.6 + O(\delta)$) for this tight case. Thus our result does separate between what can currently be done with/without advice, and we thank you for noting this is a strength of our paper. Our results show that MAC predictions are useful for other problems too (like the single facility case, and the balanced k-facilities), and we hope that these will be useful for other settings --- including the approximation for two-facility location on more general metrics --- in the near future. 2. Questions: * Question: “Why have definitions 9 and 10 been defined in generality for a pair of location estimators $f,\hat{f}$ that might be the same? It seems like they are only used in the case where $\hat{f} = f$, so why not just define them that way to begin with (which is perhaps more familiar to the audience anyway)?” Reply: In Theorem 4 we use different $f,\hat{f}$, which is why we defined it that way. If the reviewer thinks it is too confusing, we are open to changing that. * Question: “In Theorem 2, is 𝑚𝑒𝑑1(𝑋) the cost for the optimizer of the 1-median cost function?” Reply: Yes, we will clarify this. * Question: “Theorem 4, looks like $\delta < 1/k^2$ (up to constants) is necessary. Is this a limitation?” Reply: This is an interesting direction, we don’t think getting delta larger than $1/k^2$ is a barrier in general, but we don’t have better bounds yet. * Question: “I would have found it clearer to define a third set $\tilde{X}$ (which may be dependent on time if the mechanism is iterative) that represents the reported locations of the agents. Then, strategyproofness is just saying that $\tilde{X}=X$. That way, it is clear the algorithm gets the reported locations (which confused me at first), but the strategyproof property of the mechanism means agents have no reason to deviate from the truth.” Reply: We considered that option, but worried that it would add more notation to the paper. We can definitely add a sentence clarifying this point. * Question: “It would be helpful to have a short explanation of why the coordinatewise median gets 𝑑 approximation factor.” Reply: We will add this. In short it is because the coordinatewise median is the optimal solution w.r.t the L1 norm, which is at most sqrt(d) times L2 norm. * Question: “In lines 294-295, what is the randomness over? Is it randomness over the state of the world? So with probability, e.g., $1/n^2$, all of the points could be bad?” Reply: Both your statements are correct. In essence, this captures a PAC-style setting, where there is a small probability (e.g. $1/n^2$) that all points could be bad. We hedge against this by using the $O(n)$-approximate Min-Bounding-Box mechanism in this (low-probability) bad event, as we explain in appendix F.3. * Proposition: add descriptions of the algorithms and a summary table of the problem. Reply: We will add descriptions and a summary as suggested (also see the tables in the pdf file attached in the global response). * Question: “Relatedly, are there computational hardness results?” Reply: We don’t have any yet, but that’s a great question and we will continue to think about this. * Question: “Can you please briefly comment on other abstractions people have used for learned auxiliary inputs to an algorithm? And how MAC is similar / different to them? The nature of the prediction in [Agrawal 2022] is quite different.” Reply: We have a comparison of related abstractions people use for learned auxiliary inputs in the related work section 3 (lines 179-191), the model section (lines 83-103), as well as Appendix A (lines 558-591), but let us comment here on the most related work. The predictions in [Agrawal 2022] (and relatedly [Xu&Lu 2022]) are indeed quite different: they predict only the optimal facility location(s) for facility location, for one and two facilities respectively. Unlike these works (and many others), we don’t predict the optimal solution to the problem, but instead predict the input. Moreover, their measure of the prediction error is the distance between the predicted solution and the real one, while our measure is the fraction of errors, regardless of how bad each error is. This allows us to capture the property that some predictions may be arbitrarily bad (outliers), but most of the predictions are good — this fine-grained notion is difficult to achieve using a single prediction. * Small things: Reply: We will address these issues. (One clarification, though: the Lu et paper we refer to is from 2010, not 2020: [1] Pinyan Lu, Xiaorui Sun, Yajun Wang, and Zeyuan Allen Zhu. 2010. Asymptotically optimal strategy proof mechanisms for two-facility games. In Proceedings of the 11th ACM conference on Electronic commerce. 315–324. Did you have a different paper in mind?) --- Rebuttal 2: Title: Thanks for the response and clarifications. Comment: I follow your point re the approximation factor. Thanks for the clarification. But if I understand correctly, the factor $3$ you show is for second-facility location, whereas the factor $4$ Lu et al. show is for the full 2-Facility Location problem? In which case the apples-to-apples comparison that should appear in line 331 should be $3.6 + O(\delta).$ Also, please add theorem and section references for the Lu result into your paper so it is clear to the reader exactly what you are citing + comparing to. Edited to add: I see that another reviewer also had a similar confusion to me about this issue so please clarify it in the paper. Your responses for the rest sound good! Couple points: * I think adding $\tilde{X}$ as mentioned above would actually help greatly in clarification despite the fact that it adds notation. * I don't see a pdf attached in the global response. Am I looking in the wrong place? * I noticed the discussion in the related work about the abstractions for learned auxiliary inputs! I was particularly curious about the input learning-augmentation -- have there been other attempts for this kind of augmentation for related problems, e.g. clustering? If not, is studying such problems in the MAC setting interesting? If so, would suggest mentioning that in the Future Directions section! * Re Lu 2010 -- you're right; I was looking at the wrong entry, sorry! --- Rebuttal Comment 2.1: Title: Thanks for the reply Comment: Thank you for your reply, we really appreciate it and are very glad the rest of the responses sound good! Regarding the main concern: Indeed, we confirm your understanding: the factor of 3 is for the different problem of the second facility location. For an apples-to-apples comparison, we compare the ratio of 4 without predictions to the one of $3.6 + O(\delta)$ with MAC predictions - this appears in lines 110-113 in Section 2.2 "Our Results". The goal of lines 331-332 was to emphasize the biggest technical difference in the analysis (compared to the analysis of Lu et al.). However, it is not the difference in the analysis which impacts the approximation ratio the most. We completely agree that lines 331-332 are confusing in this sense and will change them to avoid this confusion and be clearer. We are also happy to add the theorem and section references of the Lu et al. result as you suggested. We hope this clarifies the issue of showing that the improvement is indeed due to MAC predictions rather than a different metric, and thank you for your suggestions that will greatly improve the clarity of our exposition. Regarding the remaining points: * Question: “I noticed the discussion in the related work about the abstractions for learned auxiliary inputs! I was particularly curious about the input learning-augmentation -- have there been other attempts for this kind of augmentation for related problems, e.g. clustering? If not, is studying such problems in the MAC setting interesting? If so, would suggest mentioning that in the Future Directions section!” * Reply: We are not entirely sure if we are interpreting "input learning-augmentation" correctly (if we’ve misinterpreted, it would be much appreciated if you could refer us to the correct lines in the related work section). If we understood correctly, you are asking about related work where the predictions are for the problem input, rather than for the optimal solution of the problem instance. Our answer is that we don’t know of other studies considering problems like offline clustering from a perspective similar to the MAC setting. We do think this is a potentially exciting direction, because even for classic algorithm design a small part of the input may contain errors. Two such examples are: using historical location data as the input, even though it accumulated some inaccuracies; and companies like Google using user location data as input, even though it can be noisy. Theorem 4 (lines 267-272) can be viewed as such results for the “balanced” k-medians clustering problem. An intriguing future direction would be to consider other clustering problems — we will add this to the Future Directions section as you suggest, thanks! We are also more than happy to continue the discussion if we did not answer your question or if additional questions arise. * Regarding the other comments: Our reply should have been “We will add descriptions and a summary table as suggested”, since we agree that this will be a great improvement to clarity! The PDF file reference was from an earlier version of the response, sorry about that. We will incorporate the remaining suggestion ($\tilde{X}$ notation), thank you! --- Rebuttal 3: Title: Thanks! Comment: * Thank you for the clarification on the approximation factor -- indeed those lines were a bit confusing, and I appreciate that you will fix them in the next version. * You interpreted "input learning-augmentation" exactly as I meant it! Apologies for the lack of clarity. Thanks for the discussion on it, and I would be excited to see future work looking at this style of "noisy" data. * Got it, okay. I appreciate the clarifications and trust the authors will make updates to the paper based on the discussion here. I am happy to increase my score from 6 to 8. Edited to add: the particular reason for skipping 7 is that if indeed there is not other work that tries to model "noisy input" to this class of problems in this way, that is a significant contribution to the community. The specific problem studied here and algorithms provided are interesting, to be sure, but the novelty and sensibility of the MAC model are perhaps the more interesting contributions. --- Rebuttal Comment 3.1: Comment: Thank you so much for increasing your score and for the engaged discussion.	Rebuttal 1: Rebuttal: We thank the reviewers for taking the time to carefully read our work and for their valuable feedback. We reply to specific points of each reviewer separately.	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Cross-Modality Perturbation Synergy Attack for Person Re-identification	Accept (poster)	Summary: The paper addresses security concerns in cross-modality person re-identification systems, focusing on systems that use both RGB and infrared images. Traditional ReID systems have primarily focused on RGB images, but the differences between RGB and infrared modalities present unique challenges. The authors propose a universal perturbation attack method designed for cross-modality ReID, which optimizes perturbations using gradients from multiple modalities. Experiments on the RegDB and SYSU-MM01 datasets demonstrate the effectiveness of this method. Strengths: 1.This work investigates vulnerabilities in cross-modality ReID models. 2.Proposes a cross-modality perturbation synergy (CMPS) attack using triplet loss to optimize perturbations that leverage shared knowledge across modalities. 3.Extensive experiments on the RegDB and SYSU datasets show the method's effectiveness and provide insights for future improvements in cross-modality ReID robustness. Weaknesses: 1.The authors use random grayscale transformations to reduce modality differences. Are the three-channel grayscale images based on visible light, infrared, or both? 2.What is the intended meaning of the decision boundary in Figure 2? 3.The Figure 3 is difficult to understand. 4.Can the method be discussed on more datasets, such as the LLCM dataset? 5.Does the size of the adversarial boundary affect the experimental results? 6.What is the overall loss function used in the paper? How are the functions discussed in Section 3.2 and Section 3.4 related? Additionally, in Section 3.4, the sequence of formulas seems inconsistent with the context. 7. The SYSU-MM01 common tests are conducted in all-search and indoor-search modes. Which mode is the experiment in Table 1 based on? It is recommended to discuss both modes. 8.The authors should select more diverse types of baseline models to verify the generalizability of the method. 9.In Algorithm 1, the CMPS attack is mentioned to use grayscale images to update perturbations, but in the ablation experiments in Table 3, they are validated as two separate modules. What is the reason for this? Technical Quality: 2 Clarity: 2 Questions for Authors: See the weaknesses above. Confidence: 5 Soundness: 2 Presentation: 2 Contribution: 3 Limitations: The authors explain the limitations of their work, and there is no negative societal impact. Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We would like to express our sincere gratitude for your thorough review and valuable feedback on our paper. Your input has undoubtedly played a pivotal role in enhancing the quality and clarity of the manuscript. Responses to the individual questions below. Reviewer’s Comment : “ ...... Are the three-channel grayscale images based on visible light, infrared, or both? ” Response: The three-channel grayscale image is based on both visible light and infrared. Reviewer’s Comment : “What is the intended meaning of the decision boundary in Figure 2? ” Response: Universal adversarial perturbations leverage the manifold hypothesis, indicating inherent structures and relationships among data. These perturbations push different sample features into a common sub-region that affects the model's accuracy. In Figure 2, we use a spherical representation of the manifold. Identical shapes with different colors represent features of the same person across different modalities. Our method generates universal perturbations that direct these features into a common sub-region. Reviewer’s Comment : “The Figure 3 is difficult to understand ” Response: We noticed your comment about the difficulty in understanding Figure 3. To address this, we have redrawn it (see Figure 1 in the rebuttal supplementary material PDF). It shows how our approach captures intrinsic associations between modalities by pushing apart feature distances of positive pairs with the same identity and pulling closer feature distances of negative pairs with different identities across modalities. Reviewer’s Comment: “Can the method be discussed on more datasets, such as the LLCM dataset? ” Response: We have supplemented the relevant experiments. The experimental results (ϵ=8) of our proposed method on the LLCM dataset[1] and the DEEN baseline[1] are shown in the table below (lower accuracy indicates better performance). \| Method \| Visible to Infrared (r=1) \| Infrared to Visible (r=1) \| \|-\|-\|-\| \| DEEN Baseline \| 62.5%\| 54.9%\| \| M-FGSM Attack\| 28.4%\| 24.8%\| \| LTA Attack \| 15.1%\| 19.5%\| \| ODFA Attack \| 26.3%\| 23.7%\| \| Col.+Del. Attack \| 8.6%\| 9.1%\| \| Our Attack \| 5.8%\| 6.4%\| LLCM is a dataset designed for cross-modality ReID under low-light conditions. Compared to other datasets, it presents more challenges for attackers due to its diverse scenarios and low-light conditions. This complexity and uncertainty make it difficult for adversarial samples to remain effective, reducing the attack success rate. [1]Zhang, Y.,et al. (2023). Diverse embedding expansion network and low-light cross-modality benchmark for visible-infrared person re-identification. In CVPR (pp. 2153-2162). Reviewer’s Comment: “Does the size of the adversarial boundary affect the experimental results? ” Response: Yes, the size of the adversarial boundary can significantly affect the experimental results. The experimental results on AGW using the RegDB dataset are as follows: \| Adversarial Boundary (ϵ) \| Visible to Thermal (r=1) \| Thermal to Visible (r=1) \| \|-\|-\|-\| \| -\| 70.0%\| 70.5%\| \| 2\| 32.7%\| 40.5%\| \| 4\| 9.6%\| 13.8%\| \| 8\| 2.3%\| 2.0%\| \| 16\| 0.3%\| 0.5% As the adversarial boundary ϵ increases, the attack effect is significantly enhanced, and the model's rank-1 accuracy drops rapidly. Reviewer’s Comment: “What is the overall loss function used in the paper? How are the functions discussed in Section 3.2 and Section 3.4 related ....... ” Response: Section 3.2 introduces the framework and overall optimization objective of our method, providing a macro overview. Section 3.4 further details the specific process of perturbation optimization under different modalities. The implementation of this method is quite flexible. Adversarial perturbations can be optimized on a per-sample basis or in batches. Section 3.4 does not explain this, which may have caused confusion regarding its relationship with Section 3.2. Additionally, adjusting the order of Formula 1 will indeed provide a better reading experience. We appreciate the reviewer pointing these out and will make the necessary optimizations. Regarding the flexibility issue, there is further discussion in subsequent questions. Reviewer’s Comment: “The SYSU-MM01 common tests are conducted in all-search and indoor-search modes. Which mode is the experiment in Table 1 based on? ” Response: For the "Visible to Infrared" scenario, we used the all-search mode. For the "Infrared to Visible" scenario, we used the indoor-search mode. We chose these modes to better align with the typical use cases and challenges presented by each cross-modality scenario. We will clarify this information in the revised manuscript to avoid any confusion. Thank you for pointing this out. Reviewer’s Comment: “The authors should select more diverse types of baseline models to verify the generalizability of the method ” Response: In the previous response, we evaluated the DEEN baseline on the LLCM dataset and, as requested by other reviewers, assessed the transferability of the proposed method on different network architectures, including IDE, PCB, and ResNet18 (see the response to Reviewer fT1U). These experiments validate the method's generalizability. Reviewer’s Comment: “ ...... CMPS attack ...... validated as two separate modules. What is the reason for this? ” Response: Separating these components allows us to assess their individual contributions to the overall method, clearly demonstrating their roles in the final performance. Different environments may require varying method components. For example, in sketch-RGB systems, grayscale images may not be effective for attack augmentation. By validating these components independently, we showcase the method's flexibility and adaptability, proving that specific enhancements improve the effectiveness of universal perturbations. --- Rebuttal 2: Comment: Dear Reviewer tAG1, As the deadline for the discussion period is approaching, we would like to kindly request your feedback on our responses. We wish to express our deepest gratitude for the time and efforts you have dedicated to reviewing our work. We sincerely hope that our detailed responses have adequately addressed all the concerns and suggestions you raised. We fully understand that you may be occupied with other commitments, but we would greatly value any comments you can provide on our responses before the deadline. Thank you for your attention to this matter. We eagerly look forward to hearing from you soon. Sincerely, 9505 Authors --- Rebuttal 3: Comment: Thank you for this feedback. I still have some concerns regarding the rebuttal. 1) The author has provided an explanation for Figure 2, but Figure 2 does not seem to convey the author's intended message. 2) The author has explained the impact of the adversarial boundary, but in my view, the choice of adversarial boundary ϵ can control the strength of the attack but does not ensure that the adversarial attack will be effective in all scenarios. Attackers may need to fine-tune for different models and datasets. How does the author address the issue that, in practical applications, it may not be possible to determine an optimal ϵ to ensure the success rate of the attack, which could increase both time and economic costs? Additionally, I still have concerns that the use of gradients from different modalities to optimize perturbations does not seem to be a new idea. Classic attack methods such as FGSM, MI-FGSM, and PGD are all based on gradient perturbations, suggesting a lack of originality. According to the author's explanation, Aug seems to be as effective as CMPS, meaning that the general random grayscale changes have actually contributed to the improved performance reported in the paper. --- Rebuttal Comment 3.1: Comment: We sincerely appreciate you taking the time to respond to our work, and we would like to clarify a few points further. Regarding your feedback on Figure 2, we take your concerns very seriously. We understand there may still be some dissatisfaction with the current version, and we are willing to spend more time to further optimize it. To maintain a compact and aesthetically pleasing layout, we kept the title of Figure 2 concise, with more detailed explanations provided in the main text. This might have contributed to the figure’s lack of immediate clarity. We will carefully consider your feedback and strive to improve Figure 2 in future iterations. Currently, research on the security of cross-modality person re-identification is still in its early exploratory stages, with infrared and thermal imaging being the primary focus scenarios in this field. Regarding your comment that "...... does not ensure that the adversarial attack will be effective in all scenarios", gradient-based methods may have limitations in improving the generalization and adaptability of attacks across more scenarios. This is indeed one of our future research directions. As we mentioned in our response to Reviewer Zepn, we will continue to address this issue in subsequent work. As for your question about "...... in practical applications, it may not be possible to determine an optimal ϵ to ensure the success rate of the attack, which could increase both time and economic costs?" generally speaking, the larger the ϵ value, the more effective the attack. The ϵ value is mainly related to the magnitude of the perturbation. In real-world applications, many tasks require a balance between the visibility of the perturbation and the effectiveness of the attack, so ϵ is typically not set too high. In most tasks, a value of 8 for ϵ is considered reasonable. The time cost is primarily related to the number of iterations set during the optimization process of the adversarial perturbation. Generally, the more iterations, the better the optimization of the perturbation, and the stronger the attack effect. Additionally, one significant advantage of universal perturbations compared to other attack methods is that they do not need to be customized for each sample (i.e., there is no need to redesign the perturbation for different samples). Although more time may be spent optimizing the universal perturbation initially, it incurs no additional time or economic costs in subsequent applications. Regarding the originality of the method, we would like to clarify further. Although FGSM, MI-FGSM, and PGD are classical gradient-based methods, they are primarily designed for single-modality scenarios and lack an intrinsic mechanism to handle the correlation of information across different modalities. This is precisely the motivation behind our research—through the collaborative optimization of information across different modalities, we propose the Cross-Modality Perturbation Synergy (CMPS) attack, a universal perturbation method that effectively addresses the security challenges in cross-modality ReID. Moreover, another key contribution of our paper lies in the theoretical analysis of the intrinsic mechanism of the proposed method, which demonstrates its effectiveness from a theoretical perspective. We hope that the reviewers will consider this contribution. As for the Aug method you mentioned, we have incorporated it as an auxiliary enhancement strategy within CMPS to further improve the generalization of cross-modality perturbations. In traditional methods like FGSM, MI-FGSM, and PGD, which typically focus on perturbation optimization in single-modality contexts, there is a lack of an intrinsic mechanism to address cross-modality differences, making it difficult to integrate enhancement methods like Aug. Our work effectively integrates Aug through the CMPS strategy, enabling it to produce more significant results in cross-modality scenarios. Once again, we thank you for your attention and suggestions on our work. Your feedback has not only helped us refine our current research but also provided direction for our future studies. We hope that our work can contribute to the security research of cross-modality ReID systems. Sincerely, 9505 Authors	Summary: This paper investigates adversarial attacks on cross-modality person re-identification (ReID) systems. It is purportedly the first study to investigate vulnerabilities in cross-modality ReID models, with the goal of evaluating the security of these systems. To this end, the paper introduces an innovative universal perturbation attack method specifically designed for cross-modality ReID. This new method includes a cross-modality attack augmentation technique, which helps the perturbation synergy attack to better bridge the gap between different modalities. Experimental results on the RegDB and SYSU datasets show that the CMPS attack significantly reduces the accuracy of ReID systems, outperforming existing traditional methods. Strengths: This paper introduces a novel perturbation attack specifically designed for cross-modality person re-identification, addressing a significant gap in the existing literature. The authors have made a notable contribution by being the first to explore vulnerabilities in these cross-modality systems. The importance of this work lies in its innovative approach to tackling the complex challenges posed by person re-identification systems that use different imaging modalities, such as RGB and infrared. The paper provides rigorous theoretical analysis and thorough experimental validation of the proposed method, demonstrating its significance both theoretically and practically. Additionally, the quality of writing is high, with the authors presenting their ideas clearly and concisely, making it accessible even to readers who are not experts in the field. Weaknesses: 1. The difference between VI-ReID and regular ReID is that VI-ReID requires matching pedestrians across different modalities. Theoretically, it is sufficient to attack the RGB features, rendering them inadequate to match the infrared image features. Can focusing solely on attacking RGB features also fulfill the requirements? 2. The article states that infrared images are grayscale images, which might not be entirely accurate. Near-infrared images appear visually similar to grayscale images and lack color information. 3. While the paper demonstrates the effectiveness of the CMPS attack in bridging the gap between RGB and infrared modalities, extending this research to a broader range of modalities would provide deeper insights into the applicability and limitations of the proposed attack method. Additionally, the current experiments are primarily focused on the RegDB and SYSU datasets. Future studies incorporating more diverse datasets from various scenarios and conditions would help validate the robustness and generalizability of this method in complex environments. Technical Quality: 3 Clarity: 4 Questions for Authors: Have the authors considered how to enhance the robustness of cross-modality ReID systems to resist attacks similar to CMPS? The paper could further expand its impact by investigating the resilience of CMPS attacks against existing adversarial defense mechanisms. By discussing or empirically evaluating the performance of CMPS attacks in the presence of adversarial training or other defense strategies, a deeper understanding of the proposed method's robustness can be gained, guiding the development of more secure cross-modality ReID systems. Confidence: 5 Soundness: 3 Presentation: 4 Contribution: 4 Limitations: Yes, the authors have adequately addressed the limitations. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We would like to express our sincere gratitude for your thorough review and valuable feedback on our paper. Your input has undoubtedly played a pivotal role in enhancing the quality and clarity of the manuscript. Responses to the individual questions below. Reviewer’s Comment: “The difference between VI-ReID and regular ReID is that VI-ReID requires matching pedestrians across different modalities. Theoretically, it is sufficient to attack the RGB features, rendering them inadequate to match the infrared image features. Can focusing solely on attacking RGB features also fulfill the requirements?” Response: Yes, theoretically, attacking only the RGB features can partially disrupt a VI-ReID system. However, this approach has significant limitations, and the effectiveness of the attack can be relatively constrained. As shown in the table below, 'RGB Attack' refers to using only RGB visible images from the cross-modality dataset RegDB for the attack. In this context, smaller values indicate better attack effectiveness. ### AGW Baseline: \| Method \| Visible to Thermal (r=1) \| Thermal to Visible (r=1) \| \|-------------------------\|---------------------------\|----------------------------\| \| AGW baseline \| 70.1% \| 70.5% \| \| RGB attack \| 15.7% \| 22.3% \| \| RGB+Infrared attack \| 5.1% \| 16.9% \| ### DDAG Baseline: \| Method \| Visible to Thermal (r=1) \| Thermal to Visible (r=1) \| \|-------------------------\|---------------------------\|----------------------------\| \| DDAG baseline \| 69.3% \| 68.0% \| \| RGB attack \| 18.3% \| 30.5% \| \| RGB+Infrared attack \| 4.6% \| 19.5% \| It can be seen that when considering only RGB, the effectiveness of the attack is limited and is even more constrained in the “Non-Visible to Visible” testing scenario. While attacking RGB features can be somewhat effective in a single RGB-infrared ReID system, its generalizability is likely poor in more complex real-world scenarios and when considering more modalities. If we focus only on attacking RGB features in the RGB-infrared ReID system, the effectiveness of the attack may significantly diminish when transferring to RGB-thermal ReID systems or even infrared-thermal ReID systems. Therefore, it is more important to research and develop universal perturbations that exhibit good transferability between different modalities to ensure the effectiveness of attacks in various practical applications. Reviewer’s Comment: “Have the authors considered how to enhance the robustness of cross-modality ReID systems to resist attacks similar to CMPS? ...... By discussing or empirically evaluating the performance of CMPS attacks in the presence of adversarial training or other defense strategies ...... guiding the development of more secure cross-modality ReID systems.” Response: Thank you for your valuable feedback. Our future work will focus on evaluating the effectiveness of CMPS attacks against existing adversarial defense mechanisms. We have conducted some experiments. We injected adversarial perturbations with a magnitude of 8 into the training samples on the RegDB dataset and then performed adversarial training by mixing the adversarial samples with the original samples. The results are shown in the table below: \| Method \| Visible to Thermal (r=1) \| Thermal to Visible(r=1) \| \|--------------------\|---------------------------\|----------------------------\| \| AGW Baseline \| 70.1% \| 70.5% \| \| Before Adversarial Training \| 2.3 % \| 2.0% \| \| After Adversarial Training \| 25.7% \| 29.4% \| The results indicate that adversarial training remains an effective defense method in cross-modality scenarios. --- Rebuttal Comment 1.1: Comment: After reading the author's defense and the opinions and responses of other reviewers, my doubts have been fully resolved. Therefore, I have decided to maintain the current rating. --- Rebuttal 2: Comment: Dear Reviewer Th4d, As the deadline for the discussion period is approaching, we would like to kindly request your feedback on our responses. We wish to express our deepest gratitude for the time and efforts you have dedicated to reviewing our work. We sincerely hope that our detailed responses have adequately addressed all the concerns and suggestions you raised. We fully understand that you may be occupied with other commitments, but we would greatly value any comments you can provide on our responses before the deadline. Thank you for your attention to this matter. We eagerly look forward to hearing from you soon. Sincerely, 9505 Authors	Summary: This paper is the first to explore the security vulnerabilities of cross-modality ReID models and proposes a universal perturbation attack method for cross-modality person re-identification (ReID) systems, called the Cross-Modality Perturbation Synergy (CMPS) attack. This method innovatively utilizes gradient information from both RGB and infrared images to generate a universal perturbation, maintaining its effectiveness across multiple modalities. Experiments conducted on the RegDB and SYSU datasets demonstrate that the CMPS method significantly reduces the accuracy of ReID models, outperforming existing traditional attack methods. This study emphasizes the necessity of considering multiple modalities in the security evaluation of ReID systems and provides new perspectives for future research. Strengths: This paper makes a notable contribution by addressing security challenges in cross-modality person re-identification (ReID) systems with a pioneering approach. It stands out as the first to explore vulnerabilities in these systems, advancing the understanding and testing of their robustness against adversarial attacks, particularly in under-explored cross-modality scenarios. By focusing on this critical gap, the paper opens new directions for security evaluation in complex multimodal environments. The novelty of the proposed attack method lies in its innovative use of aggregated feature gradients from different modality images to probe vulnerabilities in cross-modality ReID models. The writing quality is excellent, featuring clear, concise, and well-structured explanations that effectively communicate the paper's concepts. The insights provided are poised to drive improvements in the security of ReID systems. Weaknesses: 1. Figure 1 would benefit from using the same set of gallery images for both the before and after comparisons. 2. The paper exhibits inconsistencies in referencing "Table" and "Tab," as observed in lines 228 and 229. Standardizing these references would enhance readability and professionalism. Technical Quality: 4 Clarity: 3 Questions for Authors: The paper offers initial insights into the transferability of the proposed attack across various models and datasets. A more thorough investigation into factors influencing perturbation transferability, such as diverse model architectures and characteristics of cross-modality data, would advance the understanding of adversarial attacks in this domain. Such comprehensive research could elucidate the performance of perturbations in different settings, optimizing attack methods and enhancing their practical applicability. Confidence: 5 Soundness: 4 Presentation: 3 Contribution: 3 Limitations: Yes, the authors have appropriately addressed the limitations of their study. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We would like to express our sincere gratitude for your thorough review and valuable feedback on our paper. Your input has undoubtedly played a pivotal role in enhancing the quality and clarity of the manuscript. Responses to the individual questions below. Reviewer’s Comment : “A more thorough investigation ...... such as diverse model architectures and characteristics of cross-modality data, would advance the understanding of adversarial attacks in this domain ...... ” Response: We conducted adversarial transferability experiments using IDE, PCB, and ResNet18. The rank-1 transfer attack success rates (higher values indicate better transferability of the attack) are shown in the table below: \| Source \ Target Model \| IDE (Ours/Col.+Del.) \| PCB (Ours/Col.+Del.) \| ResNet18 (Ours/Col.+Del.) \| \|-----------------------\|----------------------\|----------------------\|--------------------------\| \| IDE \| 98.7% / 94.3% \| 84.5% / 81.2% \| 87.4% / 86.1% \| \| PCB \| 85.1% / 80.4% \| 97.6% / 92.8% \| 88.3% / 85.7% \| \| ResNet18 \| 81.0% / 78.5% \| 77.5% / 74.9% \| 98.2% / 95.6% \| All models exhibit high success rates for attacks against themselves, indicating vulnerabilities in recognizing and handling adversarial samples. Overall, the success rate of attacks transferring from one model to another is relatively high. Specifically, ResNet18 has the weakest defense against attacks on itself, and the attacks it generates have slightly lower transferability to other models (IDE and PCB), which may be due to differences in feature representation between ResNet18 and the other models. For the effectiveness of the proposed method in attacking more diverse modality data, please refer to the response to Reviewer fT1U. The chart shows the transferability of attacks using our method across various modality datasets (SYSU, RegDB, Sketch[1], CnMix). The Sketch ReID dataset [1] contains 200 individuals, each represented by one sketch and two photographs. The photographs of each individual were captured during daylight using two cross-view cameras. Raw images (or video frames) were manually cropped to ensure that each photograph includes only the specific individual. Additionally, we applied random channel mixing to images from the Market1501 [2] dataset to simulate a new modality dataset, which we refer to as CnMix. Market1501 includes 1,501 pedestrians captured by six cameras (five HD cameras and one low-definition camera). [1] Lu Pang,Yaowei Wang,Yi-Zhe Song,Tiejun Huang,and Yonghong Tian.Cross-domain adversarial feature learning for sketch re-identification.In Proceedings of the 26th ACM international conference on Multimedia,pages 609-617,2018. [2] Liang Zheng,Liyue Shen,Lu Tian,Shengjin Wang,Jingdong Wang,and Qi Tian. Scalable person re-identification:A benchmark.In Proceedings of the IEEE international conference on computer vision,pages 1116-1124,2015. --- Rebuttal 2: Comment: Dear Reviewer fT1U, As the deadline for the discussion period is approaching, we would like to kindly request your feedback on our responses. We wish to express our deepest gratitude for the time and efforts you have dedicated to reviewing our work. We sincerely hope that our detailed responses have adequately addressed all the concerns and suggestions you raised. We fully understand that you may be occupied with other commitments, but we would greatly value any comments you can provide on our responses before the deadline. Thank you for your attention to this matter. We eagerly look forward to hearing from you soon. Sincerely, 9505 Authors --- Rebuttal Comment 2.1: Comment: Although there is still room for improvement in this paper, considering its technical and theoretical contributions to the safety of cross-modality ReID, I have decided to maintain the current score.	Summary: This paper proposes an innovative strategy called Cross-Modality Perturbation Synergy (CMPS) attack, aimed at revealing security vulnerabilities in cross-modality person re-identification (ReID) systems. These systems are crucial in security applications, typically using RGB and infrared imaging to identify individuals under various lighting conditions and camera setups. The study highlights that current security research mainly focuses on single-modality (RGB-based) ReID systems, neglecting the complexities and potential vulnerabilities in cross-modality scenarios. Strengths: 1. By focusing on cross-modality security vulnerabilities, this paper fills a critical gap in the field of person re-identification (ReID), where previous research has primarily concentrated on single-modality (RGB-based) studies. This novel perspective is highly significant as it extends the understanding of ReID systems to real-world scenarios where different modalities are frequently used. 2. The proposed Cross-Modality Perturbation Synergy (CMPS) attack is innovative, leveraging gradient information from both RGB and infrared images to generate universal perturbations that remain effective across multiple modalities. This approach not only demonstrates theoretical originality but also provides practical value through robust experimental validation. 3. The experimental results on widely used datasets such as RegDB and SYSU convincingly demonstrate the superiority of the CMPS method compared to existing traditional attack methods, highlighting the method's effectiveness in reducing the accuracy of ReID systems. 4. This paper exhibits strong writing and organizational skills, with logically tight explanations that make complex concepts easy to understand. The comprehensive description and intuitive presentation of the methodology and experimental setup contribute to the paper's clarity and comprehensibility. Weaknesses: 1. Although the paper is clearly written, some technical sections are still quite complex. Simplifying these parts would benefit a wider audience. For example, in the section "3.2 Optimizing Loss Functions for Attacking," the derivation process from equations (4) to (11) is rather dense and might be difficult for non-specialist readers to understand. Adding more explanatory text between these equations would make it easier for a broader range of readers to follow. 2. The descriptions of "Figure" and "Fig" in lines 53 and 55 of the article are inconsistent, and they need to be carefully checked and unified. Technical Quality: 4 Clarity: 4 Questions for Authors: 1. The effectiveness of the CMPS attack method has been validated on RGB, infrared, and thermal images. Have the authors considered whether this method can be extended to more modalities, or even any modality? If so, what adjustments would be necessary to the current method? 2. The paper presents an interesting model attack scenario where universal perturbations are added to query images to mislead ReID models. Have the authors considered how to deploy such interference in real-world ReID systems? Confidence: 4 Soundness: 4 Presentation: 4 Contribution: 4 Limitations: Yes Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We would like to express our sincere gratitude for your thorough review and valuable feedback on our paper. Your input has undoubtedly played a pivotal role in enhancing the quality and clarity of the manuscript. Responses to the individual questions below. Reviewer’s Comment: “Have the authors considered whether this method can be extended to more modalities, or even any modality? If so, what adjustments would be necessary to the current method?” Response: In our subsequent work, we addressed this issue by expanding adversarial attacks to more modalities using a dual-layer optimization framework. First, we utilized image gradients within each modality to learn universal perturbations, ensuring their effectiveness in the specific modality. Then, in the second optimization layer, we employed evolutionary computation methods to search for shared features across more different image modalities. This layer of evolutionary search aimed to identify sparse perturbations that could be effectively transferred to other modalities, further optimizing and enhancing the cross-modal transferability of the universal perturbations learned in the previous step. The experimental results are shown in the table below. For example, RegDB->SYSU indicates that we optimize the universal perturbation using the RegDB dataset and then transfer it to the SYSU dataset for testing. Thermal images in the RegDB dataset lose more detailed information compared to sketch images and the channel-randomized CnMix images, and its transfer attack performance is also the worst. Therefore, we hypothesize that the smaller the gap between modalities, the better the transferability. \| Method \| r=1 \| r=10 \| r=20 \| mAP \| \|------------------\|------\|-------\|-------\|-------\| \| SYSU -> RegDB \| 19.62\| 49.70 \| 60.23 \| 15.93 \| \| RegDB -> SYSU \| 22.37\| 51.92 \| 62.17 \| 19.05 \| \| SYSU -> CnMix \| 15.81\| 31.36 \| 40.85 \| 15.02 \| \| CnMix -> SYSU \| 17.23\| 35.78 \| 45.62 \| 16.74 \| \| SYSU -> Sketch \| 17.14\| 35.10 \| 45.82 \| 16.75 \| \| Sketch -> SYSU \| 18.38\| 36.70 \| 47.82 \| 17.63 \| The Sketch ReID dataset [1] contains 200 individuals, each represented by one sketch and two photographs. The photographs of each individual were captured during daylight using two cross-view cameras. Raw images (or video frames) were manually cropped to ensure that each photograph includes only the specific individual. Additionally, we applied random channel mixing to images from the Market1501 [2] dataset to simulate a new modality dataset, which we refer to as CnMix. Market1501 includes 1,501 pedestrians captured by six cameras (five HD cameras and one low-definition camera). [1] Lu Pang,Yaowei Wang,Yi-Zhe Song,Tiejun Huang,and Yonghong Tian.Cross-domain adversarial feature learning for sketch re-identification.In Proceedings of the 26th ACM international conference on Multimedia,pages 609-617,2018. [2] Liang Zheng,Liyue Shen,Lu Tian,Shengjin Wang,Jingdong Wang,and Qi Tian. Scalable person re-identification:A benchmark.In Proceedings of the IEEE international conference on computer vision,pages 1116-1124,2015. Reviewer’s Comment : “Have the authors considered how to deploy such interference in real-world ReID systems?” Response: This research is currently in its early stages, but its potential applications and impacts have garnered significant attention. As the technology matures, attackers may develop more sophisticated methods. For instance, they could embed such perturbations into specially designed stickers or attach them to people's clothing. While these stickers or patterns may appear harmless, they could actually have a significant impact on surveillance systems. These attacks could exploit the perturbations to deliberately interfere with the images captured by surveillance cameras, thereby affecting the accuracy of person re-identification (ReID) systems. ReID systems are widely used in areas such as public safety, traffic management, and smart retail for automatically identifying and tracking individuals. Attackers could achieve several objectives through these methods: Identity Disguise: Attackers could use these perturbations to disguise themselves as others, evading detection by security systems. This could pose serious security risks in high-security locations such as airports, government buildings, or financial institutions. Surveillance Interference: The perturbations could also be used to disrupt the normal functioning of surveillance systems, preventing them from accurately capturing and identifying targets. In such cases, security personnel may be unable to timely identify and respond to potential threats or abnormal situations. Privacy Protection: On the other hand, some individuals might use these techniques to protect their privacy and avoid being tracked by surveillance systems. This could raise legal and ethical issues, especially in public spaces or monitored private areas. Overall, as research progresses and technology advances, addressing these potential attacks will become an important area of focus. This will require not only technical innovation but also legal and policy measures to ensure a balance between security and privacy. --- Rebuttal Comment 1.1: Comment: The authors solve all my quentions, and the motivation, innovation, as well as practicality of the paper are satisfactory, so I maintained the original score.	Rebuttal 1: Rebuttal: We thank all the reviewers for their detailed feedback and valuable time. We are pleased to see that the reviewers found our paper insightful (Zepn, fT1U, Th4d, tAG1), appreciated our experimental validation (fT1U, Th4d), and recognized the theoretical originality and practical value of our work (Zepn, Th4d). In this work, we proposed the Cross-Modality Perturbation Synergy (CMPS) attack method, filling a critical gap in the security research of cross-modality person re-identification (ReID) systems. Regarding the experiments, Zepn and tAG1 suggested validating the transferability of the perturbations across more diverse model architectures and cross-modality datasets. Therefore, we will supplement experiments in this area. Additionally, Th4d expressed doubts about whether attacking only RGB features would be sufficient, and we will also supplement relevant experiments to address this point. Furthermore, tAG1 pointed out some inconsistencies and confusion in our presentation. We have carefully reviewed these issues and addressed them in our individual responses to ensure clarity and consistency in the revised manuscript. Based on the reviewers' comments, we are conducting further experiments and will report the results and make certain revisions to the draft in the coming days to incorporate the reviewers' feedback. Pdf: /pdf/bc535e56ba5bb98e6c7313aedee503d50c442265.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Semantic Density: Uncertainty Quantification for Large Language Models through Confidence Measurement in Semantic Space	Accept (poster)	Summary: The paper introduces the metric "Semantic Density" to quantify the uncertainty of LLMs by measuring the distance of response embeddings in a semantic space. Strengths: - Structure: The problem is well-motivated and the paper is clearly and coherently written. - Theory: The adaptation of kernel density estimation techniques to semantic space for uncertainty quantification in NLG is novel. - Experiments: The experiments were performed on multiple datasets and various SOTA LLMs, where Semantic Density shows good empirical performance given the considered correctness metric. Weaknesses: - Theory: Semantic Density is theoretically not well grounded in uncertainty quantification theory, but proposed as an ad-hoc solution for practical application. So, although it seems intriguing to assign an uncertainty score response-wise rather than prompt-wise, uncertainty theory suggests that the (aleatoric semantic) uncertainty has to be quantified prompt-wise, no matter what ends up being sampled as the response [1]. However, since the true uncertainty score for a given prompt is unknown, the performance of an uncertainty measure is usually evaluated by how well the scores align with the correctness of the most-likely response. - Experiments: According to the experimental setup in line 897, an answer is considered to be correct if its Rouge-L to any of the reference answers is larger than 0.3 for all datasets. However, since the considered datasets usually result in short responses, a fixed threshold of 0.3 is not sufficient. For instance, in the TriviaQA question What is the last Grand Slam tennis tournament played in a calendar year? the reference answer The US Open and the sampled response The Australian Open achieve a Rouge-L of approximately 0.66. This highlights the fact that considering multiple thresholds is essential to assess the performance of uncertainty metrics. --- [1] L. Aichberger, K. Schweighofer, M. Ielanskyi, and S. Hochreiter. Semantically Diverse Language Generation for Uncertainty Estimation in Language Models. arXiv preprint arXiv:2406.04306, 2024. Technical Quality: 3 Clarity: 3 Questions for Authors: - What do the authors exactly mean by Semantic Density rebuilding the output probability distribution from a semantic perspective? (line 58) - In line 277, the authors write "After investigation, the inherent sequence likelihood returned by the original LLM was badly calibrated in these two cases.". What is meant by badly calibrated sequence likelihoods? Why didn't the authors account for this by recomputing the sequence likelihood? - There exists independent work (Kernel Language Entropy) that is closely related to Semantic Density [2]. The authors should consider discussing this in their paper. - It would be insightful to additionally report the performance of existing uncertainty estimation methods when decreasing the number of reference responses instead of only reporting Semantic Density with different models (section 4.2) - Semantic Density uses diverse beam search to sample responses, requiring hyperparameters such as diversity penalty and number of groups. How have these hyperparameters been chosen? Is the method sensitive to the specific sampling strategy? An ablation study on the performance of Semantic Density compared to existing uncertainty estimation methods would be insightful. - Have the authors considered using sampling strategies other than diverse beam search? For instance, Aichberger et al. (2024) introduced sampling semantically diverse sequences, which could be utilized to sample unique reference responses [1]. --- [2] A. Nikitin, J. Kossen, Y. Gal, and P. Marttinen. Kernel Language Entropy: Fine-grained Uncertainty Quantification for LLMs from Semantic Similarities. arXiv preprint arXiv:2405.20003, 2024. Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: The authors did not address the limitations of their work, only the limitations of existing uncertainty estimation methods. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thanks for your constructive comments, we will answer your concerns follows the order of your original comments, due to the space limitation. --- Comment: concern regarding theory Response: Thanks for this insightful comment. We have read reference [1] carefully (it was published in arXiv only after the submission deadline, so we were not aware of it before), and will address your concerns from two perspectives: First, considering the fact that LLMs sample responses stochastically given the same prompt, an uncertainty metric for each specific response has practical value. This is also reflected in reference [1], which states “Uncertainty estimation in NLG involves assessing the uncertainty of an initially generated text (output sequence) for a given prompt (input sequence)”.The prompt-wise aleatoric uncertainty metric derived in [1] was indeed used to quantify the uncertainty of the most likely response (i.e.\ the initially generated response). While this estimate provides a good first approximation, assigning the same prompt-wise uncertainty score to different sampled responses is less useful in practical use cases where the trustworthiness of specific responses matters.The main motivation of the proposed semantic density is thus to provide a solution for such use cases, i.e. to quantify the uncertainty of any specific response (not only the most likely one) that may be sampled by the LLM.. Second, as an emerging research direction, uncertainty quantification in LLMs indeed needs more unified definitions of terms related to “uncertainty”. In the literature, different definitions and usages of the term “uncertainty” can be found, and sometimes other terms like “confidence” or “certainty” are used for the same purpose. Definitions of “uncertainty of a response” and “uncertainty of a prompt” should also be defined and differentiated. We will clarify that the “uncertainty” in this paper refers to “uncertainty of a response”, and delineate the different use cases. . We will also discuss reference [1] since we believe that it forms a good theoretical foundation for this emerging direction. --- Comment: concer regarding the experiments Response: Thanks for this constructive comment. As suggested, we have added experimental results using Rouge-L with different thresholds ranging from 0.1 to 1.0. According to the results, the performance gain of semantic density is not sensitive to the choice of Rouge-L thresholds. The proposed semantic density consistently outperforms other methods across this range, further demonstrating that the results are robust. --- Response: Sorry for the confusion. We wanted to say that the original output distribution of LLMs is in sequence-of-token space, and we want to consider output distribution in a different semantic space. Theoretically, the output distribution in semantic space can be rebuilt from the output distribution in original sequence-of-token space. We will clarify this point in the revision. --- Response: Thanks for the question. Here, “badly calibrated sequence likelihoods” means the original likelihood of the LLM to sample the output token sequence is not well aligned with the correctness of the output sequence. We did not fine-tune or re-calibrate the original LLMs in our current experiments, because we wanted to evaluate the robustness of the proposed semantic density when working with existing LLMs in their original form. Post-hoc fine-tuning and calibration methods are complementary to semantic density, and they can always be applied to further improve the reliability of semantic density. --- Response: Thanks for the suggestion. We will include and discuss it in “related works”. --- Response: Thanks for the suggestion. We have added an experiment that investigates the performance change of semantic entropy when decreasing the number of reference responses. The patterns are similar for semantic entropy, but semantic density exhibits consistently better performance when the number of reference responses is reduced. We will add these results in the revision. --- Response: Thanks for the suggestion! We did not perform an extensive hyperparameter search for diverse beam search, and we used the standard default parameters. As suggested, we have added an ablation study following the setup in reference [1], which tests different choices of diversity penalty. Based on the results, a diversity penalty of 1.0 indeed provides the best performance, but the performance difference between 0.5 and 0.2 is not significant. We will add this empirical study to the revised version. --- Response: We have also tried standard multinomial sampling, and found that diverse beam search was better in generating unique and diverse generations. The SDLG sampling strategy in reference [1] is indeed a good match with semantic density, i.e., more diverse and likely reference responses would make semantic density more reliable. We will discuss it as a potential replacement for diverse beam search in the revision. --- Response: We have actually discussed the limitations of the method in several places in the original manuscript. Please see more details and justifications in section 2 of the appended NeurIPS Paper Checklist (page 15, after the references). --- Rebuttal Comment 1.1: Comment: Thank you for the rebuttal. However, I cannot locate any of the additional results you claim to have conducted for the rebuttal: > As suggested, we have added experimental results using Rouge-L with different thresholds ranging from 0.1 to 1.0. > We have added an experiment that investigates the performance change of semantic entropy when decreasing the number of reference responses. > As suggested, we have added an ablation study following the setup in reference [1], which tests different choices of diversity penalty. Could you please provide these results for further review? --- Reply to Comment 1.1.1: Title: Follow-up response to Reviewer koQE: Comment: Thanks for spending time reading our rebuttals and providing further comments! We did not include the detailed results in the initial rebuttal because this year Neurips only allows 6,000 characters in the initial rebuttal to each reviewer, urging the authors to be more concise. Moreover, only one page of PDF can be attached in the general rebuttal to include necessary tables/figures, and no external URL is allowed. Given this restriction, we have to conclude the additional experimental results with a very brief text summary in the initial rebuttal. However, we understand that providing the detailed results would be more informative to you, so we will attach all the detailed results in follow-up comments per your request. Due to the format limitation, we will use markdown tables to display all the results. Please check them in the comments following this one. We also provide some further discussions below: The most interesting results are indeed the Rouge-L threshold study that you suggested as one of your main comments. In additional to the observation that the proposed semantic density still provides overall best performance across all the tested Rouge-L thresholds, we also noticed that the absolute AUROC scores show an increasing trend for semantic density when the Rouge-L threshold is increased. This indicates that the strictness of correctness check is indeed affecting the absolute performance of the evaluated methods. The initial Rouge-L threshold of 0.3 used in the experiments was following the same setup in the original semantic entropy paper [3], aiming to make the comparisons fair. However, we agree that it is indeed more informative to include results that are under different Rouge-L thresholds. We will include all the results in the revision, and add a discussion regarding this aspect. Thanks for this constructive comment! [3] Lorenz Kuhn and Yarin Gal and Sebastian Farquhar, “Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generation”, The Eleventh International Conference on Learning Representations (ICLR), 2023 --- Rebuttal 2: Title: Detailed results for Rouge-L threshold of 0.1 and 0.5 Comment: Below are the AUROC scores when using a Rouge-L threshold of 0.1 and 0.5 (0.3 has already been shown in the original manuscript): ## Results for Rouge-L threshold of 0.1: ### CoQA \| Rouge-L >= 0.1 \| SD \| SE \| P(True) \| Deg \| NL \| NE \| PE \| \|----------------\|----\|----\|---------\|-----\|----\|----\|----\| \|Llama-2-13b-hf\|0.766\|0.623\|0.606\|0.728\|0.702\|0.556\|0.508\| \|Llama-2-70b-hf\|0.765\|0.622\|0.610\|0.715\|0.719\|0.572\|0.538\| \|Meta-Llama-3-8B\|0.727\|0.601\|0.617\|0.790\|0.632\|0.566\|0.511\| \|Meta-Llama-3-70B\|0.777\|0.606\|0.669\|0.732\|0.712\|0.542\|0.489\| \|Mistral-7B-v0.1\|0.776\|0.616\|0.667\|0.737\|0.705\|0.553\|0.508\| \|Mixtral-8x7B-v0.1\|0.766\|0.624\|0.623\|0.726\|0.707\|0.555\|0.520\| \|Mixtral-8x22B-v0.1\|0.777\|0.617\|0.646\|0.729\|0.710\|0.560\|0.525\| ### TriviaQA \| Rouge-L >= 0.1 \| SD \| SE \| P(True) \| Deg \| NL \| NE \| PE \| \|----------------\|----\|----\|---------\|-----\|----\|----\|----\| \|Llama-2-13b-hf\|0.844\|0.632\|0.583\|0.829\|0.640\|0.505\|0.490\| \|Llama-2-70b-hf\|0.824\|0.664\|0.611\|0.798\|0.696\|0.516\|0.472\| \|Meta-Llama-3-8B\|0.862\|0.572\|0.652\|0.793\|0.798\|0.480\|0.425\| \|Meta-Llama-3-70B\|0.825\|0.624\|0.656\|0.762\|0.804\|0.520\|0.491\| \|Mistral-7B-v0.1\|0.855\|0.620\|0.589\|0.822\|0.693\|0.487\|0.476\| \|Mixtral-8x7B-v0.1\|0.830\|0.654\|0.569\|0.789\|0.742\|0.541\|0.511\| \|Mixtral-8x22B-v0.1\|0.818\|0.660\|0.618\|0.758\|0.779\|0.577\|0.535\| ### Sciq \| Rouge-L >= 0.1 \| SD \| SE \| P(True) \| Deg \| NL \| NE \| PE \| \|----------------\|----\|----\|---------\|-----\|----\|----\|----\| \|Llama-2-13b-hf\|0.720\|0.570\|0.520\|0.698\|0.575\|0.458\|0.500\| \|Llama-2-70b-hf\|0.716\|0.639\|0.593\|0.704\|0.576\|0.476\|0.507\| \|Meta-Llama-3-8B\|0.755\|0.583\|0.582\|0.716\|0.633\|0.468\|0.526\| \|Meta-Llama-3-70B\|0.743\|0.588\|0.542\|0.692\|0.694\|0.490\|0.495\| \|Mistral-7B-v0.1\|0.761\|0.588\|0.578\|0.729\|0.635\|0.462\|0.468\| \|Mixtral-8x7B-v0.1\|0.751\|0.598\|0.602\|0.707\|0.675\|0.523\|0.566\| \|Mixtral-8x22B-v0.1\|0.756\|0.600\|0.613\|0.712\|0.677\|0.500\|0.525\| ### NQ \| Rouge-L >= 0.1 \| SD \| SE \| P(True) \| Deg \| NL \| NE \| PE \| \|----------------\|----\|----\|---------\|-----\|----\|----\|----\| \|Llama-2-13b-hf\|0.697\|0.589\|0.576\|0.704\|0.555\|0.521\|0.503\| \|Llama-2-70b-hf\|0.691\|0.553\|0.590\|0.701\|0.555\|0.506\|0.488\| \|Meta-Llama-3-8B\|0.707\|0.536\|0.595\|0.707\|0.553\|0.466\|0.444\| \|Meta-Llama-3-70B\|0.701\|0.573\|0.574\|0.711\|0.556\|0.503\|0.490\| \|Mistral-7B-v0.1\|0.698\|0.574\|0.598\|0.699\|0.558\|0.493\|0.454\| \|Mixtral-8x7B-v0.1\|0.716\|0.576\|0.609\|0.716\|0.588\|0.503\|0.484\| \|Mixtral-8x22B-v0.1\|0.703\|0.579\|0.584\|0.711\|0.575\|0.518\|0.517\| ## Results for Rouge-L threshold of 0.5: ### CoQA \| Rouge-L >= 0.5 \| SD \| SE \| P(True) \| Deg \| NL \| NE \| PE \| \|----------------\|----\|----\|---------\|-----\|----\|----\|----\| \|Llama-2-13b-hf\|0.791\|0.598\|0.582\|0.716\|0.701\|0.503\|0.515\| \|Llama-2-70b-hf\|0.791\|0.599\|0.559\|0.697\|0.712\|0.506\|0.527\| \|Meta-Llama-3-8B\|0.754\|0.558\|0.575\|0.789\|0.633\|0.500\|0.523\| \|Meta-Llama-3-70B\|0.790\|0.585\|0.669\|0.702\|0.694\|0.470\|0.494\| \|Mistral-7B-v0.1\|0.796\|0.599\|0.645\|0.724\|0.695\|0.495\|0.514\| \|Mixtral-8x7B-v0.1\|0.791\|0.598\|0.568\|0.709\|0.700\|0.503\|0.530\| \|Mixtral-8x22B-v0.1\|0.796\|0.593\|0.586\|0.705\|0.699\|0.505\|0.538\| ### TriviaQA \| Rouge-L >= 0.5 \| SD \| SE \| P(True) \| Deg \| NL \| NE \| PE \| \|----------------\|----\|----\|---------\|-----\|----\|----\|----\| \|Llama-2-13b-hf\|0.854\|0.593\|0.588\|0.807\|0.689\|0.479\|0.518\| \|Llama-2-70b-hf\|0.839\|0.620\|0.548\|0.773\|0.710\|0.491\|0.519\| \|Meta-Llama-3-8B\|0.869\|0.562\|0.645\|0.794\|0.799\|0.464\|0.428\| \|Meta-Llama-3-70B\|0.832\|0.616\|0.648\|0.761\|0.801\|0.504\|0.489\| \|Mistral-7B-v0.1\|0.873\|0.606\|0.580\|0.827\|0.712\|0.476\|0.472\| \|Mixtral-8x7B-v0.1\|0.855\|0.623\|0.544\|0.788\|0.767\|0.546\|0.549\| \|Mixtral-8x22B-v0.1\|0.838\|0.641\|0.585\|0.755\|0.780\|0.558\|0.569\| ### SciQ \| Rouge-L >= 0.5 \| SD \| SE \| P(True) \| Deg \| NL \| NE \| PE \| \|----------------\|----\|----\|---------\|-----\|----\|----\|----\| \|Llama-2-13b-hf\|0.796\|0.557\|0.550\|0.746\|0.704\|0.418\|0.511\| \|Llama-2-70b-hf\|0.779\|0.644\|0.569\|0.712\|0.649\|0.460\|0.548\| \|Meta-Llama-3-8B\|0.809\|0.575\|0.554\|0.732\|0.693\|0.449\|0.613\| \|Meta-Llama-3-70B\|0.800\|0.601\|0.567\|0.716\|0.716\|0.452\|0.454\| \|Mistral-7B-v0.1\|0.790\|0.578\|0.563\|0.735\|0.669\|0.433\|0.443\| \|Mixtral-8x7B-v0.1\|0.798\|0.599\|0.576\|0.721\|0.732\|0.507\|0.618\| \|Mixtral-8x22B-v0.1\|0.798\|0.603\|0.597\|0.717\|0.719\|0.487\|0.584\| ### NQ \| Rouge-L >= 0.5 \| SD \| SE \| P(True) \| Deg \| NL \| NE \| PE \| \|----------------\|----\|----\|---------\|-----\|----\|----\|----\| \|Llama-2-13b-hf\|0.723\|0.494\|0.591\|0.706\|0.528\|0.392\|0.496\| \|Llama-2-70b-hf\|0.719\|0.487\|0.503\|0.717\|0.534\|0.438\|0.486\| \|Meta-Llama-3-8B\|0.736\|0.487\|0.475\|0.718\|0.589\|0.419\|0.535\| \|Meta-Llama-3-70B\|0.774\|0.545\|0.666\|0.747\|0.641\|0.455\|0.524\| \|Mistral-7B-v0.1\|0.719\|0.518\|0.468\|0.703\|0.583\|0.441\|0.511\| \|Mixtral-8x7B-v0.1\|0.761\|0.526\|0.552\|0.737\|0.611\|0.452\|0.510\| \|Mixtral-8x22B-v0.1\|0.755\|0.526\|0.455\|0.729\|0.607\|0.473\|0.584\| --- Rebuttal Comment 2.1: Title: Detailed results for Rouge-L threshold of 0.7 and 0.9 Comment: ## Results for Rouge-L threshold of 0.7: ### CoQA \| Rouge-L >= 0.7 \| SD \| SE \| P(True) \| Deg \| NL \| NE \| PE \| \|----------------\|----\|----\|---------\|-----\|----\|----\|----\| \|Llama-2-13b-hf\|0.796\|0.577\|0.569\|0.675\|0.767\|0.494\|0.509\| \|Llama-2-70b-hf\|0.802\|0.576\|0.544\|0.662\|0.780\|0.493\|0.503\| \|Meta-Llama-3-8B\|0.759\|0.537\|0.574\|0.764\|0.667\|0.481\|0.526\| \|Meta-Llama-3-70B\|0.788\|0.570\|0.665\|0.654\|0.754\|0.456\|0.485\| \|Mistral-7B-v0.1\|0.804\|0.581\|0.612\|0.687\|0.759\|0.481\|0.501\| \|Mixtral-8x7B-v0.1\|0.802\|0.583\|0.547\|0.672\|0.768\|0.486\|0.508\| \|Mixtral-8x22B-v0.1\|0.800\|0.565\|0.562\|0.657\|0.763\|0.492\|0.515\| ### TriviaQA \| Rouge-L >= 0.7 \| SD \| SE \| P(True) \| Deg \| NL \| NE \| PE \| \|----------------\|----\|----\|---------\|-----\|----\|----\|----\| \|Llama-2-13b-hf\|0.875\|0.559\|0.590\|0.767\|0.869\|0.505\|0.513\| \|Llama-2-70b-hf\|0.874\|0.572\|0.587\|0.728\|0.871\|0.514\|0.524\| \|Meta-Llama-3-8B\|0.856\|0.517\|0.628\|0.730\|0.827\|0.432\|0.417\| \|Meta-Llama-3-70B\|0.838\|0.552\|0.624\|0.696\|0.821\|0.458\|0.461\| \|Mistral-7B-v0.1\|0.867\|0.568\|0.567\|0.769\|0.761\|0.474\|0.470\| \|Mixtral-8x7B-v0.1\|0.858\|0.575\|0.528\|0.726\|0.826\|0.516\|0.517\| \|Mixtral-8x22B-v0.1\|0.855\|0.584\|0.564\|0.693\|0.846\|0.531\|0.556\| ### SciQ \| Rouge-L >= 0.7 \| SD \| SE \| P(True) \| Deg \| NL \| NE \| PE \| \|----------------\|----\|----\|---------\|-----\|----\|----\|----\| \|Llama-2-13b-hf\|0.872\|0.577\|0.507\|0.786\|0.860\|0.422\|0.507\| \|Llama-2-70b-hf\|0.864\|0.671\|0.586\|0.732\|0.835\|0.481\|0.548\| \|Meta-Llama-3-8B\|0.865\|0.602\|0.553\|0.735\|0.855\|0.484\|0.652\| \|Meta-Llama-3-70B\|0.860\|0.641\|0.561\|0.721\|0.857\|0.474\|0.463\| \|Mistral-7B-v0.1\|0.848\|0.578\|0.564\|0.743\|0.785\|0.432\|0.415\| \|Mixtral-8x7B-v0.1\|0.843\|0.610\|0.567\|0.724\|0.832\|0.508\|0.608\| \|Mixtral-8x22B-v0.1\|0.844\|0.614\|0.597\|0.713\|0.843\|0.508\|0.600\| ### NQ \| Rouge-L >= 0.7 \| SD \| SE \| P(True) \| Deg \| NL \| NE \| PE \| \|----------------\|----\|----\|---------\|-----\|----\|----\|----\| \|Llama-2-13b-hf\|0.804\|0.494\|0.638\|0.746\|0.662\|0.378\|0.518\| \|Llama-2-70b-hf\|0.806\|0.489\|0.491\|0.758\|0.662\|0.432\|0.488\| \|Meta-Llama-3-8B\|0.789\|0.454\|0.437\|0.715\|0.742\|0.423\|0.584\| \|Meta-Llama-3-70B\|0.851\|0.557\|0.703\|0.775\|0.784\|0.471\|0.532\| \|Mistral-7B-v0.1\|0.792\|0.527\|0.410\|0.737\|0.694\|0.441\|0.544\| \|Mixtral-8x7B-v0.1\|0.825\|0.542\|0.538\|0.765\|0.704\|0.483\|0.550\| \|Mixtral-8x22B-v0.1\|0.829\|0.530\|0.407\|0.764\|0.722\|0.501\|0.640\| ## Results for Rouge-L threshold of 0.9: ### CoQA \| Rouge-L >= 0.9 \| SD \| SE \| P(True) \| Deg \| NL \| NE \| PE \| \|----------------\|----\|----\|---------\|-----\|----\|----\|----\| \|Llama-2-13b-hf\|0.802\|0.553\|0.525\|0.639\|0.797\|0.441\|0.477\| \|Llama-2-70b-hf\|0.803\|0.553\|0.481\|0.618\|0.800\|0.436\|0.470\| \|Meta-Llama-3-8B\|0.766\|0.505\|0.537\|0.735\|0.684\|0.432\|0.514\| \|Meta-Llama-3-70B\|0.799\|0.568\|0.654\|0.621\|0.786\|0.401\|0.471\| \|Mistral-7B-v0.1\|0.811\|0.566\|0.567\|0.654\|0.784\|0.426\|0.466\| \|Mixtral-8x7B-v0.1\|0.809\|0.568\|0.501\|0.636\|0.798\|0.432\|0.477\| \|Mixtral-8x22B-v0.1\|0.807\|0.544\|0.496\|0.617\|0.786\|0.433\|0.478\| ### TriviaQA \| Rouge-L >= 0.9 \| SD \| SE \| P(True) \| Deg \| NL \| NE \| PE \| \|----------------\|----\|----\|---------\|-----\|----\|----\|----\| \|Llama-2-13b-hf\|0.892\|0.547\|0.553\|0.756\|0.913\|0.468\|0.508\| \|Llama-2-70b-hf\|0.894\|0.559\|0.563\|0.709\|0.902\|0.468\|0.491\| \|Meta-Llama-3-8B\|0.855\|0.508\|0.609\|0.714\|0.838\|0.414\|0.417\| \|Meta-Llama-3-70B\|0.843\|0.541\|0.604\|0.679\|0.828\|0.426\|0.447\| \|Mistral-7B-v0.1\|0.868\|0.559\|0.544\|0.753\|0.772\|0.449\|0.447\| \|Mixtral-8x7B-v0.1\|0.867\|0.569\|0.498\|0.709\|0.844\|0.489\|0.503\| \|Mixtral-8x22B-v0.1\|0.865\|0.571\|0.535\|0.674\|0.860\|0.497\|0.547\| ### SciQ \| Rouge-L >= 0.9 \| SD \| SE \| P(True) \| Deg \| NL \| NE \| PE \| \|----------------\|----\|----\|---------\|-----\|----\|----\|----\| \|Llama-2-13b-hf\|0.890\|0.574\|0.490\|0.788\|0.880\|0.407\|0.503\| \|Llama-2-70b-hf\|0.888\|0.676\|0.577\|0.732\|0.861\|0.453\|0.526\| \|Meta-Llama-3-8B\|0.881\|0.602\|0.544\|0.734\|0.881\|0.464\|0.652\| \|Meta-Llama-3-70B\|0.876\|0.645\|0.556\|0.716\|0.883\|0.456\|0.450\| \|Mistral-7B-v0.1\|0.861\|0.574\|0.556\|0.737\|0.806\|0.412\|0.397\| \|Mixtral-8x7B-v0.1\|0.855\|0.608\|0.554\|0.721\|0.851\|0.494\|0.604\| \|Mixtral-8x22B-v0.1\|0.857\|0.620\|0.588\|0.708\|0.863\|0.490\|0.591\| ### NQ \| Rouge-L >= 0.9 \| SD \| SE \| P(True) \| Deg \| NL \| NE \| PE \| \|----------------\|----\|----\|---------\|-----\|----\|----\|----\| \|Llama-2-13b-hf\|0.845\|0.487\|0.662\|0.760\|0.734\|0.351\|0.500\| \|Llama-2-70b-hf\|0.852\|0.495\|0.471\|0.776\|0.722\|0.420\|0.481\| \|Meta-Llama-3-8B\|0.812\|0.431\|0.420\|0.702\|0.818\|0.410\|0.595\| \|Meta-Llama-3-70B\|0.882\|0.569\|0.738\|0.790\|0.838\|0.468\|0.523\| \|Mistral-7B-v0.1\|0.815\|0.502\|0.393\|0.732\|0.737\|0.427\|0.530\| \|Mixtral-8x7B-v0.1\|0.846\|0.535\|0.531\|0.769\|0.730\|0.473\|0.547\| \|Mixtral-8x22B-v0.1\|0.858\|0.527\|0.391\|0.771\|0.773\|0.504\|0.655\| --- Rebuttal 3: Title: Detailed results for Rouge-L threshold of 1.0 and two ablations studies Comment: ## Results for Rouge-L threshold of 1.0 ### CoQA \| Rouge-L = 1.0 \| SD \| SE \| P(True) \| Deg \| NL \| NE \| PE \| \|----------------\|----\|----\|---------\|-----\|----\|----\|----\| \|Llama-2-13b-hf\|0.804\|0.548\|0.513\|0.636\|0.798\|0.429\|0.472\| \|Llama-2-70b-hf\|0.807\|0.546\|0.464\|0.615\|0.799\|0.421\|0.461\| \|Meta-Llama-3-8B\|0.767\|0.495\|0.528\|0.730\|0.685\|0.420\|0.515\| \|Meta-Llama-3-70B\|0.801\|0.563\|0.644\|0.617\|0.788\|0.387\|0.467\| \|Mistral-7B-v0.1\|0.815\|0.561\|0.557\|0.651\|0.784\|0.413\|0.460\| \|Mixtral-8x7B-v0.1\|0.811\|0.565\|0.487\|0.635\|0.799\|0.420\|0.471\| \|Mixtral-8x22B-v0.1\|0.809\|0.537\|0.484\|0.612\|0.786\|0.419\|0.471\| ### TriviaQA \| Rouge-L = 1.0 \| SD \| SE \| P(True) \| Deg \| NL \| NE \| PE \| \|----------------\|----\|----\|---------\|-----\|----\|----\|----\| \|Llama-2-13b-hf\|0.893\|0.546\|0.551\|0.756\|0.914\|0.465\|0.509\| \|Llama-2-70b-hf\|0.895\|0.559\|0.560\|0.708\|0.903\|0.466\|0.490\| \|Meta-Llama-3-8B\|0.855\|0.507\|0.608\|0.714\|0.838\|0.413\|0.417\| \|Meta-Llama-3-70B\|0.843\|0.540\|0.602\|0.679\|0.828\|0.425\|0.446\| \|Mistral-7B-v0.1\|0.868\|0.559\|0.542\|0.753\|0.772\|0.447\|0.446\| \|Mixtral-8x7B-v0.1\|0.867\|0.568\|0.495\|0.709\|0.844\|0.487\|0.502\| \|Mixtral-8x22B-v0.1\|0.865\|0.571\|0.533\|0.674\|0.860\|0.496\|0.547\| ### SciQ \| Rouge-L = 1.0 \| SD \| SE \| P(True) \| Deg \| NL \| NE \| PE \| \|----------------\|----\|----\|---------\|-----\|----\|----\|----\| \|Llama-2-13b-hf\|0.890\|0.574\|0.490\|0.788\|0.880\|0.407\|0.503\| \|Llama-2-70b-hf\|0.888\|0.676\|0.577\|0.732\|0.861\|0.453\|0.526\| \|Meta-Llama-3-8B\|0.881\|0.602\|0.544\|0.734\|0.881\|0.464\|0.652\| \|Meta-Llama-3-70B\|0.876\|0.645\|0.556\|0.716\|0.883\|0.456\|0.450\| \|Mistral-7B-v0.1\|0.861\|0.574\|0.556\|0.737\|0.806\|0.412\|0.397\| \|Mixtral-8x7B-v0.1\|0.856\|0.608\|0.553\|0.721\|0.851\|0.493\|0.604\| \|Mixtral-8x22B-v0.1\|0.857\|0.620\|0.587\|0.708\|0.863\|0.490\|0.592\| ### NQ \| Rouge-L = 1.0 \| SD \| SE \| P(True) \| Deg \| NL \| NE \| PE \| \|----------------\|----\|----\|---------\|-----\|----\|----\|----\| \|Llama-2-13b-hf\|0.845\|0.487\|0.662\|0.760\|0.734\|0.349\|0.500\| \|Llama-2-70b-hf\|0.853\|0.494\|0.469\|0.776\|0.721\|0.418\|0.480\| \|Meta-Llama-3-8B\|0.813\|0.429\|0.418\|0.703\|0.819\|0.409\|0.595\| \|Meta-Llama-3-70B\|0.883\|0.569\|0.738\|0.791\|0.838\|0.467\|0.523\| \|Mistral-7B-v0.1\|0.815\|0.502\|0.392\|0.732\|0.737\|0.427\|0.530\| \|Mixtral-8x7B-v0.1\|0.847\|0.535\|0.531\|0.769\|0.730\|0.473\|0.547\| \|Mixtral-8x22B-v0.1\|0.859\|0.526\|0.391\|0.772\|0.773\|0.504\|0.655\| ## Ablation study where the number of reference responses changes for Semantic Entropy ### CoQA \| sample number \| 1 \| 2 \| 3 \| 4 \| 5 \| 6 \| 7 \| 8 \| 9 \| 10 \| \|---------------\|---\|---\|---\|---\|---\|---\|---\|---\|---\|----\| \|Llama-2-13b-hf\|0.600\|0.605\|0.616\|0.626\|0.630\|0.635\|0.633\|0.633\|0.636\|0.633\| \|Llama-2-70b-hf\|0.605\|0.624\|0.625\|0.629\|0.628\|0.625\|0.623\|0.622\|0.623\|0.621\| \|Meta-Llama-3-8B\|0.571\|0.579\|0.585\|0.598\|0.601\|0.600\|0.606\|0.609\|0.608\|0.599\| \|Meta-Llama-3-70B\|0.604\|0.597\|0.599\|0.604\|0.607\|0.608\|0.609\|0.609\|0.608\|0.608\| \|Mistral-7B-v0.1\|0.572\|0.596\|0.612\|0.617\|0.624\|0.626\|0.626\|0.628\|0.630\|0.627\| \|Mixtral-8x7B-v0.1\|0.594\|0.609\|0.619\|0.621\|0.620\|0.625\|0.625\|0.624\|0.625\|0.626\| \|Mixtral-8x22B-v0.1\|0.591\|0.603\|0.614\|0.617\|0.616\|0.615\|0.614\|0.614\|0.614\|0.614\| ### TriviaQA \| sample number \| 1 \| 2 \| 3 \| 4 \| 5 \| 6 \| 7 \| 8 \| 9 \| 10 \| \|---------------\|---\|---\|---\|---\|---\|---\|---\|---\|---\|----\| \|Llama-2-13b-hf\|0.542\|0.649\|0.672\|0.679\|0.679\|0.676\|0.675\|0.673\|0.673\|0.672\| \|Llama-2-70b-hf\|0.645\|0.670\|0.691\|0.686\|0.685\|0.683\|0.676\|0.677\|0.675\|0.677\| \|Meta-Llama-3-8B\|0.656\|0.674\|0.685\|0.685\|0.682\|0.680\|0.674\|0.669\|0.665\|0.662\| \|Meta-Llama-3-70B\|0.585\|0.615\|0.645\|0.653\|0.663\|0.666\|0.667\|0.666\|0.666\|0.663\| \|Mistral-7B-v0.1\|0.674\|0.694\|0.703\|0.707\|0.704\|0.703\|0.699\|0.693\|0.692\|0.690\| \|Mixtral-8x7B-v0.1\|0.600\|0.644\|0.678\|0.682\|0.685\|0.687\|0.687\|0.688\|0.687\|0.685\| \|Mixtral-8x22B-v0.1\|0.615\|0.655\|0.677\|0.688\|0.692\|0.693\|0.692\|0.691\|0.688\|0.686\| ## Ablation study where the diversity penalty (dp) of diverse beam search changes for semantic density (using Mistral-7B) \| AUROC \| dp=0.2 \| dp=0.5 \| dp=1.0 \| \|----------\|--------\|--------\|--------\| \| CoQA \| 0.784 \| 0.785 \| 0.788 \| \| TriviaQA \| 0.861 \| 0.863 \| 0.866 \| \| SciQ \| 0.765 \| 0.766 \| 0.771 \| \| NQ \| 0.678 \| 0.678 \| 0.680 \| --- Rebuttal 4: Title: Message to Reviewer koQE Comment: Since we won't be able to post any replies after the discussion period (ending soon), please let us know if you have any further questions. Thank you! --- Rebuttal Comment 4.1: Comment: Thank you for providing the detailed results. As a side note, these 20 tables could have been effectively summarized in a line plot (x-axis: correctness threshold, y-axis: AUROC). Overall, I have decided to increase my score to 5. --- Reply to Comment 4.1.1: Title: Response to Reviewer koQE Comment: Many thanks for your reply. We will include the line plot as you suggested in the revision. --- Rebuttal 5: Title: Final remarks Comment: I want to emphasize once more that, while the method empirically performs very well, it lacks a solid theoretical foundation within the context of current uncertainty quantification. The prevailing theory suggests that uncertainty quantification should focus on evaluating the predictive distribution (over classes, semantic clusters, etc.), irrespective of the sampled output. To draw a parallel with the typical classification setting, one also doesn't assign different uncertainty estimates to different classes sampled from the predictive distribution – to evaluate the performance of an uncertainty estimate, one uses the argmax to determine wether the model "knows" the correct class (i.e. should be certain) or "doesn't know" the correct class (i.e. should be uncertain). This principle can be similarly applied to uncertainty estimates in NLG. It should be carefully elaborated on in the updated version of the paper. --- Rebuttal Comment 5.1: Title: Response to Reviewer koQE Comment: Thanks for your final remarks. We will make sure to discuss and clarify this point in a careful way in the revised version, based on our insightful discussions. Thank you again for your time and effort!	Summary: The paper proposes a novel framework for quantifying uncertainty in LLM's responses. The authors introduce the concept of "semantic density" (SD), which measures uncertainty from a probability distribution perspective in semantic space, applicable to any pre-trained LLM without additional training. Experiments on various state-of-the-art LLMs and benchmarks demonstrate that SD outperforms existing methods in accuracy and robustness. The paper presentation is overall easy to read. Strengths: 1. The paper introduces a novel method, semantic density, that quantifies uncertainty in LLM responses using semantic information. 2. The proposed framework is clear and detailed, including its theoretical foundations and implementation details. 3. The proposed method is off-the-shelf and can be applied to other scenarios. Weaknesses: 1. The comparison with existing methods, although extensive, may not cover all possible alternatives. There are recent or lesser-known methods that also warrant consideration. 2. While the method shows promise for free-form question-answering tasks, its applicability and performance in other types of tasks (e.g., summarization, translation) are not explored, which limits the generalizability of the findings. Technical Quality: 3 Clarity: 3 Questions for Authors: 1. The literature review is not comprehensive, there are lots of related works [1, 2, 3] not mentioned or adopted in the experiment. 2. The AUROC is not enough the show the strength of the proposed model. It would be more beneficial to show Area under precision-recall curve for the misclassification detection task as well. 3. The prompt construction can have more details. In Sec. 3.2, it's worth denoting the final prompt structure, since the in-context learning examples and prompt structures can make the final result different. 4. The dataset are mostly QA tasks, it seems the model can also handle other NLG tasks. Can you elaborate more on this? [1] Ling, Chen, et al., "Uncertainty Quantification for In-Context Learning of Large Language Models." (NAACL 2024) [2] Fadeeva, Ekaterina, et al. "LM-polygraph: Uncertainty estimation for language models." (EMNLP 2023) [3] Duan, Jinhao, Hao Cheng, Shiqi Wang, Chenan Wang, Alex Zavalny, Renjing Xu, Bhavya Kailkhura, and Kaidi Xu. "Shifting attention to relevance: Towards the uncertainty estimation of large language models." ACL (2024). Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: N/A Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Comment: The comparison with existing methods, although extensive, may not cover all possible alternatives. There are recent or lesser-known methods that also warrant consideration. Response: Thanks for the suggestions. We tried to include all the mainstream uncertainty quantification methods for LLMs based on our literature review. Following your suggestion, we have done another literature search for more recent works, even including the papers that are published after the submission deadline of our current manuscript (May 22). We found another variant of semantic entropy from a recent paper published in Nature [4] (published after our submission), and we have added it into our experiments. Based on the results, the performance of the new variant of semantic entropy is similar to the original version of semantic entropy, and the proposed semantic density consistently outperforms it with different base LLMs and datasets. We will include these results in the revision. --- Comment: While the method shows promise for free-form question-answering tasks, its applicability and performance in other types of tasks (e.g., summarization, translation) are not explored, which limits the generalizability of the findings. Response: Thanks for your constructive comment. To further demonstrate the generalizability of the proposed method, we have added a summarization task with the commonly used DUC dataset. Based on the experimental results (please see detailed results in general response to all reviewers), the proposed semantic density still shows best performance compared to other counterparts, demonstrating its good generalizability. We will include these results in the revised version. --- Comment: The literature review is not comprehensive, there are lots of related works [1, 2, 3] not mentioned or adopted in the experiment. Response: Thanks for the suggestion. We have actually already included an earlier version of [1] in our literature review, we will update it into this newest version. For [2], it is a library that implements some of the existing uncertainty quantification methods for LLMs, without proposing new methods. We will include it for completeness. We will add and discuss [3] in the revised version. --- Comment: The AUROC is not enough to show the strength of the proposed model. It would be more beneficial to show Area under precision-recall curve for the misclassification detection task as well. Response: Thanks for this constructive comment. As you suggested, we have added the Area under precision-recall (AUPR) score as an additional performance metric. Please see table 1 in the attached PDF for detailed results. From the experimental results, the proposed semantic density shows consistently better performance compared to other methods, verifying its effectiveness. --- Comment: The prompt construction can have more details. In Sec. 3.2, it's worth denoting the final prompt structure, since the in-context learning examples and prompt structures can make the final result different. Response: Thanks for this constructive suggestion. To make the comparisons fair, we used the same prompt template as used in the original semantic entropy paper [5]. We will add the detailed prompt template in the revised version. --- Comment: The dataset are mostly QA tasks, it seems the model can also handle other NLG tasks. Can you elaborate more on this? Response: You are right. In principle, the proposed semantic density does not pose any restrictions on the task type, and it should work for a wide range of free-form NLG tasks. Following your previous suggestion, we have added a summarization task to demonstrate this generalizability of semantic density. We will also clarify this point in the revision. [1] Ling, Chen, et al., "Uncertainty Quantification for In-Context Learning of Large Language Models." (NAACL 2024) [2] Fadeeva, Ekaterina, et al. "LM-polygraph: Uncertainty estimation for language models." (EMNLP 2023) [3] Duan, Jinhao, Hao Cheng, Shiqi Wang, Chenan Wang, Alex Zavalny, Renjing Xu, Bhavya Kailkhura, and Kaidi Xu. "Shifting attention to relevance: Towards the uncertainty estimation of large language models." ACL (2024). [4] Farquhar, Sebastian and Kossen, Jannik and Kuhn, Lorenz and Gal, Yarin, “Detecting hallucinations in large language models using semantic entropy”, Nature 630, 625–630 (2024) [5] Lorenz Kuhn, Yarin Gal, and Sebastian Farquhar. Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generation. In The Eleventh International Conference on Learning Representations (2023) --- Rebuttal Comment 1.1: Title: Follow-up comment to Reviewer kNB4 Comment: As per the request by Reviewer koQE, we have now added the detailed results for all the newly added experiments, including the one suggested by your that adds a new variant of semantic entropy. Please see our follow-up comment in the general rebuttal above for detailed results. Thank you. --- Rebuttal 2: Title: Message to Reviewer kNB4 Comment: Since we will not be able to post any further responses after the discussion deadline tomorrow, please feel free to let us know if you have any feedback about our rebuttal, including those newly added experiments as suggested by you. Thank you for your attention!	Summary: This paper addresses the problem of LLM’s lack of uncertainty metric for the response it generates. The authors propose to use semantic density to quantify such uncertainty, as it is not restricted to any specific downstream task. In particular, the approach samples reference responses, analyzes semantic relationships, and then calculates the semantic density. Experiments on four QA benchmarks of several Llama and Mistral models are conducted, including the latest Llama 3 13B and Mistral-8x22B, to demonstrate the effectiveness and the robustness of semantic density compared to prior metrics. Strengths: * The proposed metric is not restricted to any specific task but measuring the general LLM ability * The experiments show the effectiveness of the proposed approach, outperforming the other previous metrics Weaknesses: * Only some of the llama and mistral models are tested * The results shown in Table 1 seem to be quite close for all the models (on each task), which are not so indicative for system comparison * No further analysis/discussions on different model sizes (7B vs. 70B), nor different architecture (MoE vs. Non-MoE) Technical Quality: 3 Clarity: 3 Questions for Authors: In Figure 1, different models have inconsistent performance across different tasks. Do you have any explanations? Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: Yes Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Comment: Only some of the llama and mistral models are tested. Response: Thanks for the comment. We want to clarify that at the time of submission (May 22), all the open-sourced LLMs released by MistralAI were included in the experiments, e.g., 'Mistral-7B', 'Mixtral-8x7B', and 'Mixtral-8x22B', and all the open-sourced Llama3 models were included in the experiments, e.g., ‘Llama-3-8B', 'Llama-3-70B’. For Llama2, there were three open-source models, i.e., 'Llama-2-7b', 'Llama-2-13b', and 'Llama-2-70b', and we have included both 'Llama-2-13b' and 'Llama-2-70b' in our experiments. As an older and less capable small-size LLM, 'Llama-2-7b’ is usually replaced by 'Mistral-7B' or ‘Llama-3-8B' in practical usages, so we did not include it in our initial experiments. We will add 'Llama-2-7b’ in the revision for completeness. --- Comment: The results shown in Table 1 seem to be quite close for all the models (on each task), which are not so indicative for system comparison Response: Thanks for the comment. Please allow us to further clarify how to interpret the results in Table 1, then we will address your concern. Each column in Table 1 represents one uncertainty quantification method, and each row shows the results for one base LLMs, on top of which we are applying those uncertainty quantification methods. In order to compare the performance among uncertainty quantification methods, we should look at the AUROC scores in each row, the higher the better. We have highlighted the best performing entry in boldface for each row. Regarding your concern here, the performance of other uncertainty quantification methods are not always consistent or close when applying to different base LLMs. The performances of the proposed semantic density (first column) are relatively more consistent across different models (though non-trivial differences can still be observed in some tasks). This actually indicates the better robustness of semantic density compared to other methods: it is able to provide consistently good performance when applying to base LLMs of varying sizes and structures. We will include this discussion in the revision. --- Comment: No further analysis/discussions on different model sizes (7B vs. 70B), nor different architecture (MoE vs. Non-MoE) Response: Thanks for the constructive comment. As suggested, we have added an empirical analysis that compares the performance gain of semantic density vs. semantic entropy on different groups of base LLMs. The results indicate that the performance gain of semantic density is not sensitive to the model size or architectures. --- Comment: In Figure 1, different models have inconsistent performance across different tasks. Do you have any explanations? Response: Thanks for the question. The reason is that these different LLMs are of different sizes and architectures, and since they are from different LLM families, their training pipelines and training data should also be different. It is therefore natural that their performances vary across different tasks, i.e., they have different capabilities, and they may be knowledgeable when answering one category of questions while ignorant of another topic. This is why we tried to include diverse LLMs: we want to evaluate the robustness of semantic density. We will add these discussions in the revision.	Summary: The paper proposes an approach for estimating uncertainty of LLM outputs. The proposed approach begins by sampling a diverse set of responses, analyses their equivalence using a NLI classification model, and then computes the semantic density using a kernel density estimate. Strengths: - The proposed approach seems sufficiently different from prior work and combines existing ideas meaningfully. The approach is convincingly validated in experiments. - The paper is clear for the most part. - The problem of uncertainty estimation for generation tasks is meaningful. Weaknesses: - The paper is somewhat vague in distinguishing itself from the closest prior work on Semantic Entropy - this makes its specific contribution unclear. - Some details of the implementation of semantic density are unclear. Technical Quality: 3 Clarity: 3 Questions for Authors: - Sec 3.5: Please describe how the NLI model is used for computing p_c, p_n and p_e. NLI models typically accept pairs of texts, but these probabilities seem to contain three: y_*, y_i and x. - Do I understand correctly that embedding models (discussed in Sec 3.2) are never explicitly used in Semantic Density? Instead the NLI model is relied upon for establishing equivalence between texts and for the kernel function? If yes, the current presentation comes across as a bit confusing - please consider rewriting parts of the paper to make this more explicit. - As I understand, the proposed approach only estimates uncertainty rather than explicitly calibrating the underlying model - and yet the proposed uncertainty estimation method helps improve predictive performance in Table 1. Am I understanding correctly that the underlying models are somewhat well calibrated to begin with? To put it another way, are there generation tasks where one might expect SD to not be as reliable? For example, a summarization task. If this is a reasonable understanding, please consider discussing where SD is unlikely to work well. - The differences highlighted against Semantic Entropy in Lines 105-107 are vague or inaccurate - SE considers responses in computing the SE(x) value so it is unclear how it is "prompt-wise", that being said, what are the advantages of obtaining uncertainty for a specific output and prompt pair? What does a "one-cut equivalence relationship" mean? Please consider highlighting differences more clearly and discussing the specific advantages/disadvantages that the differences result in. Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: NA Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Response: Semantic Entropy (SE) is indeed the baseline to which we compare, aiming to overcome its limitations using a different approach, i.e. Semantic Density (SD). Let us first clarify the difference. although the computation of SE involves analysis of multiple reference responses, only one SE score is obtained for each prompt: SE does not quantify the predictive uncertainty of each specific response. As a simple example, assume that given a prompt X, an LLM samples three different responses A, B, and C, among which A is the correct answer while B and C are incorrect. SE returns only one uncertainty score, representing the aleatoric uncertainty introduced by prompt X. In contrast, SD returns three different uncertainty scores, one for each specific response. This difference matters because users can get different responses from the LLM even given the same prompt. In this case, the user who gets a correct response A would be given the same SE score as another user who gets an incorrect response B. Thus, users cannot differentiate the trustworthiness of different responses for the same prompt. In contrast, SD returns different semantic density scores depending on the actual answer returned. A more trustworthy response has a high score, and thus the users can decide whether a specific response can be trusted. This fundamental difference between SE and the proposed semantic density comes from their inherently different design principles: SE is based on entropy calculation, which can only be prompt-wise, while SD is based on density estimation, which is naturally response-wise. We will add this elaborated discussion in the revision. "What does a "one-cut equivalence relationship" mean? Please consider highlighting differences more clearly and discussing the specific advantages/disadvantages that the differences result in.” As discussed in line 51-55 in the current manuscript, the "one-cut equivalence relationship" means that the original SE applies a binary measurement of the semantic relationships between two reference responses. That is, the relationship between two reference responses can only be “equivalent” or “nonequivalent”. In contrast, SD evaluates the semantic relationships among reference responses in a continuous manner: the calculation of SD estimates the degree to which the reference responses are semantically similar. Such a continuous measurement provides a more informative and accurate semantic analysis, making the resulting uncertainty score more precise and reliable. We will further clarify this point in the revision. --- Comment: Some details of the implementation of semantic density are unclear. Response: We can see you have posted specific questions following this comment, and will address them one by one below. We will add all these clarifications in the revision to make the implementation details clearer. --- Comment: Sec 3.5: Please describe how the NLI model is used for computing p_c, p_n and p_e. NLI models typically accept pairs of texts, but these probabilities seem to contain three: y_, y_i and x. Response: Each text is a concatenation of the prompt x and response y. The input to the NLI model is one pair of such texts: the first is the concatenation of x and y_i, and the second is the concatenation of x and y_. This design follows from the principle that the semantic relationship between a pair of responses (y_i and y_*) needs to be evaluated in the context of the prompt (x). We will add this clarification in the revised version. --- Comment: Do I understand correctly that embedding models (discussed in Sec 3.2) are never explicitly used in Semantic Density? Instead the NLI model is relied upon for establishing equivalence between texts and for the kernel function? If yes, the current presentation comes across as a bit confusing - please consider rewriting parts of the paper to make this more explicit. Response: That is right; thanks for pointing out the need to clarify. The SD approach aims to connect the density estimation to a semantic embedding space, which can be done either explicitly (using an embedding model) or implicitly (using a NLI model). As explained in Line 222-225, NLI models are used in the current implementation due to the lack of contextual embedding models in the existing literature. Please note that utilization of a NLI model also assumes there exists an implicit contextual embedding space that measures the semantic relationships. We will add this clarification in Section 3 of the revised version. --- Comment: As I understand, the proposed approach only estimates uncertainty rather than explicitly calibrating the underlying model - and yet the proposed uncertainty estimation method helps improve predictive performance in Table 1. Am I understanding correctly that the underlying models are somewhat well calibrated to begin with? To put it another way, are there generation tasks where one might expect SD to not be as reliable? For example, a summarization task. If this is a reasonable understanding, please consider discussing where SD is unlikely to work well. Response: The proposed semantic density does not modify the original underlying LLM. Instead, it provides an additional uncertainty measurement for each output response. In our experiments, all the LLMs are not guaranteed to be well calibrated. Indeed, the “NL” column in Table 1 can be seen as a measurement of calibration, and it varies a lot across LLMs. SD performs robustly across most such variance, but we have also highlighted one case (Line 277-280 in the current manuscript) where its performance (and that of other metrics as well) is negatively affected by a badly calibrated LLM. Good calibration is thus important for uncertainty estimation in general. We will clarify this limitation in the revision. On the other hand, we have added a summarization task (DUC2004) to the experiments. SD performs well in it, demonstrating generality across tasks. --- Rebuttal Comment 1.1: Title: Thank you Comment: Thank you for the additional results and the responses. --- Reply to Comment 1.1.1: Title: Reply to Reviewer rbw2 Comment: Thank you for spending time reading our rebuttal.	Rebuttal 1: Rebuttal: We want to thank all the reviewers for their valuable time and constructive comments. We have considered every comment from each reviewer, and added several experiments as suggested by reviewers. We believe the paper is in a much better form after incorporating constructive suggestions from all the reviewers. Below is a brief summary of the new experimental results we added during rebuttal. We will also use this space to display some of the detailed results: 1. We added a new summarization dataset as suggested by reviewer rbw2 and kNB4. Below shows the detailed results on Mistral-7B and Mixtral-8x7B: \| AUROC \| SD \| SE \| Deg \| NL \| NE \| PE \| \|--------------\|-------\|-------\|-------\|-------\|-------\|-------\| \| Mistral-7B \| 0.679 \| 0.537 \| 0.660 \| 0.673 \| 0.551 \| 0.549 \| \| Mixtral-8x7B \| 0.640 \| 0.532 \| 0.620 \| 0.636 \| 0.576 \| 0.497 \| 2. We added an experiment that uses area under precision-recall curve (AUPR) score as performance metric, as suggested by reviewer kNB4. Please see Table 1 in the attached PDF for detailed results. 3. We added an experiment that uses different rouge-L threshold for correctness evaluations, as suggested by reviewer koQE. 4. We added an experiment that uses different hyperparameters for the diverse beam search, as suggested by reviewer koQE. 5. We added an experiment that studies the effect of sampling numbers on semantic entropy, as suggested by reviewer koQE. 6. We added a comparison to a more recent variant of semantic entropy, as suggested by Reviewer kNB4. Pdf: /pdf/3a2742fa9410421323e70086bf47c7a4306a5480.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Where does In-context Learning Happen in Large Language Models?	Accept (poster)	Summary: This study primarily investigates where in-context learning occurs within GPT-style models. Specifically, it explores the stage at which a model transitions from functioning as an in-context learner to a task-specific model. By applying layer masking to the instruction and in-context examples in machine translation and coding tasks, the authors observe performance changes to understand the internal mechanisms of in-context learning. They find that certain critical layers within the model are crucial for in-context learning. Strengths: The experimental design is well-conceived and includes an analysis that elucidates the internal mechanisms of in-context learning. Weaknesses: 1. The practical utility of the findings is questionable. I doubt whether the proposed improvements to inference efficiency in Section 5 can be applied in practice. For example, critical layers differ across tasks, and even within the same task, they can vary between subtasks (e.g., en→fr vs. fr→en). Identifying critical layers typically requires significant cost. 2. The experiments are entirely based on multi-head Attention, which limits the applicability of these findings. Most current models use other attention methods, such as the grouped-query attention used in Llama-2. The findings in this paper may not apply to new attention variants, which already consider partial context attention. Technical Quality: 3 Clarity: 3 Questions for Authors: Please refer to the weaknesses section. Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 1 Limitations: -- Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We would like to thank the reviewer for their time and comments on our work. Regarding the listed weaknesses of our paper: > "The practical utility of the findings is questionable." We respectfully disagree that our findings hold little practical utility. LLMs are increasingly being adapted to, and used as, task-specific models; For instance, LLMs have shown great potential in replacing traditional supervised Machine Translation models. Our results hold incredibly high practical utility for scenarios where we require an LLM to adapt to a specific task using in-context examples and prompts, which will be used for every forward-pass of the model. As the length of the in-context examples increases (which we show does not significantly alter the position of critical layers), our results become even more relevant. > doubt whether the proposed improvements to inference efficiency in Section 5 can be applied in practice. While the exact position of critical layers is task-specific, finding them requires a one-time cost using only forward-passes of the model (e.g. no gradients or backpropagation is used). This is quite straightforward to implement, is highly reproducible, and requires no additional memory beyond forward inference. > The experiments are entirely based on multi-head Attention, which limits the applicability of these findings. Most current models use other attention methods, such as the grouped-query attention used in Llama-2. The findings in this paper may not apply to new attention variants, which already consider partial context attention. We do in fact use Llama-2 in our experiments although we did not denote this in the paper, as it was the default Llama family available through hugging face at the time. Specifically, the checkpoints we use are https://huggingface.co/meta-llama/Llama-2-7b-hf and https://huggingface.co/meta-llama/Llama-2-7b-chat-hf. We sincerely apologise for the confusion. However, we also note that (to the best of our knowledge) Llama-2 uses standard multi-head attention. _Grouped query attention (GQA) is used in the more recent Llama-3, which was released only a month ago and is therefore out of the scope of our submission._ We analyze a broad set of highly utilized LLMs which suggests that our findings are broadly relevant to the LLM community. Our overall findings (that some layers are critical to in-context learning and that attention to the entire context is no longer necessary past a critical point) are also not specific to any particular form of attention. --- Rebuttal Comment 1.1: Comment: Thank you for your reply. Let me clarify that in my previous response, I mistakenly wrote llama-3 as llama-2. As you mentioned in your reply, this method need one forward-pass for each task, which makes it practical only when there are many requests for the same task. But that's not the case when we deploy our model in reality. In practice, we receive diverse requests from different users. --- Reply to Comment 1.1.1: Comment: Thank you for clarifying and sharing your expected scenario. We would like to address this scenario, and your comments around it: > this method need one forward-pass for each task, which makes it practical only when there are many requests for the same task. But that's not the case when we deploy our model in reality. In practice, we receive diverse requests from different users. The scenario we describe of adapting a general purpose LLM to a specific task, after which the LLM processes many requests for the same task, is an increasingly popular technique. For instance, in both research [1] and industry [2], there has been a shift towards using prompted LLMs to handle machine translation, under which a fixed prompt and model is used to handle many requests for a single task (i.e. translation from one specified language to another). This is precisely a setting that we study, and we therefore argue our analysis has very real practical implications for these techniques. Thank you again for your continued engagement with us! [1] A Paradigm Shift: The Future of Machine Translation Lies with Large Language Models, Lyu et al., 2024 [2] https://www.welocalize.com/insights/google-teams-up-with-welocalize-to-test-its-adaptive-translation-llm-solution/ --- Rebuttal 2: Title: Review clarifications Comment: Dear reviewer, you raised two weakness which we provided responses to... we hope you might reconsider your overall assessment about the contributions of the paper.	Summary: This paper tries to locate where LLMs handle in-context learning (ICL) and interprets how LLMs perform ICL internally. The authors propose a layer-wise attention masking strategy and conclude that LLMs perform ICL in bottom layers. Strengths: The motivation of this paper is clear, and the research question sounds interesting. Weaknesses: However, I have several concerns about the work. 1. Layer-wise masking. The authors only release first j bottom layers and conclude that bottom layers are important. This is problematic. If the authors mask layers with a reversed order, I suppose the conclusion would change to that top layers are important. The reason is that pretrained LLMs solve task with multiple modules. And different layers may share similar functions for solving that task. Simply masking several layers or layers with specific order cannot prove whether these layers are important/useless. It’s similar to the glove game: you have 3 gloves with 2 left gloves and 1 right glove. Dropping 1 left glove randomly cannot prove this dropped one is useless, or conclude that the right one is the only necessary one. 2. Token masking. The three token masking strategies are not comprehensive. There is no discussion about the individual examples. Either dropping all of them or keeping all of them cannot explain how ICL works, since many existing works show that ICL examples affect the performance much. Overall, I think this paper tries to explore an important research question, and I would like to encourage the authors to address my two concerns. Technical Quality: 1 Clarity: 3 Questions for Authors: Line 117: can j be equal to I, i.e., (j<=i)? Confidence: 4 Soundness: 1 Presentation: 3 Contribution: 3 Limitations: See weakness. Flag For Ethics Review: ['No ethics review needed.'] Rating: 3 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We would like to thank the reviewer for their time and comments on our work. Regarding the listed weaknesses and questions: > Layer-wise masking. The authors only release first j bottom layers and conclude that bottom layers are important. Our conclusion is _not_ that bottom layers are important and top layers are not, but rather that there are critical layers. We write that “Doing so allows us to study how critical each layer is, where critical layers is loosely defined as those that have a large negative impact when masked.. (line 231-232) ”. We explicitly test the relevance of individual layers across the _entire_ model. Showing here that dropping an individual layer (layer-wise masking) significantly harms performance does suggest that this layer is important because performance would not suffer if its functionality was re-implemented by a different layer. > If the authors mask layers with a reversed order, I suppose the conclusion would change to that top layers are important. The reviewer may be referring to _layer-from-context masking_ (Figure 2,3), The masking order that we have used, retains the original order of processing that the transformer sees during training. "All masks operate from the j-th layer ($\ell_j$ ) onwards, i.e. masking from $\ell_{20}$ means causally masking out attention to all context positions from $\ell_{20:n_\ell}$, where $n_\ell$ is the total number of layers. To construct Fig 2, we increment $\ell$ from 1 to $n_\ell$ and apply the set of masks $\{m(j, u)\}^{\ell:n_\ell}$ in each experiment and observe the performance of the model" (lines 122:125) The reverse order would mean skipping several layers of attention before passing the representations to the later layers, which may result in token representations that fundamentally differ from what the later layers have seen during training. It would not be clear whether performance was impacted because the context was masked until that point, or because the masked token representations no longer match the expected representation distribution at that layer. > pretrained LLMs solve task with multiple modules. And different layers may share similar functions for solving that task. We do not present any findings in this paper that conflict with this interpretation! In our masking experiments, we only mask over the context, not the entire test input provided to the LLM. The goal of the paper is to demonstrate where in-context learning (in-context task recognition) happens, not where the LLM "solves the task". (Line 130) If this is unclear, we hope to be able to clarify. > Token masking. The three token masking strategies are not comprehensive. To recap, the three token masking strategies are * Has no instructions, and masks examples ($\overline{\texttt{Ex}}^{Mask}$) * Has instructions and masks examples ($\texttt{Instr}\overline{\texttt{Ex}}^{Mask}$) * Both instructions and examples masked ($\overline{\texttt{Instr}}\overline{\texttt{Ex}}^{Mask}$) -- “dropping all of them” We described the significance of $\overline{\texttt{Instr}}\overline{\texttt{Ex}}^{Mask}$ i.e., “dropping all of them” in Section 4.1, Layer-from Context masking. "Under this causal masking treatment masking from layer ℓ, the model must rely on the representations of the target input sentence from layer ℓ + 1 only to complete the task; if the target sentence representations do not already encode the target task (translation into a specific language) then the model will fail to generate translations." (line 126:129) To put in another way, “Dropping all of them” and showing that performance continues to be maintained past a certain layer, demonstrates that the major work of in-context learning has occurred before that layer (Figure 2, 3). This finding is extended to a varying number of In-context examples (Figure 6). > many existing works show that ICL examples affect the performance much. We agree that ICL examples are known to affect performance. Our experimental results are averaged over 5 random seeds (random in-context samples are used), to present findings which generalise beyond the choice of specific examples. > Line 117: can j be equal to I, i.e., (j<=i)? Yes, thank you for catching this typo! --- Rebuttal Comment 1.1: Title: Review clarifications Comment: Dear reviewer, if our response has helped to clarify the misunderstandings, we greatly appreciate if you could reconsider your assessment! --- Rebuttal Comment 1.2: Title: Reply Comment: Thanks for the reply. However, my concerns are not well addressed in the reply: the layer-masking strategy is problematic, and thus the following obtained conclusions are not reliable to me. Therefore, I'll keep my score.	Summary: In-context learning has emerged as an important paradigm in LLMs. In this paper, the authors attempt to characterize where models learn to “recognize” an in-context task. To do this, in-context portions (examples and/or instructions) are masked out after certain layers and are not included to generate model predictions. An advantage of this style of masking is improved cost. Their experiments give clear results, indicating that for each of the selected tasks (machine translation, code generation), there exists a cutoff layer beyond which masking is acceptable without hindering ability to recognize the task. The most clear utility of this masking is computational savings. The authors also find evidence of 3-phase in-context learning, with the last phase accounting for little to no performance improvements. Strengths: * This is an important area of research. The authors carve out a strong motivation, which is enhanced by clearly defined and executed experiments. * The paper is very well written, which makes it an interesting read. * The experiments are extremely thorough, some of them being: ex v/s Inst masking, MT v/s code, attention to context v/s input, # prompts analysis, attention heads study etc. I can tell that these took a lot of effort and will be of great importance to the community. Weaknesses: I have some concerns about the definitions of “task recognition” [more in the Questions], as well as explanations on some sections (like Sec 4.3 and 6.2). It would be important to iron these out. Technical Quality: 4 Clarity: 3 Questions for Authors: It's not clear why “task recognition” v/s actual task performance was treated as a metric here. It seems that the learnings would be very different between the two. Is task recognition in itself important enough to celebrate over computational wins? Some clarity would be good in the paper to ensure readers understand the importance of "task recognition". Also, is there a cutoff (like BLEU > 0 means task recognition)? Sec 4.3 could use better pointers. It's not clear which model is instruction tuned v/s not. Sec 6.2 presents an interesting experiment; but the figure needs to be improved. The explanations don’t match the legends of the figure (for instance, what is true/false). Also, do we mask the source sentence as well? Confidence: 4 Soundness: 4 Presentation: 3 Contribution: 4 Limitations: NA Flag For Ethics Review: ['No ethics review needed.'] Rating: 8 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for the deep appreciation of the work! > It's not clear why “task recognition” v/s actual task performance was treated as a metric here. It seems that the learnings would be very different between the two. Is task recognition in itself important enough to celebrate over computational wins? Some clarity would be good in the paper to ensure readers understand the importance of "task recognition". Also, is there a cutoff (like BLEU > 0 means task recognition)? It’s a fair point. The process of task recognition, happens over several layers. We think task performance as a metric is easier for people to understand.. Because finally the practical takeaway is that you can reach the model's ceiling task performance without needing full-processing over the context - that’s the computational win. > Sec 4.3 could use better pointers. It's not clear which model is instruction tuned v/s not. Understood, we will fix it. > Sec 6.2 presents an interesting experiment; but the figure needs to be improved. The explanations don’t match the legends of the figure (for instance, what is true/false). Also, do we mask the source sentence as well? We will improve the captioning of the figure. True/False refers to whether there are instructions provided (True) vs not provided (False). We do not mask any of the tokens, but remove the entire attention layer in Section 6.2 (as opposed to Section 3). --- Rebuttal Comment 1.1: Comment: Thanks! My score remains the same. I do think that the motivations for task recognition should be explained better in the paper.	Summary: This paper investigates where in-context learning occurs within large language models, focusing specifically on machine translation and code generation tasks. The authors introduce a "layer-from context-masking" technique to identify at which layer an LLM transitions from task recognition to task execution during ICL. They apply this method to several models including GPT-Neo2.7B, BLOOM3B, LLaMA7B (base and chat), and StarCoder2 (3B and 7B). The key finding is that models do not need to maintain attention over the entire context throughout all layers to perform the task. Instead, there appears to be a "task recognition point" after which attention to the context is no longer necessary. This point varies between LLMs but generally occurs in the middle layers. The authors characterize this as a three-phase process: initial processing where masking has little effect, a critical phase where masking greatly impacts performance, and a final phase where additional context processing yields minimal gains. The paper also explores the roles of instructions versus examples, the differences between instruction-tuned and non-instruction-tuned models, and whether these phenomena generalize across different tasks. The authors highlight the potential practical implications of their findings, particularly for inference efficiency. They estimate that up to 45% computational savings could be achieved by eliminating unnecessary context processing in later layers. Strengths: - The authors introduce a "layer-from context-masking" technique to probe the internal workings of large language models during in-context learning tasks. This method offers a fresh perspective on how these models process and utilize contextual information, providing insights that were not previously available. - The identification of a "task recognition point" and the characterization of a three-phase process in task recognition and execution are important. - The finding that attention to context can be removed after certain layers without significant performance degradation has direct practical applications for improving inference efficiency in LLMs, potentially leading to substantial computational savings. Weaknesses: - One notable weakness is the limited exploration of why different models exhibit varying behaviors in terms of their "task recognition point" and critical layers. For instance, the authors observe that GPT-Neo has more severe critical layers compared to other models but do not provide a thorough analysis of potential reasons for this difference. A more in-depth investigation into the architectural differences, training data, or other factors that might contribute to these variations would significantly enhance the paper's insights and generalizability. - The paper doesn't adequately address potential confounding factors that could influence the results. For example, the impact of different tokenization schemes across models or the potential effects of the specific prompt format used are not discussed in depth. - The paper's focus on machine translation and code generation tasks, while valuable, raises questions about the broader applicability of the findings. The authors could strengthen their work by discussing potential limitations in generalizing these results to other types of tasks or by providing a theoretical framework that explains why these findings might (or might not) extend to other domains of language model application. - The paper uses models of different sizes (2.7B to 7B parameters) but doesn't systematically analyze how model size affects the location of the "task recognition point" or the distribution of critical layers. A more structured comparison across model sizes could reveal important trends. Technical Quality: 3 Clarity: 2 Questions for Authors: 1. You observe varying behaviors across different models, particularly in terms of the "task recognition point" and critical layers. Could you provide more insight into why these differences occur? 2. Your study focuses on machine translation and code generation. How confident are you that these findings would generalize to other types of NLP tasks? 3. Your study includes models of different sizes. Do you observe any consistent trends in how model size relates to the task recognition point or the distribution of critical layers? Confidence: 3 Soundness: 3 Presentation: 2 Contribution: 2 Limitations: In the NeurIPS Paper Checklist (after appendix), they mentioned that they have discussed the limitations in the conclusion section (Line#592). However, I didn't find any such thing. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for the insightful comments on the paper and for the positive view of our work. We provide our response to the weaknesses (the questions are closely related) > One notable weakness is the limited exploration of why different models exhibit varying behaviors in terms of their "task recognition point" and critical layers. GPT-Neo has more severe critical layers compared to other models but do not provide a thorough analysis of potential reasons for this difference. Unfortunately, the differences are not due to easily observable hyperparameters like model size or architecture. To put in another way, why do large models exhibit different characteristics? Training data and training dynamics is a typical suspect. While very interesting, we feel that a thorough analysis is perhaps outside the scope of this paper. > The paper doesn't adequately address potential confounding factors that could influence the results. For example, the impact of different tokenization schemes across models or the potential effects of the specific prompt format used are not discussed in depth. We would like to discuss with the reviewer on the suggested confounding factors. * Tokenisation schemes, we’re not sure how an analysis on tokenisation scheme would be relevant to the problem being studied here. We used GPTNeo, Llama2, Bloom, Starcoder, all of which have different tokenisation schemes. * Specific prompt format. There are two main prompt formats used in the paper, reflecting the task. 1a. “Translate from {L1} to {L2}: Q: {source_sentence} A:, 1b. “Translate from {L1} to {L2}: Q: {source_sentence} A:, 2. Write a function to find the longest chain which can be formed from the given set of pairs. Q: {program_description}, A: We hope this gives the reviewer some confidence that there is sufficient coverage of the confounding factors highlighted. Instead, the potential confounding factors that we have investigated more pertinent to the research question are * With/without instructions * Number of In-context Examples * Different models Families * Instruction Tuned VS Not Instruction Tuned Models * 2 Different Tasks > The paper's focus on machine translation and code generation tasks, while valuable, raises questions about the broader applicability of the findings. The authors could strengthen their work by discussing potential limitations in generalizing these results to other types of tasks or by providing a theoretical framework that explains why these findings might (or might not) extend to other domains of language model application. Thank you for the suggestion, we will consider whether it’s possible to frame this better. > The paper uses models of different sizes (2.7B to 7B parameters) but doesn't systematically analyze how model size affects the location of the "task recognition point" or the distribution of critical layers. A more structured comparison across model sizes could reveal important trends. Thank you for the suggestion, we think this does not change the main point or contribution of the paper but acknowledge that it can be an interesting addition for extended experiments that we are happy to carry out > Limitations Most sincere apologies we seem to have missed this in the current draft... We would be extremely explicit about the scope of the experiments, and also include those the reviewer has highlighted. (exploration of different models, tasks, sizes). Currently in the paper, we have several "future work". i.e. limitations that we have not figured out. * _“It is not immediately clear why GPTNEO has such critical layers and suffers compared to the other models, although we note that this is unlikely to be due to size or model architecture as BLOOM is also around the same size as GPTNEO and performs more similarly to LLAMA. We suspect that it could be due to training data or some other factor related to the training dynamics but leave this for future work. “_ (line 245:249) * _"Potential reasons for this difference might be due to cross-entropy loss associated with task tuning for MT vs non-specific training on large corpora. We leave this as an open question for future work."_ (line 299-301)	null	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
NeuralFluid: Nueral Fluidic System Design and Control with Differentiable Simulation	Accept (poster)	Summary: The paper details a framework for design and control of complex fluidic systems with soft and hard boundaries. The paper specifically develops a fully differentiable pipeline that is able to optimize the design of the mesh to achieve the specified fluid control goal. The proficiency of the proposed framework has been demonstrated on multiple design and fluid control tasks like: (i) amplifying flow of a fluid by changing the shape of an initial boundary (ii) optimizing the position of a "neural gate" to satisfy the target outflow requirement (iii) designing an artificial heart (starting from an initial parameterized representation) to achieve a low-error match w.r.t a target simulation. The diversity of the tasks as well as task complexity and good results make the contributions in the paper worth considering. However, the paper lacks crucial details without which it is hard to fully appreciate the effectiveness of the proposed methods, hence making it hard to support publication of the paper in the present state. Strengths: * The paper tackles an interesting, challenging and important problem of developing a (fully differentiable) framework for optimal design and control of fluid flows in challenging contexts. * The results presented in the paper have been demonstrated on challenging tasks (i.e., not the usual "toy" problems tackled by other such papers) and as presented seem to be effective on the design and control tasks investigated. Weaknesses: * Although the results seem interesting and the problem the paper tackles is challenging, the paper lacks articulation of crucial details making the extent of contribution hard to appreciate. Some crucial aspects of the paper need further clarification. > Q1. How is the "initial parametric geometry" (required as input by the framework) generated? What are the feasibility constraints as far as this initial geometry is concerned? Where can a new user of this framework obtain such an initial geometry to supply to the system? An analysis of this or at least an articulation for usability by users is necessary. > Q2. Further details of the experiment setup are necessary. For example: what is the design of the PPO, CMA-ES models employed? What is the reward function for PPO and what were the architectures of the learnable components therein? > Q3. Why was `PhiFlow` chosen as the framework for comparison? Wouldn't `DiffTaichi`[1] be a more apples-to-apples comparison for measuring speedup, considering that the C++ implementation of underlying libraries similar to the current proposed framework? * Section 2.2 needs further detailing for a machine learning audience who may not be familiar with `Constructive Solid Geometry`. * Code pipeline has not been made available for review. Hence, the results are currently not reproducible. It is imperative to make code available during the review stage. ### `References` 1. Hu Y, Anderson L, Li TM, Sun Q, Carr N, Ragan-Kelley J, Durand F. Difftaichi: Differentiable programming for physical simulation. arXiv preprint arXiv:1910.00935. 2019 Oct 1. Technical Quality: 3 Clarity: 2 Questions for Authors: See questions in `Weaknesses` section. Confidence: 3 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: One improvement that can be made would be to highlight the details of the initial design specifications for the various tasks and enumerating some general prescriptions about generating good initial designs to be supplied to the pipeline. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for the careful review and insightful questions. 1. How is the "initial parametric geometry" generated? What are the feasibility constraints...? * Thank you for bringing up this important question. Usability is crucial for allowing users to specifying complex shapes enabled by our framework. We therefore designed the geometry specification process similar to existing CAD software. * For instance, a 3D component can be created by extruding a 2D shape along an axis, and users can union or intersect 3D models to form complex structures. Each 2D component is defined using a polar Bézier specification. This approach ensures that users with basic CAD software experience can effectively use our model. * For example, the heart model presented in our paper was created by specifying each heart component using six cross-sections, each made of circles with various radii and center positions. This method makes the geometry specification process intuitive and accessible. * By leveraging familiar CAD concepts, we aim to make our framework user-friendly and accessible to researchers and practitioners. We will also provide detailed documentation, visualization tools, and examples to further assist new users in generating the initial parametric geometry needed for their specific applications when releasing the codebase. 2. Code pipeline has not been made available for review. We will open-source our code upon acceptance. We have provided the anonymized version of our code at https://anonymous.4open.science/r/DiffFluidRebuttal-1D24/ for the review stage. 3. Sec 2.2 needs further detailing for a ML audience who may not be familiar with CSG. Thank you for the suggestion. We will add a more detailed description of CSG in our revised manuscript. Briefly speaking, CSG defines a hierarchical tree structure to represent volumetric geometry. Each leaf node in the tree denotes a geometric primitive (e.g., the Bezier surfaces in Sec. 2.2), and each intermediate node up to the root forms a new volumetric geometry by applying boolean operators to its child nodes, e.g., taking the union of the volumetric geometries represented by the child nodes. The root node represents the final geometry, which is formed by recursively applying boolean operators (typically unions, intersections, and subtractions) to a set of geometric primitives stored in the leaf nodes. 4. Further details of the experiment setup are necessary. What is the design of the PPO, CMA-ES models employed? What is the reward function for PPO and what were the architectures of the learnable components therein? Our PPO implementation is based on the open-sourced code of pytorch-a2c-ppo-acktr. Specifically, the actor and critic networks are both two-layer MLPs with tanh activations and a hidden layer of 64 neurons. For both controller tasks, we set the observation to be the same as the input to our gradient-based closed-loop controller. The reward function is the negative comparative of the loss function of the gradient-based closed-loop controller, plus a positive component to avoid negative rewards. Our CMA-ES implementation is based on the open-source Nevergrad. We set the population size to 10 and the metric to be the same as the loss function used for our method. We will include the details of the baseline in the Appendix. 5. Why was PhiFlow chosen as the framework for comparison? Wouldn't DiffTaichi[1] be a more apples-to-apples comparison for measuring speedup, considering that the C++ implementation of underlying libraries similar to the current proposed framework? Thank you for your valuable feedback. We chose PhiFlow for our comparison because it is an open-source, differentiable simulator specifically optimized for fluid simulation, which aligns closely with our objectives. While DiffTaichi is indeed a powerful differentiable programming tool, it serves a broader range of applications similar to Warp or JAX. However, we recognize the importance of providing a comprehensive comparison for practitioners. We have conducted additional experiments to include a comparison with DiffTaichi. In these experiments, we implemented a Conjugate Gradient (CG) iterative solver for the projection step, which is the most time-consuming component of each fluid solve, in DiffTaichi and compared its time and memory performance with our solver in 3D under 4 resolutions. The results of this comparison are detailed in Table 2. * To summarize, our implementation is approximately 3-4 times faster than DiffTaichi in both forward and back propagation. This performance gain is likely due to our efficient CUDA kernel tailored for the Laplacian operator and the rapid convergence of our MGPCG solver. Additionally, our solver uses significantly less memory than DiffTaichi, with the advantage becoming more pronounced at higher grid resolutions. At 64x64x64, DiffTaichi uses 12 times more memory. This is because DiffTaichi relies on automatic differentiation and needs to store the computational graph and values for all CG iterations, whereas our adjoint gradient method does not require storing these values. This makes our solver more suitable for long-term optimization at high resolutions, where efficient memory usage is crucial. 6. One improvement that can be made would be to highlight the details of the initial design specifications for the various tasks and enumerating some general prescriptions about generating good initial designs... Thank you for your valuable suggestion. For training fluid controllers, such as in the neural gate and neural heart tasks, we have found that initializing the network to output small actions helps achieve stable initial simulations and facilitates faster convergence of the network. In our implementation, this is accomplished by initializing all network layers with orthogonal matrices scaled to a small norm. We will include additional details on initial design in the Appendix. --- Rebuttal 2: Comment: Dear reviewer ueL6, we wanted to check if there are any remaining questions or concerns about our rebuttal. Since the author-reviewer discussion period ends tomorrow, we’d appreciate any final feedback you might have. Thank you for your time and attention. --- Rebuttal 3: Comment: Dear Reviewer, As the discussion deadline approaches, we are eager to address any remaining concerns you may have. We kindly request you to review our responses. If there is anything further we can do to facilitate the evaluation process, please let us know. We also respectfully ask that you reconsider our score based on the rebuttal provided. Thank you for your attention. Best regards, Authors --- Rebuttal Comment 3.1: Title: Official Comment by Reviewer ueL6 Comment: The author responses along with sharing of the anonymous link has enabled me to inspect the code. I am satisfied regarding the code. However, I still have concerns regarding the sensitivity of the method to the `initial parametric geometry`. But based on the additional results about `DiffTaichi` and the sharing of the code, I am able to raise my score from 4 --> 5. --- Reply to Comment 3.1.1: Comment: Dear Reviewer, Thank you for taking the time to review our work and for raising your score. Regarding your concern about the sensitivity of the method to the initial parametric geometry, we acknowledge the importance of this aspect. In our original paper, Section 4.1, we conducted an experiment on the Effects of Initialization on Optimization. Specifically, in the Shape Identifier task, which aims to identify the shape and center location of geometry parameterized by 10 parameters, we initialized geometries of various shapes with different center locations in space using 5 different random seeds. Despite the varying initial losses (ranging from 27 to 59), the optimization process proceeded smoothly, and all cases reached a final loss near zero. Additionally, in our rebuttal, we extended this analysis to more complex tasks. In Figure 2 of the rebuttal PDF, we presented an additional verification using the 3D heart controller task, which involves 7.1k neural network parameters subject to optimization. We initialized the network parameters with 5 different random seeds, resulting in different initial actuations and geometries. Despite these variations, we observed consistent convergence across all seeds, even with different initial behaviors, further demonstrating the robustness of our method. We appreciate your feedback and please let us know if you have further comments or questions.	Summary: This paper introduces a novel approach to fluidic system design and control using differentiable simulation. The authors propose a method that leverages gradient-based optimization to enhance performance and accuracy in fluid dynamics applications. Strengths: The paper demonstrates the effectiveness of their approach by comparing it to gradient-free methods such as Proximal Policy Optimization (PPO) and Covariance Matrix Adaptation Evolution Strategy (CMA-ES). The authors effectively highlight the advantages of having access to gradients, allowing for better optimization due to more information about the underlying function. In contrast, gradient-free methods approximate these gradients, which can be less efficient. The approach is particularly beneficial in scenarios where the underlying dynamics are smooth, as opposed to scenarios better suited for gradient-free methods. Weaknesses: The concept of backpropagation through time in reverse order has been extensively explored in neural ordinary differential equations (neural ODEs) and various adjoint methods literature. The paper appears to be closely related to existing work but utilizes a different discretization or numerical method. The claim of differentiability may be redundant as the equations themselves, or their adjoint operators, are inherently differentiable. The approach resembles the process of writing custom Jacobian-vector products (JVPs), which may not significantly advance the field.Although the authors outline the limitations of their method for other fluid models, they fail to address significant limitations encountered during backpropagation, such as the need to checkpoint the solution or the increasing memory use as a function of simulation length. Technical Quality: 2 Clarity: 2 Questions for Authors: The majority of the novelty comes from an efficient CUDA kernel implementation but the specifics are omitted. What specific design considerations are taken that enable this method to outperform existing solvers? Confidence: 4 Soundness: 2 Presentation: 2 Contribution: 2 Limitations: Although the authors outline the limitations of their method for other fluid models, they fail to address significant limitations encountered in many differentiable fluid simulations. Specifically,during backpropagation, such as the need to efficiently checkpoint the solution or the dependence of the amount of memory needed. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We are grateful for the reviewer’s insightful comments and questions. 1. The majority of the novelty comes from an efficient CUDA kernel implementation but the specifics are omitted. What specific design considerations are taken that enable this method to outperform existing solvers? * Because differential operators and interpolations access neighboring cells of a spatial point in all directions, we divide the whole simulation domain into cubic blocks, and each cubic block corresponds to a CUDA block. When launching a CUDA kernel, we first load the simulation data of a block into shared memory, and perform calculation efficiently on shared memory. To increase the memory throughput of the data transfer between global memory and shared memory, the simulation data of a cubic block is stored consecutively on global memory. * While we adopt a matrix-free MGPCG solver for Poisson, Phiflow uses a CG solver. Therefore, our solver has a much better convergence rate than theirs. To implement an efficient MGPCG solver, we also devised a hierarchical grid data structure on GPUs and customized CUDA kernels for prolongation and restriction operations between coarse and fine grid. Our GPU solver is highly optimized and specially tuned for fluid simulation tasks, which will be open-source. 2. ...such as the need to efficiently checkpoint the solution or the dependence of the amount of memory needed. * We are glad that the reviewer raised this limitation. Gradient checkpointing is a common technique in deep learning applications involving large models. However, our method is specifically designed for differentiable fluid simulation, where all the gradients have been manually derived for efficiency instead of relying on automatic differentiation like DiffTaichi. As a result, our method does not require the automatic differentiation workflow to store all the intermediate activations inside each timestep. In particular, our adjoint derivation of the project solve step is independent of the number of iterations in the solver, which makes our method a way better choice for advection-projection fluid simulation than any existing baselines. * To support our claim, we have conducted additional experiments to include a comparison with DiffTaichi, which uses automatic differentiation to derive gradients. We implemented a Conjugate Gradient (CG) iterative solver for the projection step, which is the most time-consuming component of each fluid solve, in DiffTaichi and compared its time and memory performance with our projection solver across four different resolutions in a 3D optimization scenario. The results of this comparison are detailed in Table 2. * To summarize, our solver uses significantly less memory than DiffTaichi, with the advantage becoming more pronounced at higher grid resolutions. For instance, at a 64x64x64 resolution, DiffTaichi uses 12 times more memory. This is because DiffTaichi relies on automatic differentiation and needs to store the computational graph and values for all CG iterations, whereas our adjoint gradient method does not require storing these values. This makes our solver more suitable for long-term optimization at high resolutions, where efficient memory usage is crucial. In conclusion, we acknowledge that gradient checkpoint is necessary when the computational graph grows, but our method has optimized the memory consumption to the best extent. --- Rebuttal Comment 1.1: Comment: Thank you to the authors for their detailed response. Based on the additional information provided, it seems that the primary contribution lies in the custom fluid solver implementation. However, the authors have not sufficiently clarified the novelty of their approach beyond the solver itself or its broader impact on the NeuRIPS community. That being said, the paper is stronger given the additional details. I will revise my score to 4 --> 5. --- Rebuttal 2: Comment: Dear reviewer QmuX, we wanted to check if there are any remaining questions or concerns about our rebuttal. Since the author-reviewer discussion period ends tomorrow, we’d appreciate any final feedback you might have. Thank you for your time and attention. --- Rebuttal 3: Comment: Dear Reviewer, As the discussion deadline approaches, we are eager to address any remaining concerns you may have. We kindly request you to review our responses. If there is anything further we can do to facilitate the evaluation process, please let us know. We also respectfully ask that you reconsider our score based on the rebuttal provided. Thank you for your attention. Best regards, Authors	Summary: The paper proposes a new set of utilities for experimenting with system design and control of viscous fluid flows on deformable domains. The contributions include (a) a differentiable NSE solver, (b) Bezier curve-based geometry parametrization, (c) an algorithm to jointly optimize a control and design objective, (d) a reinforcement learning environment interface, and (e) benchmark cases with baseline results. The results demonstrate the superiority of the differentiable solver framework over existing gradient-free approaches and pave the road for exciting research, e.g., in medical applications. Strengths: - Implementing an efficient PDE solver from scratch in C++ and CUDA and then analytically deriving gradients is a great service to the community. - The manuscript is well written and provides a good balance between theory and experimental evidence. - Efficiently parametrizing complex geometries has a great potential for bridging the gap between toy experiments and real-world problems. Weaknesses: - A. Proper figures: make the figures on pages 3 and 4 proper figures with captions. Currently, the only way to refer to them is as "the figure on paper 3 ..." - B. Solver validation: having some experience implementing numerical solvers, I know that validating the implementation is crucial. Could you add an appendix on validating the solver on an established fluid mechanics benchmark, like channel flow? The same applies to the gradients, which are typically validated by comparing them against a finite difference numerical approximation. - C. Minor issues: Line 131 "can derived"?; Line 155 "of from"? Technical Quality: 4 Clarity: 4 Questions for Authors: - Did you consider submitting to the Datasets & Benchmarks track instead of the general conference? Your contribution feels more like a benchmarking suite than machine learning research. - In the caption of Table 1, you mention that "# Frames" is not the same as the number of solver steps. What is the actual number of solver steps between two frames? Accumulating gradients over hundreds of steps often leads to exploding gradients, so why don't you have these issues if you stick to the CFL number? - Related to the previous question, using learned surrogates as PDE solvers has demonstrated great potential in overcoming the exploding gradients issue by simply learning to do as much as 200x larger time integration steps [1]. Does your framework allow for replacing the NSE solver with a learned surrogate, e.g. a U-Net or FNO? --- [1] Allen et al., "Inverse Design for Fluid-Structure Interactions using Graph Network Simulators", NeurIPS 2022 Confidence: 3 Soundness: 4 Presentation: 4 Contribution: 4 Limitations: The authors have fairly assessed the limitations of the proposed approach. Flag For Ethics Review: ['No ethics review needed.'] Rating: 8 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for appreciating our work and raising constructive suggestions. 1. Proper figures: make the figures on pages 3 and 4 proper figures with captions" We will make both inset figures proper figures in the revision. 2. Solver validation: having some experience implementing numerical solvers, I know that validating the implementation is crucial. Could you add an appendix on validating the solver on an established fluid mechanics benchmark, like channel flow? Thank you for your suggestion. We have added an experiment validating our solver using the classic Karman Vortex Street under a resolution of 512x1024. In Fig.1, we show the vortex pattern formed by a horizontal flow passing through a cylinder at three different kinematic viscosity values: $\nu = 0.0$ (inviscid fluid), $\nu = 0.002$, and $\nu = 0.02$ to recreate the classic phenomenon. We will add this experiment to the Appendix. 3. The same applies to the gradients, which are typically validated by comparing them against a finite difference numerical approximation. Indeed, it is important to validate the correctness of the gradients. During the development of our differentiable simulation, we validated the correctness of our analytical gradients for all kernels, functions, and the simulation and optimization pipeline using finite difference approximations. Below, we include the validation experiment for the end-to-end gradients of the Shape Identifier Task, which has a total of 11 optimization parameters. We compute the finite difference gradient using the central difference with a step size of 1.2e-5. Below we report the two gradients, their element-wise, as well as the vector error and difference. \|\|\|\|\|\|\|\|\|\|\|\|\| \|---\|---\|---\|---\|---\|---\|---\|---\|---\|---\|---\|---\| \|Analytical\|0.0483\|0.3935\|0.3142\|0.0459\|0.1327\|0.0670\|0.0866\|0.0081\|-0.0224\|0.5404\|-0.0579\| \|Finite Difference\|0.0484\|0.3956\|0.3137\|0.0462\|0.1341\|0.0663\|0.0864\|0.0082\|-0.0246\|0.5402\|-0.0589\| \|Absolute Difference\|-1.722e-04\|-2.090e-03\|5.196e-04\|-3.385e-04\|-1.415e-03\|7.247e-04\|2.143e-04\|-9.613e-05\|2.195e-03\|2.352e-04\|9.514e-04\| \|Element-wise Error\|0.0036\|0.0053\|0.0017\|0.0074\|0.0107\|0.0108\|0.0025\|0.0119\|0.0981\|0.0004\|0.0164\| $\lVert \text{diff} \rVert$: 0.0036 Relative Error: 0.0047 4. Did you consider submitting to the Datasets & Benchmarks track instead of the general conference? Your contribution feels more like a benchmarking suite than machine learning research. While our submission does include a suite of tasks for inverse problems in fluid environments, we believe it goes beyond merely being a benchmarking suite. Our paper introduces a novel framework that provides a comprehensive parametric geometry pipeline for specifying complex geometries and offers gradients through the geometry layer. This combination, along with our efficient solver and gradient computation implementation, enables optimization and manipulation tasks on complex shape boundaries that were previously unachievable. These contributions position our work as an advancement in the differentiable simulation community, particularly in its application to robotics, computational fluid dynamics (CFD), and inverse design. Therefore, we believe the general conference track is more appropriate for our submission as it highlights the innovative aspects of our research. 5. In the caption of Table 1, you mention that "# Frames" is not the same as the number of solver steps. What is the actual number of solver steps between two frames? Accumulating gradients over hundreds of steps often leads to exploding gradients, so why don't you have these issues if you stick to the CFL number? * Thank you for your insightful question. The issue of gradient explosion or vanishing is indeed a common problem in differentiable physics. However, we have not observed significant problems in our case, likely due to the clean gradients we provide and the stability of our numerical solver. We provide the statistics of the gradient norm over the full course of optimization on three tasks with varying complexities in Table 1. Our results do not show evidence of gradient explosion or vanishing. In practical engineering scenarios, if a gradient explosion is encountered, we implement gradient clipping and clip the gradient of the network to 1.0. We will include this detail in the implementation section of our paper to enhance the clarity and robustness of our approach. * To address your question regarding the number of solver steps, we have provided additional statistics on the actual number of solver steps in the upper part of Table 1 over one full course of optimization on three tasks. 6. ...using learned surrogates as PDE solvers has demonstrated great potential in overcoming the exploding gradients issue by ... 200x larger time integration steps [1]. Does your framework allow for replacing the NSE solver with a learned surrogate, e.g. a U-Net or FNO? Our geometry and optimization framework is designed to be orthogonal to our solver module, allowing for integration with learned NSE solvers. One advantage of our PDE solver over learned surrogates is its ability to solve any given combination of geometry boundary and initial conditions without prior training. In contrast, a learned alternative typically requires extensive training on a large dataset with various boundary conditions and geometries to achieve sufficient generalizability for geometry optimization. The design and control tasks that we highlight in this paper aim to explore novel geometry designs and control in unseen simulation conditions, which a learned surrogate might struggle to do and remains a challenging and active area of research. We acknowledge that learned surrogate models have the potential to enhance traditional differentiable physics simulators by enabling larger time steps, and we view this research direction as complementary to our work and a promising area for future development. --- Rebuttal Comment 1.1: Comment: Thanks a lot for the rebuttal and sorry for the delayed reply. Reviewing 6 papers for NeurIPS has been a ride, and yours is the last one to reply to. Overall reply: I still find this paper an important step toward doing ML on real-world-sized problems, which has been basically impossible with toy tools like PhiFlow. That's why I would keep my score, even if I'm not too happy with the current solver validation. Detailed reply: 1. Inset figures Thanks. B. Solver validation Cylinder flow is a good choice for a validation case. However, looking at the one page rebuttal PDF, the authors obviously don't know much about fluid mechanics. Let me explain. A) "Karman vortex street" is a regime of the cylinder flow, which emerges for Reynolds numbers ($Re=U D/\nu$ with free stream velocity $U$, cylinder diameter $D$ and viscosity $\nu$) between roughly 40 and 1000. Thus, providing $\nu$ in the plots is pretty much useless unless you provide $U$ and $D$ in addition or just provide $Re$. B) Validating a solver does not mean just running it and being impressed by the beauty of the images. One has to 1. configure a case for which we have a reference solution, 2. extract some statistics from the simulation for which we have this reference data, and 3. make sure that the new solver can recover this reference solution. You propose validating in the Karman vortex street regime, so you would need to set up a simulation with say $Re=50$, for which you can find a reference Strouhal number of 0.13 in [Irvine 1999](https://www.semanticscholar.org/paper/KARMAN-VORTEX-SHEDDING-AND-THE-STROUHAL-NUMBER-Irvine/181f6da07be036ac3de89e21f64ebedd28f68a90). But of course you would have to first extract this Strouhal number (which is related to the frequency of the shading) from your simulation. I hope now you understand why people in numerics spend whole PhDs on these things, and these are must-haves for credibility. C) Now, back to your rebuttal Figure 1: viscosity $\nu=0$ means $Re=\inf$, which means chaotic turbulence, which is not what your figure shows. 3. Gradient validation Looks good! 4. Benchmark track? Ok, I see the point. 5. # Frames to differentiate through This part sounds almost too good to be true, but I'm not an expert in gradient stability. I hope there is nothing wrong with your code, but adding some more details on why you don't have these gradient issues might be helpful. 6. Flexibility of framework to use other PDE solvers Ok, sounds good. --- Rebuttal 2: Comment: Dear reviewer ZAVx, we wanted to check if there are any remaining questions or concerns about our rebuttal. Since the author-reviewer discussion period ends tomorrow, we’d appreciate any final feedback you might have. Thank you for your time and attention. --- Rebuttal 3: Comment: Thank you for your detailed feedback and for providing a thorough suggestion of the validation process in fluid mechanics. Regarding your points: 1. Numerical Viscosity in Semi-Lagrangian Scheme: We acknowledge that our semi-Lagrangian scheme introduces numerical dissipation [1], which explains the results in Figure 1 in the rebuttal PDF for the chaotic turbulence case. We will add this in the discussion section of our method. 2. Validation with Reference Data: Thank you for the additional feedback. To further validate our solver numerically, we focused on validating the mid-viscosity scenario that we provided in the rebuttal PDF, corresponding to a Reynolds number of 209. For this case, we calculated a Strouhal number of 0.16, compared to the reference value of 0.18 from Irvine 1999. The observed discrepancy can be attributed to the numerical dissipation introduced by our scheme. We appreciate your insights, which have helped us better articulate the limitations and implications of our approach. Please let us know if you have further questions. [1] Jos Stam. 1999. Stable fluids. In Proceedings of the 26th annual conference on Computer graphics and interactive techniques (SIGGRAPH '99). ACM Press/Addison-Wesley Publishing Co., USA, 121–128. https://doi.org/10.1145/311535.311548	Summary: The paper aims at a fully automated pipeline for devising neural controls for complex fluidic systems with dynamic boundaries. The system consist of externally driven soft boundaries and internal complex flow behaviors. The proposed framework contains a differentiable geometry representation, a differentiable fluid simulator with solid-fluid interface handling, and a control-shape co-design algorithm using gradient-based optimization. - The 3D surface is represented by a list of 2D surfaces (represented by a set of connected Bezier curves of their control points) defining the first and last cross-section, and each key cross-sections of the geometry. More complex 3D geometries are represented by union and intersection of sub-geometries. - The fluid simulator leverages the operator-splitting method. A single simulation step comprises three sub-steps: advection, viscosity, and projection. It uses MAC grid. - The back-propagation process is used to construct the gradients of the geometry surface w.r.t. the loss function. The method is evaluated on multiple tasks, from simpler 2D tasks to complex 3D tasks (such as, neural gate controller and artificial heart design). Strengths: - The paper contains a fair amount of work to develop a differentiable fluid simulation and optimization framework, which includes a differentiable geometry representation, a differentiable fluid simulator with solid-fluid interface handling, and a gradient-based optimization framework. - The proposed methods are evaluated on multiple cases from simple 2D examples to complex 3D tasks. Besides, it's nice to see the performance profiling and comparison results in the paper. Weaknesses: It would be nice to see the framework open-sourced. Technical Quality: 3 Clarity: 3 Questions for Authors: - It might be useful to demonstrate whether gradients explode or vanish during the iterative back-propagation process. - In the experiment studies the effect of random initialization in our fluid optimization tasks, the Shape Identifier task (with #Parameter = 10) is used. Does the same conclusion hold for more complex tasks with a greater number of parameters? - How sensitive are the design results to the grid resolution? Given that the grid used for generating the design is relatively small for fluid simulations, can the designed system achieve the same level of accuracy when evaluated on a higher resolution grid? - How does the method perform when using a higher resolution grid (but not so high that the simulator cannot finish within an acceptable time)? - In Table 2: Time Performance, what's the time unit? Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The author have discussed the limitations in the paper. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for the constructive suggestions. Below we provide responses to individual questions. 1. It would be nice to see the framework open-sourced. We will open-source our code upon acceptance. We have provided the anonymized version of our code at https://anonymous.4open.science/r/DiffFluidRebuttal-1D24/. 2. It might be useful to demonstrate whether gradients explode or vanish during the iterative back-propagation process. * Thank you for your insightful point. The issue of gradient explosion or vanishing is indeed a common problem in differentiable physics. However, we have not observed significant problems in our case, likely due to the clean gradients we provide and the stability of our numerical solver. * We have included additional statistics (min,max,mean, standard deviation) on the gradient norm over the full course of optimization for three tasks with varying complexities in Table 1. Our results do not show evidence of gradient explosion or vanishing. * In practice, in case a gradient explosion is encountered, we implement gradient clipping of the gradient of the network to 1.0. We will include this detail in the implementation section of our paper to enhance the clarity and robustness of our approach. 3. In the experiment studies the effect of random initialization in your fluid optimization tasks, the Shape Identifier task (with #Parameter = 10) is used. Does the same conclusion hold for more complex tasks with a greater number of parameters? Yes, the same conclusion holds for all of our tasks. In Fig 2 we present an additional verification with the 3D heart controller task which has 7.1k neural network parameters. We initialize the network parameters with 5 different random seeds, and observe the same convergence across seeds even with different initial behaviors, showing the robustness of our method. 4. How sensitive are the design results to the grid resolution? Given that the grid used for generating the design is relatively small for fluid simulations, can the designed system achieve the same level of accuracy when evaluated on a higher resolution grid? How does the method perform when using a higher resolution grid (but not so high that the simulator cannot finish within an acceptable time)? * Thank you for raising this important question. In pure forward simulation, higher grid resolutions are necessary to achieve greater accuracy, particularly at the solid-fluid interface, which directly impacts optimization results. This is because the same continuous geometry boundary can yield different simulation results depending on the resolution, the objective values—and consequently the optimized designs—will vary across different resolutions. * To illustrate this, we have conducted an additional experiment to analyze the effect of grid resolution on design outcomes, where we first optimize for the Shape Identifier task under 128x128, then take the optimized values to 512x512, which evaluates to a loss value of 3.11. In comparison, a randomly initialized design under 512x512 evaluates to a loss value of 245.1 and optimizes to a design with loss 0.968. The results demonstrate that while higher resolutions generally improve accuracy, they also introduce variations in the optimal design due to the increased detail captured at the boundary. 5. In Table 2: Time Performance, what's the time unit? The time reported is in Seconds (s) --- Rebuttal 2: Comment: Dear reviewer grLC, we wanted to check if there are any remaining questions or concerns about our rebuttal. Since the author-reviewer discussion period ends tomorrow, we’d appreciate any final feedback you might have. Thank you for your time and attention. --- Rebuttal 3: Comment: Dear Reviewer, As the discussion deadline approaches, we are eager to address any remaining concerns you may have. We kindly request you to review our responses. If there is anything further we can do to facilitate the evaluation process, please let us know. We also respectfully ask that you reconsider our score based on the rebuttal provided. Thank you for your attention. Best regards, Authors --- Rebuttal 4: Comment: I thank the authors for the detailed response. Overall, I think this is a solid paper and I would like to keep my rating of "accept".	Rebuttal 1: Rebuttal: We thank all reviewers and the AC for their time and effort in reviewing and for insightful comments to strengthen our work. Besides the responses to individual reviewers, here we would like to highlight our contributions and new quantitative/qualitative results added in the rebuttal. 1. Contributions 1. [Motivation] Our manuscript tackles an important, challenging, and significant problem in the optimal design and control of fluid flows in complex contexts [Reviewer ueL6] and effectively bridges the gap between toy experiments and real-world problems [Reviewer ZAVx]. 2. [Method] Our method is novel, implementing an efficient PDE solver from scratch in C++ and CUDA with analytically derived gradients, providing a great service to the community [Reviewer ZAVx, Reviewer grLC]. The differentiable fluid simulation and optimization framework includes a differentiable geometry representation and fluid simulator with solid-fluid interface handling [Reviewer grLC]. 3. [Experiments] Our extensive experiments cover a range of scenarios from simple 2D examples to complex,challenging 3D tasks [Reviewer grLC], not just usual "toy" problems [Reviewer ueL6]. We also provide performance profiling and comparison results [Reviewer grLC] and highlights the advantages gradient-based optimizations compared to gradient-free methods [Reviewer QmuX]. 4. [Presentation] Our manuscript is well-written, and provides a good balance between theory and experimental evidence [Reviewer ZAVx, Reviewer grLC]. 2. New Results 1. [Code: Open-Source Release] https://anonymous.4open.science/r/DiffFluidRebuttal-1D24/ We have anonymously released our code open-source for the review stage and will officially release it upon acceptance, enabling the community to reproduce our results and build upon our work. 2. [Experiment: Solver Validation]. We validated our fluid solver using the classic Karman Vortex Street test. 3. [Experiment: Gradient Validation]. We presented a gradient validation test to compare our analytical gradient to finite-difference gradient. 4. [Experiment: Gradient Norm Analysis]. We provide statistics on gradient norm on multiple tasks during optimization to study whether gradients diminish/explode. 5. [Experiment: Step Number Statistics]. We provide statistics for solver steps on multiple tasks. 6. [Experiment: Effect of Initialization on Complex Tasks]. We provide an additional experiment on the effect of initialization on the 3D neural controller task with 7k parameters. 7. [Experiment: Memory & Time Comparison with DiffTaichi]. We compare the memory usage and computational time of our solver with DiffTaichi, highlighting the advantages of our implementation in terms of efficiency and scalability. 8. [Experiment: Effect of Grid Resolution on Optimization]. We explore how varying grid resolutions impact the optimization outcomes. 9. [Implementation Details: GPU Code Framework & Kernel Acceleration]. We detailed our GPU code framework and kernel acceleration techniques. Pdf: /pdf/3f0d1d41eaf426173af49bf636221a5f60a9d56f.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Almost Free: Self-concordance in Natural Exponential Families and an Application to Bandits	Accept (poster)	Summary: This paper discusses Generalized Linear Bandits (GLB) under the self-concordance assumption. The study successfully relaxes the limitations of existing work with an OFU-type algorithm, providing mathematically solid theories for GLB within the self-concordance family. However, the presentation could be significantly improved, and the paper's style does not align well with the venue. Strengths: This paper has a sound theoretical foundation with the relaxation of some assumptions in the existing literature. Weaknesses: The first section should provide a comprehensive overview of the study. The core concept of "self-concordance" is introduced abruptly and is not well-explained. The literature review is incomplete. Specifically, the differences between this study and the existing literature, such as [Rus+21], are not thoroughly discussed. As a result, the contribution of this study is unclear. The paper dedicates the first seven pages to the theoretical foundation and introduces the model and algorithm thereafter. Due to space constraints, these are not fully illustrated, and the paper lacks experimental results. This organization is not well-suited to this venue. Technical Quality: 3 Clarity: 1 Questions for Authors: This paper talks about "being free of exponential dependency". I would like to see what the term means in detail. Also, why "being free of exponential dependency" is important in analyses and applications? Confidence: 5 Soundness: 3 Presentation: 1 Contribution: 3 Limitations: This paper discusses the single-parameter natural exponential family. But, I believe that this family is not comprehensive enough to include most applications in the real world. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We would like to clarify a misunderstanding of our work that we do not “discuss GLB under the self-concordance assumption”. What is true that our work goes beyond this: we aim to remove this assumption for GLBs with subexponential base distribution. Now we would like to address concerns pointed out in the weakness section. + Due to the space limitation, we are unable to provide a thorough explanation for self-concordant functions but we would like to kindly remind the reviewer that references of its origin are provided in line 127 and we introduce its use in machine learning & optimization from line 28 to 46. In the future versions of our manuscript, we plan on using the extra page to flesh out the exposition around self-concordance as well strengthening the section on related works. + There is a huge body of related work, so we are incapable of summarizing them all thoroughly due to the lack of space (which we think is a common practice, in the exploding field we are in). All the related works that we know of are at least mentioned. On the issue of why [Rus+21] is not discussed in detailed. The main contribution in this paper is working out how to act in a non-stationary setting. Since we only consider the stationary setting, their contribution is irrelevant from the perspective of our paper (they avoid any difficulty that we face by assuming bounded rewards). Finally, the regret bound in [Rus+21] scales with $\kappa$ (which can be exponentially large in the dimension $d$, [8]) and is not second order (meaning the bounds does not scale with the optimal arm’s variance); the stronger earlier relevant papers are all discussed in our paper; we'd be happy to add more relevant works if needed and did the reviewer have any other suggestions. + We would like to note that our writing style naturally flows from theory to algorithms, as appreciated by reviewers Ca74 and n2uQ. The contribution of this work is to show that GLBs with subexponential base distribution possess self-concordance property. It is a result that could be interesting on its own and the application of it could go beyond GLBs as detailed in section 5. We select GLBs as a demonstration of how the self-concordance property of subexponential NEFs can be applied to address open problems in the bandit literature. Our results naturally extend the analysis techniques presented in [9]. This motivates the organization of our paper. ySjz asks the question about being free of exponential dependency. This originally comes from the very first work on GLBs [1] where the confidence width (and as a result, the regret bound) suffers from a dependency on $\kappa$ that is in worst case exponential in the norm of true underlying parameter $\theta_\star$, creating a significant gap between theoretical and empirical results. To explain why resolving exponential dependency is important, we would like to remind ySjz that algorithms with exponential dependency in relevant parameters are considered as inefficient and unpractical as the resource demands increase very rapidly with input size. Transferring this notion into decision making, or specifically bandit algorithms, algorithms with regret scaling exponentially with relevant parameters are considered to make inefficient use of samples. As is pointed out in [8], which studies an instance of GLB - logistic bandit: “$\kappa$ can be prohibitively large, which drastically worsens the regret guarantees as well as the practical performances of the algorithms.” (paragraph Limitations) and “Even for reasonable values of $S$, this has a disastrous impact on the regret bounds” (section 2). Removing this exponential dependency enables us to align the theoretical bound of UCB-type algorithms on GLBs with its empirical performance. To the best of the authors’ knowledge, there is no previous work resolving this exponential dependency for the whole class of GLBs with subexponential base distribution. We would like to address the concern about the applicability of the work. We are confused by the reviewer’s claim that natural exponential families are “not comprehensive enough to include most applications in the real world”. We interpret this sentence as asking whether NEFs enjoy revenue generating applications in the real work, which they do. To give a concrete example, consider Poisson regression, which is widely used when dealing with count data, e.g. number of insurance claims or Uber's surge pricing model. As for the theoretical nature of the work, we would like to point out that many important Neurips publications are theoretical in nature. Here is a non-exhaustive list of Neurips publications dedicated fully to theory without experimental results [2, 3, 4] and all of them are cited over 300 times. Here are works accepted last year that dedicate themselves fully to theory without experimental results [5,6,7]. We also conducted some numerical experiments. The results are available in the global rebuttal. [1]. Filippi et al. Parametric bandits: The generalized linear case. In NeurIPS 2010\ [2]. Jin et al. Is q-learning provably efficient? In NeurIPS 2018\ [3]. Kakade et al. On the Complexity of Linear Prediction: Risk Bounds, Margin Bounds, and Regularization. In NeurIPS 2008\ [4]. Antos et al. Fitted q-iteration in continuous action-space MDPs. In NeurIPS 2007\ [5]. Liu et al. Optimistic natural policy gradient: a simple efficient policy optimization framework for online rl. In NeurIPS 2023\ [6]. Yuan et al. Optimal extragradient-based algorithms for stochastic variational inequalities with separable structure. In NeurIPS, 2023\ [7]. Foster et al. Model-free reinforcement learning with the decision-estimation coefficient. In NeurIPS 2023\ [8]. Faury et al. Improved Optimistic Algorithms for Logistic Bandits. In ICML 2020\ [9]. Abeille et al. “Instance-Wise Minimax-Optimal Algorithms for Logistic Bandits.” In AISTATS 2021\ --- Rebuttal Comment 1.1: Comment: Dear Reviewer, The author-reviewer discussion period is shortly coming to an end. We were hoping to get a confirmation from you that you've considered our rebuttal, and to let us know if you have any further questions. --- Rebuttal Comment 1.2: Comment: Thanks for the detailed explanation. I understand the authors' concerns as well as n2uQ's disappointment. I agree that my understanding of fitness in this venue can be wrong. But, I still believe that this paper has a high barrier for most readers and the presentation should be improved for readers without background knowledge about GLB. I think that the authors' rebuttals are valid. I will more carefully review your manuscript based on the rebuttal and make changes in my evaluation.	Summary: The authors prove that any single-parameter natural exponential family (NEF) with subexponential (subgaussian) base distribution is self-concordant with a stretch factor that grows inverse quadratically (linearly). Strengths: - Clearly and well-written - An important theoretical contribution in establishing that self-concordance for exponential tilting comes for free, which has numerous applications in statistics and bandits (as alluded to in the Conclusion). Surprisingly, the proof consists of some concentration results combined with clever integral/infinite sum manipulations. - For the subgaussian, the authors established that the linear growth is tight by establishing a lower bound, which is technically quite interesting. - First $d\sqrt{T/\kappa_\star}$ type regret that holds for a wide range of generalized linear bandits, well beyond logistic bandits Weaknesses: - The confidence set for the OFU-GLB is nonconvex, and thus, the current algorithm is computationally intractable. There has been some progress on achieving convex confidence sets that are also statistically (regret-wise) tight -- see, e.g., [1,2]. It would be nice to write the confidence set in a convex form, as it is repeatedly alluded to during the authors' proof. - With the convex confidence set, it would be nice to see some numerical experiments, especially the exponential bandits. - The norm parameters $S_0, S_1, S_2$ were introduced but never kept track of. The dependencies on these norm parameters have been a subject of study on their own [2,3] and are known to perform well [2]. It would be nice to have those dependencies appearing in the main text as well. - Most of the discussions regarding the proof of regret analyses are relegated to the Appendix. From my perspective (heavily biased towards bandits community), the techniques used there are arguably a bit more interesting. I would really like to see the technical contributions made in the main text's Section 4, especially the self-concordance control lemmas used (Appendix E.3) and Lemma 31 and more. Comments - It would be nice to include some discussions regarding [3], which provides the first $d\sqrt{T/\kappa_\star}$-type regret for bounded generalized linear bandits but still goes beyond logistic bandits. - For each theorem statement, if not already done so, I would like to see a direct (hyper)ref to the Appendix containing its proof - Typo: "Lemma ??" in pg. 24 [1] https://proceedings.mlr.press/v130/abeille21a.html [2] https://proceedings.mlr.press/v238/lee24d.html [3] https://arxiv.org/abs/2404.06831 Technical Quality: 4 Clarity: 4 Questions for Authors: - Can the regret analyses be extended to changing arm-set case, i.e., the arm-set $\mathcal{X}_t$ varies across $t \in [T]$? - Confidence: 3 Soundness: 4 Presentation: 4 Contribution: 4 Limitations: Yes Flag For Ethics Review: ['No ethics review needed.'] Rating: 8 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thanks for your review and suggestions and we really appreciate them! For the weakness section: + We agree that the convex relaxation technique from Abeille et al [1], can be applied to our case. We adapted the proof from Abeille et al [1] and are able to apply the convex relaxation to our confidence sets as well. This was a good suggestion and thus will be added to the future version of our manuscript. + We conducted some numerical experiments on exponential bandit (as suggested by the reviewer) to verify our theoretical contributions. The results are available in the global rebuttal. + We will make the dependency on $S_0$, $S_1$ and $S_2$ explicit in the regret bound. Thank you for drawing our attention to this issue. + The techniques in section 4 follow similarly to Abeille et al [1]. Lemma 32 is borrowed from proposition 8 of Sun and Tran Dinh [2], where we tailored the technique into our specific setting. Similar use of self-concordance is also present in [1,3]. For the comment section: + We will be happy to discuss [4] in the final version. Their arm elimination technique and adaptation of rare switching are relevant. It is also nice to see that their empirical performance can surpass the performance of ECOLog, which, according to our experience, is quite competitive. + We will be happy to add hyperlinks to the appendix about the proofs of each statement. + Thanks for pointing out the typo. It was meant to be the lower bound on $\dot\mu()$, i.e., lemma 17. For the question section: Yes, our regret guarantee still holds for changing arm-sets as long as $S_2\le x^T\theta\le S_1$ holds for all $x\in \mathcal X_t$ , $\theta\in \Theta$ and $t\in [T]$. Our proof technique makes no use of the stationarity of the arm set and its inclusion was solely to facilitate a more streamlined exposition. [1]. Marc Abeille, Louis Faury, Clement Calauzenes. “Instance-Wise Minimax-Optimal Algorithms for Logistic Bandits.” In International Conference on Artificial Intelligence and Statistics (2021). [2]. Tianxiao Sun and Quoc Tran-Dinh. “Generalized self-concordant functions: a recipe for Newton-type methods.” In Mathematical Programming 178 (2017): 145 - 213. [3]. David Janz, Shuai Liu, Alex Ayoub and Csaba Szepesvari. “Exploration via linearly perturbed loss minimisation.” In International Conference on Artificial Intelligence and Statistics (2024). [4]. Ayush Sawarni, Nirjhar Das, Siddharth Barman, Gaurav Sinha. "Generalized Linear Bandits with Limited Adaptivity." ICML 2024 Workshop: Aligning Reinforcement Learning Experimentalists and Theorists. --- Rebuttal Comment 1.1: Comment: Thank you for the responses, and apologies for getting back so late. After reading through the responses to my and other reviewer's reviews, I'm satisfied with the authors' responses and intend to keep my score.	Summary: The paper investigates the self-concordance properties of single-parameter natural exponential families (NEFs) with subexponential tails. It provides two main contributions: first, it demonstrates that NEFs with subexponential tails are self-concordant with polynomial-sized parameters, and second, it applies these findings to generalized linear bandits (GLBs). The authors derive novel second-order regret bounds for GLBs that are free of exponential dependence on the problem parameters. This result extends the applicability of optimistic algorithms for GLBs to reward distributions such as Poisson, exponential, and gamma. Strengths: - The results on the self-concordance property of NEFs are definitely interesting and general, going beyond its application to GLBs. They can be interesting to many other problem settings (as mentioned by the authors themselves). - Not only do the authors provide an algorithm for GLBs, but it guarantees a second-order regret bound. This is particularly desirable to achieve better data adaptivity. - The results are presented in a clear manner, with clear definitions and helpful examples. Weaknesses: - It appears that the algorithmic results in this work tightly rely on the knowledge of some parameters of the NEF. Parameter-free results are quite important and have become relevant, especially in the past few years. - The paper could benefit from a slightly more detailed comparative analysis with existing methods, highlighting the advantages and potential trade-offs of the proposed approach in various scenarios, and how these prior results would fit in the setting considered in this work. - The papers could benefit from experimental results, although it is very clear that this is a theoretical paper. Minor details: - Many references have "et al." instead of the full list of authors. This should be fixed. Technical Quality: 3 Clarity: 3 Questions for Authors: - Do the authors believe it possible to lift prior knowledge on parameters such as $S_0$, $L$, $c_1$, and $c_2$ in designing efficient algorithms for GLBs with NEF rewards? Confidence: 2 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The authors addressed potential limitations. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thanks for reviewing our manuscript and we are delighted at your appraisal of our work. A question was asked “Do the authors believe it possible to lift prior knowledge on parameters such as $S_0$, $L$, $c_1$ and $c_2$ in designing efficient algorithms for GLBs with NEF rewards?” To the best of the authors’ knowledge, existing parameter free algorithms on multi-armed bandits (linear bandits) still require the knowledge of subexponential (subgaussian) parameters or the upper bound of the reward [1], [2], [3]. Hence the knowledge of subexponential parameters (i.e., $c_1$, $c_2$) may be still needed. The knowledge of $S_0$ can be lifted as the information we need about $S_0$ can be provided by $S_1$ and $S_2$. Judging from the present work on parameter-free bandit algorithms [3], the knowledge of $S_1$ and $S_2$ cannot be lifted as [3] designs their confidence set using the upper bound of the true underlying model parameter $\theta_\star$ which plays a similar role to $S_1$ and $S_2$ in our work. The knowledge of $L$ can be lifted as it is worst-case polynomial in $\max(1/(c_1-S_1), 1/(c_2-S_2))$. This bound is oftentimes pessimistic hence we leave the dependency on $L$ in the bound and knowing a tighter bound on the variance definitely helps in the performance. Hence, removing dependencies on knowledge of subexponential/subgaussian parameter and knowledge of the bound of the parameter norm, $S$, are promising directions for future research and remain open in the bandit literature. We now address concerns in the weakness section. + For more detailed comparative analysis, we can compare our bandit algorithm with subgaussian base distribution and we will be happy to add it to the camera ready version of the manuscript (assuming the paper gets accepted). Specifically, we will point out the setting in this work is the most general in the sense that we consider GLBs with subexponential rewards while all the previous work we know of consider bounded rewards or subgaussian rewards. For subgaussian rewards, we will emphasize that [4,5,6,7] still depend on $\kappa$. Russac et al [7], also employs self-concordance in GLBs but they assume bounded reward and focuses on addressing non-stationarity of the environment – their bounds also scale with $\kappa$ in the leading term, which can be exponentially large for logistic bandits. Janz et al [8], consider a similar setting to ours. They assume the moment generating function of the base distribution $Q$ is defined over the entire real line. This implies that $Q$ does not have a tail as heavy as an exponential distribution hence less general than our setting. + For experiments, we provided some results in the global rebuttal. + For the minor details, thank you for drawing our attention to the formatting of our references! This will be addressed in future versions of our submission. [1]. Shinji Ito (2021). “Parameter-free multi-armed bandit algorithms with hybrid data-dependent regret bounds”. In COLT 2021\ [2]. Yifang Chen, Chung-Wei Lee, Haipeng Luo, Chen-Yu Wei. “A new algorithm for non-stationary contextual bandits: efficient, optimal and parameter-free.” In COLT 2019\ [3]. Kei Takemura, Shinji Ito, Daisuke Hatano, Hanna Sumita, Takuro Fukunaga, Naonori Kakimura, Ken-ichi Kawarabayashi. “A parameter-free algorithm for misspecified linear contextual bandits.” In AISTATS 2021\ [4]. Sarah Filippi, Olivier Cappe, Aurélien Garivier, Csaba Szepesvári. Parametric bandits: The generalized linear case. In NeurIPS 2010.\ [5]. Kwang-Sung Jun, Lalit Jain, Blake Mason, Houssam Nassif. Improved Confidence Bounds for the Linear Logistic Model and Applications to Bandits. In ICML 2021.\ [6]. Aadirupa Saha, Aldo Pacchiano, Jonathan Lee. Dueling RL: Reinforcement Learning with Trajectory Preferences. In AISTATS 2023\ [7]. Yoan Russac, Louis Faury, Olivier Cappé, Aurélien Garivier. Self-Concordant Analysis of Generalized Linear Bandits with Forgetting. In AISTATS 2021.\ [8]. David Janz, Shuai Liu, Alex Ayoub and Csaba Szepesvari. “Exploration via linearly perturbed loss minimisation.” In AISTATS 2024.\ --- Rebuttal Comment 1.1: Comment: I thank the authors for the response. I have no further questions and am keeping my positive score.	null	null	Rebuttal 1: Rebuttal: We would like to thank you all for the time and effort spent in reviewing our manuscript! We are glad that the reviewers appreciate our theoretical contributions on NEFs (reviewer Ca74 & reviewer n2uQ), our contributions to the bandit literature on second-order regret guarantee for GLBs with subexponential rewards (reviewer Ca74 & reviewer n2uQ) and our writing style (reviewer Ca74 & reviewer n2uQ). A general concern was raised about the lack of experiments and we understand the concern and conducted some experiments -- as a sanity check of our theoretical results. The setting of the experiment is as follows. We will be happy to use the extra space in the paper for including a little more thorough experimental verification of our theoretical results. + We conduct experiment on exponential bandits, i.e., the base distribution is an exponential distribution and as a result the reward distributions are also exponential. + The dimension $d$ of the true underlying parameter $\theta_\star$ is $d=2$ + The number of arms $\|\mathcal X\|=20$. + The maximum variance is $0.25$, i.e., for all $t\ge 1$, $\max_{x\in \mathcal X}\mathrm{Var}[Y_t\|X_t=x]=0.25$ . + The experiment consists of 60 runs with a horizon of 5000. + The failure probability $\delta$ is set to be 0.05. + The regularizer is set to be $\lambda=2$ and $\gamma_t(\delta)$ to be the theory suggested value below line 922: $$\gamma_t(\delta) = \sqrt{\lambda}\left(\frac{1}{2M}+S_0\right)+\frac{2Md}{\sqrt{\lambda}}\left(1+\frac{1}{2}\log\left(1+\frac{tL}{\lambda d}\right)\right)+\frac{2M}{\sqrt\lambda}\log(1/\delta)$$ The results are available in the pdf attached. Here are some explanations: + The first figure displays the mean regret along with standard deviation. The regret attained appears to be "sublinear". + The second figure is a log-log plot to display the growth rate of the regret. The slope gradually approaches 0.5, i.e., the growth rate of regret approaches to $\sqrt T$, which confirms our theoretical bound. Pdf: /pdf/345f687028e2049aba10a202f7fc8cc3ac6209b5.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
NeuroGauss4D-PCI: 4D Neural Fields and Gaussian Deformation Fields for Point Cloud Interpolation	Accept (poster)	Summary: Point Cloud Interpolation (PCI) is the task of predicting intermediate point cloud features from a sparser representation, often to construct point cloud representations for intermediate time frames. Contrary to interpolation in other fields, point clouds are largely unstructured and do not preserve consistent information across different sequence frames, and thus cannot be addressed adequately with classical interpolation functions such as linear interpolation. To properly represent point clouds in a latent space for learned approaches, a method that respects the volumetric nature of point distributions is crucial for minimising noisy artifacts caused by the unordered nature of point clouds. This paper proposes three new components of PCI learning architectures that address this necessity. First, a Gaussian clustering function is used to group point sets into distinct regions, which are less prone to misrepresenting unintended variations in point cloud data, and facilitates a necessary structure for PCI. To my understanding, with the sparse latent representations, interpolation is achieved by first using Radial Basis Functions (RBF) to provide an initial smooth estimate of the interpolated Gaussian cluster sequence, followed by a learned graph-based network to determine a final interpolation based on the composition of RBF sequences from every cluster. Strengths: The paper is technically sound with strong results against state-of-the-art methods in PCI of dynamic environmental LiDAR scenes. The methodology presentation is largely clear and well structured. A detailed ablation study is provided to demonstrate the importance of each component for effective PCI based on standard Chamfer Distance and Earth Mover Distance metrics. Weaknesses: Section 1: Introduction - The introduction writing structure is quite unconventional, and repeats itself word for word in the contributions statement. I suggest the introduction of the proposed method be explained in more detail with regards to its overall architectural structure, to incorporate a consistent flow with the presentation of the method's components. - The mentioned challenges of PCI are sporadic and inconsistent with the way PCI is introduced as a research problem. The use of a mathematical formula to introduce PCI takes away from the intended motivation of PCI-centric research, and is therefore difficult to link to each challenge. e.g. If solving Eq.(1) is the goal, what does the representation of "multiple unordered point clouds" have to do with it? This is unclear with the current presentation. - Figure 1 is a mess of graphs and qualitative examples that belong as separate (sub)figures in the Experiments section. The introduction of Figure 1 in the beginning of the work is inappropriate. What is the expected ground truth for the right side figures? It is unclear what the right side figure is trying to demonstrate. Section 2: Related works - Like the introduction, the presented explanation is centred around explaining mathematical formulae, rather than intuitively presenting technical problems and expressing it as formulae if necessary. It is generally unnecessary for the formula to be understood in order to analyse the current state of research for each subsection. For this reason, by linking the motives of past research to solving an otherwise arbitrary formula, the flow of the related works section is unclear. - L81: "for efficient:" appears to be in error. Section 3: Methodology - 1), 2), 3) are not labelled in the diagram itself, and thus can be difficult to associate. - Figure 3 fails to visualise the purpose of each component, i.e. RBF Activator, Gaussian/Feature Interpolators, in the proposed method. It is generally expected that a flowchart is used to both illustrate the information flow of the system, and provide labels for the purpose, i.e. I/O, of each component. Mathematical equations are highly ineffective for this. Technical Quality: 3 Clarity: 1 Questions for Authors: 1. Figure 2: Is it correct to call the output of the soft-clustering process "spheres"? The figure appears to describe "ellipsoids" rather than consistent radius spheres. 2. Outlier removal in Section 4.2/Table 2 appears to improve the results of the method quite significantly. How does it affect other state-of-the-art methods? Confidence: 4 Soundness: 3 Presentation: 1 Contribution: 3 Limitations: Yes, limitations of the method are discussed briefly in the manuscript regarding its applicability in practical scenarios. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We appreciate your meaningful suggestions and questions, and we will address each of them in our response. ## Q1.1: Non-traditional writing structure of the introduction. A1.1: We will rigorously revise our introduction structure according to your recommendations. Due to space constraints, please refer to the end of our response to A1 for the detailed revision plan. ## Q1.2: Sporadic PCI challenges and unclear logical relationship to Formula 1. A2: We appreciate your feedback and will clarify that "multiple unordered point clouds" refers to the inherently unordered nature of input point cloud signals. To enhance clarity and logical flow, we will separate the introduction of PCI concepts from the discussion of current challenges in the main text. Additionally, we will provide a detailed explanation for each term in Equation 1. ## Q1.3: Inappropriate introduction of Figure 1 at the beginning. A3: We greatly appreciate your valuable feedback on Figure 1. We agree that introducing detailed experimental results at the beginning of the paper may not be ideal. Our original intent was to quickly showcase our method's advantages, including: 1. Interpolation accuracy across various frame intervals 2. Performance with different data sparsity levels 3. Effectiveness on both human body and autonomous driving datasets To address your concern, we will: 1. Split the existing Figure 1 2. Move qualitative and quantitative results to the experimental section 3. Ensure readers fully understand our method before encountering these results Regarding the right side of Figure 1, we will provide further explanations in our PDF response (Fig. 4). The following is the revised Introduction outline, and we will re-revise the text strictly according to your suggestions: 1. Point Cloud Interpolation (PCI) - Concept and application scenarios, incorporating Equation 1 - Clear explanation of each term in Equation 1 2. PCI Challenges and Research Significance - Point cloud data characteristics and resulting challenges - Complexity of spatio-temporal dynamic modeling - Difficulty in generalizing from sparse temporal samples 3. NeuroGauss4D-PCI: Key Components and Their Roles a. Iterative Gaussian Cloud Soft Clustering - Structured representation for unordered point clouds - Geometric feature capture addressing data irregularity b. Temporal RBF-GR Module - Complex non-linear temporal dynamics modeling - Smooth interpolation between sparse temporal samples c. 4D Gaussian Deformation Field - Long-term motion trend and non-rigid deformation capture - Cross-frame geometric consistency maintenance d. 4D Neural Field - Fine-grained spatiotemporal detail representation - Multi-scale dynamic modeling complement to Gaussian representation e. Fast Latent-Geometric Feature Fusion Module - Adaptive combination of Gaussian and neural features - Handling of varying point densities and enhanced spatiotemporal modeling 4. Innovations and Contributions - Novel 4D representation combining Gaussian soft clustering and neural field features - Continuous time modeling via Temporal RBF-GR module - Advanced 4D Gaussian deformation field using graph convolutions ## Q2: Unclear flow in the related works section A2: We will improve the related works section by: 1. Reorganizing the structure of each subsection (neural fields, 3D Gaussian splatting, and point cloud interpolation) 2. Reducing reliance on mathematical formulas 3. Correcting grammatical errors ## Q3.1: Unlabeled components in Figure 2 A3.1: We will revise Figure 2's caption to match the module names in the diagram and avoid using numbering: Figure 2: NeuroGauss4D-PCI architecture. The system processes input point clouds (X, Y, Z, T) and a predicted time T_pred. Latent Feature Learning occurs via Fourier Basis Encoding and Neural Field. Gaussian Representation is achieved using Iterable Gaussian SoftClustering. Temporal Modeling employs the RBF-GR Module. The 4D Deformation Field integrates latent features and temporal information. Feature Fusion is performed by the Fast-LG-Fusion module. Finally, Point Cloud Generation is accomplished using a Prediction Head. This pipeline enables effective spatiotemporal modeling and interpolation of point clouds. ## Q3.2: Figure 3 fails to visualize component purposes A3.2: We've enhanced Figure 1 in the PDF reply as follows: 1. Gaussian Ellipsoid Visualization: Added pre- and post-interpolation Gaussian ellipsoids, showing model inputs and outputs. 2. Intermediate Process Visualization: Included visualizations of intermediate products to illustrate data transformation. 3. Component Functionality: Clarified inputs, outputs, and functions of RBF-GR module components. 4. Information Flow Diagram: Will add a flow diagram in the final revision, annotating each component's role and data flow. ## Q4: Incorrect terminology in Figure 2. A4: Using "sphere" to describe soft clustering output is indeed inaccurate.. We will: - Change "Gaussian spheres" to "Gaussian ellipsoids" in Figure 2's caption and explanation - Review and correct all related descriptions in the main text ## Q5: Impact of outlier removal on other methods A5: Outlier removal improved results for all tested methods. Here's a comparison: \| Methods \| CD ↓ \| EMD ↓ \| \|-----------\|--------\|---------\| \| NSFP \| 1.75 \| 132.13 \| \| NSFP† \| 1.72 \| 129.05 \| \| NeuralPCI \| 0.80 \| 97.03 \| \| NeuralPCI† \| 0.75 \| 83.56 \| \| Ours \| 0.78 \| 95.95 \| \| Ours† \| 0.72 \| 78.66 \| Note: † indicates results with outlier removal. NeuroGauss4D-PCI benefits most from outlier removal due to: 1. Our Gaussian representation amplifies the benefits of outlier removal. 2. Clean data significantly enhances our 4D deformation field's accuracy. 3. Outlier removal maximizes our Temporal RBF-GR module's effectiveness. --- Rebuttal Comment 1.1: Comment: Thank you for the response. The new figures, explanations, and results are much needed improvements to the original submission. I am inclined to increase my rating in order to reflect the technically sound and adept contributions of the paper, provided that its presentation is acceptable in the final version. --- Reply to Comment 1.1.1: Title: Response to Reviewer 2Dkp Comment: Thank you very much for your response and valuable feedback. We deeply appreciate your recognition of our revised paper. Your constructive comments have greatly improved the quality of our research. We will do our utmost to further refine the presentation of our paper according to your suggestions, ensuring that the final version meets your expectations. Once again, thank you for your time and insights.	Summary: The paper presents a novel model, “NeuroGauss4D-PCI,” for point cloud frame interpolation, a popular but challenging 3D computer vision task in real-world scenarios such as Lidar point cloud densification. The model outperforms existing PCI methods on the most popular benchmark datasets, DHB and NL-Drive, showcasing scalability to tasks like auto-labeling and point cloud densification. Strengths: - The paper is well written and well-organized, a good review of related works supports the motivation, the experiment is well designed, and the results and additional information are satisfied. - Although I’m not an expert in developing such algorithms in detail, as a user from the application side, I can understand that using 4D Gaussian deformation fields and temporal radial basis function Gaussian residual modules to capture complex spatiotemporal dynamics is a novel approach. Weaknesses: - There are no details of the experiment platform or discussion of the computational efficiency of the proposed method. - The potential of NeuroGauss4D-PCI seems significant. But as we all know, NeuralPCI was said to be the best model for PCI until now. A more detailed comparison with this model could be crucial in providing valuable insights and strengthening the paper's contribution to the field. Technical Quality: 4 Clarity: 3 Questions for Authors: I don’t have additional detailed questions for this paper, as I may not be good enough to understand all the details of the proposed algorithm. Confidence: 3 Soundness: 4 Presentation: 3 Contribution: 3 Limitations: I wonder if it is convincing that all are testing their work on only two open datasets used in this paper. Flag For Ethics Review: ['No ethics review needed.'] Rating: 8 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We sincerely appreciate your positive feedback on our paper's organization, literature review, experimental design, and results. Your recognition of our novel approach using 4D Gaussian deformation fields and temporal radial basis function Gaussian residual modules to capture complex spatiotemporal dynamics is particularly encouraging. We are grateful for your detailed comments and will address each of your concerns in the following responses. ## Q1: Discussion on computational efficiency A1: - Experimental Platform: Our algorithm was tested on a platform equipped with an NVIDIA RTX 3090 GPU. - Computational Efficiency: We recorded detailed computational costs for different point cloud sizes: Table 1: Time consumption statistics (in seconds) \| Processing Step \| 1024 points \| 8192 points \| \|:-------------------------------------------\|------------:\|------------:\| \| Single Frame \| \| \| \| Time Encoding \| 0.0003 \| 0.0003 \| \| 4D Neural Field \| 0.0007 \| 0.0008 \| \| RBF-GR+4DGD \| 0.0041 \| 0.0034 \| \| LG-fusion \| 0.0004 \| 0.0028 \| \| Prediction Head \| 0.0005 \| 0.0023 \| \| Loss Calculation \| 0.0048 \| 0.0022 \| \| Total (Single Frame) \| 0.0108 \| 0.0118 \| \| Sequence (4 Frames) \| \| \| \| Loss Backpropagation + Optimizer Update \| 0.0567 \| 0.0590 \| \| Total (One Sequence Iteration) \| 0.0753 \| 0.1572 \| - Efficiency Analysis 1. Single frame processing: Only 0.0118 seconds for 8192 points, demonstrating high efficiency. 2. Sequence processing: 0.1572 seconds for a 4-frame sequence (8192 points/frame), or about 157.2 seconds for 1000 iterations. 3. Preprocessing optimization: Iterative Gaussian Cloud Soft Clustering module moved to preprocessing stage, running once per sequence (~1 second) instead of every iteration. 4. Weight freezing: DGCNN and SelfAttention network weights frozen to reduce updatable parameters. ## Q2: Detailed comparison with NeuralPCI. A2: We appreciate the reviewer's valuable feedback and recognition of NeuroGauss4D-PCI's potential. As requested, we have expanded our comparison with NeuralPCI: 1. Visual comparison in Figures 1, 6 and 7 in the original paper. 2. Quantitative comparisons across various point cloud densities, frame intervals, datasets, and metrics are presented in Tables 1 and 2, and Figure 1 in the original paper. Key advantages of NeuroGauss4D-PCI over NeuralPCI include: 1. Structured Representation: Our iterative Gaussian soft clustering module provides a structured temporal point cloud representation, better capturing geometric features and spatio-temporal dynamics. NeuralPCI, in contrast, directly inputs spatial and temporal coordinates to an MLP. 2. Spatio-temporal Modeling: Our Temporal RBF-GR module and 4D Gaussian deformation fields enable more precise modeling of complex non-rigid deformations and non-linear trajectories, particularly beneficial for long time spans and complex dynamic scenes. 3. Feature Fusion: Our fast latent-geometry fusion module adaptively combines implicit features from neural fields with explicit geometric features from Gaussian deformation fields, enhancing spatio-temporal correlation modeling. These improvements collectively contribute to NeuroGauss4D-PCI's superior performance in various challenging scenarios. ## Q3: Convincingness of testing on only two open datasets. A3: Thank you for raising this important question. I understand your concerns about the potential limitations of testing only on two open datasets, as well as the reliability of the experimental design and results of all the work. 1. Dataset Representativeness: - DHB (object-level) and NL-Drive (large-scale autonomous driving) represent two major application scenarios in point cloud interpolation. - NL-Drive combines KITTI, Argoverse, and Nuscenes datasets, offering diverse, real-world autonomous driving environments. - These datasets cover a wide range from fine-grained object deformations to complex, large-scale scenes. 2. Fair Comparison: - We benchmark against state-of-the-art methods including IDEA-Net, PointINet, NSFP, PV-RAFT, NeuralPCI, and 3DSFLabelling. - We use results provided by Zheng et al. in the NeuralPCI paper, validating their experimental outcomes for consistency. 3. Open-source Verification: - All compared algorithms are open-sourced, enhancing result credibility and reproducibility. - We conducted independent experiments using NSFP and 3DSFLabelling's open-source code on the test set, further ensuring fair and accurate comparisons. 4. Extensibility Validation: - We demonstrate NeuroGauss4D-PCI's potential in related tasks such as auto-labeling and point cloud upsampling, showcasing its versatility and adaptability. This comprehensive approach aims to establish the reliability and broad applicability of our method across diverse scenarios in point cloud interpolation. --- Rebuttal Comment 1.1: Comment: Thanks for the detailed response and the additional experiment. I am satisfied with the current version. and my recommendation will not change from the previous one. --- Reply to Comment 1.1.1: Title: Response to Reviewer ddrR Comment: Thank you very much for your valuable feedback and recognition of our work. We will do our best to improve the quality of our work based on your suggestions, ensuring that the final version meets your expectations. Finally, thank you again for your time and insights.	Summary: The paper introduces NeuroGauss4D-PCI, a model designed to address the challenges of point cloud interpolation (PCI) by using Gaussian soft clustering and a 4D neural field to model complex non-rigid deformations in dynamic scenes. The model excels in capturing spatial and temporal dynamics from sparse data, showing superior performance on object-level and large-scale datasets. Strengths: It is interesting to utilize Gaussian clustering and 4D neural fields for solving PCI problems. Weaknesses: 1. The color scheme of the figures in the article is very poor, making many details difficult to discern. 2. Point cloud interpolation is a relatively niche direction in point cloud analysis. The author should more clearly emphasize the significance of studying this issue. 3. The most related work reported in this work might be the CVPR 23 paper Neuralpci. Does that mean no more recent related works? Technical Quality: 3 Clarity: 1 Questions for Authors: 1. How does NeuroGauss4D-PCI ensure robustness against varied data sparsity in real-world scenarios? 2. Can the model handle rapidly changing dynamic scenes, such as explosions or quick animal movements? 3. What are the computational costs associated with training and inference, and how do they compare to simpler models? 4. How does the model perform under conditions of significant occlusion or sensor noise? Confidence: 4 Soundness: 3 Presentation: 1 Contribution: 2 Limitations: 1. The complex interactions between Gaussian fields and neural networks may hinder understanding and tuning of the model. 2. The high computational demand may limit deployment in time-sensitive applications. Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We sincerely thank the reviewer for their insightful questions and provide detailed responses below ## Q1: Poor color scheme. A1: We commit to redesigning the color scheme in our main text to improve visibility and readability. For your reference, we've implemented this new color scheme in our PDF response. ## Q2: Emphasize the significance of research direction. A2: We will reemphasize the research significance of this task in our paper: 1. Bridges the gap between current sensor limitations and high-frequency data demands in autonomous driving and AR. 2. Improves object tracking and motion prediction in dynamic environments. 3. Facilitates world model construction and AI-generated 3D content. 4. Supports multi-sensor synchronization, auto-labeling, and point cloud densification. Our supplementary materials demonstrate these applications, highlighting PCI's versatility and potential across various 3D vision tasks. ## Q3: Latest relevant works. A3: NeuralPCI (CVPR 2023) is the most recent specialized study on point cloud interpolation in our citations. While 3DSFLabelling (CVPR 2024) addresses related tasks, it focuses on 3D scene flow rather than sequence interpolation. Recent applications of point cloud interpolation include skeletal animation generation (PC-MRL, arXiv 2024) and optimal transport evaluation (CL+SW2, WACV 2024). ## Q4: Ensuring robustness to different data sparsities. A4: NeuroGauss4D-PCI achieves robust performance across data sparsity levels due to: 1. Adaptive Representation: Gaussian soft clustering extracts meaningful features even from sparse data. 2. Flexible Temporal Modeling: RBF-GR module interpolates smoothly between frames, regardless of point density. 3. Multi-scale Capture: 4D Gaussian fields model both global structure and local details, adapting to varying sparsity. These components synergistically handle different data densities. Our algorithm's robustness across diverse point cloud densities is demonstrated by these results: \| Point Cloud Size \| NSFP \| PV-RAFT \| PointINet \| NeuralPCI \| 3DSFLabelling \| Ours† \| \|:----------------:\|:----:\|:-------:\|:---------:\|:---------:\|:------------:\|:----:\| \| 1024 \| 6.81 \| 6.92 \| 5.64 \| 5.04 \| 6.19 \| 4.01 \| \| 2048 \| 4.01 \| 3.98 \| 3.10 \| 2.59 \| 3.41 \| 2.00 \| \| 4096 \| 2.60 \| 2.51 \| 1.70 \| 1.38 \| 1.80 \| 0.99 \| \| 8192 \| 1.80 \| 1.65 \| 1.10 \| 0.80 \| 1.19 \| 0.72 \| \| 16384 \| 1.30 \| 1.21 \| 0.72 \| 0.48 \| 0.92 \| 0.38 \| ## Q5: Handling rapidly changing dynamic scenes？ A5: In our response PDF (Fig. 2), we present visualizations of frame interpolation predictions for scenarios involving long intervals and rapid motion patterns. Our predicted results demonstrate strong alignment with ground truth. ## Q6: Training and inference costs comparison. A6: Our model's computation costs for different point cloud sizes are detailed below: \| Processing Step \| 1024 points \| 8192 points \| \|:-------------------------------------------\|------------:\|------------:\| \| Single Frame \| \| \| \| Time Encoding \| 0.0003 \| 0.0003 \| \| 4D Neural Field \| 0.0007 \| 0.0008 \| \| RBF-GR+4DGD \| 0.0041 \| 0.0034 \| \| Fast LG-fusion \| 0.0004 \| 0.0028 \| \| Prediction Head \| 0.0005 \| 0.0023 \| \| Loss Calculation \| 0.0048 \| 0.0022 \| \| Total (Single Frame) \| 0.0108 \| 0.0118 \| \| Sequence (4 Frames) \| \| \| \| Loss Backpropagation + Optimizer Update \| 0.0567 \| 0.0590 \| \| Total (One Sequence Iteration) \| 0.0753 \| 0.1572 \| Note: The Iterative Gaussian Cloud Soft Clustering module runs only once in the preprocessing stage, taking about 0.2248 seconds, and is not included in the table. For 8192 points, our model takes 0.1572 seconds per iteration, or about 157.2 seconds for 1000 iterations. Simpler models like NeuralPCI take about 60 seconds for 1000 iterations, while more complex models like 3DLSFLabelling take over 10 minutes for a single point cloud pair. Our algorithm's time consumption is within an acceptable range for optimization-based methods designed for accuracy. ## Q7: Performance under occlusion or sensor noise? A7: Figures 2 and 3 in our response PDF demonstrate our model's visual results under significant occlusion and various noise conditions, respectively. The results show that our model maintains acceptable accuracy even in these challenging scenarios. ## Q8: Complex interactions between modules. A8: Our experiments demonstrate that integrating Gaussian fields with neural network features consistently yields performance improvements, regardless of the specific fusion method employed: \| Method \| DHB (×10⁻³) \| NL-Drive \| \|:--------------\|:----------------------\|:-----------------------\| \| \| CD ↓ \| EMD ↓ \| CD ↓ \| EMD ↓ \| \| Baseline \| 0.49 \| 2.99 \| 0.80 \| 98.03 \| \| LG-Cat \| 0.42 \| 2.69 \| 0.79 \| 97.36 \| \| Fast-LG-Fusion\| 0.44 \| 2.48 \| 0.78 \| 95.95 \| The combination provides: Gaussian fields capture spatial structure and global information, while neural networks learn complex non-linear mappings and local features. ## Q9: High computational cost limiting real-time applications. A9: As shown in the runtime analysis in Answer 6, our algorithm's computational cost falls within an acceptable range. Our approach, similar to NeRF, is a coordinate-based, per-scene fitting method primarily designed for offline optimization of individual scenes. --- Rebuttal Comment 1.1: Comment: Dear Reviewer Z54i, We greatly appreciate your time and expertise in reviewing our work. Your insightful feedback is invaluable for improving our paper. In our rebuttal, we have: - Addressed all your concerns - Improved figure clarity - Emphasized research significance - Highlighted recent related work Our response demonstrates NeuroGauss4D-PCI's effectiveness across various scenarios through: - Visualizations - Tables - Detailed computational cost analysis With only about 20 hours left in the author-reviewer discussion period, we kindly request your feedback. Your thoughts on any remaining concerns are crucial for our paper's improvement. Thank you sincerely for your time and effort. Best regards, The Authors of Paper #7315	Summary: This paper proposes a novel method for point cloud interpolation, which aims to address complex non-rigid scenarios. It turns point clouds into 3D Gaussians via iterative soft clustering, and then utilizes several 4D spatio-temporal modules to fuse latent features with neural fields. Specifically, this paper employs the temporal radial basis function for Gaussian interpolation, the graph convolutional network for feature extraction and the attention module for feature fusion. Comprehensive experiments demonstrate the leading performance across indoor and outdoor datasets, along with a thorough ablation study for the proposed components. Strengths: - It is the first to introduce 3D Gaussians for point cloud interpolation, which shows great performance in modeling non-rigid deformations and non-linear trajectories. - The proposed 4D Gaussian deformation fields leverage temporal graph convolutions for spatio-temporal feature aggregation. - The experiments are conducted on multiple datasets, including indoors and outdoors. It is also compared on the scene flow benchmark to demonstrate its effectiveness. And the ablation study is comprehensive for each proposed module. Weaknesses: - The proposed method is overly complex and redundant, which shows a trivial combination of existing modules and limited contribution. Moreover, the proposed modules lack strong motivation and necessity, and the interpretability of the intermediate features is difficult to clarify. - According to the Supplementary Material, nearly two hours of optimization time is required for just four frames of input, which is much more than the previous method. The problem may lie in the design of proposed method, which is not suitable for an optimization-based approach, but rather a learning-based approach. For example, some feature extraction or fusion may not be meaningful or necessary for a single sample fitting. Technical Quality: 3 Clarity: 3 Questions for Authors: - This paper may not be related to the work of 3DGS series. It just uses 3D Gaussians but has nothing to do with "splatting". Also, the proposed method is more similar to the super-point concept or the Gaussian Mixture Model in clustering and should be discussed. - Does DGCNN use pre-trained models or is it trained from scratch? Retraining DGCNN for each optimization can be time consuming and may not be meaningful for fitting individual samples. - In the Temporal RBF-GR Module, the 3D Gaussian needs to be interpolated, so how to ensure the correspondence? Also, is it feasible to visualize the Residual Gaussian to prove its reasonableness and validity? - Quantitative comparisons of efficiency with other methods. It would be better to analyze the training/inference time for each module. In addition, can the proposed method be extended to more frames or more points of input, and what is the corresponding efficiency? typo: - L136 - "Table4.2"? - missing arrows of ACC_S and ACC_R in Table 3 Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: - The entire framework can be further simplified and improve its efficiency. - Additional supervision or constraints can be introduced for 3D Gaussians rather than only points. - Use more challenging datasets beyond DHB. In Table 1, the results for both Squat and Swing sequences are 0.00, which may need to retain higher precision or change to other datasets. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your insightful critique. ## Q1: Algorithm complexity and limited contributions A1: Due to space constraints, we kindly refer you to Reviewer xq5Q's Q1 for the explanation on model complexity. We apologize for any inconvenience. Design Motivation: - Gaussian Soft Clustering: Structures multiple unordered point clouds, improving upon methods like NeuralPCI - Temporal RBF-GR Module: Overcomes linear motion assumptions of methods such as PointINet - 4D Gaussian Deformation Fields: Captures complex motion patterns over extended time spans, surpassing scene flow-based approaches Key Innovations - 4D Gaussian representation for spatiotemporal features - Temporal RBF-GR for smooth parameter interpolation - 4D Gaussian Graph Convolutional Deformable module for spatiotemporal learning Improved Interpretability - Uses explicit geometric principles: Gaussian means (μ), covariance matrices (Σ), deformation fields ## Q2: Long optimization time and suitability for optimization-based approach A2: Following your Q4 suggestion, we've significantly reduced the algorithm's runtime. Our core components suit optimization methods because: Temporal RBF-GR, 4D Gaussian Deformation: Optimize meaningful mathematical parameters. 4D Neural Field: Expresses highly complex non-linear functions through optimization. ## Q3: Relationship to 3D Gaussians, splatting, and clustering A3: Relationship to 3DGS: - Uses 3D Gaussians, inspired by 3DGS concepts - Doesn't employ "splatting" techniques - Will reduce 3DGS discussion in the paper Our method uses EM-like clustering and GMM concepts, enhanced by DGCNN and self-attention for Gaussian deformation, focusing on point cloud interpolation. Detailed relationships will be clarified in the main text. ## Q4: DGCNN training approach A4: - Moved Iterative Gaussian Cloud Soft Clustering to preprocessing stage - Froze weights of DGCNN and SelfAttention networks - Networks now act as fixed feature extractors Performance Impact - Model with frozen weights performs comparably to original model \| Methods \| Longdress \| \| Loot \| \| Red&Black \| \| Soldier \| \| \|-----------------------\|-----------\|------\|--------\|------\|-----------\|------\|---------\|------\| \| \| CD \| EMD \| CD \| EMD \| CD \| EMD \| CD \| EMD \| \| NeuralPCI \| 0.70 \| 4.36 \| 0.61 \| 4.76 \| 0.67 \| 4.79 \| 0.59 \| 4.63 \| \| Ours \| 0.68 \| 3.69 \| 0.59 \| 4.12 \| 0.65 \| 4.20 \| 0.57 \| 4.14 \| \| Ours (Freeze weight) \| 0.69 \| 3.92 \| 0.59 \| 4.03 \| 0.66 \| 4.51 \| 0.57 \| 4.13 \| Efficiency Gains - Processing time for 4-frame sequence (8192 points) reduced to 0.1572 seconds. - Iterative Gaussian Cloud Soft Clustering now takes about 0.2248 seconds in preprocessing For detailed timing of individual model components, please refer to our response to Reviewer xq5Q's Q9. ## Q5: 3D Gaussian correspondence during interpolation, and residual Gaussian visualization. A5: Reason: 1. Each Gaussian is uniquely identified and tracked across all timesteps. 2. Gaussian parameters evolve smoothly over time via RBF interpolation. 3. Self-attention mechanism ensures coherent global deformation. Residual Gaussian visualization provided in Figure 1 of response PDF. ## Q6: Model efficiency analysis for more frames/points, and writing corrections A6: 1. Detailed timing for each module provided in reviewer xq5Q's A9 for 1024 and 8192 points. 2. For optimization time comparisons across models with varying frame counts and point cloud sizes: \| Method \| 4 Frames \| \| \| 6 Frames \| \| \| 8 Frames \| \| \| \|:--------------\|:--------:\|:-------:\|:-------:\|:--------:\|:-------:\|:-------:\|:--------:\|:-------:\|:-------:\| \| \| 1024 pts \| 8192 pts\| 16384 pts\| 1024 pts \| 8192 pts\| 16384 pts\| 1024 pts \| 8192 pts\| 16384 pts\| \| 3DSFLabelling \| 0.1324 \| 0.3620 \| 0.7500 \| 0.1986 \| 0.5430 \| 1.1250 \| 0.2648 \| 0.7240 \| 1.5000 \| \| NeuralPC \| 0.0447 \| 0.0861 \| 0.1924 \| 0.0671 \| 0.1292 \| 0.2886 \| 0.0894 \| 0.1722 \| 0.3848 \| \| Ours \| 0.0753 \| 0.1572 \| 0.3948 \| 0.1130 \| 0.2358 \| 0.5922 \| 0.1506 \| 0.3144 \| 0.7896 \| The time consumption of our algorithm is within a reasonable range. 3. Writing corrections: "Table 4.2" reference on line 136 and missing arrows for ACC_S and ACC_R in Table 3. ## Q7: Framework simplification for improved efficiency A7: Framework simplified as described in A4, significantly improving efficiency. ## Q8: Additional supervision for 3D Gaussian distributions A9: Explored two additional constraints: Gaussian Distribution Consistency Constraint: Similar to the Smoothness Loss in the paper, we enforced continuity and consistency between Gaussian distributions of adjacent time steps. Local Anisotropy Constraint: We quantified the similarity of local directional and structural features by comparing covariance matrices of corresponding local regions in target and predicted point clouds. Results: \| Constraint \| Dataset \| CD \| EMD \| \|------------\|---------\|----:\|----:\| \| Baseline \| DHB \| 0.44 \| 2.48 \| \| \| NL-Drive \| 0.78 \| 95.95 \| \| Gaussian Consistency \| DHB \| 0.43 \| 2.53 \| \| \| NL-Drive \| 0.79 \| 95.06 \| \| Local Anisotropy \| DHB \| 0.44 \| 2.39 \| \| \| NL-Drive \| 0.79 \| 93.22 \| Precision remains nearly constant, but at the cost of increased computation time. ## Q9: Evaluation on more challenging datasets A10: 1. Evaluated on NL Drive dataset (KITTI, Argoverse, Nuscenes) in Table 2 of paper. 2. Additional testing on Waymo dataset: \| Method \| CD \| EMD \| \|----------------\|-----:\|------:\| \| 3DSFLabelling \| 0.72 \| 83.07 \| \| NeuralPC \| 0.51 \| 60.94 \| \| Ours \| 0.48 \| 50.71 \| These results further validate our model's effectiveness in complex, real-world autonomous driving scenarios. --- Rebuttal Comment 1.1: Comment: Thanks for your efforts during the rebuttal, which addressed most of my concerns. For the efficiency improvements that make a big difference from the original version, I hope that the authors will clearly modify the relevant content in the final version and include as much as possible the additional issues mentioned in the review and the corresponding experiments. Based on this, I would keep my positive rating.	Rebuttal 1: Rebuttal: We sincerely thank the Area Chair for their time and effort in handling our paper, and all reviewers for their detailed and valuable suggestions, which are crucial for improving our work. The reviewers have positively acknowledged our method's novelty, impact, accuracy, and potential, as highlighted below: Our proposed methodology presents a novel approach to addressing the Point Cloud Interpolation (PCI) challenge, introducing 3D Gaussian representation for PCI (Reviewer ZfCH) and innovatively combining Gaussian clustering with 4D neural fields (Reviewer Z54i). The use of 4D Gaussian deformation fields and temporal radial basis function Gaussian residual modules is noted as an innovative method for capturing complex spatiotemporal dynamics (Reviewer ddrR). The method demonstrates excellent performance in non-rigid deformation and non-linear trajectory modeling (Reviewer ZfCH). The experimental design is considered comprehensive and reasonable, including evaluation on multiple indoor and outdoor datasets (Reviewers ZfCH, 2Dkp) and detailed ablation studies (Reviewers ZfCH, 2Dkp). Results show our method outperforming existing approaches on standard evaluation metrics (Reviewers xq5Q, 2Dkp). Additionally, the paper's organization, writing quality (Reviewers ddrR, 2Dkp), and review of related work supporting the research motivation (Reviewer ddrR) are commended. After careful analysis of all comments, the main issues can be summarized as: 1. Model structure complexity 2. Algorithmic efficiency of components 3. Model's adaptability to varying frame numbers and point cloud densities 4. Latest PCI research and its significance 5. Performance in complex scenarios (noise, rapid motion, occlusion) 6. Writing errors, structural clarity, and figure readability 7. Performance on challenging datasets and impact of outliers We have meticulously revised the manuscript based on these valuable suggestions. Due to space constraints, we've provided concise responses here, with detailed illustrations and experimental results in the reviewer-specific replies. Brief responses to the main issues: 1. While our model comprises multiple components, each addresses specific PCI challenges. We've clarified component relationships and demonstrated their effectiveness through ablation studies. 2. We provide detailed timing statistics for each component across various point cloud sizes. 3. Our model shows robust performance across different point cloud densities (1024 to 16384 points) and frame intervals, with comparative results demonstrating superior performance in various scenarios. 4. We've re-explained the latest PCI research and its specific significance. 5. Visualizations in our response demonstrate effective interpolation under occlusion, noise, and rapid motion conditions, maintaining good alignment with ground truth. 6. We will address all mentioned and potential writing and presentation issues, improve figure clarity, and resolve terminology inconsistencies to enhance overall readability and comprehension. 7. We've tested on challenging datasets like Waymo and provided comparative results. Outlier removal benefits all methods, with our approach showing the most significant improvements due to its Gaussian representation and temporal modeling capabilities. We look forward to engaging in further discussions with you over the next few days. We are eager to address any remaining concerns you may have about our paper and are committed to providing comprehensive clarifications to ensure the highest quality of our research. Once again, we extend our sincere gratitude to the Area Chair and all reviewers for their invaluable input and dedication! Pdf: /pdf/e91054a61e18f1698389489e53b7d107ff7a439a.pdf	NeurIPS_2024_submissions_huggingface	2,024	Summary: This paper proposes a method, NeuroGauss4D, to tackle the problem of 4d point cloud interpolation. NeuroGauss4D consists of the following 5 components: 1. "Iterative Gaussian Soft Clustering": a module to encode the scene to Gaussian representation with DGCNN features (map: X, Y, Z, T -> Gaussians(Mu, Cov, Feat)). 2. "4D Neural Field": a neural field with Fourier features and MLP to capture spatio-temporal features in latent space (map: X, Y, Z, T -> latent). 3. "Temporal RGB-GR": a module with temporal radial basis functions to interpolate Gaussian parameters in continuous time (map: Mu, Cov, Feat, T -> ΔMu, ΔCov, ΔFeat, ΔT). 4. "4D Gaussian Deformation Field": a module that take Gaussian parameters (Mu, Cov, Feat) and the latent features as input to predict the motion and feature deformation field (map: Mu, Cov, Feat, T -> deformation field). 5. "Fast-LG-Fusion": an attention mechanism that fuses the latent features (FL) and the geometric features (FG, from the deformation field) to predict the point cloud at the target time step (map: FL, FG, T -> point cloud). Strengths: 1. This method shows the application of dynamic Gaussian representation to the problem of 4D point cloud interpolation. 2. This method outperforms previous methods on the set of evaluations provide by the author. Weaknesses: 1. This method shows the application of dynamic Gaussian representation to the problem of 4D point cloud interpolation, which is a good idea. However, the execution of the idea seems to make the method overly complex. NeuroGauss4D-PCI's pipeline contains 5 different components, where a mixture of representations are used. Besides more hand-tuning for hyperparameters and longer training time, this complexity could make it hard to interpret the fundamental principles and the key components behind the full model. 2. It seems that the method is not very efficient. For example, the "Iterable Gaussian Soft Clustering" procedure shown in Algorithm 1 is only capable of taking one timestamp of point cloud (N, 3) as input, which means that this has to be done for each timestamp of the point cloud sequence. 3. Similar to the point above, the method might be limited on the size of the point cloud sequence that it can handle. For example, line 218 says "we sample the input points to 1024 for object-level scenes and 8192 for autonomous driving scenes". A point cloud of 1024 points in autonomous driving scenes is very small, which could limit the method's applicability to real-world scenarios. The authors can provide more information on how the method will perform when we have a larger point cloud size or a longer sequence of point clouds. 4. The author provides rich information about the method, which is good, but the clarity of the writing can be improved. Some of these are mentioned in the "Questions" section, and it would be nice to include them in future versions of the paper. There are other inconsistencies in the paper, for example: - Equation 1 uses 0-based indexing, but line 29 uses 1-based indexing. - Line 109 has an extra double quote. - Line 117 says "Iterative Gaussian Cloud Soft Clustering" but the Figure 2 uses "Iterable Gaussian ...". - Equations shall be written as part of a sentence, not as separate sentences (Eq. 5, 8, 9, 10, 11; and also Eq. 4). Technical Quality: 3 Clarity: 2 Questions for Authors: 1. It would be good to clarify in paper the exact meaning of "Frame-1, Frame-2, and Frame-3" in Table 2. Does it mean that we fit the scene with frame {0, 4, 8, 12, ...}, and then we evaluate on frame {1, 2, 3, 5, 6, 7, 9, 10, 11, ...}, and we call frame {1, 5, 9, ...} as Frame-1, frame {2, 6, 10, ...} as Frame-2, and frame {3, 7, 11, ...} as Frame-3? 2. In Table 5, when we say "4 frames of point clouds sampled at regular 3-frame intervals", does it mean that for each scene, we only train on 4 frames {0, 4, 8, 12} and we evaluate on 9 frames {1, 2, 3, 5, 6, 7, 9, 10, 11}? If this is the case, why do we only train on these 4 frames but not fit the full point cloud sequence of the scene in the raw dataset? 3. In line 456, when we say "initial frame at time step 0 and the final frame at time step 1", what do the "0" and "1" refer to? For example, in equation 1, it is clear that there can be time steps larger than 1, e.g. time step 4, 8, etc. Is the "0" and "1" in line 456 referring to some form of normalized time step? So, what exactly is the time step gap (in seconds) between the training frame and evaluation frames? 4. From equation 1, it seems that the method only fits one model for one whole scene, which is good. Can you confirm this? 5. In line 476 we report the "average training time is ∼ 1.31 seconds per iteration". Per my understanding, this "iteration time" means the training iteration. It is not clear if the time includes "Iterative Gaussian Cloud Soft Clustering" (which has to be done for each time step), and other feature extraction steps. It would be more clear to give a high-level timing number, for example, could you report "how long does it take to fit a full of ~X training frames each containing ~Y number of points"? Confidence: 4 Soundness: 3 Presentation: 2 Contribution: 2 Limitations: Yes, the authors have discussed the above. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We appreciate your thorough review and valuable feedback. Here are our responses to your questions: ## Weaknesses ### Q1: Is the method overly complex with its 5 components? A1: Our method is designed for efficiency and effectiveness: 1. Parameter Efficiency: NeuroGauss4D-PCI uses only about 0.1 million parameters, significantly fewer than similar methods requiring millions. 2. Logical Pipeline: Our components form a clear sequence: a) Structure point clouds b) Model temporal evolution c) Capture fine details d) Fuse information 3. Component Breakdown: - Gaussian Soft Clustering: Organizes unstructured point clouds - Temporal RBF-GR Module: Enables smooth temporal interpolation - 4D Gaussian Deformation Field: Simulates long-term motion trends - 4D Neural Field: Captures high-frequency details - Fusion Module: Combines geometric and latent features 4. Benefits: - Improved Interpretability - Reduced Parameter Count Each component addresses specific challenges in point cloud interpolation. ### Q2: Is it inefficient that the algorithm must perform operations on each timestamp of the point cloud sequence? A2: NeuroGauss4D-PCI is designed for per-scene optimization, not real-time processing. - Processes single-frame point clouds sequentially - Accumulates loss across the entire sequence - Performs backpropagation and optimization after processing all frames Single-frame processing takes about 10ms. The majority of computation time is spent on backpropagation and parameter updates after processing the full sequence. Nevertheless, optimizing a large-scale LiDAR scene requires only 2-3 minutes. ### Q3: Can the method handle large point cloud sizes or sequences? A3: We use different point cloud sizes for distinct scenarios: - Object-level scenes: 1024 points. (Aligns with Idea-net) - Autonomous driving scenes: 8192 points. (Consistent with NeuralPCI) We also provide quantitative comparisons of different point cloud densities: Table 1: Quantitative comparison results on NLDrive dataset with different input point cloud densities. \| Point Cloud Size \| NSFP \| PV-RAFT \| PointINet \| NeuralPCI \| 3DSFLabelling \| Ours† \| \|:----------------:\|:----:\|:-------:\|:---------:\|:---------:\|:------------:\|:----:\| \| 1024 \| 6.81 \| 6.92 \| 5.64 \| 5.04 \| 6.19 \| 4.01 \| \| 2048 \| 4.01 \| 3.98 \| 3.10 \| 2.59 \| 3.41 \| 2.00 \| \| 4096 \| 2.60 \| 2.51 \| 1.70 \| 1.38 \| 1.80 \| 0.99 \| \| 8192 \| 1.80 \| 1.65 \| 1.10 \| 0.80 \| 1.19 \| 0.72 \| \| 16384 \| 1.30 \| 1.21 \| 0.72 \| 0.48 \| 0.92 \| 0.38 \| ### Q4: How will you improve writing clarity? A4: We will: - Unify to 0-based indexing - Remove punctuation errors - Use consistent terminology - Integrate equations into sentences ## Questions ### Q5: Clarify "Frame-1, Frame-2, and Frame-3" in Table 2. A5: We use frames {0, 4, 8, 12} as input and evaluate on frames {5, 6, 7}. ### Q6: Explain the training and evaluation process in Table 5. A6: We optimize on frames {0, 4, 8, 12} and evaluate on {5, 6, 7}. We also present experimental results for both shorter and longer frame intervals: Table 2: Comparison of CD errors (×10^-2^) for different methods across various time intervals \| Time Interval (frames) \| NSFP \| PV-RAFT \| PointINet \| IDEA-Net \| NeuralPCI \| 3DSFLabelling \| Ours \| \|:----------------------:\|:----:\|:-------:\|:---------:\|:--------:\|:---------:\|:-------------:\|:----:\| \| 1 \| 0.69 \| 0.78 \| 0.91 \| 1.01 \| 0.49 \| 0.69 \| 0.39 \| \| 2 \| 0.98 \| 0.86 \| 0.913 \| 1.02 \| 0.52 \| 0.73 \| 0.40 \| \| 3 \| 1.22 \| 0.90 \| 0.92 \| 1.03 \| 0.53 \| 0.89 \| 0.42 \| \| 4 \| 1.48 \| 1.03 \| 0.99 \| 1.09 \| 0.63 \| 1.03 \| 0.43 \| \| 5 \| 1.87 \| 1.30 \| 1.132 \| 1.192 \| 0.72 \| 1.12 \| 0.46 \| \| 6 \| 2.01 \| 1.38 \| 1.23 \| 1.32 \| 0.90 \| 1.30 \| 0.48 \| \| 7 \| 2.20 \| 1.502 \| 1.41 \| 1.48 \| 1.06 \| 1.48 \| 0.51 \| \| 8 \| 2.42 \| 1.83 \| 1.77 \| 1.50 \| 1.31 \| 1.80 \| 0.54 \| \| 9 \| 2.83 \| 2.02 \| 1.81 \| 1.76 \| 1.48 \| 1.99 \| 0.57 \| Our method shows the lowest CD error across all time intervals. ### Q7: Explain the time steps "0" and "1" in line 456. A7: We normalize all input times to 0-1 to handle different sequence lengths, simplify training, and enhance generalization. ### Q8: Does the method fit one model per scene? A8: Yes, NeuroGauss4D-PCI uses per-scene fitting, allowing high-quality interpolation at any time point after a 3-minute optimization. ### Q9: Can you provide detailed timing information? A9: Here's our time consumption breakdown: Table 3: Algorithm Time Consumption Statistics \| Processing Step \| 1024 points \| 8192 points \| \|:-------------------------------------------\|------------:\|------------:\| \| Single Frame \| \| \| \| Time Encoding \| 0.0003 \| 0.0003 \| \| 4D Neural Field \| 0.0007 \| 0.0008 \| \| RBF-GR+4DGD \| 0.0041 \| 0.0034 \| \| LG-fusion \| 0.0004 \| 0.0028 \| \| Prediction Head \| 0.0005 \| 0.0023 \| \| Loss Calculation \| 0.0048 \| 0.0022 \| \| Total (Single Frame) \| 0.0108 \| 0.0118 \| \| Sequence (4 Frames) \| \| \| \| Loss Backpropagation + Optimizer Update \| 0.0567 \| 0.0590 \| \| Total (One Sequence Iteration) \| 0.0753 \| 0.1572 \| Note: The Iterative Gaussian Cloud Soft Clustering module runs only once in the preprocessing stage, taking about 0.2248 seconds, and is not included in the table. The total time for one sequence iteration includes the processing time for 4 single frames plus additional sequence-level operations. --- Rebuttal 2: Comment: I thank the author for the rebuttal responses, where most of my concerns are covered. Score increase 4->5. --- Rebuttal Comment 2.1: Comment: Dear Reviewer xq5Q, Thank you for your consideration and the increased score. We appreciate your feedback and will incorporate your suggestions in our final paper. Best regards, Authors of Paper #7315	null	null	null	null	null	null
Efficient and Sharp Off-Policy Evaluation in Robust Markov Decision Processes	Accept (poster)	Summary: This paper proposes a statistical theory for off-policy evaluation given observational data from an unknown transition kernel of an original MDP, possibly under policies the same as or different from the target policy. This paper focuses on the situation of environment shift, i.e., the transition kernel of the MDPs at test time can shift from the original MDP to a certain extent. These transition kernels are assumed to be center around the observational transition kernel. This paper proposes new algorithms and sharp estimators for robust estimation of policy value. The proposed estimation method has several desired properties.. First, it is semiparametrically efficient, with a $\sqrt{n}$-rate of estimation even when certain nuisance functions are estimated at slow parametric rates. The estimator is also asymptotically normal which enables easy statistical inference. Even when the nuisance functions are estimated with bias, the estimator is still constant. Numerical simulations verify the efficiency and sharpness of the proposed estimator. Strengths: Significance: 1. This paper focuses on an important and challenging theoretical problem of policy evaluation under transition kernel shift. This is a very realistic and probably more common scenario compared to the classical OPE setting where only the policies shift. 2 This paper presents a credible statistical theory for policy evaluation under transition kernel shift and the existence of nuisance functions. The statistical analysis shows that strong statistical guarantee can be achieved for the proposed estimator. Quality: this paper has a good quality. 1. The paper has a solid theoretical analysis, with well specified definitions and theorems. Weaknesses: 1. This paper is purely theoretical and thus it is very hard to evaluate the practicability of the proposed estimation framework. The numerical simulation also only covers a very simplified synthetic environment. Thus it is unclear how useful or computationally efficient the proposed estimation framework really is. 2. I feel this paper is missing a discussion of the line of work on OPE under POMDP. It seems that the OPE on POMDP is naturally connected with the topic of this paper, though I am not very familiar with that line of work. Minor: 1. The notation of this paper is a bit heavy. For example, the plus-minus sign confused me for a while when I read about its meaning (“read twice”) at the bottom of page 3. But this is not a big issue and is sort of understandable given the complex framework of this paper. 2. This paper is a bit hard to read for readers unfamiliar with this topic. No example or demonstration of any kind is given. Technical Quality: 3 Clarity: 2 Questions for Authors: Please see weakness. Confidence: 3 Soundness: 3 Presentation: 2 Contribution: 2 Limitations: Yes. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Dear reviewer kuGv, thanks for acknowledging the importance of our problem and the strengths of our theoretical results. Please find our responses to your questions below: W1: "This paper is purely theoretical and thus it is very hard to evaluate the practicability of the proposed estimation framework. The numerical simulation also only covers a very simplified synthetic environment. Thus it is unclear how useful or computationally efficient the proposed estimation framework really is." Author's Response: Thank you for the feedback. We would like to offer the following clarifications about usefulness and computational efficiency of our framework: 1. While our paper is indeed theoretical, it builds upon the well-established marginal sensitivity model (MSM) framework, which has been practically validated in numerous prior studies (e.g. Kallus and Zhou 2021 "Minimax-Optimal Policy Learning under Unobserved Confounding", Bruns-Smith and Zhou 2023 "Robust Fitted-Q-Evaluation and Iteration under Sequentially Exogenous Unobserved Confounders", and Dorn and Guo 2021 "Sharp Sensitivity Analysis for Inverse Propensity Weighting via Quantile Balancing", and many more). Thus, we can be assured that the MSM framework is useful to the broader causal inference community. 2. Our experiments, though synthetic, serve as a crucial proof of concept. We deliberately designed a synthetic environment where the ground truth $V^-$ is known, allowing us to compute the true error and show that our method converges the fastest. 3. Regarding computational efficiency, our method is compatible with neural nets as demonstrated in our experiments. Hence, our method offers comparable computational efficiency to standard OPE methods such as doubly robust estimation. This scalability ensures that our approach remains practical for larger-scale applications. W2: "I feel this paper is missing a discussion of the line of work on OPE under POMDP. It seems that the OPE on POMDP is naturally connected with the topic of this paper, though I am not very familiar with that line of work." Author's Response: Thanks for bringing up OPE for POMDPs. Indeed, there are several relevant lines of work in this area, each making unverifiable assumptions to identify the confounded policy value: 1. Namkoong et al. (2020) assume confounding occurs at only one step; 2. Shi et al. (2022) require access to auxiliary mediators; 3. Bennett and Kallus (2023) utilize bridge functions from proximal causal inference. Our approach builds on the well-established Marginal Sensitivity Model (MSM) from Tan (2006) to bound policy value in the absence of assumptions that point-identify the value given observations. Our key contribution is providing statistically optimal (semiparametrically efficient) estimators for the sequential "RL" setting, whereas prior estimators for the MSM were limited to single-step scenarios. Some of this was discussed in our related works section (Sec 1.1). We will add more discussion to the camera-ready. W3: "The notation of this paper is a bit heavy. For example, the plus-minus sign confused me for a while when I read about its meaning (“read twice”) at the bottom of page 3. But this is not a big issue and is sort of understandable given the complex framework of this paper." Author's Response: Thanks for the feedback about plus-minus. To improve readability for the camera-ready, we will focus on the minus case only in the main text and dedicate an appendix section to the symmetric plus case. W4: "This paper is a bit hard to read for readers unfamiliar with this topic. No example or demonstration of any kind is given." Author's Response: We concur that the topic is quite technical and many concepts & notations from stats and RL are required to achieve the mathematical rigor consistent with past works addressing similar topics. To help with clarity, we will dedicate another appendix section to discuss examples, both further elaborating on our experiments, and how the MSM can be useful in real applications (e.g. as in Bruns-Smith and Zhou 2023). Thanks again for your helpful feedback. We hope we have addressed your concerns and please let us know if you have any additional questions. --- Rebuttal Comment 1.1: Comment: Thank you for your feedback. I will take all the responses into consideration during the discussion and decision session. In the paper revision, please make sure to (i) adding the above discussion in the paper revision to make the paper clearer and easier to read; (ii) adding results on real-world dataset, such as the health dataset mentioned in the rebuttal and perhaps other appropriate datasets. Best, reviewer	Summary: This paper studies the problem of evaluating a policy under best- and worst-case perturbations to a Markov decision process (MDP), given transition observations from the original MDP. The first contribution is the robust Q learing algorithm for CVaR problem, the second contribution is the estimation of robust visitation distribution in the function approximation setting and their complexity bounds. Strengths: The problem studies in this paper is of significant practical importance, which is to evaluate the worst/best performance over an uncertainty set. The authors designed algorithms and derived their complexity bounds, which are shown to be optimal. Weaknesses: - The authors seem to be using offline and off-policy interchangably, which is misleading and confusing. - One important challenge in offline reinforcement learning is due to partial coverage and distribution shift. However, this paper does not explicitly define the single-policy concentrability coefficient that measures the gap between the sampling distribution $\nu$ and the target policy $\pi$, and therefore did not consider this key challenge in the offline setting. - The notations are unnecessarily complicated, and many are used without being defined. For example, in algorithm 1 line 6, the hat on top of the expectation, and the subscript of the expectation is not clear. - There are many technical assumptions that remain unjustified. Please justify each of the assumptions, and provide examples when those assumptions can be satisfied, and how to verify those assumptions in practice. - The perturbation model in eq. (1) is unjustified. It could happen easily that $\Lambda(s,a)$ is zero or infinite for some $(s,a)$. The authors shall explain why this perturbation model is of interest, and why this model is superior over existing uncertainty set models, e.g., those defined by KL divergence, TV. Technical Quality: 3 Clarity: 1 Questions for Authors: - There are several other important papers on robust offline reinforcement learning that are missing in this paper, e.g., Double Pessimism is Provably Efficient for Distributionally Robust Offline Reinforcement Learning: Generic Algorithm and Robust Partial Coverage Jose Blanchet, Miao Lu, Tong Zhang, Han Zhong Distributionally Robust Model-Based Offline Reinforcement Learning with Near-Optimal Sample Complexity Laixi Shi, Yuejie Chi Comparison with existing robust offline RL is not clear in this paper. - The writing of this paper needs to be improved. Is Section 3 and Algorithm 1 only about CVaR? Confidence: 4 Soundness: 3 Presentation: 1 Contribution: 2 Limitations: na Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Dear reviewer ghkS, thanks for acknowledging the strengths of the theoretical results. Please find our responses to your questions below: W1: "The authors seem to be using offline and off-policy interchangably, which is misleading and confusing." Author's Response: We agree this may be confusing and will use "off-policy" consistently in revising since we focus only on evaluation. W2: "One important challenge in offline reinforcement learning is due to partial coverage and distribution shift. However, this paper does not explicitly define the single-policy concentrability coefficient that measures the gap between the sampling distribution $\nu$ and the target policy $\pi$, and therefore did not consider this key challenge in the offline setting." Author's Response: The concentrability coefficient is defined in Line 208, and it makes an appearance in our guarantee for robust FQE. Note that our concentrability coefficient differs from the one from standard OPE since the target policy's distribution is under the adversarial MDP. We will make this more apparent in the revision. We will also clarify how concentrability makes an appearance in the (efficient) variance our estimator achieves (namely, $\Sigma$ on Line 304). In particular, $\Sigma=\mathbb E[(\frac{\mathrm{d}d^{\pm,\infty}(s)}{\mathrm{d}\nu(s)})^2(\frac{\pi_{\mathrm t}(a\mid s)}{\nu(a\mid s)})^2(r(s,a)+\gamma \rho^\pm(s,a,s';v^\pm,\beta^\pm)-q^\pm(s,a))^2]$. That is, the amount of distribution shift (in the adversarial MDP) makes an explicit appearance in the (minimal) variance of robust evaluation. W3: "The notations are unnecessarily complicated, and many are used without being defined. For example, in algorithm 1 line 6, the hat on top of the expectation, and the subscript of the expectation is not clear." Author's Response: Thanks for catching, we use the \hat on top of $\mathbb{E}$ to denote empirical expectation (in this case, over the second split of $\mathcal{D}_i$). For the camera-ready, we will try to simplify and reduce notation (e.g. we will focus the main text on the - case, rather than presenting both -/+ cases together). However, we do want to concede that the nature of orthogonal ML and semiparametric statistics is inherently very technical and many concepts / notations are needed to achieve the mathematical rigor consistent with past works addressing similar topics. W4: "There are many technical assumptions that remain unjustified. Please justify each of the assumptions, and provide examples when those assumptions can be satisfied, and how to verify those assumptions in practice." Author's Response: We justify and discuss each of the assumptions right before / after they are stated. For example, Assumption 3.2 is discussed in lines 193-195; Assumption 3.3 in 199-200; Assumption 4.3 in Lines 254-255. We concede that these justifications are rather brief but we do note that our assumptions are standard and known in the OPE literature (Munos and Czepesvari 2008, Uehara et al. 2021). To improve readability, we will add more discussions about these assumptions for the camera-ready. W5: "The perturbation model in eq. (1) is unjustified. It could happen easily that $\Lambda(s,a)$ is zero or infinite for some $(s,a)$. The authors shall explain why this perturbation model is of interest, and why this model is superior over existing uncertainty set models, e.g., those defined by KL divergence, TV." Author's Response: Our perturbation model is a natural generalization of the celebrated Marginal Sensitivity Model (MSM; Tan 2006 [56]) from causal inference, which has been validated by many follow-up papers (e.g. Kallus and Zhou 2021 "Minimax-Optimal Policy Learning under Unobserved Confounding", Bruns-Smith and Zhou 2023 "Robust Fitted-Q-Evaluation and Iteration under Sequentially Exogenous Unobserved Confounders", and Dorn and Guo 2021 "Sharp Sensitivity Analysis for Inverse Propensity Weighting via Quantile Balancing", and many more). For example, the MSM importantly captures settings where the behavior policy and transition kernels may be perturbed by unobserved confounders, which is not captured by any those defined by KL or TV. Since the uncertainty set is a modeling choice there is no "superiority" of one over another, but the MSM does nicely capture possible unobserved selection effects. We elaborate on this point in Lines 84-93. Line 135 specifies $\Lambda(s,a)\in[1,\infty)$. Q1: "There are several other important papers on robust offline reinforcement learning that are missing in this paper" Author's Response: Thanks for pointing out these two papers. Both papers are for the task of robust offline policy learning (OPL, i.e. learning a robust policy), whereas we focus on the task of robust off-policy evaluation (OPE, i.e. evaluating a policy's performance under distribution shift). Both are important problems with their own challenges. In practice, even if one is using robust policy learning, robust OPE is still of paramount interest, as it allows policy makers to reliably assess the actual performance of the learned policy under environment shifts or confounding. We will certainly add more discussion about robust policy learning and cite the papers you mentioned. Q2: "Is Section 3 and Algorithm 1 only about CVaR?" Author's Response: Yes, they are for robust Bellman equations with $\lambda \mathbb{E}+(1-\lambda)\text{CVaR}$. Indeed, one of our key insights is that the confounding-robust uncertainty set of Eq (1) can be equivalently expressed by the above robust Bellman equation, leading to tractable solutions in Sec 3 and Alg 1. We highlight that our approach can be easily extended to deal with other convex risk measures such as entropic risk or mean-variance (Markowitz), which we leave for future work. Thanks again for your helpful feedback. We hope we have addressed your concerns and please let us know if you have any additional questions. --- Rebuttal Comment 1.1: Comment: Thank you for the detailed response. W1 addressed W2 Addressed W3 not clear from the rebuttal W4 the reviewer would like to see why those assumptions are reasonable assumptions and how can they be satisfied in practice. W5 why it cannot be zero or infinity? Q1 and Q2 are addressed. --- Rebuttal 2: Comment: Dear Reviewer ghkS, Thanks for specifying your questions and for taking the time to consider our response. We will now answer them in order: W3 not clear from the rebuttal. To clarify, the $\hat{\mathbb{E}}_D$ notation (where $D$ is a dataset of points $x_1, \dots, x_n$) is defined as follows. For any function $f(x)$, we define $\hat{\mathbb{E}}_D[f(x)]=\frac{1}{n}\sum_if(x_i)$. In other words, $\hat{\mathbb{E}}_D$ is the empirical expectation for the dataset $D$. In the revision, we will directly use the $\frac{1}{n}\sum_if(x_i)$ in Alg 1, Line 6 to avoid using this notation. W4 the reviewer would like to see why those assumptions are reasonable assumptions and how can they be satisfied in practice. We are happy to provide clarifications on why these assumptions are reasonable and when they are satisfied. We now discuss each assumption in the paper. Assumption 3.2. This assumption posits that the quantile regression step succeeds in Alg 1. Quantile regression is a well-established problem with many classical algorithms for doing so: for example, Meinshausen and Ridgeway showed that random forests can learn conditional quantiles and this satisfies Assumption 3.2 where the $err_{QR}$ converges to zero as the number of datapoints grows to infinity (Theorem 1 of Meinshausen and Ridgeway 2006). More recently, there are also effective deep RL approaches that successfully use neural networks to learn quantiles, such as QR-DQN (Dabney et al 2018a) and IQN (Dabney et al 2018b). These approaches have obtained state-of-the-art results in Atari and can also be used to satisfy this assumption. Assumption 3.3. The Bellman completeness (BC) assumption posits that the $Q$ function class is closed under the (robust) Bellman operator. BC is a standard assumption for proving convergence in offline RL (Xie et al. 2021) and has also appeared in prior robust MDP works (Panaganti et al 2022; Bruns-Smith and Zhou 2023). In fact, BC is necessary for TD-style algorithms to succeed; without it, TD can diverge or converge to bad fixed points, e.g. Tsitsiklis and Van Roy, 1996 showed such a counterexample. Since our Algorithm 1 is based on TD, it is quite natural for our results to also rely on BC. Assumption 4.2. This is a mild regularity assumption that simply requires (i) the outputs of our function class to have bounded outputs and (ii) the thresholding function $V^\pm(s')-\beta^\pm(s,a)$ to be continuously distributed around the point $0$. We note that our algorithms do not crucially rely on (ii); if the distribution is discrete, we can use the discrete form for CVaR. Assumption 4.3. This assumption is a realizability assumption for importance-weighted estimators (i.e. Algorithm 2). The first part (i) simply requires that our density function class $\mathcal{W}$ to realize the density ratio and can be satisfied as we increase our function class's expressivity. The second part (ii) posits that our adversary function class $\mathcal{F}$ is rich enough to capture the error terms that take the form $\mathcal{J}'(w-w^\pm)$ for $w\in\mathcal{W}$. We note that both (i) and (ii) are monotone in the function class size and can be satisfied by making functions more expressive (i.e. increasing size of neural network). Regarding Assumption 4.3, we remark that our algorithms and theory are in fact robust to violations. In particular, we proved in Appendix I that the error from Algorithm 2 will depend gracefully on the approximation errors to Assumption 4.3 (as we formalized in Assumption I.1). In fact, this robustness also holds for the BC assumption (Assumption 3.3), i.e. our bounds will gracefully degrade with the robust Bellman error: $\epsilon_{be} = \min_{q\in\mathcal{Q}}\max_{q'\in\mathcal{Q}}\\|\\|q-\mathcal{T}^\pm_{rob}q'\\|\\|_2$. We will add the robustness-to-BC result in our revision. To conclude, our theory and algorithms are robust even when these assumptions fail to hold exactly. W5 why it ($\Lambda$) cannot be zero or infinity? Recall that $\Lambda$ is a parameter chosen by the user to capture the magnitude of perturbations $U$, which ought to satisfy $\Lambda^{-1}(s,a) \leq \frac{dU(s'\mid s,a)}{dP(s'\mid s,a)} \leq \Lambda(s,a)$. Since the definition implies $\Lambda^{-1}(s,a)\leq\Lambda(s,a)$, we have that $\Lambda(s,a)\geq 1$ so it cannot be $0$ and must be at least $1$. The infinity case is possible: if $\Lambda(s,a)=\infty$, then $U(s'\mid s,a)$ is allowed to be arbitrarily different from $P(s'\mid s,a)$, and our robust evaluation would evaluate the best- or worst-paths, i.e. what is the maximum or minimum possible cumulative reward. This setting was also studied by Du et al. 2023. Thank you again so much for the detailed feedback and for taking our responses into consideration. Please let us know if you have more questions and we will do our best to answer them promptly. Thank you again for your valuable efforts in reviewing our paper. Title: Response to Reviewer ghkS --- Rebuttal 3: Title: More Citations Comment: Citations [1] Du, Yihan, Siwei Wang, and Longbo Huang. "Provably efficient risk-sensitive reinforcement learning: Iterated cvar and worst path." ICLR 2023. [2] Meinshausen, Nicolai, and Greg Ridgeway. "Quantile regression forests." Journal of machine learning research 7.6 (2006). [3] Dabney, Will, et al. "Distributional reinforcement learning with quantile regression." Proceedings of the AAAI conference on artificial intelligence. Vol. 32. No. 1. 2018a. [4] Dabney, Will, et al. "Implicit quantile networks for distributional reinforcement learning." International conference on machine learning. PMLR, 2018b. [5] Panaganti, Kishan, et al. "Robust reinforcement learning using offline data." Advances in neural information processing systems 35 (2022): 32211-32224. [6] Tsitsiklis, John, and Benjamin Van Roy. "Analysis of temporal-diffference learning with function approximation." Advances in neural information processing systems 9 (1996). [7] David Bruns-Smith and Angela Zhou. Robust fitted-q-evaluation and iteration under sequentially exogenous unobserved confounders. arXiv preprint arXiv:2302.00662, 2023. [8] Xie, Tengyang, et al. "Bellman-consistent pessimism for offline reinforcement learning." Advances in neural information processing systems 34 (2021): 6683-6694. --- Rebuttal Comment 3.1: Comment: Dear reviewer, the open discussion period is nearing the end. We hope our responses addressed your concerns. If you feel that they have we would greatly appreciate if you update your score accordingly. If you still have questions let us know. We worked hard to be thorough while clear in our response and address all questions raised. Thank you again!	Summary: This paper studies off-policy evaluation problems in robust Markov decision processes, where the environment dynamics may change over time. The authors consider a perturbation model that modifies the transition probability up to a given multiplicative factor. They first propose two new algorithms for learning the Q-value function $Q$ and the density ratio function $w$. Then, they design a new policy value estimator based on the estimated nuisance parameters. The authors provide a theoretical analysis of the new algorithms and estimators, along with numerical experimental results to verify their effectiveness. Strengths: a. The studied problem of off-policy evaluation in robust MDPs is interesting and meaningful. b. The theoretical analysis is solid. The proposed $Q$-function estimation algorithm achieves a $\widetilde{\mathcal{O}}(n^{-1/2})$ rate for parametric classes. More importantly, the proposed orthogonal estimator in Section 5 has a second-order dependence on the estimation error of nuisance parameters. As a result, it only requires the rate of nuisance parameter estimation to be faster than $n^{-1/4}$ to achieve an $n^{-1/2}$ rate. c. The numerical results align with the theoretical analysis; the orthogonal estimator consistently achieves the best performance compared to the $Q$ estimator and $w$ estimator. Weaknesses: a. This paper considers a perturbation model where the ratio between the modified transition kernel and the nominal kernel is bounded by a sensitivity parameter. In Algorithms 1 and 2, the learner needs access to the parameter $\Lambda(s,a)$. However, it is unclear how to estimate $\Lambda(s,a)$ in real-world scenarios. Additionally, the authors claim that the perturbation model is more general and captures confounded settings. More detailed analysis and explanations are needed to support this claim. b. Algorithm 2 requires solving a minimax optimization problem, which is usually very time-consuming in practice. In the experiments, the authors use an iterative method as an approximation. Is there any theoretical analysis for that implementation? c. Additional experiments using real-world datasets would help to better demonstrate the practical applicability of the proposed algorithms. Minor: Redundant content in line 194 Technical Quality: 3 Clarity: 3 Questions for Authors: See weakness part. Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: N/A Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Dear reviewer QdT5, thank you for your review and positive feedback on our work. We appreciate your recognition of the problem's significance, our theoretical contributions, and the alignment of our numerical results with the theory. Motivation for perturbation model If the cause of the perturbation is unobserved confounding, a common approach to set $\Lambda(s,a)$ is to conduct an ablation study by withholding one feature of the state at a time. In a clinical setting, for example, smoking status or BMI could be withheld one by one, and the ratio in (1) calculated. A practitioner could then set $\Lambda(s,a)$ by assuming that an unobserved confounder could induce a shift in the transition kernel up to, say, twice the maximum $\Lambda(s,a)$ observed in the ablation study (see [1]). Another approach is to consider multiple $\Lambda(s,a)$ values until a specific condition (e.g., the lower bound of the value being less than $\alpha$, or less than 0 if $r \in [-1, 1]$). For instance, [2] studied the effect of smoking on lung cancer and found that unobserved confounding had to be nine times larger in smokers ($\Lambda = 9$) than in non-smokers to negate the measured negative effect of smoking. Since other features in the data had smaller $\Lambda$ values (ranging from 1 to 3), the conclusion was that there is at least some negative effect of smoking despite the observational dataset being affected by unobserved confounding. We will add this discussion to the final draft. Our perturbation model has a one-to-one correspondence to the MSM model in the confounded setting, which places a constraint on the ratio of confounded and unconfounded policies (rather than the transition kernels). Specifically, our perturbation model implies the policy MSM and therefore it subsumes the confounded setting. However, the reverse is only true for $A=2$. For $A>2$, a bound on the policy ratio imples only a loose bound on the ratio of transition probabilities, thus yielding non-sharp bounds for $A>2$. This discussion is included in the related literature section. Minimax optimization problem A couple of points regarding the hardness of the minimax optimization problem and proposed solution: 1. In general these kinds of minimax problems given by conditional moment conditions can be efficiently solved. For example, [4] show that an iterative procedure of solving a sequence of T least squares regression problems and cost-sensitive classification problems can guarantee a $log(T)/T$-approximate solution (which works via a reduction to no-regret learning, similar to the original theoretical analysis of boosting.) 2. The solution we used is somewhat similar to that mentioned above, although differs a little. It can be seen as a special case of [5] motivated by the observation of [6] that such OWGMM estimators are equivalent to minimax estimators. The sieve-based procedure of [5] has strong theoretical guarantees of consistency and semiparametric efficiency when the sieve is grown sufficiently fast (as the number of data points $n$ increases), and we augment this kind of estimator by adding extra functions to the sieve via a similar no-regret style procedure as in [4], by iteratively computing the OWGMM estimator and finding the worst-case adversary function. This augmentation does nothing to subtract from its existing theoretical guarantees, but we find is empirically very helpful. Furthermore, since we compute the worst-case adversary at each iteration, it gives a computational certificate of how close to min-max optimality each iterate is, which can make the procedure trustworthy in practice. In terms of computation, this algorithm just involves minimizing a convex loss function a fixed number of times, and so is computationally efficient. We will provide some discussion of this. Additional experiments For the final version of the manuscript, we will include results using real-world healthcare data. Specifically, we will demonstrate how our method extends to complex, real=world scenarios via a case study using MIMIC-III data for off-policy evaluation of learned policies for the management of sepsis in the ICU with fluids and vasopressors (see [3] for example). [1] Hsu, J.Y. and Small, D.S., 2013. Calibrating sensitivity analyses to observed covariates in observational studies. Biometrics, 69(4), pp.803-811. [2] Cornfield, J., Haenszel, W., Hammond, E.C., Lilienfeld, A.M., Shimkin, M.B. and Wynder, E.L., 1959. Smoking and lung cancer: recent evidence and a discussion of some questions. Journal of the National Cancer institute, 22(1), pp.173-203. [3] Killian, T.W., Zhang, H., Subramanian, J., Fatemi, M. and Ghassemi, M., 2020. An empirical study of representation learning for reinforcement learning in healthcare. arXiv preprint arXiv:2011.11235. [4] Dikkala, N., Lewis, G., Mackey, L., & Syrgkanis, V. (2020). Minimax estimation of conditional moment models. Advances in Neural Information Processing Systems, 33, 12248-12262. [5] Hansen, L. P. (1982). Large sample properties of generalized method of moments estimators. Econometrica: Journal of the econometric society, 1029-1054. [6] Bennett, A., & Kallus, N. (2023). The variational method of moments. Journal of the Royal Statistical Society Series B: Statistical Methodology, 85(3), 810-841. --- Rebuttal Comment 1.1: Comment: Thank you for the detailed response. I will maintain my positive score. However, I also suggest that the authors should make an effort to simplify the notation and enhance the readability of the paper.	Summary: This paper studies statistically-efficient robust/optimistic (e.g., worst- or best-case within the uncertainty set $\mathcal{U}$) off-policy evaluation with bounded Radon-Nikodym uncertainty sets centered around known nominal models. It proposes novel algorithms for computing robust/optimistic Q functions, and provides theoretical analysis for them. It further claims that the sharp and efficient estimators are optimal in the local-minimax sense, and provides preliminary experimental results to support the claim. Strengths: * The paper seems to include a wide collection of new theoretical results, with assumptions clearly stated and proofs attached. * The problem itself is simple, fundamental, and stated in an comprehensible way. Weaknesses: * The writing of this paper needs to be improved, at least for non-experts in this specific area. * Frankly speaking, I'm having a lot of trouble following the paper, or even understand the problems and the results. Though I have to admit that I major in CS and don't have a strong statistics background. * First and foremost, it doesn't seem like the $\pm$ superscript is doing any good here, except confusing the reader for the first few moments. If I were to write this paper, I would just sell the story of "robust OPE", and say a sentence or two on how to re-interpret it as a optimistic evaluation scheme (I do think negating rewards is easier to understand). * Some sentences are broken and not fully comprehensible (e.g., lines 193~195), some notations are left undefined before their first use (e.g., the $\frac{dU}{dP}$ notation, which I regard as Radon-Nikodym derivative), and some paragraphs are duplicated with subtle differences (e.g., Lemma 4.1 and G.1). * The literature review part (Section 1.1 and Appendix B) seems to be very incomplete, and some paragraphs seem irrelevant (e.g., lines 84~104). Since this is a paper on robust OPE, a more comprehensive review on existing works regarding robust MDPs and OPE methods is definitely needed, especially a comparison on the settings and the bounds. * As far as I'm concerned, the flow of the whole paper needs major revision. For example, it's unclear why we need to estimate $w^{\pm}$ in Section 4, until in the estimator for $V^{\pm}\_{d\_1}$ is proposed in Section 5. Another issue is that I don't fully get the point why we need a few more complex procedures to estimate $V^{\pm}\_{d\_1}$ after we've got the estimates for $Q^{\pm}$. Besides, the key results are not explained in plain English (e.g., given the sentences between lines 211 and 217, I still don't see clearly what Theorem 3.4 means. What is the typical order of $\varepsilon^{\mathcal{Q}}_n$? What about the $\mathrm{err}$ term?) * Simply put, Sections 3~5 are not well-motivated, the results are not intuitively interpreted, and their connections need to be further specified. * Personally, I expect to first see a full overview of the proposed algorithm and the "ultimate" end-to-end sample complexity result (which is now hidden in the paragraph "Putting everything together" on lines 316~322) to get the big picture, before diving into all the technical details introducing the subroutines. * Since I'm not an expert in this area, I don't fully understand the technical details. (*To AC:* Please do take other reviewers' opinions for technical soundness. I've tried hard but failed to fully check the proofs.) * Specifically, I don't follow the proofs in Sections E.5 (for the second part of Theorem 5.3), G.1 (for Lemma 3.1) and G.2 (for Lemma 4.1). The latter two don't seem like legit proofs in my opinion. Technical Quality: 2 Clarity: 1 Questions for Authors: * Why do you use bounded Radon-Nikodym derivative for defining ambiguity sets, as I haven't seen people doing this? Does it have any connections with other "distances", e.g. total variation, KL-divergence, or Wasserstein distance? Confidence: 2 Soundness: 2 Presentation: 1 Contribution: 3 Limitations: There are a few sentences discussing limitations of the setting, but a summary is missing. Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Weakness: Paper is difficult to read Thank you for your detailed feedback on how the quality of writing in the paper could be improved. On some level, this is a very difficult research topic to present in a way that is easily accessible without at least some background in stats and/or causal inference, because of the topics that it considers (i.e. related to semiparametric efficiency theory, orthogonal ML, etc.) It is typical that papers on such topics, including many of the papers that we cite related to causal inference, double/debiased machine learning, or semiparametric efficiency theory, are similarly technically dense. Also, our work is cross-disciplanary between these research areas and RL too, so there is the additional challenge of making it accessible to both audiences, while also being technically rigorous enough for both. However, it is not our intention for the paper to be inaccessible, and we will work hard on improving its readability and accessibility for the final camera ready version, following the helpful advice of you and other reviewers. In particular, regarding your specific suggestions on improving readability: - Use of $\pm$: Our use of the $\pm$ notation is as a succinct way to denote that there are two different quantities being defined. For example, for the operator $\mathcal{T}^\pm$ defined in Lemma 3.1 in terms of $\text{CVaR}^\pm$, we are succinctly defining two different operators: $\mathcal{T}^+$, which is defined in terms of $\text{CVaR}^+$, and $\mathcal{T}^-$, which is defined in terms of $\text{CVaR}^-$. This was done because, ultimately, we are presenting estimators for both the worst-case and best-case policy values under the sensitivity model. However, we understand that this notation can be somewhat confusing and cumbersome, and so we propose the following change to the final camera ready version, which would eliminate all $\pm$ notation: 1. Instead of discussing both the best and worst cases (+/-) simultaneously, we will provide results only for worst case (-) in the main text. 2. We will add a brief discussion about how the best-case version can be reduced to the worst-case version for a transformed MDP. (This reduction works by replacing all rewards $r(s,a)$ with $1-r(s,a)$, and then replacing the final estimator $\psi$ with $1-\psi$.) - Definition of notations / writing quality: Thank you for pointing out these issues, we will do a thorough edit of the paper to fix all such writing issues and ensure that all non-standard notations are defined. Regarding the Radon-Nikodym derivative, we would argue that this is standard probability theory notation, but we will clarify. - Literature Review: The part of the literature review that you highlighted is actually specifically about unobserved confounding in both sequential / non-sequential decision making, not about robust-MDPs (which, other than the works we cite and discuss, do not allow for unobserved confounding). Given limited space we focussed our literature review on the areas most related to our paper (focussing on settings that allow for unobserved confounding), and relegated our discussion of the literature on robust MDPs more generally to Appendix B ("other related works"). However, we will add some clearer pointers to this discussion in the related work section in the main paper. - Ordering of Content in Paper: We acknowledge the feedback here, and can understand how the order of the paper may seem unintuitive for readers unfamiliar with the related literature. We believe the current order is inuitive for readers familiar with similar orthogonal policy value estimators in non-robust settings, which are defined in terms of $Q$ and $W$, however it could be made more accessible. Therefore, we propose to present these existing orthogonal estimators for non-robust MDPs before Sections 3-5, explaining how they are defined in terms of $Q$/$W$. In addition, at this location we will foreshadow the Seciton 5 result that our estimator generalizes this estimator, using robust versions of the $Q$/$W$ functions, which are the $Q$/$W$ functions for the worst-case MDP. After this motivation, sections 3/4 will naturally follow, as they describe how to identify and estimate the robust $Q$/$W$ functions that we just introduced/defined. Similarly, section 5 will naturally follow after these as it puts together how these robust $Q$/$W$ functions are combined in the more general estimator that was previously foreshadowed. In order to make space for this, we will move some of the more technical content that is less important for the overall narrative to the appendix. Weakness: Issues in Proofs While we are open to feedback on how the presentation of our proofs could be improved, we have gone to great lengths to ensure that these results are technically sound. Could you please provide specific details about your claim that "the latter two don't seem like legit proofs in my opinion" about our proofs of Lemma 3.1 / Lemma 4.1 during the discussion period? This is a vague statement and we are not sure how to respond without more specific detail about what you find problematic with these proofs, but we are happy to defend the technical details of our proofs. Q1: Why do you use bounded Radon-Nikodym derivative for defining ambiguity sets? We use this definition to allow for full generality to state spaces that could be either continuous or discrete, or some combination of the two. For discrete state spaces, this Radon-Nikkodym (RN) derivative is just the ratio of transition probabilities, whereas for continuous state spaces, this RN derivative is just the ratio of probability densities. In either case, as discussed in the paper, this definition comes naturally from generalizing the standard marginal sensitivity model used in causal inference in the single decision (i.e. non-RL, or horizon=1) setting. We will clarify this further in the final paper. --- Rebuttal Comment 1.1: Title: Thanks for the responses! Comment: I appreciate the authors' efforts to settle my questions and concerns, especially their open attitude towards adjusting the presentation and flow of the paper. When I say I cannot follow the proofs, I'm not implying that the proofs are technically wrong or suspicious. Rather, I just cannot get through certain steps or sentences. For a few examples: * The equation on line 657 seems to happen only with high probability, and the following sentence on line 658 doesn't make any sense to me (What is $n_K$? Why does it matter here?) * In Appendix G.1, I don't know how to relate the equation between lines 717 and 718 to the statement of Lemma 3.1 (specifically, the form of $\mathcal{T}_{\mathrm{rob}}$. Besides, there is a typo in the equation (nothing after $\mathrm{sup}$). * In Appendix G.2, two proof sketches are provided, but it's better to present only one in a clear and rigorous way. I understand that I'm probably not the target audience of this paper (lol), and this is a tough (and kind of ignorant) decision, but I decide to keep my rating for now. --- Rebuttal 2: Comment: Thank you very much for specifying your questions about the technical appendix. We greatly appreciate the detailed review – this helps us improve our paper. We will answer them in order: * "The equation on line 657 seems to happen only with high probability" You are correct: this occurs with high probability, which is why we used the big-O in probability ($O_p$) notation in this expression. This in fact is simply a restatement of the display equation just above this line, arising from Chebychev's inequality. Recall that $a_n=O_p(b_n)$ iff for any $\eta>0$ we have $P(a_n/b_n\geq \epsilon)\leq\eta$ for some $\epsilon>0$. This is precisely what we get from the display by letting $\epsilon=1/\sqrt{\eta}$ with $a_n=\varepsilon_k$ and $b_n=\mathrm{Var}[\epsilon_k\mid \mathcal D_k)]^{1/2}$ and the probability $P$ being conditional on $\mathcal D_k$, $P(\cdot\mid\mathcal D_k)$. We will add a sentence here to make it extra clear. * "the following sentence on line 658 doesn't make any sense to me (What is $n_K$ Why does it matter here?)" Here we are simply defining $n_K$ in-line as $n/K$, being the size of the dataset $\mathcal D_k$, to make extra clear why the asymptotics are the same whether we take $n\to\infty$ or the size of the fold (wrt which we are taking Chebychev) to infinity. This is to clarify that the conditional big-O in probability ($O_p(\cdot\mid \mathcal D_k)$) indeed makes logical sense here. Again, we will add a sentence here to make it extra clear. * "In Appendix G.1, I don't know how to relate the equation between lines 717 and 718 to the statement of Lemma 3.1 (specifically, the form of $\mathcal{T}_{rob}$). Besides, there is a typo in the equation (nothing after $\sup$)." Firstly, thank you for catching the typo: the missing expression after the $\sup$ is $\mathbb E_{G}[f(s')]$. That this completes the proof follows by the definition of $G$ in line 715. In particular, inverting the definition, each feasible $U$ in the supremum in the definition of $\mathcal{T} _ {rob}$ can be equivalently expressed as $U = \Lambda^{-1}(s,a)P + (1-\Lambda^{-1}(s,a))G$ where $G$ satisfies the constraints in line 717. Thus, the supremum in $\mathcal{T} _ {rob}$ can be expressed as $\Lambda^{-1}(s,a)$ times the expectation under the nominal $P$, and $(1-\Lambda^{-1}(s,a))$ times the sup over $G$, i.e. $\sup_{U: \Lambda^{-1}(s,a)\leq \frac{dU(s'\mid s,a)}{dP(s'\mid s,a)}\leq \Lambda(s,a)}\mathbb{E} _ U[v(s')\mid s,a] = \Lambda^{-1}(s,a)\mathbb{E} _ P[v(s')\mid s,a] + (1-\Lambda^{-1}(s,a))\sup_{G\ll P: \\|dG(\cdot\mid s,a)/dP(\cdot\mid s,a)\\| _ \infty\leq \tau^{-1}(s,a)}\mathbb{E} _ G[v(s')]$. Finally, line 717 observes that the latter term is equivalent to CVaR, which is proved in Section 3.4 of [3]. Thank you for bringing up this question. Explaining the completion of the proof certainly merits another line or two -- although it follows from the previous lines, it can be made easier to follow. * "In Appendix G.2, two proof sketches are provided, but it's better to present only one in a clear and rigorous way." Thank you for the feedback. We hoped to provide intuition to the reader by providing two ways to think about this, but we do understand that a clear complete proof may be the most instructive. Here is a complete proof we can add here in the appendix: Fix any $s,a$ and let $\tau=\tau(s,a)$. Fix any function $v(s')\in\mathbb{R}$. We want to show that the worst-case $U^+ = \arg\max _ {U\in\mathcal{U}(P)} \mathbb{E} _ U[v(s')\mid s,a]$ has a closed form expression as shown in line 725. By the proof of Lemma 3.1 above, we can rewrite $U^+(s'\mid s,a) = \Lambda^{-1}(s,a)P(s'\mid s,a) + (1-\Lambda^{-1}(s,a)) G^+(s'\mid s,a)$, where $G^+ = \arg\max _ {G\ll P: \\|dG(\cdot\mid s,a)/dP(\cdot\mid s,a)\\| _ \infty\leq \tau^{-1}(s,a)}\mathbb{E} _ G[v(s')]$. Thus, it suffices to simplify $G^+$. To do so, we invoke the premise that the CDF of $v(s')$ is differentiable at $\beta^+ _ \tau$, i.e. $F _ v(\beta^+ _ {\tau,F _ v}(s,a)\mid s,a)=1-\tau$. This implies that the CVaR is exactly the conditional expectation of the $1-\tau(s,a)$-fraction of best outcomes, i.e. $\text{CVaR}^+ _ \tau(v(s')\mid s,a) = \mathbb{E}[v(s')\mid v(s')\geq\beta^+ _ \tau(s,a),s,a]$, which in turn is equal to $\tau^{-1}\mathbb{E}[v(s')\mathbb{I}[v(s')\geq\beta^+_\tau(s,a)]\mid s,a]$. Thus, $G^+(s'\mid s,a) = \tau^{-1}P(s'\mid s,a) \mathbb{I}[v(s')\geq\beta^+ _ \tau(s,a)]$. This concludes the proof for the $+$ case. The proof for the $-$ case is symmetric and follows identical steps. Thank you again so much for the detailed feedback about the technical appendix. Citations [1] Chernozhukov, Victor, et al. "Double/debiased machine learning for treatment and structural parameters." (2018): C1-C68. [2] Kallus, Nathan, and Masatoshi Uehara. "Double reinforcement learning for efficient off-policy evaluation in markov decision processes." Journal of Machine Learning Research 21.167 (2020): 1-63. --- Rebuttal Comment 2.1: Comment: Dear reviewer, the open discussion period is nearing the end. We hope our responses addressed your concerns. If you feel that they have we would greatly appreciate if you update your score accordingly. If you still have questions let us know. We worked hard to be thorough while clear in our response and address all questions raised. Thank you again.	null	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Double-Ended Synthesis Planning with Goal-Constrained Bidirectional Search	Accept (spotlight)	Summary: The paper addresses the synthesis planning problem where constrains are taken into account. To that end, the authors propose a double-ended synthesis planning grounded with bidirectional search to ensure that the added constrains are met. They show experimentally that their proposed approach helps with solve rate as well as reduction in number of node expansion. Strengths: - The paper presents a novel idea. - The real-world aspect of having constraint is addressed in this paper - Experiments have a clear objective and look sound. Weaknesses: - See the questions section. - Proof of soundness and completeness of algorithm 1 is missing. In particular, what can be said about the properties of this algorithm? - This paper provides a novel contribution for synthesis planning, but I fail to see its broader impact to the community (its significance is of narrow scope). Technical Quality: 3 Clarity: 3 Questions for Authors: 1. Why Bi-directional search? Have you tried other search algorithms? You can potentially still define goal constrains and be in the forward search algorithm and ensure those goals are met. Forward search algorithms with heuristic search can address soft and hard constraints on goals or even on the full trajectory. Some examples follow. While these examples are from Automated planning literature, perhaps some can be relevant in this context. Note the specification of constraints in Linear Temporal Logic, as well as heuristics to meet these constraints has been a topic of interest in several publications. 1. https://www.cs.toronto.edu/~sheila/publications/bai-mci-aim08.pdf 2. https://www.sciencedirect.com/science/article/pii/S0004370208001975 3. https://cdn.aaai.org/ICAPS/2005/ICAPS05-019.pdf 2. Could there be multiple solutions to the general synthesis planning problem defined in Section 2.2. If so is the notion of cost you mentioned taken into account? Also is the algorithm in section 3.2 going to favor the least costly solution? If so do you have a proof of that? 3. Is starting material-constraints the same as the goal constraints? 4. Can you point to where in the paper you discuss how you learned the goal-conditioned cost network offline (mentioned in the abstract). Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: Authors discuss limitations and those are not concerning (re societal impact, etc). Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your feedback and questions, they bring up some interesting discussion points that will help improve our work! --- Reviewer: _Proof of soundness and completeness of algorithm 1..._ Response: We agree that some detail regarding algorithm 1 is missing and will add the following justification in the final manuscript. The purpose of Algorithm 1 is to add the $N$ “best” forward reactions to add to the search graph given a particular reactant $m_1$ from which we want to eventually reach some target molecule $m_2$. If we had access to the complete reaction graph $\mathcal{G}$, we could find the $N$ reactions that use $m_1$ as a reactant that minimize the total cost to reach $m_2$ in $\mathcal{G}$. Thus, $f_t(m_1, m_2)$ would yield the set of templates corresponding to these $N$ reactions, and for each of the bidirectional templates $t_i$, $f_b(m_1, m_2, t_i)$ would yield the missing reactant $m_{3,i}$ in the reaction. We instead approximate $\mathcal{G}$ with the partial reaction graph $G_{\text{FWD}}$ and train neural networks to predict the best templates and building blocks using the reactions in $G_{\text{FWD}}$. Thus, to perform a forward expansion in DESP on $m_1$ conditioned on $m_2$, we approximate $f_t$ with a trained forward template model and return the $N$ most likely templates to apply to $m_1$. For each template, if the template is unimolecular, we can simply apply the template $m_1$ and add the reaction to the search graph. For bimolecular templates, we instead use a building block model that approximates $f_b$ to predict the missing building block $m_3$. The model predicts the fingerprint of $m_3$, and we perform a $k$-nearest neighbors search on our building block set $\mathcal{B}$ to retrieve the $k$ best building blocks to use as $m_3$. Finally, we apply the bimolecular template to $m_2$ and each retrieved building block and add the reaction to the search graph. The forward expansion algorithm relies on some limiting assumptions, which we touch on in the paper. Particularly, we ignore the existence of $\geq$3-component reactions, and assume that the missing reactant $m_3$ is a member of $\mathcal{B}$, thus precluding “convergent” bottom-up synthesis plans. --- Reviewer: _...I fail to see its broader impact to the community..._ Response: We would argue that a novel contribution to synthesis planning is in itself a contribution of broad significance to the scientific community. Synthesis planning is a crucial component in the formulation and discovery of most of our medicines, as well as desirable agrochemicals and materials used across a wide swath of industries. Anecdotally, we have received interest in the algorithm from chemists, chemical engineers, and pharmaceutical companies. --- Reviewer: _Why Bi-directional search?..._ Response: Thank you for the constructive feedback and references! Our implementations of the unidirectional search baselines (including our top-down guided ablation, Retro* + D) do define the starting material goal constraints, and we posited that bidirectional search may be well suited for affording efficiency gains on this task. We find that DESP outperforms all baseline methods on the task, and the ablation study demonstrates that bidirectional search contributes to the improved performance. We believe that these results provide a solid empirical case for the utility of bidirectional search in synthesis planning. Though there are many exciting avenues for improvement of either unidirectional or bidirectional search with preferences and/or constraints, we view such explorations as out of the scope of this paper. --- Reviewer: _Could there be multiple solutions..._ Response: Thank you for raising this question. For a given target, it is essentially guaranteed that there are many solutions to the general synthesis planning problem. In spite of this, the problem is intractable for many targets without the use of ML or heuristics to prune the search space, so we frame the problem as efficiently finding _some_ solution rather than finding the optimal solution. In any case, knowing that each reaction step is costly in the real world motivates our evaluation in Table 3 of average number of reaction steps as an indicator of quality / cost. Our heuristic cost networks are also trained with this notion of cost in mind--the training labels correspond to the optimal number of reaction steps (to reach the specified goal molecule) based on the reaction corpus. A limitation of DESP is that the first route found is not necessarily the cost-optimal route. First, each end of our search is a variant of Retro. As proven in [1], the unidirectional search only guarantees an optimal solution on termination with admissible heuristics, which our neural networks do not provide. Second, even with an admissible heuristic, bidirectional A search does not guarantee optimality upon meeting [2]. We emphasize that chemists generally care more about obtaining multiple reasonable routes quickly than obtaining the theoretically optimal route, and our evaluations are designed accordingly. Nevertheless, we will summarize the discussed limitations and outlook in our final manuscript. --- Reviewer: _Is starting material-constraints the same as the goal constraints?_ Response: Yes, thank you for raising this question; we will make an effort to be more clear / consistent about such terminology in the final version. --- Reviewer: _Can you point to where in the paper you discuss how you learned the goal-conditioned cost network offline..._ Response: Section 3.4 discusses the high level procedure and loss function, while details (including Figure 5) can be found in Section A.4. --- [1] Chen, B. et al. "Retro: Learning Retrosynthetic Planning with Neural Guided A Search". _ICML_ (2020). [2] Kaindl & Kainz. "Bidirectional Heuristic Search Reconsidered". _JAIR_ (1997). --- Rebuttal Comment 1.1: Title: Reply to rebuttal Comment: Thank you for answering my questions. I think more details on Algorithm 1 is definitely needed even the full proof of soundness and correctness. --- Reply to Comment 1.1.1: Title: Proof of soundness and correctness Comment: Thank you for your response. We provide a proof of soundness and completeness below. --- Assume that we have access to all unimolecular and bimolecular reactions that involve at most one non-buyable (forming $G_{\text{FWD}}$), giving us access to target functions $f_t$ and $f_b$ (as described in our response). We prove that Algorithm 1 is sound and complete for $N = 1$ and $K = 1$. Consider the set of routes $S$ for which $m_1$ is a leaf node and $m_2$ is a root and no such route in $G_{\text{FWD}}$ has lower total cost. On input $m_1, m_2$, the algorithm is sound if the algorithm only adds a reaction $R$ involving $m_1$ if $R$ is in some route in $S$. We call such $R$ an _optimal reaction_. Additionally, the algorithm is complete if it adds an optimal reaction for any input. Since we know $f_t$ and $f_b$, our algorithm computes $f_t(m_1, m_2)$ (and $f_b(m_1, m_2, f_t(m_1, m_2))$ if necessary) which comprises an optimal reaction by the definition of the functions. Thus, the algorithm is sound and complete. --- In practice, we do not have $f_t$ and $f_b$ and instead approximate them with neural networks, meaning that the algorithm is not sound or complete. This applies to any expansion policy of an existing CASP tool and justifies the use of search with higher branching ratios ($N$ and $K$), as the expansion policy will only sometimes give the “optimal reaction” as its top-1 output. Thus, we believe that the provided proof is somewhat tautological and does not significantly enhance our contributions. In any case, we will provide more detail about Algorithm 1 into our final version, incorporating our initial response and the discussed properties of CASP expansions.	Summary: The paper considers computer aided synthesis planning with applications to retrosynthetic analysis in chemistry where the goal is to find a reaction route from purchasable materials to a target molecule. The latter is an important problem with real applications in areas such as drug discovery. In the current landscape of algorithms for retrosynthetic analysis the common practice is to assume reachability to arbitrary materials thus failing to address an important constraint where using specific molecules is most desired. Therefore, the paper proposes a bi-directional graph search algorithm that is restricted to using a user specified set of purchasable basic materials. The algorithm called DESP is guided by a heuristic function derived from a goal-conditioned cost network (neural network) learned offline from a set of valid chemical reactions. The empirical evaluation is carried out on standard benchmarks for retrosynthetic analysis. The results show clearly that the new bi-directional search algorithm improves considerably over existing state-of-the-art algorithms for this domain. Strengths: - The paper considers an important problem in AI and develops a new more efficient search algorithm to solve it optimally. Specifically, bi-directional search (although a well established search method) appears to be a novel application to retrosynthetic analysis. - The paper is well written and organised. It is therefore relatively easy to follow. The quality of the presentation is overall quite good. - The experimental evaluation is sound and covers well most of the prior work in terms of competing algorithms. The results are presented in a relatively clear manner and therefore it is fairly easy to understand the performance gains achieved by the proposed method. Weaknesses: I was not able to find any major weakness in this paper. Perhaps including a small numerical example to show more clearly how the node values are computed and updated during search would help improve the quality of the presentation. Technical Quality: 3 Clarity: 3 Questions for Authors: - What is dn() and rn() refering to in Equations 3-6? Are these values related to the proof and disproof numbers from the A* algorithm proposed by [Kishimoto et al, 2019]? Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The limitations of the proposed method are discussed fairly clearly in the paper. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your review and positive reception of our paper! Addressing your comments: --- Reviewer: _I was not able to find any major weakness in this paper. Perhaps including a small numerical example to show more clearly how the node values are computed and updated during search would help improve the quality of the presentation._ Response: This is a great suggestion! We have created such a figure (Figure 1 in author rebuttal) and will include it in the final version of the paper. --- Reviewer: _What is dn() and rn() refering to in Equations 3-6? Are these values related to the proof and disproof numbers from the A* algorithm proposed by [Kishimoto et al, 2019]?_ Response: Thank you for the question. $rn(m\|G)$ is actually a quantity directly from the Retro* algorithm of Chen et al. [1]. It represents the “reaction number,” the total estimated cost of synthesizing a particular molecule $m$ based on the current search graph. $dn(m\|G)$ is an analogous quantity that we developed in order to incorporate the guidance from the synthetic distance values as well. $rn(m\|G)$ is more specifically described in Section A.2, and $dn(m\|G)$ can be better understood by our explanation in Section A.5, as well as the new Figure 1 we have included in the author rebuttal. We will make sure these quantities are clearly described in the final version of the paper. --- [1] Chen, B. et al. "Retro: Learning Retrosynthetic Planning with Neural Guided A Search". _ICML_ (2020). --- Rebuttal Comment 1.1: Comment: Thanks for the clarifications.	Summary: This paper proposes a bidirectional search algorithm for chemical synthesis, in the case where we also have certain "part of the way there" molecules that we would like to include in the discovered synthesis route. Strengths: The paper is very clearly written, with lots of great notation and detail provided. Despite not being familiar with this area, I found the high level ideas easy to follow. I am familiar with top-down and bottom up program synthesis, so I can follow the high level ideas. But I am not very knowledgable about chemical synthesis and the literature on it. I did not closely read the details of the algorithm, other than trying to understand the high level additions compared with the Retro* baseline. The fact that I could still get a lot of technical value from the paper, despite not paying attention to the chemistry details, and thinking of it just as a generic synthesis-y problem, is to be commended and a sign of the paper's strength and significance. The results look good. Bidirectional search seems useful to apply to chemical synthesis, especially to the problem studied. it really seems like great technical caliber has been applied to this problem. Care and precision is applied to creating the algorithm. Weaknesses: By adding bidirectional search, the algorithm gets a bit complicated. Due to my lack of familiarity with the area, I'm not 100% sure how to weigh the complexity vs performance tradeoff, but I am inclined to ignore it given how clearly the algorithm is described and how easy the high level motivation for it is. Technical Quality: 4 Clarity: 4 Questions for Authors: - Is the BFS top-down only or bottom-up only? Would it be useful to include a "bidirectional BFS" baseline? Suggestions/typos: - I would suggest including a high level explanation of how Retro* compares with DESP in the main text . it sounds like Retro* is top-down only, and DESP = Retro* + synthetic distance + bottom up expansions? - it might be good to include more details about the compared baselines during the paper. In particular, what is Retro+$D$? the appendix only describes Retro. This is almost certainly clear to someone who reads through all the details of the approaches and understands them (Retro* + D just adds the synthetic distance D to Retro, somehow based on how Retro and the current work works, and the appendix probably meant ...) but to clarify, the appendix describes Retro* as DESP without bottom-up expansions. So, at a high level, is Retro* just top-down only, and DESP is bidirectional, plus the synthetic distance? - line 106 typo, two front-to-end's You should check out this reference: https://dl.acm.org/doi/pdf/10.1145/3571226. They use "cuts", which I believe are similar in that using certain "cuts" lets you stake out some target in the "middle" of the search and then split the synthesis problem into two problems, one of reaching the midpoint, and then going from the midpoint to the target. (I haven't read this paper in a while, and sort of forget it, so I might be wrong) - Maybe this is relevant to addressing the convergent synthesis limitation? not sure. Confidence: 3 Soundness: 4 Presentation: 4 Contribution: 4 Limitations: The limitations section looks great! Flag For Ethics Review: ['No ethics review needed.'] Rating: 8 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your review and the kind words about our work! We address your comments one by one. --- Reviewer: _By adding bidirectional search, the algorithm gets a bit complicated. Due to my lack of familiarity with the area, I'm not 100% sure how to weigh the complexity vs performance tradeoff, but I am inclined to ignore it given how clearly the algorithm is described and how easy the high level motivation for it is._ Response: Thank you for pointing this out. We agree that the bidirectional search introduces complexity, though we would argue that some amount of increased complexity is inherent (and not unnecessary) to a double-ended search. One area to tackle the increased complexity is the forward expansion policy (Algorithm 1), which is more complex than the retro expansion policy (Algorithm 2), as some templates necessitate a second model call and k-NN search over a large database. Synthesizable molecular generation is rapidly attracting more attention ([1], [2], [3] published since we submitted this paper), and we believe a simpler or more elegant method of performing the bottom-up search can likely be integrated in future work. While it cannot trivially be plugged into DESP, ChemProjector (Luo et al. [1]), for instance, demonstrated that a lone transformer architecture can improve bottom-up planning performance by directly decoding the actions to perform, comprising an arguably less complex overall algorithm. --- Reviewer: _Is the BFS top-down only or bottom-up only? Would it be useful to include a "bidirectional BFS" baseline?_ Response: The BFS is top-down only. The new baseline is a great idea! We have performed the bidirectional BFS experiment and attached the updated results table in the author rebuttal (Table 3). We find that the bidirectional BFS results in fewer node expansions on average than uni-directional BFS, but does not consistently outperform uni-directional baselines like MCTS or Retro. Thank you for the suggestion. --- Reviewer:* _I would suggest including a high level explanation of how Retro* compares with DESP in the main text . it sounds like Retro* is top-down only, and DESP = Retro* + synthetic distance + bottom up expansions?_ Response: Thank you for the suggestion. Your understanding is correct, and we will make this more explicit in the final version! --- Reviewer: _it might be good to include more details about the compared baselines during the paper. In particular, what is Retro+D? the appendix only describes Retro. This is almost certainly clear to someone who reads through all the details of the approaches and understands them (Retro* + D just adds the synthetic distance D to Retro, somehow based on how Retro and the current work works, and the appendix probably meant ...) but to clarify, the appendix describes Retro* as DESP without bottom-up expansions. So, at a high level, is Retro* just top-down only, and DESP is bidirectional, plus the synthetic distance?_ Response: Yes, your understanding is correct. “Retro* + D” is DESP as described in Section 3.2 but without any bottom-up expansions to serve as an ablation. As with our last response, we will make these distinctions more clear in Section 4.1. We have also included Table 2 in the author rebuttal to summarize the evaluated algorithms and their components. We will include this in the appendix of the final manuscript and hope this helps with some of the points of confusion. --- Reviewer: _line 106 typo, two front-to-end's_ Response: Thank you for pointing this out! We will fix that. --- Reviewer: _You should check out this reference: https://dl.acm.org/doi/pdf/10.1145/3571226. They use "cuts", which I believe are similar in that using certain "cuts" lets you stake out some target in the "middle" of the search and then split the synthesis problem into two problems, one of reaching the midpoint, and then going from the midpoint to the target. (I haven't read this paper in a while, and sort of forget it, so I might be wrong) Maybe this is relevant to addressing the convergent synthesis limitation? not sure._ Response: Thank you for the reference; it brings to mind some very interesting starting points for future work and seems related to ideas we’ve been thinking about as well. The divide-and-conquer or “middle-out” approach sounds like an intriguing method for synthesis planning and would likely naturally extend from DESP. Using something like a “cut” to break a synthesis planning task for a particularly complex molecule into subgoals (i.e. by predicting a key intermediate) also intuitively seems like a promising avenue. We will incorporate these general future directions and the reference into Section A.8! --- [1] Luo, S., Gao, W., et al. “Projecting molecules into synthesizable chemical spaces” _ICML_ (2024). [2] Koziarski, M., et al. "RGFN: Synthesizable Molecular Generation Using GFlowNets" _arXiv:2406.08506_ (2024). [3] Guo, J. & Schwaller, P. "Directly Optimizing for Synthesizability in Generative Molecular Design using Retrosynthesis Models" _arXiv:2407.12186v1_ (2024). --- Rebuttal Comment 1.1: Comment: Thank you for your response to each of my questions and comments! I have no further questions and will maintain my score of 8.	Summary: the authors propose a new algorithm for double ended synthesis planning. while this problem has received attention from the community a few decades ago, this has recently not been studied at all. Strengths: - addresses an important outstanding problem in the community - sound experimentation from the chemistry perspective Weaknesses: - none really Technical Quality: 4 Clarity: 3 Questions for Authors: - results from the PAroutes paper and recent work by Tripp et al and Maziarz et al indicate that there are signficantly less or even no differences between the different uni-directional search algorithms than prior work (Chen et al; Retro*) imply. My suggestion would be more clearly flag which baseline implementation of the various algorithms used in the maintext, and also give the used hyperparams for all search algorithms. Confidence: 4 Soundness: 4 Presentation: 3 Contribution: 3 Limitations: n/a Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your review! We address your comments and suggestions as follows: --- Reviewer: _results from the PAroutes paper and recent work by Tripp et al and Maziarz et al indicate that there are signficantly less or even no differences between the different uni-directional search algorithms than prior work (Chen et al; Retro) imply._ Response:* Thank you for bringing this up. Though these papers perform evaluations on a different problem setting and with different test sets (other than USPTO-190), our results on the starting material-constrained task also find relatively small differences between the two widely used uni-directional search algorithms (MCTS and Retro) on both USPTO-190 and our new benchmark sets. We will make note of this in the final version of the manuscript. --- Reviewer:* _My suggestion would be more clearly flag which baseline implementation of the various algorithms used in the maintext, and also give the used hyperparams for all search algorithms._ Response: Thank you for the suggestion! While we do outline the various baselines and relevant hyperparameters in the “Multi-step algorithms” paragraph of Section 4.1, we will also add a table to summarize descriptions of our implementations and algorithm-specific hyperparameters to make this more clear. We have included such tables in the author rebuttal (Tables 1 and 2) and will incorporate them in our final manuscript. --- Rebuttal Comment 1.1: Comment: Thank you! Again: great paper!	Rebuttal 1: Rebuttal: We thank all reviewers for their thoughtful feedback and comments. We have addressed stated weaknesses, questions, and comments in the individual rebuttals. We also include a single page PDF containing additional tables and a figure as referenced in the rebuttals. Pdf: /pdf/298cab975cce58e6f0da2de0f8aba9dfacbc4048.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Towards Principled Graph Transformers	Accept (poster)	Summary: This paper introduces a novel architecture called Edge Transformer (ET) for graph learning tasks. The ET leverages global attention on node pairs instead of individual nodes and demonstrates strong empirical performance without relying on positional or structural encodings. The authors show that ET has the expressive power of 3-WL and achieves competitive results on algorithmic reasoning and molecular regression tasks. Strengths: 1、ET bridges the gap between theoretical expressivity and practical performance. 2、The paper provides comprehensive empirical evidence demonstrating that the Edge Transformer outperforms existing theoretically motivated models and competes well with state-of-the-art models in various graph learning tasks. Weaknesses: 1、The total number of parameters for the model is not provided in the parameter table. 2、While ET is more efficient than some other high-order transformers, it is still significantly inferior to most graph transformers with O(n^2). This limits the applicability of ET. 3、The author's contribution is confined to applying the ET model to the graph, without proposing their own method. Technical Quality: 2 Clarity: 2 Questions for Authors: 1、Can you provide possible ways to reduce the complexity of ET? 2、Can you provide the total number of parameters for ET on each dataset? See Weaknesses 1. 3、Why has the performance changed so much compared to the submitted version of ICML in 2024? Especially on the Searching dataset. 4、What do Average and All algorithms represent respectively? Confidence: 5 Soundness: 2 Presentation: 2 Contribution: 2 Limitations: See Weaknesses. Flag For Ethics Review: ['No ethics review needed.'] Rating: 1 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for their effort and are happy to address the concerns raised by the reviewer. First, the reviewer states > The total number of parameters for the model is not provided in the parameter table > We provide the parameters for each model in the general response above. As can be observed, on the molecular regression tasks, the ET is well within the 500K parameter budget. Next, the reviewers says > While ET is more efficient than some other high-order transformers, it is still significantly inferior to most graph transformers with O(n^2). This limits the applicability of ET > See our general response for a discussion of the practical usefulness of the ET. In summary, we argue that there exists still plenty of application and interest for a model with high runtime complexity, particularly, if this complexity can be translated into strong predictive performance. Finally, the reviewer says > The author's contribution is confined to applying the ET model to the graph, without proposing their own method > See our general response for a discussion on the novelty and contribution of our work. In summary, we argue that the novelty of our work does not come from proposing a new method. Rather, the main contribution of our work is in providing a connection between the ET, systematic generalization and graph learning. ### Questions Further, we are happy to address the question of the reviewer below. First, the reviewer asks > Can you provide possible ways to reduce the complexity of ET? > As our work is partly motivated by demonstrating that high expressivity can also result in strong empirical performance, we do not aim to reduce the theoretical complexity of the ET in this work. At the same time, we show that in practice, the high runtime and memory cost can be reduced by leveraging a parallelizable implementation, together with low-level GPU optimizations; see the limitation section in our paper. More generally, while the ET may not be applicable to large graphs yet, we regard our work as a first step at a theoretical understanding of equivariant graph transformers with high expressive power that also perform strongly in practice. Next, the reviewer asks > Why has the performance changed so much compared to the submitted version of ICML in 2024? Especially on the Searching dataset. > In a previous version, we had not included the graph features that are available in CLRS, and used by baseline models, into the ET. These features proved particularly useful on the Searching datasets, explaining the improved performance. Finally, the reviewer asks > What do Average and All algorithms represent respectively? > In “Average”, we average performance across the six algorithm classes, whereas in “All algorithms” we average performance over all algorithms. We want to ask the reviewer to increase their score if they are satisfied with our response. We are happy to answer any remaining questions. --- Rebuttal Comment 1.1: Comment: Considering that the performance of this version achieves about 30% improvement than that of ICML version on Searching dataset, while it decreases on Strings and Geometry datasets, I believe the emprical results are not convincing. Moreover, I think the response is not reasonable.	Summary: In this paper, the authors show that Edge Transformer, a global attention model operating on node pairs, has 3-WL expressive power when provided with the right tokenization. Experiments results also show that the Edge Transformer has competitive performance on molecular regression tasks and algorithmic reasoning. Strengths: 1. This paper proposes a concrete implementation of the Edge Transformer, and proves that it has an expressive power of 3-WL. 2. The proposed ET has superior empirical performance on molecular regression and neural algorithmic reasoning tasks. Weaknesses: 1. My major concern is the real usefulness of ET, since the high runtime and memory complexity may offset the importance of ET, though the authors discuss it in Limitations. Also, it is not clear what is the parameter count, which raises the question that the better performance of ET may be mainly from large number of parameters. 2. It seems that the ET in this paper is mainly from existing work, and the difference needs to be explained. Technical Quality: 3 Clarity: 3 Questions for Authors: 1. The ET in this paper is a variant of existing ones, due to the specific tokenization. But it is not quite clear to me what are the main differences of the tokenization compared with existing ones, and why this tokenization can help the 3-WL. It would be good if the authors provide more details. 2. In Table 1, ET with RRWP has a little bit lower performance on QW9. Can the authors elaborate on this? Since generally, transformers with positional encodings will lead to improved performance. 3. The authors emphasize that the designed ET can achieve superior performance even without positional encodings. But maybe as an open question, if incorporated with PEs, will the theoretical results change? [1] Comparing Graph Transformers via Positional Encodings, ICML 2024 Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: Scalability limitations are discussed. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for their effort and are happy to address the concerns raised by the reviewer. First, the reviewer states > My major concern is the real usefulness of ET, since the high runtime and memory complexity may offset the importance of ET > See our general response for discussion of the practical usefulness of the ET. In summary, we argue that there exists still plenty of application and interest for a model with high runtime complexity, particularly, if this complexity can be translated into strong predictive performance. Next, the reviewer says > Also, it is not clear what is the parameter count, which raises the question that the better performance of ET may be mainly from large number of parameters > We provide the parameter counts in the general response. We want to highlight that on ZINC and Alchemy, we adhere to the 500K parameter budget and that the ET’s strong performance cannot be explained by a comparatively large number of parameters. Finally, the reviewer says > It seems that the ET in this paper is mainly from existing work, and the difference needs to be explained > See our general response for a discussion on the novelty and contribution of our work. In summary, we argue that the novelty of our work does not come from proposing a new method. Rather, the main contribution of our work is in providing a connection between the ET, systematic generalization and graph learning. To still answer the question about the difference between the ET in our work and the original ET, note that on the architectural side, we provide a sufficient tokenization and readout for the ET to simulate 2-FWL. In what follows, we provide a detailed explanation in response to the reviewer’s first question, which also touches on this concern. ### Questions The reviewer asks > But it is not quite clear to me what are the main differences of the tokenization compared with existing ones, and why this tokenization can help the 3-WL > We are happy to provide further details on the proposed tokenization for the ET. For the tokenization to be sufficient for the 2-FWL, the initial embeddings of each node pair need to injectively encode the initial colors of each node, as well as an indicator of whether the nodes are connected by an edge. Such a tokenization is already vaguely described in the original paper (https://arxiv.org/abs/2112.00578). In this work, we merely formalize this tokenization such that it can be used in our formal proofs. Other than the tokenization and readout, we do not modify the ET at all. Next, the reviewer asks > In Table 1, ET with RRWP has a little bit lower performance on QW9. Can the authors elaborate on this? Since generally, transformers with positional encodings will lead to improved performance > We suspect that adding positional encodings (PEs) only translates to improved empirical performance if the PEs provide additional features either useful for expressivity or directly for prediction. However, since the ET already has a high base expressivity, on this particular task, the additional RRWP encodings may not be useful for either distinguishing graphs or directly for predicting the targets and instead lead to slight overfitting. A takeaway from this finding may be that the base expressivity of the ET is often enough, as the RRWP encodings do not prove substantial for the good performance of the ET. On the other hand, models such as the SOTA graph transformer GRIT rely on PEs for good performance; see https://arxiv.org/abs/2305.17589, Table 5. Finally, the reviewer asks > But maybe as an open question, if incorporated with PEs, will the theoretical results change? > We agree with the reviewer that this is an interesting question for future work. In particular, if one were able to show that RRWP encodings can distinguish graphs indistinguishable by the 3-WL, one would obtain a theoretical guarantee that ET+RRWP leads to increased expressivity. At the same time, we regard it as a strength of the ET that the model does not rely on PEs but can still successfully leverage them, if provided and informative on the given task; see e.g., our results on ZINC 12K. We want to ask the reviewer to increase their score if they are satisfied with our response. We are happy to answer any remaining questions. --- Rebuttal Comment 1.1: Comment: Thank the authors for clarifications and explaining the main contributions. Though this paper does not propose a new model, it is a solid paper. I am happy to increase my rating.	Summary: This paper applies Edge Transformer (ET) to the field of graph learning. It is proved that ET has 3-WL expressivity with cubic complexity, which is more efficient than existing 3-WL models. Experiments on BREC benchmark clearly demonstrate its expressive power. Results on the other three molecular datasets and CLRS benchmark are also provided. Strengths: - It proves ET has 3-WL expressive power and demonstrates excellent results on BREC benchmark. Even though it has $O(n^3)$ complexity, it is still more efficient than other 3-WL models. - It shows good performance on real-world graph learning tasks. - The paper is well-written and easy to follow. Weaknesses: - My major concern is about empirical evaluation. - While I appreciate ET's excellent theoretical expressive power, I find it is needed to include more benchmark datasets in graph learning (e.g., OGB, moleculeNet, GNN benchmark, Long Rang Graph Benchmark, Zinc-full, etc) to comprehensively demonstrate its practical predictive power compared with state-of-the-art (SOTA) methods, e.g., those graph transformers Grit, Exphormer, GraphGPS, etc. - Besides datasets from algorithmic reasoning, currently, in my opinion, ET is only evaluated on two widely-used graph benchmark datasets with performance reported from very recent SOTA methods, i.e., Zinc-12k and Alchemy-12k, making it hard to assess ET's practical performance. Although QM9 is also a popular dataset, the adopted setting is less common. Meanwhile, Zinc-12k is just a small subset of Zinc-full, and it has recently been shown that being good at Zinc-12k does not necessarily lead to the best performance on Zinc-full [1]. - It would be interesting to see its long-range modeling capability on the LRGB benchmark as it's a transformer. - In terms of the evaluation of expressive power, it would be better to include SOTA methods such as those subgraph-GNNs, potentially also discussing their complexity compared to ET. [1] Wang, X., Li, P., & Zhang, M. (2024). Graph as Point Set. ICML 2024. Technical Quality: 2 Clarity: 4 Questions for Authors: - How does the setting of QM9 used in this paper differ from the setting that is commonly used in equivariant GNNs (e.g., EGNN, DimeNet, etc)? It would be better if this description could be put in the paper, making it self-contained. - Are there any particular benefits to having an expressive model without using PE or SE? I consider the major benefit would be on the computation side as computing PE can be $O(n^2)$, but ET has already had $O(n^3)$ complexity. So, for the claim in the paper, is it just because it would be more challenging to analyze expressive power with PE/SE, therefore it would be easier to understand a model's expressive power without using them? - I feel like depending on how PE is used, it is still possible to analyze the expressive power, e.g., via graph substructure counting. Can the authors discuss the works such as graph as point set and those subgraph-GNNs? Because they may also use PE, while proving their expressive power via graph substructure counting. Confidence: 4 Soundness: 2 Presentation: 4 Contribution: 2 Limitations: See above. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for their effort and are happy to address the concerns raised by the reviewer. Regarding evaluation, the reviewer says that > I find it is needed to include more benchmark datasets in graph learning […] to comprehensively demonstrate its practical predictive power compared with state-of-the-art (SOTA) methods, e.g., those graph transformers Grit, Exphormer, GraphGPS > as well as > Besides datasets from algorithmic reasoning, currently, in my opinion, ET is only evaluated on two widely-used graph benchmark datasets > and > It would be interesting to see its long-range modeling capability on the LRGB benchmark as it's a transformer > While we certainly evaluate the ET only on a subset of all possible graph learning benchmarks we argue that our results already provide a comprehensive view on the predictive performance of the ET. In particular, we evaluate the ET on three different types of benchmarks: - Molecular property prediction (ZINC, Alchemy, QM9) - Algorithmic reasoning (CLRS) - Graph isomorphism testing (BREC) Most notably, the CLRS benchmark contains a total of 30 different datasets and includes a variety of graph-, node- and edge-level tasks. In addition, the CLRS benchmark inherently evaluates models on size generalization, a problem recently highlighted as an important challenge in graph learning; see https://arxiv.org/abs/2402.02287, Section 3.1, Challenge III.4. Hence, we argue that CLRS is a high-quality benchmark and note that it is also widely adopted; see e.g., https://arxiv.org/abs/2209.11142, https://arxiv.org/abs/2403.04929, https://arxiv.org/abs/2402.01107, https://arxiv.org/abs/2404.03441, https://arxiv.org/abs/2312.05611, https://arxiv.org/abs/2210.05062. Finally, note that our concrete selection of tasks is partly also to validate our theoretical findings and not only to demonstrate SOTA performance on the most popular datasets; see also our remark in the general response on the intended scope of our work, in particular, regarding an insightful theoretical and empirical investigation of the ET. The above being said, we worked hard during the rebuttal to provide encouraging preliminary results on two additional datasets, see below. ### PCQM4Mv2 We evaluate on one random seed, as is common on this benchmark. \| Model \| Num. parameters \| Validation MAE \| \| --- \| --- \| --- \| \| GraphGPS-small \| 6M \| 0.0938 \| \| GRIT \| 17M \| 0.0859 \| \| TokenGT \| 50M \| 0.0910 \| \| ET \| 6M \| 0.0911 \| \| ET \| 17M \| 0.0883 \| ### ZINC-full We evaluate on 2 random seeds. The ET has 283,969 parameters. \| Model \| Test MAE \| \| --- \| --- \| \| SignNet \| 0.024 $\pm$ 0.003 \| \| Graphormer \| 0.052 $\pm$ 0.005 \| \| Graphormer-GD \| 0.025 $\pm$ 0.004 \| \| GRIT \| 0.023 $\pm$ 0.001 \| \| PST \| 0.018 $\pm$ 0.001 \| \| ET+RRWP \| 0.028 $\pm$ 0.002 \| Notably, on PCQM4Mv2 our 6M model outperforms the GraphGPS model at the same parameter budget while also being on par with transformer models such as TokenGT which has almost 5x as many parameters. On ZINC-full, we observe that the results of the ET are competitive with the best models, albeit not SOTA results. We note that achieving SOTA results on new datasets typically involves extensive hyper-parameter tuning. Due to the limited time during the rebuttal we were only able to test a few configurations and also at only a fraction of the number of epochs (1000 instead of 2000 on ZINC-full and 40 instead of 200 on PCQM4Mv2) of the baseline models. Nonetheless, our results indicate that with more time for properly tuning hyper-parameters and running the same number of epochs, the ET is a viable contender for SOTA results on both datasets. Finally, the reviewer says > In terms of the evaluation of expressive power, it would be better to include SOTA methods such as those subgraph-GNNs, potentially also discussing their complexity compared to ET > We refer the reviewer to Wang and Zhang 2023 (https://arxiv.org/abs/2304.07702), Table 2. Here, the authors have already evaluated a variety of subgraph GNNs on BREC. Most notably, the ET beats 7 out of 9 models on this benchmark. In what follows, we address the question of the reviewer. First, the reviewer asks > How does the setting of QM9 used in this paper differ from the setting that is commonly used in equivariant GNNs > In this work, for QM9, we adopt the setting used for SpeqNets (https://arxiv.org/abs/2203.13913), where tasks are learnt jointly and the resulting MAE is the average across all tasks, where we note that all targets are normalized by subtracting the mean and dividing by the standard deviation. We follow this setting to enable a comparison to the higher-order WL SpeqNets. We will add this description to the paper and plan to include results on QM9 in the more widely adopted single-task setting in the future. Next, the reviewer asks > Are there any particular benefits to having an expressive model without using PE or SE? […] because it would be more challenging to analyze expressive power with PE/SE, therefore it would be easier to understand a model's expressive power without using them? > and mentions that > I feel like depending on how PE is used, it is still possible to analyze the expressive power, e.g., via graph substructure counting > While it is true that the expressive power of PEs can be understood, in general, we argue that knowing which PEs to add is typically highly task-dependent; see e.g., the study in GraphGPS (https://arxiv.org/abs/2205.12454), as PEs are typically based on graph heuristics. This also holds for subgraph GNNs, where assumptions have to be made about the type of substructures that are relevant for downstream tasks. In contrast, the ET without any additional PEs already performs strongly, across tasks in molecular regression, algorithmic reasoning and graph isomorphism testing. We want to ask the reviewer to increase their score if they are satisfied with our response. We are happy to answer any remaining questions. --- Rebuttal Comment 1.1: Comment: I have read the authors' response and other reviews and intend to keep the original rating.	Summary: This work proposes an Edge Transformer (ET), a global attention model operating on node pairs instead of nodes. Authors theoretically demonstrate that ET has 3-WL expressive power with the proper tokenization. Experimental results demonstrate that the proposed model outperforms other theoretically aligned models in terms of predictive performance. Additionally, ET competes with state-of-the-art models in algorithmic reasoning and molecular regression tasks without relying on positional or structural encodings. Strengths: 1. The paper is well-written. All technical steps are easy to follow. 2. The proposed triangular attention is interesting and novel. 3. ET achieves impressive results for both molecular regression and algorithmic reasoning tasks. Weaknesses: 1. Previous work [1] has demonstrated that graph transformers (GTs) with proper positional encodings (PEs) can be more powerful than any WL test. Therefore, it is unclear why the authors aim to develop a model with 3-WL expressive power, which cannot be more expressive than prior GTs (e.g., [1]). Notably, given the cubic complexity of the proposed ET, computing PEs is no longer a scalability bottleneck. Consequently, if ET empirically outperforms GT+PE, it essentially implies that the WL hierarchy is not a meaningful metric in practice, undermining the purpose of building a 3-WL expressive model. 2. While the authors mention how to apply ET for node-level tasks, they provide no corresponding results. Given the cubic complexity of ET, it is likely not scalable to most graphs for node-level tasks. 3. Some relevant GT models haven't been discussed or compared (e.g., [1-3]). [1] Kreuzer et al., "Rethinking Graph Transformers with Spectral Attention", NeurIPS'21. \ [2] Zhu et al., "On Structural Expressive Power of Graph Transformers", KDD'23. \ [3] Deng et al., "Polynormer: Polynomial-Expressive Graph Transformer in Linear Time", ICLR'24. Technical Quality: 3 Clarity: 3 Questions for Authors: N/A Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: Please refer to the Weaknesses section for details. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for their effort and are happy to address the concerns raised by the reviewer. First, the reviewer says > Previous work [1] has demonstrated that graph transformers (GTs) with proper positional encodings (PEs) can be more powerful than any WL test > The work in [1] presents a universality result for transformers with Laplacian encodings. However, the transformer in [1] is not equivariant to node permutations, since the Laplacian encodings are not invariant to sign- and basis changes in the underlying eigenvalue decomposition. While a universal model is more expressive than any WL test, it is questionable whether the transformer in [1] is able to learn permutation equivariance from limited data. Theoretically, we expect worse generalization from non-equivariant models on graph tasks; see e.g., Petrache and Trivedi [2]. In fact, the lack of permutation equivariance could well explain the worse empirical performance of the model in [1] compared to the ET, e.g., on ZINC 12K. In summary, our theoretical results should be viewed under the assumption of permutation equivariance, where 3-WL is considered to have very strong expressive power. Next, the reviewer says > While the authors mention how to apply ET for node-level tasks, they provide no corresponding results > We refer the reviewer to the experiments on the CLRS benchmark. There, many tasks involve node- and edge-level predictions. The reviewer also mentions that > Given the cubic complexity of ET, it is likely not scalable to most graphs for node-level tasks. > We agree that the ET currently cannot be scaled to thousands of nodes and that most large-scale transductive node tasks are out of scope for the ET. Nonetheless, our results on CLRS indicate that the ET can be effectively used for node-level tasks. Finally, the reviewer mentions that > Some relevant GT models haven't been discussed or compared (e.g., [1-3]) > We are happy to include those models into our discussion. In particular, we will add a paragraph discerning expressivity results for permutation equivariant models as compared to non-equivariant but universal models such as the one in [1]. We want to ask the reviewer to increase their score if they are satisfied with our response. We are happy to answer any remaining questions. ### References [1] Kreuzer et al., Rethinking Graph Transformers with Spectral Attention, 2021 https://arxiv.org/abs/2106.03893 [2] Petrache and Trivedi, Approximation-Generalization Trade-offs under (Approximate) Group Equivariance, 2023 https://arxiv.org/abs/2305.17592 --- Rebuttal 2: Title: Follow-up Comment: Thanks for authors' detailed response. By node-level tasks, I’m actually referring to some larger graphs for node classification (e.g., citation/biological networks) rather than neural algorithmic reasoning tasks. I’m interested in seeing how well the proposed approach scales with larger graphs. >We want to ask the reviewer to increase their score if they are satisfied with our response. I'm really not a big fan of explicitly asking reviewers to change their scores in this way. Authors could say "reconsidering their score" instead. That said, I do appreciate the major contributions of this work and increase my score to 7.	Rebuttal 1: Rebuttal: We thank all reviewers for their time and effort and the valuable feedback they provided for our work. Here, we address two common concerns. In addition, we provide parameter counts for each dataset. ### On the novelty and contribution of our work Here, we address the concern that our work is not novel because we do not propose a new architecture. Indeed, we adopt the existing ET architecture, with almost no modifications. At the same time, we want to point out that novelty does not solely originate from proposing novel architectures. Concretely, we regard the main contribution of our work as establishing the connection between the ET, its systematic generalization capabilities and graph learning (Sections 3 and 4). In particular, we provide two highly non-trivial proofs that show that the ET has exactly 3-WL expressive power. Our empirical study (Section 5) is aimed at both validating the theoretical findings, as well as demonstrating that the ET can effectively translate its expressive power into strong empirical performance. As such, our work should be viewed as a theoretical and empirical investigation rather than proposing a novel method. ### On the practical usefulness of the ET Here, we address the concern of the practical usefulness of the ET and the results in our paper, given its cubic runtime and memory complexity. As already addressed in our limitations section, the ET has indeed a high runtime and memory complexity. At the same time, we want to highlight that the ET shows very strong performance on smaller graphs, in particular, on molecular graphs. As such, we believe the ET to be very useful in the context of molecular representation learning. Here, we want to highlight TGT (https://arxiv.org/abs/2402.04538) and AlphaFold 3 (https://www.nature.com/articles/s41586-024-07487-w), two recent works that use models with a triangular attention mechanism for learning molecular representations. In particular, both works compute attention scores over triplets of nodes. Although the attention mechanism in these works differs from the one in the ET, their strong performance demonstrates nonetheless the usefulness of studying triangular-style attention and its impact in molecular representation learning. Most notably, the authors of TGT refer to https://arxiv.org/abs/2302.05743 to motivate their work, arguing that > 3rd-order interactions are crucial for geometric understanding, yet ≥4th-order interactions add little/no benefit at much higher computational cost > In addition, the ET performs particularly well on CLRS. We refer the reviewer to the CLRS paper (https://arxiv.org/abs/2205.15659) as well to https://arxiv.org/abs/2105.02761, for an in-depth discussion of the potential use-cases of algorithmic reasoning in neural networks. ### Number of parameters Here, we report the number of parameters of the ET without positional encodings. \| Dataset \| Num. parameters \| \| --- \| --- \| \| ZINC 12K \| 280,897 \| \| Alchemy 10K \| 295,356 \| \| QM9 \| 257,916 \| \| CLRS \| 1,371,264 \| \| BREC \| 58,112 \| Here, we report the number of parameters of ET+RRWP. \| Dataset \| Num. parameters \| \| --- \| --- \| \| ZINC 12K \| 283,969 \| \| Alchemy 10K \| 298,428 \| \| QM9 \| 260,988 \|	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Association Pattern-aware Fusion for Biological Entity Relationship Prediction	Accept (poster)	Summary: The paper introduces an innovative perspective, namely association pattern, for biological entity relationship prediction (e.g., drug-target protein-adverse reaction). The authors first summarize the characteristics of existing perspectives and emphasize the importance of the association pattern. Next, the association patterns of certain entity nodes are sampled in the constructed graph based on the defined distance and then serve as tokens for self-attention to fuse similar semantic information. Additionally, the bind-relation enhancement module can effectively reconstruct the missing feature and thus generate hard negative samples for further improving the performance. Extensive experiments on biological datasets demonstrate the effectiveness of the proposed method. Strengths: 1. The perspective of triple-wise association patterns, which takes the actual meaning of each entity and their connections into account, is novel and explainable. 2. The paper comprehensively discusses the advantages of the proposed method compared with existing non-graph, graph, and hypergraph perspectives. Moreover, the related works on biological entity relationship prediction and path-based graph mining are elaborated. 3. The paper provides a clear and detailed description of each part of the method, and the formulas used in the paper seem correct. The overall design of the method is rather reasonable. 4. Extensive experiments on biological datasets demonstrate the effectiveness of the proposed method. The reveal of the intrinsic biological mechanism can indeed promote the deployment of the method in real-world scenarios. 5. The association pattern-aware perspective appears to apply to commonly used graph benchmarks or tasks, which can be leveraged to enhance existing graph-based methods. Weaknesses: 1. The bind-relation feature reconstruction appears to be a standalone component that requires extra separate training, resulting in a two-stage process for the method. Additionally, such a design may influence the entire optimization process and distract the training flow, how to alleviate that? 2. Generalization and extension issues have not been discussed. The pattern's length is fixed to 3, which may make the method not work when facing longer-range relationships. Are there any feasible solutions for sampling patterns with different lengths? 3. Complexity has not been discussed. Some details are also not clear enough, such as in Line 167, could the authors provide details on how the position encoding is designed? In Fig. 2, the meaning of the dotted line "Bind-relation Feature" needs more explanation. The "add" operation is not reflected in Section 4.3. Please explain the meaning of the dotted line "Bind-relation Feature". Technical Quality: 3 Clarity: 3 Questions for Authors: Q1: The paper does not give a specific explanation of $L_{BE}$ (see Line 224). Please give a specific explanation of $L_{BE}$. Q2: In Table 1, the authors appear to have not reported the statistical measures like standard error. Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The authors have adequately discussed the limitations. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for all the comments. We believe we have addressed all the concerns and are happy to follow up in the discussion phase. > W1: The bind-relation feature enhancement module needs extra separate training? A: Thanks for pointing this out. Our description may not be entirely clear, and the overall architecture is actually quite straightforward. The core components are two complementary modules: Association Pattern-aware Fusion (APF, Section 4.2), Bind-relation Enhancement (BE, Section 4.3) with their corresponding losses. * Training strategy. Actually, the method does not adopt two completely independent training stages, but rather achieves it through an alternating training strategy. Specifically, the BE module is trained for the first 4 epochs of every 5-epoch cycle, followed by the APF module, which is trained for the final epoch of each cycle. During the training of each module, the parameters of the other one are frozen. Moreover, this design satisfies the need of generating hard negative samples for the APF module, hence the BE module requires initial and additional training. * Loss funtions. The BE losses (Eq. 7 & Eq. 8) are utilized to supervise the reconstruction of missing pairwise feature and the generatation of hard negative samples. Consequently, the BE module necessitates additional initial training to prevent low-confidence negative samples for the APF module. Following this, the supervised loss $\mathcal{L}_{APF}$ (Eq. 10) is utilized to determine the positive triplet samples and these negative samples generated from the BE module. Hence, the total loss function is formulated as $\mathcal{L}(o) = \mathcal{L}\_{\text{BE}}(o) \cdot (1 - \left\lfloor \frac{o \mod 5}{4} \right\rfloor) + \mathcal{L}\_{\text{APF}}(o) \cdot \left\lfloor \frac{o \mod 5}{4} \right\rfloor$, where $o$ represents the current epoch; $\lfloor \cdot \rfloor$ denotes the floor function; $\text{mod} $ denotes the modulo operation. We will make the description of the entire architecture more clear for understanding. > W2: Generalization issues about sampling patterns with different lengths. A: Thanks for advice. As shown in Table R2 (response PDF), the proposed method has been extended with variable-length settings and thus applied on the molecular property prediction tasks. See Q3 of reviewer ugjG for details. > W3.1: Computation complexity. A: Thanks for concern. The computation complexity depends on the number of entity nodes and sampled patterns, and we discuss the solution for complexity explosion. Please refer to Q1 & L1 of reviewer ugjG for details. > W3.2: Details about how the position encoding designs. A: Thanks for your feedback. First, we would like to clarify that the purpose of designing this position encoding is to enable the model to recognize the relative position of the selected entity node in relation to these patterns. This function is analogous to how the Transformer [A] and ViT [B] architectures handle the relationship between "tokens/patches and their positions." Specifically, in Association Pattern Sampling (APS) block, the $N$ sampled patterns are assigned to certain node $v$ according to the defined distance. On the one hand, each sampled pattern consists of three entity nodes with $F$-dimension feature embedding, and thus the feature embedding of each pattern is denoted as $\mathbb{R}^{3F}$, which represents the concatenation of the original node feature embeddings, thereby obtaining the feature vector $\mathbf{P}_v \in \mathbb{R}^{N \times(3F)}$ of all the $N$ sampled patterns; on the other hand, each sampled pattern has a distance label defined in Line 154-158 with node $v$. To connect the pattern feature embeddings with the corresponding position information $\mathbf{D}_v \in \mathbb{R}^N$, we provide a position encoding layer $\text{POS}(\cdot)$ which represents a map function from $\mathbb{R}^N$ → $\mathbb{R}^{N \times(3F)}$, and finally integrate $\mathbf{P}_v$ and $\text{POS}(\mathbf{D}_v)$, thereby outputting the enhanced embedding for the next Association Pattern-aware Interaction (API) block. > W3.3: Explanations for "Bind-relation Feature" and "add" operation in Fig. 2. A: Thanks for detailed observation. Line 194-199 shows two main functions of the BE module: (1) to reconstruct the missing pairwise feature; (2) to generate hard negative samples. The "Bind-relation Feature" in Fig. 2 actually denotes the above missing pairwise future. Hence, the blue dotted line "delivers" the BE pairwise feature to the APF module, and the icon $\oplus$ "integrates" the two feature embeddings from the BE module and the APF module. Finally, the enhanced feature embedding is fed into the predictor. The above integrating process has been mentioned in Line 219-220, and we will highlight the description with a more separate and clear paragraph. > Q1: Specific explanation of $\mathcal{L}_{BE}$ (Line 224). A: Thanks for careful reading and feedback. The $\mathcal{L}_{BE}$ actually denotes the supervised loss of the BE module. The calculation is defined in Line 209, which is equal to the $\mathcal{L}_2$. We will modify $\mathcal{L}_2$ in Line 209 to $\mathcal{L}\_{BE}$. > Q2: Standard error in Table 1? A: Thanks for the concern regarding statistical measures. As mentioned in the Appendix B.3.1 and Checklist Q7, each result of these methods in Table 1 is calculated from the average of 5-fold cross-validation experiments with four different scenarios. However, the significant variation in prediction difficulty across different scenarios makes it relatively unreasonable to provide an error bar for all 20 results. Hence, to demonstrate the statistical validity of Pattern-BERP, we have provided all the raw experimental results in Supplementary Materials. References [A] Vaswani et al., Attention is all you need. NeurIPS, 2017. [B] Dosovitskiy et al., An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale. ICLR, 2020. --- Rebuttal Comment 1.1: Title: To Authors Comment: I thank the clear and comprehensive response, and my concerns have been mainly addressed especially on the generalization issue, so I raise my final voting to 7. Please provide such discussions in camera-ready. --- Reply to Comment 1.1.1: Comment: We appreciate your acknowledgment of our responses in addressing your concerns. The relevant discussions regarding the extension of variable-length patterns will be elaborated in the final version. Your insights are crucial in enhancing the quality of our work. Thank you once again for the thoughtful review.	Summary: This paper presents a novel approach to predicting relationships among biological entities by addressing limitations in current deep learning methods that focus solely on entity-centric information. The authors introduce an association pattern-aware fusion method that integrates association pattern information into entity representation learning. Additionally, they develop a bind-relation module to enhance low-order message passing by considering strong low-order entity associations. Extensive experiments on three biological datasets demonstrate significant improvements compared to advanced baselines. The paper also provides detailed explanations of the interpretability of association patterns, highlighting intrinsic biological mechanisms and potential real-world applications. Strengths: - The introduction of an association pattern-aware fusion method is innovative. It effectively integrates association pattern information into entity representation learning, which is a novel approach compared to traditional entity-centric methods. - The method includes several interconnected modules such as association pattern sampling, pattern-aware interaction, and bind-relation enhancement. Extensive experiments on three biological datasets demonstrate significant improvements compared to advanced baselines. - The method provides detailed explanations of the interpretability of association patterns. This helps in understanding the intrinsic biological mechanisms, making the results more transparent and useful for real-world applications. Weaknesses: - The proposed model involves multiple modules and several hyperparemeters. Some hyperparameters (such as the number of attention head) are vary on different datasets. The authors may aslo need to add hyperparameter study for loss-balanced coefficient and the threshold for bind-relation prediction probability. - The approach may not scale well with increasing dataset sizes or more complex biological networks due to its computational requirements and the need for extensive pattern sampling and interaction modeling. - The proposed model involves multiple components such as hypergraph convolution, pattern-aware fusion, and bind-relation enhancement, which can be computationally intensive. This might limit its applicability for large-scale real-world datasets or in environments with limited computational resources. The author may also need to provide inference speed study with some of the baselines. Technical Quality: 3 Clarity: 3 Questions for Authors: Please see the weaknesses. Confidence: 2 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: They provide a limitation section in the appendix. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for all the comments. We believe we have addressed all the concerns and are happy to follow up in the discussion phase. > W1.1: Some hyperparameters (such as the number of attention heads) vary on different datasets. A: We appreciate your valuable feedback. Actually in the machine learning field, performing grid search for hyperparameters is a common practice across different datasets or tasks to achieve optimal results. Therefore, given the significant differences in distribution and association sparsity among datasets, it is entirely reasonable for us to obtain distinct optimal hyperparameter sets, including the number of attention heads mentioned by the reviewer. > W1.2: More hyperparameter studies for loss-balanced coefficient and the threshold for bind-relation prediction probability. A: Thanks for your careful reading. We provide additional hyperparameter studies as follows: * Loss-balanced coefficient $\alpha$. Since the final prediction task involves predicting the associations among entity A, B, and C, we intuitively consider the two tasks of A→B and B→C to be of equal importance and thus the $\alpha$ is set to 0.5 by default. Here, we attempt to adjust $\alpha$ from 0.1 to 0.9, and the results are shown below (the hits@1 with default $\alpha$=0.5 is 93.94). The hits@1 performance of the default setting surpasses other ablation settings. \| coefficient $\alpha$ \| hits@1 \| coefficient $\alpha$ \| hits@1 \| \| -------------------- \| ------ \| -------------------- \| ------ \| \| 0.1 \| 92.91 \| 0.6 \| 92.79 \| \| 0.2 \| 93.87 \| 0.7 \| 93.25 \| \| 0.3 \| 93.86 \| 0.8 \| 93.66 \| \| 0.4 \| 93.32 \| 0.9 \| 93.23 \| * Threshold $\gamma$ for bind-relation prediction probability. Bind-relation prediction is fundamentally a binary classification task, so setting the threshold to 0.5 by default is quite common. Here, we also attempt to adjust the threshold $\gamma$ from 0.1 to 0.9, and the results are shown below (the hits@1 with default $\gamma$=0.5 is 93.94). The hits@1 performance of the default setting surpasses other ablation settings. It is noteworthy that when $\gamma$=0.1, the generation of negative samples is extremely hard as defined in Eq. 9, and thus the BE module cannot provide valid hard samples. \| threshold $\gamma$ \| hits@1 \| threshold $\gamma$ \| hits@1 \| \| ------------------ \| ---------------- \| ------------------ \| ------ \| \| 0.1\| No Valid Samples \| 0.6\| 92.17 \| \| 0.2\| 91.88 \| 0.7\| 93.67 \| \| 0.3\| 92.91 \| 0.8\| 93.88 \| \| 0.4\| 93.48 \| 0.9 \| 93.81 \| > W2: Computation complexity explosion for huger dataset or more complex biological networks. A: Thanks for your valuable insight. As discussed in Q1 by reviewer ugjG, the total complexity of the entire graph is denoted as $ \mathcal{O}\left(\|\mathcal{V}\| \cdot (N^2 \cdot d + N \cdot d^2 + N \cdot d \cdot f) \right)$, where $\|\mathcal{V}\|$ represents the number of entity nodes, $N$ represents the number of sampled patterns, the dimensions of all input pattern features and hidden features in MHA layer are $d$ and the hidden features in FFN layer is $f$. It is evident that computational complexity is primarily determined by the number of entity nodes $\|\mathcal{V}\|$ and the number of sampled patterns $N$. Hence, when encountering larger datasets or more complex biological networks, we can employ the following two strategies to avoid a computation complexity explosion: (1) Graph Sampling. Processing large graph data requires significant computational resources. By sampling smaller subgraphs [A], computational resource consumption can be significantly reduced, improving the speed and efficiency of algorithms; (2) High-confidence Pattern Selection. As shown in Fig. 4 (g)-(i), reducing $N$ from 100 to 5 across three datasets slightly decreases performance but still surpasses these baselines. Thus, adjusting the sampling quantity is acceptable to effectively reduce time complexity. Furthermore, to test on larger and diverse datasets, our approach is refined to capture variable-length patterns and applied to large-scale molecular property datasets. As shown in Table R2 (response PDF), the association patterns significantly enhance atom (analogous to entity nodes in this study) representations and improve prediction performance. > W3.1: Limitation of applying in large-scale real-world datasets or environments with limited computational resources. A: Thanks for your further concern regarding the real-world scenarios. As discussed in W2, the computation complexity can be controlled through some reasonable strategies, such as graph sampling and pattern selection. Moreover, substantial computational resources are typically deployed on central servers in the field of bioinformatics, unlike the field of computer vision, which often requires deployment on resource-constrained devices. > W3.2: Inference speed study compared to baselines. A: Thanks for highlighting this aspect. We provide the inference speed comparison with other methods as follows and present the inference time of each 100 samples with milliseconds. Compared to the baseline methods, the difference in inference time for our method is constant and even faster than several baselines. \| Method \| DMD (ms) \| DDC (ms) \| DPA (ms) \| \| ---------------- \| -------- \| -------- \| -------- \| \| RF \| 0.36\|0.66\| 0.57 \| \| MLP \| 0.18\| 0.21 \| 0.26 \| \| CP\| 8.98\| 9.19 \| 10.25\| \| Tucker\| 7.92 \| 8.84 \| 7.96\| \| CoSTCo\| 0.75 \| 1.51\| 3.15\| \| GCN \| 0.80 \| 0.99\| 1.95\| \| GraphSAGE \| 0.81 \| 0.95\| 1.92\| \| GAT \| 1.18 \| 1.61 \| 3.11 \| \| GIN \| 0.72\| 1.14 \| 1.86\| \| DHNE \| 0.29 \| 0.29 \| 0.39\| \| HyperSAGNN \| 0.63 \| 0.69\| 0.56\| \| HGSynergy \| 0.64 \| 0.89\| 1.55 \| \| MCHNN (CPU-only) \| 8.65 \| 9.54 \| 13.72 \| \| Pattern-BERP \| 1.28 \| 1.24\| 2.96\| References [A] Hu and Lau, A survey and taxonomy of graph sampling. arXiv, 2013. --- Rebuttal Comment 1.1: Title: To Authors Comment: Thanks for your responses. I think my rating is reasonable and fair. --- Reply to Comment 1.1.1: Comment: Thanks for your efforts and the considerable recognition of our paper. The quality of the manuscript will be greatly improved in accordance with your valuable comments.	Summary: The author proposed a deep learning method, termed the Pattern BERP method, designed to elucidate the potential associations among triple-wise biological entities. This method innovativly incorporates association pattern information into the entity representation learning. Moreover, it employs two additional bipartite graphs to enrich the binary relation information extracted from triple entities. Evaluated on three biological datasets, the proposed method demonstrates superior performance compared to non-graph, graph-based, and hypergraph-based methodologies. This work is noteworthy not only for its impressive predictive accuracy but also for its potential applicability in real-world scenarios. Strengths: 1. The concept of k-hop neighbors on a hypergraph has been defined, incorporating pattern-similar triples information as neighbors into each hypernode. 2. The information of triples has been decomposed into pairwise relationships, and these features have been injected into the backbone network. 3. A parameter-based negative sampling technique has been introduced, which is more efficient compared to random sampling. Weaknesses: 1. The interpretation provided for the model is not entirely persuasive. The analysis of the relationship between peptide-based micro-molecular drugs and small-molecular chemical drugs is unconventional and lacks commonality. 2. While the concept of association pattern-aware fusion is highly innovative and appropriately highlighted as the main focus of the paper, its contribution for model performance seems not to be impressive, especially in Table 5 and Table 6. 3. The model is overly complex, with multiple stages of tasks and losses, which may lead to difficulties in optimization. 4. The role of the triple information has been simplified to a single chain pattern from A to B to C. Technical Quality: 3 Clarity: 2 Questions for Authors: 1. The abbreviation "APF" (association pattern fusion) is not defined in the text at line 219. It is essential to provide the full name when first introduced for clarity. 2. In equation (11), the LBE is not updated every epoch, which contradicts the description in the text. 3. The manuscript features two bipartite graphs in Figure 2, yet it remains unclear whether these graph features are integrated with hypergraph features. Additionally, the role of the blue dotted line arrow, which is not discussed in the text, needs clarification to enhance understanding of the graphical representations. 4. Although the association pattern-aware fusion is novel and central to the paper's title, its contribution for model performance seems not to be impressive. Specifically, while Table 2 shows significant impairment in performance on the DDC dataset without the association pattern interaction (API), Tables 3 and 4 for the DMD and DPA datasets suggest that the Binding-relation Feature Reconstruction (BFR) for bipartite graphs predominantly enhances performance. It may be misleading to attribute the main contribution of the work solely to APF given these findings. 5. The model interpretation in Figure 3 lacks persuasiveness, as Drug #52, a peptide with numerous sub-group structures, is not ideal for visualization comparison with other compound drugs. Furthermore, in equation (3), the attention mechanism is applied across different triple entities, not just one. Analyzing only the drugs without considering the other two entities in the figures is insufficient. At minimum, the roles of the other two entities should be elucidated to provide a more comprehensive analysis. 6. Equation 2 describes the generation method of the distance matrix D and the distance token 𝐷𝑣. How is the specific position embedding done on line 167? Is the initial pattern 𝑃 directly concatenated from the three nodes? 7. In the bind-relation enhancement, why is only the bipartite graph between AB and BC considered? Why not consider AC? Not all multi-entity relationships have a clear chain pattern from A to B to C. 8. Following up on question 7, how are relationships defined between two entities in Equations 7 and 8? Confidence: 3 Soundness: 3 Presentation: 2 Contribution: 2 Limitations: The model lacks practical application scenarios. It primarily learns from the interaction network of existing entities such as drugs, diseases, and symptoms. Such methods generally struggle to predict the relationships between a completely new entity and the existing entities in the network. Moreover, the relationships within the network are already well-known. The more important task is to uncover new and potential relationships. The comprehensiveness and accuracy of the existing relationships are merely the tasks designed by the model itself. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for all the comments. We believe we have addressed all the concerns and are happy to follow up in the discussion phase. > W1: The provided interpretation study lacks absolute persuasiveness. A: Thanks for your insight. There are two additional interpretation cases in Fig. R1 (response PDF), which shows the common patterns closely linked to the original drug node reflect the mechanism that acts on the cell wall and envelope and thus influences microbe physiological activities, thus treating diseases. In contrast, the low-contribution pattern causes cell death by inhibiting protein synthesis. We will provide detailed text descriptions for interpretation cases in the future. > W2: The contribution of APF seems not to be impressive in Table 5&6. Which module contributes more to three different datasets? A: Thanks for your valuable feedback. The situation arises due to significant differences in the distribution and sparsity of these three datasets (see Appendix Table 3). Table 2 shows that APF's contribution stands out in the DDC. However, in the relatively sparse DMD and extremely sparse DPA, there are fewer high-confidence patterns associated with entity nodes (some nodes link to only one pattern), reducing the APF module's effectiveness. In the future, as biological association datasets grow larger and denser, APF's pattern exploration will yield more expressive representations, making its contribution more impressive. > W3: Overly complex model architecture with multiple stages of tasks and losses. A: Thanks for concern. The core components are two complementary modules: Association Pattern-aware Fusion (APF), Bind-relation Enhancement (BE) with their corresponding losses. Due to the limited response characters, please refer to W1 of reviewer UqdA for details. > W4: The triple information is simplified to a single chain pattern from A to B to C. A: Thanks for pointing this out. In this study, the triplet relationship we investigate is defined as the A→B→C pattern due to dataset limitations, making it challenging to collect substantial longer physiological pathway data. As noted in the Limitation section, we plan to extend to longer pattern pathways and have already obtained some preliminary results. > Q1: Full name of APF when first introduced. A: Thanks for careful reading. The abbreviation APF denotes Assocaition Pattern-aware Fusion, which will be introduced in Line 149. > Q2: Ambiguity for total loss function in Section 4.4. A: Thanks for carefulness. The total function is revised by the rule: BE module trains for the first 4 epochs of each 5-epoch cycle; APF module trains for the final epoch. Please refer to W1 of reviewer UqdA for details. > Q3: Unclear description for bipartite graph feature in Fig. 2 and its caption. A: Thanks for pointing it out. The bipartite graph features are integrated with hypergraph features, represented by the blue dotted line arrow. Please refer to W3.3 of reviewer UqdA for details. > Q4: The peptide is not ideal for visualization comparison with other compound drugs. A: We understand your concern. Additional cases in Fig. R1 (response PDF) are both discussed with small molecule drugs. > Q5: The roles of the other two entities should be elucidated in the interpretation study. A: Thanks for highlighting this aspect. Due to insufficient dataset information, we cannot obtain identifiers for Microbe and Disease entities, which are directly processed into feature vectors in the original DMD dataset [17]. In the future, we will focus on intrinsic interpretation using more comprehensive datasets. > Q6: Details about how the position embedding works (line 167). Is the initial pattern $P$ directly concatenated from the three nodes? A: Thanks for pointing it out. The purpose of designing this position encoding is to enable the model to recognize the relative position of the selected entity node in relation to these patterns. Please refer to W3.2 of reviewer UqdA for details. In this work, each sampled pattern consists of three different types of entity nodes representing a reaction pathway. These patterns may contain common knowledge (see Fig. 2), aiding in learning more expressive representations for entity nodes. Additionally, in the Limitation section, we propose exploring variable-length patterns to identify more representative pathways. > Q7: Why not consider A→C in the bind-relation enhancement? A: Thanks for your concern. Our focus is on the triplet relationships like Drug→Protein→ADR discussed in the paper. Typically, a drug interacts with a target protein, triggering signals that cause various activities, some manifesting as ADRs like vomiting or diarrhea. Therefore, we did not consider a direct A→C relationship, as there is no connection in this context. However, we acknowledge your perspective on broader multi-pathway relationships where a direct A→C could exist. We will consider it for future tasks. > Q8: The defined relationships between two entities in Equations 7 and 8. A: Thanks for highlighting this aspect. In this paper, A→B and B→C have clear biological associations, reflected in the data through labels. However, the A→C relationship is determined by modeling new negative samples A→B→C (Bottom right of Fig. 2, Line 211-217). > L: The model struggle to predict the relationships between a completely new entity and the existing entities in the network, thus lacking practical application scenarios. A: Thanks for guidance on future direction. Our core goal is to uncover common association patterns between biological entities, which remain unchanged with the addition of new nodes. Conversely, by linking new nodes to existing ones through common patterns, we aim to uncover new potential relationships. Of course, we highly appreciate your viewpoint. The current model design indeed lacks the ability to introduce new entity nodes. We will improve it in the future to facilitate the practical application. --- Rebuttal Comment 1.1: Comment: Thanks for detailed response. I have raised the score. --- Reply to Comment 1.1.1: Comment: We appreciate your effort on our paper and the recognition of our responses. Your unique insights and detailed review have significantly enriched our work, allowing us to further refine this manuscript. Thank you once again for your valuable feedback.	Summary: This work presents a novel approach - Pattern-BERP - for the prediction of biological entity relationships, it utilises entity association patterns as opposed to a lot of existing research that focuses primarily on entity-centric information mapping and aggregation. The evaluation is done on three different biological datasets (DMD, DDC, DPA), and compared against a range of different approaches including non-graph, graph-based and hypergraph-based ones. The results show state-of-the-art performance across the board (an increase from 2 to 10 points over the next best method). The authors also do an ablation study, showing the importance of each component and demonstrating the relative improvement. Strengths: A novel idea presented in an easy-to-understand way. Manuscript is nicely written and clear, with a broad impact. An extensive evaluation concerning methods, state-of-the-art results and a detailed ablation study. Weaknesses: This is a very general method but it was tested on only one dataset type and relatively small datasets. Would be great to see it expanded in the future. Technical Quality: 3 Clarity: 3 Questions for Authors: Similar to the limitations field, I'd be very interested in an explanation of how the computation complexity of Pattern-BERP scales with the number of entities and associations. Is it possible to provide a bit more theory behind the success of your method compared to others? The justification for the association pattern-aware fusion to me seems mostly intuitive rather than theoretical. Is there a way to extend the method to capture variable-length pathways? Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: It would be great to see a longer discussion on limitations: my primary concerns are complexity explosion and very large datasets. Would be great to see a bit of a theoretical analysis (or even empirical) on how it scales for millions of entities or associations (which are not rare in the domain). The interpretability section focuses on only drug #52, it would be great to see that expanded, as making conclusions from one example is bit of a stretch. Real-world applications might be a bit of an overstatement, while it is possible, nothing was really tested or proven. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for all the comments. We believe we have addressed all the concerns and are happy to follow up in the discussion phase. > W: Possibility to test on more dataset types and relatively huge datasets? A: We appreciate your insight. Firstly, we clarify that the limited associations in this study result from current research constraints, despite large Cartesian products in Appendix Table 3. Previous works [15-17,19] also used similar dataset types. To test on larger, diverse datasets, our approach is refined to capture variable-length patterns and applied to large-scale molecular property datasets. As shown in Table R2 (response PDF), the association patterns significantly enhance atom (analogous to entity nodes in this study) representations and improve prediction performance. > Q1: How the computation complexity of Pattern-BERP scales with the number of entities and associations? A: Thanks for your concerns. The most critical module is undoubtedly the APF, which aggregates multiple patterns across different entity nodes. This module includes Multi-Head Attention (MHA) and FeedForward Network (FFN). For an entity node with $N$ sampled patterns from the APS module, the input and hidden features in the MHA layer are of dimension $d$, and hidden features in the FFN layer are $f$, and the query, key, and value matrices are derived from the same input sequence and share length $N$. In APF, the primary operations include scaled dot-product attention, multiplication of attention weights and values, MHA linear transformation, and FFN linear projection. The time complexity is expressed as $\mathcal{O}(N^2 \cdot d + N \cdot d^2 + N \cdot d \cdot f)$. Hence, for the entire graph, the total complexity is $\mathcal{O}\left(\|\mathcal{V}\| \cdot (N^2 \cdot d + N \cdot d^2 + N \cdot d \cdot f)\right)$, where $\|\mathcal{V}\|$ is the number of entity nodes. Moreover, Table R1 (response PDF) shows the GPU usage of Pattern-BERP scaling with the number of entities and patterns. > Q2: Theory behind the success of the method. A: Thanks for highlighting this point. Pattern-BERP is regarded as an empirical method. It extracts common patterns or rules from large bio-associated datasets, similar to k-means clustering. Given a triplet dataset $\mathcal{D}=\\{\mathbf{x}\_1,\mathbf{x}\_2,\ldots,\mathbf{x}\_n\\}$ and $k$ common patterns, our goal is to minimize the total distance of samples to their respective pattern centers within the same pattern. First, initialize the pattern centers $\mathbf{m}\_1,\mathbf{m}\_2,\ldots,\mathbf{m}\_k$. Next, assign each sample to the nearest pattern center by computing $j=\arg\min_k \\\|\mathbf{x}\_i-\mathbf{m}\_k\\\|$. Then, update the pattern centers using $\mathbf{m}\_j=\frac{1}{\|C_j\|}\sum_{\mathbf{x}\_i \in C_j}\mathbf{x}\_i$, where $C_j$ is the set of samples assigned to pattern $j$. Iterate these assignment and update steps until the pattern centers converge. The objective function to minimize is $J=\sum_{j=1}^{k}\sum_{\mathbf{x}\_i \in C_j} \\\|\mathbf{x}\_i - \mathbf{m}\_j\\\|^2$, and by minimizing $J$, Pattern-BERP extracts representative biological association patterns effectively. In the future, additional corresponding theoretical analysis will be provided in detail. > Q3: Method extension to capture variable-length pathways. A: Thanks for constructive advice. As discussed this limitation in Appendix Section C, we strived to extend the method to capture variable-length patterns after the paper submission. Since now, the proposed method has been optimized with variable-length settings and thus applied on the molecular property prediction tasks to enhance the atom (in line with entity in this paper) representation in the molecular graph. Table R2 (response PDF) demonstrates the effectiveness of variable-length association patterns. > L1: Discussion on very large datasets and complexity explosion. A: We understand your primary concern. Regarding computation complexity, the discussion in Q1 indicates that the decisive factors are the number of entity nodes $\|\mathcal{V}\|$ and the number of sampled patterns $N$. Hence, when encountering larger datasets or more complex biological networks, we can employ the following two strategies to avoid a computation complexity explosion: (1) Graph Sampling. By sampling smaller subgraphs [A], computational resource consumption reduces significantly, boosting algorithm speed and efficiency; (2) High-confidence Pattern Selection. As shown in Appendix Fig. 4 (g)-(i), reducing $N$ from 100 to 5 across three datasets slightly decreases performance but still surpasses these baselines. Thus, adjusting the sampling quantity is acceptable to effectively reduce time complexity. Moreover, Table R1 (response PDF) shows the GPU usage varying from the number of sampled pattern across three datasets with significant differences in the number of entities and associations. The inference time compared to baselines can be found in W3.2 of reviewer 4Nwa. > L2: Interpretability analysis of more cases. A: Thanks for your insight. There are two additional interpretation cases in Fig. R1 (response PDF), which shows the common patterns closely linked to the original drug node reflect the mechanism that acts on the cell wall and envelope and thus influences microbe physiological activities, thus treating diseases. In contrast, the low-contribution pattern causes cell death by inhibiting protein synthesis. > L3: Restate real-world applications of the proposed method. A: Thanks for pointing this out. Actually in Appendix Section C, we would have intended to discuss the possibility of applying our proposed APF-BERP in real-world scenarios and the corresponding limitations. Due to limited resource and time, we cannot indeed validate it with enough real tests or proofs. We will restate the confusing description about the real-world applications. References [A] Hu and Lau, A survey and taxonomy of graph sampling. arXiv, 2013. --- Rebuttal Comment 1.1: Title: All clear Comment: Thank you for the answers, all is clear. --- Reply to Comment 1.1.1: Comment: Thank you for your time and effort on our paper. We are delighted to hear that our responses are clear and satisfactory. Your thorough review and constructive feedback have significantly contributed to the refinement of our manuscript.	Rebuttal 1: Rebuttal: We thank all reviewers for the time spent reviewing the paper and recognizing the significance ("with a broad impact" – ugjG, "noteworthy" & "impressive predictive accuracy" & "more efficient" – m3DY, "significant improvements" – 4Nwa), novelty ("novel idea" – ugjG, "highly innovative" – m3DY, "innovative" & "a novel approach" – 4Nwa, "novel and explainable" & "reasonable" – UqdA) of our research direction, the quality of the presentation ("nicely written and clear" & "presented in an easy-to-understand way" – ugjG, "clear and detailed" & "comprehensively discusses" – UqdA), and applicability ("potential applicability in real-world scenarios" – m3DY, "more transparent and useful for real-world applications" – 4Nwa). We have endeavored to consider the feedback as comprehensively as possible, leading to a revision process that significantly honed the paper. We have addressed every point in our responses and are happy to follow up on any aspect during the discussion phase. Specifically, we have tackled stated weaknesses (W), questions (Q), and limitations (L) with detailed answers (A). Additionally, we have included a single-page PDF containing extra referenced figures and tables to further clarify our points. Furthermore, we have strived to balance making all necessary changes within the given space constraints. However, due to the response length limitations, our answers to some common but important problems that require detailed explanation may refer to the response provided to another reviewer, indicated by the statement "please refer to the response for another reviewer." We sincerely apologize for any inconvenience this may cause. Finally, we would like to express our appreciation once again for the reviewers' constructive comments and careful reading, which undoubtedly lead to enhancing the quality of our work. Pdf: /pdf/962e8e2ed064fe5abcdb95659b0be40eafb1a159.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Warped Diffusion: Solving Video Inverse Problems with Image Diffusion Models	Accept (poster)	Summary: This paper aims to address video inverse problems using image diffusion models. By viewing videos as sequences of warping transformations between frames, the authors propose a novel approach called warped diffusion from a continuous function space perspective. Specifically, warped diffusion includes a Gaussian process-based noise-warping technique and a post-hoc equivariance self-guidance method to enhance temporal consistency. Experiments on video super-resolution and inpainting validate the effectiveness of warped diffusion. Moreover, warped diffusion first demonstrates superior performance with latent diffusion models such as SDXL. Strengths: 1. The proposed method is well-motivated with well-constructed formulations. 2. The paper is well-written. 3. The visualization results are impressive. Weaknesses: 1. As illustrated in Table 1 and Figure 3, the proposed GP Noise Warping performs worse than "How I Warped Your Noise" in terms of warping error. The core performance improvement appears to come from the equivariance self-guidance. 2. As mentioned in Section G.3, the equivariance self-guidance is inefficient. Although the proposed GP Noise Warping is more efficient than "How I Warped Your Noise," the overall process can be more time-consuming. Technical Quality: 3 Clarity: 3 Questions for Authors: 1. "How I Warped Your Noise" operates in a zero-shot manner using pretrained video editing diffusion models without requiring additional training. Is it possible for warped diffusion to also function in a zero-shot manner? 2. I am curious about the effectiveness of warped diffusion with just the equivariance self-guidance alone, without the GP noise warping. 3. What would the performance be like if the equivariance self-guidance technique were integrated into "How I Warped Your Noise"? Would it surpass the current performance of warped diffusion? Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The limitations and societal impacts have already been discussed in the paper. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the Reviewer for their time and their high-quality review. We are glad that the Reviewer appreciated the importance of the problem we are solving, the presentation of our work, and our experimental results. In what follows, we do our best to answer the questions raised by the Reviewer. `As illustrated in Table 1 and Figure 3, the proposed GP Noise Warping performs worse than "How I Warped Your Noise" in terms of warping error. The core performance improvement appears to come from the equivariance self-guidance.` We believe there is some misunderstanding here. In Table 1, no noise warping is happening (hence no comparison with the How I Warped Your Noise work). The reported results are for the generation of the first frame of a video. The results show that finetuning with correlated noise does not compromise performance. We will clarify this further to avoid confusing the reader. In Figure 3, we measure equivariance with respect to translation by an integer amount of pixels. For this deformation, the How I Warped Your Noise warping mechanism and the proposed GP Warping are essentially the same: both mechanisms just shift the input noise by the appropriate number of pixels. This is explained in Lines 315 to 318 in the paper. We intentionally chose to compare on this task because it simplifies the How I Warped Your Noise method's implementation (for which no reference code is available). Since for this task, GP Noise Warping and How I Warped Your Noise are essentially the same algorithm, the reason there is some small performance difference is that we are applying the warping to different models: the GP Noise Warping uses the finetuned model with correlated noise while the How I Warped Your Noise paper uses the finetuned model with independent noise. We will clarify this point in the paper and we thank a lot the Reviewer for raising it. `As mentioned in Section G.3, the equivariance self-guidance is inefficient. Although the proposed GP Noise Warping is more efficient than "How I Warped Your Noise," the overall process can be more time-consuming.` We agree with the Reviewer that the overall process can be more time-consuming if guidance is used. Our paper has two major contributions: (1) a principled framework for noise warping (GP Warping) and (2) a guidance method to enforce the equivariance of the underlying network (self-guidance). The How I Warped Your Noise paper is a warping method and hence when we compare the speed with this baseline, we measure the time needed for warping (see Lines 357). Our warping method (contribution (1)) is 16x faster and it generates images at higher resolution. That said, it is true that sampling guidance (contribution (2)) will significantly increase the sampling time. Namely, as we mention in Section G.3., we need ~2.67x the time needed without guidance for every single step and we run it for twice the number of steps, leading to an overall ~5.34x slowdown compared to not using guidance. For full transparency, we will move this discussion to the main paper and we thank the Reviewer for bringing up this important point. `"How I Warped Your Noise" operates in a zero-shot manner using pretrained video editing diffusion models without requiring additional training. Is it possible for warped diffusion to also function in a zero-shot manner?` This is a very important point and we thank the Reviewer for raising it. Our method cannot work in a zero-shot manner since it requires a model that is trained with correlated noise. We mention this in the paper, but we will explicitly add it to the Limitations Section (Section F). As we show in the paper, with minimal finetuning it is possible to get a model trained with independent noise to work with correlated noise (Table 1), but still, some amount of finetuning is required, as the Reviewer correctly pointed out. `I am curious about the effectiveness of warped diffusion with just the equivariance self-guidance alone, without the GP noise warping.` This is a great question. We ran some preliminary experiments for super-resolution on real-videos and we found that omitting the warping significantly deteriorates the results when the number of sampling steps is low. We found that increasing the number of sampling steps makes the effect of the initial noise warping less significant, at the cost of increased sampling time. We will include this discussion in the camera-ready version of our paper and we thank a lot the Reviewer for raising this important point. `What would the performance be like if the equivariance self-guidance technique were integrated into "How I Warped Your Noise"? Would it surpass the current performance of warped diffusion?` This is an excellent question. We believe that adding self-guidance to the How I Warped Your Noise paper would significantly improve the results. Unfortunately, there is no way to check this for general transformations because there is no reference implementation for us to try. We tried this for the integer shift transformation (for which the implementation becomes trivial) and the How I Warped Your Noise + self-guidance method matched the performance of our proposed algorithm. We will include this experiment in the camera-ready version of our work and we thank a lot the Reviewer for raising this insightful question. We hope our response addresses your concerns and that you consider increasing your rating. --- Rebuttal 2: Comment: I appreciate the authors' efforts in addressing my concerns. After reviewing the other reviewers' comments and the authors' responses, I have decided to maintain my original score. I would like to see the authors include the discussions and experiments in the response to their final revision. --- Rebuttal Comment 2.1: Title: Thank you for acknowledging our rebuttal Comment: We thank the Reviewer for acknowledging our rebuttal. We will make sure to include the discussions and experiments in the camera-ready version of our work. We thank the Reviewer once again for their time and for helping us improve our work!	Summary: This paper addresses the challenge of temporally correlated inverse problems by employing an image diffusion model. The authors introduce a technique termed Warped Diffusion, which incorporates an equivariance self-guidance mechanism. This mechanism ensures that the generated frames maintain consistency when subjected to warping transformations. The paper demonstrates the application of this technique in the context of video inpainting and video super-resolution through a series of experiments. Strengths: 1. The paper is presented in a structured manner, with illustrations that aid in understanding. The content is coherent and follows a logical sequence. 2. The authors offer an analysis of noise warping and equivariance self-guidance, providing both intuitive explanations and theoretical underpinnings. 3. 3. The experiments are extensive to support the claim. Weaknesses: 1. The authors report the noise warping speed at Line 357. We recommend that the authors also include the complete inference time required to process an entire video, which would provide a more comprehensive understanding of the method's efficiency. 2. We suggest that the authors provide more video results to further demonstrate the capabilities and limitations of the proposed method in various scenarios. 3. It is observed that the inpainted regions in the video inpainting examples remain static, such as the cat in the video not exhibiting motion. All apparent motion seems to be attributed to camera movements, with no optical flow present within the inpainted regions. We would appreciate an explanation for this phenomenon and its implications on the video inpainting process. Technical Quality: 3 Clarity: 3 Questions for Authors: See the weaknesses. Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The authors have adequately discussed the limitations and negative societal impact in the paper. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the Reviewer for their time and insightful review. We are very glad that the Reviewer appreciated the presentation of our work, the theoretical underpinnings of our formulation and the strong empirical performance of our method. `The authors report the noise warping speed at Line 357. We recommend that the authors also include the complete inference time required to process an entire video, which would provide a more comprehensive understanding of the method's efficiency.` We have some additional discussion regarding sampling time in Section G.3. of the Appendix. Processing a 2-second video takes roughly ~5 minutes on a single A-100 GPU. We will move this discussion to the main paper, as recommended by the Reviewer. `We suggest that the authors provide more video results to further demonstrate the capabilities and limitations of the proposed method in various scenarios.` We thank the Reviewer for their suggestion. We include more results on the [project webpage](https://anonneurips2024.github.io/) as recommended by the Reviewer. We will de-anonymize this webpage and make it available to the public upon acceptance of our work. `It is observed that the inpainted regions in the video inpainting examples remain static, such as the cat in the video not exhibiting motion. All apparent motion seems to be attributed to camera movements, with no optical flow present within the inpainted regions. We would appreciate an explanation for this phenomenon and its implications on the video inpainting process.` We thank the Reviewer for raising this question. Our proposed framework is not constrained to static examples and can work with real optical flows, as demonstrated for the super-resolution task. Inpainting is a much harder inverse problem that super-resolution and thus maintaining consistency for real flows might be more challenging. We did not experiment with real video inpainting in this paper but we plan to include some examples for the camera-ready version. We hope our response addresses your concerns and that you consider increasing your rating.	Summary: The paper follows a previous work on noise-warping methods for video inverse problem. The authors proposed instead of giving temporally consistent noise maps to the DM, using a continuous function space representation for DM directly can serve more complex spatial transformations and results in better temporal consistency in the generated videos. They demonstrated the proposed method on video inpainting and super-resolution. Strengths: The proposed method is novel in terms of using Gaussian processes to handle the noise function so that no mapping is required for the noise. The authors derived the equivariance for deformation and by satisfying this the gaussian process is used to guide the generation to be consistent under the warping transformation. To avoid additional training, a sampling mechanism was proposed to ensure this satisfaction at inference time. Weaknesses: The key statement in the paper is the importance of the equivariance of the DM to achieve temporal consistancy. The authors argued that the previous work "How I Warped Your Noise" performed badly when the DM is not equivariant. However, there are no explicit examples or solid proof on this statement. The proposed method for noise warping is more like offering another perspective than showing the failing reasons of the other work. Furthermore, for super-resolution experiments, the authors did not provide comparison against "How I warped your noise". Even though they elaborated that the authors of "How I warped your noise" acknowledged to them that the work does not result in temporal consistency, I believe it is still better to include the comparison given how many super-resolution cases were presented in that work. If they don't provide the code, the authors may consider modify the one they have for the inpainting experiments and list out the comparison for more convincing results. Technical Quality: 3 Clarity: 2 Questions for Authors: 1. It is not clear to me why the function space diffusion models need to be equivariant with respect to the underlying spatial transformations. I can imagine the necessity, but in your derivation, I don't see the proof that you stated you provide. Can you provide explicit examples or solid proof on this statement? 2. Why in fig 3 how i warped your noise seems to be in the second place in terms of error, but in table 2, the method seems not to outperform any other baselines? Confidence: 4 Soundness: 3 Presentation: 2 Contribution: 2 Limitations: The authors did not address any limitations Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the Reviewer for their time and their valuable review. We are glad that the Reviewer appreciated the novelty of our work. In what follows, we do our best to answer some remaining questions. `The authors argued that the previous work "How I Warped Your Noise" performed badly when the DM is not equivariant. However, there are no explicit examples or solid proof on this statement. The proposed method for noise warping is more like offering another perspective than showing the failing reasons of the other work.` Our framework has two components: (1) the GP warping scheme, and (2) the self-guidance method at inference time. In Figure 3 of the paper, we show that (1) is not enough: both GP noise warping and the How I Warped Your Noise baseline still have significant warping error. Self-guidance is essential to further decrease the warping error because the DM is not equivariant. This is also illustrated in Row 2 of Figure 1: the How I Warped Your Noise warping scheme fails to produce consistent results because the underlying DM is not equivariant. If the Reviewer wants further clarification on this point, we would be happy to provide it. `Furthermore, for super-resolution experiments, the authors did not provide comparison against "How I warped your noise". Even though they elaborated that the authors of "How I warped your noise" acknowledged to them that the work does not result in temporal consistency, I believe it is still better to include the comparison given how many super-resolution cases were presented in that work. If they don't provide the code, the authors may consider modify the one they have for the inpainting experiments and list out the comparison for more convincing results.` We thank the Reviewer for their suggestion! We provide comparisons for the super-resolution task with How I Warped Your Noise in the case of integer translation in the following anonymous links: 1) [(Self-) Warping Error with respect to previous generated frame in pixel space](https://anonneurips2024.github.io/assets/self_warping_pixel_error_wrt_prev_frame.pdf) 2) [(Self-) Warping Error with respect to first frame in pixel space](https://anonneurips2024.github.io/assets/self_warping_pixel_error_wrt_first_frame.pdf) These results are similar to what's given in Figure 3 of the paper and will be included in the camera-ready version of our paper. Once again, we thank the Reviewer for suggesting this important experiment. `Why in fig 3 how i warped your noise seems to be in the second place in terms of error, but in table 2, the method seems not to outperform any other baselines?` We believe the Reviewer might have misunderstood this part. Figure 3 shows the Warping Error and the How I Warped Your Noise paper gets the second (best) place. This is consistent with the first column (Warping Error) of Table 2 which places again the GP in the second best place in terms of warping error. The rest of the columns of Table 2 measure the quality of the generated images (but not temporal consistency across frames). Any warping mechanism sacrifices some quality for temporal consistency. This has been also reported in the How I Warped Your Noise paper (see Table 1, page 7 of the paper). Our results in Table 2 are consistent with this finding. Hopefully, this clarifies the question raised by the Reviewer. `The authors did not address any limitations` We would like to bring to the Reviewer’s attention Section F of our Appendix. In this Section, we state several limitations of our work. To increase the visibility of this Section, we will bring it to the main paper in the next-revision of our work. `It is not clear to me why the function space diffusion models need to be equivariant with respect to the underlying spatial transformations.` The formalization of this statement follows from the definition of the video that we use in this paper. We define a video such that the next frame is given as a deformation of the last frame. If the generative model is not equivariant w.r.t. this transformation, then its output will no longer satisfy this definition of a video. We argue that since optical flows are a useful tool for video modeling and have been empirically successful, this definition of a video, through the optical flow, is a reasonable one. In terms of empirical proof, Figure 1 shows that the robot keeps changing if you don't have equivariance. We hope our response addresses your concerns and that you consider increasing your rating. --- Rebuttal Comment 1.1: Comment: Thank you for your response, especially for providing the comparisons for the super-resolution task and clarifying my misunderstanding on table 2. However, I am still not convinced about the "equivariant" statement. I understand your formulation and approach, but I don't agree other approaches "failure" automatically prove your statement. --- Reply to Comment 1.1.1: Title: Further Clarifications Comment: We agree with the reviewer that we have not proven other approaches will not work. Indeed, let us consider the following argument. We'll work with $H$ a Hilbert space of real-valued functions over the domain $D = [0,1]^2$. Consider first the following definition of a video: A two-frame video is a pair of functions $f_0, f_1 \in H$ such that there exists a bounded, injective map $T: D \to \mathbb{R}$ with the property that $f_1(x) = f_0 \big ( T^{-1}(x) \big )$ for all $x \in T(D) \cap D$. Now let $G: H \to H$ be a generative model for which there exists some $\xi_0 \in H$ such that $G(\xi_0) = f_0$. Then following holds: if $G$ is equivariant w.r.t. to $T$ then the pair $\big ( f_0, G(\xi_0 \circ T^{-1}) \big )$ is a two-frame video. This follows from the definition of equivariance as $G(\xi_0 \circ T^{-1}) = G(\xi) \circ T^{-1} = f_0 \circ T^{-1} $ on $T(D) \cap D$. Certainly, the other direction does not hold true. In particular, it does not follow that if $\big ( f_0, G(\xi_0 \circ T^{-1}) \big )$ is a two-frame video then $G$ is equivariant w.r.t. $T$. Therefore we agree with the reviewer that we have not proven that equivariance is necessary, however, we have proven that it is sufficient. We will explicitly point this out in the camera-ready version. This lack of necessity stems from the fact that our definition of a video is weak and allows many possible pairs to be videos. One natural way of strengthening it is as follows: Let $\mathcal{T}$ denote the set of bounded, injective maps on $D$ then a two-frame video is a pair of functions $f_0,f_1 \in H$ such that the following problem admits a unique maximizer \[\max_{T \in \mathcal{T}} \big \{ \|T(D) \cap D\| : f_1(x) = f_0 \big ( T^{-1}(x) \big ) \text{ for all } x \in T(D) \cap D \big \}.\] In particular, we enforce that there is a unique deformation which keeps the maximum number of pixels in frame. From uniqueness, it now follows that: the pair $\big ( f_0, G(\xi_0 \circ T^{-1}) \big )$ is a two-frame video if and only if $G$ is equivariant w.r.t. to $T$. We thank the reviewer for bringing this to our attention and are happy to discuss the mathematical modeling of videos in the camera-ready version further. If that's not what the Reviewer was looking for, please let us know and we will try our best to incorporate the Reviewer's feedback in our camera-ready.	Summary: This paper proposes a self-guidance equivariance approach using the Image Diffusion model for generating temporally consistent videos. In previous work HOW I WARPED YOUR NOISE[1], noise is warped across frames to ensure the noise maps are temporally consistent. However, temporally consistent noise maps do not guarantee temporally consistent output. In this work, the authors address this issue. The proposed self-guidance equivariance enforces that the generated frames remain consistent under the warping transformation. The proposed method can generate more consistent results. In their experiments, the authors conducted comparisons on video inpainting and superresolution. It is worth noting that the proposed method outputs consistent content in the inpainting area across frames. Strengths: - Problem Setup - The problem seems reasonable and important, especially in the case of video inpainting. Compared to other video applications, any temporary inconsistent case can create a dramatic failure case. See Figure 1. - Temporal consistent results. - In this work, the authors show how the proposed equivariance self-guidance improves video inpainting results and superresolution. - More efficient noise warping. - Compared to the previous work [How I Warped Your Noise], this work improves the inference time by up to 16 times. Weaknesses: - Better illustration and explanation of how the `self-guidance Equivariance` works. The main novelty of the paper is the self-guidance equivariance, which improves performance compared to previous work, HOW I WARPED YOUR NOISE [1]. However, it is not easy to understand how it works in Figure 2. The current Figure 2 only shows its role and the input and output in the overall system but does not describe its function. Besides, this figure seems to provide more information about how to use optical flow to guide the warping process of noise. - Inpainting examples and usefulness? Do the warped noise and self-guidance Equivariance work for generating "moving objects" in video inpainting? According to the formulation and the generation results, it seems it will favor generating "still objects" in the video inpainting case because it will easily meet the "warped" mechanism. - Experiment Design. Experiments in Section 4.1 are not needed (or do not provide a useful argument) in the paper. Previous works have shown that warped noise is better than independent noise across the frames in a video. The only contribution here is that the fine-tuned version performs better than the un-fine-tuned version. The finding seems unrelated to the paper or provides quite limited information. Technical Quality: 3 Clarity: 2 Questions for Authors: - A better way to illustrate how the proposed Equivariance Self-Guidance works. - A proper figure would be better instead of just formulations. - See Point 2 in Weakness; can the proposed method handle cases where the object is moving or has different actions in the video inpainting case instead of being still? Confidence: 3 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: For the limitations, the authors mention that in some situations, the work may fail. It would be helpful to also provide the corresponding failing examples, such as the second and third examples mentioned in Appendix F Limitations. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the Reviewer for their thoughtful review. We are glad to see that the Reviewer appreciated many aspects of our submission, such as the importance of the problem we are addressing and the experimental benefits we are obtaining. In what follows, we do our best to address any remaining concerns. `[...] it is not easy to understand how it works in Figure 2. [...] A proper figure would be better instead of just formulations.` We thank the Reviewer for their comment. We agree that Figure 2 should be improved. Following the recommendation of the Reviewer, we updated the figure to show that the self-guidance is applied in each step of the ODE sampler. The figure is now available at the (anonymous) project website and at [this link](https://bashify.io/i/veUk9P). We plan to include this update in the camera-ready version of our work. If there is any more feedback, we would be glad to incorporate it. `Do the warped noise and self-guidance Equivariance work for generating "moving objects" in video inpainting? According to the formulation and the generation results, it seems it will favor generating "still objects" in the video inpainting case because it will easily meet the "warped" mechanism.` We thank the Reviewer for their insightful question. The proposed framework should work for moving objects in video inpainting as long as the optical flow map is available and there are no occlusions. That said, as the Reviewer correctly points out, for realistic videos, the estimation of the optical flow map might be noisy. We will make this point more explicit in our paper and we will include videos of moving objects in the camera-ready version of our work. We thank again the Reviewer for bringing up this important point. `Experiments in Section 4.1 are not needed (or do not provide a useful argument) in the paper. Previous works have shown that warped noise is better than independent noise across the frames in a video. The only contribution here is that the fine-tuned version performs better than the un-fine-tuned version. The finding seems unrelated to the paper or provides quite limited information.` We respectfully disagree with the Reviewer on this point. Typically, diffusion models are trained with i.i.d. noise. In Section 4.1, we show that one can finetune a state-of-the-art diffusion model to work with correlated noise as input. Before finetuning, Stable Diffusion XL will produce unrealistic images when the sampling chain is initialized with correlated noise. Our experiments show that post-finetuning, the model can handle spatially correlated noise in the input without compromising performance. To the best of our knowledge, spatially correlated noise has not been shown effective in prior work (note that this is different from prior works on video generation that use temporally correlated noise). Our GP Warping mechanism requires models that can handle correlated noise. Hence, these fine-tunings are essential for the rest of the paper. We will clarify this point in the main paper to avoid confusing the reader. `For the limitations, the authors mention that in some situations, the work may fail. It would be helpful to also provide the corresponding failing examples, such as the second and third examples mentioned in Appendix F Limitations.` We definitely agree with the Reviewer and we thank them for encouraging us to make negative results publicly available. * Equivariance of the decoder. Sometimes, the decoder is not equivariant with respect to the underlying transformation. We noticed that this is a common failure for text rendering. This can be better illustrated with an example. The generated latent video [here](https://anonneurips2024.github.io/assets/videos/3_output_latent_video.mp4) appears equivariant. However, the decoded version of this video, found [here](https://anonneurips2024.github.io/assets/videos/3_output_video.mp4) is not equivariant. Specifically, the produced text changes from one frame to the other. * Correlation artifacts: For extreme deformations, there is a distribution shift between training and inference which leads to correlation artifacts. This has already been observed in the prior work, How I Warped Your Noise. In [this](https://warpyournoise.github.io/docs/assets/videos/SuperRes/Bear/adv.mp4) example from the project website, there appears to be a colored wave near the back of the bear. This is an example of a correlation artifact. Such artifacts also appear sometimes in our work, e.g. see the texture artifacts that appear in the final frame of [this](https://anonneurips2024.github.io/assets/videos/216_output_video.mp4) generated video. We will definitely include these failure cases in our camera-ready version and we thank again the Reviewer for raising this important point. We hope our response addresses your concerns and that you consider upgrading your rating. --- Rebuttal Comment 1.1: Comment: Thanks for the clarification, and I'm happy to see the improved version. I might be confused by the wording in Section 4.1. I understand that performance improves after finetuning, which is already useful across all machine learning tasks and areas. This improvement is expected. Given the limited space, I would prefer combining Section 4.1 with other ablation studies and including more diverse experiments in the full paper. --- Reply to Comment 1.1.1: Title: Thank you for acknowledging our rebuttal Comment: Dear Reviewer, thank you for reading our rebuttal; we are happy you appreciated the improved version. If there are no other major concerns, we would greatly appreciate it if you could increase your rating of our submission. We understand your suggestion now and will incorporate it in the camera-ready version of our work to improve the presentation of our work. Thank you again for your time and for helping us to strengthen our work!	null	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Seeing Beyond the Crop: Using Language Priors for Out-of-Bounding Box Keypoint Prediction	Accept (poster)	Summary: This paper focuses on an interesting and inherent problem in top-down human pose estimation; that is out-of-box prediction in a top-down paradigm. The core of the solution is to utilize the semantic context by giving proper text prompts to CLIP. Specifically, a cropped image is first given to a pre-trained CNN model to extract initial features and obtain a coarse prediction. Then the visual features from CNN, the coarse prediction of the person, and the semantic information from CLIP are concatenated and input to a transformer decoder to obtain the final prediction. The method is capable of solving the occluded points in the crowded scene and breaking the limits from the bounding box in the top-down model. Strengths: 1. This paper focuses on a very interesting topic that indeed requires a deeper investigation. 2. Having semantic information from text prompts is a quite novel and effective way of solving the occlusion and out-of-box points. 3. The paper is in general well-written and easy to follow. Weaknesses: 1. Poor visualisation. Qualitative results are only compared with HRNet. More visualization should be shown to validate the effectiveness of the proposed method. 2. A few images are very ambiguous. Especially, the Figure 1. (b). There is no notation for x, y, and colors. The caption said it is the text embedding and such embedding loses the global structure. Why did it lose the global structure? 3. In terms of performance, there is indeed an improvement. However, how many of them are coming from the unseen points? i.e. Is the source of improvement from unseen points or a more accurate estimation of the seen points? After all, the whole pipeline is a coarse-to-fine prediction with additional text information. Therefore, the seen points should also benefit. If the major improvement does not come from the unseen points, then the major problem proposed by this paper still remains unsolved. Technical Quality: 3 Clarity: 2 Questions for Authors: 1. One statement in the introduction that I do not agree with is "Contemporary deep learning-based pose estimation methods predominantly follow a top-down approach" between line 27 and line 28. Bottom-up and one-stage models are also important parts of human pose methods. In fact, bottom-up models have their own merits such as real-time inference and bounding-box independent predictions. I suggest revising this statement. 2. It would be better if the authors could make a further explanation on using normalizing flow to estimate the human poses. I think it is quite interesting as this method was published in 2021 and is quite rare in recent work. Many other papers like PETR directly regress pose with the decoder. Then it is natural to ask Why use normalizing flow? What is the impact if we directly regress the pose? These two points may need further discussion. 3. What is the exact text prompt used in the given method? 4. The authors also claimed that the previous method ignored the global spatial relation between points. Yet it is still unclear to me how the author's method solves this problem. In the introduction, it is claimed that transformers are used to solve the problem. But it is too general to convince me. Confidence: 4 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: No negative societal impact are found. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: W1. Qualitative Results: More qualitative comparisons with ViTPose and HRNet are shown in Figure 1 of the rebuttal document. From the figure, it is evident that excluding the stick from the bounding box is much more beneficial as it reduces the noise present in the image. --- W2. t-SNE visualization of text embeddings: Figure 1(b) of the main paper depicts the t-SNE visualization of the text embeddings generated from keypoint-specific text prompts. The two axes x and y represent the two reduced dimensions dimension1 and dimension 2 respectively. The different colours represent whether they are upper-body or lower-body joints, with red representing upper-body joints, blue representing lower-body joints and green representing the hip joints. In the paper, we mention that from the figure, it is evident that while these embeddings maintain positional structure within the upper-body joints (the shoulders are placed above the elbows which are placed above the wrists, following the pose of a human standing normally) and the lower-body joints (knees placed above ankles), they fail to maintain positional structure between the upper-body and lower-body joints (elbows and wrists are placed below knees and ankles in the plot which does not follow the pose of a human being). This has been explained in lines 41 to 46 in the introduction of the paper. --- W3. Improvement on unseen keypoints: As demonstrated in Table 1, the unseen keypoints (stick top, stick heel, and stick toe) contribute significantly to the overall improvement of TokenCLIPose. Specifically, an improvement of 4%, 6.4%, and 7.35% is observed on the three keypoints respectively when compared to the second-best model (ViTPose). On the other hand, the seen keypoints (human) only improve by 1.76\%. Similar trends are observed when experimentation was done on the Lacrosse dataset in Table 2. Hence, it is evident that major improvements come from the unseen keypoints. --- Q1. We intended to say that most of the state-of-the-art works [1-4] follow a top-down approach. However, we will revisit this statement and update it in our camera-ready version. --- Q2. Thank you for noting our use of normalizing flows and asking an insightful question! We would like to explain this choice of ours by first stating the limitations of standard regression losses and then explain the reason behind using normalizing flows. Limitations of standard loss functions: Directly regressing poses using a standard $\ell_2$ or $\ell_1$ loss is not desirable as it is vulnerable to ambiguous and noisy labels [5] which is prevalent in our setting due to high motion-blur. This is primarily because applying a standard distance function as our loss function is equivalent to assuming the distribution of the output probability distribution. For example, the loss function when we assume the output probability distribution to be a Gaussian with constant variance is equivalent to the standard $\ell_2$ loss. Similarly, the loss function when we assume the output probability distribution to be a Laplacean with constant variance is equivalent to the standard $\ell_1$ loss. Why normalizing flows? On the other hand, we learn the deviation between the predicted probability distribution and ground-truth probability distribution, which is estimated by a flow model, and minimize the deviation using MLE. By doing so, we get more robust predictions. We validate the impact of this Residual log likelihood (RLE) loss through an ablation study by replacing it with the standard $\ell_2$ loss. Upon doing so, we get a mean PCKh accuracy of 75.22\%, resulting in a 1.06\% performance drop. --- Q3. Addressed in C2 of the author rebuttal --- Q4. Our difference over existing multimodal methods: Existing multimodal 2D pose estimators [6] align the image features around each keypoint to their corresponding text embeddings using a contrastive loss. This pushes the image features to be similar to the text embeddings. However, this is not desirable as the text embeddings do not capture global positional structure (showcased in figure 1(b) of the main paper and discussed in W2). This is what we explain in lines 41-46 of the main paper. In order to overcome these limitations, we use these text embeddings as priors and initialize our learnable keypoint tokens (also referred to as text tokens) using these text embeddings. This provides our model with the inductive priors required for robust prediction without biasing them completely towards the text embeddings. This is mentioned in lines 47-51 in the main paper. --- References:- [1]: Xu et al., ViTPose: Simple Vision Transformer Baselines for Human Pose Estimation, NeurIPS 2022. [2]: Sun et al., Deep High-Resolution Representation Learning for Visual Recognition, CVPR 2019. [3]: Li et al., TokenPose: Learning Keypoint Tokens for Human Pose Estimation, ICCV 2021. [4]: Yang et al., TransPose: Keypoint Localization via Transformer, ICCV 2021. [5]: Li et al., Human pose regression with residual log-likelihood estimation, ICCV 2021. [6]: Hu et al., LAMP: Leveraging Language Prompts for Multi-person Pose Estimation, IROS 2023. --- Rebuttal Comment 1.1: Comment: Thank you for your detailed response. Most of my concerns have been properly addressed, though I have a few additional points I’d like to discuss: 1. As part of the ongoing discussion regarding the use of normalizing flow, I believe the method provides an explicit probability distribution for keypoint estimation, correct? If so, I’m curious whether the standard deviation of each prediction can be directly used as an uncertainty measurement or confidence score. If the method already employs this approach, could you please share the performance results? If not, I suggest testing this on the CrowdPose dataset, as its evaluation protocol (based on COCO) is highly sensitive to accurate confidence estimation of poses. Demonstrating improved performance in this area could potentially strengthen the paper. 2. Several reviewers have noted that the test dataset appears limited and relatively simple in terms of occlusion challenges. I recommend evaluating the method on the OCHuman [1], which has gained popularity recently for methods addressing occlusion. This could provide more robust evidence of the method’s effectiveness under challenging conditions. 3. Regarding the concern (C3) on how the text guides the model in predicting the exact location of unseen points, it would be helpful if the authors could visualize the attention map between the text prompt and the visual features (e.g., between F_text and F_vis or between F_text and F_loc). My assumption is that the attention between F_vis and F_loc (both visual features) struggles to focus on out-of-box regions because these regions (e.g., white regions if I am correct) lack visual similarity to in-box visual features. Thus, there is no hope to recover any useful information through the these visual features (F_vis and F_loc). However, text features might not rely on visual similarity and could direct attention to broader regions, including out-of-box areas. In my point of view, this visualization could be more persuasive to other reviewers than simply citing other papers to support the intuition behind this idea. I understand that addressing these points may require additional experiments, which would take time. Therefore, I won’t factor the response to these discussions into my final rating, even if no further experimental results are provided. Finally, I noticed that most reviewers initially gave a negative rating, and I agree with many of their proper and valid points. I would like to see their feedback on the rebuttal before making my final decision. Also hope it will help to convince other reviewers through address a few of my concerns. [1] Pose2Seg: Detection Free Human Instance Segmentation --- Reply to Comment 1.1.1: Comment: We would like to thank the reviewer for their invaluable comments and suggestions. 1. Standard deviation as confidence score: Thanks for noting such minute details and raising this point! The results that we reported are using the standard deviation directly as a confidence measure. 2. OCHuman Evaluation: We appreciate the reviewer’s suggestion of evaluating our model on OCHuman. However, since the OCHuman dataset does not contain any train set, the general scheme followed by the research community is to train the model on COCO dataset and test it on OCHuman. This is difficult for us due to memory constraints as one complete training run on the COCO dataset takes approximately 4-5 days. Hence, this would not be possible before the rebuttal deadline. Moreover, in order to showcase robustness under occlusions, we did conduct experiments on CrowdPose, the largest occlusion benchmark. 3. Impact of text prompts: Thanks for the suggestion. We would like to point out that apart from citing other relevant research, we have also conducted quantitative experiments (Tables 4 and 6 of the main paper) showcasing the benefit of using text prompts on the accuracy of our model. Hence, we believe we have successfully demonstrated the positive impact of text prompts. Moreover, we agree that adding visualisations will further bolster our motivation behind utilizing text and will include them in our camera-ready version.	Summary: This paper proposes a text-guided keypoint localization method that can detect keypoint that is out-of-input image. The proposed method only crops person area and abandons the object area, then adopts language prior to predict keypoint that is out-of-input image. To verify the effectiveness of the proposed method, this paper also introduces a Ice-Hockey keypoint detection dataset. Experiments on CrowdPose demonstrate the effectiveness of the proposed method. Strengths: 1. Utilizing text to represent the spatial relationships of keypoints is reasonable and straightforward. The proposed TokenCLIPose can effectively model the keypoint relationship and estimate unseen keypoints accurately. 2. This paper is well-written and easy to understand. Weaknesses: The proposed method is not well suited to the introduced tasks such as Ice-Hockey. Abandoning the visible object is not a good solution because the model cannot make perfect prediction on out-side objects. For occluded keypoints, it is not bad because we can only guess the position, it is acceptable that the prediction is not so accurate. But for visible keypoints of hockey stick in Fig. 1(a), the predicted results are not acceptable. A better way to handle unnecessary visual features is to separate the object and person and perform keypoint localization on each individually. I think the proposed method can be used to perform the occluded/out-of-box keypoint localization, but not to solve the Human-Object Keypoint Localization tasks such as Ice-Hockey. The introduced task and dataset cannot fully demonstrate the effectiveness of the proposed method. It is better to introduce the method from the perspective of occluded or out-of-box keypoint localization, abandoning the Ice-Hockey tasks and background and conduct more experiments on occluded keypoint localization benchmarks such as OCHuman. Technical Quality: 3 Clarity: 3 Questions for Authors: In Weakness Confidence: 5 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The authors say they show the failure cases of the prooposed method, but I do not find them in the manuscript. Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: W1. (a) Excluding the sticks: The concern of abandoning the visible object is addressed in the author's rebuttal. (b) Individual localization of human and stick: We would like to thank the reviewer for raising an insightful question of estimating the pose of human and their extension separately. While this might seem interesting, works on human-object interaction [1-3] and 2D pose estimation [4] showcase that the pose of the human and the extension are closely related, and can be used to refine each other’s pose. Our experiment on individual and joint pose estimation shown in Table 4 of the rebuttal document also demonstrates an improvement in the accuracy of human pose when jointly trained with the stick. (c) Efficacy of our method to solve human-object Keypoint Localization: We also appreciate the reviewer's suggestion of introducing this paper from the perspective of occluded keypoint localization. However, we disagree with the reviewer’s comment that our method cannot solve human-object keypoint localization. Through our extensive qualitative and quantitative experiments, we have demonstrated the superior performance of our model in comparison to SOTA approaches. --- References:- [1]: Yao et al., Modeling mutual context of object and human pose in human-object interaction activities, CVPR 2010. [2]: Gupta et al., Observing Human-Object Interactions: Using Spatial and Functional Compatibility for Recognition, TPAMI 2009. [3]: Delaitre et al., Learning person-object interactions for action recognition in still images, NeurIPS 2011. [4]: Neher et al., HyperStackNet: A Hyper Stacked Hourglass Deep Convolutional Neural Network Architecture for Joint Player and Stick Pose Estimation in Hockey, CRV 2018	Summary: The paper argues that using images including both humans and interacting objects introduces unnecessary visual features that hinder pose estimation performance. To address this, the paper claims that treating objects as unseen to predict interacting object poses can achieve better results and proposes a TokenCLIPose solution. The method is evaluated on the Hockey and Lacrosse datasets, which contain images from a total of 11 video clips. Strengths: The paper is generally clear and the method uses language information to improve pose estimation. Weaknesses: The experiments and comparisons are not convincing and the experiments are weak. (1) The paper conducts its main experiments on the Hockey and Lacrosse datasets. However, these datasets are too small, comprising only 11 video clips. (2) The paper claims that predicting object poses using human-only images performs better than using human-and-object images. However, the paper lacks in-depth analysis, and the experiments are insufficient to support this claim. The reviewer disagrees, arguing that observation is more accurate than imagination when an appropriate framework is used. (3) The major contribution of the paper is not clearly defined. (4) The paper did not discuss and compare with bottom-up methods, which are popular for human pose estimation. (5) In Line 136, the text encoder simply encodes class-related information/names of each keypoint, which the reviewer argues cannot tackle the challenge of unseen keypoints in the image. (6) Typos, such as "we curate two new sports dataset" and "Experimentations". Technical Quality: 2 Clarity: 2 Questions for Authors: See Weaknesses. Confidence: 4 Soundness: 2 Presentation: 2 Contribution: 2 Limitations: No discussion on limitations is provided. Flag For Ethics Review: ['Ethics review needed: Data privacy, copyright, and consent', 'Ethics review needed: Data quality and representativeness'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: W1. (a) Custom dataset size: To the best of our knowledge, this is the first work to address the problem of extension pose estimation and create a dataset for the task. Since pose estimation is a task that is heavily dependent on labels, we spent a lot of time collecting precise manual annotations. Though the reviewer might feel 11 video clips might be less, the number of annotations that we collected still sum up to a sizable 11630 images for ice hockey and around 300 for Lacrosse (used for zero-shot pose estimation). (b) SOTA results on large dataset (CrowdPose): Moreover, one of our main experiments is conducted on the CrowdPose dataset (Table 3 of the main paper) is a benchmark dataset from the literature that has atleast four times more human images when compared to the Ice hockey dataset. The results show that TokenCLIPose outperforms existing state-of-the-art architectures on this CrowdPose dataset as well. This shows that irrespective of the dataset size, our network performs better when keypoints are unseen. --- W2. Exclusion of stick from the bounding box: This is addressed in C1 of the author rebuttal. --- W3. Main contributions: Our main contributions are as follows:- - We reformulate the extension pose estimation problem as an out-of-bounding box keypoint detection problem by explicitly leaving out the extensions, and leverage the human features and keypoint-specific text prompts to robustly estimate the human and extension pose. - Existing multimodal pose estimators try to align the image features with the keypoint-specific text embeddings using a contrastive loss. However, upon visualizing these text embeddings, we find out that this is not desirable as the embeddings do not maintain global structure (as shown in Fig. 1(b) of the main paper). Hence, we use them as additional priors and initialize our learnable keypoint tokens (also referred to as text tokens) with these text embeddings rather than biasing our model completely towards these text embeddings. - Realizing the lack of datasets for extension pose estimation, we introduce 2 datasets: an ice hockey and a Lacrosse dataset. Furthermore, we show that our model outperforms the existing SOTA approaches by 4.36\% and 2.35\% respectively. - We further demonstrate our model’s robustness to occlusions by conducting experiments on the CrowdPose dataset, where we outperform the SOTA top-down approaches by 3.8\%. --- W4. Why not bottom-up? Most of the SOTA techniques [2-5] implicitly follow a top-down approach. This is mainly because they lead to more accurate predictions [1]. Hence, we compare with top-down approaches. --- W5. How do text prompts contain exact location? This is addressed in C3 of the author rebuttal. --- W6. Thanks for spotting the typos. We will update it for the camera-ready submission. --- References:- [1]: Jiang et al., RTMW: Real-Time Multi-Person 2D and 3D Whole-body Pose Estimation, arXiv 2024. [2]: Xu et al., ViTPose: Simple Vision Transformer Baselines for Human Pose Estimation, NeurIPS 2022. [3]: Sun et al., Deep High-Resolution Representation Learning for Visual Recognition, CVPR 2019. [4]: Li et al., TokenPose: Learning Keypoint Tokens for Human Pose Estimation, ICCV 2021. [5]: Yang et al., TransPose: Keypoint Localization via Transformer, ICCV 2021. --- Rebuttal Comment 1.1: Comment: Thank you for the authors' responses. However, like Reviewer 9Npr, many of my concerns remain unaddressed. The experiments do not convincingly support the main claim.	Summary: This paper introduces the problem of estimating the keypoints of humans together with a stick-like object that the human interacts with, i.e. hockey stick or lacrosse stick (which is referred to as "extension" in this paper). The paper claims that prior works on 2D human pose estimation cannot be naively extended to this task by simply using a larger cropped image containing the human and the object together, because it would introduce unnecessary features and hurt performance. To resolve this issue, the paper proposes the TokenCLIPose method, which focuses solely on human using a tight crop bounding box and utilizes keypoint-specific text embeddings from CLIP to predict out-of-bounding-box keypoints of the stick objects. Specifically, it uses a CNN to extract features from images and obtain a coarse estimation of human keypoints in the bounding box with an MLP. Subsequently, it feeds the image features, coarse keypoints features and the keypoint-specific text embeddings of the stick keypoints from a CLIP text encoder to a transformer to obtain a final keypoint estimation result. The experimental results indicate their method outperforms previous 2D human keypoint estimation methods in their newly curated datasets for this new setting, as well as on the CrowdPose dataset with multi person scenarios that have severe occlusion. Strengths: 1. The paper is reasonably well-structured and the motivation and approach are described well. 2. The integration of features from foundation models, like CLIP, for keypoint detection is original in general, but I am unsure why it would be beneficial in the particular application scenario proposed in this paper. 3. The experiments on various dataset show that the proposed method outperforms related works. Weaknesses: 1. The proposed problem of detecting keypoint of cropped out objects seems artificial, and it remains unclear if predicting the keypoints of cropped objects is actually necessary. One important ablation study that needs to be shown is to train TokenCLIPose on images that are not artificially cropped, and instead contain both the human and the stick together. It seems that if the text embedding is helpful for locating keypoints of unseen objects, it should also help when the in the bounding box. 2. The description of adopting the keypoint-specific text embeddings for predicting the keypoints of unseen keypoints is unclear. Why should the text embeddings contain any information of the location of unseen objects in not explained and not studied sufficiently in the experiments. 3. How are the baseline methods in the experiments adapted to the newly proposed task? This is not discussed at all. The number of keypoints for the extensions seems to vary between experiments. How do you adapt human pose estimation methods for this new task and why do these methods fail in this setting? This should be explained in more detail. 4. The proposed method should be compared to more recent works like ViTPose++ (TPAMI 2023) and BUCTD (ICCV 2023). The latest works used for comparison in the submission are ViTPose (NeurIPS 2022) and HRFormer (NeurIPS 2021). As this paper works on a different setting than classical human pose estimation, it is important to discuss why existing 2D human pose estimation methods are limited in dealing with this setting. 5. What are the text prompts used for the Text-based Keypoint Encoder? There is no explanation regarding this essential part of the method. 6. This method is only verified with simple objects like hockey sticks and lacrosse sticks. A core open question is how the method would generalize to more complicated structures like chairs? Technical Quality: 2 Clarity: 2 Questions for Authors: In addition to the questions contained in the previous section: 1. How is the visualization of Figure 1(b) obtained? 2. For the ablation study in Table 4, what is the result of only combining text token and image token? Confidence: 3 Soundness: 2 Presentation: 2 Contribution: 2 Limitations: The paper shows failure cases, but only limited quantitative results are shown and there is no discussion about these failure cases. Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: W1. Training TokenCLIPose with sticks included: To assess TokenCLIPose's performance on uncropped images, we extended our experiments on the uncropped images (images that contain both players and their sticks). As shown in Table 2 of the rebuttal document, the performance drops by 4.51\% resulting in a mean accuracy of 71.77\%. These results reinforce our hypothesis that expanding the field-of-view introduces unnecessary visual features which hinder model accuracy. --- W2. Impact of text prompts: This is addressed in C3 of the author rebuttal. --- W3. (a) Baseline training details: Baseline methods are trained from scratch on the extended bounding boxes (boxes that contain human and stick). All models are trained on the Ice hockey dataset to predict 15 keypoints (12 human + 3 stick). For the zero-shot setting, we directly use the ice hockey trained models on our Lacrosse dataset and infer predictions. Specifically, we discard the 15th keypoint predicted by the model, since the Lacrosse dataset has only 14 points (12 human + 2 stick). The human keypoints are the same for both the Lacrosse and Ice hockey datasets. We understand that we have failed to include this detail and will update this in the camera-ready version. (b) Why do Baselines fail? These methods fail in this setting primarily due to the expansion of the bounding boxes, which increases the field-of-view. This introduces unnecessary visual features as depicted in Figure 3 of the rebuttal document. which confuses the model and leads to suboptimal predictions. --- W4. (a) Why not ViTPose++ and BUCTD? ViTPose++ deals with heterogeneous body keypoint categories thereby adopting task-agnostic and task-specific feed-forward networks in transformers. BUCTD uses a hybrid approach that combines the strengths of bottom-up and top-down methods. Thus, since we focused on improving over top-down approaches with task-specific fixed keypoints we avoided both these frameworks. (b) ViTPose++ results: However, for completeness, we trained ViTPose++ on the ice hockey dataset which resulted in a mean PCKh of 72.09\% underperforming by 4.19\% when compared to TokenCLIPose as shown in Table 3 of the rebuttal document. --- W5. What are the text prompts? This has been explained in C2 of the author rebuttal. --- W6. Experiments on “simpler” objects: To the best of our knowledge, this is the first work to address the problem of extension pose estimation and create a dataset for the task. Since pose estimation is a task that is heavily dependent on labels, we spent a lot of time collecting precise manual annotations. Also, the setting in which the objects are considered is highly dynamic, making the task extremely challenging. This can be seen in Tables 1 and 2 of the main paper as existing SOTA methods struggle to estimate the object pose. Hence, we politely disagree with the reviewer that we consider simple objects and find it unfair to criticize us on the data front as we are the first to address the problem. --- Q1. Figure 1(b) explanation: The visualization in Figure 1(b) of the main paper is a t-SNE plot of each of the keypoint prompts used to describe the human keypoints. --- Q2. Text and image tokens ablation: Combining text and image tokens resulted in a mean PCKh of 75.72\%. Thank you for spotting the missed ablation. We will add it in the camera-ready version. --- Rebuttal Comment 1.1: Comment: I appreciate the effort of the authors, however, it remains unclear to me why cropping out the object of interest from the image actually improves the performance. The argument made is that this introduces irrelevant features, but this should only be a problem in a limited data setting where the model starts overfitting on the background, is that correct? This hypothesis could be even verified with synthetic data rendered with computer graphics in cluttered backgrounds. To me, and it seems also several other reviewers, the paper does not sufficiently study when and why the model fails when the stick is included in the crop. Demonstrating a performance decrease in the results is a necessary initial step, but since the result is very unintuitive, I would expect a more in-depth study of the reasons for this problem. --- Reply to Comment 1.1.1: Comment: Thank you for taking the time to review our rebuttals. We believe we have conducted comprehensive experiments that sufficiently illustrate the rationale behind our approach of cropping out sticks. Specifically: 1. Noise Influence: We have demonstrated the influence of noise by comparing our model with ViTPose on two different data splits—one with predominantly visible keypoints and another with a mix of visible and noisy keypoints, as presented in Table 1 of our rebuttal document. 2. Training on Human+Stick Bounding Boxes: We have further validated our approach by training our model on datasets containing human+stick bounding boxes, as shown in Table 2 of our rebuttal document, which underscores the efficacy of our work. 3. Qualitative Performance: Finally, we have provided qualitative evidence of our model's superior performance in noisy conditions in Figure 1, where noisy regions are clearly marked. Given these extensive evaluations, we are unsure what additional experiments would be necessary to further validate our hypothesis. If there are specific experiments or analyses you would like to see, we would greatly appreciate your guidance in this matter.	Rebuttal 1: Rebuttal: Dear Reviewers, We would like to thank all the reviewers for providing constructive feedback that helped us improve the paper. We are delighted that the reviewers recognized the originality of our work in incorporating language to predict out-of-bounding box keypoints (R1, R4), significance of our focus on the interesting topic (R4), the effectiveness of our method in modeling spatial relationship between keypoints (R3), and the substantial improvement over the existing SOTA (R1, R4). Throughout the rebuttal, we refer to the reviewers in the following manner: {Reviewer 9Npr: R1, Reviewer F7X8: R2, Reviewer AetR: R3, Reviewer 9aCe: R4}. We address some of the common concerns here. The concerns have been paraphrased as multiple reviewers had similar concerns and questions. --- ### C1. Counter-intuitiveness of excluding the extension from the bounding box (R2 and R3) ### Training TokenCLIPose with sticks included: To showcase the effectiveness of cropping out the hockey stick, we train our model on the extended bounding boxes (containing both the human and stick) and report the results in Table 2 of the rebuttal document. From the table, we can see that including the stick in the bounding box deteriorates our model’s performance by 4.51\%, resulting in 71.77\% mean accuracy. Impact of noise: Furthermore, in order to investigate the impact of noise on the final predictions, we record the performance of ViTPose and TokenCLIPose under two different data split-ups in Table 1 of the rebuttal document. Specifically, the ice hockey dataset is divided into 2 sets, one with images that predominantly contain visible keypoints (referred to as A) and the other with images that contain both visible and noisy (partially visible) keypoints (referred to as B). The results demonstrate that ViTPose outperforms TokenCLIPose (ours) by 2.49\% when only split-up A was used but underperforms by 4.36\% when split-up B is used. While our method might seem counter-intuitive, these experiments explicitly demonstrate that existing models aren't robust enough to noise necessitating the need for smaller bounding boxes. The distribution of the visibility of keypoints across frames is shown in Figure 2 of the rebuttal document. --- ### C2. What are the text prompts for each keypoint? (R1 and R4) ### The text prompts corresponding to each keypoint used in TokenCLIPose are as follows:- \| Joint \| Text Prompt \| \|----------------\|-----------------------------------------------------------------------------------\| \| Left Shoulder \| left shoulder of a person \| \| Right Shoulder \| right shoulder of a person \| \| Left elbow \| left elbow of a person \| \| Right elbow \| right elbow of a person \| \| Left wrist \| left wrist of a person \| \| Right wrist \| right wrist of a person \| \| Left hip \| left hip of a person \| \| Right hip \| right hip of a person \| \| Left knee \| left knee of a person \| \| Right knee \| right knee of a person \| \| Left ankle \| left ankle of a person \| \| Right ankle \| right ankle of a person \| \| Stick Top \| top portion of the stick opposite to the blade of a hockey stick held by a person \| \| Stick Heel \| intersection of the blade and the shaft of a hockey stick \| \| Stick Toe \| end portion of the blade that is farthest away from the shaft of a hockey stick \| --- ### C3. How do text embeddings contain any information about the exact location of the unseen keypoints? (R1 and R2) ### Our choice of using text prompts to tackle the challenge of unseen keypoints is guided by recent works on 3D pose estimation [1] which use language to interpolate missing poses temporally, and image inpainting [2-3]. Furthermore, the authors have demonstrated in Tables 4 and 6 of the main paper that the proposed network drops in performance significantly without text prompts (by 3.35\%). --- Summary: We address a critical yet overlooked problem: joint pose estimation of humans and extensions (objects that humans hold and interact with), and overcome the limitations of existing SOTA top-down approaches on this task. Our approach is counter-intuitive yet impactful: we propose excluding the extension from the bounding box and predicting keypoints beyond the bounding box, thereby challenging the standard practice of including all keypoints within a bounding box. To achieve this, we utilize language priors along with bounding box features through keypoint-specific text prompts. To evaluate our method, we introduce the first dataset with labeled human and extension poses from broadcast ice hockey videos. We also perform zero-shot evaluations on a self-curated Lacrosse dataset to showcase our model’s generalizability. Finally, to showcase our model’s robustness to occlusions, we conduct experiments on the CrowdPose dataset. Please see our reviewer-specific feedback for more information. References:- [1]: Tevet et al., Human Motion Diffusion Model, ICLR 2023. [2]: Ni et al., NUWA-LIP: Language-guided Image Inpainting with Defect-free VQGAN, CVPR 2023. [3]: Zhang et al., Text-Guided Image Inpainting, MM 2020. Pdf: /pdf/44e0cfc01ae00804fd6b73eecb18ce768a5b0ece.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Where's Waldo: Diffusion Features For Personalized Segmentation and Retrieval	Accept (poster)	Summary: The authors propose a novel approach without any additional training for Personal retrieval and segmentation tasks, which focus on identifying specific instances within a dataset. The existing methods struggle to locate a desired instance when other instances within the same class are presented. They propose to utilize the features from a pre-trained text-to-image diffusion model and design a Personal Features Diffusion Matching method. The proposed method outperforms on both existing datasets and the new dataset which is proposed in this paper. Strengths: + The idea of introducing the features from the text-to-image diffusion models to handle the personal retrieval and segmentation problem is interesting. + The authors propose a new approach called PDM which requires no training or fine-tuning, no prompt optimization, or any additional models. + The authors explore the hidden textural and semantic information in the layers and blocks in the diffusion model. + The authors construct a new benchmark includes videos with multiple instances from the same category. Weaknesses: - The logical flow before the Method Section of this paper needs to be adjusted. It is hard to understand what the authors want to do and the problem they want to address, although the utilization of features from diffustion models and the PDM itself is somewhat clear. - The form of the task in the this paper is not clear. "... a dataset based on an input image and a short description of the reference instance." in Line.1-2 "this work focuses on the case where only class names are provided." Line.102-103 ... Line.103-105 As observed in the figures, the input information includes reference images, target images, and the class name (some of them are optional) - I think the SUPERVISED models for personal retrieval and segmentation, which need a large amount of annotated data, and the SELF-/WEAKLY-SUPERVISED foundation models are not in the same aspect. The authors should rearrange the related works and the motivation of their work. - The authors should list their contributions to help the readers better understand thier work. - The visualized results in both the main text and appendix do not fully capture the problem the authors aim to address. Few of them present the situation where a desired instance appears together with other instances of the same class. - There is a lack of sufficient theoretical justification for why the authors choose diffusion models and why the features of diffusion models can achieve the capabilities that the authors expect. Only using "These models have the capability to generate an infinite array of objects and instances, each exhibiting unique appearances and structures. Line.33-34" and the two examples in Figure 2 is not enough. Technical Quality: 3 Clarity: 2 Questions for Authors: Please refer to the Weakness part. Additional comments: 1. The authors need to clearly define the form of the task and formally present the settings for differernt scenarios. 2. The Figure 3 is hard to understand. Why "dog" is not fed into the diffusion features extraction in I_t branch? As F^s_t is features from the cross attention, what information is used to calculate the cross attention with I_t? 3. The authors should explain why using the features from diffusion models and provide theoretical justification. They should figure out the differences between the diffusion models and the other models (e.g. common resnet, ViT, Vision Mamba, Transformer+KAN, ..., and the other variants, why not choose other SoTA foundation models). Why they can present the textural and semantic information? Confidence: 4 Soundness: 3 Presentation: 2 Contribution: 2 Limitations: NA Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for finding our approach novel and the ides of our method interesting. We address your comments below. Q1: The logical flow before the method section needs to be adjusted. The authors should rearrange the related works and the motivation of their work. The authors should list their contributions. A1: We appreciate the reviewer's valuable feedback and their contribution to improving our paper. We will make sure to rearrange the related works and the motivation of our work to improve the logical flow leading up to the method section. We will make a clear distinction between supervised and self/weakly supervised foundation models in the text and tables. We will also explicitly list our contributions to highlight the key aspects and innovations of our work. Q2: It is hard to understand what the authors want to do and the problem they want to address. A2: This paper addresses Personalized Retrieval and Personalized Segmentation, where a user provides a reference image and either a mask or the object's class name (lines 1-2, 101-102 in the paper). Personalized retrieval aims to find database images with the exact object from the reference image, while personalized segmentation seeks to segment the specified object in new images and videos. We demonstrate that features from pre-trained diffusion models achieve high zero-shot performance on these tasks without training or fine-tuning (please refer to Section 3.1 for details). Lastly, we further point to major drawbacks with current personalized retrieval and segmentation benchmarks and offer two new alternative benchmarks. We show that our approach (PDM) suppresses all supervised and self-supervised methods on all benchmarks. We will make sure that these issues are better emphasized in the revised version. Q3: What is the “short description” mentioned in the paper? A3: The “short description” is the “class name” (as we use in lines 1-2, 101-102, 124, 157). We will make sure to clarify this in the final version. Q4: Visualized results do not present the situation where a desired instance appears together with other instances of the same class. A4: Due to space constraints, we cropped the images in the figures to focus on the relevant objects among other similar objects. We will include more examples without cropping and enlarge the images in the final version. Q5: Why using diffusion features and not other models? A5: The fundamental difference between diffusion models and the other models listed by the reviewer is that they are generative, in the sense that they focus on p(image\|text). The diffusion training objective (i.e., coarse-to-fine reconstruction loss) requires the model to generate informative features for every object. This is different from other, non-generative models, some of which use image-level contrastive learning objectives (e.g. CLIP), and others use image-level discriminative objectives (Resnet, ViT). Such image-level discriminative or contrastive objectives often remove information about specific instances and objects [4]. Furthermore, current diffusion models contain a self-attention component which controls how some parts of the image depend on other parts. This allows the model to generate coherent objects and makes the model contain an explicit representation of object instances. For additional details, please refer to recent papers on diffusion features [1,2,3]. We will clarify and add this discussion to the final version. Q6: Figure 3 is hard to understand. Why "dog" is not fed into the target branch? A6: We thank the reviewer for their feedback. We will make sure to simplify the figure in the final version. This figure illustrates the flow of our algorithm and aligns with the algorithm described in Section 3. Colors are used to differentiate between "Appearance" (green) and "Semantic" (yellow) features. In this figure, a reference image of a dog labeled "dog" and a target image are provided. Both images and the class name undergo feature extraction (see L155-156). The reference and target branches follow the same process, making it irrelevant which branch receives the class name. Q7: What information is used to calculate the cross attention with the target image? A7: Semantic similarity is calculated as the cross attention between class name token $C$ and the semantic feature map $F^{S}_{t}$ as detailed in lines 170-172 and Eq. 6. [1] Tang et al. (2023) “Emergent Correspondence from Image Diffusion”. [2] Lue et al. (2023) “Diffusion Hyperfeatures: Searching Through Time and Space for Semantic Correspondence”. [3] Zhang et al. (2023) “A Tale of Two Features: Stable Diffusion Complements DINO for Zero-Shot Semantic Correspondence”. --- Rebuttal Comment 1.1: Comment: Thank you for the detailed explanation. After reading the authors' response, most of my concerns have been resolved. The motivation and proposed method in this work are interesting. The presentation could be further improved to some extent. However, after reading the comments from other reviewers, I have the same problems as Reviewer 8kmZ. PDM has a weakness in terms of inference speed and is limited by the robustness of the used diffusion model, especially as generative models struggle to generate certain types of objects effectively. --- Rebuttal 2: Comment: Thank you for your feedback. Regarding the robustness of diffusion features, our experiments show they are effective across a wide range of concepts, outperforming *both supervised and self-supervised methods on various benchmarks*. What tools would the reviewer suggest to further validate the robustness? We believe that as better and faster diffusion models are released, PDM can be applied to achieve more robust features and thus better performance. Introducing PDM will indeed allow further research in this direction. As for the inference speed, it is indeed a limitation as noted in our paper. We currently achieve feature extraction in half a second, making it applicable to a variety of tasks. As inversion methods improve, our approach will also speed up.	Summary: The paper introduces Personalized Diffusion Features Matching (PDM), a novel zero-shot approach that utilizes pre-trained text-to-image diffusion models for personalized image retrieval and segmentation without requiring additional training. PDM extracts and fuses semantic and appearance features from an off-the-shelled diffusion model to accurately identify and segment unique instances, even when multiple similar objects are present. It demonstrates superior performance on various benchmarks, outperforming both self-supervised and supervised methods. The authors also address limitations in current datasets by proposing new benchmarks that include challenging scenarios with multiple instances from the same category. Despite its reliance on image inversion, which may affect performance, PDM offers a significant advancement in the field of personalized instance retrieval and segmentation. Strengths: 1. The paper is well organized, clearly written, and easy to follow, especially for the motivation clarification. 2. The experimental observation and justification of the effect of self-attention and cross-attention in the diffusion model are insightful. 3. The proposed method is technically sound and well-motivated. 4. The contribution is sound, consisting of new observations, methods, and more practical benchmark settings. 5. The proposed method is training-free and seems to have great transferability. Weaknesses: I didn't find a major weakness Technical Quality: 4 Clarity: 4 Questions for Authors: 1. It is suggested that some works related to semantic-level feature matching and their applications [1,2] be added to the related work section. 2. (Just constructive suggestions for future works). I am curious whether a similar or more profound phenomenon about attention will appear in DiT [3] and stable video diffusion [4]. Can the method be extended to these more advanced architectures [3,4]? [1] Lindenberger, P., Sarlin, P. E., & Pollefeys, M. (2023). Lightglue: Local feature matching at light speed. In Proceedings of the IEEE/CVF International Conference on Computer Vision (pp. 17627-17638). [2] Li, W., Liu, X., & Yuan, Y. (2022). Sigma: Semantic-complete graph matching for domain adaptive object detection. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (pp. 5291-5300). [3] Peebles, W., & Xie, S. (2023). Scalable diffusion models with transformers. In Proceedings of the IEEE/CVF International Conference on Computer Vision (pp. 4195-4205). [4] Blattmann, A., Dockhorn, T., Kulal, S., Mendelevitch, D., Kilian, M., Lorenz, D., ... & Rombach, R. (2023). Stable video diffusion: Scaling latent video diffusion models to large datasets. arXiv preprint arXiv:2311.15127. Confidence: 4 Soundness: 4 Presentation: 4 Contribution: 3 Limitations: N/A Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for finding our approach insightful, technically sound with great transferability and our paper to be well motivated and easy to follow. We kindly address your comments below. Q1: Cite relevant work. A1: Thank you for your feedback. We will make sure to cite these papers in the final version. Q2: Can the method be extended to DiT and stable video diffusion? A2: We thank the reviewer for their suggestion. We are optimistic that PDM can be applied to DiT and video diffusion models. First, recent studies [1] identified structural and appearance features in vision transformer-based models. Second, it was not hard to find instance-features in several Unet models, SDXL and SDv2.1. Thus, we assume that other diffusion models will also exhibit comparable instance features. We appreciate the reviewer's insightful question, and we leave this for future work. [1] Tumanyan et al. (2022) “Splicing ViT Features for Semantic Appearance Transfer”. --- Rebuttal Comment 1.1: Comment: Thanks for the clarification. I have read all the responses. The proposed method can perform better after fine-tuning, which shows more significant potential in benchmark performance. Considering the new observations, clear motivations, methodology designs, and dataset contributions, I would like to keep my original score because this can be seen as a great contribution to the prior work DIFT that explores diffusion features. --- Reply to Comment 1.1.1: Comment: Dear reviewer, Thank you for the positive and insightful feedbacks	Summary: This paper explores the use of text-to-image diffusion models for personalized retrieval and segmentation tasks. The authors introduce a novel method called PDM (Personalized Features Diffusion Matching), which leverages intermediate features from pre-trained text-to-image models for personalization tasks without requiring additional training. PDM demonstrates superior performance across multiple benchmarks, surpassing many supervised methods. Additionally, the paper identifies deficiencies in existing datasets and introduces a new benchmark dataset that effectively addresses the challenges presented by traditional datasets in scenarios involving multiple instances of the same class. This new dataset focuses on complex scenes containing multiple instances of the same class, further validating PDM's efficiency and accuracy in precisely handling and locating multiple similar instances. Strengths: 1.This paper introduces a novel challenge in personalized retrieval and segmentation tasks involving complex scenes with multiple instances of the same class. In response to this scenario, the authors have constructed a new benchmark dataset and devised a novel method—PDM (Personalized Features Diffusion Matching), which ingeniously combines appearance and semantic features to address the issue of multiple instances within the same category. This approach is quite innovative. 2.The overall structure of the paper is logically organized and easy to understand, and the figures greatly assist in comprehension. Overall, the paper is excellently written. Weaknesses: 1.The authors simply take the average of appearance and semantic features as the overall diffusion features without considering a weighted fusion of these two features. This approach may lead to errors in segmentation or retrieval on some datasets, as it fails to balance the contribution between different features effectively. 2.There may be some issues with the process of generating the personalized multi-instance retrieval and segmentation dataset, such as the randomness in selecting video frames. While this approach improves the efficiency of data generation, it could mislead model training and evaluation if the chosen frames lack sufficient feature diversity or have quality issues. 3.Although the paper conducts extensive experiments in personalized retrieval and segmentation tasks and briefly supplements with ablation study results of key components in the appendix, and qualitatively analyzes the differences from other methods, ensuring comprehensive experimentation, there are still shortcomings. The ablation experiments are only conducted for multi-instance retrieval, which does not prove the importance of key components in multi-instance segmentation. It would be beneficial to include experiments addressing this aspect as well. Technical Quality: 3 Clarity: 3 Questions for Authors: 1.Given your mention that the method's performance might depend on the success of image reconstruction quality, I am curious about how you have managed to enhance image reconstruction quality to achieve such impressive results with your approach. 2.Have you considered more complex ways of combining appearance and semantic features? If so, why did these approaches not yield better results, and what are your thoughts on this? 3.Why opt for random selection of video frames without addressing potential quality issues in the generated data? How do you manage this randomness to ensure fairness and consistency across different methods tested on this data? Confidence: 5 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The authors briefly discuss the limitations of their method in the conclusion but do not provide any viable future solutions. Could the authors possibly offer some feasible ideas or directions for addressing these limitations in future work? Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your feedback. We are encouraged that you find our approach innovative, the challenge novel and our paper to be excellently written. We address your comments below. Q1: Have you considered more complex ways of combining appearance and semantic features? A1: We thank the reviewer for their suggestion. In the paper, we chose feature averaging to avoid training or hyperparameter tuning on labeled data. Following the reviewer's suggestion, we tested a weighted combination of semantic and appearance features: $wF_{appearance} + (1-w)F_{semantic}$. We split the PerMIR and ROxford-Hard [1] datasets into training (20%) and test sets (80%), and optimized $w$ on the training sets. The table below shows that when a training set is available, weighted fusion improves results. We also plan to explore learnable fusion methods with advanced techniques in future work. We will include this analysis in the final version. \| \| ROxford-Hard \| PerMIR \| \|---------------\|--------------\|--------\| \| Avg (in the paper) \| 53.2 \| 71.2 \| \| Wegithed Avg \| 58.4 \| 76.9 \| Q2: In the proposed multi-instance benchmarks, selected frames may lack feature diversity or suffer from quality issues. How do you ensure fairness and consistency across methods despite randomness? A2: We appreciate the reviewer’s comment. Random frame selection was done once during dataset preparation to ensure fair comparisons among all methods. We manually inspected the frames for quality and diversity, finding them acceptable and adequate given the BURST [2] dataset’s quality and video length. In response to this comment, we further quantified frames quality and diversity. Using the CLIP model, we found an average cosine similarity of 0.17 between frames, indicating low similarity (compared to 0.31 for adjacent frames) and thus high diversity. For quality, the mean SSIM between dataset frames and a random ImageNet subset was 13.2 (compared to 11.8 for ImageNet samples, higher values indicate better quality). We will clarify and include this analysis in the final version. Q3: Missing ablation study for Personalized Segmentation. A3: Following this comment, we now added the following ablation study for personalized segmentation: (1) Object Mask Instead of Class Name: In this scenario, we considered the case where the class name is not provided, but an object mask is available. We tested this configuration on PerMIS, resulting in a mIOU of 45.0% compared to the original 42.3% when using the class name. The bIOU was 89.2% compared to the original 86.8% when using the class name. This shows that using an object mask leads to improved segmentation performance, indicating its potential as a valuable alternative when class names are not available. (2) Appearance vs. Semantic Maps: We examined the individual contributions of the Appearance and Semantic maps to the final similarity map. For this experiment, we used each map independently as the final similarity map, ignoring the other. When using only the Appearance Map, we achieved a mIOU of 30.2%, compared to 24.9% when using only the Semantic Map. Both results are significantly lower than our original mIOU of 42.3% when using both maps and averaging them. These findings underscore the necessity of integrating both maps to achieve optimal performance in the final similarity map, and eventually in personalized matching. We thank the reviewer for this feedback. We will make sure to add this ablation study to the final version. Q4: How did you manage to enhance image reconstruction quality? A4: We simply build on recent advances in inversion with diffusion models [3, 4]. For SDXL-turbo, using [3] for inversion results in a PSNR of 24.1, close to the upper bound of 26.3 set by the diffusion VAE. This high PSNR indicates good reconstruction quality and hence high-quality features. Q5: Could the authors suggest ways to address the limitations in future work? A5: Image inversion is the primary limitation of our method, and thus it falls into a different line of work. We did not focus on developing new inversion techniques within the scope of this study. Note that our method is agnostic to the inversion approach, allowing us to adopt faster and more accurate methods developed by the community in the future. [1] Radenovic et al. (2018) “Revisiting oxford and paris: Large-scale image retrieval benchmarking”. [2] Athar et al. (2023) “Burst: A benchmark for unifying object recognition, segmentation and tracking in video”. [3] Pan et al. (2023) “Effective real image editing with accelerated iterative diffusion inversion”. [4] Garibi et al. (2024) “ReNoise: Real Image Inversion Through Iterative Noising”. --- Rebuttal Comment 1.1: Title: Official Comment by Reviewer JGDB Comment: Thanks for your detailed response. I would keep my score by a comprehensive consideration of the paper's contribution and experimental results. --- Reply to Comment 1.1.1: Comment: Dear reviewer, Thank you for the positive and insightful feedbacks	Summary: This paper introduces a novel approach called Personalized Diffusion Features Matching (PDM) for personalized retrieval and segmentation tasks. Most current self-supervised and supervised methods struggle to accurately identify specific instances within a dataset when multiple instances from the same class are present. So the proposed PDM method leverages intermediate features from pre-trained text-to-image diffusion models. PDM combines semantic and appearance cues to accurately locate and segment specific instances within target images. Strengths: * its an innovate use of pretrained model (already available foundation models ) in a zero shot setting. This is beneficial for people without a lot of compute and good for environment. * the proposed method combines both appearance and semantic similarity, which is a well motivated design Weaknesses: * the authors used features from stable diffusion, which is text guided image generation model. its not that fair to compare to DINOv2 or SAM since those models were not trained with text supervision. * the method depends on diffusion inversion, which is quite slower than other segmentation methods. the authors used sdxl-turbo to mitigate the latency but its unclear the impact on quality * the method seems only applicable to Unet diffusion models. its unclear if it works on DiTs Technical Quality: 3 Clarity: 3 Questions for Authors: * what is the performance difference if PDM uses SDXL-turbo vs non-turbo? SDXL-turbo was notorious for not able to reproduce good quality details such as small human faces or limbs. * how does PDM performance vary wrt to the strength of the underlying diffusion model? * in table 2, the authors show openCLIP+PDM and DINOv2+PDM. what happens if you compute OpenCLIP+DINOv2+PDM? Confidence: 2 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: yes the authors adequately address the limitations. Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your detailed and insightful feedback. We believe we address all your concerns below. Q1: It is not fair to compare PDM to Dinov2 or SAM since those models were not trained with text supervision. A1: We thank the reviewer for the comment. The paper compared two types of baselines: (1) Baselines trained *with* text supervision (CLIP and OpenCLIP; See Table 2, Figure 5b and Figure S2) and (2) baselines without supervision, to be consistent with the literature [1,2,3]. Following this comment, we add comparisons with more methods trained with text supervision. Specifically, we evaluated personalized retrieval with features from BLIP2 [4], GLIP [5], and SLIP [6], on the PerMIR dataset. The table below shows that PDM outperforms all text-image models by a large margin. We will add this experiment and additional details in our revised manuscript/suppl. \| Model \| mAP \| \|------------------------\|------\| \| CLIP (in the paper) \| 20.9 \| \| OpenCLIP (in the paper)\| 26.7 \| \| GLIP [5] \| 31.2 \| \| BLIP [4] \| 33.3 \| \| SLIP [6] \| 35.9 \| \| PDM (ours) \| 73.0 \| Q2: How does PDM performance and quality vary with the underlying diffusion model? A2: Thank you for the insightful question. Indeed, it is not clear a-priori that similar features with comparable quality can be found in other diffusion models. To answer this question, we repeated the feature finding process in two diffusion models: SDXL, and SDv2.1. We then ran new experiments for the Personalized Image Segmentation task using two datasets, PerSeg [7] and PerMIS. The table below reports segmentation performance using three diffusion models: (1) SDXL-turbo (results taken from the paper), (2) SDXL, and (3) SDv2.1. We also report the run time for feature extraction per image and the mean PSNR of images to measure inversion-reconstruction quality. The results show that one can find PDM features for other diffusion models (SDv2.1 and SDXL) that produce better results than SDXL-turbo in terms of PSNR, mIoU and bIoU. Their inversion reconstruction time is 10x slower because they require more inversion steps. We will report and discuss these results in the final version. \| \| PerSeg \| \| PerMIS \| \| \| \| \|---\|---\|---\|---\|---\|---\|---\| \| \| mIoU \| bIoU \| mIoU \| bIoU \| feature extraction run time / image (sec) \| mean PSNR \| \| SDXL-turbo (in the paper) \| 95.4 \| 79.8 \| 42.3 \| 86.8 \| 0.5\| 24.1 \| \| SDXL \| 97.0 \| 80.9 \| 44.8 \| 87.7 \| 5\| 25.9 \| \| SDV2.1 \| 95.9 \| 80.1 \| 43.7 \| 87.1 \| 5\| 25.8 \| Q3: The method seems only applicable to Unet diffusion models. A3: The paper focused on UNet-based diffusion models because they are currently the most widely-used text-to-image models. We are optimistic that similar features can be found in other diffusion models, for the following reasons. First, recent studies [8] identified structural and appearance features in vision transformer-based models. Second, it was not hard to find instance-features in several Unet diffusion models. Thus, we assume that other diffusion models (such as DiTs) will also exhibit comparable or better instance features. We appreciate the reviewer's insightful question, as it highlights a promising avenue for future research. Q4: What happens if you compute OpenCLIP+DINOv2+PDM? A4: Following this question, we tested a combination of DINOv2 and PDM. Naturally, there are many ways to combine several features, and here we followed the protocol from [9,10]. We first used OpenCLIP to select the 400 most similar images to each query image. Then, we selected 100 images with highest DINOv2 scores, and then ranked them using PDM. We tested the combined method for personalized retrieval in two datasets: PerMIR and ROxford-Hard. In PerMIR, this method achieved a mAP of 70.2%, compared to 69.9% for OpenCLIP + PDM and 70.8% for Dinov2 + PDM. In ROxford-Hard, it achieved a mAP of 58.3%, compared to 57.7% for OpenCLIP + PDM and 62.1% for Dinov2 + PDM. This approach shows a slight improvement over OpenCLIP + PDM but underperforms compared to Dinov2 + PDM, likely due to OpenCLIP's less effective retrieval capabilities. [1] Tang et al. (2023) “Emergent Correspondence from Image Diffusion”. [2] Lue et al. (2023) “Diffusion Hyperfeatures: Searching Through Time and Space for Semantic Correspondence”. [3] Zhang et al. (2023) “A Tale of Two Features: Stable Diffusion Complements DINO for Zero-Shot Semantic Correspondence”. [4] Li et al. (2023) “BLIP-2: Bootstrapping Language-Image Pre-training with Frozen Image Encoders and Large Language Models”. [5] Li et al. (2022) “Grounded Language-Image Pre-training”. [6] Mu et al. (2022) “SLIP: Self-supervision meets Language-Image Pre-training”. [7] Zhang et al. (2023) “Personalize Segment Anything Model with One Shot”. [8] Tumanyan et al. (2022) “Splicing ViT Features for Semantic Appearance Transfer”. [9] Shao et al. (2023) “Global Features are All You Need for Image Retrieval and Reranking” [10] Zhu et al. (2023) “R2Former: Unified Retrieval and Reranking Transformer for Place Recognition” --- Rebuttal Comment 1.1: Comment: thank you for the detailed rebuttal --- Reply to Comment 1.1.1: Comment: Thank you for reading our response and for your feedback. We believe that it should have addressed your main concerns. If there are any remaining (or new) issues, we would love to get a chance to address them.	Rebuttal 1: Rebuttal: Dear Reviewers and ACs, We were happy to see that reviewers found our approach “novel”, “innovative” (All), “well-motivated" (R1, R3) and recognized its potential as a “significant advancement in the field of personalized instance retrieval and segmentation” (R3). Additionally, they acknowledged our tasks and benchmarks as “novel” (R1,R3), “practical”, and “challenging” (R1, R2, R3), and found our method to be “insightful”, “easy-to-follow” and “excellently written”, with “superior performance” (R2, R3) compared to current SoTA approaches. We have addressed the reviewers' concerns in our rebuttal and are open to further discussion. Your input has been instrumental in improving our paper.	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Non-geodesically-convex optimization in the Wasserstein space	Accept (poster)	Summary: This paper introduces and analyzes an optimization scheme, termed "semi-FB Euler", for a particular minimization problem over the Wasserstein space $P_2(R^d)$: $\min_\mu \mathcal{F}(\mu) = \int (G-H) d\mu + \mathcal{H}(\mu)$, where $G$ and $H$ are convex functions over $R^d$ and $\mathcal{H}$ is a functional that is convex over generalized geodesics. Namely, "semi-FB Euler" is defined by equation (4) of the paper: starting from some $\mu_0$, $$\begin{cases} \nu\_{n+1} = (I + \gamma \nabla H)\_{\sharp} \mu_n, \\\\ \mu\_{n+1} \in \arg\min\_{P\_2(R^d)} \int G d\mu + \mathcal{H}(\mu) + \frac{1}{2\gamma} W\_2^2(\cdot, \nu\_{n+1}). \end{cases}$$ (The second step, called a JKO step, is assumed solvable for the theoretical parts of the paper.) Convergence to critical points of $\mathcal{F}$ is established under mild regularity assumptions, both asymptotically (Theorem 1) and with non-asymptotic rates (Theorems 2, 3). Under a Lojasiewicz inequality assumption, convergence to a minimizer is established with non-asymptotic rates (Theorems 4, 5). Numerical illustrations with synthetic data are provided, in which an input-convex neural network is used to implement the JKO step. Strengths: This work provides mathematically rigorous grounding for an infinite-dimensional optimization scheme, by working out explicit regularity conditions that ensure well-definedness and asymptotic convergence. The precision and attention to rigor are appreciable. The paper is clearly written and well-structured. It also provides an appropriate level of background information on the Wasserstein geometry. Compared to the closely related work "The Wasserstein proximal gradient algorithm" ([56] Salim, Korba, Luise, 2020), numerical experiments using input-convex neural networks (following [44] Morkov et al., 2021) illustrate that the JKO step can indeed be implemented in general, although computational costs are not discussed. Weaknesses: The proposed "semi-FB Euler" corresponds to a forward-backward splitting scheme of $\mathcal{F}$ into $\mathcal{F}_1(\mu) = \int (-H) d\mu$ and $\mathcal{F}_2(\mu) = \int G d\mu + \mathcal{H}(\mu)$ in the Wasserstein optimization geometry. (Incidentally, the name "semi-FB Euler" can be misleading, as it is really a forward-backward scheme.) So the setting considered in this paper is very similar to that of "The Wasserstein proximal gradient algorithm" ([56] Salim, Korba, Luise, 2020), which corresponds to the case where $H$ is concave and $G=0$. In fact, it seems that the only way that convexity of $G$ comes into play in the proofs, is to ensure convexity of $\mathcal{F}_2$ over generalized geodesics. (Please do correct me if this is incorrect.) With this in mind, the contributions of this paper are to study what happens when $-H$ is concave in $\mathcal{F}_1(\mu) = \int (-H) d\mu$, as opposed to convex in [56]. It seems that concavity of $-H$ is used for: 1. the existence of a Borel measurable selector $S$ for the subdifferential $\partial H$ (section A.1), but it is not essential to the paper; 2. the descent lemma (Lemma 1); 3. quadratic growth of $\\|S\\|^2$ under quadratic growth of $H$ (Lemma 4 and proof of Thm 1 line 706); 4. it seems that convexity of $H$ is implicity used in the very last step of the proof of Thm 1 (line 735). (Incidentally, please make the last step of the proof of Thm 1 more explicit.) In summary, compared to the setting of [56], which corresponds to $-H$ being smooth and convex, this work shows that if $-H$ is concave, then the forward-backward algorithm (with a good choice of the selector $S$ when $H$ is non-differentiable) converges for any choice of step-size $\gamma$. I find this theoretical contribution interesting, but I am not sure if it is sufficiently significant. Besides, there is also the weakness, acknowledged by the authors (line 362) that the proposed algorithm relies on a JKO step which is computationally expensive. Hence my overall rating for this submission. Technical Quality: 4 Clarity: 3 Questions for Authors: - Please address the points in "Weaknesses". - The items 1.-4. in "Weaknesses can also be guaranteed if, instead of $-H$ concave, one assumes $H$ is smooth (which is Assumption 5) and $\gamma$ is small enough (see [56, Thm 5] for item 2 and [56, Lemma 2] for item 4). Could your results be extended to the case where $H$ is smooth instead of convex? If yes, then this could be another way to show theoretical guarantees for forward-backward schemes outside of the convex case (in the spirit of your conclusion, line 393). - What are the "interesting avenues for future work" mentioned in the conclusion? Confidence: 4 Soundness: 4 Presentation: 3 Contribution: 1 Limitations: The authors adequately addressed the limitations. Flag For Ethics Review: ['No ethics review needed.'] Rating: 3 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for the positive comments on our work. We hope the reply below can highlight our contribution. Strengths *"Computational cost...": as the answer to reviewer 7EW7, we will discuss the computational cost of the JKO in the revised version. Weaknesses* *``the setting considered in this paper is very similar to": our problem setting is much more general than that of ([56], Salim, Korba, Luise - NeurIPS2020). Having some concavity looks simple yet the whole objective structure becomes much more expressive. The expressivity can be acknowledged from the following result: any continuous function can be approximated by a sequence of DC functions over a compact, convex domain [Bačák11]. [Bačák11] Bačák, M., & Borwein, J. M. (2011). On difference convexity of locally Lipschitz functions. Optimization, 60(8-9), 961-978.* By that, we mean that the structure is semantically simple but powerful mathematically. Saying that the convexity in [56] is replaced by the concavity in our work does not entirely reflect our framework, hence the contribution. We should look at the whole landscape of the objective function (potential energy + internal/interaction energy), and it would be more complete to say that our work replaces the geodesic convexity in [56] by geodesic difference-of-convexity. Apart from the theoretical contribution mentioned by the reviewer, we think there are two more elegant contributions: (1) The use of the DC function for the potential energy already allows us to tackle sampling from log-DC density -- which is a large class of densities (instead of log-concave "and" log-smooth density as in ([56] Salim, Korba, Luise, 2020)). (2) The way we separate $\mathcal{E}_G$ into the JKO part and leave $\mathcal{E}_H$ for the push-forward is non-trivial and is already a contribution (in our opinion). It differs from the common mindset of applying forward to the potential and backward to the internal energy. Our approach makes both steps tractable, i.e., the optimal map of the forward is computable and the optimal map of the backward is characterizable. Moreover, if we started from [56] with the old mindset and with a mere curiosity of what happens if we replace convex $H$ with concave $-H$, we would not do so in the first place and rather abandon the idea because there are not so many ``log-convex" distributions out there. For these reasons, we also would like to retain the name "semi-FB Euler" to address its non-triviality and distinguish it from [56]. In terms of theory, the use of the concave $-H$ is correctly mentioned by the reviewer. However, we think the existence of $S$ is actually essential because it allows us to work with non-differentiable $H$ (as in Theorem 2). Without this concavity, we have to use more sophisticated subdifferential notions for $H$ like Clarke or Frechet [Clarke90] in the non-differentiability realm. These notions are difficult to work with, and they can be ill-posed (the subdifferential set is empty). [Clarke90] Clarke, F. H. (1990). Optimization and nonsmooth analysis. Society for Industrial and Applied Mathematics. *``Please make the last step of the proof of Thm 1 more explicit": the equation between lines 734 and 735: $\gamma^{-1}(T_{\mu_}^{\nu_} - I) \in \partial (\mathcal{E}_G + \mathscr{H})(\mu^)$. By the definition of $\nu^$ in line 678, $\nu^ := (I+\gamma S)$#$\mu^$, and since $S$ is the gradient field of a convex function $H$, that push-forward is optimal, i.e., $T_{\mu^}^{\nu^} = I + \gamma S$. Plug this in the above formula, we get $S \in \partial(\mathcal{E}_G + \mathscr{H})(\mu^)$. On the other hand, since $H$ is convex, $S \in \partial \mathcal{E}_H(\mu^)$ [4, Proposition 4.13]. We will add these explanations in the revised version. About the computational challenge of the JKO, please refer to our answer to reviewer 7EW7. Questions* *``Could your results be extended ...": We think our results are totally applicable for $L$-smooth potentials with small $\gamma$ as suggested. Note that, any $L$-smooth function is a DC function (see our paragraph Why difference-of-convex structure). Therefore, while the suggestion is nice, it does not extend our work any further. The true extension could be that instead of geodesically-concave potential $-\mathcal{E}_H(\mu)$, we can consider a more general geodesic concavity not necessarily given in the form of potential energy. What are the "interesting avenues for future work": Those include, for example, the extension mentioned in the previous answer. Moreover, we can also investigate non-geodesically-convex problems in different Wasserstein spaces (either with different base space than $\mathbb{R}^d$, or different cost functions instead of squared Euclidean distance). For example, in [Section 5, Lambert2022], in the case of mixture of Gaussian Variational Inference, the base space for the Wasserstein space is $BW(\mathbb{R}^d)$ (Bures–Wasserstein space) instead of $\mathbb{R}^d$, i.e., we are minimizing over $\mathcal{P}_2(BW(\mathbb{R}^d))$ (Wasserstein space over Bures–Wasserstein space). This adds one layer of complexity and, as a consequence, convexity is lost in that space and, quoting from page 9 [Lambert2022], ``we lose many of the theoretical guarantees". We can extend the discussion when we have one page extra for the final version. [Lambert2022] Lambert, M., Chewi, S., Bach, F., Bonnabel, S., & Rigollet, P. (2022). Variational inference via Wasserstein gradient flows. Advances in Neural Information Processing Systems, 35, 14434-14447.* --- Rebuttal 2: Comment: Thank you for clarifying what your contributions are. However, this clarification makes the significance of this work less convincing than I initially thought. The title of the submission "Non-geodesically-convex optimization in the Wasserstein space" indicates that 1. your audience is one that is interested in optimization questions; 2. you consider objective functionals which are non-convex, and the go-to condition in the non-convex optimization literature is smoothness. However your submission is actually about Difference-of-Convex optimization in the Wasserstein space, which is quite different, both in its application cases and in the kind of theory involved for the analysis. I understand the general appeal of the DC assumption, given the approximation result you cited ("any continuous function $f$ can be approximated by a sequence of DC functions $g-h$ over a compact, convex domain"). But a) this approximation result does not say how to choose the splitting $g-h$ in a usable way for optimization [please correct me if incorrect], and besides b) you do not prove such an approximation result for the Wasserstein space. Another argument in favor of studying DC functions on the Wasserstein space, instead of smooth ones, might be that your analysis holds under quite few assumptions. But, particularly in a venue such as NeurIPS, a theoretical analysis only has value when it applies (or there are reasons to think it will apply in the future) to (i) an algorithm _and_ (ii) a setting of practical interest. Now - (i) after reading your answer to Reviewer 7EW7, it is still unclear to me that the algorithm you analyze (using a proximal step in Wasserstein space) has hopes of becoming efficiently implementable. If, as you say, methods proposed 2 years ago allow for faster computation, then it is up to you to implement them. - (ii) The example setting you promoted most, namely sampling from a log-DC measure, deserves more discussion. Sampling problems of this form typically arise in Bayesian inference, where the target measure is a posterior likelihood which can be quite involved. It is not at all clear how to choose a splitting of it (or rather of its log) in a tractable way. For these reasons, I downgrade my rating from 4 to 3. Nonetheless I remain open to further discussion. My recommendation to the authors would be to exploit their (technically interesting!) analysis into a full-fledged study of DC optimization in the Wasserstein space. (I realize that this is not easy to incorporate into the current submission unfortunately.) PS1: I understand that your analysis can be extended to the case where the objective $\mathcal{F}$ is of the form $\tilde{\mathcal{G}} - \tilde{\mathcal{H}}$ where $\tilde{\mathcal{G}}, \tilde{\mathcal{H}}$ are general geodesically convex functionals, instead of $\tilde{\mathcal{G}}$ being linear ($\tilde{\mathcal{G}} = \mathcal{E}_{-H}$ and $\tilde{\mathcal{H}}= \mathcal{H} + \mathcal{E}_G$ in the paper). My comments above implicitly assume this extension. PS2, regarding the name semi-FB Euler: I do not have a strong opinion on the matter, but I would like to point out that choosing such a name does not contribute at all to convey the non-triviality of the method, and that this name would be quite awkward in the context of the natural extension mentioned in PS1 (with general $\tilde{\mathcal{G}} - \tilde{\mathcal{H}}$). --- Rebuttal Comment 2.1: Comment: We thank the reviewer for the response. *The title of the submission "Non-geodesically-convex optimization in the Wasserstein space" indicates...* We agree that smoothness (L-smooth) is the go-to condition when there is no convexity. As we understand, the reviewer advocates for this class of L-smooth nonconvex functions. We also assume we are talking about the nonconvexity of $F$ in the potential part, $\mathcal{E}_F$ (inducing the nonconvexity along Wasserstein geodesics). We emphasise is that the class of L-smooth functions is just a subclass of DC functions thanks to the well-known result: if $F$ is L-smooth, then it admits the following DC decompositions: (1) $F(x) = (F(x) + (\eta/2) \Vert x \Vert^2) - (\eta/2) \Vert x \Vert^2$ or (2) $F(x) = (\eta/2) \Vert x \Vert^2 - ((\eta/2) \Vert x \Vert^2 - F(x))$ whenever $\eta \geq L$. In other words, our results readily apply to the class of $L$-smooth functions raised by the reviewer. Nevertheless, we can explicitly mention in the abstract that the nonconvex structure we are studying is DC. *given the approximation result you cited...* The result we cited advocates the richness of the class of DC functions since it is a universal approximator for any continuous function over a compact region. Obtaining explicit DC decomposition for a given function has been studied thoroughly in the DC programming literature. It is known that many objective functions have natural DC decomposition (we are talking about the $F$ part in the potential) (see, e.g., [Nouiehed19, Lethi05]). We can add a paragraph to discuss the explicit decomposition in the revised version of the paper. Note that, in Appendix C.1 and C.2 in our submission, we already provided two concrete examples of the DC decomposition for the log of the Gaussian mixture and also von Mises-Fisher with distance-to-set prior, demonstrating that it can be done in practice. We can point out DC structures of other types of non-log-concave densities, including the posterior, as suggested. [Nouiehed19] Nouiehed, M., Pang, J. S., \& Razaviyayn, M. (2019). On the pervasiveness of difference-convexity in optimization and statistics. Mathematical Programming, 174(1), 195-222. [Lethi05] H. A. Le Thi, \& T. Pham Dinh (2005). The DC (difference of convex functions) programming and DCA revisited with DC models of real world nonconvex optimization problems. Annals of operations research, 133, 23-46. *Another argument in favor of studying DC functions on the Wasserstein space, instead of smooth ones, might be that your analysis holds under quite a few assumptions: This is indeed why we focus on DC class (containing L-smooth class), and we will make this advantage even more clear in the revised version. We already made an attempt to explain that in the paragraph Why difference-of-convex structure* and will make it more pronounced. *(i) It is still unclear to me that the algorithm you analyze (using a proximal step in Wasserstein space) has hopes of becoming efficiently implementable: our work is mainly theoretical, in the same vein as in ([56], Salim, Korba, Luise - NeurIPS2020). (ii) The example setting you promoted most, namely sampling from a log-DC measure, deserves more discussion: It is possible to discuss the DC structure of posterior distributions more extensively in the revised version. The splitting of the posterior depends on two terms: log-likelihood and log-prior. If we assume that the likelihood is nice enough, i.e., log-L-smooth, it is already DC with known splitting as above (of course, other structures can also be considered). The log-prior is normally not smooth to model sparsity or low rank (LASSO, group LASSO, SCAD, Capped-$\ell_1$, PiL, etc). Most of them have some explicit DC structure [Lethi15]. [Lethi15] Lethi, H. A., Dinh, T. P., Le, H. M., \& Vo, X. T. (2015). DC approximation approaches for sparse optimization. European Journal of Operational Research, 244(1), 26-46.* *My recommendation to the authors would be to exploit their (technically interesting!) analysis into a full-fledged study of DC optimization in the Wasserstein space*: this is a promising future research direction. However, our current paper is already technically large (26 pages or so), and integrating all of this into the current version makes it overly heavy. Moreover, we did not study the suggested class initially because we did not find any practical problems with the concave part given in a more general form than the potential energy.	Summary: This work, of a theoretical nature, considers the problem of minimizing a functional $$\mathcal{F}$$ over the space of probability measures of the form $$\mathcal{F}(\mu) = \int (G(x) - H(x)) d\mu(x) + \mathcal{H}(\mu)$$ where $G,H$ are convex potentials and $\mathcal{H}$ is (typically) the negative entropy (the work actually extends to functionals $\mathcal{H}$ that are convex along generalized geodesics). This setting substantially differs from standard optimization in the space of probability measure in that $\mathcal{F}$ is not convex along generalized geodesics, the standard assumption to establish convergence of gradient flows in this spaces, following the seminal work of Ambrosio, Gigli and Savaré. Nonetheless, the "difference of convex functions" (DC) structure enables the derivation of a two-step scheme to minimize $\mathcal{F}$. Namely, given a current iterate $\mu_n$, one first computes $\nu_{n+1}$ using a forward (explicit) Euler scheme _using only the concave term_ $-H$, then obtain $\mu_{n+1}$ using a backward (implicit) iterate on the convex (along generalized geodesics) term $\mu \mapsto \braket{G,\mu} + \mathcal{H}(\mu)$. This approach is referred to as a _semi_ forward-backward (FB) Euler scheme, seen as a variation of the known FB scheme (which would process similarly, but performing an explicit iterate on $G-H$ and an implicit iterate on $\mathcal{H}$). In contrast to the standard FB scheme, this semi-FB scheme that leverages the DC structure enables the derivation of strong theoretical guarantees: existence of accumulation points that are critical points of $\mathcal{F}$, and under additional standard assumptions ($\sim$ PL inequality), convergence rate toward the global minimum of $\mathcal{F}$. Strengths: The presentation of the work is extremely clear. It is exposed in a pedagogical way, motivations are clear and results are stated formally. The authors obtain strong theoretical guarantees in a scope more general than the restricted _convex along generalized geodesics_ one. The DC framework in the context of Wasserstein-based optimization seems to be a promising playground for further research. The proposed approach is elegant to me, in that it is simple yet seems very powerful, and seems reasonably usable in practice. Weaknesses: 1. While I understand that the paper is mostly theoretical, the "from theory to numeric" side may be enhanced (typically, putting some of the material of Part B, in particular Algorithm 2, to the main body). 2. Still targeting numerical applications, the approach seems somewhat limited in that the numerical experiments, according to the appendix, have been run on a fairly powerful hardware and yet took a couple of hours to run, while they remain at the proof-of-concept level on toy datasets. 3. Though this does not diminishes the intrinsic quality of the paper, the paper relies on technical proofs deferred to the appendix and I could not proofread all of them. I read the proof of Lemma 1 and Theorem 1, which seem correct to me, and quickly check other proofs but cannot guarantee the correctness of the theorems (though they look sounded)---which are nonetheless the main (if not unique) contributions of the work. I understand that this is not the authors fault, but I wanted to stress that point in my review. Minor aspects: - It may be better to use $\tau$ instead of $\gamma$ to denote the step-size in JKO schemes, since $\gamma$ is often used to denote a transport plan. - I believe it's better to avoid starting sentences with mathematical symbol. That makes the document a bit easier to read. See for instance line 117 "continuous w.r.t. $\mathcal{L}^d$. $\mu$-a.e. stands..." is a bit confusing. Technical Quality: 3 Clarity: 4 Questions for Authors: 1. Genuine question: is there any convergence in the regime $\gamma \to 0$ toward a limit curve $(\mu_t)_t$, and if so does it coincides with the usual Wasserstein gradient flow of $\mathcal{F}$? Said differently, is it true that the (time-continuous) Wasserstein gradient flow of the KL for a log-DC target distribution converges globally? (As a consequence of the fact that the sequence $(\mu_n)_n$ you build do converge globally in that case) Confidence: 3 Soundness: 3 Presentation: 4 Contribution: 3 Limitations: NA Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for your positive comments on our work. Weaknesses *[1.]* We will put some material from Part B (discussion on the ICNN approach for the JKO as well as Algorithm 2) into the main text as suggested when we have some extra space. *[2.]* We agree with this limitation. Please see also our reply to reviewer 7EW7. As answered to reviewer 7EW7, there are some recent works [A-Melis22, Fan22] proposing new strategies to compute the JKO that scale better. [A-Melis22] Alvarez-Melis, D., Schiff, Y., & Mroueh, Y. (2022). Optimizing functionals on the space of probabilities with input convex neural networks. Transactions on Machine Learning Research. [Fan22] Fan, J., Zhang, Q., Taghvaei, A., & Chen, Y. (2022). Variational Wasserstein gradient flow. International Conference on Machine Learning. *[3.]* As authors, we also try our best to ensure everything is mathematically correct. *Minor aspect.* Thanks for the suggestion. We will replace $\gamma$ with some other symbol and also revise all the sentences carefully. *Question.* It is sensible to expect such behaviours of the time-continuous limit of semi-FB-Euler. We think the hypotheses raised by the reviewers are very likely to hold because the semi-FB-Euler is stable and has sufficient regularity. However, we have not really studied that limit and it is not necessarily easy to prove such hypotheses. This could be an interesting future research avenue. --- Rebuttal Comment 1.1: Title: Thanks Comment: Thank you for taking time answering my review :-)	Summary: This work focuses on the optimization in the Wasserstein space of a functional which is a sum of an internal energy (convex along a generalized geodesic) and of a potential energy, whose potential is a difference of convex functions. To solve such problem, the authors propose to generalize the semi Forward-Backard Euler scheme to the Wasserstein space, and study it theoretically, showing the convergence in general settings. Finally, they demonstrate the convergence of the algorithm on two toy objectives. Strengths: - This paper is well written and clear. - To minimize functionals obtained as difference of convex functionals, it introduces the semi-forward backward Euler scheme, and it shows its convergence under different reasonable assumptions. - The theoretical analysis seems rigorous and complete, as it shows the convergence in different settings and under different criteria (e.g. the paper provides a descent lemma, convergence of a subsequence towards a critical point, convergence in gradient, and convergence to the minimum under PL inequality). Weaknesses: This is mainly a theoretical work. Thus, the following weaknesses on the experiment section and on the method are minor in my opinion. - As underlined in the experiment section, the scheme involves to compute the JKO operator, which is computationally costly as it requires neural networks to solve it - The experiments focus on 2D toy examples Technical Quality: 3 Clarity: 3 Questions for Authors: The focus of the paper is on functionals obtained as a sum of a potential and an internal energy. Could the analysis be done with more general DC functionals (e.g. with interaction energies.). I guess yes since the MMD is presented in the introduction as being such a functional. It would also have been nice to test the semi Forward-Backward scheme on the MMD, as it is not geodesically convex, and does not converge well without tricks such as adding noise (e.g. for Gaussian kernel). Assumption 2 supposes that the sublevel sets are compact w.r.t the Wasserstein topology. Are there easy examples of functionals which satisfy this (e.g. those used in the experiment section)? Typos: - In the abstract, I found the sentence line 3 "When the regularization term is the negative entropy, the optimization problem becomes a sampling problem where it minimizes the Kullback-Leibler divergence between a probability measure (optimization variable) and a target probability measure whose logarithmic probability density is a nonconvex function." weird as it is not specified that the objective function is a potential. - Line 14: "can be considered gradient descent": lack a word? Rating: 7 Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The authors have acknowledged the limitations in the main text Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for constructive and positive comments on our work. Weaknesses *the scheme involves to compute the JKO operator, which is computationally costly..., toy examples: Please also refer to our reply to reviewer 7EW7. Since we use [Mokrov21] in our JKO step, our work is equally costly. There are some recent works [A-Melis22, Fan22] that propose new strategies to compute the JKO that scale better. [Mokrov21] Mokrov, P., Korotin, A., Li, L., Genevay, A., Solomon, J. M., & Burnaev, E. (2021). Large-scale Wasserstein gradient flows. Advances in Neural Information Processing Systems, 34, 15243-15256.* [A-Melis22] Alvarez-Melis, D., Schiff, Y., & Mroueh, Y. (2022). Optimizing functionals on the space of probabilities with input convex neural networks. Transactions on Machine Learning Research. [Fan22] Fan, J., Zhang, Q., Taghvaei, A., & Chen, Y. (2022). Variational Wasserstein gradient flow. International Conference on Machine Learning. Question *``Could the analysis be done with more general DC functionals": Yes, our framework can handle interaction energies (e.g., MMD) as discussed in the context paragraph and Appendix A.2. Applying semi-FB Euler to MMD as suggested is a good research direction which we can consider in the near future. ``Assumption 2 supposes that the sublevel sets are compact...": As far as we know, there is no easy check for it when the base space for the Wasserstein space is $\mathbb{R}^n$. If the base space is instead compact ($X \subset \mathbb{R}^n$, $X$ is compact, the Wasserstein space is the space of all finite 2nd-moment probability distributions whose supports are contained in $X$), the compactness of sublevel sets would be easier to verify since the coercivity of $\mathcal{F}$ is a sufficient condition. In turn, to check coercivity, one sufficient condition is that the potential grows fast enough at infinity, e.g., if $\mathscr{H}$ is the entropy, we need $F(x) \gtrsim c \Vert x \Vert^2$. Nevertheless, this is not the case here since we wanted to consider $\mathbb{R}^n$ but not $X$. Note, however, that the compactness assumption is only used for Theorem 1. In fact, we only need the compactness of the generated sequence {$\mu_n$} in the proof. Therefore, in the final version, we will remove Assumption 2 and instead assume that the sequence {$\mu_n$} is compact inside Theorem 1. Typos*: We will proofread the paper and correct the typos as suggested.	Summary: This paper studies minimization algorithms for functionals on the Wasserstein space with the following difference of convex functions (DC) structure: $$ \min_{\mu \in \mathcal{P}_2(X)} \mathcal{F}(\mu) := \int (G(x) - H(x)) d\mu(x) + \mathcal{H}(\mu), $$ where $G$ and $H$ are convex functions and $\mathcal{H}$ is convex along (generalized) geodesics in the Wasserstein space. The main motivation for this problem is that it is the sampling analog to difference of convex functions problems in optimization, giving a problem of intermediate difficulty between convex and true non-convex. The authors also mention an application to maximum mean discrepancy. They study a modified forward Euler sceme which they refer to as "semi FB Euler", where given a current iterate $\mu_n$ they update as $$ \mu_{n + 1/2} := (I + \gamma \nabla H) \mu_n, $$ and then $$ \mu_{n + 1} := JKO_{\gamma(H+ E_G)}(\mu_{n + 1/2}). $$ A similar scheme was considered in [1,2] but with the difference that the function $G$ was included in the first step but not in the second; the motivation for this difference is that it more closely aligns with DC programming. One benefit of this modification is that $\mu_{n + 1/2}$ is pushed forward by an optimal transport map, which makes the problem more tractable. The main focus of the work are various convergence results for the above scheme, including an asymptotic result as well as results on the norm of a gradient analog and the distance between $0$ and the sub-differential. The authors also consider convergence under a gradient domination condition, and conclude with some numerics. [1] Wibisono, Andre. "Sampling as optimization in the space of measures: The Langevin dynamics as a composite optimization problem." Conference on Learning Theory. PMLR, 2018. [2] Salim, Adil, Anna Korba, and Giulia Luise. "The Wasserstein proximal gradient algorithm." Advances in Neural Information Processing Systems 33 (2020): 12356-12366. Strengths: - This paper is, to my knowledge, the first to consider the difference of convex functions setting. - The above bullet leads the authors to propose a modified algorithm compared to previous literature, and means that their convergence results are generally novel. - The work is rigorous and quite mathematically clear. Weaknesses: - The Łojasiewicz condition is not verified to hold in any settings other than their the standard case of KL minimization. - The problem is somewhat far from practice, firstly because the JKO step is very challenging to implement in practice, and secondly because the setting the authors study is only motivated by one application, to maximum mean discrepancy functionals. They do mention a connection to two-layer neural networks in the "Context" section on page 2 but this was impossible to understand from the little they wrote. - The proofs don't yield explict constants in their results, which is important because there could be hidden dimension-dependence. Technical Quality: 3 Clarity: 3 Questions for Authors: - The thorough introduction to Wasserstein space is much appreciated, but perhaps it could be largely moved to an appendix so that more space is left in the main text for more discussion of applications and high-level ideas of the proofs. - Please give more space to the connection to two-layer neural networks mentioned in the "Context" section on page 2. - Since it is a general fact (see, e.g. [1]) that a gradient domination condition implies that $d(x, x)^2 <= C(F(x) - F(x))$, I feel that Theorem 5 should either be removed, or stated as a corollary in an appendix and just mentioned as a brief remark in the main text. [1] Otto, Felix, and Cédric Villani. "Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality." Journal of Functional Analysis 173.2 (2000): 361-400. Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The authors have adequately addressed the limitations. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for the thoughtful and positive comments on our work. Weaknesses *$\bullet$ "The Lojasiewicz condition...": We agree that the Lojasiewicz condition is usually used in the case of KL divergence. However, the condition also almost holds for the case of Maximum Mean Discrepancy (MMD) (under mild assumptions). Recall that MMD involves the interaction energy: \begin{align} \mathcal{F}(\mu) = \dfrac{1}{2} D_{\text{MMD}}(\mu^,\mu)^2:=\dfrac{1}{2} \int \int k(x,y) d\mu(x) d\mu(y) + \int{F(x)} d\mu(x) + C \end{align} where $D_{\text{MMD}}$ is the MMD distance, $F(x)=-\int{k(x,y)}d\mu^(y)$, $C$ does not depend on $\mu$ and $k$ is a stationary kernel, i.e., $k(x,y) = W(x-y)$ for some $W$. The Wasserstein gradient of $\mathcal{F}$ is given by \begin{align} \nabla_W \mathcal{F}(\mu) = \nabla F + \nabla W * \mu \end{align} where denotes the convolution. Under some regularity conditions of the kernel, it is known that (inequality (62) in [Arbel19] with some notational change) \begin{align} 2(\mathcal{F}(\mu)-\mathcal{F}(\mu^)) \leq \Vert \mu^-\mu\Vert_{\dot{H}^{-1}(\mu)} \times \int{\Vert \nabla_W \mathcal{F}(\mu) \Vert^2} d\mu(x) \end{align} where $\Vert \mu^-\mu\Vert_{\dot{H}^{-1}(\mu)}$ is the weighted negative Sobolev distance. This is almost the Lojasiewicz condition for $\mathcal{F}$. The only requirement to make it real Lojasiewicz is that $\Vert \mu-\mu^\Vert_{\dot{H}^{-1}(\mu)}$ is bounded uniformly for all $\mu$. However, this is tricky. Nevertheless, the point is that we only use the Lojasiewicz condition for the generated sequence {$\mu_k$}, so all we need is the above quantity to be bounded along that sequence, and this boundedness seems natural and is usually assumed (as in [Prop.7, Arbel19]). We will add this discussion in the revised version. [Arbel19] Arbel, M., Korba, A., Salim, A., & Gretton, A. (2019). Maximum mean discrepancy gradient flow. Advances in Neural Information Processing Systems, 32. *$\bullet$ "JKO step is very challenging": The bottleneck of the JKO computation using [Mokrov21] is the logdet(Hessian), (scales cubically w.r.t. data dimension) and training an NN at each step. If we trade some accuracy for scalability, we can use stochastic log determinant estimators as in [A-Melis22], leading to quadratic complexity. We are also aware of a recent work that replaces the gradient of ICNN by a residual neural network, leading to remarkable speeding [Fan22]. Therefore, we believe the scalability issue of the JKO and hence our proposed method can be resolved shortly. [Mokrov21] Mokrov, P., Korotin, A., Li, L., Genevay, A., Solomon, J. M., & Burnaev, E. (2021). Large-scale Wasserstein gradient flows. Advances in Neural Information Processing Systems, 34, 15243-15256.* [A-Melis22] Alvarez-Melis, D., Schiff, Y., & Mroueh, Y. (2022). Optimizing functionals on the space of probabilities with input convex neural networks. Transactions on Machine Learning Research. [Fan22] Fan, J., Zhang, Q., Taghvaei, A., & Chen, Y. (2022). Variational Wasserstein gradient flow. ICML. *--``only motivated by one application, to maximum mean discrepancy functionals": our work is not only motivated by maximum mean discrepancy but also (and mainly) by sampling from log-DC densities, which existing samplers fail to address. This is a very rich class of (nonconvex) densities and it would be helpful to have another independent survey on DC structures of commonly-used densities. --"connection to two-layer neural networks": The connection between MMD and the problem of infinite-width one hidden layer neural network is briefly mentioned in [Salim20, Appendix B.2]. We can add a pointer to that and can even briefly present it for completeness. [Salim20] Salim, A., Korba, A., & Luise, G. (2020). The Wasserstein proximal gradient algorithm. Advances in Neural Information Processing Systems, 33, 12356-12366.* *$\bullet$``The proofs don't yield explicit constants": we can discuss the complexity w.r.t. dimensionality (to some extent). However, yielding explicit dimension-constant is very tricky, especially since the ICNN family is only a subfamily of convex functions, and we do not know how close the solution given by ICNN is to the true optimal transport map. So, obtaining the overall complexity that includes the JKO computation is probably impossible in practice. Question* *$\bullet$ ``The thorough introduction...": Thanks for the suggestion. However, we think it would be beneficial for the readers to have Wasserstein's geometry background in the main text, and we also need all those notions to present our results precisely, so moving them to the appendix is a bit difficult. In the final version with one page extra, we will extend the experiment section, e.g., move the practical scheme in the appendix to the main text. $\bullet$``Please give more space...": as answered above, we can add a pointer to [Salim20, Appendix B.2] or can briefly discuss it for completeness. $\bullet$ ``Since it is a general fact...": It is known that Log-Sobolev implies Talagrand [Otto00]; consequently, KL divergence controls Wasserstein distance in such a case. We can discuss this connection in our paper. However, Theorem 5 is much more general than that and cannot use the above implication. First, we work with a general regularizer $\mathscr{H}$, so the objective is not KL divergence. Second, even when $\mathscr{H}$ is the negative entropy, resulting in KL divergence, we consider the general Lojasiewicz exponent $\theta \in [0,1)$. At the same time, the above implication applies only for $\theta=1/2$ (the case of Log-Sobolev inequality). Therefore, Theorem 5 is not simply a corollary of Theorem 4. [Otto00] Otto Felix and Cédric Villani. "Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality." Journal of Functional Analysis 173.2 (2000): 361-400* --- Rebuttal Comment 1.1: Title: Thanks for your response Comment: With regard to the Lojasiewicz condition, it is interesting that it can almost be satisfied in the MMD case, but I would emphasize that the reason the log-Sobolev inequality is so important is that it holds uniformly. In particular, the gap between a PL inequality at some points versus a PL inequality everywhere can be very large and difficult to bridge. Also, I still don't find the connection to MMD particularly convincing, so this setting is not completely convincing anyways. With regard to the fact that gradient domination implies quadratic growth: sure, the case where $(f(x) - f(x_*))^\theta \leqslant C\\|\nabla f(x)\\|$ is not explicitly proved in [1], but the proof can be quite easily modified to handle that case. At a minimum, you should add citations to [1] and [2]. Note also that using their results you could likely simplify your proofs and make the constants more explicit. With regard to your remaining points, thanks for your responses. Overall, my opinion of the work has not substantially changed, so I leave my score as-is. [1] Otto, Felix, and Cédric Villani. "Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality." Journal of Functional Analysis 173.2 (2000): 361-400. [2] Karimi, Hamed, Julie Nutini, and Mark Schmidt. "Linear convergence of gradient and proximal-gradient methods under the polyak-łojasiewicz condition." Machine Learning and Knowledge Discovery in Databases: European Conference, ECML PKDD 2016, Riva del Garda, Italy, September 19-23, 2016, Proceedings, Part I 16. Springer International Publishing, 2016. --- Reply to Comment 1.1.1: Comment: Thank you for the response. We will incorporate those suggestions into the final version of the paper.	Rebuttal 1: Rebuttal: We thank all the reviewers for their thoughtful, constructive, and high-quality reviews. We reply to each reviewer in their comment section.	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
RL-GPT: Integrating Reinforcement Learning and Code-as-policy	Accept (oral)	Summary: The authors present a framework to give LLMs the ability to code and train RL agents as a tool for completing tasks. They perform experiments in MineDojo. Strengths: Experiments: Barring the standard deviation issue mentioned in teh weaknesses, the results are a significant improvement over Plan4MC. Idea: the method of using RL as a tool for crafting subfunctions to complete tasks via LLMs is interesting, intuitive, and simple. Weaknesses: Minor Issues: - some relevant related works using LLMs to train RL agents: [https://rlvlmf2024.github.io/,](https://rlvlmf2024.github.io/) https://mihdalal.github.io/planseqlearn/, https://clvrai.github.io/boss/, https://clvrai.github.io/sprint/, https://instructionaugmentation.github.io/, https://gimme1dollar.github.io/lift/, Clarity: - The term “Code-as-Policy” is introduced without definition or citations in the introduction. Is this a common term? Is this referring to the [Code as Policies](https://code-as-policies.github.io/) paper? This will confuse readers who haven’t seen this term before. - The related works section doesn’t do a great job differentiating this work against prior work. For example section 2.2 doesn’t mention the current work in relation to prior work at all, same with the first paragraph of 2.3. - The method section isn’t really clear, it’s missing details, references to appendix sections, or references to figures clarifying things. Examples: - L133: If the focus is not on the reward function then how is the reward obtained? - L136: “A dedicated token is allocated for [integrating high-level actions]…” how is this trained or used? - L181: What are the inputs and outputs of $C$? image observatoins or other details from the environment state? - Overall, there’s not enough examples or details here to understand the method and how things are learned/trained without having to thoroughly dig through the appendix. For space reasons obviously not all details can be here, but I think this methods section can be rewritten to be much better. - Experiments: - L230 “It costs 3k steps for harvesting a log” what does this mean? This is the minimum number of timesteps required? or is this the empirical number the RL agent that the authors trained requires? - L232: please link to a specific section in the appendix. Experiments: - There are no standard deviations on any numbers, or information about # seeds in the main paper. How many seeds did you run? - Task-directed Voyager seems like a very direct comparison that uses LLMs for everything instead of RL. Why is this not compared? Technical Quality: 2 Clarity: 2 Questions for Authors: See weaknesses Confidence: 3 Soundness: 2 Presentation: 2 Contribution: 3 Limitations: Yes, but i think it's typical to include this in the main paper instead of the appendix. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Dear Reviewer ep8Y, Despite the negative score, we really appreciate your detailed review. We address your questions below. Q1. Related works. A1. Thanks for mentioning these papers. We will add some of them to the related work part in the revision. - RL-VLM-F introduces visual feedback to the reward function design. - Plan-Seq-Learn combines motion planning and RL skills to solve long-horizon tasks, using LLM as the high-level planner. - BOSS chains short-term skills to construct long-term skills with LLM supervision. - SPRINT uses LLMs to relabel instructions. - DIAL uses foundation models for dataset augmentation. - LiFT uses foundation models for task instruction proposal and reward design. The motivation, technical novelty, and experimental results of our work distinctively set it apart from these works: - Our motivation is to equip LLMs with RL capabilities to explore environments and autonomously decide which actions to learn using RL. - Our technical novelty involves inserting high-level actions coded by LLMs into the RL action space. - Our main results demonstrate that our agent can successfully determine which actions to learn and complete long-horizon targets in Minecraft. We will modify Sections 2.2 and 2.3 following your suggestions. Q2. Code-as-Policy. A2. Sorry for the confusion. Yes, the definition of "Code-as-Policy" in this paper refers to LLMs writing code that is then executed in the environment to control the agent. We will reference this paper to clarify this concept. Q3. Writing issues. A3. Thanks for these valuable suggestions! - L133: It means our agent will not focus on reward design. Instead, default reward functions, such as sparse rewards and distance rewards, are used for agent training in the environment. - L136: It means that one of the output dimensions of the RL network will represent the coded high-level action. This high-level action will be executed when the network selects that option. - L181: You can find the outputs in lines 185 to 187. The inputs are simply observations from the environment, as shown in Tab. 10. We will clarify our method based on your suggestions in future versions. Q4. Experiment issues. A4. Thanks for these valuable suggestions! - L230: For these tasks, the maximum exploration steps are capped at 3K. We will compare the success rate for these tasks. More details can be found in Tab. 16. - L232: It is linked to Section C. - Seeds: For quantitative ablation studies on harvest tasks, we used 3 seeds. Due to the large number of tasks, the rest were tested on 1 seed. This approach aligns with practices in the field. Given the low simulation speed of the Minecraft game, other significant works, such as VPT [1], also report outcomes based on a single RL training seed. [1] Video PreTraining (VPT): Learning to Act by Watching Unlabeled Online Videos, 2022 Works like Voyager focus solely on high-level planning, using human-coded skill libraries to bypass the need for low-level control. Our method integrates both high-level planning and learning low-level skills, directly addressing the challenge of playing the Minecraft game using keyboard and mouse actions. RL is necessary to acquire low-level policies autonomously. - We are the first agent that utilizes an RL training pipeline as a tool and decides which actions to be learned by RL. - We are the first to incorporate GPT-coded actions into the RL action space, enhancing the sample efficiency for RL. - The critic agent is similar to Voyager, but Voyager doesn't have a two-level hierarchical framework since it only contains high-level planning. Here is a system-level comparison table: \| Method \| long-horizon task \| low-level control \| sample-efficiency \| self-improvement \| \| ---- \| ---- \| ---- \| ---- \| ---- \| \| MineAgent \| ✗ \| ✔ \| ✗ \| ✗ \| \| VPT \| ✔ \| ✔ \| ✗ \| ✗ \| \| DEPS \| ✔ \| ✗ \| ✔ \| ✗ \| \| Voyager \| ✔ \| ✗ \| ✔ \| ✔ \| \| RL-GPT \| ✔ \| ✔ \| ✔ \| ✔ \| --- Rebuttal Comment 1.1: Comment: Thanks for the response!. Overall, due to NeurIPS' rebuttal format, I cannot determine how the writing issues will be addressed (unless authors provide direct quotes for each part). However, I have re-read the paper again, with the proposed changes in mind, and I also saw some areas where I simply missed the author's text in answering some of my questions. Regarding experiments, I fundamentally disagree that experiments in simulation should only be run with 1 seed. VPT does use just one seed, but just because one paper uses one seed doesn't mean that should be the standard everywhere. I'm raising my score but keeping it at a borderline simply due to this standard deviation issue as I believe the paper itself has merit. --- Reply to Comment 1.1.1: Comment: Thank you for your thoughtful feedback and for raising your score! We appreciate your insights and will carefully revise the writing issues you highlighted. We also take your point about using multiple seeds seriously and will incorporate experiments with multiple seeds in the revision.	Summary: This paper introduces RL-GPT, a hierarchical framework that uses LLMs to first break down complex embodied tasks into sub-actions that are suitable for coding or learnable through RL, and then write codes or RL configurations to execute the actions. The authors evaluate the framework on MineDojo benchmark and the challenging ObtainDiamond task, showcasing better performance and efficiency compared to existing baselines. Strengths: 1. The integration of RL training pipeline is novel and generally applicable to other domains. 2. Strong empirical results on Minecraft tasks. Detailed ablation studies on key design choices. 3. The paper is clearly written and well presented. Weaknesses: The proposed framework is only evaluated on the MineCraft games, which the GPTs have extensive knowledge about due to the massive relevant contents on the internet. It's unclear if the framework could be easily extended to novel domains like simple MuJoCo simulated environments, new games, or more real-world tasks, e.g. navigation or household tasks with real robots. Technical Quality: 3 Clarity: 4 Questions for Authors: 1. Have you tried using any smaller / open-source LLMs instead of GPT-4? How does the performance change? 2. When the fast agent fails to code up a sub-action, how does the slow agent decide if it should further break down the action into steps, or use an RL training pipeline? 3. Does the framework keep an archive of solutions (high level plans + codes / RL agents)? Confidence: 4 Soundness: 3 Presentation: 4 Contribution: 3 Limitations: Yes. Flag For Ethics Review: ['No ethics review needed.'] Rating: 8 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Dear Reviewer efny, Thank you for appreciating our work with valuable suggestions. We address your questions below. Q1. Generalization to other environments. A1. We acknowledged this concern and addressed it to some extent in Appendix Section D. It is difficult to find real-world environments like Minecraft, which require both high-level planning and low-level control. We applied our methods to some robotic tasks that demand both long-horizon planning and precise motor execution. Some results are shown in Fig. 7 and Fig. 8 in the attached pdf. - Kitchen Environment Training: Fig.7 illustrates the RL training process in the Kitchen environment[1]. The vertical axis represents the success rate, and the horizontal axis represents the number of training steps. Inserting coded motion planning into the action space accelerates learning. Our method learns faster compared to the baseline. - Furniture Environment Demonstration: In Fig.8, we present a qualitative demonstration of the Furniture environment[2]. The motion planning action effectively aids in hole-finding tasks during table and chair assembly. The baseline struggles to find the correct location at the same training step. [1] Relay Policy Learning: Solving Long-Horizon Tasks via Imitation and Reinforcement Learning, 2019 [2] Furniture Assembly Environment for Long-Horizon Complex Manipulation Tasks, 2021 Additionally, VLMs can be integrated into our critic agent, enabling future expansion to vision-based environments like driving, as shown in Fig. 9 of the attached pdf. Simple MuJoCo simulated environments may not be ideal for our method due to their focus on low-level controls and lack of high-level planning or decision-making. However, our method performs well in some cases, as illustrated in Fig. 10. For instance, GPT-4 can code an action to reverse the car and then move it forward based on the topography. Modifications are needed for different domains, such as adjusting the task descriptions in the prompts. The powerful zero-shot capability of GPT should ensure generalization ability. Q2. Smaller / open-source LLMs. A2. Thanks for this good question! Here is the comparison on the ''harvest a log'' task. The performance of Claude is similar to GPT-4. Vicuna-13b has lower performance due to its poor coding ability. Mixtral-8x7B works much better than Vicuna-13b. Open-sourced methods are continuously improving, making them promising for future agent development. \| LLMs \| Success Rate \| Dead loop \| \| ---- \| ---- \| ---- \| \| Vicuna-13b \| 0.36 \| 0.8 \| \| Mixtral-8x7B \| 0.55 \| 0.5 \| \| Claude \| 0.64 \| 0.3 \| \| GPT-4 \| 0.65 \| 0.3 \| Q3. When the fast agent fails to code up a sub-action. A3. Thanks for this good question! When the fast agent is unable to code an action, it implies that at least part of the action requires RL training. The slow agent will decompose this action, which is a process of gradually analyzing which specific sub-action needs RL. For the steps that can be coded, the code is written. If decomposition fails to resolve the issue after a certain number of iterations, the task will be handed over to RL. Q4. Keeping an archive of solutions. A4. Yes, both successful coded actions and well-trained RL networks will be preserved during agent optimization. They will be executed as skills with specific names, similar to Voyager's vector database. --- Rebuttal Comment 1.1: Comment: Thanks for the response. I have increased my score given the additional results. --- Reply to Comment 1.1.1: Comment: Thank you for recognizing our work and raising the score. We sincerely appreciate your valuable suggestions and will ensure they are incorporated in the revision.	Summary: This work is a variation of the code as policies, which utilizes LLMs to write code robotic policies in code snippets. This work examines minecraft, proposing that certain tasks can be composed into two sets: those solvable using LLM generated code and those best left to be solved using a standard RL agent. They utilize 2 LLM prompting styles. The first is for an LLM agent which decomposes tasks and determines which ones can be learned as code or using RL. The 2nd actually implements the code and inserts it into the action space for use by the RL agent. A critic LLM determines if the action was successful and how to improve it. This is used for iterative improvement of the code generating LLM. Strengths: This deals with one of the most important problems in utilizing LLMs and code as policies, the fact that some actions are just not well suited for code and should be learned using standard RL. Ablations including removing the critic are shown. The improvements in Minecraft appear to be substantial. Overall, the paper presents a good improvement in an area of interest to many RL researchers. I generally support acceptance of this work if the limitations/broader impact are discussed. Weaknesses: Alot of manual design is needed for each specific environment. A large amount of calls to an LLM API are used and this method becomes very expensive quickly. I would like to see how VLMs could be leveraged in other environments. The work does not explore envs outside of Minecraft. I would like to see how applications of this work could extend to other common RL envs. Technical Quality: 3 Clarity: 3 Questions for Authors: Can the authors discuss the broader impact of this method in envs outside of Minecraft and how it can apply to other types of environments in robotics? Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: Limitations are clearly the expense of this work, could the authors discuss a bit more about this? Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Dear Reviewer m13r, Thank you for appreciating our work with valuable suggestions. We address your questions below. Q1. Manual design is needed for each specific environment. A1. Yes, we acknowledge that some manual design is necessary. However, compared to existing agents like Voyager, which require humans to write low-level action code, our RL training reduces manual design by 90%. As LLMs' zero-shot capabilities continue to advance, the need for manual design will further decrease. Q2. Expensive API call. A2. Thanks for this good question! We agree that calling API has a cost. Here are the statistics. We count the average tokens on different tasks for the first 3 iterations. \| \| iter-1 \| iter-2 \| iter-3 \| \| ---- \| ---- \| ---- \| ---- \| \| tokens \| 10K \| 15K \| 16K \| GPT-4-32k will cost $0.12 per 1,000 tokens. The newly released GPT-4o Mini will be more cost-effective. Here is the comparison on the ''harvest a log'' task. Vicuna-13b has lower performance due to its poor coding ability. Mixtral-8x7B works much better than Vicuna-13b. Open-sourced methods are continuously improving, making them promising for future agent development. \| LLMs \| Success Rate \| Dead loop \| \| ---- \| ---- \| ---- \| \| Vicuna-13b \| 0.36 \| 0.8 \| \| Mixtral-8x7B \| 0.55 \| 0.5 \| \| Claude \| 0.64 \| 0.3 \| \| GPT-4 \| 0.65 \| 0.3 \| Q3. How VLMs could be leveraged in other environments? A3. Thanks for this good question! VLMs can function as more effective critic agents in our framework. While LLMs can only indicate whether the agent succeeded with its coded actions, VLMs can explain why it failed in the environment. As shown in Fig. 9 of the attached pdf, GPT-4V provides more detailed feedback across different environments. For example, in Minecraft, it can identify that the agent keeps attacking the ground instead of finding the cow. In the driving simulation environment, it can note that the vehicle is gradually drifting off the road. This feedback can be used by both our fast and slow agents for self-improvement. Q4. Generalization to other environments. A4. We acknowledged this concern and addressed it to some extent in Appendix Section D. It is difficult to find real-world environments like Minecraft, which require both high-level planning and low-level control. We applied our methods to some robotic tasks that demand both long-horizon planning and precise motor execution. Some results are shown in Fig. 7 and Fig. 8 in the attached pdf. - Kitchen Environment Training: Fig.7 illustrates the RL training process in the Kitchen environment[1]. The vertical axis represents the success rate, and the horizontal axis represents the number of training steps. Inserting coded motion planning into the action space accelerates learning. Our method learns faster compared to the baseline. - Furniture Environment Demonstration: In Fig.8, we present a qualitative demonstration of the Furniture environment[2]. The motion planning action effectively aids in hole-finding tasks during table and chair assembly. The baseline struggles to find the correct location at the same training step. [1] Relay Policy Learning: Solving Long-Horizon Tasks via Imitation and Reinforcement Learning, 2019 [2] Furniture Assembly Environment for Long-Horizon Complex Manipulation Tasks, 2021 Modifications are needed for different domains, such as adjusting the task descriptions in the prompts. The powerful zero-shot capability of GPT should ensure generalization ability.	Summary: The paper introduces RL-GPT, a novel framework that integrates Large Language Models (LLMs) with Reinforcement Learning (RL) to enhance the performance of LLM-based agents in complex, embodied environments. The primary goal is to address the limitations of LLMs in executing intricate logic and precise control, especially in open-world tasks like those found in the Minecraft game. The RL-GPT framework employs a two-level hierarchical approach, consisting of a slow agent and a fast agent. The slow agent is responsible for decomposing tasks and determining which actions can be coded directly, while the fast agent generates the corresponding code and integrates RL configurations. This division of labor allows for efficient handling of both high-level planning and low-level execution. Key contributions of the paper include: 1. Two-level hierarchical framework to determine which actions should be learned by RL and which ones can be coded (e.g. in a python). 2. The introduction of a mechanism where high-level actions coded by LLMs are appended to the RL agent’s action space, instead of only relying on low level actions. 3. Empirical validation showing that RL-GPT outperforms traditional RL methods and existing LLM agents in the Minecraft environment, particularly excelling in the ObtainDiamond task and other MineDojo tasks. In experiments, RL-GPT demonstrated superior performance, achieving state-of-the-art (SOTA) results in several tasks, including rapidly obtaining diamonds and excelling in long-horizon tasks with limited computational resources. Strengths: Originality: - The paper proposes a novel integration of RL and LLMs, leveraging the strengths of both to improve task efficiency in open-world environments. - The fast agent's method of combining code-as-policy with RL by inserting high-level coded actions into the RL action space is a creative and original solution that sets RL-GPT apart from other frameworks. Quality: - Claims are well supported by extensive experimental results, comparing with previous SOTA methods in MineDojo Clarity: - The paper is generally well-written and structured, with detailed explanations of the framework components and their interactions. - Figures and tables effectively illustrate the performance improvements and workflow of RL-GPT. Significance: - There is often a question about the what is the right abstraction level for LLM agents to operate on: high level APIs/code-as-policies, or low level mouse/keyboard, etc. RL-GPT addresses this by trying to leverage the both, with the higher level actions appended to the RL agent’s action space. - The state-of-the-art performance in MineDojo tasks highlights its potential impact on the field, though the focus on Minecraft limits the generalizability of the results. Weaknesses: 1. The work focus on Minecraft, while useful as a testbed, may not fully represent the range of challenges present in other open-world environments. Expanding the scope of testing to other domains would enhance the significance of the work 2. While the integration approach is novel, the individual components (LLMs, RL, task decomposition) are well-known techniques. The paper could benefit from a more explicit discussion of how these components are synergistically combined to create a unique solution. 3. Some sections, particularly those describing the two-loop iteration process and the role of the critic agent, could benefit from more detailed explanations or examples to improve understanding. I am aware that the full prompts are included in the appendix and they do not fit in the main paper, however. Technical Quality: 3 Clarity: 3 Questions for Authors: 1. The slow agent can all a sub-action that the RL agent executes. But can the fast agent which uses “code as policies” also call the RL agent inside its loop? 2. What is the architecture and inputs of the PPO RL agent? In particular, it was said that “PPO is limited to a set of skills”: how is the sub-action (e.g. “Harvest log” sub-action 2 in Figure 3) from the slow agent represented to the policy network? Is it just a one-hot vector (“PPO is constrained to a limited set of skills”), or are you encoding the sub-action text instruction as an embedding vector, etc., or are you learning a different set of policy weights for each sub-action, or something else? 3. How would the proposed framework adapt to other open-ended environments beyond Minecraft? Are there specific modifications required for different domains? 4. (RL Interface Ablation) Do you have any hypotheses on why the action space reconstruction is more effective than designing the reward function? Is the action space shortening the horizon of the task and makes the reward less sparse? 5. Table 4: is this showing the %? In Section 4.4, it was reported as 0.34% and 0.65% success rate. Was this a typo and it’s supposed to be 34% and 65% success percentage for crafting a table? Post rebuttal: I have increased the score after the rebuttal. Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 4 Limitations: The authors acknowledge some limitations of their work, notably the reliance on the capabilities of LLMs and the potential challenges in generalizing to unseen data. However, there are additional limitations and assumptions that could be more explicitly addressed: 1. The approach assumes an environment with a structured observation space that can support coding as policies. This might not be feasible in more complex or less structured environments. Environments need to be compatible with the two-level hierarchical framework and provide sufficient information for task decomposition and action coding. It’ll be helpful to provide guidelines for adapting the framework to different types of environments, including those with less structured observation spaces. 2. The framework's reliance on multiple interacting agents and iterative refinement could complicate implementation and debugging. The need for specific prompts and hand written examples add to the complexity, making it challenging for broader adoption. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Dear Reviewer LWBp, Thank you for appreciating our work with valuable suggestions. We address your questions below. Q1. Generalization to other environments. A1. Thanks for this suggestion! We acknowledged this concern and addressed it to some extent in Appendix Section D. It is difficult to find real-world environments like Minecraft, which require both high-level planning and low-level control. We applied our methods to some robotic tasks that demand both long-horizon planning and precise motor execution. Some results are shown in Fig. 7 and Fig. 8 in the attached pdf. - Kitchen Environment Training: Fig.7 illustrates the RL training process in the Kitchen environment[1]. The vertical axis represents the success rate, and the horizontal axis represents the number of training steps. Inserting coded motion planning into the action space accelerates learning. Our method learns faster compared to the baseline. - Furniture Environment Demonstration: In Fig.8, we present a qualitative demonstration of the Furniture environment[2]. The motion planning action effectively aids in hole-finding tasks during table and chair assembly. The baseline struggles to find the correct location at the same training step. [1] Relay Policy Learning: Solving Long-Horizon Tasks via Imitation and Reinforcement Learning, 2019 [2] Furniture Assembly Environment for Long-Horizon Complex Manipulation Tasks, 2021 Yes, modifications are needed for different domains, such as adjusting the task descriptions in the prompts. The powerful zero-shot capability of GPT should ensure generalization ability. Q2. How are these components synergistically combined? A2. Thanks for this suggestion! The key technical novelty is illustrated in Fig.2 of the paper. Incorporating high-level actions generated by LLMs into the RL action space captures the core ideas presented. This core design allows the agent to choose between RL and code-as-policy. Q3. More detailed explanations or examples. A3. Thanks for this suggestion! - Slow Agent: This agent will decide which parts can be coded and which parts should be learned. The first iteration loop is designed to correct decision-making errors. - Fast Agent: This agent will code the coding tasks from the slow agent. The second iteration loop is designed to correct coding errors. - Critic Agent: The critic agent provides feedback from the environment for each code execution. The output from the critic agent after one step serves as feedback for the fast agent, while outputs from a sequence of steps serve as feedback for the slow agent. Q4. Can the fast agent also call the RL agent inside its loop? A4. Sorry for the confusion. The fast agent cannot perform RL training. Its role is to generate code based on the requirements provided by the slow agent. Q5. The architecture and inputs of the PPO RL agent. A5. Sorry for the confusion. Yes, we will learn the weights for each RL sub-action (marked orange in Fig. 3). 1. The "Harvest log" is sent from the slow agent to the fast agent in text format. 2. The fast agent generates high-level codes for the action. 3. Coded actions are inserted into the RL action space. 4. RL training is performed after this insertion. Q6. Action space vs reward function. A6. Thanks for this good question! We have conducted ablation studies, as shown in Tab. 5. Using an action space with higher-level actions can shorten the task horizon and reduce reward sparsity. This design is more efficient as it leverages the coding ability and common sense of LLMs. For instance, LLMs understand that it takes 10 attacks to break a tree. When designing a reward function, even though "10 attacks" yields a high reward, randomly sampling those 10 individual attacks is a time-consuming process. In contrast, with action space design, an action like "attack 10 times" can be directly generated, resulting in an immediate high reward. Q7. Typos. A7. Thank you for pointing that out. The correct values are 34% and 65%. We will correct this in the revision. --- Rebuttal Comment 1.1: Comment: Thank you for the detailed response addressing my questions and concerns regarding generalization to other environments, how the components are combined and more detailed explanations. I have increased my score to 7. --- Reply to Comment 1.1.1: Comment: Thank you for your insightful comments and questions, which have greatly improved the quality of our paper. We deeply appreciate your recognition and the score increase! We will carefully integrate the results discussed with you into the revision.	Rebuttal 1: Rebuttal: Dear all reviewers, We sincerely thank your effort in the review with valuable comments and suggestions. We appreciate reviewers _LWBp_, _m13r_, and _efny_ for recognizing our work. Additional figures are attached in the _6379_rebuttal_figs.pdf_, which we will reference in the following specific responses. Pdf: /pdf/a3aef9af7e7a2bb6d174622f46a60aefe4e6e069.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Robot Policy Learning with Temporal Optimal Transport Reward	Accept (poster)	Summary: This paper extends the vanilla optimal transport-based proxy reward method in imitation learning by 1) masking out distant steps within a trajectory in the optimization of the transport plan and 2) considering neighbouring steps in the reward estimate Strengths: - the paper is well written and organized, with rich benchmarking experiments and comparisons - strong experimental results in comparison to baselines Weaknesses: - the novelty is incremental, focusing on two additions to vanilla OT - the presentation of the central claim seems to contradict the rationale behind the two additions to OT (see the question below). - some result analyses contain plain observations, lacking in-depth insights - missing discussion on why learning from demonstration performs worse in door-lock and window-open tasks (sec. 4.3), important for understanding the efficacy scope of the proposed extension; in contrast, RL with simply binary reward performs well in the twos - no insights on why important components vary across tasks (sec. 4.4), beneficial for understanding the sensitivity of the proposed extension - ablation of $k_c$ and $k_m$ in sec. 4.4 is good, but a high-level guide for choosing them under different task conditions would benefit others following this work and be important for understanding the generalisation capability of the two additions - as to sec. 4.6, the description of the pixel-based setting is a bit over-simplified, the author can instead put detailed explanations in the appendix - sec. 4.7 feels like a case-by-case study; it does not relate to the method's efficacy and the paper's central claim - minor comment: - a brief description of the nine meta-world tasks (and task length) would provide an overview of task complexity - a detailed example of computing group-wise cosine similarity is missing. Including this would help clarify the value of introducing $k_c$ in the cost estimate, especially concerning the example on the right side of Figure 4 Technical Quality: 2 Clarity: 2 Questions for Authors: ### Presentation of the central claim - in section 3.1.2, how does the permutation study with ADS connect to the first observation; is being oder-invariant within a trajectory problematic? Which proposed component (masking scheme or context embeddings) addresses this? Further, how does the 1st observation relate to the claim that existing methods overlook temporal information (e.g., lines 44-45)? - what exactly is meant by overlooking temporal information? eq. 5 already counts all future steps in calculating the original OT proxy reward for current state. Why incorporate temporal information? - the paper claims to incorporate this information (lines 144-145), but doesn't the masking scheme weaken the influence of future/distant steps (lines 149-152), while context embedding enlarges it (lines 168-169)? This divergence causes confusion about the central claim of mitigating the issue of overlooking temporal information (e.g., lines 8-12, 45-47) - Introducing context embeddings (section 3.2.2) seems to contradict the second observation in section 3.1.2 (lines 116-117) as considering later steps could add noise to the reward estimate of the current state-action pair. ### Methodology - is the context cost matrix in eq. 9 used in the optimisation of transport plan $\mu$ in eq 4, or just for reward inference in eq. 5? ### Experimental results - in Figure 6, the average of TemporalOT appears less than 7.5 but is reported to be 8.4 in Table 1. - in Figure 2, which step does $o_2$ correspond to? better to add x-y labels and mark $o_2$, $o_3$ to the reward curve on the right - misspecified value for TaskReward in Door-lock env, according to Figure 9, the mean value is around 60. Similarly, the Window-open env mean value should be around 30 - which $\epsilon$ values were used in the experiments (or are they determined after optimizing equation 7), and how do they affect the task performance? - the 4th baseline OT needs more explanation, though I can roughly guess how online OT differ from offline OT ### Discrepancy in ASD vs. OT performance - unsure about why ASD performs worse than vanilla OT in some tasks as shown in Table 1? I understand this paper adopts a more challenging experimental setup, with varying goals per episode and only two demonstration videos provided. However, in the benchmarking results of the ASD paper, ASD achieves over 80% success in the basketball task within 1M steps, significantly higher than OT's performance (around 10%), as shown in Figure 11 of Appendix C.2. This trend is also observed in the lever-pull task. Yet, Table 1 in this paper shows the opposite comparison between ASD and vanilla OT for these tasks. Could you explain this discrepancy? ### Minor points - Figure 1, five steps should be -> six steps? the scheme is not indicative of the magnitude of reward $r_a$ or $r_b$; what does $a_2^a$ differ from $a_2^b$? - It would be better to indicate in the caption of Table 1 that the values represent success rates, even though this is mentioned in section 4.1, as tables should be self-contained Confidence: 4 Soundness: 2 Presentation: 2 Contribution: 2 Limitations: - authors acknowledge the limitations of the work, and their comments are fair - it's unclear how different pretrained visual encoders will influence OT's efficacy under the same conditions; a discussion on this topic would be helpful - nonetheless, the authors discuss the broader impact of their work, including immediate societal implications, and suggest a straightforward solution, which is appreciated Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for the detailed and constructive comments. ## Questions > Q1: Presentation of the central claim Due to the importance of this point and limited space, we have clarified the motivation/central claim in the common reply (top) on Clarifications on motivation. In short, the permutation study provides empirical evidence that the conventional OT-reward (Eq 5) is order-invariant (1st obs), since the frame order in the expert trajectory is fully discarded. > Q2: What exactly is meant by overlooking temporal information? How does 1st obs relate to it We meant overlooking the temporal order information (apologize and will revise). Since Eq 5 is order-invariant, methods using it will overlook order info. We further detailed on this in C1. > Q3: Doesn't the masking scheme weaken ... while context embedding enlarges.... Both scheme are for incorporating the temporal order information (C2). This seems to be caused by the term "temporal information". We replaced it with "temporal order information" in the revised paper. > Q4: Introducing context embeddings seems to contradict the second observation The context length $k_c$ (i.e., 2-3) is much smaller than the trajectory length (i.e.,100-200). In observation 2, we discuss the distraction from distant states (i.e.,100-200 steps). The context embedding with a small context length $k_c$ will have a small influence on the distraction issue as discussed in observation 2. > Q5: Is the context cost matrix in Eq9 used in the optimization of transport plan 𝜇 in Eq4, or just for reward inference in Eq5? The context cost matrix in Eq9 is used in both transport plan optimization and reward inference. > Q6: In Figure 6, the average of TemporalOT appears less than 7.5 but is reported to be 8.4 in Table 1 This is because we plot a smoothed evaluation curve. Table 1 reports the result at the last step: (7+7+11+10+7)/5 = 8.4. Figure 6 plots a smoothed curve: (5+4.33+8+9.33+7)/5 = 6.73. Logs are available in PDF-Table 1 in the uploaded PDF. > Q7: $o_2$ in Figure 2 $o_2$ is the 40th step. > Q8: Misspecified value for TaskReward Sorry that we made a mistake when plotting Fig 9. We extracted the same number of data samples for TaskReward from the evaluation log as other baselines, and thought it corresponds to1e6 steps. But actually it is 5e5 steps since it uses doubled evaluation frequency. PDF-Fig 7 is the corrected figure matching Table 1 > Q9: Effect of 𝜖 We follow the parameter setting from ADS where 𝜖=0.01. PDF-Fig 6 from the PDF file shows the ablation for different 𝜖. The entropy coefficient 𝜖 controls the sparseness of the transport plan 𝜇. A large value will generate a 𝜇 closer to uniform distribution. > Q10: Discrepancy: Table 1 shows the opposite comparison between ASD and vanilla OT for basketball and lever-pull Sorry about the confusion. OT in the ADS paper corresponds to OT0.99 in Table 1 of our paper. By comparing OT0.99 with ADS, we can see that the results are not opposite, with ADS outperforming OT0.99 on basketball and lever-pull tasks. The overall performance drop is indeed due to the more challenging experimental setup as you mentioned. > Q11: Figure 1, five steps ... what does $a^a_2$ differ from $a^b_2$ Sorry that steps is a confusing term and we changed it to steps of transitions. $r_b$ is larger than $r_a$ since $a^b_2$ leads to a success grasp ($a^a_2$ fails resp.) and matches demo better. Thanks for all the good suggestions and will include the improved figure in revision. > Q13: Different pretrained visual encoders Thanks for the suggestion and we will add more discussions in revision. In this work, we follow the standard setting [ADS] and use a pre-trained ResNet50 to extract the visual embedding. Other visual encoders could also be used. We also run some experiments quickly to compare different visual encoders in PDF-Fig 2 in the uploaded PDF file. In PDF-Fig 2, we compare three different ResNet variants (ResNet18, ResNet50, ResNet152). PDF-Fig 2 indicates that a reasonably good visual encoder is usually enough to extract effective visual embeddings for computing OT rewards in RL. ## Weaknesses > W1: Novelty To the best of our knowledge, we are the first to discuss how to leverage temporal order information in computing OT rewards for training an RL agent. As an initial attempt on this topic, we aim to address this problem from a minimalist perspective. Though being simple, the method is effective and could be a good starting point to inspire others to reproduce and build upon. > W2: Bad performance in door-lock and window-open Because these two tasks have strict success conditions, i.e., the door-lock task is defined as solved only when the knob rotates to 60°. IL proxy reward is not accurate enough for such details, i.e., 55° w.r.t. 60°. > W3: Important components vary across tasks When long distance distraction is the main bottleneck, temporal mask is the key. When inaccurate transport cost is the main bottleneck, context embedding is the key. > W4: How to choose of $k_c$ and $k_m$ A small value of $k_c$=3,4 is effective enough for a context information-augmented OT cost, while a larger value will oversmooth the cost information. $k_m$ relates to the length of the expert trajectory L. Setting $k_m$ to around 0.1L is a good rule of thumb. > W5: Example of computing group-wise cosine similarity In Figure 4, we use $k_c=3$. The transport cost between $o_1$ and $o^E_2$ is: $\hat c(o_1, o^E_2) = 1 - \left[\mathrm{cos}(f(o_1),f(o^E_2))+\mathrm{cos}(f(o_2),f(o^E_3))+\mathrm{cos}(f(o_3),f(o^E_4))\right]/3$. ## Other > Caption of Tab 1; details about sec 4.6 in appendix; comments on sec 4.7; description of meta-world; more explanation on the 4th baseline ... Thanks for all the other comments (cannot list all due to space; all received, thanks!) and we have revised paper accordingly. --- Rebuttal Comment 1.1: Comment: Many thanks to the authors for thoroughly addressing my concerns and adding the extra experimental plots, much appreciated. I found the clarifications on C2 helpful and suggest (if possible) incorporating them into sec. 3 when introducing new techniques. It would also be great if you could include the insights from W3 and W4 in the discussion section. I have just a few other points: - Is the context cost matrix in eq. 9 used in optimizing the transport plan $\mu$ in the new objective (eq. 5)? It seems NO as shown in Fig. 4. If yes, shouldn’t the formulation of eq. 6 and 7 reflect the context cost matrix $\hat{C}$? - Regarding W2, you mention that the "IL proxy reward is not accurate enough for such details." How is this generally true for imitation learning (IL)? --- Rebuttal 2: Comment: > S1: I found the clarifications on C2 helpful ... It would also be great if you could include the insights from W3 and W4 in the discussion section... It is great to know that we have successfully resolved the confusions and addressed most of the questions you had, and only a few other points need discussions (as done below). We greatly appreciate many of the great points you raised that help to improve the quality of the paper (e.g. the clarifications on C2 and insights from W3 and W4). We will definitely include them in the revised paper (e.g. into Sec. 3 and discussion section respectively). > S2: Cost Matrix in Figure 4 The context cost matrix is used in optimizing the transport plan 𝜇. We apologize for the confusion. After carefully understanding the point you raised, we realized that it is caused by our order of introducing the two components of TemporalOT. Our original intention was to organize Section 3.2.1 and Section 3.2.2 to introduce the two components of TemporalOT in a progressive way starting from vanilla OT: firstly introducing temporal mask M in Section 3.2.1, and then the component for improving the cost matrix calculation in Section 3.2.2. Figure 4 in the main paper is also organized under the same reasoning. Thanks to your reminder, now we realized that this might introduce some confusions if we want to understand the whole method from the first section only (e.g. Eqn.(6) and Eqn.(7)) if there is no explicit reminder around Eqn.(6) and Eqn.(7) (or Figure 4 Left) saying the $C$ in Eqn.(6) and Eqn.(7) (respectively Figure 4 Left) will be upgraded with a context embedded version $\hat C$ later. We are planning to introduce the Context Embedding based Cost Matrix (Eqn.(9)) in the original paper before Eqn.(6). Figure 4 will also be updated accordingly: 1) introduce Context Embedding on the left and then 2) temporal mask based OT on the right with the Cost Matrix notation $C$ changed to $\hat C$. We believe this can resolve the confusion as pointed by you. Thanks again and we will also include this change into the revision together with the ones as mentioned in reply to Suggestion 1 (S1). We would thanks the reviewer sincerely again for all the great advice that helps to further improving the presentation quality of the paper. > S3-1. IL proxy reward is not accurate enough for such details Thank you for the question. We are sorry for the inaccurate and confusing "IL" term. By "IL proxy reward", we actually meant "visual similarity-based reward", i.e. reward calculated based on the visual similarity between the policy trajectory and reference trajectories. The term "IL" term is really unnecessary here, sorry for the confusion. It is easy to understand that due to factors such as viewpoint, occlusion, object sizes etc, sometimes it can be challenging to differentiate subtle differences in images, e.g., the knob being turned to 55° (task failure) vs a knob being turned to 60° (task success). While there is a clear difference if a low-dimensional knob angle sensor is provided (which is the case in low-dimensional state based reward), the visual signal based reward does not have the luxury of accessing the knob angles directly, leading to the challenges as mentioned above. > S3-2: How is this generally true for imitation learning (IL) Sorry for the usage of the confusing "IL" terms as explained above. It was an inaccurate term we used to describe the visual similarity based reward and we didn't intent to pass any implication on the Imitation Learning in our original response. After clarifying all the confusions, we can provide some of our understanding on visual observation based imitation learning. Based on our understanding, some of the challenges we observed in visual-similarity based reward calculation could also appear in imitation learning in several cases: - Imitation-learning with visual reward: this is the category that aligns with the line of works in ADS etc and this paper, which actually formulate IL into an RL form with the help of the visual similarity reward. This is easy to understand since the visual-reward calculation is directly impacted as explained above. - Visual BC-type of imitation learning: behavior cloning (BC)-type of IL methods does not require the proxy reward so the reward part is not an issue. However, if visual observation is used as the policy input, differentiating subtle differences based on visual observations is similarly challenging and will likely to impact policy learning in our opinion. Moving forward, general techniques that can improve on these aspects can potentially improve both the visual-similarity based proxy reward (the line of works in ADS etc and in this paper) and visual similarity-based imitation learning. This is a very interesting direction for future work, with potential impacts on multiple fields. Title: To Reviewer GZSS: Explanations for Figure 4 and proxy reward --- Rebuttal 3: Title: To Reviewer GZSS: A gentle reminder Comment: Dear Reviewer GZSS, As we are approaching the end of the rebuttal period, we want to send a gentle message to you confirming that our reply to your followup question on "Figure 4 and proxy reward" has been successfully received (it seems that there was an issue with the OpenReview system, as it did not send out notification emails for some reason when we posting our replies, and we didn't receive any email notifications after we posted the replies; so we send this message just in case it also happened to you), and we also want to confirm the reply has addressed your followup questions on "Figure 4 and proxy reward". Looking forward to your confirmation and thanks again for your time and efforts in reviewing our paper and providing detailed, constructive comments. We greatly appreciate many of the great points you raised that help to improve the quality of the paper, and we enjoyed the interaction with you during the discussion period. We will definitely incorporate the valuable clarifications and insights formed in our discussion into the revised paper. --- Rebuttal Comment 3.1: Comment: Thanks to the authors for their responses, which clear up my follow-up questions and offer details on visual-similarity-based reward calculation and imitation learning. I appreciate the added clarity.	Summary: This work proposes a reinforcement learning method from a few expert demonstrations based on optimal transport. It incorporates temporal information into the framework of optimal transport reward so that the agent can focus on more relevant information in learning. The work proposes two simple tricks to achieve this, i.e., a masking mechanism and context embedding-based cost matrix. The experiments in simulated robotic control benchmarks show that the proposed temporal OT converges to a higher success rate than imitation learning and inverse reinforcement learning methods that do not consider temporal information. Strengths: The paper is clearly motivated. It points out a major weakness of OT-based reward calculation, that is the temporal information not being considered, and proposes a simple solution that applies a temporal mask to the cost matrix. Weaknesses: 1. TemporalOT uses a manually designed diagonal-like matrix as the mask on the transportation plan, which could be ineffective when the learning policy has not been close to the expert or gets stuck at early-stage behaviors. Have the authors tried other design choices for the temporal mask or tried to make it a part of the learning? 2. As a robot learning paper, it would be better to apply the algorithm to real robots similar to previous OT-based methods (e.g., [18]). Technical Quality: 3 Clarity: 3 Questions for Authors: The variance of the baseline ADS is quite large in some environments shown in Fig. 7. Is there any explanation/discussion on it? Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: As shown in the learning curves, the proposed algorithm requires ~1e6 timesteps to converge, which may limit its practical use for real robots. I think initializing the policy with imitation learning, then tuning it with TemporalOT might converge faster. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for the detailed, constructive review and insightful comments. Your valuable comments helped us to further improve the quality of the paper. Responses to the questions are below: > Q1: Try other design choices for the temporal mask or try to make it a part of the learning Thanks for the great question. We used the current design in the paper is because: - We want to use a simple and easy to understand design to illustrate the benefits of incorporating temporal information into OT rewards; - The current design is interpretable, easy to implement and computationally cheap. To mitigate the issue that the agent could get stuck at early-stage behaviors, here, we introduce a variant of TemporalOT that uses a dynamic mask for each trajectory. We begin with some notations: - The agent trajectory is $\tau = (o_1, \cdots, o_T)$ and the expert trajectory is $\tau^E = (o^E_1, \cdots, o^E_T)$. - We compute a cosine similarity based transport cost matrix $\hat C\in\mathbb R^{T \times T}$ as Eq 9. - For each step $o_i$ in the agent trajectory, we compute a mask window $M_i\in\mathbb R^{1 \times T}$ where $M_i(j)$=0 or 1 for $1\le j \le L$. In the current paper, we use a variant of the diagonal matrix with a mask window size $k_m$: $$ M_i(j) = \begin{cases}1, &\text{if } j \in [i-k_m, i+k_m] \\\\0, &\mathrm{otherwise} \end{cases} $$ In the added experiment, we learn a dynamic mask window for each step as follows: $$ M_i(j) = \begin{cases}1, &\text{if } j \in [c-k_m, c+k_m] \\\\0, &\mathrm{otherwise} \end{cases} $$ Here, we select the window center index as $c = \arg\min_j \hat C(i, j), j \in [0, i]$. This means we select an index $j$ in the expert trajectory that has the least transport cost w.r.t $o_i$. We further add a constraint $j \in [0, i]$ to avoid looking into distant future steps as pointed out in Section 3.1.2. The experiment results are shown in PDF-Fig 4 of the attached PDF. We can observe that this learning-based temporal mask slightly outperforms our previous rule-based temporal mask. We have been focusing on using a simple and effective approach to illustrate the main point of the paper, and therefore did not try to learn the temporal masks. We do agree with your intuition that learning temporal masks is a very promising direction to pursue. > Q2: As a robot learning paper, it would be better to apply the algorithm to real robots similar to previous OT-based methods Thanks for the suggestion. We apologize that simulated environments are mainly used in experiments. The reason is that we currently have no real robots at hand. At the same time, in our humble opinion, benchmarking different methods under the same setting in simulation also provide valuable empirical verifications on the effectiveness of different methods. We fully agree with you that it is important to validate the effectiveness of the proposed method in real-world scenarios. We are very willing to deploy our algorithm to real robots once physical robots are available in the future. > Q3: High variance of ADS in some environments. Thanks for the great question. Actually, the ADS baseline also shows high variance in its original paper [ADS]. The main reasons are: - ADS uses the naive OT reward definition (Eq 5) that depends on the whole trajectory. Such a global scope sometimes introduces noisy information from far away steps. Therefore, we can observe that both the ADS and OT show high variances in Figure 4, 5, 10, 11, 12 from the ADS original paper. - Moreover, the discount factor changes during the training in ADS. This makes the TD target less stable. Sometimes, such a changing discount factor will lead to a change in the Q-value function and the learned policy. In some tasks, the less stable ADS policy will also lead to high variance. > Q4: As shown in the learning curves, the proposed algorithm requires ~1e6 timesteps to converge, which may limit its practical use for real robots. I think initializing the policy with imitation learning, then tuning it with TemporalOT might converge faster. Thanks for the question. Using imitation learning to initialize the robot policy and then fine-tuning it with TemporalOT will very likely to help converge faster. One thing to note is that the demos used in our work and previous literature [e.g. ADS] are assumed to be action-free videos. Therefore, many of the standard action-based imitation learning approaches are not applicable, preventing a simple imitation-based policy pre-training. To do policy pre-training, state-based imitation learning approach should be used. However, the proposed approach is actually a type of state-based policy learning approach already. From this sense, although we can further improve sample efficiency with pre-training, it can be regarded as a factor that can be used by all baselines. Therefore, for fair comparison in this work, we place all the baseline methods on the same footing without policy-pre-training. On the other hand, to verify the point raised in your comment and go beyond the settings used in this work, we did some quick experiments with action-inclusive demonstrations. In PDF-Fig 5 of the attached PDF file, the BC Pretrain baseline refers to pre-training the policy with imitation learning. In addition, the BC Loss baseline refers to using both imitation learning loss and RL-loss for policy training throughout. We can observe that both BC Pretrain and BC Loss show performance gain in terms of sample efficiency, which confirms your intuition. References [ADS] Liu et al., Imitation Learning from Observation with Automatic Discount Scheduling, ICLR 2024 --- Rebuttal Comment 1.1: Comment: Thank you for the rebuttal. I appreciate the added results regarding other design choices of temporal masks. I have some follow-up questions: In PDF-Fig 5, why does the curve for "BC pretrain" start from a success rate of 0 instead of a positive success rate learned by BC? I am asking the BC and fine-tuning results to see how many offline demonstrations and how many online interactions are required to obtain a reasonable success rate, and to justify how practical the algorithm is for potential real-world applications. --- Rebuttal 2: Comment: It is great to know that we have successfully addressed most of your questions. We appreciate your great efforts in reviewing our paper that helped to improve our work. As to your follow-up question on "BC pretrain" results in PDF-Fig 5 at step-0, we apologize that this was caused by a setting that was inappropriate for methods with pre-training in generating the plot. BC-pretrain has a success rate around 10.8 $\pm$ 9.2 at step-0 for Door-open task (consistent with the result reported in Table 1 of the main paper). What happened was when we generated PDF-Fig 5, the first step of actual evaluation happens at 2e4 steps which was set according to all the online learning methods (such as ADS and TemporalOT, which only start to learn after collecting some online samples via environmental interactions). A default success rate of zero is used since all these methods always have a zero success rate at the step-0 (essentially before any training). The issue was that for generating PDF-Fig 5, we forgot to adapt the script for BC-pretrain method to run evaluation at step-0 and used a default success rate of zero. While this makes sense for the online learning methods (w.o. pre-training) as explained above, for BC-pretrain, it is inappropriate since it has a non-zero success rate before any online training because of the pre-training. Also in order to reflect the original values, we didn't apply smoothing in PDF-Fig 5, therefore the curve values remains at zero at step 0 (some curves in Figs elsewhere e.g. main paper with minor non-zero values at step 0 are due to smoothing, and the raw values are zero). To resolve the confusions and maintain consistency in presenting the results, we are planning to change PDF-Fig 5 in to a Table as shown below to be included in our revised paper (due to the reason that while Figures are good for comparing the general trends across the training period, Table is more suitable in this case since it directly shows the raw results at the actual evaluation steps and makes it easier to to compare the pre-train-only performance and the pre-train+online training performance). \| \| 0 \| 2e4 \| 4e4 \| 6e4 \| 8e4 \| 1e5 \| 5e5 \| 1e6 \| \| ------------------------------------------------- \| ----------- \| ---------- \| ------------ \| ------------ \| ------------ \| ------------ \| ------------ \| ------------ \| \| BC [pure-offline, param fixed after pre-training] \| 10.8 $\pm$ 9.2 \| - \| - \| - \| - \| - \| - \| - \| \| TemporalOT [pure online] \| 0.0 $\pm$ 0.0 \| 2.0 $\pm$ 4.0 \| 0.0 $\pm$ 0.0 \| 0.0 $\pm$ 0.0 \| 5.0 $\pm$ 10.0 \| 16.6 $\pm$ 32.2 \| 57.8 $\pm$ 37.1 \| 78.4 $\pm$ 12.4 \| \| TemporalOT with BC-pretrain [offline-to-online] \| 10.8 $\pm$ 9.2 \| 6.8 $\pm$ 8.4 \| 25.0 $\pm$ 18.5 \| 42.8 $\pm$ 22.2 \| 48.6 $\pm$ 25.9 \| 55.4 $\pm$ 12.0 \| 70.8 $\pm$ 8.2 \| 82.0 $\pm$ 2.4 \| We can observe that: 1. BC without any online training has relatively low success rate (10.8 $\pm$ 9.2) 2. TemporalOT achieved relatively high success rate after 1e6 environmental steps (78.4 $\pm$ 12.4) 3. Incorporating pretraining (Temporal OT with BC-pretrain) helps to further improve the sample efficiency. We want to clarify as already done in the original rebuttal reply that our default setting in the main paper is an action-free-demo setting. For this ablation study, we go beyond this setting and use action labels which are required by BC. 4. For TemporalOT with BC-pretrain, one can notice a small success rate drop (which recovers later) at the initial phase when we transit from offline to online training (step0->step2e4->step4e4). This is an "initial-dipping" phenomenon as also being reported in previous literature and can be improved by designing more specific offline-to-online methods [O2O, PEX etc]. In summary, incorporating offline pre-training into TemporalOT does show promising improvements to further boost the sample efficiency and indicate practical paths to generalizing and applying TemporalOT in real world applications (thanks for sharing your insights with us on this!). And we believe the offline-to-online training paradigm in general [O2O, PEX etc], although out-of-the scope of the current paper (which only focus on the online training setting) is a powerful one for real-world robotics applications and we plan to pursue it in our future work. References [O2O] Yu et al. Actor-Critic Alignment for Offline-to-Online Reinforcement Learning, ICML 2023 [PEX] Zhang et al. Policy Expansion for Bridging Offline-to-Online Reinforcement Learning, ICLR 2023 Title: To Reviewer M6BJ: Explanation for PDF-Fig 5 --- Rebuttal Comment 2.1: Comment: Thank you for the additional explanation. My questions are addressed and I will raise the score to 5. --- Reply to Comment 2.1.1: Title: To Reviewer M6BJ: Thank you for your positive feedback and for raising the score Comment: We thank Reviewer M6BJ for your positive feedback on the rebuttal and thank you for raising the score. We greatly appreciate your efforts in reviewing the paper and your valuable comments that have helped to further improve the quality of the paper.	Summary: This paper proposes several improvements on top of the Optimal Transport reward for inverse reinforcement learning. The key observation is that the traditional OT-based reward does not consider the temporal information, i.e., it is invaraint to the order of the state-action pairs in a trajectory, and that the reward is not defined over state-action pairs but over a whole trajectory, so later transitions in the trajectory would affect the reward of an early state-action pair, which does not follow the standard definiation of reward in RL. This the key technique the paper proposes is to introduce a mask for the transport plan, such that only temporaily neighboring states between expert and the agent will be considered when computing the reward. It futher proposes a technique to futher improve the computation of the cost matrix in the OT reward. Experiments are conducted on 9 metaworld tasks, and the proposed masked OT rewards outperform several previous baselines. Ablation studies are also conducted to help understand some design choices. Strengths: - This paper studies an important problem in the formulation of the OT-based reward, which is it being non-temporal (invariant to the order of the trajectory). - The paper is well-written and easy to follow. - The proposed algorithm is simple yet effective, and it achieves better performances than prior methods in the experiments. - The experiments are thorough, with results compared on 9 environments, and with ablaiton studies that are very helpful for understanding how each component helped to improve the performance. Weaknesses: - The proposed method to restrict the temporal information works by masking the transport plan to only include temporaily nearby states. This "temporaily nearby" is measured using the distance between the time step indexes, which assumes that the time interval between each step, or the time scale, is similar between the agent and the expert. I am wondering how general this is true. I encourage the authors to think of cases where this assumption might be broken and add some discussion on how the method would work & can be extended to work in such cases. Technical Quality: 3 Clarity: 3 Questions for Authors: Please refer to the weakness section. Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: Yes. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for your positive review and insightful comments! Your valuable comments helped us to further improve the quality of the paper. Responses to the questions are below: \| Q: The proposed method to restrict the temporal information works by masking the transport plan to only include temporarily nearby states. This "temporarily nearby" is measured using the distance between the time step indexes, which assumes that the time interval between each step, or the time scale, is similar between the agent and the expert. I am wondering how general this is true. I encourage the authors to think of cases where this assumption might be broken and add some discussion on how the method would work & can be extended to work in such cases. Thanks for the great question. Our work indeed inherits an implicit assumption from learning from demonstration literature: - The agent has a similar movement speed as the expert. Under this assumption, using the distance between the time step indexes is a simple and effective strategy to represent temporal affinity information. We will make this clear in our revised paper. As to your question on wondering how general this is true, we do admit that this assumption can be broken if the discrepancy between expert-agent movement speed / trajectory alignment is large enough. Here we share some quick empirical results that we were able to finish within the limited time on investigating the performance v.s. discrepancy (more results with the complete transition phase, i.e. the stage that it starts to fail due to increased discrepancy, will be added to the appendix of revised paper). We have done experiments to use double speed expert demonstrations, where we get the demos by sampling the original expert trajectory every 2 steps. PDF-Fig 3 in the uploaded PDF file shows the experiment results. Though the expert trajectory length is only half of the agent trajectory length, the proposed TemporalOT method is still effective under a such setting. This experiment provides some positive empirical evidence that there are some tolerance in terms of the deviation from the assumption (discrepancy). In addition to these empirical investigations, as a future extension, we may need to further generalize the definition of temporal affinity accordingly, potentially at a more abstract level. For example, we can first learn to infer the intention/latent goal of the agent and then compute the OT reward w.r.t. the intentions [Ghosh et al., 2023]. This is a very interesting direction that is worth exploring in future work. References [Ghosh et al., 2023] Reinforcement learning from passive data via latent intentions, ICML 2023 --- Rebuttal Comment 1.1: Title: Official Comment Comment: I want to thank the authors for the detailed and well-written response, and for adding a new experiment within the short rebuttal period of time. I don't have further questions and I remain positive about the paper. --- Rebuttal 2: Title: To Reviewer FnLe: Thank you for your positive feedback Comment: We thank Reviewer FnLe for your positive feedback on the rebuttal. We greatly appreciate your efforts in reviewing the paper and your valuable comments that have helped to further improve the quality of the paper.	Summary: The authors introduce TemporalOT, a learning-based proxy reward that incorporates temporal information. via using a mask mechamism and context-embeddings based cost matrix. They implemented the TemporalOT-RL based on ADS implementation, conducted thorough experiments on Meta-world benchmark focusing on the a challenge setting where there are only two demonstrations available and outperformed the OT-based reward baseline. Strengths: 1. The motivation of incorporating temporal information into OT-reward is clear. 2. The paper is well-written and easy to follow. 3. The experiments are thorough and convincing 4. The ablation study of no-mask, no-context, discount factor, number of demonstrations is very sufficient. Weaknesses: See Questions Technical Quality: 3 Clarity: 3 Questions for Authors: 1. Could the author analyze what potential property of the push task makes it different that ADS outperforms TemporalOT? 2. Does the author intend to incorporate visual encoder training instead of fixed pre-trained? Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: Performance relies heavily on the demonstration quality and visual encoder effectiveness. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We would like to thank the reviewer for the positive review and for the efforts in reviewing our work! Your comments are valuable in helping us to further improve the quality of the paper. Responses to the questions are below: \| Q1: Could the author analyze what potential property of the push task makes it different that ADS outperforms TemporalOT? Thanks for raising this point. The goal of the push task is to move the red cylinder to a target position (green dot) on the surface of the table, as illustrated in Figure10 (C) in the appendix. Usually, we can solve a task by focusing on the robot arm trajectory in the demo, i.e., open a door. However, we need to pay special attention to the red cylinder in the push task and move it to the exact target position. ADS performs better in this task because: - Firstly, the red cylinder is quite small compared to the red robot arm. Therefore, the cosine similarity based OT reward usually contains more information about the robot arm than the red cylinder. The agent is likely to focus on imitating the robot arm movement and ignores the small red cylinder. - Secondly, ADS uses a larger 𝛾 than TemporalOT due to its adaptive discount scheduler. From the comparison of OT0.99 and OT0.9 in Table 1 of the main paper, we can observe that using a larger discount factor indeed helps to improve performance. The benefit of using the adaptive discount scheduler in ADS is significant for the push task because the larger 𝛾 encourages the RL agent to look into more future steps via TD-learning and assign higher weight for future rewards. This is important because the OT reward is generally more noisy in the push task than the other tasks due to the small size of the red cylinder. For example, the OT reward $r_t$ at step $t$ is sometimes not that accurate but the OT reward $r_{t+3}$ at step $t+3$ is more accurate and contains more useful information about the red cylinder. Under a such circumstance, a larger 𝛾 will let the agent pay more attention to $r_{t+3}$ and learn a more accurate Q-value function and policy accordingly. In the experiment, we always use 𝛾=0.9 to match the initial 𝛾 value in ADS and the second best baseline OT0.9. We added experiments to run TemporalOT with a larger discount factor 𝛾=0.99. From PDF-Fig 1 in the uploaded PDF file, we can observe that TemporalOT with a larger discount factor achieves better performance in the push task. \| Q2: Does the author intend to incorporate visual encoder training instead of fixed pre-trained visual encoder? Thanks for the great question. The reason for using a fixed pre-trained visual encoder in our work is mainly following standard settings in literature [e.g. ADS paper], which removes the factor of visual encoder learning and helps us to focus on reward structure design. Although it is not the main focus of this work, we can definitely incorporate visual encoder training instead of using a fixed pre-trained visual encoder. For example, we have the following different strategies to train the encoder: - In the pixel-based setting, we unfreeze the encoder in the critic and use the Q-learning loss to optimize the encoder. - We can also adopt some existing representation learning methods for RL to train the encoder, i.e., ATC [Stooke et al., 2021]. Intuitively, this has the potential to further boost overall performance by reducing the potential domain shift issue, better capturing task-relevant signals, etc. Since the main focus of our current work is to demonstrate the effectiveness of adding temporal information to the OT rewards in RL, we follow standard setting in literature in order to make the comparison clear and consistent and leave the incorporation of visual encoder training as an interesting future work. \| Q3: Rely on demonstration quality and visual encoder effectiveness. Thanks for the comment. Demonstration quality. We agree with you that this is a common limitation of imitation learning (IL). Since our method is closely related to IL, TemporalOT also faces this common issue. On the other hand, unlike many other IL methods that require a large diverse dataset of high-quality demonstrations, TemporalOT is designed to work with only a few expert demonstrations. For example, we only provide TemporalOT with two expert trajectories in the experiments. Such a small number of expert demonstrations makes our method more practical than the other IL methods, which require more expert demonstrations. Visual encoder. We leverage the visual encoder to extract embedding for each image and compute the cosine similarity based transport cost. Since this is also a common component shared by baseline methods such as OT and ADS, any reasonably effective visual encoder can be used to make the comparison fair. In this work, we follow the experiment setup in ADS and use a pre-trained ResNet50 to extract the visual embedding. Other visual encoders could also be used. Following your suggestion, we also run some experiments quickly to compare different visual encoders in PDF-Fig 2 in the uploaded PDF file. In PDF-Fig 2, we compare three different ResNet variants (ResNet18, ResNet50, ResNet152) using the checkpoints from torchvision. We can observe that ResNet50 and ResNet152 encoders show similar final performances. Here, ResNet18 underperforms the other two encoders because it is quite weak, such that sometimes it fails to capture the key information of the image. PDF-Fig 2 indicates that a reasonably good visual encoder is usually enough to extract effective visual embeddings for computing OT rewards in RL. Given the rapid development of computer vision models, we can easily build our own model with some strong open-sourced vision encoder checkpoints. Moreover, we can incorporate visual encoder training, as discussed in Q2, to further improve performance. References [Stooke et al., 2021] Decoupling Representation Learning from Reinforcement Learning, ICML 2021	Rebuttal 1: Rebuttal: # To all the reviewers: Thanks for the reviews and summary of key paper changes We thank all the reviewers (R1-hYj8, R2-FnLe, R3-M6BJ and R4-GZSS) for their time and efforts in reviewing the paper. The reviewers appreciated that: - The motivation is clear and the problem is important (R1-hYj8, R2-FnLe, R3-M6BJ, R4-GZSS). - The paper is well-written and easy to follow (R1-hYj8, R2-FnLe, R4-GZSS). - The proposed method is simple and effective (R1-hYj8, R2-FnLe, R3-M6BJ). - The experiments are thorough (R1-hYj8, R2-FnLe, R4-GZSS). We have further improved the paper according to the valuable suggestions from all reviewers. Below is a summary of the key changes made to the current paper. We: - added experiments for $\gamma$=0.99 on the push task (R1-hYj8) (c.f. PDF-Fig 1) - added experiments to compare different visual encoders (R1-hYj8, R4-GZSS) (c.f. PDF-Fig 2) - added experiments to use double speed expert demonstrations (R2-FnLe) (c.f. PDF-Fig 3) - added experiments to use different masks (R3-M6BJ) (c.f. PDF-Fig 4) - added experiments to incorporate BC pre-trained policy (R3-M6BJ) (c.f. PDF-Fig 5) - added ablations for $\epsilon$ parameter (R4-GZSS) (c.f. PDF-Fig 6) - re-generated Figure 9 by fixing a plotting issue that caused a mis-match with the results in Table 1 (R4-GZSS) (c.f. PDF-Fig 7) - added clarifications and discussions on the assumptions of TemporalOT (R3-M6BJ, R4-GZSS). - added more detailed explanations for the experiment results (R4-GZSS). We greatly appreciate the efforts the reviewers spent on helping to improve our work and we are deeply grateful for all the valuable suggestions. We have carefully addressed each comment and improved our work accordingly. We hope they are helpful to address the concerns the reviewers had previously. We would love to hear feedback from all the reviewers. # Clarifications on motivation The motivation of this work has been well-perceived by R1-hYj8, R2-FnLe and R3-M6BJ (e.g. quoted from their reviews respectively: R1-hYj8: "the motivation of incorporating temporal information into OT-reward is clear"; R2-FnLe: "this paper studies an important problem in the formulation of the OT-based reward, which is it being non-temporal (invariant to the order of the trajectory)"; R3-M6BJ: "the paper is clearly motivated. It points out a major weakness of OT-based reward calculation"). Here we try to make some further clarifications to help resolve any potential confusions R4-GZSS seems to have (we apologize to R4-GZSS for any potential confusions we caused and we will resolve them below and also in the revised paper). We decide to re-clarify the motivation here since it is one of the most crucial prerequisite to better understand the method and resolve many related questions and confusions. Another reason to list it here is that it could be useful to readers from a broader audience later after the reviews and rebuttals are made public. > C1: Is being order-invariant within a trajectory problematic? Why order information matters in OT-based RL? Temporal order information is very important and being oder-invariant within a trajectory is problematic. More specifically, in the standard OT-reward (Eq. 5), the order information is discarded and the frames from the demo sequence are treated as bag-of-temporally-collapsed frames. In our view, collapsing the temporal axis drops arguably one of the most important characteristic features of temporal information. More concretely, consider a demo trajectory of 𝜏1 = (S1, S1, S2), meaning first to stay at S1 and then move to S2, and we want to imitate this behavior. However, if order information is discarded as in standard OT-reward (Eq. 5), from the perspective of reward, there is no ability to differentiate between 𝜏1 and some other (undesired) trajectories, e.g. 𝜏2 = (S1, S2, S1) (first move to S2 and move back to S1). Therefore, it is possible for the policy to converge to a solution that generates trajectories like 𝜏2, which is undesirable. In summary, discarding the temporal ordering information in reward calculation makes the reward on top of it under-constrained, which in consequence increases the possibility of converging to undesired solutions. This motivates us to investigate how to address this issue by incorporating temporal ordering information. > C2: Motivation of the proposed method. Which proposed component (masking scheme or context embeddings) addresses the lacking of ordering issue in the standard OT-reward? Both masking scheme and context embeddings contribute to the final overall performance and are incorporated into different stages in the algorithmic pipeline. As a brief recap, the pipeline of standard OT-based RL is as follows: (Stage 1) Transport cost matrix => (Stage 2) OT reward => (Stage 3) RL training Temporal mask. We leverage the mask mechanism to incorporate temporal affinity and therefore the order information. This is the component that is designed to address the lacking of ordering issue in the standard OT-reward explicitly (Stage 2). Context embedding. This is a component for improving the quality of the cost matrix (Stage 1) by incorporating nearby context information. This component contribute to the inclusion of temporal ordering implicitly (and at a coarser temporal scale), by the incorporating of a temporal window as context for cost calculation (e.g. frames outside of the temporal window will not be considered in cost calculation). We realized that the roles of these two components might not be well clarified in the original submission. We apologize to R4-GZSS for any potential confusions we caused and will resolve them in the revised paper. Pdf: /pdf/f2dd5fcc5c5087921c68a0f7ca265e7bd10dfe42.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
A Best-of-both-worlds Algorithm for Bandits with Delayed Feedback with Robustness to Excessive Delays	Accept (poster)	Summary: This paper studies the best-of-both-worlds (BOBW) algorithms for MAB with delayed feedback. Compared to previous results, it eliminates the need for prior knowledge on maximum delay $d_{\text{max}}$, and the regret scales with the number of “outstanding observations” ($\sigma_{\text{max}}$) rather than with the delay length as in the previous works. Technique-wise, this is achieved through a new round skipping rule, a new implicit exploration loss estimator, and advanced analysis. Strengths: The regret guarantee is significant in the sense that it scales with the number of missing information, rather than how much it is delayed as in previous work. In the latter case, even if there’s only one single delay, it incurs linear regret if this delay is $T$, which however is safeguarded by the regret guarantee in this paper. Such phenomenon has been achieved soly in either stochastic or adversarial regime before, but not in BOBW. To achieve this, the authors propose new techniques in both algorithm design and regret analysis. Weaknesses: 1. I feel that the words "distribution drift/shift" comes from nowhere in the introduction. Its meaning is not clear to me in the context of delayed bandits, but no sufficient explanation is provided. A reader may not figure it out until the Analysis Section. 2. The authors use both “multiarm” and “multi-arm” inconsistently. The latter is commonly used. 3. The contribution summary may need polishing. Points 2-4 (Line 118) seems too detailed. Currently they are not informative, they could be merged, or not even necessarily included in the contribution summary in my opinion. 4. The author may consider elaborating more on Line 181-183, i.e., why the additional $K^{1/3}$ factor is a price for BOBW guarantee (in the analysis). This could be an interesting point to BOBW researchers. 5. When introducing Lemma 2 for the first time (around Line 202), it would be good to briefly talk about what are the key elements to achieve it, rather than let the readers figure it out in the long proof later. Is it due to the analysis (virtual rearrangement) only, or also the skipping rule and/or implicit exploration? 6. These two works on feedback-delayed bandits should be relevant, but they are not discussed in this paper. One in stochastic regime [1] and the other in adversarial regime [2]. References: [1] Yang, Yunchang, Han Zhong, Tianhao Wu, Bin Liu, Liwei Wang, and Simon Shaolei Du. "A Reduction-based Framework for Sequential Decision Making with Delayed Feedback." In Thirty-seventh Conference on Neural Information Processing Systems. 2023. [2] van der Hoeven, Dirk, Lukas Zierahn, Tal Lancewicki, Aviv Rosenberg, and Nicoló Cesa-Bianchi. "A Unified Analysis of Nonstochastic Delayed Feedback for Combinatorial Semi-Bandits, Linear Bandits, and MDPs." In The Thirty Sixth Annual Conference on Learning Theory, pp. 1285-1321. PMLR, 2023. Technical Quality: 3 Clarity: 2 Questions for Authors: 1. Why do some citations have no year? E.g., “analysis of Zimmert and Seldin” in Line 58 2. Is the word “outstanding observations” existing in the delayed-feedback literature or named for the first time by the authors? It is just the number of missing observations, right? If so, I personally just feel that the wording is not very informative/natural. 3. Is the idea of “skipping” reflected only through the regret analysis, or both the algorithm design and analysis? From Algorithm 1, I think it is the latter, but Line 86-89 seems to mean the former. 4. Since the BOBW guarantee is obtained through the self-bounding trick, can we directly obtain a regret bound for the intermediate $C$-corrupted regime? Confidence: 3 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: Yes Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Weaknesses: 1. We will add a clarification around Lines 48-49, where the term is first used. Technically, the distribution drift is the ratio $x_{t+d_t,i} / x_{t,i}$ of the probability of playing action $i$ at round $t+d_t$, when the observation arrives, to the probability it had when it was played at round $t$. 2. Thanks, we will fix it. 3. Thanks for the suggestion. 4. We had to decrease the skipping threshold of Zimmert and Seldin (2020) to control the distribution drift that is due to the loss shift (see Appendix B.2 in the supplementary material). More explicitly, $K^{1/3}$ comes from a bound on the weighted average of loss estimates in Equation (25) that is bounded in Lemma 9. For now we do not know how to remove this factor, but we expect that it might require a different analysis of the distribution drift. 5. The core of Lemma 2, which relates drifted regret to the actual regret, is based on Lemma 3, which controls the distribution drift using implicit exploration and skipping. The factor of 1/4 in front of $\overline{Reg}\_T$ in Lemma 2 and the summation of implicit exploration terms come from Lemma 3. Virtual rearrangement of arrivals is needed in the proof of Lemma 2, because at the moment we have no other way to analyze multiple simultaneous arrivals. Lemma 5, which analyzes Algorithm 2 for virtual rearrangements, shows that the additional delay caused by the rearrangements is small (limited by $\sigma_{\max}^t$). 6. Thanks for the references. * Questions:** 1. It is a common practice to use \citeauthor{...} command on repeated mentions of the same paper within a short text span distance, whenever it does not lead to confusion which work is being mentioned. We hope it was not confusing in Line 58. We can add a year if necessary. 2. The term “outstanding observations” was introduced by Zimmert and Seldin (2020). An observation is considered “outstanding” from the moment an action from which it originates is played to the moment it is revealed to the algorithm. 3. Skipping is done both in the algorithm and in the analysis. 4. Yes, it is straightforward to obtain a bound for $C$-corrupted regime. --- Rebuttal Comment 1.1: Comment: I'd like to thank the authors for the response. For now, I do not have any other concerns, but I suggest that the authors could improve the writing in furture versions, including (but not limited to): 1. Clarifying "distribution drift/shift", as the meaning here is different from that in supervised learning (which is more well-known). 2. Improving the contribution summary. 3. Giving more details about the extra $K^{1/3}$ factor. 4. Overall, making a clearer roadmap about the analysis. Currently, it's a bit too dense in my opinion. 5. Including those two papers I mentioned, and some discussions (especially [2], the one for adversarial environment and hence is related to FTRL/OMD, why the analysis therein fails to obtain the guarantees here). I keep my score unchanged as of now and lean towards acceptance. --- Reply to Comment 1.1.1: Title: Response Comment: We thank the reviewer for additional input, which we will incorporate in the final version. A clarification concerning [2]: the work [2] focuses on adversarial setting only, and they assume that either the delays $d$ are fixed, or the total delay $D$ and the maximal delay $d_{\max}$ are known. The focus of our work is on BOBW bounds, on handling excessive delays with no prior knowledge of delays, and on eliminating the dependence on $d_{\max}$. So the challenges addressed by us are very different from theirs. We also note that [2] explicitly state in their Discussion that skipping cannot be applied with their approach, meaning that it is unable to handle delay outliers, and that their bounds depend on $d_{\max}^2$, meaning that even a single delay of order $\sqrt{T}$ would make their bounds linear in $T$.	Summary: This paper proposes a new best-of-both-world algorithm for bandits with a delayed feedback model. The results simultaneously achieve the latest upper bounds for delayed feedback in stochastic and adversarial (up to a factor). The algorithm design utilizes an implicit exploration estimator and the skipping set. The analysis contains new technical methods for handling the relationship between drifted and standard regrets. Strengths: The reviewer thinks this paper is a nice piece of theoretical work. It has several strengths as follows, 1. This paper's introduction concisely and clearly discusses this work and its relation (both result and theoretical tool aspects) to previous work. This is very helpful for readers to understand the research background and new contribution. 2. The best-of-both-world theoretical results of this paper combine the known best stochastic and adversarial upper bounds (with a $K^{1/3}$) factor for bandits with delay and improve upon the latest results on the same topic. Weaknesses: The reviewer is uncertain whether this paper reaches the NeurIPS bar for the following weaknesses reasons: 1. The algorithm design itself needs to be more novel. The only new component the reviewer notices is the implicit exploration estimator, which was also related to prior works in adversarial bandits. 2. The algorithm design is not optimized. For example, the skipping set $\mathcal{S_{t}}$ is always expanding, which is counterintuitive: (1) As the threshold $d^t_{\text{max}}$ is non-decreasing, there should exist observations, previous belongs to the skipping set, with delay less than the increased new threshold. Why does the algorithm design not add these skipped observations to the non-skipped set? (2) Even for observations belonging to the skipping set, when their observations are finally revealed, why does the algorithm not consider the kind of observations? If considered by the decision-making, both types of observations can help improve the algorithm's performance. Even if this modification cannot reduce the regret upper bound, it should be able to improve the algorithm's empirical performance. Technical Quality: 3 Clarity: 3 Questions for Authors: 1. The reviewer needs clarification on some proof steps. For example, by the definition of the drift regret, the benchmark is the estimated loss $\hat \ell_{i^}$, but when it comes to the stability-penalty decomposition at the beginning of Appendix A, the benchmark becomes the actual loss $\ell_{i^}$, which looks inconsistent. Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: Yes Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: > The algorithm design itself needs to be more novel It is very common for BOBW algorithms to bear close resemblance to the adversarial algorithms they are derived from, because it allows inheritance of the adversarial regret guarantees. For example, the EXP3++ algorithm (Seldin and Slivkins, 2014) only makes a small modification to the exploration distribution of the well-known EXP3 algorithm, and the Tsallis-INF algorithm (Zimmert and Seldin, 2021) is essentially identical to the INF algorithm designed by Audibert and Bubeck (2010) for adversarial bandits. The major contribution of many BOBW papers, including ours, is the stochastic analysis that stays within the predefined framework of the parent adversarial algorithm, which only allows minor algorithmic modifications due to the necessity to preserve the adversarial regret guarantees. The preservation of the algorithm design is, therefore, a desired feature. The value and technical sophistication of these contributions, including ours, should not be underestimated though. We introduced several important algorithmic and analytical tools: 1. We are the first to control the distribution drift without altering the learning rates, by using implicit exploration and skipping (Lemma 3). Prior work controlled the drift by damping the learning rates using knowledge of $d_{\max}$, but this technique adds $d_{\max}$ linearly to the regret bound and fails in presence of just a single outlier of order $d_{\max}$. 2. Implicit exploration design is very delicate, because it has to be sufficiently large to control the drift, but at the same time sufficiently small, because it adds up linearly to the bound. We have designed an implicit exploration scheme that does not ruin neither the stochastic nor the adversarial bound (Lemma 4). Note that our implicit exploration scheme depends on the delays, but not the losses. Therefore, it has a great potential to be useful in other settings with delayed feedback. 3. We have also derived the first approach to relate drifted and non-drifted regret in presence of delay outliers (Lemma 2). This contribution involves introduction of the greedy rearrangement algorithm (Algorithm 2) and drift control by Lemma 3. Prior work has only allowed to relate drifted regret and the actual regret, when the delays were bounded by $d_{\max}$, and it was adding $d_{\max}$ linearly to the regret bound. Thus, it was failing in presence of even a single delay of order $T$. We believe that our contribution has the potential to bring a transformative effect to the field of BOBW learning with delayed feedback. * > The algorithm design is not optimized - Concerning (1): when an observation is processed at time $t$ it modifies the playing distribution $x_t$ at time $t$. If at time $t$ we would decide to go back to some old observations, the actual delay from the moment the action was played to the moment it is reconsidered would remain above the updated threshold, so it would not be possible to add it back. - Concerning (2): while it feels wasteful to drop observations, we note that the cardinality of the skipped set is smaller than the regret bound, which is in turn sublinear in the total number of observations. Processing of skipped observations would add a lot of pain in the analysis, but add nothing in terms of the bound (because of matching lower bounds), and almost nothing in terms of empirical performance, because of the small size of the skipped set relative to the total number of observations. * Q1: We are sorry, it is a typo. It should be $\hat \ell_{t, i_{T}^{}}$ at the end of the display between Lines 328 and 329 in Appendix A. References** Y. Seldin and A. Slivkins. One practical algorithm for both stochastic and adversarial bandits. ICML, 2014. J-Y. Audibert and S. Bubeck. Regret bounds and minimax policies under partial monitoring. JMLR, 2010. --- Rebuttal Comment 1.1: Comment: The reviewer thanks the authors for their responses. The reviewer will maintain their score for now.	Summary: This paper studied the best of both world algorithms for arbitrary delayed feedback. The proposed algorithm does not require prior knowledge of maximum delay $d_{\max}$ and avoids its linear dependence in the regret bound. To this end, they proposed the implicit exploration that works for the best-of-both-worlds guarantees. The key idea is to relate the number of outstanding observations $\sigma_{\max}$ so as not to rely on the boundness of delays. Strengths: - The first proposal of implicit exploration for BoBW settings. The algorithm is based on FTRL with a hybrid regularizer where a skipping technique is employed, which becomes crucial for the BoBW guarantee. - When the maximal number of outstanding observations $\sigma_{\max}$ is smaller than maximum delay $d_{\max}$, the proposed method provided a much better bound than [Masoudian et al. 2022]. Weaknesses: I only see it for writing. The current main paper more focus on the explanation of the result comparison with [Masoudian et al. 2022]. Although the authors detailed a summary of technical proof in the main text, a more intuitive, and higher-level explanation of algorithmic parts would be appreciated when introducing the proposed technical scheme. For example, the paper does not provide a detailed explanation of the selection of regularizers or learning rates intuitively. For example, what makes analysis challenging due to aiming BoBW bounds could be more highlighted. I guess the additional challenge for dealing with stochastic cases, from [Zimmer and Seldin, 2020] that already uses the FTRL algorithm with a hybrid regularizer, has already been addressed by [Masoudian et al. 2022], but by missing these explanations, it would be hard for readers to see the clear picture of inherently technical challenges of BoBW algorithm for delayed feedback. Technical Quality: 3 Clarity: 2 Questions for Authors: How can we interpret implicit exploration term $\lambda_{s,t}$? (Is this inspired by controlling the bias term due to an implicit exploration scheme in order to make it applicable to a best-of-both-worlds setting?) Confidence: 3 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: n.a Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: A detailed explanation of the selection of regularizers or learning rates: The learning rates and regularizers were taken directly from Zimmert and Seldin (2020), because we had to have the adversarial regret guarantee. The intuition behind the choice of regularizers is that the adversarial regret bound, $\sqrt{KT} + \sqrt{dT\log K}$ for fixed delays $d$, and the construction of the matching lower bound combine a lower bound for bandits to show the necessity of the $\sqrt{KT}$ term, and a full information lower bound to show the necessity of the $\sqrt{dT / logK}$ term. The negative Tsallis-entropy regularizer with power 1/2 is optimal in the bandit setting, and the negative entropy regularizer is optimal in the full information setting, and the combination achieves the optimal regret bound in the delayed feedback setting. The learning rate $\eta_t$ is the standard learning rate for bandits, and the learning rate $\gamma_t$ is the standard full information learning rate. We refer to Zimmert and Seldin (2020) for further details. The primary challenge addressed by our work is that these regularizers and learning rates also work in the stochastic setting. We make a small adjustment of $\gamma_t$ by a constant due to adjusted skipping. * What makes analysis challenging due to aiming BoBW bounds: First, we want to emphasize that our focus is on BoBW analysis in presence of delay outliers, and that the work of Masoudian et al. (2022) cannot handle delay outliers, because even a single delay outlier of order $T$ renders both their stochastic and adversarial regret bound linear. Concerning analytical challenges: the stochastic part of our analysis is based on control of the distribution drift (the ratio $x_{t+d_t,i} / x_{t,i}$ of the probability of playing action $i$ at round $t+d_t$, when the observation arrives, to the probability it had when it was played at round $t$). Control of the distribution drift is the most commonly used approach in bandits with delayed feedback, also used by Masoudian et al. (2022). So far the only way to control the distribution drift was by damping the learning rate, but it only applies when the maximal delay $d_{\max}$, which corresponds to the control range, is known, and it adds $d_{\max}$ linearly to the regret bound. Therefore, this technique fails in presence of delay outliers. We are the first to achieve control of the distribution drift in presence of delay outliers. In order to achieve it we introduced several important algorithmic and analytical tools: 1. We are the first to control the distribution drift without altering the learning rate. Our control is based on a combination of implicit exploration, which is used to control the drift due to the change of regularizer, and skipping, which is used to control the drift due to the loss shift (Lemma 3). 2. The challenge in designing a successful implicit exploration scheme is that implicit exploration has to be sufficiently large to control the ratio, but at the same time sufficiently small, because it adds up linearly to the bound. We have shown that the contribution of our implicit exploration to the bound, $\sum_{t=1}^T \lambda_{t,t+\hat d_t}$, does not ruin neither the stochastic nor the adversarial bound (Lemma 4). 3. We have also derived the first approach to relate drifted and non-drifted regret in presence of delay outliers (Lemma 2). Prior work has only allowed to relate the two when the delays were bounded by $d_{\max}$, and it was adding $d_{\max}$ linearly to the regret bound. Thus, it was failing in presence of even a single delay of order $T$. We believe that all these tools will find additional applications in other learning settings. Finally, we note that the analysis of Zimmert and Seldin (2020) only applies in the adversarial setting. It is unknown whether their analysis technique, which is not based on distribution drift, can be applied in the stochastic setting. * Interpretation of implicit exploration terms $\lambda_{s,t}$: The role of $\lambda_{s,t}$ is to control the distribution drift (the ratio $x_{t+d_t,i} / \max(x_{t,i}, \lambda_{t,t+d_t})$). To control the ratio it cannot be too small, but since $\sum_{t=1}^T \lambda_{t,t+\hat d_t}$ adds up linearly to the bound, it cannot be too large either. Note that $\lambda_{s,t}$ only depends on the delays, but not the losses. --- Rebuttal Comment 1.1: Comment: Thank you for providing a detailed response. I have read the reviews and responses from the other reviewers as well, and then I will keep my score (leaning towards acceptance).	Summary: The authors consider the multi-armed bandit problem with delayed feedback, where the loss of a chosen arm is observed several rounds later. In this setting, nearly optimal algorithms have been developed for both stochastic and adversarial environments, as well as best-of-both-worlds (BOBW) algorithms that perform well in both regimes. However, the regret upper bounds of existing BOBW algorithm by Masoudian et al. (2022) has gaps compared to the regret upper bounds of algorithms designed specifically for adversarial environments (Zimmert and Seldin, 2020) and stochastic environments (Joulani et al., 2013) and in particular the algorithm by Masoudian et al. require the prior knowledge of the maximal delay before the game starts. To address this issue, the authors propose an algorithm that achieves a regret upper bound without knowing the maximal delay in advance. To achieve this, the authors introduce a new framework of implicit exploration, demonstrating that this framework can be effectively combined with techniques that skip observations associated with excessive delays. Strengths: The differences from existing research are thoroughly discussed. Technically, the introduction of the implicit exploration framework to achieve BOBW regret bounds without using the maximal delay is novel. Fine-tuned adjustments are made to achieve BOBW while employing implicit exploration. Additionally, how the parameter $\lambda$ is utilized in the proof is clearly explained and discussed throughout the proof. Weaknesses: One concern is that the differences between this paper and existing research might not be sufficient. While the authors propose an algorithm that works in both adversarial and stochastic environments, the foundation for handling excessive delays seems to have been largely established by Zimmert and Seldin (2020) (and Masoudian (2022)). I was unable to check all the proofs in detail, but they appear to be generally correct. However, there seems to be large room for improvement in the overall explanation. Many explanations are not contextualized, making the proofs difficult to read. For instance, Lemmas 11 to 13 are directly taken from Masoudian et al. (2022). However, the algorithm in Masoudian et al. (2022) differs from the one proposed by the authors, so it is unclear whether these results are directly applicable. Technical Quality: 3 Clarity: 2 Questions for Authors: The authors are expected to discuss to what extent the results from Zimmert and Seldin (2020) and Masoudian et al. (2022) can be used in their study. Confidence: 4 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: not applicable Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Concerning the novelty of our approach to handling excessive delays: First, we want to emphasize that the work of Masoudian et al. (2022) is unable to cope with excessive delays, because even a single delay of order $T$ renders their regret bound linear in both stochastic and adversarial environments. The work of Zimmert and Seldin (2020) only copes with excessive delays in the adversarial regime. It is the only work on delayed feedback and adversarial losses known to us that is not using control of the distribution drift in the analysis, but it is unknown whether their analysis technique can be applied to stochastic losses to obtain BOBW results. The stochastic part of our analysis is based on the more broadly used approach based on control of the distribution drift (the ratio $x_{t+d_t, i} / x_{t,i}$ of the probability of playing action $i$ at round $t+d_t$, when the observation arrives, to the probability it had when it was played at round $t$). So far the only way to control the distribution drift was by damping the learning rate, but it only works when the maximal delay $d_{\max}$, which corresponds to the control range, is known, and it adds $d_{\max}$ linearly to the regret bound. Therefore, this technique fails in presence of delay outliers. We are the first to achieve control of the distribution drift in presence of delay outliers. In order to achieve it we introduced several important algorithmic and analytical tools: 1. We are the first to control the distribution drift without altering the learning rate. Our control is based on a combination of implicit exploration, which is used to control the drift due to the change of regularizer, and skipping, which is used to control the drift due to the loss shift (Lemma 3). 2. The challenge in designing a successful implicit exploration scheme is that implicit exploration has to be sufficiently large to control the ratio, but at the same time sufficiently small, because it adds up linearly to the bound. We have shown that the contribution of our implicit exploration to the bound, $\sum_{t=1}^T \lambda_{t,t+\hat d_t}$, does not ruin neither the stochastic nor the adversarial bound (Lemma 4). 3. We have also derived the first approach to relate drifted and non-drifted regret in presence of delay outliers (Lemma 2). Prior work has only allowed to relate the two when the delays were bounded by $d_{\max}$, and it was adding $d_{\max}$ linearly to the regret bound. Thus, it was failing in presence of even a single delay of order $T$. We believe that all these tools will find additional applications in other learning settings. * Clarification concerning the use of Lemmas 11 to 13, which were taken from Masoudian et al. (2022):** We recall that $\overline{Reg}\_T= \sum_{t=1}^T x_{t,i}\Delta_i$. Substitute this definition into the inequality in Line 435. Lemmas 11 to 13 are used to bound three parts of the inequality in Line 435 by finding the worst-case choice of $x_{t,i}$ for each of the parts. Since the worst-case choice of $x_{t,i}$ is algorithm-independent, the lemmas can be applied. We will add the clarification to the paper. --- Rebuttal Comment 1.1: Title: Response Comment: I appreciate the authors' response. Since the authors addressed my concerns, I will raise the score from 5 to 6. However, as with bmXx, I expect improvements in the overall writing, particularly in the appendix. --- Reply to Comment 1.1.1: Comment: Thanks for raising the score. We will use input from all the reviewers to improve the writing.	null	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Partial observation can induce mechanistic mismatches in data-constrained models of neural dynamics	Accept (poster)	Summary: The authors investigate whether dynamical systems models that are statistically fit to neural data recapitulate the same dynamical mechanisms of the circuit. Commonly, neuroscientists only measure activity from a small fraction of neurons within a circuit. Under this constraint, the authors show examples where the model learns fundamentally different dynamical mechanisms. If true, this would be of great significance to the computational neuroscience community and an important cautionary tale. Strengths: There are a lot of good things to say about this paper. The motivating question is very interesting and important. The mathematical framing and analysis is elegant. The introduction and discussion sections are skillfully written to target the computational neuroscience community, and I think the paper has the potential to be very impactful within this community after some revisions. Weaknesses: I very much liked the big picture idea of this paper. However, in various parts of the paper, the writing is unclear and left me confused on details. The interpretation of certain findings should be clarified. I am optimistic about being to raise my score during the discussion period if these weaknesses can be addressed. * In section 2, the authors fit a linear dynamical system model with 5 latent dimensions (line 113) to 5% of neurons sampled from a feedforward chain circuit. The model fails to recapitulate the feedforward chain and instead learns a line attractor. Critically, there are two distinct but non-mutually exclusive explanations for this result: (a) 5 latent dimensions is not enough to capture the line attractor, or (b) the partial observation of 5% of the circuit is insufficient. The title and abstract of the paper exclusively favor explanation (b). However, on lines 127-132 the authors do not mention (b) and instead put forth (a), "[if] the data constrained model has fewer neurons, it cannot realize a feedforward chain with sufficiently long memory". Here, the recurrent dynamics in the LDS happen within a 5-dimensional latent space, so I assume that the authors mean "fewer neurons" to mean the relatively low dimensionality of the latent space. * I would like to see the result in section 2 more systematically investigated as follows. Let `N` denote the number of neurons in the teacher circuit (feedforward chain). Let `d` denote the latent dimensionality of the LDS model, and let `n` denote the number of neurons that are measured / observed for fitting the LDS model. I am interested to see whether the LDS model still fails to learn a feedforward chain when `N` is large (e.g. maybe 1000) and `n = d` is big but still a small fraction of the overall system (e.g. `n = d = 100`). Additionally, it would be elucidating to see an example where `N = n` (i.e. fully observed circuit), but a low-dimensional dynamical model is assumed `d < n`. The purpose of these additional experiments is to clarify whether the problem is that `n` $\ll$ `N` (as suggested by the title / abstract), or whether the real problem is that `d` $\ll$ `N`, or whether both are a problem. * Figure 3 seems to get at some of these concerns, but I think the paper will be much clearer if the above comments are addressed in Figure 1 as well. * In Figure 3, it is still a little unclear to me whether subsampling, per se, is the problem. If I understand the construction of the teacher network properly, as `D` increases, the timescale of the feedforward chain also increases. It is harder for the student network to match this timescale with a chain, leading it to instead learn a line attractor. I would like to see an experiment where the timescale of the feedforward chain is kept constant while increasing `D` (e.g. by inserting multiple copies of each neuron in the feedforward chain). In this case, when you randomly sample `d` neurons for the student network, do the learned dynamics still fail to capture a feedforward chain for large `D`? An affirmative answer would seem to be more in agreement with the main claims of the title and abstract. A negative answer would still be interesting, but would change the interpretation of the paper to be more in line with the idea that a mismatch in dimensionality is the core of the problem instead of sub-sampling. Technical Quality: 3 Clarity: 3 Questions for Authors: See "Weaknesses". Confidence: 5 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: Limitations are adequately discussed. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for their careful critiques of our work, which have helped us further strengthen our paper. Below we respond to their comments on Weaknesses of our work: * The reviewer brings up an excellent point---that both partial observation and the selection of a latent dimension much smaller than the number of observed neurons could contribute to why the feedforward chain in the experiment of Section 2 is misidentified as a line attractor. We set up the experiment to parallel how data-constrained models are often fit in practice, with both partial observation and an explicit bias towards smaller latent dimensions, but appreciate the concern that this leaves room for multiple explanations as to why the mismatch we found occurs. However, since partial observation even in the absence of an explicit bias towards small latent dimensions already bounds model dimension to be smaller than that of the teacher network, the quoted explanation we provide was intended to implicitly also support explanation (b). Nonetheless, we will provide further clarification on this point and our interpretation of the findings here. * We agree that the experiment you propose would be fruitful in disentangling explanations (a) and (b), and as such have performed a sweep of LDS models of various latent dimensions and observability conditions, fit to the same functionally feedforward chain as in Fig. 1b. In particular, using the suggested notation, we fit models with a latent dimension $d = n-1$ (the $-1$ accounts for the fact that the LDS fitting procedure we use requires latent dimension to be strictly less than the observation dimension) to a functionally feedforward teacher circuit performing the same integration task (as in Fig. 1b). We performed fits at various values of $n$, up to the suggested fraction of $n = 0.1N$. In addition, as suggested, we fit LDS models of small latent dimensions $d \in \{2, 3, \dots, 6\}$ at full observability. The results demonstrate that the mechanistic mismatch we observe persists even if partial observability is the only driver of restricted model dimension. Further, the second experiment demonstrates that a model of small latent dimension will still learn a line attractor-like mechanism even at full observability. This finding is consistent with the quoted explanation of lines 127-132. * We agree that an experiment with a fixed length feedforward chain while increasing $D$ could further clarify how the results of Fig. 3 should be interpreted. We interpret the suggested connectivity for such an experiment proposed by the reviewer as resembling synfire chain connectivity. Specifically, we consider teacher networks with connectivity $B = \frac{1}{k}\delta_{i+1,j} \otimes \mathbf{1}_{k\times k}$, where $k$ is the number of copies of each neuron in the chain. Here, the $\frac{1}{k}$ factor is included to ensure that all the nonzero singular values of $B$ remain equal to $1$ as the number of copies $k$ is scaled up. We compute the learned student matrix for a random selection of $d=50$ observed neurons in the limit of long observation time $T$, for fixed chain length $D/k = 50$ and values of $k \in \{2^0, 2^1, \dots 2^6\}$. For each value of $k$, we report the top two eigenvalues, time constants, and singular values of the learned student networks, averaged over $10$ random observed neuron selections, sampled without replacement. The results are consistent with the interpretation that neither a feedforward chain, nor a line attractor (or any persistent timescale mechanism) are learned when $D$ is increased in this manner. Specifically, as $k$ is increased, the learned timescales approach the intrinsic neuronal timescale $\tau$, ruling out persistent timescale mechanisms, and the learned singular values fall well below $1$, ruling out a feedforward chain-like structure. Thus, as in Fig. 3, the student still does not learn a feedforward chain, but fails to do so in a different manner. Plots for the latest experiments are included in the global response. --- Rebuttal Comment 1.1: Title: Thanks for the additional experiments Comment: Thanks for the additional experiments. My interpretation of them is that both neuron subsampling and latent dimension restriction are problems for creating a dynamical mismatch. It would be great to see follow up work on this that carefully disentangles these two effects further. I'm raising my score to a 6, as I think the paper does a good first pass characterization of this important phenomenon. --- Reply to Comment 1.1.1: Comment: Thank you for your prompt response; we are glad that the additional experiments addressed some of your concerns. We agree that both subsampling and latent dimensionality restriction contribute towards the bias towards line-attractor-like mechanisms, and certainly intend to follow up on our findings in future work. As you say, this is just the first step!	Summary: The authors address provide a cautionary tale for how data-constrained RNN models can mis-identify the dynamical structure underlying neural population computations when only a subset of the neural population is observed ("partial observation"). Empirical case studies are provided, whereby data-constrained student networks are trained from partial observation of synthetic teacher networks. The analyzed dynamics of the trained student networks differed from those of the teacher network in several teacher network setups. When teacher networks performed integration of a stimulus input via a feedforward chain dynamic, student networks were found to be biased to recover a line attractor dynamic under certain conditions. Mismatched student-teacher dynamics were also shown when teachers were linear noise-driven networks with non-normal dynamics or low-rank connectivity. The final case study provided details similar propensities for mismatched student-teacher dynamics when all networks are non-linear. Strengths: - Originality: The overall message and cautionary tale is indeed original (although see related work in Weaknesses). - Quality: The case study examples are well chosen and illustrative of the potential for mismatched student-teacher dynamics. The experiments appear well controlled and visualizations are intuitive and elegant. - Clarity: Overall, the writing is clear and appropriately didactic. - Significance: Recent years have seen a proliferation of data-constrained model development and interest in interpreting the corresponding trained models. Thus, this cautionary tale message is quite significant and timely. While perhaps beyond the scope of this work, solutions to the problems exposed, even if only hypothesized, could improve the significance of this work. Weaknesses: - Minor: There is a line of related work from Chethan Pandarinath's group on interpretable data-constrained models that should be referenced if not explicitly discussed. For example: Sedler, Andrew R., Christopher Versteeg, and Chethan Pandarinath. 2023. “Expressive Architectures Enhance Interpretability of Dynamics-Based Neural Population Models.” Neurons, Behavior, Data Analysis, and Theory, March, 1–22. https://doi.org/10.51628/001c.73987. Technical Quality: 3 Clarity: 4 Questions for Authors: - If I understood correctly, the student models applied throughout were designed to provide a one-to-one mapping from hidden units in the student RNN to observed teacher unit activity. Other data-constrained architectures do not rely on such design constraints--in particular, LFADS [11] and Neural ODEs [33] attempt to reproduce single-trial neural recordings (or teacher activity) via a readout from the RNN hidden activity space, thus allowing the RNN expressivity to be decoupled from the size of the observed neural population. To what extent might some of the described mismatches be artifacts of the limited expressivity of RNN models whose individual units are constrained to directly match observed teacher unit activity? To be concrete, in the integration example, too few units in the student network was explained as a cause for the student network mis-identifying a line attractor motif when the teacher actually employed a feedforward chain (lines 127-132; and Figure 1b). Would a mismatch still appear by when fitting partial observations using a less-constrained architecture like LFADS? - Minor: The intro paragraph beginning on line 34 lists a number of challenges for data-constrained models. Why is it important for us to consider all of these limitations when only the partial observability is addressed in this work? There may be an opportunity to clarify the exposition here. - Minor: Line 66: "even under relatively ideal conditions where the input to a circuit is either perfectly known or white noise". In the white noise case, were known inputs not provided to the student networks? This sentence could benefit from clarification. Confidence: 4 Soundness: 3 Presentation: 4 Contribution: 3 Limitations: The authors did not include an explicit "Limitations" section, and beyond a brief sentence in the author checklist, limitations of the techniques are not discussed explicitly in the manuscript. I would encourage the authors to consider stating some of the limitations of their studies and the particular model class chosen for the student RNNs. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for their appreciation of our work. Below we address some of the concerns and questions that they raise: #### Weaknesses: * We thank the reviewer for pointing out the work of Pandarinath's group, which we unfortunately missed citing in our initial manuscript. We will add the suggested references. #### Questions: * While the analytically tractable setup we describe in Section 3 is indeed constrained to a one-to-one mapping from units in the student and units in the teacher, we would like to emphasize that the motivating experiment described in Section 2 was actually performed with a latent variable model (LDS) that does not have such a constraint (See lines 109-113). Further, for our results on low-rank non-normal teacher dynamics (Section 3.1), we showed experiments in a supplementary figure that found that the spurious slow directions we derived analytically for the one-to-one mapping setup still occurred in LDS models (Supplementary F.5). We did not experiment with LFADS because it is a spiking model, whereas we focus on rate-based models throughout. Moreover, to the best of our knowledge, there's not a straightforward way of extracting spectral information from LFADS weights to make claims about attractor dynamics, whereas this can and has been done for LDS. * We describe the limitations of data-constrained models in detail here to help frame why the insights that are derived from such models are often rather course-grained (attractor-like properties rather than individual synaptic weights). Further, it motivates our analytical setup in Section 2, which includes two of the four stated limitations (partial observation and neuronal noise), and justifies why we focus on recovery of spectral properties over other possible criteria (e.g., weight recovery). Lastly, the discussion of these limitations supports the overall message that even in a best-case scenario where the other two limitations are ignored, data-constrained RNNs are inductively biased towards fitting (possibly spurious) attractor-like solutions. * In the white noise case, the students were only driven by noise; there are no known additional inputs. We will reword that sentence to make this distinction clearer. --- Rebuttal Comment 1.1: Comment: Thank you for these responses. I stand by my original evaluation. I wish the authors all of the best with this work. --- Reply to Comment 1.1.1: Comment: Thank you again for your valuable and positive feedback, which has helped us improve our manuscript!	Summary: Deriving a mechanistic understanding of neural circuits from observations (neural recordings) is a fundamentally ill-posed problem. This paper explores and exposes this issue in controlled theoretical settings. Specifically, the authors focus on two aspects: the intrinsic biases of data-constrained surrogate models and the partial observability of the data. They demonstrate these pitfalls in both linear and non-linear systems. Strengths: This is a beautifully written paper, clear and concise. The examples are well motivated. The theoretical and experimental analyses are mathematically tight. Moreover, the issue of fitting models to partially-observed data and deriving mechanistic insights from such surrogate models is a pertinent one for neuroscience today, given the developments in recording techniques and data-driven modeling. Weaknesses: While the problem formulation is intuitive and well-motivated, the settings considered here are exceptionally constrained. This paper would greatly benefit from and be practically more useful if the authors provided scenarios where observed data has more than one plausible mechanistic explanation and how one would go about falsifying each hypothesis. The authors allude to perturbation analyses as a solution, but once again, the interpretations are unclear when we lack a "ground truth." Are there existing biological neural datasets that the authors can use to expose possible misinterpretations of circuit mechanisms? This question of system identification has been of long-standing interest in neuroscience. Coupled with surrogate modeling, there is a big literature on simulation-based inference and adjacent topics that would be worth adding as discussion in this current manuscript. Some representative references: Flexible and efficient simulation-based inference for models of decision-making. Boelts et al. (2022) Fast Inference of Spinal Neuromodulation for Motor Control using Amortized Neural Networks. Govindarajan et al. (2022) The frontier of simulation-based inference. Cranmer et al. (2020) Technical Quality: 4 Clarity: 4 Questions for Authors: Please refer to the weaknesses section above. Confidence: 4 Soundness: 4 Presentation: 4 Contribution: 3 Limitations: Please refer to the weaknesses section above. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for their careful reading of our manuscript, and are grateful for their positive assessment. Below we respond to their comments on the Weakenesses of our work: * We are glad the reviewer found our formulation of the problem intuitive, and agree that the settings we consider are constrained. However, we would argue that they are not exceptionally so. In particular, we emphasize that the integrator networks in Figure 1 do in fact have multiple plausible mechanistic explanations; by examination of the activity and network outputs alone we could not discern that the example in 2a is a line attractor, while that in 2b is a feedforward chain. Given the mismatch in the fitted and ground-truth flow fields, one could experimentally distinguish these hypothesis based on perturbing the activity of the integrator neurons in this circuit. This could be accomplished, for instance, through optogenetic stimulation (see e.g. O'Shea, Duncker, et al. 2022, or very recent work by Vinograd et al. 2024 posted after the NeurIPS submission deadline). Carefully investigating when perturbations can sensitively distinguish between mechanistic hypotheses is an important topic, but lies beyond the scope of the present work. * We agree with the reviewer that it would be interesting to expose possible misinterpretations of circuit mechanisms in existing biological datasets. However, for the purpose of the present paper we prefer to maintain our focus on synthetic data with known mechanisms, so that we can map out when mismatch in model mechanism arises. This is also motivated by the fact that conclusively demonstrating misinterpretation of mechanism in biology would require experimental manipulations; as we are not in a place to carry out such experiments, for the moment we prefer to take a more conservative approach rather than suggesting particular targets for future study. We will a discussion on this broader point, to our work. * We thank the reviewer for drawing our attention to the simulation-based inference literature, and will expand the discussion section to reflect its connections with our work. --- Rebuttal Comment 1.1: Title: acknowledging author rebuttal Comment: Thanks for your response. I've read the rebuttal and comments of other reviewers. I still think this is a good paper, but the rebuttal itself does not provide any further information. If working with biological datasets is beyond the scope of this paper, I think at least a discussion of how one can even "detect" a potential mismatch in the absence of known mechanisms seems like an important addition to the study, given the framing of the paper and its relevance for neuroscience. I'm keeping my original evaluation. Good luck to the authors! --- Reply to Comment 1.1.1: Comment: Thank you again for your careful evaluation! We will add a discussion of potential approaches to detecting mismatch to our manuscript, and certainly intend to follow up on this question in depth in future work.	null	null	Rebuttal 1: Rebuttal: We thank the referees for their careful reading our our manuscript, and are gratified by their positive appraisal of our work. Here, we would like to address two common points of concern. ## Title and Framing First, we would like to clarify why we frame the title and abstract to focus on partial observation rather than dimensionality mismatch in general: Partial observation is a near-universal property of data-constrained models in neuroscience, whereas restricted latent dimensionalities only apply to a subset of such models (many methods exist for fitting one-to-one mappings between student units and observed teacher units, such as FORCE, BPTT, and the MAP inference procedure we describe). Our latest experiments, the quoted reasoning of lines 127-132, and the second paragraph of the Discussion all suggest that dimensionality mismatches arising from restricted latent dimensions also contribute to the observed mechanistic mismatches. However, our analytical results only apply to the setting without the additional latent dimensionality restriction. Extending our theoretical analysis to latent variable models is an important objective of our future work. Consequently, to reflect our contributions accurately, we focus on partial observation in the title and abstract, using wording that does not rule out other possible sources of mismatch. We reiterate that we do discuss restricted latent dimensions as an additional driver of bias towards attractor-like solutions in the Discussion (paragraph 2). We nonetheless agree that this point should be expanded on, and will discuss it further in the context of our latest experiments. ## Solutions Second, we agree with the reviewers that it is important to provide an avenue to resolve the issues we highlight in our work. As we mentioned in our manuscript and discuss in our reply to Reviewer njnf, one approach to validating putative attractor structure is to examine responses to perturbations of neural activity, for instance using optogenetics. However, we believe that it is important to focus the present manuscript on documenting the space of failure modes before we can formulate a useful proposal as to how they can be addressed. In our revised manuscript, we will expand our discussion of possible approaches using targeted optogenetic perturbations, and caveats thereof. Pdf: /pdf/414924d56fc6aba0a2119b3198b480f5ff284ec2.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
EfficientCAPER: An End-to-End Framework for Fast and Robust Category-Level Articulated Object Pose Estimation	Accept (poster)	Summary: This paper proposes EfficientCAPER, a novel method for category-level articulated object pose estimation from input point cloud. The proposed method first estimates the 6D pose of the free part (or static part), then uses this estimated 6D pose to transform the input point cloud into canonical space, and finally segments and regresses the pose of each part. The authors experiment on both synthetic and real-world datasets, showing that the proposed method outperforms existing methods. Strengths: - The proposed method is simple but efficient as shown in Table 2. - The idea of transforming the input point cloud into its canonical space seems to be straightforward but it appears not to have been done in previous works. - The proposed method outperforms existing works on both synthetic and real-world datasets. Weaknesses: - The paper misses many important related works such as CAPTRA, Ditto. While these methods do not work in the exact same setting, these methods are relevant and it is worthy to discuss the difference with the proposed method. - I found the paper is not well-written, making it difficult to understand the true contribution of the paper. - In Table 3, the authors show the results to prove the robustness of the proposed method against self-occlusion. The self-occlusions are sometimes quite very high such as 80-100%. It would be helpful to know in which cases the object can be occluded at this high rate, along with qualitative samples. Technical Quality: 2 Clarity: 1 Questions for Authors: - Please show some qualitative samples of object being self-occluded at 80-100%. Confidence: 3 Soundness: 2 Presentation: 1 Contribution: 2 Limitations: No, the authors did not mention explicitly the limitation of the proposed method. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for taking the time to read this paper and for asking these meaningful questions. Below we respond in detail to your questions. *W1: The paper misses many important related works such as CAPTRA, Ditto. While these methods do not work in the exact same setting, these methods are relevant and it is worthy to discuss the difference with the proposed method. Our work involves estimating articulated objects, while CAPTRA[1] focuses on the tracking task. In terms of translation, CAPTRA utilizes CoordinateNet to predict normalized coordinates, whereas our approach directly regresses it, which enhances efficiency. Ditto[2] is a model based on implicit neural representations, capable of learning and reconstructing the 3D geometry of articulated objects from visual observations through interactive perception, but it does not perform pose estimation. For the joint parameter estimation module, Ditto uses implicit decoding of axis parameters and states from camera point clouds. Still, our work implicitly decodes axis parameters and explicitly decodes the state in the canonical space. We will incorporate more significant related work in the revised version. W2: I found the paper is not well-written, making it difficult to understand the true contribution of the paper. We have summarized our contributions in the introduction from line 71 to line 80. In short, our key contributions are pose canonicalization and joint-centric articulation pose modeling method. Additionally, we will add a concluding statement at the end of the method section to highlight the contributions of our approach in the revised version. W3&Q1: In Table 3, the authors show the results to prove the robustness of the proposed method against self-occlusion. The self-occlusions are sometimes quite very high such as 80-100%. It would be helpful to know in which cases the object can be occluded at this high rate, along with qualitative samples. We presented some cases with severe self-occlusion and qualitative results in Figure 3 in the attached PDF*. The category drawer suffers from severe self-occlusion due to its complex structure and constrained parts with small size. Thanks to our joint-centric pose modeling, our method can effectively address self-occlusion issues and demonstrate robustness to varying levels of self-occlusion. Therefore, both qualitative and quantitative results show the potential that our method can achieve superior performance on objects with more complex structures. [1] CAPTRA: CAtegory-level Pose Tracking for Rigid and Articulated Objects from Point Clouds. 2021. ICCV. [2] Ditto: Building Digital Twins of Articulated Objects from Interaction. 2022. CVPR.	Summary: The paper investigates category-level articulated object pose estimation with a new framework. The framework consists of two stages, including the first for estimation the pose of the free parts using decoupled rotation representation and the second for estimation the pose of the constrained parts by predicting the joint parameters and states as replacements. Experimental results on ArtImage, ReArtMix, and RobotArm demonstrate the outstanding pose estimation performance for articulated objects. Strengths: 1.An end-to-end Category-level Articulated object Pose EstimatoR composed of two stages for free parts and constrained parts. 2.Free part pose estimation with decoupled rotation and constrained part pose estimation with joint state replacement. 3.Experimental results demonstrate that the proposed method achieves the less object pose estimation error in comparison with other methods on ArtImage, ReArtMix, and RobotArm. Weaknesses: 1.The proposed method is called EfficientCAPER, which indicates that the running efficiency is a key factor. However, the expression of this is lacked. For one thing, the reason that why the proposed method can achieve higher FPS than other methods should be explained more clearly. For another, the detailed discussion of running time is also suggested to add. 2.In Table 2, experiments on the effect of articulation pose canonicalization are conducted. However, different metrics (Joint State Error and 3D Scale Score) are used. It is suggested to use the same metrics (Rotation Error, Translation Error (m) and 3D IOU) as Table 1, which can prove the effect of articulation pose canonicalization more clearly. 3.The experimental results demonstrate obvious improvements in Tables 1,3,4. What is the key contribution to the improvements? It is suggested to add more ablation experiments to show this. Technical Quality: 3 Clarity: 3 Questions for Authors: 1.What is the main difference and challenge of category-level articulated object pose estimation in compared with category-level object pose estimation? 2.It is interesting that what is the performance of the category-level object pose estimation methods (like GPV-Pose) on ArtImage, ReArtMix, and RobotArm? Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The authors have adequately addressed the limitation. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your review, and for your thoughtful comments and questions. They will certainly help improve the revised paper. Below we respond in detail to your questions. *W1: The proposed method is called EfficientCAPER, which indicates that the running efficiency is a key factor. However, the expression of this is lacked. For one thing, the reason that why the proposed method can achieve higher FPS than other methods should be explained more clearly. For another, the detailed discussion of running time is also suggested to add. The analysis of inference time is reported in Section 5.2. More discussions are in below: (1) Compared to some dense prediction methods like NOCS, we do not perform point-by-point predictions, achieving lower computational costs and faster running speed; (2) Our method is end-to-end without any time-consuming post-procession like OMAD (It estimates coarse pose and uses a retrieval-based method to get refined results). W2: In Table 2, experiments on the effect of articulation pose canonicalization are conducted. However, different metrics (Joint State Error and 3D Scale Score) are used. It is suggested to use the same metrics (Rotation Error, Translation Error (m) and 3D IOU) as Table 1, which can prove the effect of articulation pose canonicalization more clearly. The joint state is the key target after canonicalization, which is a more intuitive metric in our proposed joint-centric perspective. We additionally provide estimated results of the constrained part with the same metrics as Table 1 in the main paper, it shows that the canonicalization module employed in the second stage is beneficial for estimating the pose of constrained part. \| Category \| APC \| Rotation Error (°) \| Translation Error (m) \| 3D IOU (%) \| \| ------------ \| --- \| ------------------- \| --------------------- \| ---------- \| \| Laptop* \| \| 5.1 \| 0.073 \| 84.8 \| \| \| ✔ \| 3.3 \| 0.071 \| 87.9 \| \| Eyeglasses \| \| 8.8, 9.7 \| 0.113, 0.094 \| 78.4, 79.2 \| \| \| ✔ \| 7.2, 5.8 \| 0.109, 0.089 \| 82.3, 84.3 \| \| Dishwasher \| \| 3.3 \| 0.096 \| 79.3 \| \| \| ✔ \| 2.6 \| 0.085 \| 83.9 \| \| Scissors \| \| 5.9 \| 0.112 \| 69.5 \| \| \| ✔ \| 5.1 \| 0.099 \| 69.2 \| \| Drawer \| \| 1.2, 1.2, 1.2 \| 0.102, 0.124, 0.100 \| 81.8, 80.5, 83.6 \| \| \| ✔ \| 1.2, 1.2, 1.2 \| 0.086, 0.090, 0.080 \| 87.1, 87.1, 88.4 \| \| *W3: The experimental results demonstrate obvious improvements in Tables 1,3,4. What is the key contribution to the improvements? It is suggested to add more ablation experiments to show this. As shown in Table 2 in the main paper, it is justified that canonicalization contributes greatly to the framework, so we conducted the ablation study for this module. Our pose canonicalization operation facilitates better learning of joint parameters and states. Additionally, we also conducted an ablation study in articulation pose modeling. We use GPV-Pose to directly output the poses of all parts of the category laptop under part-centric(i.e., treating each part of the articulated object as an independent rigid object), the result shows that our joint-centric modeling method is beneficial to the estimation of the constrained part. \| Category \| Pose Modeling Method \| Rotation Error ($^\circ$) \| Translation Error (m) \| 3D IOU(%) \| \|----------\|-----------------------\|--------------------------\|-----------------------\|-----------\| \| Laptop* \| Part-centric \| 10.5, 12.7 \| 0.205, 0.275 \| 49.1, 46.3\| \| \| Joint-centric \| 2.3, 3.3 \| 0.065, 0.071 \| 88.2, 87.9 \| \| Furthermore, we explore the effect of the backbone. We have conducted an ablation study on category laptop to estimate the pose of free part , using the MLP, 3D-GC, HS-Encoder as backbones respectively. The results in the table below show that the choice of HS-Encoder is effective. \| Category \| Backbone \| Rotation Error ($^\circ$) \| Translation Error (m) \| 3D IOU(%) \| \|----------\|------------\|---------------------------\|-----------------------\|-----------\| \| Laptop \| MLP \| 20.5 \| 0.203 \| 23.8\| \| \| 3D-GC \| 7.5 \| 0.099 \| 76.3\| \| \| HS-Encoder \| 4.8 \| 0.073 \| 85.4\| \| *Q1: What is the main difference and challenge of category-level articulated object pose estimation in compared with category-level object pose estimation?* Estimation complexity: Compared to rigid objects can be represented by a single pose, describing their position and orientation in 3D space. Category-level articulated object pose estimation involves objects with articulated parts that can move relative to each other while obeying kinematic constraints. This adds complexity as the pose estimation not only involves determining the overall object pose but also capturing the poses of its articulated parts and joint parameters. Severe self-occlusion: Category-level articulated object pose estimation will increase dimensionality and variability which may cause self-occlusion. Severe self-occlusion will lead to poor performance, especially where smaller parts are obscured by larger parts from certain camera views. As discussed in section 4.2 in the main paper, the joint-centric pose modeling method can effectively alleviate the issue. *Q2: It is interesting that what is the performance of the category-level object pose estimation methods (like GPV-Pose) on ArtImage, ReArtMix, and RobotArm?* We have conducted this experiment(shown in Table in W3), directly regressing pose in part-centric modeling method has inferior performance, since the part-centric pose modeling method does not take count into kinematic constraints.	Summary: This paper introduces a new approach for estimating the pose of category-level articulated objects. The proposed framework, EfficientCAPER, aims to address the challenges of kinematic constraints, self-occlusion, and optimization requirements. The method eliminates the need for optimization post-processing by utilizing a joint-centric pose modeling mechanism. The approach is evaluated on three diverse datasets: ArtImage, ReArtMix, and RobotArm, demonstrating its effectiveness and generalization ability. Strengths: 1. EfficientCAPER introduces a joint-centric articulation pose modeling mechanism, which differs from traditional part-centric approaches. This mechanism allows the learning of each part’s pose as a joint state representation, improving the network's ability to handle self-occlusion and kinematic constraints. 2. The method splits the pose estimation process into two stages. First, it estimates the pose of the free part using a decoupled rotation representation. Then, it canonicalizes the input point cloud to estimate the poses of constrained parts by predicting joint parameters and states. 3. EfficientCAPER eliminates the need for intermediate variable estimation or optimization procedures, making the pose estimation process more efficient and straightforward. Weaknesses: 1. The method heavily relies on the accuracy of the free part pose estimation. Any error in this stage can propagate and affect the estimation of the constrained parts. 2. Although the method is tested on three datasets, the datasets might not cover all possible variations and complexities of real-world articulated objects. This might limit the generalizability of the method to new, unseen categories. 3. There is no clear definition of what constitutes a free part. The concept appears to be relative, and each part could potentially be considered a free part depending on the context (like the two parts of scissors). This ambiguity might complicate the learning process. 4. The difference between a free part and a root part is not well-defined, and they seem to be essentially the same. 5. it is not clear in the method section if the free part is pre-defined. As in the ablations, there are inputs with free-part only. Technical Quality: 3 Clarity: 3 Questions for Authors: Please check the weakness w.r.t free part. Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: NA Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We appreciate that the reviewer understands and recognizes the contributions of this work. We address the main concerns as follows. *W1: The method heavily relies on the accuracy of the free part pose estimation. Any error in this stage can propagate and affect the estimation of the constrained parts. As shown in Table 1, our method has earned satisfactory results in estimating poses both the free part and the constrained part. While our method does exhibit cumulative errors, even in datasets of high complexity such as RobotArm, we have also achieved notably superior results compared to the baseline approaches. W2: Although the method is tested on three datasets, the datasets might not cover all possible variations and complexities of real-world articulated objects. This might limit the generalizability of the method to new, unseen categories. We follow the suggestion from A-NCSH that the number of rigid parts and kinematic structures is constant for all the objects in the same category, and the goal is to estimate the pose of unseen objects within the category. We consider objects in the physical world to generally fall into two categories: rigid objects and articulated objects. Articulated objects can be further classified into two types—those with rotational joints and those with prismatic joints. Our datasets already include both types of articulated objects, including highly complex ones like robot arms. Therefore, our method can generalize to both kinds of articulated objects within the same category. W3: There is no clear definition of what constitutes a free part. The concept appears to be relative, and each part could potentially be considered a free part depending on the context (like the two parts of scissors). This ambiguity might complicate the learning process. For the pose estimation of the free part in the first stage, we input all parts of the articulated object together, treating them as a rigid object without distinguishing between the free and constrained parts. Since all the parts can rotate around each other interchangeably, for simplicity, we pre-define the free part according to the joint location (this configuration is interchangeable), all objects share the same setting within the intra-category. For the pose estimation of the constrained part in the second stage, we first canonicalize the point clouds via the prediction from stage 1 to align the free part. Then the network tries to learn the joint state, which is distinguished from canonical space and rest state(please see Figure 1 in the attached PDF). The Parts with obvious movement are considered constrained parts, whose poses are optimized by our joint-centric modeling way. W4: The difference between a free part and a root part is not well-defined, and they seem to be essentially the same. Please check Figure 2 in the attached PDF, we show the main difference between a free part and a root part. It predominantly suggests two ways in defining root part for articulation structure: Definition I: the root part is defined as the world, and there is a fixed joint connecting the world to the base part (this definition is known in PartNet-Mobility dataset from SAPIEN[1]). In this definition, the root part is a virtual part that contains no physical parts. Definition II: the root part is directly defined as the base part known in AKB-48 dataset [2]. In this work, the free part is more similar to definition II of AKB-48 in terms of the physical base part in the articulation structure, but the differences are: (1) we name the part type following the kinematic motion type, i.e. we assume there is a free joint accompanying with the free part. So every part's pose in the articulated object can be converted to the task that how to estimate the joint parameters and state. (2) "free" means it can move at arbitrary position and rotation in the 3D space, while "constrained" means the part's motion is limited to the free part's motion. W5: It is not clear in the method section if the free part is pre-defined. As in the ablations, there are inputs with free-part only. Free part and constrained part is our proposed articulation modeling way in this work, where the free part is pre-defined for each category. As it is stated in our work, there are two stages to solving the articulation pose estimation. The first one is to canonicalize the object by predicting the free part's pose and the second one is to predict the joint states of constrained parts (since it is obviously easy to predict joint state in canonical space). In this case, we find that only free part input in the first stage might cause symmetry problem that affects the canonicalization performance. Thus, we provide an ablation study in A.5.1, that shows when the whole object is inputted, the free part pose estimation can be achieved better so the canonicalization is more accurate. Note that in this ablation study, we only investigate the effect of input on the first stage. [1] SAPIEN: A SimulAted Part-based Interactive ENvironment. CVPR. 2020. [2] AKB-48: A Large-scale Real-world Articulated Object Knowledge Base. CVPR. 2022. --- Rebuttal Comment 1.1: Comment: Thank you for the rebuttal and the detailed explanations provided. While I appreciate the clarifications, I still have concerns regarding the definition of free part and how to define it for category. Given these concerns, I tend to maintain my original rating. That said, I am OK if other reviewers strongly advocate for the acceptance of this paper. --- Reply to Comment 1.1.1: Comment: Thanks for your reply, here, we give a clearer definition of the free part and how it works for category. Definition: The free part used in this work mainly refers to a relative concept, in other words, we divide the K* rigid parts of an articulated object into 1 free part and K-1 constrained part. The free part enjoys 3D of freedom transformation, while the constrained part can only conduct relative motion (1D of freedom transformation) under the free part. For each category, we tend to choose the part that is semantically the base as the free part, and this definition follows a uniform setting across the intra-category. Thank you again for your time and effort. If our rebuttals do not address your concerns to some extent, we would be happy to have further discussions. Your feedback is an important reference for us to improve the quality of our paper, and we attach great importance to it. We look forward to your reply.	Summary: This paper introduces an end-to-end framework designed for category-level articulated object pose estimation. Specifically, it addresses the complexity of articulated objects by using a joint-centric approach that divides the task into two stages: estimating the pose of free parts and then the constrained parts. The method is evaluated on three datasets, demonstrating its effectiveness. Strengths: 1.The paper is well-organized and easy to follow. 2.It is interesting to estimate the category-level articulated object pose from the joint-centric perspective. 3.The proposed method is shown to be effective on different datasets. Weaknesses: 1.It is not clear to me how the free part is defined. Actually, the “free” and “constrained” are defined relatively and can be changed in some sense. Will this cause the ambiguity in the estimation? 2.In the paper, it is claimed that the part-centric can fix the self-occlusion issues, but I didn’t fully understand how the proposed “Joint-Centric Articulation Pose Modeling“ can handle this effectively. 3.The framework takes a cascaded architecture, and I am wondering how the free part pose estimation in the first stage will affect the following constrained part estimation. 4.For the ArtImage dataset, the translation estimation of the proposed method is not stable, and for the “Scissors” case, its performance is much worse than others in terms of rotation and translation errors. More expatiation is expected. Technical Quality: 3 Clarity: 3 Questions for Authors: Please refer to the weakness part. Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The limitations are discussed in the supplementary material. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your valuable comments and evaluation on our submission. Please find our response below. *W1: Unclear definition of the free part with relative change against the constrained part. The "free" and "constrained" parts are indeed interchangeable, however, this does not cause ambiguity in the estimation process. Concretely, for the pose estimation of the free part, all parts of the articulated object will be input together, treating them as a rigid object without distinguishing between the free and constrained parts. Since all the parts can rotate around each other interchangeably, for simplicity, we pre-define the free part according to the joint location(this configuration is interchangeable). In the second stage, we first perform pose canonicalization via the prediction from stage 1 to align the free part. Then the network tries to learn the joint state, which is distinguished from canonical space and rest state. The Parts with obvious movement are considered as constrained parts, whose poses are optimized by our joint-centric modeling way (please see Figure 1 in the attached PDF). W2: It is claimed that the part-centric can fix the self-occlusion issues, but I didn’t fully understand how the proposed “Joint-Centric Articulation Pose Modeling“ can handle this effectively. In the proposed joint-centric modeling, the degrees of freedom for the constrained part are reduced from 3D to 1D (due to kinematic constraints from the joint), and this 1D constraint information is well reflected in the joint state. Therefore, even in the cases of severe self-occlusion, the network can still learn the joint state from few point clouds, regressing 1D directional information naturally performs better than regressing 3D direction information, achieving superior performance. W3: The framework takes a cascaded architecture, and I am wondering how the free part pose estimation in the first stage will affect the following constrained part estimation. As mentioned in Section 4.4 in the main paper, this strategy can be conducive to the following aspects: (1) We use the predicted pose of free part to align the free part, transforming the joint state estimation task from camera space to canonical space, making sure the network can effectively learn the joint state in canonical space. This is a simple and efficient way but still under-studied in existing works (see reviewer Gf45); (2) The canonicalization process applied to the point cloud eliminates the effects of varying joint configurations in movable rigid parts. This process reduces uncertainty, enhances stability and accuracy, and provides both shape and kinematic priors, significantly aiding in the regression of joint states. The ablation study in Table 2 validates these advantages. W4: For the ArtImage dataset, the translation estimation of the proposed method is not stable, and for the “Scissors” case, its performance is much worse than others in terms of rotation and translation errors. More explanation is expected*. Estimating translation in category-level pose estimation is challenging. As shown in Table 1, the translation error of constrained part is higher than free part, since it relies on the estimation of free part and joint parameters. However, compared to baselines achieving state-of-the-art performance only for specific categories, our method can achieve comprehensive performance in each category. For category scissors, typically exhibit complex shapes and partially symmetrical features. This complexity makes it challenging to accurately capture the details of scissors, while symmetry may lead to multiple possible poses.	Rebuttal 1: Rebuttal: Dear Reviewers, Please see the attached PDF for a one-page PDF with a summary of added experimental figures. We are appreciated by the positive comments of the reviewers on the novelty and significance of our method (Reviewers UxV6, UsR2, cXQd, Gf45), readability (Reviewer UxV6), effectiveness (Reviewers UxV6, UsR2, Gf45), and notable improvements compared with state-of-the-art methods (Reviewers cXQd, Gf45). We provide point-to-point responses to each reviewer. We look forward to engaging in further discussion with the reviewers, answering questions, and discussing improvements. Pdf: /pdf/f10c37b3b6870561700b79ba1705693263753a80.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
LISA: Layerwise Importance Sampling for Memory-Efficient Large Language Model Fine-Tuning	Accept (poster)	Summary: This paper proposes an parameter-efficient finetuning (PEFT) method, LISA, that only finetunes some sampled layers while freezing the rest for some certain iterations, and resample the finetuned layers later. To validate LISA's effectiveness, the authors benchmark it on various tasks, like instruction-following, medical QA, math problems, across various sizes of LLMs. The results show that LISA shares a similar GPU memory consumption as LoRA, 1.5x speedup than LoRA for training, better or comparable to LoRA and Full Finetuning for various tasks. The main contributions of this paper are: 1. The proposed method is simple, easy to be applied; 2. The experiments are thorough and consistent to support LISA's effectiveness. Strengths: 1. The paper is well-written and easy to follow; 2. The proposed method, LISA, is simple and practical; 3. The experiments are thorough, and the results are better than the baselines. Weaknesses: 1. Lack of novelty. LISA is very similar to the method proposed in the paper [46] in the references. [46] proposes to pretrain a model layer-by-layer, while LISA shuffles the training order and finetune some for a period. Such novelty is not enough. In addition, the authors don't apply their finding, i.e. skewed weight-norm distribution across layers, to design a better sampling method. Instead, they apply uniform sampling, which makes the finding less relevant. BTW, the finding is very similar to a previous work [2] (Figure 4). 2. Lack of experimental details about the optimizer states, and unfair comparison. Compared to LoRA, LISA basically finetunes the whole model, which means the optimizer states stay the same as Full Finetuning. Since the oprimizer states occupy as twice memory as the model's, I assume LISA offload them to CPU. This part is not explicitely stated, nor in the limitation section. When comparing the training time, the authors only compare the forward and backward time (Figure 4), and ignore the latency introduced by the offloaded optimizer states, which is unfair since LoRA doesn't need to offload. 3. Lack of important ablation study. The benefit of LISA is from the training of the whole model in a layer-by-layer manner. Actually, we can also apply LISA to LoRA. I.e. we can use a very large size LoRA and only finetune the sampled LoRAs. In this way, LoRA has a larger number of trainable parameters, which might close the gap between LISA and LoRA. 4. Unintuitive results without further analysis. The most surprising result is that LISA outperforms full finetuning quite often, which is against our intuition. It also casts a doubt: how do you choose the hyper-parameters (like Table 15)? And what is the error bar for the main results. [1] A fast learning algorithm for deep, Geoffrey E. Hinton, Simon Osindero, Yee-Whye Teh [2] Parameter-Efficient Fine-Tuning without Introducing New Latency, Baohao Liao, Yan Meng, Christof Monz Technical Quality: 3 Clarity: 2 Questions for Authors: See weakness. Confidence: 4 Soundness: 3 Presentation: 2 Contribution: 2 Limitations: The authors discuss in the Limitation section. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thanks for the feedback. To address the raised concerns, we have provided additional clarifications and experiments, the details are listed as follows, Weakness 1: Lack of novelty. > LISA is very similar to the method proposed in the paper [46] in the references... In addition, the authors don't apply their finding, i.e. skewed weight-norm distribution across layers, to design a better sampling method. Instead, they apply uniform sampling, which makes the finding less relevant. BTW, the finding is very similar to a previous work [2] (Figure 4). Thanks for the valuable comments. We would like to emphasize that LISA's major novelty lies in its successful applications in LLMs, which significantly reduce memory consumption and improve the training speed of LLMs. In contrast, [46] is a paper in 2006 that focused on training of deep belief nets. Their settings are vastly different. Regarding the non-skewed weight-norm distribution claim, this may be a misunderstanding. The distribution in LISA is indeed skewed, as the embedding and linear head layers are always unfrozen during the training. We will add additional clarifications in Section 3.2 to make it clearer for readers. Concerning similarity to Figure 4 in [2], again, their settings are different, as the observations of [2] is made in encoder-only models, e.g. Roberta, while LISA focuses on decoder-only LLMs. In addition, we would like to emphasize again that the observation itself only serves as a motivation of our work, LISA's main novelty still lies in its successful applications in LLMs. Weakness 2: Lack of experimental details about the optimizer states, and unfair comparison > Compared to LoRA, LISA basically finetunes the whole model, which means the optimizer states stay the same as Full Finetuning. Since the oprimizer states occupy as twice memory as the model's, I assume LISA offload them to CPU. This part is not explicitely stated, nor in the limitation section. When comparing the training time, the authors only compare the forward and backward time (Figure 4), and ignore the latency introduced by the offloaded optimizer states, which is unfair since LoRA doesn't need to offload. Thanks for the feedback. We would like to kindly remind the reviewer that there may be some miscommunications, which lead to the false impressions here. In our implementation for all the experiments, the model will be reinitialized every time, so the optimizer is only applied to the trainable parameters and has the same or less memory consumption as LoRA, just as shown in Table 1 of the paper. Because of this, there is no need to offload the optimizer states to CPUs, let alone the latency of offloading optimizer states for LISA. We will emphasize these implementation details in our papers to avoid misunderstandings. Weakness 3: LISA + LoRA experiment. > The benefit of LISA is from the training of the whole model in a layer-by-layer manner. Actually, we can also apply LISA to LoRA. I.e. we can use a very large size LoRA and only finetune the sampled LoRAs. In this way, LoRA has a larger number of trainable parameters, which might close the gap between LISA and LoRA. Thank you for the suggestion. It is valid to combine LoRA with LISA. But if this approach works, logically it is just another proof of the effectiveness of LISA, not the opposite. Actually, LISA is orthogonal to most low-rank techniques, and there have already been published papers that combine LISA with GaLore [3]. Since the combination of those techniques already merits another paper, we intended to leave that part for future works. In addition, we have evidence showing that this simple combination does not work easily. As demonstrated in the table below, LoRA + LISA achieves similar performance as LoRA, but still significantly worse than LISA. The detailed results can be found in the attached rebuttal PDF. \| Model \| Method \| MMLU (5-shot) \| AGIEval (3-shot) \| WinoGrande (5-shot) \| \|----------------\|----------\|--------------------\|-----------------------\|-----------------------\| \| LLaMA-2-7B \| Vanilla \| 45.87 \| 25.69 \| 74.11 \| \| \| FT \| 45.66 ± 0.09 \| 27.02 ± 0.10 \| 75.06 ± 0.13 \| \| \| LoRA \| 45.50 ± 0.07 \| 24.73 ± 0.04 \| 74.74 ± 0.09 \| \| \| GaLore \| 45.56 ± 0.05 \| 24.39 ± 0.11 \| 73.32 ± 0.12 \| \| \| LISA + LoRA \| 45.34 ± 0.41 \| 25.55 ± 0.66 \| 72.64 ± 0.24 \| \| \| LISA \| 46.21 ± 0.12 \| 26.06 ± 0.08 \| 75.30 ± 0.11 \| Weakness 4: Unintuitive results. > The most surprising result is that LISA outperforms full finetuning quite often, which is against our intuition. It also casts a doubt: how do you choose the hyper-parameters (like Table 15)? And what is the error bar for the main results. Thank you for the question. The intuition of this surprising effect can be attributed to the implicit regularization effect of LISA's layerwise freezing strategy, as mentioned in lines 245-250, where LISA and LoRA favor different types of tasks, implying the regularization tendency under different freezing strategies. The hyperparameter search process can be found in Appendix B.3, and we have conducted additional multi-trial experiments to address the raised concerns, please refer to the attached PDF for detailed results. > Reference: > [1] Geoffrey E. Hinton, Simon Osindero, and Yee-Whye Teh. A fast learning algorithm for deep belief nets. Neural Computation, page 1527–1554, Jul 2006. > [2] Liao, Baohao, Yan Meng, and Christof Monz. "Parameter-efficient fine-tuning without introducing new latency." arXiv preprint arXiv:2305.16742 (2023). > [3] Li, Pengxiang, et al. "OwLore: Outlier-weighed Layerwise Sampled Low-Rank Projection for Memory-Efficient LLM Fine-tuning." arXiv preprint arXiv:2405.18380 (2024). --- Rebuttal Comment 1.1: Comment: Thank you for the clarification and new eperiments. I'm willing to increase my score. --- Reply to Comment 1.1.1: Title: Thanks very much for your positive feedback! Comment: Dear Reviewer kABp, We sincerely thank you for your positive feedback and the time you dedicated to reviewing our rebuttal. It brings us great joy to learn that our response has addressed your concerns and contributed to increasing the score from 4 to 5. As the score is still borderline, we are wondering if there are any major concerns regarding our current revision. It would be our great pleasure to provide further clarifications and results to address any additional doubts. Your suggestions really help a lot to improve our work and make the justification of our method more complete. We also greatly appreciate your recognition of the simplicity of our algorithm, the quality of our paper, and the contribution it makes. Once again, we would like to express our appreciation for your valuable comments during the reviewing process. Best regards, Authors. --- Rebuttal 2: Title: Thank you very much for the valuable feedback! Comment: Dear Reviewer kABp, Thank you very much for your valuable feedback! We truly hope that our new results can help clarify the concerns. We appreciate the time you have spent on reviewing our paper and providing us with the constructive comments. Please let us know if there are any concerns remaining. If you find our response to have addressed your concerns, it would mean very much to us if you could consider raising the score.	Summary: This paper proposes a lighter alternative to LoRA, LISA, based on using importance sampling to periodically choose a subset of layers to optimize. It is motivated by observations on the norm of parameter updates made during training with LoRA, compared to full parameter fine-tuning. Experiments are made comparing LISA with LoRA and full parameter fine-tuning on memory efficiency, and moderate/large fine-tuning and continual pre-training. Supplementary experiments are made on the hyperparameters of LISA and training sensitivity. Results show that LISA uses less memory than LoRA and achieves better results on most tasks. The paper also presents a discussion including theoretical properties of LISA. Strengths: - The method proposed by this paper is of obvious interest for efficient training. - The experimental results presented are convincing, and seem to indicate that the method is promising. Weaknesses: - The main issue I have with this paper is that the approach presented does not seem to actually use Importance sampling: the weights of the $E$ and $H$ layers are fixed to $1.0$, and the intermediate layers have uniform weights. Besides, the presentation of the distribution and rates used in Section 3.2 is rather unclear. Technical Quality: 3 Clarity: 3 Questions for Authors: - While the choice of that sampling distribution seems motivated by observation on LoRA, there seems to be shortcuts taken, particularly on fixing $E$ and $H$. Is there anything more to motivate this ? Did you try more extensive experiments with only $E + H$ ? - Can you relate your approach with those mentioned in Section 2.2, focusing on layer-selection ? Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: - The limitations have been addressed. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We would like to offer our sincere thanks for all your constructive comments and recognition of our contributions. We really appreciate it. Here we will address the raised concerns one by one. Weakness: Sampling Strategy. > The main issue I have with this paper is that the approach presented does not seem to actually use Importance sampling: the weights of the $E$ and $H$ layers are fixed to $1.0$, and the intermediate layers have uniform weights. Besides, the presentation of the distribution and rates used in Section 3.2 is rather unclear. Thank you for the valuable feedback! Importance sampling serves as the motivation of our algorithm, which emphasizes the difference between layers. To avoid misunderstandings, we will definitely clarify that in our revisions. Regarding the presentation issue in Section 3.2, we will add the description for different layers accordingly, such as $E$ and $H$, to make it clearer. Question 1: Fixing $E + H$ layers. > While the choice of that sampling distribution seems motivated by observation on LoRA, there seems to be shortcuts taken, particularly on fixing $E$ and $H$. Is there anything more to motivate this ? Did you try more extensive experiments with only $E+H$ ? Thank you for your insightful question! Yes. Besides the motivation we mentioned in the paper, we also found that fixing $E+H$ significantly hurts the performance, indicating the importance of those two layers. To further understand the effect of $E+H$ layers, we conducted additional experiments on LISA with only $E+H$ layers: \| Model \| Method \| MMLU (5-shot) \| AGIEval (3-shot) \| WinoGrande (5-shot) \| MT-Bench \| \|----------------\|----------------\|---------------\|------------------\|---------------------\|---------------\| \| TinyLlama \| Vanilla \| 25.50 \| 19.55 \| 59.91 \| 1.25 \| \| \| FT \| 25.62 ± 0.10 \| 21.28 ± 0.07 \| 62.12 ± 0.15 \| 2.21 ± 0.16 \| \| \| LISA ($E+H$) \| 25.49 ± 0.14 \| 20.75 ± 0.21 \| 60.43 ± 0.19 \| 2.18 ± 0.31 \| \| \| LISA \| 26.02 ± 0.13 \| 21.71 ± 0.09 \| 61.48 ± 0.08 \| 2.57 ± 0.25 \| \|\|\|\|\|\|\| \| Mistral-7B \| Vanilla \| 60.12 \| 26.79 \| 79.24 \| 4.32 \| \| \| FT \| 61.70 ± 0.13 \| 28.07 ± 0.12 \| 78.85 ± 0.12 \| 4.64 ± 0.12 \| \| \| LISA ($E+H$) \| 61.49 ± 0.12 \| 27.66 ± 0.07 \| 77.93 ± 0.11 \| 4.51 ± 0.27 \| \| \| LISA \| 62.09 ± 0.10 \| 29.76 ± 0.09 \| 78.93 ± 0.08 \| 4.85 ± 0.14 \| \|\|\|\|\|\|\| \| LLaMA-2-7B \| Vanilla \| 45.87 \| 25.69 \| 74.11 \| 3.29 \| \| \| FT \| 45.66 ± 0.09 \| 27.02 ± 0.10 \| 75.06 ± 0.13 \| 4.75 ± 0.16 \| \| \| LISA ($E+H$) \| 45.88 ± 0.12 \| 25.82 ± 0.15 \| 73.48 ± 0.22 \| 4.63 ± 0.35 \| \| \| LISA \| 46.21 ± 0.12 \| 26.06 ± 0.08 \| 75.30 ± 0.11 \| 4.94 ± 0.14 \| As shown in the Table, LISA ($E+H$) can achieve reasonable performance but is still no match for LISA. Question 2: Layer-selection related works. > Can you relate your approach with those mentioned in Section 2.2, focusing on layer-selection ? Thanks for your constructive comments! Compared with the mentioned works, LISA's simple selection strategy makes it much easier to understand and implement, which reduces theoretical difficulties in analysis and engineering difficulties in practice. In contrast, Autofreeze [1] adopts a heuristic rule based on gradient norm changes to select layers, which is difficult to analyze in theory and not quite easy to control in practice. Autofreeze also focuses more on encoder-only models such as BERT, while LISA emphasizes its applications in LLMs. Freezeout [2] and SmartFrz [3] are facing the same issues as well, which progressively freeze layers, or adopt a NN-based predictor to guide the selection respectively. These heuristic-driven approaches are hard to obtain theoretical guarantees, and their empirical properties may vary as the backbone network changes. In addition, both Freezeout and SmartFrz focus on Computer Vision tasks, while LISA is adopted mostly in LLM settings. We will definitely include the aforementioned discussions in our revisions. > Reference > [1] Liu, Y., Agarwal, S., & Venkataraman, S. (2021). Autofreeze: Automatically freezing model blocks to accelerate fine-tuning. arXiv preprint arXiv:2102.01386. > [2] Brock, A., Lim, T., Ritchie, J. M., & Weston, N. (2017). Freezeout: Accelerate training by progressively freezing layers. arXiv preprint arXiv:1706.04983. > [3] Li, S., Yuan, G., Dai, Y., Zhang, Y., Wang, Y., & Tang, X. (2024). Smartfrz: An efficient training framework using attention-based layer freezing. arXiv preprint arXiv:2401.16720. --- Rebuttal Comment 1.1: Comment: I would like to thank the authors for their rebuttal, the clarifications and the supplementary results ! I have updated my Soundness rating, and maintain my global rating recommanding acceptance. --- Reply to Comment 1.1.1: Title: Thank you so much for your valuable feedback! Comment: Dear Reviewer K468, We sincerely appreciate your time in reviewing our rebuttal and examining our new results. We are delighted to learn that our response successfully addressed your concerns and contributed to an increase in the _Soundness_ rating. Your constructive advice is really helpful in enhancing the completeness and quality of our paper! Once again, we sincerely appreciate your valuable feedback and consideration. Best regards, Authors	Summary: This paper proposes a new optimization algorithm called Layerwise Importance Sampled AdamW (LISA) for large language model (LLM) fine-tuning. The authors observe the skewed weight norms across different layers in the Low-Rank Adaptation (LoRA) method and use this observation to develop LISA, which randomly freezes certain layers during optimization. Experimental results show that LISA outperforms LoRA and full parameter training in various downstream fine-tuning tasks, demonstrating its effectiveness and memory efficiency. Strengths: (1) The paper addresses an important problem in the field of large language models, which is the high memory consumption during training. The proposed LISA algorithm provides a memory-efficient alternative to the existing LoRA method. (2) The authors provide a clear motivation for their work and thoroughly analyze the layerwise properties of LoRA, which leads to the development of LISA. This analysis adds valuable insights to the field. (3) The experimental results demonstrate the superiority of LISA over LoRA and full parameter training in various downstream tasks. The authors provide detailed comparisons and evaluations, supporting the claims made in the paper. (4) The paper is generally well-written and easy to follow. (5) The design of the proposed "Layerwise Importance Sampling AdamW" is quite interesting and novel, which may be generalized in other related LLM's variants. Weaknesses: (1) I am curious whether the authors will open-source their implementation? Since efficient training techniques are important to this field, it would be beneficial to have an easy-to-use implementation. In addition, it would be helpful if the authors provide more information on their hyperparameter tuning strategy in the experiments, like how do you choose the best hyperparameters? (2) The some parts of the writing and layout needs improvement. For example, there are too many capitalized letters like line 6 "Parameter Efficient Fine-Tuning". I do not see any reason to capitalize every words. In addition, the figures should be re-organized like Figure 2. (3) The authors seem to define 65B as a boundary for small language models and large language model (see line 56). Just curious, are there any justification or relevant claims? Since there are more and more small language model research nowadays and they are mainly focusing on 1B-7B, it would be interesting to have a clear definition in our community. Technical Quality: 3 Clarity: 3 Questions for Authors: None Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 4 Limitations: The limitation is fine with me. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We would like to offer our sincere thanks for all your constructive comments and recognition of our contributions. We really appreciate it. Here we will address the raised concerns one by one. Weakness 1: Open-Source Implementation. > I am curious whether the authors will open-source their implementation? Since efficient training techniques are important to this field, it would be beneficial to have an easy-to-use implementation. In addition, it would be helpful if the authors provide more information on their hyperparameter tuning strategy in the experiments, like how do you choose the best hyperparameters? Thank you for your questions! The LISA algorithm has been integrated into several third-party libraries, such as LMFlow [1] and Axolotl [2], which have almost full support for single-GPU settings, and basic support for multi-GPU settings. The full support for multi-GPU settings will be available soon. For hyperparameters, we conducted extensive hyperparameter searches for learning rates for SFT, LoRA, and LISA, as well as for $K$ and $\gamma$ for LISA. Details can be found in Appendix B.3 of the paper. Weakness 2: Writing and layout improvement. > The some parts of the writing and layout needs improvement. For example, there are too many capitalized letters like line 6 "Parameter Efficient Fine-Tuning". I do not see any reason to capitalize every words. In addition, the figures should be re-organized like Figure 2. We appreciate your feedback and will definitely improve these aspects in our revisions. Specifically, we will correct the unnecessary capitalization, such as in "Parameter Efficient Fine-Tuning," and reorganize the figures, including Figure 2, to enhance clarity and readability. Weakness 3: Definition of small language models. > The authors seem to define 65B as a boundary for small language models and large language model (see line 56). Just curious, are there any justification or relevant claims? Since there are more and more small language model research nowadays and they are mainly focusing on 1B-7B, it would be interesting to have a clear definition in our community. In our experiment, we classify language models that can fit within a single 8xA40 (48GB) server as small language models ($\le$ 65B). This classification is based on practical considerations of model deployment and resource requirements. We will provide a more detailed description and clarify that in our revisions. By the way, to the best of our knowledge, 2B is normally the boundary for mobile LLMs, and 8B normally represents the boundary for single-GPU-trainable LLMs. > Reference: > [1] Shizhe Diao, Rui Pan, Hanze Dong, KaShun Shum, Jipeng Zhang, Wei Xiong, and Tong Zhang. 2024. LMFlow: An Extensible Toolkit for Finetuning and Inference of Large Foundation Models. In Proceedings of the 2024 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies (Volume 3: System Demonstrations), pages 116–127, Mexico City, Mexico. Association for Computational Linguistics. https://github.com/OptimalScale/LMFlow > [2] Axolotl: https://github.com/axolotl-ai-cloud/axolotl	null	null	Rebuttal 1: Rebuttal: Thank you very much for all the constructive comments and suggestions! To further address every reviewer's concerns, we have included additional results in the attached PDF file. Please kindly refer to the file for more details. Pdf: /pdf/fa3c4e412a2f589b4f18b55046ec332437040868.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Transformers Learn to Achieve Second-Order Convergence Rates for In-Context Linear Regression	Accept (poster)	Summary: The authors show that when trained on ICL tasks encoding a regression problem, the layers of a transformer implement an implicit higher order optimization method. They contrast this with prior work on this subject that suggest that the transformer in this setting implicitly implements a preconditioned gradient method. They also construct a transformer capable of implementing this proposed algorithm. Strengths: There appears to be a better match between the layers of the transformer and iterations of iterative newtons method as compared to the iterations of the gradient methods they consider. Weaknesses: 1. In the comparisons to Iterative Newton: If the Transformer had 40 layers do you expect that each layer would implement a single iteration or that it would match more layers of IN overall? In other words, is there something fundamental about taking 3 layers together to compute one iteration? 2. Does the transformer also match the higher order methods when solving other problems? That is, if the objective was not OLS for linear regression? The problem with studying only linear regression is that subsequent layers interpolating between 0 and the OLS solution is somewhat what one would “expect”. Not matching with GD fits into this interpretation because GD exhibits an oscillatory behavior for ill-conditioned problems that an “interpolator” would have no reason to match. 1. What happens to Appendix A.3 when we compare the transformer to the appropriately preconditioned GD? 2. Figure 15 is only an illustration of the best matching iterations. I have two concerns with this. The construction given in the paper is theoretical and not necessarily the one used by actual transformers (it is also deeper than 3 layers). I think this reduces the impact of saying that iterative newton matches every third layer of the transformer, since even GD is matching (though with a varying number of iterations). And the match quality of GD after those varying number of iterations is not much worse. Technical Quality: 3 Clarity: 3 Questions for Authors: 1. What happens to the covariates across layers? To implement these algorithms, the transformer needs to implicitly compute some second order moment of the original data, but at each layer can only work with the “modified covariates” at that layer. It would be interesting if these quantities somehow turned out to be invariant across layers. 2. Is it fair to say that ReLU activations don’t hurt performance? Softmax seems to be pretty crucial, or why would people go to the trouble of implementing something that has a larger run-time? Even most of the works cited only say it isn’t much worse, sometimes. Also, it seems softmax is used for the experiments in this work anyway, and ReLU is only used for some of the layers in the construction. imo this is not a big issue, just pointing it out. 3. I dont understand the description of the Iterative Newtons Method (Page 3). It seems $S$ is an empirical covariance, and then $M_k$ is just a function of $S$. What is the purpose of computing the intermediate $\hat{w}_k^{\text{Newton}}$ (other than to show that they match the Transformer)? Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: Yes Flag For Ethics Review: ['No ethics review needed.'] Rating: 3 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for detailed comments and suggestions. We are pleased that the reviewer agrees that our experiments show a better match between the layers of the transformer and iterations of iterative newtons than when compared with gradient descents. ## Matching between Transformer layers and Iterative Newton steps We believe this is some degree of misunderstanding by the reviewer. As shown in the heatmap in Figure 3 (left), one Transformer layer is implementing 3 iterations of Newton steps, not the other way around as the reviewer suggested. The reviewer can also take a look at Figure 21 on a 24-layer transformer model, where each layer is approximately implementing one Newton step until convergence. ## Generalization to other problems We believe that linear regression is the right starting point to understand how transformers perform in-conext learning. It would be interesting to see the extensions to logistic regression, classification, and even non-convex problems. However, this is beyond the scope of this paper. ## Not matching GD is expected Garg et. al. [1] empirically showed that Transformers, when performing in-context linear regression, match the ordinary least-squares (OLS) solution. However, what remains unclear and what is the main focus of this paper, is how Transformers converge to the OLS solution. We wouldn’t say not matching GD is expected because many existing work claims that Transformers converge to the OLS solution via Gradient Descent (GD) [2,3,4,5]. The main contribution of this work is to show that (1) empirically, Transformers can converge exponentially faster than GD, which suggests that they emulate higher-order optimization methods; (2) theoretically, there is a construction of Transformers to implement a particular higher-order optimization method – the Iterative Newton’s method. ## Comparison with Precondition GD We would like to emphasize that even with well-conditioned data, our experiments show Transformers and Newton converge exponentially faster than Gradient Descent. Under the well-conditioned case, preconditioning would not do anything because the preconditioner (inverse of the Hessian matrix) is identity. Even under the ill-conditioned case, where the preconditioner is not identity, one needs to compute the inverse of the Hessian matrix first, where such inverse computation is already computationally heavy and involves second-order information, and to compute the inverse efficiently, one needs to use the Iterative Newton’s Method. In our setup, the eigenbasis of the covariance matrix $\Sigma$ is sampled at random, so there is no way the Transformer stores the preconditioner during training so they need to compute the inverse at ICL inference time. ## Weakness 2.2: mismatch between theoretical construction and empirical Transformers There is some degree of misunderstanding from the reviewer about our main claim and we would like to reiterate our claim and evidence. - First, we don’t claim that Iterative Newton is the algorithm that a trained Transformer model is implementing. What we really claim is that Transformers learn some algorithm that convergence exponentially faster than the gradient descent method, and algorithms with such log log convergence rate fall into the same category of “higher-order” optimization methods, where Iterative Newton is one of them. We do believe that convergence rate is a solid categorization of optimization algorithms. We also note the $\Omega(\log(1/\epsilon))$ lower bound of gradient-based methods [1] and it is not possible to improve Gradient Descent’s convergence rate without using second-order methods. - Second, our empirical results show that Transformers share the same convergence rate as Iterative Newton and such results can categorize Transformers as a higher-order method, and they are all exponentially faster than Gradient Descent algorithms. Please refer to Fig 3 for the well-conditioned case, Fig 15 for the ill-conditioned case, and Fig 21 for deeper transformers. The intuition why we don’t believe Transformers are doing GD is that, for example in Fig 3 (right), there is no way for one Transformer layer (from layer 7 to layer 8) to implement 500 gradient descent steps. - Finally, we show expressivity results that Transformers can indeed implement Iterative Newton’s method, a representative higher-order method. ## Covariates across layers We would like to humbly ask the reviewer to clarify the question. We also would like to point to our theoretical proof that the intermediates $M_k$ do not need to be stored in each layer. In this case, it will be difficult to extract the exact intermediate covariates. ## ReLU activation As the reviewer pointed out, this is not a bit issue as many existing work studies either linear attention (no activation applied to attention layers) or with ReLU activations. ## Purpose of computing $w^{\mathrm{Newton}}_{k}$ It allows us to compute the convergence rate of algorithms, for which one needs to show the relationship between $\|\|w_{k+1} - w_{\star}\|\|$ and $\|\|w_{k} - w_{\star}\|\|$ for the optimal solution $w_{\star}$. In this case, we need to compute the intermediate $w^{\mathrm{Newton}}_{k}$. Moreover, $w^{\mathrm{Newton}}_{k}$ is needed to make predictions on any test sample, and we can measure how good each iteration has been by looking at the errors on test samples. --- Rebuttal Comment 1.1: Comment: Thank you for your response. I did have a misunderstanding that several layers in the transformer are used to implement a single iteration of the higher order method. Rather it is the other way. I was coming at this from the perspective that perhaps there are some weights that implement the algorithm you propose, (like Theorem 5.1, but one the transformer actually learns). My main concern is that the observations here might be very specific to OLS for linear problems. The way it is solved traditionally (without transformers) this is just a quadratic problem. There have been many works in this space (those cited in the section on "Do Transformers implement Gradient Descent?"), but as far as I know, none of them consider learning any other function class, whereas this seems like a very natural question. Since a lot of these observations are empirical, it would make the message more powerful if these results could be demonstrated on non-linear regression problems. Considering the prior work, I think this paper presents an interesting ``closer look". But I wonder if we can hope that these insights would extend even to problems that are not quadratic. Would it be feasible in the remaining time to get a heat map for the similarity in weight when the ground truth is a single ReLU neuron, or the similarity in errors when the ground truth is a small MLP? Regarding the question about the covariates, what I was getting at is that an $L$ layer transformer can be thought of as an $L-1$ layer transformer with inputs that are the outputs of the actual first layer. I was just wondering if the new $x_i, y_i$ can be directly interpreted in any way. There must be some way that you can view the last $L-1$ layers as running an optimization algorithm to solve the problem presented by the outputs of the first layer. Is this optimization problem the same as the one the full transformer is running (but with one (or three) less iterations)? --- Rebuttal 2: Title: References Comment: [1]Shivam Garg, Dimitris Tsipras, Percy Liang, Gregory Valiant. What Can Transformers Learn In-Context? A Case Study of Simple Function Classes. In NeurIPS, 2022 [2] Johannes von Oswald, Eyvind Niklasson, E. Randazzo, Joao Sacramento, Alexander Mordvintsev, Andrey Zhmoginov, and Max Vladymyrov. Transformers learn in-context by gradient descent. In International Conference on Machine Learning, 2022. [3] Ekin Akyurek, Dale Schuurmans, Jacob Andreas, Tengyu ¨ Ma, and Denny Zhou. What learning algorithm is incontext learning? investigations with linear models. The Eleventh International Conference on Learning Representations, 2024 [4] Kwangjun Ahn, Xiang Cheng, Hadi Daneshmand, and Suvrit Sra. Transformers learn to implement preconditioned gradient descent. Advances in Neural Information Processing Systems 36. 2024 [5] Yu Bai, Fan Chen, Haiquan Wang, Caiming Xiong, and Song Mei. Transformers as statisticians: Provable in-context learning with in-context algorithm selection. Advances in neural information processing systems, 36. 2024 --- Rebuttal 3: Title: Additional Non-Linear Experiments Comment: Thank you for your thoughtful suggestions and comments. We have conducted an additional experiment on a non-linear function class: 2-layer neural network with ReLU activations, a setting also studied by pioneering work, Garg et. al. (2022) in Fig. 5(c) in their NeurIPS 2022 paper version. Please refer to https://anonymous.4open.science/api/repo/transformer_icl_neurips_rebuttal-2E55/file/Transformer_ICL_rebuttal_additional.pdf for experimental results. TL;DR: Transformers still converge superlinearly, and exponentially faster than GD -- indicating higher-order optimization in-context. In the same prompt setup $(x_1, y_1, \cdots, x_t, y_t)$, each $y_k$ is generated by $y_k = a^\top \mathrm{ReLU}(Wx_k + v) + b$. There are 100 neurons, aka, the hidden size, and the problem dimension $d$ is still 20. As shown in Figure 3a, even on 2-layer neural network tasks, Transformer shows superlinear convergence rates. As shown in Figure 3b, Transformer shows an exponentially faster convergence rate than GD’s, because GD’s steps are shown in log scale and the trend is linear – similar to Figure 9 in the main paper. Although our title indicates the study mainly focuses on linear functions, we find the extension to non-linear functions quite meaningful. We will make the experiments extending to non-linear function classes more thorough and include more discussions in the camera-ready version. --- Rebuttal 4: Title: Question about the covariates Comment: In analogy to many optimization algorithms, what's updated along the iterations are the estimators $\hat{w}$ than the covariates $x_i, y_i$. We can understand by analogy to any other iterative method, such as GD. The final $L-1$ steps of GD solve some problem whose input is the solution to the first step, $\hat{w}_1$. However, the $x_i, y_i$ for the linear regression instance would not change, it’s just that the optimization algorithm starts with a better estimate. In analogy to Newton, the goal is to compute better and better estimates of the inverse covariance iteratively. Please let us know if you have further questions. --- Rebuttal 5: Comment: Dear Reviewer, as the discussion period is about to end, we would like to know if our newest experiments on two-layer MLP with ReLU activation (thread here: https://openreview.net/forum?id=L8h6cozcbn&noteId=7Gu8rWpfSn) have cleared out any of your concerns. We are also happy to answer any further questions. Thanks!	Summary: This paper demonstrates that transformers learn to approximately perform higher order algorithms, building on the previous works that demonstrate that transformers can approximate gradient descent which is a first-order algorithm. For the problem of linear-regression, it is empirically shown that that prediction errors of transformer are similar to that of iterative Newton's method, and so are their corresponding rates of convergence. Further, it is shown by explicit construction of weights how a $k+\mathcal{O}(1)$ layers of transformers can implement $k$ steps of the Newton's method. Strengths: (1) The work provides a very good understanding of how transformers can efficiently solve (even ill-conditioned) linear regression problems, which is of interest to the research community. (2) This paper establishes that transformers are better algorithmic engines than other deep learning models (for example, LSTMs, in Figure 6 of Appendix A.2.1). (3) The performance of the trained transformer is very close to that of a higher-order algorithm, even though transformer is not trained for different number of layers $\ell$ separately (only the ReadOut layer is retrained). This demonstration strongly supports the crucial claim that the representations after each layers learned by the transformers in fact mimic the updates of some higher-order algorithm. (4) The experiments are well-executed and their presentation is commendable. (5) The proof of the main theoretical contribution (Theorem 5.1) is very clean. Weaknesses: (1) Although the result is very interesting that leads to a better understanding of the abilities of a transformer, there is little direct impact in terms of application. Technical Quality: 3 Clarity: 4 Questions for Authors: (1) The effect of the number of layers is that the prediction after each layer progressively improves. However, one might also be interested in the effect of embedding dimension on the rate of convergence, which is not discussed. I am curious if you have any comments on this? Confidence: 4 Soundness: 3 Presentation: 4 Contribution: 3 Limitations: (1) Within the scope of the problem, there is no specific limitation that requires attention (pun intended). Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for their detailed comments and suggestions. We are pleased they find our work valuable in demonstrating how transformers efficiently solve linear regression problems, including ill-conditioned ones. They appreciate our comparison showing transformers as superior to models like LSTMs, and acknowledge our experimental results show strong evidence that transformers resemble higher-order algorithms. We thank the reviewer for commending our well-executed experiments, clear presentation, and clean proof of our main theorem. ## Direct Impact We acknowledge that this is a more interpretability and theoretical work whose direct impact to applications is unknown. However, we believe that interpretability could be useful in general, for example, it facilitates our understanding of architectures, and motivates us to make reliable changes in the future. ## Impact of Hidden Dimension Size Empirically, we ablate 12-layer 1-head transformers with different hidden dimensions: 64, 32, 16, and 8. Please see results in the Figure 2 in the rebuttal PDF. We find that transformers with hidden dimensions 64 and 32 are able to converge to the OLS solution. On the contrary, transformers with hidden dimensions 16, and 8 could not. Theoretically, as stated in Theorem 5.1, the hidden dimensions in our theoretical construction require a size of $\mathcal O(d)$, where $d$ is the dimension of the linear regression problem. That being said, as long as the hidden dimensions are of order $\mathcal O(d)$, transformers are able to converge to the OLS solution, and the higher-order optimization methods are learned in-context. This coincides with our empirical results, where $d = 20$ and the hidden dimensions need to be $\mathcal O(d)$. --- Rebuttal Comment 1.1: Comment: I read the rebuttal and my doubts have been addressed adequately. I shall maintain my score. Thank you. --- Reply to Comment 1.1.1: Comment: Dear reviewer, Thank you for discussing with us and we appreciate your support for our paper.	Summary: This work investigated the ability of transformers to implement higher-order optimization methods for in-context learning of linear regression tasks. The authors considered a noiseless linear regression setting and compared the output of each layer of TF with few steps on gradient descent (GD), online gradient descent (OGD), iterative Newton's method, and empirically showed that the output has a linear trend with the iterations of the Newton's method but an exponential trend with GD's iterations. Therefore, they concluded that TFs are more likely to implement high-order methods instead of first-order method for ICL tasks. They also performed experiments on ill-conditioned tasks and observed similar trends. In addition to the experiments, they theoretically proved that there exists a polynomial size TF that can implement iterative Newton's method. Strengths: The paper is well-written. The experimental results and their implications are well-discussed. The similarity metrics used to compare different algorithms are reasonable. Novel theoretical results on the approximation ability of TFs are proved. Weaknesses: Assumption on the linear regression tasks. This work considered a noiseless setting in which the optimal predictor in the OLS. It is unclear to what extent the observations in this work can be generalized the setting where the noise exists. Technical Quality: 3 Clarity: 3 Questions for Authors: What is the choice of stepsize for GD? Is it optimal? Would different choices of stepsize for GD affect the exponential trend shown in Figure 3 (right)? Do similar observations appear in linear regression tasks with non-zero noise? For example, in this case, would TF perform high-order optimization methods to learn the optimal ridge predictor? Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: This work compared the outputs of TFs and some first-order/higher-order algorithms and concluded that TFs are more likely performing higher-order optimization based on the similarity of their outputs. However, this does not imply that TFs internally implement Newton's method or any other specific higher-order method. This work focused on ICL with linear regression tasks. It is unclear if TFs still behave like higher-order methods in other convex ICL tasks (e.g., logistic regression for classification) and what TFs approximate if the learning task is non-convex. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for detailed comments and suggestions. We are pleased that the reviewer thinks our experimental results and their implications are well-discussed. We are happy to see that the reviewer regards our theoretical results novel, our comparison metrics reasonable, and our paper well-written. ## Generalization to noisy problems We thank the reviewer for this suggestion. We run experiments on noisy linear regression with a noise standard deviation of $\sigma = 0.1$. Please refer to Figure 1 in the rebuttal PDF for detailed results. We observe that in noisy setup, transformers and iterative Newton’s method still share the same convergence rate, and are both exponentially faster than GD. Additionally, under the noisy linear regression setup, the closed form solution would be $\hat{w} = (X^\top X + \lambda I)^\dagger X^\top y$. Our theoretical construction stills holds with slight modifications: replacing $S = X^\top X$ by $S = X^\top X + \lambda I$. We will discuss this more clearly in our next revision. ## Choice of step size for GD Notice that the optimal step size for GD is $\eta = \frac{2}{\beta + \gamma}$ where $\beta$ and $\gamma$ are the smallest and largest eigenvalues for $S = X^\top X$ respectively. However, each sequence is sampled randomly and will have different optimal $\eta$, and it would be an unfair comparison if extra computations are allowed for eigenvalues of $S$ – which involves computing higher moments of $S$ if using numerical methods, for example, power methods. To circumvent this, we sampled 10,000 sequences and computed the average optimal step size $\bar{\eta} = \mathbb E[\eta]$ and used the same step size $\bar{\eta}$ for GD. Empirical, we showed that transformers match Iterative Newton’s convergence rate. Theoretically, Iterative Newton’s convergence rate is exponentially faster than GD with optimal step sizes (see lines 121 and 130). Combining the two, we can deduce that transformers will also be exponentially faster than GD with optimal step sizes. ## Generalization to logistic regression and classification, or even non-convex problems We believe that linear regression is the right starting point to understand how transformers perform in-conext learning. It would be interesting to see the extensions to logistic regression, classification, and even non-convex problems. However, this is beyond the scope of this paper. --- Rebuttal Comment 1.1: Comment: Thanks for the clarification and additional experiments. My questions have been answered and I will update my score. --- Rebuttal Comment 1.2: Title: Thanks Comment: Dear reviewer, Thank you for discussing with us. We appreciate your updated score and your support for our paper.	Summary: In the paper the authors study the nature of in-context learning in transformers. Starting from the hypothesis of previous work on the fact that transformers may internally implement gradient descent algorithms to correctly perform linear regression on test data, the authors put forward the theory that transformers actually implement a different, higher-order algorithm. The authors back their claim with empirical evidence on the convergence rate of the algorithm across layers, and they provide a theoretical construction for the implementation of Newton's iterative algorithm using the transformer architecture. Strengths: I believe that the idea that transformers implement a higher-order algorithm for linear regression is intriguing, and I think that the empirical evidence provided by the authors definitely rule out the possibility that transformers simply implement gradient descent and not a more sophisticated algorithm. Weaknesses: The limit of the work is two-fold: (1) the authors only provide circumstantial -- and not direct -- evidence that the network is learning a higher-order algorithm, and the provided evidence on ill-conditioned data actually seem to contradict the theory that the network is actually implementing Newton's iterative method and not something ever more sophisticated; (2) there is quite a bit of mismatch between the empirical and the theoretical results: there is a 8-layer baseline required for the proposed construction to work that doesn't seem to appear in the experiments, and 8 is quite a large number for the setting presented in the paper (e.g., in Figure 2 the transformer seem to achieve small error already after 8 layers). Technical Quality: 3 Clarity: 3 Questions for Authors: What do you think may be causing the mismatch between the theoretical and the empirical results, i.e., what do you think is the limit of your construction? Do you think that it may be improved, e.g, by some additional architecture components, or by the substitution of softmax instead of ReLU? Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: N/A Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for detailed comments and suggestions. We are pleased that the reviewer thinks our ideas intriguing and empirical evidence convincing. ## Evidence for higher-order is indirect Our main evidence is the convergence rate. We do believe that convergence rate is a solid categorization of optimization algorithms where higher-order methods will have $\log\log(1/\epsilon)$ rates whereas first-order could only achieve $\log(1/\epsilon)$ rates. We also note the $\Omega(\log(1/\epsilon))$ lower bound of gradient-based methods and it is not possible to improve Gradient Descent’s convergence rate without using second-order methods. ## contradiction in ill-conditioned case There might be some degree of misunderstanding about our ill-conditioned experiments. Our experiments show that both Transformers and Newton’s method are not susceptible to ill-conditioned data – a common trait for higher-order optimization methods. In both well-conditioned and ill-conditioned experiments, our heatmaps (Fig 3 and Fig 15) show that one Transformer layer could implement three Newton iterations, which indicates that Transformers could implement some algorithms even more complicated and stronger than Iteratvie Newton’s method. However, they are still higher-order optimizations with a similar convergence rate to Newton’s method, ## Mismatch between the empirical and the theoretical results Surely, there’s a mismatch between empirical and theoretical results for the initial constant number of layers needed, but they are both $\mathcal O(1)$. Empirically, we observe there’s an $\mathcal O(1)$ number of layers needed for a warmup: the initial layers where transformers cannot show improvements in prediction errors. Please see Figure 2(a) for 12-layer transformers, 2 layers at the beginning are reserved for warmup; in Figure 21 for 24-layer transformers with iterative newton, 4 layers are reserved at the beginning. Similarly, our theoretical construction needs 8 layers, but it still lands in the category of $\mathcal O(1)$. Our main focus for theoretical construction is to show that, to implement $k$ Newton steps, we need $k + \mathcal O(1)$ Transformers layers, with a particular focus on the 1-to-1 correspondence between intermediate layers and Newton steps. Admittedly, we didn’t optimize our construction for the $\mathcal O(1)$ constant number of layers needed to initial layers. There could be alternative constructions with a smaller amount of warmup layers than 8, but that’s not the main focus of our theoretical analysis. There could be many causes for the mismatch of the constant. For example, the number of layers of the Transformers, the hidden dimension size, etc. At the same time, optimization algorithms used to train these Transformers could also be another factor on the empirical side. On the theoretical side, as the reviewer pointed out, the substitution of softmax activation by ReLU could be an important factor. Nonetheless, matching the exact number between empirical and theoretical results would be tedious but matching the number within the same complexity of $\mathcal O(1)$ is simply what’s presented in this paper. --- Rebuttal Comment 1.1: Comment: Thank you for your valuable comments. I will keep my positive score. --- Reply to Comment 1.1.1: Comment: Dear reviewer, Thank you for discussing with us and we appreciate your support for our paper.	Rebuttal 1: Rebuttal: We sincerely thank the reviewers for their time and effort in reviewing our work. We are encouraged that the reviewers praise our work for providing a very good understanding of how transformers can efficiently solve linear regression (p5Dq) and find our ideas of higher-order optimization intriguing (F4MD). We are happy to see that reviewers find our experiments thorough (vdXr) and well-executed (p5Dq), our results reasonable (J6bG) and convincing (vdXr, F4MD), and their implications are well-discussed (dusD). We are also pleased to see the reviewer commend our theoretical results (dusD, p5Dq). Finally, we are delighted to see reviewers find our paper well-written (vdXr, dusD) and our proof clean (p5Dq). We conducted two additional experiments per the reviewers’ comments and the results are attached in the PDF: - Noisy Linear Regression. As reviewer dusD suggested, we conduct additional experiments on noisy linear regression problems, and find our claim that transformers learn high-order optimization methods in-context still holds in noisy linear regression setups. - Varying Hidden Dimension Sizes. As reviewer p5Dq suggested, we ablate on the hidden dimensions of transformers, and observe the resonance between empirical results and our theoretical claim that a hidden dimension of $\mathcal O(d)$ is necessary for Transformers to converge to the OLS solution and thus learn higher-order optimization methods in-context. We have addressed the comments in the responses to each reviewer and will incorporate all feedback into the paper. Pdf: /pdf/c4ba8b2f2daadbfe15c08144c3b4ed7230d3b345.pdf	NeurIPS_2024_submissions_huggingface	2,024	Summary: This paper studies in-context learning in transformers, and find that gradient descent converges more slowly than transformers/Newton's method for linear regression. Previous works proposed that transformers do in-context learning using gradient-based algorithms, based on experiments with linear regression tasks. This paper suggests that transformers use a higher-order optimization method rather than a first-order method, for linear regression. The evidence for this is as follows: (1) transformers converge to the OLS solution at a similar rate as iterative newton. The predictions after each layer match those of Newton's method after a proportional number of iterations. (2) GD requires a much larger number of steps (exponentially many) to match the transformer's errors. The problem setup/experimental setup is similar to prior works in this area - in each example sequence, they sample a weight vector $w$, and a matrix $\Sigma$ which is from some distribution over PSD matrices (in some of the experiments, $\Sigma$ is an identity matrix, and in others, $\Sigma$ is ill-conditioned). The examples $x_i$ within the sequence are sampled from a Gaussian with covariance $\Sigma$. They use the following metrics to measure similarity between transformers/other algorithms (namely Newton's method and GD): 1. Similarity of errors - cosine similarity of the errors that two algorithms achieve. On a given data sequence of length $n$, they take the vector of errors that each algorithm achieves on $y_2, \ldots, y_{n + 1}$, where for $y_i$, the algorithm is given $x_1, y_1, ..., x_i$. Then, they take the cosine similarity between these two error vectors. 2. Similarity of induced weights - fit a weight vector to the predictions of this model, and compare two algorithms by comparing their induced weight vectors (on the same sequence of in-context examples). 3. Matching steps between algorithms - Let $p_a$ be a particular number of steps taken by algorithm A. Then, the best matching number of steps for algorithm B is the one that maximizes the cosine similarity with algorithm A at step $p_a$. The results in Figure 2 show that the middle layers of transformers converge at a superlinear rate, similarly to Newton's method. Figure 2 also shows that gradient descent has a sub-exponential convergence rate, and gets slower as the number of steps increases. It requires a much larger number of iterations. They also match the steps between transformers and Newton's method and GD (in other words, for each layer L of the transformer, find the step of Newton's method/GD whose predictions are the most similar to the transformer at layer L). Figure 3a shows that there is a linear relationship between the transformer layer index and the corresponding step index of Newton's method. (Figure 8, which matches steps based on weight vectors instead of errors, seems to show a stronger linear trend.) Strengths: - The experiments are thorough and successfully show that transformers can learn optimization algorithms much faster than gradient descent. - The paper is very well-written. Weaknesses: - As the authors mention, the experiments ultimately show that transformers behave more similarly to some higher-order method, rather than Newton's method in particular. In some cases, transformers can behave differently from Newton's method as well. - For instance, in Figure 20 (left), it could be argued that the transformer converges even faster than iterative Newton's method, i.e. the relationship between the iteration of Newton's method and the transformer layer index is not exactly linear. For instance, layer 14 of the transformer seems to correspond to about 4 iterations of Newton's method. - It would be useful to clarify the difference between the takeaway of this paper and e.g. Garg, et al. (2022), which finds that transformers can match ordinary least-squares very closely. - If this submission shows that transformers learn Newton's method in particular, then the difference would be clear. This work gives evidence that transformers learn faster than GD, but somewhat less strong evidence that transformers learn a particular algorithm. Garg, et al. (2024) "What Can Transformers Learn In-Context? A Case Study of Simple Function Classes" ================================== The authors clarified my questions in the rebuttal - I am increasing my score from 6 to 7. Technical Quality: 4 Clarity: 4 Questions for Authors: - Figure 5, left, seems to be showing a drastic difference between the performance of transformers and Newton's method. This may be because the red curve only uses 5 steps of Newton's method. Is the result different if more steps of Newton's method are used? Confidence: 4 Soundness: 4 Presentation: 4 Contribution: 2 Limitations: Yes. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for detailed comments and suggestions. We are pleased that the reviewer thinks our experiments are thorough and successfully support our main claim. We are also happy to see the reviewer thinks our paper is well-written. ## In some cases, Transformers can behave differently from Newton's method Admittedly, Transformers could behave slightly differently compared to Newton’s method as the reviewer pointed out. This could come from optimization noises during training or probing. Additionally, we are not claiming trained Transformers models are exactly implementing Iterative Newton’s method and this is why our title says “higher-order method” rather than “Newton’s Method”. Our main claim is that Transformers resembles a class of optimization algorithms, and a slight deviation from Newton’s method wouldn’t hurt such claims. ## Clarify the difference between this paper and Garg et. al. Garg et. al. empirically showed that Transformers, when performing in-context linear regression, match the ordinary least-squares (OLS) solution. However, what remains unclear is how Transformers converge to the OLS solution. One common hypothesis is that Transformers converge to the OLS solution via Gradient Descent (GD), while the main contribution of this work is to show that (1) empirically, Transformers can converge exponentially faster than GD, which suggests that they emulate higher-order optimization methods; (2) theoretically, there is a construction of Transformers to implement a particular higher-order optimization method – the Iterative Newton’s method. ## Whether Transformers evidently learn a particular algorithm Again, we are not claiming trained Transformers models are exactly implementing Iterative Newton’s method. We also compared Transformers with many alternative higher-order optimization methods such as Conjugate Gradient and (L-)BFGS, and the conclusion is that Transformers are learning a particular class of algorithms, that are utilizing higher-order information. ## LSTM only matches 5-step Newton’s Method Yes. As shown in Fig. 6(c), LSTMs couldn’t improve with more layers and the errors are still quite large. This implies that LSTMs could only converge to an estimator $\hat{w}_{LSTM}$ that achieves the same performance as Iterative Newton’s method after only 5 steps, which is far from converging to the least squares solution. --- Rebuttal Comment 1.1: Comment: Thank you for the reply. I agree that this work goes beyond Garg, et al. by explicitly analyzing how the rate at which transformers converge to the OLS solution, depends on the number of layers. I will update my score. --- Reply to Comment 1.1.1: Title: Thanks! Comment: Dear reviewer, Thank you for discussing with us. We appreciate your updated score and your support for our paper.	null	null	null	null	null	null
Pessimistic Backward Policy for GFlowNets	Accept (poster)	Summary: The paper successfully identifies and addresses the under-exploitation problem in the flow matching of GFlowNets. The proposed method, Pessimistic Backward Policy (PBP-GFN), adjusts the probabilities of backward trajectories to improve exploration and exploitation, achieving superior performance in various benchmarks. Strengths: - This paper first identifies the significant issue in conventional GFlowNets—under-exploitation due to unobserved flow in backward trajectories. - The paper provides a clear and detailed explanation of the methodology, including the training process and the loss function used for the backward policy. Weaknesses: - The PBP-GFN introduces additional complexity to the training process of GFlowNets. Pessimistic training of backward policy might be computationally expensive or hard to tune in different settings. The author should discuss this in the updated version of the paper. - In the experiment sections, this paper does not compare with some new GFlowNets methods, such as [1, 2], that claim improvement over the baselines. I wonder (1) Are PBP-GFN's results better than [1, 2]? (2) Can we combine the pessimistic backward policy with strategies, such as those in [1, 2], to further improve performance? I understand that each paper deals with GFlowNets from a different perspective, therefore, I am ok if not all answers are yes. - There are some missing references that are also quite relevant to the topic. [3,4] - I would raise my scores if my concerns are resolved. [1] Kim, M., Yun, T., Bengio, E., Zhang, D., Bengio, Y., Ahn, S., & Park, J. (2023). Local search gflownets. arXiv preprint arXiv:2310.02710. [2] Jang, H., Kim, M., & Ahn, S. (2023). Learning Energy Decompositions for Partial Inference of GFlowNets. arXiv preprint arXiv:2310.03301. [3] Chen, Y., & Mauch, L. (2023). Order-Preserving GFlowNets. arXiv preprint arXiv:2310.00386. [4] Tiapkin, Daniil, et al. "Generative flow networks as entropy-regularized rl." International Conference on Artificial Intelligence and Statistics. PMLR, 2024. Technical Quality: 2 Clarity: 3 Questions for Authors: - When minimizing the negative log-likelihood in Eq.5, how to ensure, or do we need to ensure that the sum of the backward probability on a state is 1, and why the total amount of backward flows will not change claimed in line 157? In the provided codebase "PBP.train_proxy", it seems the sum of log_pb_actions will change, and the total number of flows will change. - This paper includes MIS from [1]. Can you include more difficult graph combinatorial optimization problems from [1], such as maximum cut? (Maximum clique is not necessary since it is related to MIS) [1] Zhang, D., Dai, H., Malkin, N., Courville, A., Bengio, Y., & Pan, L. (2023). Let the flows tell: Solving graph combinatorial optimization problems with gflownets. arXiv preprint arXiv:2305.17010. Confidence: 3 Soundness: 2 Presentation: 3 Contribution: 2 Limitations: Please see the Weaknesses part. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Dear reviewer WPBt, We express our deep appreciation for your time and insightful comments. In what follows, we address your comments one by one. --- W1. The PBP-GFN introduces additional complexity, which may be expensive or inpractical in some settings. Can the authors provide a discussion on this point? We clarify that the training of the pessimistic backward policy does not require significant overhead and is practical in most cases, as it only requires computing the gradients of the negative log-likelihood for the given trajectories. This requires similar or higher complexity than the conventional backward policy but less than the sub-structure backward policy. Especially, this complexity (i.e., the computation of gradients) would be minor for real-world problems with expensive reward evaluations, e.g., molecular docking tools or wet-lab experiments. We will update our future manuscript to reflect these points. --- W2. Compared to independent lines of research for exploitation, e.g., local search GFN and LED-GFN, (A) does PBP-GFN show superior results, and (B) can we combine PBP-GFN with these approaches to further improve performance? To address your comments, we conducted new experiments by (A) comparing PBP-GFN with local search and LED-GFN and (B) combining PBP-GFN with them. Note that (B) is trivial since our pessimistic backward policy is orthogonal to local search and LED-GFN that address off-policy sampling and local credits. We present the results in Figure C(a) and Figure D(a) of our rebuttal PDF. One can see that PBP-GFN (A) shows similar performance compared to local search GFN and LED-GFN, and (B) further improves performance when combined with them. --- W3. There are some missing references that are also quite relevant to the topic [2,3]. Thank you for your valuable suggestions! We will incorporate them into the related works section of our future manuscript. --- Q1. (A) How to ensure the sum of the backward probability on a state is $1$, and (B) the provided codebase "PBP.train_proxy" seems change the sum of `log_pb_actions`, so the total backward flows will change. We would like to clarify that (A) is trivial. When we implement the backward policy using softmax, i.e., $\sum_{s\in\text{parent}(s')}P_B(s\|s')=1$, the summation of the backward probability on a state satisfies $\sum_{\tau\in\mathcal{T}(x)}P_B(\tau\|x)=\sum_{(s_0\rightarrow\cdots\rightarrow s_T)\in\mathcal{T}(x)} {\prod_{t=0}^{T-1}P_B(s_t \|s_{t+1})=1}$, by iterating the law of total probability over entire trajectories. Note that we do not constrain $\sum_{\tau\in\mathcal{B}(x)}P_B(\tau\|x)$ for observed trjajectories $\tau \in \mathcal{B}(x)$ to be equal to one, but maximize it. For (B), we would like to clarify that the sum of `log_pb_actions` corresponds $\log P_B(\tau\|x)=\sum_{t=0}^{T-1} \log P_B(s_t\|s_{t+1})$ for the given trajectory. The change of this does not affect the total amount of backward flow, i.e, $R(x)\sum_{\tau \in \mathcal{T}(x)}P_B(\tau\|x)$, as $\sum_{\tau \in \mathcal{T}(x)}P_B(\tau\|x)=1$ is always guaranteed over the entire trajectories. --- Q2. This paper includes MIS. Can you include more difficult graph combinatorial optimization problems from [1], such as maximum cut? Indeed, we previously tried other graph combinatorial optimization problems from [1], e.g., the maximum cut problem, but could not reproduce the official results even when using the official implementation. For example, the official score for the maximum cut problem is around $700$, but running their implementation yields a score of $2000$ during the initial training round. To alleviate your concerns, we report the result of PBP-GFN applied to the maximum cut problem in Figure D(c) of our rebuttal PDF. --- [1] Let the Flows Tell: Solving Graph Combinatorial Problems with GFlowNets, NeurIPS 2023 [2] Order-Preserving GFlowNets, ICLR 2024 [3] Generative Flow Networks as Entropy-Regularized RL, AISTATS 2024 --- Rebuttal Comment 1.1: Comment: Thank you for the detailed clarifications and additional experiments. I decide to raise my score to 6. --- Rebuttal 2: Comment: Dear reviewer WPBt, We are happy to hear that our efforts have addressed your concerns! We also appreciate your insightful comments on our works.	Summary: The authors present a problem with GFlowNets training that originates from not having seen backward trajectories for a particular terminal state. The authors show that because of the lack of observed trajectories, the backward flows underestimate the probabilities for the observed flows, resulting in a (forward) policy that may not match the reward distribution. The authors propose to mitigate the problem by increasing backward flows for the observed trajectories. The authors provide experimental results in eight different environments, showing the superior performances of their method in terms of mode discovery and distribution fitting. Strengths: 1. Well-written motivation for the problem described. 2. The solution presented is well-motivated and clearly described. 3. The experiments include well-studied environments and baselines, showing the method's performance in exploitation. Weaknesses: 1. The discussion about lacking backward flow given the unseen trajectories is valid. In practice, one can mitigate this by having a uniform backward policy with a reward-prioritized replay buffer [1], which also can increase the probability a trajectory yielding high rewards, thereby tackling the mentioned problem. I feel adding this baseline will improve the paper. 2. As an exploitation method, at least one experiment with a larger state-space should be useful to show its performance in larger state-spaces. Hypergrid with a larger dimension and horizon can be one option for this. [1] Shen, Max W., et al. "Towards understanding and improving gflownet training." International Conference on Machine Learning. PMLR, 2023. Technical Quality: 3 Clarity: 3 Questions for Authors: 1. What is the hypermeters for GAFN in Figure 9? Were the hyperparameters tuned for the experiments? 2. The example in Figure 3 raises a question: if $P_B(x\|\tau)[i]$ is maximized, $P_B(x\|\tau)[j] \approx 0; j \neq i$, thereby matching it will cause $P_F(x\|\tau)[j] \approx 0; j \neq i$. In smaller state-space, it may not be a problem, but in a larger state-space, this should be an issue as it may cause $p(x) \approx 0$ where x necessitates action j whose probability we've just made approximately 0. Curious to hear what you think about this/whether you've done experiments in large-scale environments. Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: Yes. Limitations are adequately addressed. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Dear reviewer CTvM, We express our deep appreciation for your time and insightful comments. In what follows, we address your comments one by one. --- W1. One can mitigate under-exploitation using a reward-prioritized replay buffer. Adding this as a baseline will be helpful. We clarify that our experiments on the bag and RNA sequence have already incorporated the reward-prioritized buffer into all baselines and our method (Appendix B). Since the pessimistic backward policy and the reward-prioritized buffer are orthogonal, they are not directly comparable and one can combine them to train GFlowNets. Nevertheless, to further address your comments, we also considered PBP-GFN without a reward-prioritized buffer and compared it with baselines using a reward-prioritized buffer. We present results in Figure C(b) of our rebuttal PDF. One can observe that the pessimistic backward policy (1) yields similar performance improvements compared to the reward-prioritized buffer, and (2) further improves their performance when combined with it. --- W2. As an exploitation method, at least one experiment with a larger state-space could be useful, e.g., larger hyper-grid. We first clarify that our molecule generation environment considers a sufficiently large state space sized up to $10^{16}$ [1]. To further address your suggestion about a larger hyper-grid, we conducted additional experiments on $40\times 40 \times 40 \times 40$ hyper-grid. To the best of our knowledge, this is larger than any hyper-grid experiment conducted in the literature. We present the results in Figure D(b) of our rebuttal PDF. One can observe that our method still shows superior results compared to considered baselines. --- Q1. What are the hyperparameters for GAFN? For GAFN, we searched for the coefficient $\alpha$ of intrinsic rewards within $\{1 \mathrm{e-}1, 1 \mathrm{e-}2, 1 \mathrm{e-}3\}$. We designed the random network to have the same architecture as the policy network, but with an output dimension of one, and used a learning rate of $1 \mathrm{e-}3$ for this network. --- Q2. In a large state space, PBP-GFN may cause $P_F(x)\approx 0$ when $x$ necessitates an action $j$ but PBP-GFN have made probability of $j$ approximately $0$. Curious to hear what you think about this and whether you've done experiments in large-scale environments. We think that such a potential reduction in the exploration of unobserved objects is natural due to the exploration-exploitation trade-off. As PBP-GFN enhances the exploitation, this may reduce exploration for the unobserved objects in the large state space (discussed in Limitation section). However, we would like to clarify that one can simply relax this issue by reducing the learning rate for the pessimistic backward policy or incorporating an exploration-focused off-policy sampling method to observe $x$ with $P_F(x)\approx 0$. Furthermore, it is worth noting that our method has already shown good performance in a large state space, e.g., molecule generation sized up to $10^{16}$. This implies that our method is still effective in environments with large state space, as exploitation is also significant for them. --- [1] Trajectory balance: Improved credit assignment in GFlowNets, NeurIPS 2022 --- Rebuttal Comment 1.1: Comment: Thank you for your rebuttal. I think the method’s promise is weakened because of Q2. Since it is an exploration method, further analysis of this phenomenon in a large state space is required. Hence, I would like to keep my score. --- Rebuttal 2: Comment: Dear reviewer CTvM, Thanks you for your response. We appreciate your insightful and constructive feedback for improving our paper in many aspects. Additionally, we would like to emphasize that we have already empirically analyzed the reduction of exploration (as an exploitation method) in large state spaces by measuring the diversity of high-score objects (Figure 7(c)). However, we observed no particular reduction in practice. In our future manuscript, we will also incorporate an analysis of the case where our PBP-GFN may reduce exploration (Figure B of rebuttal PDF) and discuss mitigation strategies with contents from (u41F-W4,5). We hope that this addresses your concerns.	Summary: This paper proposes a pessimistic backward policy for GFlowNets (GFN), which maximizes the expectation of observed backward trajectories. This paper points out the under-exploitation of high-reward objects for previous GFN training methods and provides a deep analysis of this problem. Extensive experiments validate the superior performance of the proposed method. Strengths: - This paper is well-written. The illustrations of the proposed method are clear, and the toy examples provided are easy to understand. - This paper proposes a simple yet effective method to address the problems of under-exploitation in GFN training. - Extensive experiments on 8 benchmarks validate the efficacy of the method. Weaknesses: Does the auxiliary objective introduced in Eq. 5 affect the original GFN training objective? Since higher probabilities are assigned to the backward transitions of observed trajectories, could this impact the original assumptions of TB, DB, and other objectives? Do you observe instability during training after some episodes, once the model has seen a sufficient number of samples? Technical Quality: 2 Clarity: 3 Questions for Authors: - How do you estimate Eq. 5 in practice? This is an important component of the method, but it is not described. - What's the meaning of $N$ in algorithm 1? Why does this method need multi-round gradient updates? Confidence: 3 Soundness: 2 Presentation: 3 Contribution: 2 Limitations: Limitations have been discussed in this paper. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Dear reviewer smvU, We express our deep appreciation for your time and insightful comments. In what follows, we address your comments one by one. --- W1. Does the pessimistic training objective affect the original assumption of GFlowNets training objective? Our pessimistic training objective does not affect the original assumption of GFlowNet objectives, e.g., DB, TB, and subTB. The assumption of them, i.e., flow matching over entire trajectories $\tau \in \mathcal{T}$ constructs target Boltzmann distribution, is valid for any design of backward policy, i.e., degree of freedom [1,2]. Our pessimistic training objective only modifies this backward policy within the GFlowNet objectives. --- W2. Did you observe any instability during training after the model had seen a sufficient number of samples? In our experimental setup, we observed no particular instability after the model had seen a sufficient number of samples. --- Q1. How do you estimate Equation (5) in practice? In practice, we estimate the gradients of Equation (5) using the stochastic gradients computed with mini-batch randomly sampled from the buffer $\mathcal{B}$, as described in Algorithm 1. We will update our future manuscript to better reflect this point. --- Q2. What's the meaning of $N$ in Algorithm 1, and why does pessimistic training require multi-round gradient updates with $N$? As you mentioned, $N$ is a hyperparameter that specifies the number of update rounds for training the pessimistic backward policy. We require this as we use stochastic gradients to minimize Equation (5), which involves multi-round updates over multiple mini-batches. --- [1] GFlowNet Foundations, JMLR 24 [2] Trajectory balance: Improved credit assignment in GFlowNets, NeurIPS 2022 --- Rebuttal Comment 1.1: Comment: Thanks for your response and hard work. After reading your rebuttal and other reviews, I've decided to maintain my score. --- Rebuttal 2: Comment: Dear reviewer smvU, We also appreciate your insightful comments. Thank you again for your time and effort for improving our paper!	Summary: This paper addresses the under-exploitation of high-reward objects in Generative Flow Networks (GFlowNets) due to the limited observation of trajectories during training. The authors propose PBP-GFN (Pessimistic Backward Policy for GFlowNets), which modifies the backward policy to maximize the observed backward flow, aligning it closer to the true reward. They argue that this pessimistic training scheme encourages the forward policy to assign higher probabilities to high-reward objects, even if they are under-represented in the observed trajectories. Experiments across eight benchmarks, including hypergrid, molecule, and RNA sequence generation, demonstrate that PBP-GFN improves the discovery of high-reward objects while maintaining object diversity. Strengths: * The paper tackles an important issue in GFlowNet training – the potential for under-exploration of high-reward objects due to the sparsity of observed trajectories. This issue is particularly relevant in complex domains with vast trajectory spaces. * The proposed solution, PBP-GFN, is conceptually simple and intuitive. Maximizing the observed backward flow to align with the true reward directly addresses the identified problem of under-exploitation. * The paper provides extensive experimental results across a variety of tasks, showcasing the effectiveness of PBP-GFN in enhancing the discovery of high-reward objects. Weaknesses: * While the intuition behind PBP-GFN is clear, the paper lacks a strong theoretical analysis to support its claims. The "error bound" analysis in Appendix A is limited in scope and doesn't offer a comprehensive understanding of the algorithm's convergence properties or its impact on the target Boltzmann distribution. * The core idea of modifying the backward policy in GFlowNets has been explored in prior works [1, 2, 15]. PBP-GFN, while achieving promising empirical results, doesn't present a significant conceptual departure from these existing approaches. Its primary contribution appears to be a specific strategy for maximizing the observed backward flow, but the paper lacks a detailed comparison and analysis of how this strategy differs from or improves upon existing techniques. * The paper primarily focuses on metrics like the number of modes discovered and the average top-100 score. While these metrics are relevant for measuring exploration and exploitation, they provide a limited view of the overall quality and diversity of generated samples. Evaluating PBP-GFN on more comprehensive downstream task-specific metrics would strengthen the paper's claims. * While the paper claims that PBP-GFN maintains object diversity, the pessimistic training scheme inherently introduces a bias towards the observed trajectories. This bias could potentially lead to a reduction in exploration and the generation of degenerate or less diverse samples, especially in domains with significant uncertainty or where observed trajectories are not truly representative of the target distribution. A deeper analysis and empirical evaluation of this potential bias would be useful. * The performance of PBP-GFN heavily relies on the quality and representativeness of the observed trajectories. In scenarios where the initial observed trajectories are biased or incomplete, PBP-GFN could amplify these biases, hindering the discovery of truly novel and high-reward objects. The paper doesn't address this sensitivity or propose mitigation strategies. * The paper mainly compares PBP-GFN with other backward policy design methods. However, it doesn't provide a thorough comparison with other exploitation-focused techniques in GFlowNets, such as local search GFlowNets [3] or those focusing on higher-reward trajectories [2]. This limited comparison weakens the paper's claim of achieving superior performance in discovering high-reward objects. [1] Trajectory balance: Improved credit assignment in gflownets [2] Towards understanding and improving gflownet training. [3] Local search gflownets [4] Maximum entropy gflownets with soft q-learning Technical Quality: 3 Clarity: 3 Questions for Authors: Please refer to weaknesses section above. Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: N/A. Flag For Ethics Review: ['No ethics review needed.'] Rating: 3 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Dear reviewer u41F, We express our deep appreciation for your time and insightful comments. In what follows, we address your comments one by one. --- W1. The paper lacks a strong theoretical analysis to support claims. We agree that our paper lacks a strong theoretical analysis since we mainly focus on empirical performance improvements. We note that a strong theoretical analysis would be challenging (though valuable) since it requires thinking about the optimization landscape of GFlowNets, where no theoretical results have been made. Hence, we chose to provide insights in Appendix A by analyzing our PBP-GFN under strong assumptions. --- W2. Compared to existing backward policies [1,2,3], this work (A) does not present a significant conceptual departure and (B) lacks a detailed comparison. We respectfully disagree with (A). Unlike existing backward policies that focus on under-exploration or credit assignment issues, PBP-GFN is designed to tackle a new under-exploitation problem stemming from the unobserved backward flow. Next, to resolve (B), we will incorporate the following detailed comparisons with the existing backward policies in our future manuscript. - While uniform backward policy [1] and MaxEnt backward policy [3] assign a fixed probability to the backward transition for enhancing exploration, our pessimistic backward policy learns the probability of the backward transition for enhancing exploitation. - While conventional backward policy [1] and sub-structure backward policy [2] may enhance the exploitation by learning the backward flow to align with the forward flow or to improve the credit assignments, they do not directly reduce the unobserved backward flow and do not resolve the under-exploitation stemming from that. --- W3. Current metrics are insufficient to capture overall quality and diversity. Downstream task-specific metrics would strengthen the paper's claims. We would like to clarify that we have already incorporated downstream task-specific metrics following prior studies [1,3,4]. We consider the Tanimoto similarity and edit distance to measure the diversity of molecules and RNA sequences, respectively. To further address your comments on the overall sample quality, we provide the relative mean error [2] which measures the distance between the mean values of the empirical generative distribution and the target Boltzmann distribution. We present the results in Figure A of our rebuttal PDF. One can see that our method shows superior performance. --- W4. PBP-GFN may reduce exploration in domains with significant uncertainty or where trajectories are not representative of the target distribution. A deeper analysis and empirical evaluation of this are recommended. To address your comments, we consider a scenario where the observed trajectories are not representative of the target distribution. In this domain, an unobserved high-reward trajectory may largely overlap with an observed low-reward trajectory. Then, to explore the high-reward trajectory, one should assign a relatively high probability to the low-reward trajectory, i.e., the opposite of the case requiring exploitation. We examplify and analyze this scenario in Figure B of our rebuttal PDF, which (1) illustrates how pessimistic training may reduce exploration by enhancing the exploitation of observed high-reward trajectories and (2) provides an empirical evaluation of the exploration. One can observe that PBP-GFN may reduce the exploration in considered settings. Despite the potential reduction of exploration, we would like to clarify that our method is still effective as exploitation is significant in most environments. As discussed in Limitation section, there is no free lunch in the exploitation-exploration trade-off. One can futher control the trade-off by interpolating PBP-GFN with explorative GFNs, e.g., MaxEnt, which can be an interesting future work direction. --- W5. PBP-GFN can amplify biases in initially observed trajectories, hindering the discovery of novel objects, but the paper does not address this or mitigation strategies. As you mentioned, our method may struggle to discover novel objects when heavily biased towards initially observed trajectories. However, we would like to clarify that such failure cases are rare in practice, as demonstrated in extensive experiments. Furthermore, to mitigate the bias towards initially observed trajectories, one can reduce the learning rate of the pessimistic backward policy in the initial training rounds. Additionally, incorporating exploration-focused sampling, e.g., a noisy policy, can address this issue. We will add a discussion about this potential risk and mitigation strategies in our future manuscript. --- W6. The paper lacks a comparison with other exploitation techniques, e.g., local search or reward-prioritized buffer. First, we clarify that local search and reward-prioritized buffers are sampling methods for off-policy training, that are orthogonal to our pessimistic backward policy, i.e., the methods are not directly comparable. One can combine both approaches to improve performance further. Note that we have already used the reward-prioritized buffer to implement our method and baselines (Appendix B). Nevertheless, to address your comments, we verify the effectiveness of PBP-GFN by comparing or combining the pessimistic backward policy with local search and reward-prioritized buffer. We present the results in Figure C of our rebuttal PDF. One can observe that our method (1) shows similar performance compared to other techniques and (2) consistently improves the performance when combined with them. --- [1] Trajectory balance: Improved credit assignment in GFlowNets, NeurIPS 2022 [2] Towards understanding and improving GFlowNet training, ICML 2023 [3] Maximum entropy GFlowNets with soft Q-learning, AISTATS 2024 [4] Local search GFlowNets, ICLR 2024 --- Rebuttal Comment 1.1: Comment: Dear Reviewer u41F, We appreciate your constructive feedback for improving our paper in many aspects. We have provided the requested analysis, discussions, and experiments. We are curious whether our rebuttal has resolved your concerns. Thank you again for your time and effort.	Rebuttal 1: Rebuttal: Dear reviewers (u41F, smvU, CTvM, and WPBt) and area chairs, We are deeply grateful for the time and effort you spent reviewing our manuscript. In what follows, we summarize our rebuttal PDF and planned revisions. --- ### Summary of rebuttal PDF Our rebuttal PDF provides the following contents: - Figure A provides experiments on a new metric for the overall quality of generated samples (u41F-W3). - Figure B presents a synthetic example for the case where our PBP-GFN may reduce exploration (u41F-W4). - Figure C and Figure D(a) present the results of comparing and combining PBP-GFN with methods that improve exploitation (u41F-W6, CTvM-W1, WPBt-W2). - Figure D(b) and Figure D(c) present the results on additional benchmarks (CTvM-W2, WPBt-Q2). --- ### Summary of planned revisions We will update our future manuscripts to incorporate the following contents that have been addressed in our rebuttal: - Clarification of the detailed conceptual differences with existing methods for backward policy modification (u41F-W2) - Clarification of detailed implementations for pessimistic training (smvU-Q1) - Additional references relevant to the topic (WPBt-W3) - Additional experimental results measuring overall sample quality (u41F-W3) - Additional experimental results comparing with other methods that improve exploitation (u41F-W6, CTvM-W1, WPBt-W2) - Additional experimental results on the large-scale hyper-grid (CTvM-W2) - Analysis for the case where our PBP-GFN may reduce exploration (u41F-W4) - Discussion of the strategies for mitigating risks in exploitation (u41F-W4,5) - Discussion of additional time complexity (WPBt-W1) Pdf: /pdf/16568a311598b0a6bf873b1b61f9124d2ef72228.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Symmetries in Overparametrized Neural Networks: A Mean Field View	Accept (spotlight)	Summary: This paper studies the Mean-Field limit of generalized shallow neural networks after learning with Wasserstein gradient flow under data augmentation, feature averaging or equivariant architectures as well as standard training. The provided results provide insights into learning with symmetries by covering two notions of invariant laws on the parameter space, varying assumptions on the data distribution and preserved symmetry over the course of training. Strengths: The paper provides several deep and quite general theoretical results on learning with symmetries in the mean-field limit. Although the results are quite technical, the authors manage to present them in good clarity and embedded in the related literature of mean field limits of shallow models. Considering the examples of Data Augmentation, Feature Averaging and Equivariant Architectures seems natural and provides several interesting insights, for example the equivalence of DA, FA and even free training under symmetric data. Weaknesses: The paper already seems quite complete and well written and I could not identify significant weaknesses. The following weaknesses are only minor points: - The description of Figure 1 is hard to parse. Markers like (a)-(d) could reduce ambiguity of what is meant by a column. - The markers in Figure 2 should be larger and it is unclear to me which additional insight to draw from the second row. As I am not an expert in the mean-field and Wasserstein gradient flow literature, I did not verify the correctness of all proofs, and did not double-check the claimed novelty. Typos: 22: lastly, 65 and 66: b=N?, 75: Definition name in bold for consistency?, 120: […], 275: will, 329: a heuristic Technical Quality: 4 Clarity: 3 Questions for Authors: - How close is your setting to practical neural networks trained with SGD? In future work, are there hopes to extend your mean-field theory results to deep networks or to SGD with large learning rates and edge of stability dynamics? Similarly is the entropy regularization merely theoretically pleasing or also practically feasible? - Can GNNs or Transformers also be encoded in your class of equivariant architectures? If so, these example would significantly broaden the target audience. - In future work, in which ways could Assumption 1 be relaxed? Confidence: 2 Soundness: 4 Presentation: 3 Contribution: 4 Limitations: The authors adequately acknowledge the main limitations of the paper. These limitations lie beyond the scope of this paper, but pose interesting directions for future work: - The provided results are only asymptotic and only consider gradient flow on shallow models as opposed to edge of stability dynamics in finite deep models. - The practical relevance of the findings and proposed algorithm at finite width for practical architectures, datasets and optimization procedures could be empirically verified. In particular, does vanilla training remain SI throughout training beyond the simple student-teacher setting? Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for their thorough reading and the relevant comments and suggestions. Regarding the detected weaknesses of the paper, we will make sure to address them by providing clearer descriptions of the relevant figures, and correcting the detected typos. For instance, we shall complement the description of Figure 2, emphasizing the role of the second row as a “parallel” view of the plane ${\cal E}^G$, that allows us to visually check that particles indeed remain inside it (see Figure 5 for an example where this doesn’t occur). We next address the questions posed by the reviewer: Q1: Regarding practical NNs, the entropy term in practice, and extensions to deep networks and edge-of-stability (EoS) dynamics. - In our Global Response, we provide a deeper discussion regarding the applicability of our setting to practical NNs. Namely, we stress that the MF limit is closer to real applications than other asymptotic regimes, and that our numerical experiments correspond to quite “practical” settings (a “usual” single-hidden-layer NN architecture trained with the “usual” SGD). That is, despite our results being “asymptotic”, we believe they are applicable to reasonably practical NN implementations (with relatively normal width $N$). - Regarding the entropy-regularization, despite it being mostly a theoretical tool to ensure uniqueness and global convergence, it also corresponds in practice to considering a “noisy/Langevin” SGD dynamics. Indeed, when taking the limit $N\to \infty$, the presence of properly scaled noise in the SGD dynamic exactly translates to the appearance of the entropy term in the WGF. Therefore, in a sense, the entropy term is truly realized in practice through the introduction of noise. - We most surely hope to extend our results to general deep neural networks, for which we believe that some of the symmetry-related theorems (Section 3.3) might still hold. As discussed in our Global Response, however, this requires a more mature (and unified) mean-field theory of deep neural networks, which is yet to be established. - We haven’t specifically looked into SGD with large learning rates and EoS dynamics, but it indeed seems to be an interesting direction for future work. Now, we know that some of our proofs (e.g. for Theorems 3 and 4) can be applied in the setting of works like [18], where the MFL is established under a fixed learning rate (which may be large, and doesn’t necessarily decrease with N). This can be seen as a first preliminary result in the suggested direction. Q2: Regarding applicability on GNNs and Transformers. As mentioned to other reviewers (see Global Response), very commonly applied equivariant architectures (such as CNNs and GNNs) can be exactly modeled in our setting: either as “shallow” models, or as large ensembles of multilayer models; and such that ${\cal E}^G$ exactly encodes the desired EA. To clarify this point, we will include a section in the Supplementary Material where some of these relevant examples will be explicitly modeled in our framework (e.g. a “shallow” GNN, under the right action of $G = S_n$ on $\cal Z$). As for Transformers, it is well known that they can be seen as a particular type of GNN; and so, in particular, they can also be modeled using our framework (again, as "shallow" Transformers or also large ensembles of Transformers). Q3: Regarding Assumption 1. We believe that only a couple of our assumptions are truly fundamental for achieving our results; namely, the convexity and joint invariance of $\ell$, and the joint-equivariance of $\sigma_$. On the other hand, some of the more “technical” assumptions we believe can be relaxed. For instance, it is known (see e.g. [9, 51]) that the boundedness of $\sigma_$ can be replaced by assumptions on the data distribution $\pi$ (e.g. bounded “finite-moments”, or compact support). Also, passing through the Wasserstein sub-Gradient Flow (as in [13]), and considering weak solutions, we believe that some of the differentiability constraints on $\ell$ and $\sigma_$ could be potentially lifted. Regarding the Limitations* Generally speaking, we plan on tackling many of the detected limitations of our results in upcoming works. Namely, we will be sure to continue experimenting with our results (particularly, Theorems 5 and 6) on more realistic and practical datasets (i.e. beyond the simple student-teacher setting). We also comment on the applicability of our work in our General Response. --- Rebuttal Comment 1.1: Title: Thank you Comment: I thank the authors for their thoughtful response and thorough work. I am satisfied with the changes promised in the global response and I will keep my positive evaluation. --- Reply to Comment 1.1.1: Comment: We thank the reviewer for their comment, and are very happy for their positive evaluation. Thanks again!	Summary: The paper investigates the learning dynamics of neural networks with several symmetry-leveraging techniques from a mean-field perspective. The main result indicates that optimizations with data augmentation and feature averaging (and the corresponding Wasserstein gradient flows) are equivalent in the mean-field limit under mild assumptions, while equivariant architecture may suffer from limited expressivity. Moreover, for equivariant data, freely-trained models also have the mean-field flow remaining in the set of strongly invariant distributions if initialized there, which is supported by the experiments. Finally, the authors propose a heuristic to discover equivariant architectures by gradually expanding the equivariant subspace. Strengths: * The math in the paper is rigorous and detailed. Complete proofs and abundant examples and remarks are provided. As more of a practitioner myself, I can understand the main ideas of the paper without much difficulty, though I did not check the proofs carefully. * The experiments are compact and well-designed, clearly supporting the theoretical results. Weaknesses: * This is not essentially a weakness, but the theoretical results don't bring many interesting insights to me. They mostly match my existing intuitions. E.g. for equivariant data, freely-trained models tend to have the same training dynamics as symmetry-aware models. I will leave it to other reviewers to comment on the theoretical significance of these results. * I suggest the authors provide more detailed explanations about some mathematical terminology, e.g. the pushforward of a probability measure; dt-a.e. standing for almost everywhere wrt dt. This could make the paper more accessible to the general audience. Technical Quality: 3 Clarity: 3 Questions for Authors: * Can you explain what is the connection between jointly equivariant and equivariant? The way I understand it is that we have some group actions on $\mathcal Z$ induced from the definition of joint equivariance, i.e. $\sigma_* (\rho_g x, M_g z) = \hat\rho_g \sigma_(x,z)$. In other words, $M_g$ is determined by the group action on data and the model architecture. Then, if $M_g z = z$, then a NN model parametrized by $z$ is equivariant. Is this correct? Proposition 5 states that equivariant architectures can lead to optimal solutions provided some universality conditions. How restrictive are these conditions? * Is the property of data equivariance (defined in L150) equivalent to the marginal distribution on $\mathcal X$ being invariant and the function $f: \mathcal X \to \mathcal Y$ being equivariant, given that the mapping from $\mathcal X$ to $\mathcal Y$ is deterministic? If so, would it be too restrictive to assume the invariance of $\pi_\mathcal X$? * In Section 4.1, the authors show that SI-initialized but freely-updated models remain in $\mathcal E^G$ for large $N$s. This is indeed an interesting phenomenon. I wonder if this is related to the exact WI-initialized teachers. Can you provide, in addition to the arbitrary particles in Appendix D, the WI-initialized particles? Most likely, sampling from the pushed-forward empirical measure would result in a non-symmetric teacher, but there's a chance that the WI teacher might contain two pairs of symmetric parameters (e.g. $\theta_1^, g\theta_1^, \theta_2^, g\theta_2^$) and another singled out, making it mostly equivariant. After all, if the teacher is not equivariant, then the data is not equivariant, and the assumptions in Theorem 5 do not hold. * Section 4.2 reminds me of another work on discovering symmetry [1], which initially specifies a large candidate group and discovers the subgroup symmetry by inspecting the weights of relaxed group convolution filters. Can you comment on the connection between your method and theirs? ## References [1] Wang, Rui, et al. "Discovering Symmetry Breaking in Physical Systems with Relaxed Group Convolution." Forty-first International Conference on Machine Learning. Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The authors have discussed the limitations. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer’s insightful feedback. We will address the signaled weaknesses in our final version, including in the Appendix a table with relevant notation and further reference for the main concepts. We will also further stress those aspects that, we believe, go beyond the usual intuition on symmetrically-trained NNs. These include the non-trivial, quite interesting fact that models freely-trained on equivariant data, stay for big N within the space of equivariant parameters; and the non-necessarily intuitive difference between two types of parameter distributions that naturally produce equivariant models: WI measures (which define them in general), and SI measures (which encode traditional “Equivariant Architectures” and have possibly fewer approximation guarantees). We next answer the questions posed: Q1: About the connection between jointly equivariant and equivariant In the setting of traditional NNs, the group action $M$ is determined by the action on data and on the model architecture (as displayed in Sect. A.4); and indeed a NN model parameterized by $z$ s.t. $M_g z = z$ for all $g\in G$ corresponds to an equivariant architecture (thus, an equivariant model). A slight subtlety is that a shallow NN model can combine different $z_i$, e.g. $(1/N).\sum_{i=1}^N \sigma_(x,z_i)$, thus being an equivariant function without all the $z_i$ satisfying $M_g.z_i = z_i$ (i.e. without explicitly having an "equivariant architecture" in the traditional sense). This is the core principle behind WI distributions. Further details on the assumption of $\sigma_$ being jointly equivariant (i.e. equivariant in both arguments) are given in our Global Response. Q2: Regarding Proposition 5 Depending on the group considered and the architecture itself, these conditions may be generally satisfied. As mentioned in the Sect. A.4, important architectures such as CNNs and GNNs (see [35, 58, 59] for further discussion) are known to be “first-order-universal”, which implies that, taking the infinite-width limit in our setting, universality in the target class of models is guaranteed. We will elaborate more on this in Section A.4 in the final version. Q3: On the property of data equivariance in L150 The reviewer is right. In general, $\pi$ G-equivariant implies $\pi_{\cal X}$ G-invariant [BT20]. Further, if $\pi$ is equivariant and such that $Y = f(X)$ for some function $f: \cal X \to \cal Y$, Prop.10 in Sect. A.3 implies $f$ is a G-equivariant function $\pi_{\cal X}$-a.e. Conversely $\pi_{\cal X}$ G-invariant plus $Y = f(X)$ for $f$ as before implies $\pi$ G-equivariant. As discussed in the literature (e.g. [10, 24, 34]), assuming $\pi_{\cal X}$ G-invariant might seem restrictive in some settings (e.g. in image classification, one shouldn’t assume that “images can arrive with any possible orientation” when training), but such assumption is reasonable when “exploiting symmetries” does make sense. As mentioned in remarks after Theorems 3 and 5, one could also just neglect the assumption of $\pi$ being equivariant, and introduce the inductive bias by applying data augmentation (which forces the marginal on $\cal X$ to be G-invariant). Notice also that $\pi$ “equivariant” is usually more general than the situation discussed above, including models like $Y = f(X) + \xi$ with $f$ as before, and suitable random noises $\xi$ possibly correlated to $X$. Q4: On SI-initialized but freely-updated models remaining in ${\cal E}^G$ for large N The exact WI-initialized teacher particles are a key part of our empirical result, as they make the teacher equivariant and thus the data distribution equivariant too. We mentioned the WI-initialized particles only implicitly in Appendix D (in terms of the symmetrization of the empirical measure), but they are exactly as stated by the reviewer: for every particle $\theta_i$, the symmetrized version has both $\theta_i$ and $g.\theta_i$, with $g$ the non-trivial element of $S_2$. Explicitly (omitting the scale parameter and the transposition for clarity), they are given by: $\theta_1 = (-1, 0, 0, 0.5)$, $g.\theta_1 = (0.5, 0, 0, -1)$ $\theta_2 = (0.5, 1, 0, 1)$, $g.\theta_2 = (1, 0, 1, 0.5)$ $\theta_3 = (-0.5, 0.3, 1, 0)$, $g.\theta_3 = (0, 1, 0.3, -0.5)$ $\theta_4 = (0, -1, -0.5, 1)$, $g.\theta_4 = (1, -0.5, -1, 0)$ $\theta_5 = (0.7, -0.7, 0.5, 0.7)$, $g.\theta_5 = (0.7, 0.5, -0.7, 0.7)$ Note that, besides them being symmetric pairs, none of these particles lie within ${\cal E}^G$ (given by vectors of the form $(a, b, b, a)$ for $a,b \in \mathbb{R}$), making the empirical demonstration of Theorem 5 quite remarkable from our point of view. Q5 on Section 4.2 and work on symmetry-discovery We were unaware of [WHG+23] and will properly reference it. As in our work, their method starts with the most constrained architecture (in our case, the null space), respecting symmetry w.r.t. the largest possible group; and symmetries are then "broken" as models are trained on data. Their method seemingly works “one-shot”, while using a weighted combination of group convolutional filters to find “symmetry-breaks”; ours iteratively constructs an invariant linear subspace of the parameter space by adding dimensions as symmetries are broken. Our Theorem 5 guarantees that our method won’t leave ${\cal E}^G$, and part of our future work is establishing symmetry-breaking guarantees for our heuristic (comparable to their Proposition 3.1). The latter is discussed around L.1535 in Section C.3.2. in light of the MF interpretation. Finally, both methods aren’t really discovering the “underlying symmetry” of the data, but rather “optimizing architectures” compatible with such symmetries (be it the “right” subspace of equivariant parameters, or the “right” weights for each convolutional filter). Identifying the true underlying structure of symmetries is a much harder problem that is yet to be tackled in both cases. --- Rebuttal Comment 1.1: Comment: Thank you for your response. My concerns have been addressed, and I'm happy to keep the current recommendation. I have some more comments about Q4&5. For Q4, how many particles are there in the WI-initialized teacher? Originally I thought it was 5, as you mentioned in L1585. But the WI distribution $(\nu_{\theta^}^{N_})^G$ has support on 10 (5 pairs of) points. Do you randomly sample 5 particles from this distribution, or do you include all 10 points? If it is the latter case, then the teacher is indeed strictly equivariant. For Q5, I think the difference between "discovering the symmetry of the data" and "optimizing model architectures compatible with data symmetries" is subtle. I feel these two objectives are often connected to each other. In [1], for example, one can tell from the optimized architecture what is the maximal symmetry in data. This is also done in [2] but in a quite different way, by solving the Lie derivative constraint wrt a non-equivariant network. Conversely, one can also start by discovering the data symmetry and design equivariant architectures accordingly [3]. These works may be relevant if you plan to further investigate the idea in Sec 4.2. [1] Discovering Symmetry Breaking in Physical Systems with Relaxed Group Convolution. ICML 2024. [2] LieGG: Studying Learned Lie Group Generators. NeurIPS 2022. [3] Generative Adversarial Symmetry Discovery. ICML 2023. --- Reply to Comment 1.1.1: Comment: Thank you very much for your response, and we are happy as well for your positive recommendation. Regarding your follow-up questions: Regarding L.1585, we agree that the current phrasing can easily lead to confusion, and we will be sure to change it in the final version. We only wanted to refer to the arbitrary teacher having 5 particles and, indeed, as you have noticed, the WI teacher has exactly 10 particles (which are the ones we provide in our original rebuttal). Namely, it is exactly $G$-equivariant (and not just an empirical sample from a $G$-equivariant measure). As we mention in our original rebuttal, the current version “implicitly” mentioned both of these facts, as from our remarks in lines 196-203 and the phrase in line 1587-1588; but we will surely make this clear and explicit in our final version. We do want to stress that the exact equivariance of the WI teacher doesn’t mean the problem is any easier. Since the WI-teacher’s particles don’t live in ${\cal E}^G$, one intuitively would believe that the freely-trained particles of a NN (initialized within ${\cal E}^G$) would prefer to “escape” ${\cal E}^G$ in order to better approximate the teacher. However, as shown by our numerical experiments, this doesn’t happen, and the particles remain (up to numerical error) within ${\cal E}^G$. Regarding Q5, we deeply thank you for the provided references and ideas. We will be sure to consider them for our upcoming works regarding the topic.	Summary: This work studies the symmetric structure of the model and data structures with respect to the action of $G$ and studies the Wasserstein gradient flow (WGF) for learning overparameterized neural networks under the mean-field (MF) regime. In particular, the authors consider data augmentation (DA), feature averaging (FA), and equivariant architecture (EA) as symmetry-leveraging techniques. They show that for symmetric data, DA and FA follow the same dynamics by exploiting weakly and strongly invariant laws (WI and SI) on the parameter space. In particular, the following statements are given. - DA and FA are equivalent in terms of optimal values and also equivalent to standard training (free training) for WI measures (Theorem 2). - Furthermore, this equivalence is shown over the space of general measures when the data distribution is equivalent (Corollary 2). - WGF for an invariant functional preserves weak invariance of the measure (Theorem 3 and Corollary 3). Moreover, there is an equivalence of WGF for DA, FA, and free training under suitable conditions. Strengths: The paper proposes the notion of WI and SI and proves several equivalences between DA, FA, and free training. These results indicate when these techniques (DA and FA) are meaningful. Weaknesses: - This work mainly focuses on two-layer neural networks; hence, it is unclear if the results can be applied to deep neural networks. - The results, especially for WGF, seem to fully rely on the mean-field limit $N\to\infty$. Hence, it’s unclear whether the theory has some implications for finite-neuron settings. - (Minor) The paper is somewhat hard to follow because of the numerous notations. I suggest including a table that summarizes these notations. Technical Quality: 3 Clarity: 2 Questions for Authors: - In Theorem 4, the noisy SGD (4) involves the projection step of the noise. I think such a projection is non-trivial in general. Are there any practical examples? - Is WGF essential for the results in Section 3.3? Do similar results hold for other dynamics (e.g., underdamped version)? Confidence: 3 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: Limitations are addressed in the paper. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for their relevant feedback about the paper. We will make sure to address the detected weaknesses in our final version, specifically: W1: Regarding our work mainly focusing on two-layer neural networks. As mentioned in our Global Response, the full MF theory for deep NNs is an open, active research endeavor, in which sustained progress is being done. We think that a significant part of our results can be extended to settings in which MF results on deep models are (or will be) available; this has been left for future work, however, since the involved technicalities are usually quite intricate. Nevertheless, as noted in our Global Response, our current setting already allows to go far beyond two-layer NNs (and we will be sure to further stress this in the core of our work). Indeed, our "activations" $\sigma_$ are general functions on parameter spaces that can, by themselves, encode complex deep architectures (including e.g. kernels in CNNs, heads in Graph Attention Networks, etc). Thus, the resulting "shallow models" can represent large stacks of such (jointly-trained) multilayer “units”; i.e. deep models which, although not fully general, are way more interesting than single-hidden-layer NNs. Finally, as put forward in most of the growing literature on the MFL of overparametrized NNs (see references cited in the paper), the MF behavior can already become apparent for reasonable/realistic finite values of $N$; which speaks to a possibly broad applicability of such framework. Along this line, see our comments below regarding W2. W2: On our results fully relying on the mean-field limit as $N\to \infty$ and the theory having no clear implications for finite $N$* Although not fully conclusive, the MFL and its associated WGF is one of the most promising approaches to mathematically explain the generalizability capacity of the SGD training dynamics of overparametrized NNs. Furthermore, it is the asymptotic approximation of NNs known to better describe their feature learning capabilities [36, 37, 38, 46]. In practice, as shown both by experiments in those papers and by our numerical results, the MF viewpoint provides truly useful insights (and new results) on the training dynamics, that manifest themselves even for relatively small numbers of neurons (1000 was enough in our case). But not only does the MF theory provide new insights for finitely many (though large numbers of) neurons, that would be unaccessible from a fixed $N$ standpoint (as is the case for Theorem 5). Ongoing research in this field (based on theoretical tools such as propagation of chaos, optimal transport, WGFs and functional inequalities, see e.g. [9,18]) also has the potential to provide non-asymptotic estimates and quantitative answers to concrete questions with practical implications (e.g. How many neurons and training steps should be enough in order to attain a given level of generalization/population error? Which architecture/training method takes better advantage of given, limited resources?). We thus expect the MF theory to increasingly bring useful insights and concrete implications for finite-neuron settings, including for the issues addressed in this work. We will give further details on non-trivial implications of our theoretical results, for the finite-N setting, in the final version of our work. W3: On the paper being somewhat hard to follow because of the numerous notations As stated in our Global Response, we will include a table explaining our relevant notation. We now address the proposed questions: Q1: Regarding the projected noisy SGD dynamics. - Indeed, as we also mention in the core of our work, computing the projection onto ${\cal E}^G$ is a highly complex problem (see [23, 24]) that can’t always be efficiently solved in practice. However, our alluded results hold even taking $\beta = 0$; that is, without including any projected noise (and thus, without ever needing to compute it). - As mentioned in our remarks and our experimental results, any shallow NN with all parameters initialized at {0}, being trained freely with traditional SGD and without noise, will satisfy Theorems 5 and 6 in the MF limit. We believe that the previous conditions (modulo the shallowness of the NN and taking a big N) are all fairly easy to achieve in practice. In fact, this is exactly the case of our numerical experiments (where we never assume to know G and never explicitly compute such projection; see our Global Response for details). - The projection of the noise is only included as a tool to allow for easy “global convergence” guarantees for the dynamic within the space of SI-distributions (following the traditional MF literature on the topic [9, 28, 38], among others): a “general” noise cannot be used, as it would always remove the dynamic from ${\cal E}^G$. In short, the projection of the noise in (4) is far from being fundamental in the proofs of Theorems 5 and 6, and their further application. Q2: Regarded dynamics beyond the WGF - In general, we remained within the domain of the classical WGF dynamics following the cited (standard) MF literature on the topic; without looking much into other variants of the dynamics, but also without discarding the applicability of our results therein. - Indeed, we believe Theorems 3 and 4 to be “natural” results, and expect them to hold for many potentially different training dynamics (e.g. Wasserstein sub-Gradient Flows [13], underdamped dynamics [FW23], annealed dynamics [12], among many others). - From [24], we know that Theorem 5 holds in a finite-N setting when exact DA is applied during training. The interesting MF phenomenon is that it also holds under free training with randomly sampled data (Theorems 5 and 6). This result doesn’t seem immediate to generalize for other asymptotic dynamics (e.g. annealed or underdamped), and we thus consider it an interesting question to be tackled in future work. --- Rebuttal Comment 1.1: Comment: Thank you for the detailed response. The authors have adequately addressed my concerns. Given the strength of the paper, some limitations seem negligible. I will raise my evaluation. The discussion provided in the general comments will significantly help readers understand the importance and applicability of the theory. --- Reply to Comment 1.1.1: Title: Thank you Comment: We thank you for pointing out your concerns, as they have undoubtedly helped us provide a clearer exposition of our central ideas and contributions in the final version of our paper. We are also thankful for your positive comments and the evaluation adjustment.	Summary: This paper presents a mean-field analysis on a class of overparameterized neural networks that are expressed as an ensemble of $N$ units, trained with SGD under symmetries in data distribution and possible use of symmetry-leveraging techniques (data augmentation, feature averaging, and equivariant architectures). While the analysis is based on prior work on mean-field analysis on the same class of neural networks e.g. based on Wasserstein gradient flows [1], the contribution of this work is in extending to learning under symmetries. The setup is as follows: - In considered neural networks, a unit computes $\sigma_:(\mathbf{x},\theta_i)\mapsto\hat{\mathbf{y}}$ and the network computes $\Phi_{\theta}^N:(\mathbf{x},\theta)\mapsto \frac{1}{N}\sum_{i=1}^N\sigma_(\mathbf{x},\theta_i)$. - Overparameterization means the width $N\to\infty$, yielding a limiting ensemble $\Phi_\mu$ where $\mu$ is understood a probability measure on the space of parameters $\theta_i$. - The parameters $\theta$ are optimized using noisy SGD. The mean-field theory of the neural networks considered above [1] aims to analyze the training dynamics of the limiting ensemble $\Phi_\mu$, given that its optimization using a convex loss function becomes a convex optimization problem (unlike $\Phi_{\theta}^N$ which induces non-convex optimization) and that its global optimum may be approximated by training $\Phi_{\theta}^N$ with a large width $N$. Specifically, it is known that SGD on $\Phi_{\theta}^N$ approximates Wasserstein gradient flow on $\Phi_\mu$ in the scaling limit $N\to\infty$ under certain assumptions, which then, under certain assumptions, converges to the global optima of the convex optimization problem. Given the background, the paper presents a mean-field analysis given that the data generating distribution is possibly under a symmetry described by a compact group $G$, and symmetry-leveraging techniques are possibly used. The authors consider data augmentation, feature averaging (i.e. symmetrization; also called the Reynolds operator), and equivariant architectures, in accordance to literature [2]. The idea for the analysis is to distinguish between two types of symmetries for the measure $\mu$ on parameters: weakly-invariant and strongly-invariant, where weakly-invariant refers to an invariant measure on the subspace containing possibly non-invariant elements, and strongly-invariant refers to a measure on invariant subspace. The authors first show in Section 3.1 that, given that the unit $\sigma_(\cdot, \cdot)$ is jointly equivariant, $\Phi_\mu$ is equivariant if and only if $\mu$ is weakly-invariant. Then, feature averaging (and data augmentation) can be understood as being related to weakly-invariant distributions obtained through symmetrization, and equivariant architecture is related to strongly-invariant distributions. The authors then, in Section 3.2, begin mean-field analysis on optimality under a set of assumptions including that the unit $\sigma_(\cdot, \cdot)$ is jointly equivariant (Assumption 1), and show that: - (Proposition 3) Optimizing with respect to an invariant loss function yields a weakly-invariant optimum if it has a unique minimizer, - (Corollary 1) If input data distribution is invariant, optimizing under data augmentation and feature averaging are equivalent and corresponds to approximating the symmetrized version of mean of the labeling function, - (Corollary 2) If data distribution is equivariant, optimizing under data augmentation and feature averaging provide no advantage, - (Proposition 4 and 5) But even when data distribution is equivariant, equivariant architectures (i.e. strongly invariant measures $\mu$) may not achieve the optimum with respect to a given invariant loss function, unless universality properties that are "good enough" for the given data distribution are assumed. Then, in Section 3.3, the authors provide mean-field analysis on training dynamics, and show that: - (Theorem 3, Corollary 3, and Theorem 4) Under an invariant loss function and Assumption 1 (among others), a training dynamics $\mu_{0:t}$ following the Wasserstein gradient flows yields a unique weakly-invariant solution $\mu_t$. If the data distribution is equivariant, from Corollary 2 this result applies to freely-trained neural networks without symmetry leveraging techniques, and data augmentation and feature augmentation again provide no advantages. - (Theorem 5 and 6) Under an invariant loss function and Assumption 1 (among others), a training dynamics $\mu_{0:t}$ starting at a strongly-invariant initial condition $\mu_0$ and following the Wasserstein gradient flows yields strongly-invariant solutions $\mu_t$. Importantly, this means that if the data distribution is equivariant, $\mu_t$ stays strongly-invariant throughout training even though it is not explicitly forced or constrained to be invariant. Furthermore, equivariance of data distribution can be dropped if one of the symmetry leveraging techniques are used, which all yield coinciding solutions. In Section 4, the authors provide synthetic experiments focusing on validating Theorem 3-6, and then propose and demonstrate an empirical method for finding good equivariant architecture for the task at hand (i.e. the most expressive among invariant subspace) by training according to Theorem 5 and 6 until convergence. [1] Lenaic Chizat and Francis Bach. On the global convergence of gradient descent for over-parameterized models using optimal transport. Advances in neural information processing systems, 31, 2018. [2] Clare Lyle, Mark van der Wilk, Marta Kwiatkowska, Yarin Gal, and Benjamin Bloem-Reddy. On the benefits of invariance in neural networks. arXiv preprint arXiv:2005.00178, 2020. Strengths: - S1. The paper targets an important and challenging problem of understanding training dynamics of overparameterized neural networks under symmetries and their leveraging. The technical approach that applies mean-field analysis of generalized shallow neural networks [1] to learning under symmetries is original as far as I am aware. - S2. The paper considers three types of symmetry-leveraging techniques: data augmentation, feature averaging, and equivariant architectures. These three are sufficiently general to represent currently used techniques [2]. The descriptions as well as strengths and weaknesses of each technique discussed in Section 2.3 are correct. - S3. The authors' approach of imposing distributional symmetries on the measure $\mu$ to describe equivariant architectures as strongly-invariant (and feature averaging as weakly-invariant given that the unit $\sigma_(\cdot, \cdot)$ is jointly equivariant) is interesting and could be potentially useful in future work. - S4. The results presented in Section 3 and 4 are interesting, in particular Theorems 5 and 6 which shows that overparameterization and equivariant units, combined with equivariant data distribution or symmetry leveraging, leads to the property that strongly-invariant parameter initialization stays strongly-invariant throughout the training even without explicit constraints to do so. (But also see W1.) [1] Lenaic Chizat and Francis Bach. On the global convergence of gradient descent for over-parameterized models using optimal transport. Advances in neural information processing systems, 31, 2018. [2] Clare Lyle, Mark van der Wilk, Marta Kwiatkowska, Yarin Gal, and Benjamin Bloem-Reddy. On the benefits of invariance in neural networks. arXiv preprint arXiv:2005.00178, 2020. Weaknesses: - W1. I have concerns regarding Assumption 1, which is a key assumption underlying Section 3 and assumes that the unit $\sigma_:(\mathbf{x},\theta_i)\mapsto\hat{\mathbf{y}}$ is jointly equivariant with respect to the input $\mathbf{x}$, the parameters $\theta_i$, and the output $\hat{\mathbf{y}}$. This assumption states that we have already (partially) baked in the symmetry constraint to our model class. This may be natural for analyzing equivariant architectures, but does not coincide with the practical uses of data augmentation and feature averaging (e.g. please see [2]), as they are generally applied to an arbitrary, non-equivariant function, while in the setup of this work they are applied on already equivariant units. This limits the usefulness of the results regarding data augmentation and feature averaging. Perhaps the setup of this work could be relevant to symmetry breaking in already equivariant architectures [3], but I am not entirely sure. - W2. In Line 92-93, the authors claim that "Note that requiring an infinite and i.i.d. sample from $\pi$ is key when letting later $N\to\infty$. This is not truly a restriction, since one can always sample from the empirical distribution of finite data points". This seems problematic since (1) if we can infinitely sample from $\pi$, then we have access to it, which violates basic assumptions in machine learning (Line 82), and (2) if we infinitely sample from an empirical distribution supported on finite set of data points, the resulting distribution would not be $\pi$, and consequently the SGD scheme in Equation (1) would not be optimizing the objective in Equation (2). (Please correct me if I am wrong.) - W3. The writing of the paper could be in general improved. For example, the paper uses an excessive number of abbreviations (MF, MFL, NN, SL, DA, FA, EA, WI, SI, WGF, RMD, V), which is hurting readability. It would be also helpful to provide an example of a measure and its (non-equivalent) invariant symmetrization and projection in Definition 5; these are important concepts that are used in all later sections, but I was not able to directly grasp them from reading the text. For example, considering a uniform distribution on $[0, 1]\subset\mathbb{R}$, and a multiplicative group {1, -1} acting on $\mathbb{R}$ by multiplication, may be sufficiently informative. - W4. The architecture discovery algorithm proposed in Section 4.2 was a bit questionable to me, since the architecture of the ensemble is already specified (at least up to a significant portion) by the jointly equivariant unit(s) $\sigma_*(\cdot,\cdot)$, and the algorithm searches for their parameters within a strongly-invariant regime. I am not sure why this algorithm can be understood as doing architecture discovery, instead of doing the usual parameter optimization. - W5. Currently, it is not immediate how the study of the ensemble considered in the paper would benefit the development of practical neural networks that leverage symmetry. Showing how some of the currently used symmetry-leveraging deep neural networks can be viewed as such ensembles could be informative in this directions. [2] Clare Lyle, Mark van der Wilk, Marta Kwiatkowska, Yarin Gal, and Benjamin Bloem-Reddy. On the benefits of invariance in neural networks. arXiv preprint arXiv:2005.00178, 2020. [3] Rui Wang, Elyssa Hofgard, Han Gao, Robin Walters, and Tess E. Smidt, Discovering symmetry breaking in physical systems with relaxed group convolution, arXiv preprint arXiv:2310.02299, 2023. Technical Quality: 3 Clarity: 2 Questions for Authors: Please see the Weaknesses section. Confidence: 3 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: The authors have partially addressed limitations of their work, for example in Section 5. Since the discussions are currently scattered across the main text, I encourage the authors to gather them in a dedicated limitations section. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for their careful reading and relevant feedback on the paper. We will incorporate an explicit Limitations section in the Appendix of the revised version, as well as a simple yet clarifying example of the different notions of symmetric distributions (e.g. if ${\cal Z}=\mathbb{R}$ with the multiplicative action of $G=$ { -1, 1 }, setting $\mu = \delta_x$ for $x \neq 0$, we get $\mu^G = \frac{1}{2} (\delta_x + \delta_{-x})$, and $\mu^{{\cal E}^G} = \delta_0$). The beginning of our Global Response mentions other clarifying sections we plan to add. We next address the perceived weaknesses: W1 Your concerns regarding the “a priori knowledge” of symmetries that’s encoded in the fact that $\sigma_$ is assumed jointly-equivariant, are generally justified, but miss a key point in the setting of the paper. We refer the reviewer to our Global Response, where we provide thorough revision of the assumption of $\sigma_$ being jointly-equivariant (also partially addressed in Appendix A.4; we will be sure to make it more explicit in the core of our work). In short, $\sigma_$ can describe many configurations beyond single-hidden-layer NNs, and the property of it being jointly-equivariant doesn’t necessarily imply that “everything inside it” needs to be equivariant as well. For instance, if we take $\sigma_$ to be the “traditional” single-hidden-layer NN and we consider the group action on $\cal Z$ to be trivial on the hidden layer; then all our results apply with no constraints on the architecture whatsoever (see our Global Response and the proof of Proposition 4). In particular, DA, FA and “vanilla” training with distributionally equivariant data are still tightly related in terms of their optimization and WGFs (regardless of the properties of the inner activation). More interestingly, when $M$ is taken to be a more intricate action (and the unit $\sigma_$ respects it), the EAs are also more attractive, and our results on DA and FA work just as well. W2* We agree with you on the fact that performing SGD with an infinite i.i.d. sequence sampled from $\pi$ is not equivalent to sampling infinitely many times with replacement from a (finite) given empirical measure $\pi_k$, “previously” obtained by sampling $k$ points from $\pi$. What we wanted to stress is that, from the theoretical point of view, our treatment of the first and second cases (often respectively called “population SGD” and “empirical SGD” in the literature) is indistinct and can be applied to both situations. We will rewrite said statement, to make our intent clearer. We also agree that having access to an infinite i.i.d. sequence of a given law can be considered a way of “accessing” the whole distribution but, of course, we do not expect this to be the actual application setting. Our results, as well as the whole MF approach to NNs, should be understood as an approximation that is valid for a large enough i.i.d. sample. W4 We believe that our discovery heuristic can be nicely justified through our numerical experiments. As mentioned in our Global Response, our experiments are run with a traditional single-hidden-layer NN without any specific regard for the architecture (by default, code frameworks often apply activations pointwise). In particular: - We assume only that the symmetry group acts via permutations, and little to no care is put into truly encoding anything into $\sigma_$ (see our Global Response for further discussion). In particular, we never assume to “know” the group $G \leq S_n$ encoding data symmetries. - We simply initialize our architecture with all parameters being 0, and let it train unconstrained for a set number of epochs. Theorem 5 guarantees that such training will never leave the subspace ${\cal E}^G \leq \cal Z$, which is possibly of much lower dimension than $\cal Z$ (e.g. imagine convolutional layers as a subspace of all possible linear layers between images). - Our heuristic iteratively discovers ${\cal E}^G$, by capturing the directions on which the trained parameters “break” the symmetry (under the assumption that this indeed happens). Despite not explicitly “discovering” new ways of building NNs, it does provide the “most expressive weight-sharing scheme” that respects data symmetries. It also yields a “basis” for such space, allowing to later build NNs with $dim({\cal E}^G) << dim(\cal Z)$ parameters. - Indeed our heuristic is only doing parameter optimization, but our theory (cf. Theorem 5) guarantees that it will never leave a strict, possibly much smaller subspace of $\cal Z$. In short, the “discovery” part is that we start knowing little to nothing about our data symmetries (e.g. only that they are given by a finite group acting via permutations), and we end up with a way of building strongly-equivariant NN (i.e. more “parameter-efficient” than what we started with) in the smallest possible parameter subspace signaled by the data itself. W5* Architectures such as DeepSets, GNNs and CNNs (which are massively used in practice) were key pieces of inspiration for the development of our work. Namely, we know that our “unit” $\sigma_$ allows for modeling such equivariant architectures both as wide single-hidden-layer networks, and as large ensembles of multilayer NNs (both in such a way that $\cal Z$ is a large linear space and ${\cal E}^G$ represents exactly the desired EA). We will be sure to include a section in the Supplementary Material where some of these practical examples shall be described in detail. Knowing this, and despite the theoretical nature of our work, we believe that our results in Section 3 could provide key guarantees and ideas for users of practical equivariant architectures. --- Rebuttal Comment 1.1: Comment: Thank you for the comprehensive rebuttal. I am trying to technically understand the response on the joint-equivariance of single-hidden-layer NN when the group acts trivially on the hidden layer (regarding W1). Following Line 65-67, let $\mathcal{X}=\mathbb{R}^d$, $\mathcal{X}=\mathbb{R}^c$, and $\mathcal{Z}=\mathbb{R}^{c\times b}\times \mathbb{R}^{d\times b}\times \mathbb{R}^b$, $z = (W, A, B)\in \mathcal{Z}$, $\sigma:\mathbb{R}^b\to\mathbb{R}^b$, and $\sigma_(x,z)\coloneqq W\sigma(A^\top x+B)$. From Line 170-171, the joint-equivariance is written as $\sigma\_* (\rho\_g \cdot x, M\_g \cdot z) = \hat{\rho}\_g \sigma\_* (x,z)$ for all $g,x,z\in G\times \mathcal{X}\times \mathcal{Z}$. Now let $M\_g$ be a trivial action. Then joint-equivariance is required as $\sigma\_* (\rho\_g \cdot x, z) = \hat{\rho}\_g \sigma\_* (x,z)$, or equivalently $W\sigma(A^\top \rho\_g \cdot x+B) = \hat{\rho}\_gW\sigma(A^\top x+B)$, for all $g,x,z\in G\times \mathcal{X}\times \mathcal{Z}$. As far as I am aware, this is not true in general; let $A=0$, $\sigma=\mathrm{id}$, $W=I$, and let $B\in\mathbb{R}^b$ have distinct entries, then we have $\sigma\_* (\rho\_g \cdot x, z) = B$ which is not equal to $\hat{\rho}\_g \sigma\_* (x,z) = \hat{\rho}\_gB$ for faithful actions $\hat{\rho}_g$. Therefore I do not see how joint-equivariance holds for single-layer NNs if the group acts trivially on the hidden layer. Am I missing something? --- Reply to Comment 1.1.1: Comment: We thank you very much for your response, and we will take the opportunity to provide a clarifying example for the question at hand. As noted in Lines 1012-1016, under the same example you are considering, the “natural” action of $G$ on the parameter space ${\cal Z} = \mathbb{R}^{c \times b} \times \mathbb{R}^{d \times b}\times \mathbb{R}^b$ corresponds to taking, for $g \in G$ and $(z = W, A, B) \in \cal Z$: $$M_g.z = M_g.(W, A, B) := (\hat{\rho}_g.W.\eta_g^T, \rho_g.A.\eta_g^T, \eta_g.B). $$ This is what we refer to as the “intertwining action” on the layer parameters, as it recalls the traditional definition of an intertwinning linear map from representation theory (also, see the discussion on lines 165-180). Notice that, indeed, this involves the action of the group on the corresponding input/output spaces of each layer (e.g. from $\mathbb{R}^d$ to $\mathbb{R}^b$ and from $\mathbb{R}^b$ to $\mathbb{R}^c$). In our original rebuttal, notice that we referred to “a trivial action on the intermediate layer”, and not plainly “a trivial action”. Indeed, we referred to taking $\eta$ to be trivial, rather than $M$ itself; the latter, as you have correctly noticed, doesn’t work in general. Thanks to the orthogonality (and linearity) of our group action, a similar development to yours yields, for any $\sigma: \mathbb{R}^b \to \mathbb{R}^b$, any $g \in G$ and for any $z = (W, A, B) \in \cal Z$: $$\sigma_(\rho_g.x, M_g.z) = \sigma_(\rho_g.x, (\hat{\rho}_g.W.\eta_g^T, \rho_g.A.\eta_g^T, \eta_g.B)) =(\hat{\rho}_g.W.\eta_g^T). \sigma((\rho_g.A.\eta_g^T)^T.(\rho_g.x) + \eta_g.B)$$ $$ = \hat{\rho}_g.(W.\eta_g^T. \sigma(\eta_g. A^T.(\rho_g^T.\rho_g).x + \eta_g.B)) = \hat{\rho}_g.(W.\eta_g^T. \sigma(\eta_g. (A^T.x + B)))$$ Namely, it is enough that $\sigma: \mathbb{R}^b \to \mathbb{R}^b$ is $G$-equivariant (w.r.t. the action of $\eta$) in order to get $\sigma_$ to be jointly equivariant. Indeed, this would yield: $$\sigma_(\rho_g.x, M_g.z) = \hat{\rho}_g.(W.\eta_g^T.\eta_g. \sigma(A^T.x + B)) = \hat{\rho}_g.(W.\sigma(A^T.x + B)), $$ as required. This justifies our claims about the pointwise activations and/or the use of a Norm-ReLU activation to ensure the joint-equivariance of $\sigma_$ for different levels of complexity of $G$ (and its action on the intermediate layer). More specifically, if this action on the intermediate layer $\eta$ is taken to be trivial, any function $\sigma: \mathbb{R}^b \to \mathbb{R}^b$ is $G$-equivariant w.r.t. $\eta$ (indeed, $\sigma(\eta_g.x) = \sigma(x) = \eta_g.\sigma(x)$); i.e. no matter the inner activation function $\sigma$, under this action $M$, $\sigma_$ is jointly-equivariant. In the end, a trivial $\eta$ assumes “no action of the group on the latent space”; and so we only act on the parameters on the dimensions defined by the data: e.g. $\rho$, that acts on $\cal X$, will act only on $A$ on the left; and $\hat{\rho}$, that acts on $\cal Y$, will act only on $W$ on the left as well. This readily generalizes to the case where $\sigma_$ represents a whole multilayer unit, for which we take the action on parameters to be trivial on the hidden layers, but not on the input and output layers (where it acts according to the data). Indeed, no matter the inner activations, such $\sigma_$ would be jointly equivariant with respect to such group action. As we also mention in our original rebuttal, a “trade-off” follows from considering such a “boring” group action $M$: the space ${\cal E}^G$ might not represent very “interesting” equivariant architectures. This doesn't seem too problematic since it wouldn’t be the use case if $\sigma$ didn’t respect any sort of equivariance to begin with. It does, however, allow to state that DA and FA are tightly related, even for unconstrained architectures. This also makes sense when we consider that DA and FA only interact with NN models through the input and output layers. We hope to have clarified your question with this example, and we’re open to answer further questions if required.	Rebuttal 1: Rebuttal: We thank all reviewers for their insights. We here present information to help transversally clarify some of their questions. References from the manuscript are mentioned as presented therein; new references follow the format at the end of this response. First, for better understandability of the paper, in the Appendix we will add: a table explaining relevant notation/abbreviations; a summary for a wide audience on fundamental notions used in the paper; a summary of Limitations clarifying its applicability; and an explanation on how some well-known equivariant architectures (CNNs, GNNs, DeepSets) enter our setting. We next give general context on how close our setting is to practical applications of NNs: - Despite the MF limit of NNs being a theoretical tool, it is the asymptotic regime that most closely describes the actual behavior of large NNs during training (as compared e.g. to the Neural Tangent Kernel), and we believe truly useful insight can be obtained from it: our experiments show that the predicted MF behavior emerges in practice already for finite, not too large $N$ (1000 was generally enough), in reasonable practical settings of shallow NNs (standard pointwise sigmoid activation and objax’ default SGD training were used). - A fully unified, satisfactory MF theory for deep NNs is still an open, actively tackled question (for advancements on it see e.g. [SS21],[NP23]). We believe some of our key results (e.g. Theorem 3) can be extended to such settings, undoubtedly in a future research line. Notice though that $\sigma_$ can by itself encode a complex deep architecture (see below), and the resulting shallow model can represent way more interesting structures than single-hidden-layer NNs (e.g. ensembles of such multilayer “units” trained in parallel). We also clarify further the “jointly-equivariant” assumption on $\sigma_$: - We defined our shallow models through an abstract, general $\sigma_$, termed “activation” in the MF literature, but more complex in general than the “usual” activations. Since no constraints (beyond being orthogonal) are put on the action of $G$ on $\cal Z$, this “joint-equivariance” plays a key role in connecting the G-action on the data with the one on parameters. It doesn’t, however, imply that all “inner components” of $\sigma_$ are equivariant. - The joint-equivariance of $\sigma_$ can encode a wide range of situations and allows us to find interesting results beyond particular choices of architecture. It also encodes possible trade-offs between “freedom” in the architecture and “intricacy” of the group action $M$. - In “traditional” single-hidden-layer NNs (cf. Appendix A.4) $\sigma_$ is defined in terms of a “usual” activation function $\sigma:\mathbb{R}^b \to \mathbb{R}^b$ on the hidden layer and $M$ in terms of G-actions on the data (via $\rho$ and $\hat{\rho}$) and on the hidden layer (via $\eta$). These choices determine how constraining the “jointly-equivariant $\sigma_$” assumption is. For instance: If $\eta$ is trivial (i.e. $\eta \equiv id_{\mathbb{R}^b}$), any single-hidden-layer NN is jointly-equivariant, regardless of $\sigma:\mathbb{R}^b \to \mathbb{R}^b$ (see e.g. the proof of Prop. 4). Similarly, any multilayer architecture under a G-action acting trivially on the hidden layers (but not on input/output), also results in a jointly-equivariant $\sigma_$. Thus, our results apply to general architectures if the G-action on $\cal Z$ is well chosen. The catch is that, under such G-actions, the equivariant architectures encoded in ${\cal E}^G$ might end up being uninteresting (and so, Theorem 5 loses part of its punch); however, results relating DA, FA and vanilla training still apply. - If G acts via permutation of input coordinates (as commonly for finite groups), $\sigma_$ will be jointly-equivariant for any activation function $\sigma:\mathbb{R}^b \to \mathbb{R}^b$ applied pointwise (a common practice). The same holds in many other interesting cases involving finite groups (e.g. $Z_n \times Z_n$ acting on square images, $S_n$ acting on graphs/sets, etc). This discussion is also tackled in [24] regarding a similar assumption. For a more complex (possibly infinite) group acting orthogonally on the data and parameters (with non-trivial $\eta$), for $\sigma_$ to be jointly-equivariant we have to restrain the chosen $\sigma:\mathbb{R}^b \to \mathbb{R}^b$. For instance, an O(b)-equivariant $\sigma$ (e.g. a Norm-ReLU) would grant our results to apply; but this particular choice could potentially harm the model’s expressiveness and applicability. Last, we thank the reviewers for pointing out relevant references. We shall properly cite [WHG+23] in Section 4.2. We have also become aware of the work [HC23] describing a result comparable to Corollary 3, but in the particular case of ReLU activations and under a single symmetry transformation. We think our work branches far beyond both mentioned papers, and proper references for them will be included. References - [BT20] Benjamin Bloem-Reddy and Yee Whye Teh. 2020. Probabilistic symmetries and invariant neural networks. J.Mach.Learn.Res. 21, 1, Article 90 (January 2020), 61 pages. - [FW23] Qiang Fu and Ashia Wilson. Mean-field Underdamped Langevin Dynamics and its Space-Time Discretization. In: arXiv preprint arXiv:2312.16360 (2023). - [HC23] Karl Hajjar and Lénaïc Chizat. On the symmetries in the dynamics of wide two-layer neural networks. Electron.Res.Arch., 31(4):2175–2212, 2023. - [NP23] Phan-Minh Nguyen and Huy Tuan Pham, A rigorous framework for the mean field limit of multilayer neural networks. Math.Stat.Learn. 6 (2023), no. 3/4, pp. 201–357 - [SS21] Justin Sirignano, Konstantinos Spiliopoulos (2021) Mean Field Analysis of Deep Neural Networks. Maths.Oper.Res.47(1):120-152. - [WHG+23] Rui Wang, Elyssa Hofgard, Han Gao, Robin Walters, and Tess E. Smidt, Discovering symmetry breaking in physical systems with relaxed group convolution, arXiv preprint arXiv:2310.02299, 2023.	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Distribution Learning with Valid Outputs Beyond the Worst-Case	Accept (poster)	Summary: This paper follows up on the line of study initiated in the work "Actively Avoiding Nonsense in Generative Models" by Hanneke et al. 2018. The model studied in that paper is as follows: we are given data generated by a distribution $P$ over a domain $X$. A certain fraction of the domain $X$ is labeled "valid" and the rest is "invalid"; $P$ is only supported over valid samples. We are given access to an oracle that tells us whether any point $x \in X$ is valid or not. Our goal is to obtain a distribution $\hat{q}$, which minimizes a certain loss, subject to not having too much mass on the invalid fraction of the domain. More precisely, our benchmark is against a specified family of distributions $Q$. Let $q^\star$ be the distribution that minimizes a loss function among all the distributions $q \in Q$ that are fully supported on valid data. The distribution $\hat{q}$ we return should suffer an excess loss of at most $\epsilon_1$ compared to $q^\star$. Furthermore, the mass that $\hat{q}$ assigns to invalid samples should be at most $\epsilon_2$. To obtain such a $\hat{q}$, we can do 2 actions: 1) obtain iid samples from the data distribution $P$ 2) issue queries to the validity oracle. To obtain the required $\hat{q}$, we ideally want both our sample complexity as well as query complexity to be polynomial in $1/\epsilon_1$, $1/\epsilon_2$ and possibly also in the range of the loss function (i.e., if it is bounded in $[0,M]$ for $M < \infty$). Among other results, the paper by Hanneke et al. 2018 shows that 1) If the learning algorithm is proper (constrained to return a distribution in $Q$), then even with infinite running time and infinite samples from $P$, it must issue at least $2^{\Omega(1/\epsilon_1)}$ queries to the validity oracle. 2) If the learning algorithm is improper, it can return $\hat{q}$ satisfying the required criteria with $O(M^2 \log \|Q\|/\epsilon_1^2)$ samples from $P$ and $O(M^2\log\|Q\|/\epsilon_1^2\epsilon_2)$ queries to the validity oracle. These results are stated for a very general class of loss functions (just bounded, monotonic decreasing). The main contribution of this work is to study under what specialized settings the guarantees of Hanneke et al. 2018 can be improved, especially in the number of validity queries that learning algorithms require. The authors study two different scenarios, and obtain improved query complexities for each. First, the authors consider a setting where 1) the true data distribution $P$ also belongs to the benchmark class $Q$ 2) the loss function is simply the log-loss function i.e. $l(x)=\log(1/\hat{q}(x))$ (where we are abusing notation so that $\hat{q}(x)$ is the density that $\hat{q}$ assigns to $x$). The former is a "realizability" condition, and the latter is natural since in practice, a default training choice is to maximize the likelihood of the observed data, which is equivalent to minimizing the log-loss. For this setting, the authors present an algorithm that obtains the desired $\hat{q}$ with no queries to the validity oracle at all---but now, the algorithm requires $\tilde{O}(\log\|Q\|/\min(\epsilon_1^2, \epsilon_2))$ samples, as compared to the $O(M^2\log\|Q\|/\epsilon_1^2)$ samples required by the more general improper algorithm of Hanneke et al. 2018. (Note that the log-loss is not bounded at all, and it helps to think of the comparison when $M$ is a constant). The learning algorithm simply returns the distribution in $Q$ that minimizes the emipirical loss, but suitably mixed with the uniform distribution over the domain $X$. Thus, under the assumptions of realizability, and with a specific loss function, the punchline is that validity comes easily from random examples themselves. The analysis uses classic tools from hypothesis testing like the Neyman-Pearson lemma (this is where the realizability assumption as well as the log-loss shows up). The authors also argue that the sample complexity dependence on $\epsilon_2$ is more-or-less optimal---any proper learner must necessarily use $1/\epsilon_2$ samples (although it still might be possible that improper learners, like the one the authors produce, can do better). Second, the authors return to the more general setting considered by Hanneke et al. 2018, i.e., $P$ need not belong to $Q$, and the loss function is a monotone decreasing function bounded in $[0,M]$. However, now the crucial assumption is that validity oracle, which is a function that maps $X$ to {0,1}, belongs to a function class $V$ of bounded VC dimension $d$. Here again, the authors obtain a natural algorithm that uses fewer validity queries than the one by Hanneke et al. 2018. First, the algorithm obtains a distribution from $Q$ that minimizes empirical loss. Then, the algorithm obtains extra samples from $P$ (in fact, from $P$ mixed with $\hat{q}$), and invokes the validity oracle on this sample, to obtain valid/invalid labels for all the examples so obtained. Then, the algorithm finds a function $\hat{v}$ in $V$ that agrees with this labeling as much as possible. Finally, $\hat{q}$ obtained in the previous step is re-normalized to only have mass on points that are rendered valid by $\hat{v}$. The authors show that this algorithm works (when all the distributions in $Q$ have at least a constant mass on valid examples) with a sample complexity of $O(M^2\log\|Q\|/\epsilon_1^2)$ and query complexity of $\tilde{O}(d/\min(\epsilon_1,\epsilon_2))$. Note that the latter is still an improvement (in the dependence on $\epsilon_1, \epsilon_2$). The authors are also able to prove a result without the assumption of constant valid mass, albeit with a slightly worse query complexity (that is still better than that of Hanneke et al. 2018) and which only works for the capped-log-loss. Finally, the authors comment on ways to improve the query complexities of their results in this setting. Strengths: The authors present an interesting, suitably exhaustive and strong set of results for natural "special" cases of the problem of validity-constrained distribution learning. Both the settings that the authors study (realizability with log-loss, as well as validity oracle in a bounded VC class) in the paper are natural beyond-worst case instances of the problem, and may well form a reasonable model of practical scenarios. The gains in the realizable setting are particularly impressive---it is nice to see that one can in principle do away with the validity oracle, while also maintaining near-optimal sample complexity. Even in the second setting, which just adds the additional assumption of a bounded VC validity region over those of Hanneke et al. 2018, the authors obtain improved query complexities. Overall, the suite of results feels satisfying and paints a meaningful beyond-worst case picture of the problem. Weaknesses: While I do find the study compelling, if I am to nitpick and search for weaknesses, I will say that there are no proof sketches whatsoever for the main theorems in the body. Notably, the content is still well under the page limit, and hence I suggest that the authors at least attempt to summarize the main steps used in the proofs of their results in the main body. Also, certain points and sentences could have used more elaboration and verbosity, to make the reading slightly less heavy. For example, lines 251-252 were not coherent to me and seemed like a mouthful, and similarly, at a few other places, I felt like more exposition could have been useful for the reader. Technical Quality: 4 Clarity: 4 Questions for Authors: Here are a few questions that came to my mind as I was reading (some may not be well-formed/basic misunderstandings): 1) In the guarantee of Theorem 1, isn't $q^\star= P$? maybe it would help to write a remark saying this. 2) From a skim, the exponential lower bound for proper learners in Hanneke et al. 2018 uses the coverage loss function. Do you think that such a bound for proper learners might also hold under non-realizability with the log-loss? Basically, I am trying to see if the reason for the exponentially many samples can be isolated to non-realizability alone, or if it also requires the unnatural loss function 3) In lines 250-252, what do you mean by the "realizable complexity"? Shouldn't this be "proper sample complexity" instead? Isn't it possible that there exists an improper learner in the realizable setting that gets something smaller than $1/\epsilon_2$? 4) Just to clarify, in Algorithm 2, in line 4, is it true that all the samples obtained in the previous line from $P$ will be labeled as valid by the validity oracle? I this only really saves a constant factor, but still, these samples need not be queried to the oracle. 5) From a skim of the proofs in the Appendix, it seems that the log-loss is only used to the degree that it is equivalent to likelihood maximization (e.g. in the proof of Lemma 6). If that is the case, can you say something more generic, that your results also hold for any loss functions that get minimized when the likelihood of the observed data gets maximized? If this is not the case, could you point out where exactly the exact form of the log-loss (i.e. $l(x)=\log(1/q(x))$ is crucial in your arguments? 6) I may be wrong and misunderstanding the measure notation, but it seems to me that in the equation block at line 470, in the second line, the $f^n_P(x)$ shouldn't be there. This is because, at least in the discrete case with pmfs, $\sum_x \min(p(x), q(x)) = 1-TV(p,q)$ (note that there is no $p(x)$ multiplying the $\min$ in the summation). 7) Could you explain a little more as to why in Algorithm 2, one needs to obtain samples from the mixture of $P$ with $\hat{q}$? Why do the samples from $\hat{q}$ end up being necessary? --- Minor typos: Line 112: typo any \ Line 136 any choice of \ Line 142 samples \ Line 249 means of \ Line 250-252 is not coherent and can use some elaboration \ Line 286 $d$ should be $D$ Confidence: 4 Soundness: 4 Presentation: 4 Contribution: 4 Limitations: The authors have adequately addressed limitations as far as I can see. Flag For Ethics Review: ['No ethics review needed.'] Rating: 8 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for taking the time to read our work with such attentiveness, and write such a detailed review. We will work to clarify the writing in the next version, and agree that some proof intuition can be added. Answers to the reviewer's questions can be found below: 1) This is correct: in the realizable case $q^* = P$. Theorem 1 was phrased in terms of $q^*$ mostly for notational consistency, but we should note the confluence here. 2) While we do not have a formal result, our impression is that the driving issue here is not the coverage loss, but the sort of extreme case of non-realizability they construct. When the supports of the distributions in the model class $\mathcal{Q}$ have so little overlap with the data generating distribution $P$, there is no way to ascertain which models are valid and which aren't without something close to exhaustively searching through them. The choice of loss does not feel helpful in resolving this -- for example, there is nothing about the maximum likelihood model $q$ that guarantees any sort of validity in the worst case. 3) Our writing in this paragraph is imprecise, and will be cleaned in the next version. By "realizable complexity" we were referring to the fact that $P \in \mathcal{Q}$ in the setting of Theorem 1. Given that the lower bound only applies to proper learners, the reviewer is correct in saying that it's possible there is an improper algorithm that surpasses the $\Omega(1/\epsilon_2)$ lower bound. That said, this feels to us somewhat unlikely given that the improperness of Algorithm 1 arises so that we can control the loss -- it is done so that we don't output a hypothesis that is small in total variation to $P$ but large in KL-divergence. From the perspective of invalidity, small total variation to $P$ is sufficient. 4) The reviewer is correct: the samples from $P$ do not need to be queried for validity, and updating the algorithm to reflect this saves a constant factor. We left this detail out originally, but will add it to Algorithms 2 and 3 in the next version. 5) The reviewer is correct that likelihood maximization is really what's doing most of the legwork in Theorem 1 (via Lemma 6). There is one other feature of the log-loss (see Lemma 8) which we use in Theorem 1 and Theorem 4: for mixture distributions $f_M(x) = (1-\epsilon) f_q(x) + \epsilon f_{r}(x)$, the form of the log-loss admits the inequality $\log(1/f_M(x)) \leq 2\epsilon + \log(1/f_q(x))$. In the case of Theorem 1, this allows us to argue that mixing with the uniform distribution does not degrade the loss too much. There are definitely some nice generalizations that can be made. 6) This is a good catch. The $f^n_P$ outside of the minimum in line 470 is a typo. The proof is correct when it is removed. 7) We use samples from both $P$ and the ERM in Algorithm 2 is so that we get a single estimate of the validity function $\hat{v}$ which has a high probability of agreement with the true validity function $v$ under samples from both distributions. Basically, we use the accuracy of the estimate $\hat{v}$ under $P$ to ensure that the loss of the returned distribution is small, and the accuracy of the estimate $\hat{v}$ under the ERM is to bound the invalidity. If we could return a distribution constructed by "accepting/rejecting" samples from the ERM using the true validity function $v$, we'd have perfect validity, but under an estimate of $v$, we need to make sure this estimate doesn't disagree too much with $v$ precisely under the proposal distribution $\hat{q}_{ERM}$, or too many invalid samples may be leaked. --- Rebuttal Comment 1.1: Title: Response to rebuttal Comment: Thank you for the response. Please do revise the submission to reflect the discussion above. I maintain my score of 8, and believe this work should be accepted. Great job!	Summary: The paper proposes a method for vastly improved validation query efficiency in validity-constrained distribution learning by relaxing the requirement for worst case settings of distributions, loss function and true validity function. Strengths: The paper makes good high level arguments for why regarding common case instead of worst case settings can be appropriate in some situations. The proposed algorithm makes sense and are supported by mathematical derivations of its low error and high validity guarantees given assumptions on the space of learnable distributions. The theorems look valid, though I didn't check the proofs. Weaknesses: A more in depth discussion of situations where one could clearly afford the proposed relaxation versus those where it might not be prudent enough would be helpful for justifying it. Technical Quality: 3 Clarity: 3 Questions for Authors: - Confidence: 2 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: Yes. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We appreciate the review, and will try to address the weaknesses they point out. We would argue that most practical situations are likely closer to the regime of realizability explored in the first half of this paper than the case where no model in the model class is a reasonable approximation for the data generating distribution, the setting which motivates algorithms in previous work [1]. It also seems that valid regions of space are "learnable" in practice, motivating the second half of the paper where the validity function is known to lie in a bounded complexity class. For example, [3] found empirical success on the problem of post-editing GANs by coaxing GANs towards their restriction to "valid" parts of space. [1] Hanneke, S., Kalai, A., Kamath, G., & Tzamos, C. (2018). Actively Avoiding Nonsense in Generative Models. https://arxiv.org/abs/1810.06988 \ [3] Kong, Z., & Chaudhuri, K. (2022). Data Redaction from Pre-Trained GANs. https://arxiv.org/abs/2206.14389 --- Rebuttal Comment 1.1: Comment: Thanks for the response! The point I mentioned in the review is that in different practical situations, the assumption might or might not be valid. Even if it is valid in most situation, some guidelines or measurable prerequisites that make the assumption more likely to safely hold would be helpful. This is however a minor point for the overall paper, and I'm maintaining my score.	Summary: The paper considers the problem of learning generative models under validity constraints. Specifically, given data from a distribution and an oracle that tells whether a particular datapoint is valid, the goal is to output a generative model from a hypothesis class Q whose output has a small loss epsilon_1 (compared to the best model in Q) while ensuring the output is valid with high probability (1 - epsilon_2). The objective is to achieve this with minimal training samples and validity queries to the oracle. Previous work on this problem showed a negative result: exp(1/epsilon_1) validity queries are needed to properly learn the generative model. For improper learning, they show that O(log(Q)/(epsilon_1^2 epsilon_2)) validity queries suffice. This work aims to improve these results by making further assumptions. For example, it is shown that if the true data-generating distribution P is assumed part of class Q, then a minor modification of empirical risk minimization can achieve the loss and validity requirements with O(log(Q)/min(epsilon_1^2, epsilon_2)) samples and no validity queries. Additional results are provided, assuming a bound on the VC dimension of the class to which the validity oracle belongs. Strengths: The paper makes concrete improvements to the bounds established in previous works (under certain assumptions). Weaknesses: While the problem of generative modeling under validity constraints has been introduced citing practical concerns, it is unclear if the results or algorithms in this paper add much to generative modeling in practice. Therefore, the significance and relevance of these results are unclear. Technical Quality: 3 Clarity: 2 Questions for Authors: Could the authors elaborate on any practical insights that can be derived from the algorithms and bounds presented in this work? Confidence: 3 Soundness: 3 Presentation: 2 Contribution: 2 Limitations: See the weaknesses section. It would be great to include a discussion of insights for practice. Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We appreciate the review, and agree that the next version of the paper should furnish more practical insight. We mainly see these results as a first attempt at studying the problem of learning a valid generative model from the opposite perspective of [1], which paints learning in this setting as a complex endeavor. In practice, generative models do often suffer from invalidity issues, leading to a variety of techniques for mitigating this issue, many of which are quite intuitive and feasible [2, 4, 5, 6]. We hope this work can spark further investigation into uncovering natural settings where practical algorithms can be effective. Lemma 2 -- which shows that validity naturally arises when the data distribution $P$ is in the model class $\mathcal{Q}$ -- is intended to shed light on what learning a valid generative model is like when the model class $\mathcal{Q}$ contains good approximations of the "validity-filtered" data distribution. While the rates in Lemma 2/Theorem 1 hold only for the realizable case, we would argue that this setting likely a more faithful representation of generative modeling in practice than the more general setting of [1], where much of the complexity seems to come from the possibility that all models in $\mathcal{Q}$ bare little to no resemblance to the data generating distribution $P$. Basically, our claim here is that learning the distribution well is really what needs to be done – if you’ve learned well in this setting, you’re unlikely to generate invalid outputs. In the second half of the paper, we consider the possibility of learning the validity function and restricting the ERM model to the learned "valid" part of space. One recent applied work [3] similarly considers post-editing GANs by "learning the data distribution restricted to the complement of the [valid part of space]". Explaining the success of such schemes that operate on the estimation of the validity function requires relaxations of the original learning model of [1], where the validity function cannot be estimated well with a polynomial number of queries. [1] Hanneke, S., Kalai, A., Kamath, G., & Tzamos, C. (2018). Actively Avoiding Nonsense in Generative Models. https://arxiv.org/abs/1810.06988 \ [2] Kaneko, T., & Harada, T. (2021). Blur, Noise, and Compression Robust Generative Adversarial Networks. https://arxiv.org/abs/2003.07849 \ [3] Kong, Z., & Chaudhuri, K. (2022). Data Redaction from Pre-Trained GANs. https://arxiv.org/abs/2206.14389 \ [4] Schramowski, P., Brack, M., Deiseroth, B., & Kersting, K. (2023). Safe Latent Diffusion: Mitigating Inappropriate Degeneration in Diffusion Models. https://arxiv.org/abs/2211.05105 \ [5] Malnick, S., Avidan, S., & Fried, O. (2023). Taming Normalizing Flows. https://arxiv.org/abs/2211.16488 \ [6] Liu, J., Xu, J., & Wang, Y. (2022). Efficient Retrieval-Augmented Generation: An Empirical Study of Practical Techniques. https://arxiv.org/abs/2210.04610 --- Rebuttal Comment 1.1: Comment: I appreciate the authors' response. While I agree that this work adds nuance to the prior work by Hanneke et al., the high-level takeaways and the algorithms do not seem to contribute significantly beyond what is already established in the practice of generative modeling. Therefore, I will maintain my original score.	Summary: This paper studies distribution learning with invalidity constraints. It assumes that the algorithm has access to an oracle that provides validity queries, and targets to reduce the total amount of queries to the oracle while achieving comparable learning guarantees to previous counterparts. By specifying the loss function and restricting the hypothesis class, the paper achieved improved sample/query complexity of $\tilde{O}(\log{\lvert Q\rvert}/\min(\epsilon_1^2,\epsilon_2))$ (from previous $\tilde{O}(\log\lvert Q\rvert/\epsilon_1^2\epsilon_2)$ of Hanneke et al. 2018). Additionally, by assuming that the validity function is from a VC-class with VC-dim $D$, then the query complexity can be further reduced to $\tilde{O}(D/\min{\epsilon_1,\epsilon_2})$. Strengths: This paper considers a nontrivial problem, learning a generative distribution with validity verification. It contributes to the literature of both generative networks and distribution learning. On the other hand, it improves the query efficiency of the learning algorithm by specifying or restricting the class of distribution, loss function, class of validity functions. The progress on improving the query efficiency, see summary, looks a bit incremental; however, requires delicate handling in the algorithmic design and analysis. The theoretical analysis looks sound to me. Weaknesses: There are some typos. Line 136: choice of. Line 237: "is true for .. for .." To name a few. Some parts are a bit unclear, for example, Line 37: "while achieving polynomial bounds on the number of validity queries, uses relative large number of validity queries". It is unclear what the "relative large number" is comparing to. Line 232-233: "attainable, at least improperly". Does this mean that the algorithm can output an improper hypothesis? Is this due to the mixture of the ERM with the uniform distribution? Then, is proper learning achievable? In addition, the format for the references is not unified. Some references are missing the information for venues. Technical Quality: 3 Clarity: 2 Questions for Authors: Do all algorithms run in exponential time, i.e. computationally inefficient? Confidence: 3 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: I have no concerns on the potential negative societal impact. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for looking closely at our work, and apologize for sometimes being less clear than we should. In line 37 ("while achieving polynomial bounds on the number of validity queries, uses relative large number of validity queries''), what we were referring to is that the improper algorithm of Hanneke et al. makes $\tilde{O}(1/\epsilon_1^2 \epsilon_2)$ validity queries, which looks large relative to the quadratic dependence one is used to seeing. It's an open question what the right query complexity is for the general case discussed by Hanneke et al. [1]., so this sentence should probably be reworked. In line 232-233 ("guarantees for the log-loss are attainable, at least improperly"), the reviewer is correct in assuming that by invoking “improper” learning here, we are referring to the fact that we output a mixture of the ERM and the uniform distribution in Algorithm 1. Satisfying the loss requirement with a proper learner will in general require many more samples than $\tilde{O}(1/\min(\epsilon_1^2, \epsilon_2)$, as there may be some $\tilde{P} \in \mathcal{Q}$ which is very close in total variation to $P$, but has infinite KL-divergence from $P$. With regard to computational considerations, the algorithms are in general inefficient. For efficiency, one needs access to an efficient ERM routine over the distribution class $\mathcal{Q}$ -- in this sense, our work follows in the line of original work of Hanneke et al. [1]., who assume access to an efficient (constrained) ERM oracle for computational efficiency. In the cases of Algorithms 2 and 3, one also needs access to an efficient ERM routine over the VC class. It's true that many important VC classes do not admit efficient ERM. [1] Hanneke, S., Kalai, A., Kamath, G., & Tzamos, C. (2018). Actively Avoiding Nonsense in Generative Models, https://arxiv.org/abs/1810.06988 --- Rebuttal Comment 1.1: Title: Official Comment by Reviewer yKWM Comment: Thank you for your response. It will be helpful to include the discussion in the revision.	null	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
LoCo: Learning 3D Location-Consistent Image Features with a Memory-Efficient Ranking Loss	Accept (poster)	Summary: This work focuses on the best strategy to pre-train a feature extractor network optimized to be invariant wrt to the viewpoint in the image. To do so the authors use a dataset of paired views from which they extract pairs of positive patches (same 3D point in two different views) and negatives (different 3D points). Given these sets a feature extractor model is trained for patch retrieval using a loss proposed by the authors. In particular the paper starts from the existing Average PRecision Loss and adapts it to make it significantly more memory efficient. Provided with the data and the loss the authors train a tiny CNN adapter on top of Dino features to make them more robust wrt to the viewpoint. The performance of the trained model is evaluated on few ad-hoc benchmarks (multi view feature consistency, consistency of panoptic segmentation and visual place retrieval) where the proposal achieves improvements wrt to the competitors. Strengths: + Presentation: the paper is very well written and presented. The paper has a straightforward core idea and contribution and the author make a good job at motivating and explaining it. + Reusable: the proposed improved ranking loss can likelly be re-used for other tasks that require some form of metric learning and it’s not specifically tailored for the multi-view consistency use case. As such the contribution of this work can probably extend to nearby fields. + Efficiency: the proposal seems to be quite effective even when training somewhat shallow models on somewhat small datasets (although what the author train is a residual model on top of a pre-trained Dino one). This is quite interesting as it shows that a relatively small learning budget is enough for learning multi-view consistency. Weaknesses: a. Limited experimental validation: while the author tested their model against competitors across 3 tasks, these are mostly internal comparisons on tasks that would privilege the proposed model. In particular, Table 1 where the method has the biggest gains, is basically measuring the performance on the task LoCo was trained on vs models that were not trained for the task (except for LoCUS). Regarding LoCUS in table 1 it is shown with a † that has no match in the caption of the table, following the rest of the paper I’m assuming it means that the method only has dimensionality 64 for features. It would have been interesting to include in the evaluation some of the correspondence based tasks that CroCo-v2 has been exploring like stereo depth estimation, optical flow or relative pose estimation. b. Generalization: the model is trained on samples from matterport3D and evaluated on unseen scenes from Matterport and on scenes from ScanNet. This constrains quite a lot the scenarios being tested and does not give insight on the generalization capabilities of the proposed method. For example how would it perform in very different scenarios like an outdoor scene? Note that there are plenty of dataset for evaluation of correspondences method that could be used for this task like [MegaDepth](https://www.cs.cornell.edu/projects/megadepth/) c. Potential unfair comparison to competitors: the closest competitor that has been trained with a comparable objective to the one proposed by the authors is LoCUS that according to the evaluation in Tab.1 and Tab. 2 achieves consistently worse results. However LoCUS uses only 2 FC layers on top of the features f a frozen DINO (500K parameters) while the proposed methods use a full CNN (~20M parameters), as such the comparison is not particularly fair. It would have been interesting to have a version of the LoCo method trained in the exact same settings as LoCUS (models and data) to verify what is the gain or losses of the proposed new loss function compared to the one introduced in LoCUS. Technical Quality: 3 Clarity: 4 Questions for Authors: Questions 1. Can you comment on weakness [b] and whether generalization is to be expected or very limited? 2. Can you comment on weakness [c] Typos * L 166: Eq. 12 → Eq. 3? Confidence: 4 Soundness: 3 Presentation: 4 Contribution: 3 Limitations: Limitations have been adequatelly discussed in the manuscript. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your detailed and constructive review. We appreciate your positive remarks regarding the presentation, efficiency, and potential reusability of our proposed method. We also acknowledge the valuable concerns you’ve raised and address them below. --- Weakness (a): Limited experimental validation We understand your concern regarding the focus of our experimental validation on tasks where our model excels. These tasks were chosen to highlight the core strengths of our approach in a controlled setting. For tasks like surface normal prediction and monocular depth estimation (as reported in, e.g., El Banani et al. [12]), the correct prediction depends not just on the scene geometry, but also on the camera pose. Our work however explicitly aims to make the features location-consistent and thereby invariant to changes in camera pose. The LoCo-trained features therefore lack crucial information for such tasks. In their experiments on optical flow and stereo depth estimation, CroCov2 [44] fine-tune their entire (pre-trained) network rather than training a comparatively small probe. Experiments of that scale were beyond our computational resources. In the appendix, we provide an evaluation on Visual Place Recognition, which further demonstrates the versatility and utility of the features learned by our method across different applications. --- Weakness (b): Generalization capabilities We appreciate the concern regarding generalization and agree that this is an important aspect of any method’s robustness. Due to computational limitations, we were constrained to training relatively small models on indoor scene datasets. In performing well on many unseen diverse indoor environments, the models do demonstrate the capability to generalise to unfamiliar environments. Due to the circumscribed training domain, we do not expect these models to perform well on environments with a larger domain shift (such as outdoor environments), where performance would mostly depend on the degree of their similarity with the training domain. However, the training method we propose is designed to be fully general and adaptable to a variety of settings. While our current experiments focus on indoor scenes, the methodology itself should be applicable to other scenarios and domains without significant adjustments. --- Weakness (c): Potential unfair comparison to competitors We appreciate your concern about the comparison between our method and LoCUS, given the differences in model architecture and parameter count. To address this, we conducted additional experiments, as detailed in our global author response, where we fine-tuned the LoCUS architecture using our memory-efficient loss. These experiments reveal that while our method does not outperform LoCUS in all tasks in terms of accuracy, it significantly enhances memory efficiency. This efficiency is what unlocks the training of larger models that produce higher-dimensional feature vectors within the same computational budget, leading to substantial overall performance improvements. The ability to scale up model capacity while maintaining computational feasibility is a key advantage of our approach, illustrating its potential beyond the specific settings and model scales we tested. We do however appreciate the importance of having this apples-to-apples comparison in the paper. --- Typos We will correct the typo on Line 166 (Eq. 12 → Eq. 3) and address the missing match for the dagger symbol in Table 1 before publication. We appreciate your attention to detail in pointing these out. --- We hope these clarifications address your concerns and provide additional context for evaluating our work. We are confident that our paper offers valuable contributions, particularly in advancing methods for training location-consistent feature extractors in a memory-efficient manner. We appreciate your careful consideration of our work and look forward to any further feedback. --- Rebuttal Comment 1.1: Title: Acknowledgement Comment: Thank you authors for submitting a detailed rebuttal. I would suggest to incorporate the result of LocUS (w Loco architecture) in the future versions of the work because they help quantifying the effect on performance of the tradeoff introduced by the memory optimized loss function used. --- Reply to Comment 1.1.1: Comment: Thank you - we will definitely include this result in our revision and agree that it helps more concretely pinpoint the advantages of the proposed approach.	Summary: The paper introduces a memory efficient loss for location consistent image features. The paper addresses the problem of high memory footprint of previous work, by significantly reducing the memory footprint, by 3 orders of magnitude. Memory efficiency is achieved by sampling the positive pairs from a smaller subset and using a threshold on similarity differences between pairs, and discarding the pairs with gradients close to 0, which do not contribute to the loss. To compensate for the non-uniform sampling, some correction terms are added to the loss. Strengths: * Significant memory footprint reduction (3 orders of magnitude), allowing for larger batch sizes * Identifying that the gradients from most pairs are close to 0 and don't contribute to the losses. * Analysis of correction to the batched loss function. Weaknesses: * relies on existing 3D mesh reconstruction of the environment (for segmentation masks of individual objects in the scenes) -- this limits evaluation to datasets with existing mesh reconstructions. * while direct comparison with LoCUS on the same feature dimension is not possible due to high memory consumption, it would be interesting to see a comparion with LoCo on a feature dimension d=64 (Tab 2) for a fair comparison. Technical Quality: 3 Clarity: 3 Questions for Authors: How does LoCo perform with features coming from different models (e.g. DINO vs DINO v2)? Confidence: 2 Soundness: 3 Presentation: 3 Contribution: 4 Limitations: - limited to datasets with 3D reconstructions available. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your thoughtful and encouraging review. We appreciate your recognition of the strengths of our work, particularly in terms of the memory efficiency gains and the analysis of the correction to the loss function. Below, we address your concerns and questions in more detail. --- Weakness 1: Reliance on existing 3D mesh reconstruction for evaluation We understand your concern regarding the reliance on 3D mesh reconstructions for the Scene-Stable Panoptic Segmentation task. However, we would like to clarify that this requirement is only necessary for evaluation purposes, not for training or general application of the LoCo features. The primary goal of this task is to highlight the improved location-consistency of our trained LoCo features compared to existing feature extractors. While it is true that this evaluation necessitates datasets with 3D reconstructions, we believe that this is not a significant limitation. Several existing datasets provide this data, and our method's ability to perform well in this setting demonstrates its robustness and applicability in scenarios requiring high-precision spatial understanding. The improvements in location-consistency, as demonstrated in this task, are transferable to other tasks that do not necessarily require 3D meshes. --- Weakness 2: Comparison with LoCo at a feature dimension of d=64 We appreciate your suggestion to include a comparison between LoCo and LoCUS at a feature dimension of d=64 for a more direct comparison. In the global author response, we provided additional results for fine-tuning the LoCUS architecture using our memory-efficient loss. While it is true that a direct comparison at a high feature dimension is challenging due to memory constraints, our additional experiments demonstrate that even at a low feature dimension our method offers significant improvements in memory efficiency while maintaining strong performance. The improvements seen with larger models trained using our method further validate the value of our modifications to the loss function and training algorithm in overcoming memory limitations. This supports the scalability and robustness of our approach across different architectures and feature dimensions. --- Question: Performance of LoCo with features from different models (e.g., DINO vs. DINOv2) In response to your question about the performance of LoCo with features from different models, we have provided additional results using a DINOv2 ViT-Base backbone in the global author response. These results show that our method significantly outperforms the original DINOv2 feature extractor in tasks requiring accurate pixel correspondences. While the performance with the DINOv2 backbone is slightly lower than with the DINOv1 backbone, this likely arises from the differences in the patch size of the backbone, which affects the granularity of the feature map. Nevertheless, the fact that training with our method improves multi-view consistency with different backbone architectures demonstrates its flexibility and effectiveness across various feature extraction models. --- Limitations: Dataset requirements We acknowledge the limitation regarding the availability of 3D reconstructions in certain datasets. As discussed, this requirement is specific to the evaluation of certain tasks and not an inherent limitation of our method. The technique we propose is broadly applicable and can be adapted to other datasets and tasks that do not require 3D reconstruction data. --- We hope these clarifications address your concerns and provide a deeper understanding of the contributions and versatility of our work. We appreciate your constructive feedback and believe that our paper makes a valuable contribution to the field of vision foundation models, particularly in improving memory efficiency and multi-view consistency. Thank you again for your careful review and for the opportunity to improve our work through your insights. --- Rebuttal Comment 1.1: Comment: I would like to thank the authors for their responses and the other reviewers for their thoughtful feedback and questions. I think the motivation of choice of Matterport (raised by Reviewer jhZZ ) and apples to apples comparison with LocUS (raised by Reviewer aW6W) should make it to the main paper, emphasizing the reduced memory footprint of the proposed method. --- Reply to Comment 1.1.1: Comment: Thank you, we will include these in the main paper to better reflect the setting and contributions of our proposed approach.	Summary: This paper presents a new training scheme for vision foundation models. The key goal of the paper is to enhance the multi-view consistency of vision foundation models. To this end, the paper revisits the idea from soft average precision, and applies the idea for training vision foundation models. Specifically, the loss loosely enforces similar score values for positive patch pairs, unlike explicitly enforcing positive / negative affinities to reach a pre-designated value as in conventional contrastive learning approaches. The authors further propose pruning positive and negative samples during backpropagation to ensure memory efficiency. Experiments demonstrate that the proposed method can outperform tested baselines in local feature matching, panoptic segmentation, and visual place recognition. Strengths: 1. The paper tackles an important task in training vision foundation models, namely enforcing multi-view consistency. 2. The presentation is clear and straightforward to follow. 3. The proposed pruning scheme enables training multi-view consistent vision foundation models at a much smaller computational cost than existing approaches. Weaknesses: 1. My major concern is with the experiments. First, it is unfair to compare existing vision foundation models directly against the proposed method, since the method is additionally trained using Matterport3D data. The baselines in Table 1 should also have been additionally fine-tuned on Matterport3D. Further, since the paper is proposing a generic loss function applicable to any pre-trained vision foundation model, the technical contributions would have been better elucidated if the method improved multi-view consistency for other vision foundation models as well, for example pre-trained DINOv2 features. 2. The motivation for setting the saturation threshold to 0.076 in L220 is unclear. Why is the gradient being 0.2% of the "maximum gradient of the sigmoid function" important for training models with the proposed loss? 3. The technical contributions of the paper is unclear. From a methodological point of view, the paper adapts soft average precision loss from prior literature with a threshold-based pruning to ensure memory efficiency, which is not strongly novel. Further, the experimental results are largely limited to fine-tuning a small CNN operating on top of DINO features. Therefore the scalability of the proposed training scheme is unclear. Technical Quality: 2 Clarity: 2 Questions for Authors: Please refer to the weaknesses section above. Below are a few additional questions: 1. What are the exact computational requirements of the paper? The only place that I could find hardware requirements was L302. Is a single RTX8000 GPU all we need? 2. What is the reason for training the model on Matterport3D? I feel datasets such as ScanNet will contain a much more diverse range of scenes. Since the only model being trained is the feature refinement CNN, training on ScanNet will not be prohibitively expensive. Confidence: 5 Soundness: 2 Presentation: 2 Contribution: 1 Limitations: Yes the limitations are stated in the supplementary material. Flag For Ethics Review: ['No ethics review needed.'] Rating: 3 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your thorough review and for highlighting both the strengths and weaknesses of our work. We appreciate your feedback, and we would like to address your concerns in detail below. --- Weakness 1: Fairness of comparisons and generalization of the proposed method We understand your concern regarding the comparison with existing vision foundation models. However, we would like to clarify that our training and evaluation strategy is designed to test generalization across diverse scenes and datasets, not just on Matterport3D. Specifically, we evaluate on different environments than those used in training, including environments from a different dataset (ScanNet), ensuring that our network is not simply overfitting on the training set, but instead learning transferable and generalizable features. Regarding the inclusion of a DINOv2 backbone, we have extended our experimental analysis to include results with a DINOv2 ViT-Base backbone (as described in the global author response). The results show clear performance improvements over the original DINOv2 features, which supports the general applicability of our method across different backbone architectures. This new evidence strengthens the claim that our method improves multi-view consistency in a broader context. --- Weakness 2: Motivation for the saturation threshold $\Delta$ The threshold $\Delta$ is indeed a key hyper-parameter in our method, and its selection is crucial for balancing memory efficiency with the accuracy of the loss function approximation. The chosen value for $\Delta$ represents a trade-off: a smaller $\Delta$ leads to greater memory savings but can also introduce distortions to the loss function, affecting the training dynamics. We selected $\Delta$ such that the gradient at $\sigma(\Delta)$ is 0.2% of the maximum gradient of the sigmoid function. This choice allows us to achieve significant memory savings (by a factor of approximately 5) while minimizing the distortion of the loss gradients. In this way, we ensure that the memory efficiency gains do not come at the expense of training stability or performance. The ablations provided in Table 1 of the paper offer insight into these trade-offs, showing how different values of $\Delta$ impact both memory usage and model performance. We agree that the explanation for our specific choice could have been more explicit in the paper, and we appreciate your feedback on this. We believe that our current justification is grounded in practical considerations of training efficiency and accuracy, and we have provided empirical evidence to support it. --- Weakness 3: Technical contributions and scalability concerns We would like to emphasize that our approach is more than just an adaptation of the LoCUS architecture with threshold-based pruning. The pruning mechanism we propose is based on a detailed analysis of the gradient behavior, and it includes correction terms to ensure that the loss remains unbiased. We also address the bias in existing batch implementations of the general Smooth-AP loss, deriving the compensating correction terms necessary if using this loss for mini-batches, as is always the case in practice. This addresses a fundamental flaw in this loss function as used in the literature. Overall, our careful loss design addresses the challenges associated with unbiasing the loss signal, improving the memory efficiency and stabilising the gradients, making our method a significant contribution beyond a simple combination of existing techniques. Regarding scalability, we agree that larger-scale experiments would be beneficial to fully explore the potential of our approach. However, even within the computational constraints we had, we observed consistent performance improvements with increased model size, as evidenced by our experiments with the LoCUS architecture. This suggests that our method scales well, at least within the range we were able to test. We hope that future work, possibly with greater computational resources, will further validate the scalability of our approach on larger foundation models. --- Questions and Additional Clarifications 1. Computational Requirements: As noted in our paper, our experiments were conducted using a single RTX8000 GPU, with each training run taking approximately 1.5 days. This setup reflects the memory efficiency of our method, making it accessible even for researchers with limited computational resources. 2. Choice of Matterport3D Dataset: The method most similar to ours, LoCUS, trained its models on the Matterport3D dataset only, so we followed their choice to avoid additional confounding factors in comparing the two methods. The Matterport3D dataset is particularly suitable for our task of enforcing multi-view consistency due to its diversity and the way it captures varied viewpoints of the same scene through panorama cropping. We acknowledge that ScanNet is another valuable dataset; however, due to its trajectory-based data collection, there is less viewpoint variation per scene compared to Matterport3D, which influenced our dataset selection. --- We hope these clarifications address your concerns and provide a better understanding of the contributions and significance of our work. We appreciate your thoughtful feedback and believe that our additional explanations and results strengthen the case for our contributions. We respectfully invite you to reconsider your assessment of our work in light of the additional evidence and explanations provided. Thank you once again for your time and effort in reviewing our submission. --- Rebuttal Comment 1.1: Comment: Thank you for the response. While the rebuttal has allayed some of my concerns, I am willing to keep my initial rating. Here is why: 1. I acknowledge that the authors have conducted experiments regarding generalization on other datasets such as ScanNet. However, my major concern was that all the tested baselines should have been fine-tuned on the training dataset for LoCo (i.e., Matterport3D), and then be evaluated on the test set. Otherwise, the comparisons will not be fair, since only LoCo had access to the multi-view information from Matterport3D. 2. Regarding the motivation of the saturation threshold, I am still not clear why "0.2% of the maximum gradient of the sigmoid function" is a key desiderata for choosing its value. Where does the number "0.2%" come from? The authors' explanation is not sufficient to clarify their decision on the saturation threshold value. --- Reply to Comment 1.1.1: Comment: Thank you for considering our response and for clearly outlining your main concerns. We appreciate the opportunity to address your remaining concerns and provide further clarification below: 1. We acknowledge the concern and will include this fine-tuning experiment in the final revision; we need more time to complete this for all compared methods. However, we would like to emphasise that one of the compared methods (CroCo-v2) is already trained with a multi-view loss on a very much larger multi-view dataset (a combination of simulated Habitat images and real images from ARKitScenes, MegaDepth, 3D Street view, IndoorVL; a total of 5.3 million image pairs) than Matterport3D and so has a significant advantage over LoCo, especially on the ScanNet experiments. LoCo’s better performance on the validation tasks highlights the benefits of explicitly including location-consistency as a goal of the loss function. 2. The 0.2% threshold is arbitrary, albeit selected empirically (see Table 1 of the paper). It represents a trade-off between performance and memory-efficiency. Setting it to 0.2% of the maximum gradient leads to minimal impact on the gradient signal (and minimal impact on performance) while achieving a 5x memory reduction. In this respect it resembles other hyperparameters used in training algorithms, e.g. learning rates, where the practitioner’s choice is guided by empirical performance rather than theoretical guarantees of optimality. We hope these additional clarifications address your concerns more comprehensively. We are committed to improving our work and appreciate the constructive nature of your feedback. Thank you once again for your valuable insights.	null	null	Rebuttal 1: Rebuttal: We thank all reviewers for their careful reading and thoughtful comments. In this section, we outline the additional ablations and evaluations requested by the reviewers, which are presented in the PDF attached to this response. ## Pixel Correspondence Estimation (Table 1) ### LoCo with DINOv2 Backbone As requested by reviewers jhZZ and YTBi, we provide results where the DINO backbone used in the original submission is replaced by the DINOv2 ViT-Base backbone ("LoCo w/ DINOv2 backbone"). The resulting features significantly outperform the original pre-trained DINOv2 features (also reported in Table 1) for finding accurate pixel correspondences, showing its advantage in tasks that require location-consistent features. However, it slightly underperforms the LoCo model trained with the DINO-ViT-Base8 backbone used in the original submission. We hypothesize that this arises from the coarser feature map of the DINOv2-ViT-Base14 backbone compared to the DINO-ViT-Base8 backbone. ### LoCo with LoCUS architecture As requested by reviewers YTBi and aW6W, we also provide results where the network architecture used in the original submission is replaced by that used in LoCUS ("LoCo w/ LoCUS architecture"). This model outperforms the original LoCUS model for small viewpoint changes, but underperforms for image pairs with larger viewpoint changes. This illustrates that the improvements in memory efficiency do not by themselves lead to improvements in performance, but that they allow for the training of larger models and higher-dimensional feature vectors with the same computational budget, the effect of which far outweighs any performance decrease due to our loss function and training algorithm changes. ## Panoptic Scene-Stable Segmentation (Table 2) ### LoCo with DINOv2 Backbone For this task, the LoCo model trained with the DINOv2 backbone only outperforms the original DINOv2 feature extractor on some of the metrics. This is likely attributable to the coarser feature map of this backbone, which leads to less fine-grained patch-level supervision during training. ### LoCo with LoCUS architecture For this task, the LoCUS architecture trained with the LoCo algorithm performs worse than the original LoCUS model. For this ablation, we trained for the same number of epochs as our other LoCo models, and so cannot rule out that the vision transformer blocks in the LoCUS architecture require longer training times than the convolutional layers of the LoCo model. As before, this result illustrates the value in our efficiency improvements as they ultimately unlock the training of larger models with larger feature dimensions. Pdf: /pdf/adb3016a9304ebf52461c2cd6fe0f5deafc47e96.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Simple and Effective Masked Diffusion Language Models	Accept (poster)	Summary: The paper introduces a masked diffusion language modeling (MDLM) framework that enhances the performance of diffusion models in generating high-quality text, closing the gap with autoregressive methods. By applying an effective training strategy and a simplified objective function, MDLM achieves state-of-the-art results among diffusion models on language benchmarks. The approach is shown to be simple yet effective, with potential applications beyond language, including biological sequence modeling. Strengths: - The method is well motivated and well designed based on the previous works SEDD - The story is well told for better understanding. Weaknesses: - In Figure 1, unmasking loss is misleading. What's the difference between the red and yellow colors? Which tokens should we enforce the losses on? - In Line 38, "Simple" seems overstated. I couldn't quickly understand the method, even though I have some background in diffusion models and sequence modeling. - In Line 168, there are too many experimental details about the network structure and tokenizer changes, making it unclear how to prove the method works. This, in turn, suggests that the proposed method is not so simple. - The sampling steps for diffusion-based methods should be highlighted in Table 1 and other related tables. - In Line 178, the semi-autoregressive part is not clear to me. I lose track of how it works. The need for semi-autoregressive models is not well-motivated. It's a common replacement trick used in diffusion models. The author should explain it. - In Table 5, memory should also be included. Secondly, Mamba is more favorable for longer token numbers. The authors should also compare with Mamba under various token numbers: 1k, 5k, 10k, and 20k. - The paper needs to provide the mathematical proof for the continuity equation, showing that $ u_t $ in the equation generates the probability path $ p_t $. It should also highlight the connection to the continuous case. - In Line59, several works about using flow-based method is missing,[1][2] - In LIne65, citation missing, Chapell's discrete flow matching paper - Better discuss with this work: https://arxiv.org/abs/2406.03736 [1]. Language Rectified Flow: Advancing Diffusion Language Generation with Probabilistic Flows [2]. Flow Matching for Conditional Text Generation in a Few Sampling Steps Overall, the authors claim the method is simple, but it’s not as simple as they claimed. Additionally, there are many issues with the presentation and experimental parts. Therefore, I am inclined to weakly reject this paper. Technical Quality: 3 Clarity: 3 Questions for Authors: As above Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: Yes Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Title: Response to wXn1 (1/3) Comment: We want to thank the reviewer for their constructive feedback. We address specific comments and questions below. --- ### **Concern 1: What is “simple”? It was hard to understand the method. We use the term “simple” because our algorithm is very similar to BERT except for a small change: a random masking rate. Please see the general response for how one of our main contributions, the SUBS parameterization and continuous time perspective, allow us to simplify the training objective. We will clarify the method by providing the following pseudocode in the next version of the paper. We use $x$ to denote a one-hot word embedding, and $m$ is a one-hot vector encoding the mask token. Algorithm: MDLM Training: Inputs: dataset $\mathcal{D}$, monotonic masking schedule $\alpha_t : [0,1] \to [0,1]$, BERT-like model $x_\theta$. 1. repeat** 1. $\mathbf{x}^{1:L} \sim \mathcal{D}$ // Sample a sequence of length L from dataset (can be a batch) 2. $\mathbf{z}^\ell_t \sim \text{cat}(\mathbf{z}^\ell_t; \alpha_t \mathbf{x}^\ell + (1 - \alpha_t)\mathbf{m})$ $\forall 1 \leq \ell \leq L$ for random $t \sim \mathcal{U}[0, 1]$ // Mask each token $\mathbf{x}^\ell$ independently with masking rate $\alpha_t$ to obtain the latent $\mathbf{z}^{1:L}_t$. 3. Update weights $\theta$ of denoising (BERT) model $\mathbf{x}_\theta$ by gradient descent step on $\nabla_\theta \frac{\alpha'\_t}{1 - \alpha\_t} \sum_{\ell} \log \langle \mathbf{x}\_\theta^\ell(\mathbf{z}^{1:L}_t), \mathbf{x}^\ell \rangle$ // Note: this is simply a “weighted” BERT-style loss until converged The only differences relative to BERT are that at step (1.2), $\alpha_t$ is a constant, and in step (1.3.) there is no weighting term in front of the cross-entropy loss. Otherwise the training algorithms are equivalent! Indeed, one could even take an off-the-shelf pre-trained BERT and with minimal modifications to the training loop, render it a generative model (Table 4) with an principled ELBO objective and sampling algorithm. Additionally, unlike previous works, such as CTMC [1] and SEDD [2], which rely on the machinery of continuous-time Markov chains, our work admits a straightforward generation algorithm based on ancestral sampling that we present below: Algorithm: MDLM Sampling / Inference 1. $\mathbf{z}^{1:L}_1 =$ [MASK, MASK, …, MASK] // Sampling process starts with all MASK tokens. 2. for t = {$1, \frac{T-1}{T}, \dots, \frac{1}{T}$} do 1. $s \xleftarrow{} t - \frac{1}{T}$ 2. $\mathbf{z}^\ell_{s} \sim \text{Cat}(\mathbf{z}^\ell_s; \frac{(1 - \alpha_s)\mathbf{m} + (\alpha_s - \alpha_t)\mathbf{x}_\theta(\mathbf{z}_t)}{1 - \alpha_t} )$ if $\mathbf{z}_t^\ell = \text{[MASK]}$ else $\mathbf{z}_s^\ell = \mathbf{z}_t^\ell$ $\forall 1 \leq \ell \leq L$. 3. $\mathbf{z}^{1:L}_t \xleftarrow{} \mathbf{z}^{1:L}_s$ end for 3. return $\mathbf{z}_0$ To further underscore the simplicity of our method, we highlight the minimal form of our variational lower bound, Equation 10, which ends up being a weighted average of BERT-style losses: $\mathcal{L} = \mathbb{E}\_q\int_{t=0}^{t=1}\frac{\alpha\_t'}{1-\alpha\_t} \log \langle\mathbf{x}_\theta(\mathbf{z}_t), \mathbf{x}_0\rangle dt$ In summary, our work presents a principled approach to turn widely-used bi-directional language models into generative ones. --- Rebuttal 2: Title: Response to wXn1 (2/3) Comment: ### Concern 2: MDLM involves a number of hyper-parameters. It is unclear these are same for baselines, and whether the comparison is fair. We stress that our experiments use exactly the same hyper-parameters (tokenizer, network structure, training set, optimizer settings, etc.) across every model that we have implemented (AR, SEDD, which is the current state-of-the-art in discrete diffusion, MDLM, as well as models in other tables such as D3PM). \| \| SEDD \| MDLM \| AR \| \| --- \| --- \| --- \| --- \| \| Tokenizer \| `bert-base-uncased` for LM1B / `gpt-2` for OWT \| `bert-base-uncased` for LM1B / `gpt-2` for OWT \| `bert-base-uncased` for LM1B / `gpt-2` for OWT \| \| Architecture \| DiT \| DiT \| DiT \| \| Context size \| 128 for LM1B / 1024 for OWT \| 128 for LM1B / 1024 for OWT \| 128 for LM1B / 1024 for OWT \| \| Train steps \| 1M steps \| 1M steps \| 1M steps \| \| Perplexity ($\downarrow$) on LM1B (1M train steps) \| 32.79 \| 27.04 \| 22.32 \| \| Perplexity ($\downarrow$) on OWT \| 24.10 \| 23.21 \| 17.54 \| To further clarify: in Section `3.5.1`, we specifically highlighted architectural details used in MDLM that contribute to a performance relative to the results in the original D3PM paper. However, our main tables compare against key baselines (SEDD, AR, and D3PM, which is MDLM after all ablations) with the same architecture. --- ### **Concern 3: It is unclear how semi-autoregressive sampling works. Naively, diffusion models only generate fixed-length sequences. Semi-autoregressive sampling allows diffusion to produce arbitrary-length sequences by generating (via diffusion) a block of text that is conditioned on previously generated blocks of text (blocks previously obtained via diffusion). Algorithm: MDLM Semi-AR sampling** Generates a Sequence of length $B \times L$ where $L$ is the context length of the diffusion model. 1. $S = \phi$ // We start with a null sequence. 2. $\mathbf{x}^{1:L} =$$[MASK]^{1:L}$ // Sampling process starts with all MASK tokens. 3. for $i$ = {${1, \dots, B - 1}$} do 1. Unmask all masked tokens in $\mathbf{x}^{1:L}$ using the MDLM Sampling algorithms as described above. 2. $S \xleftarrow{} S \cup \mathbf{x}^{1:L/2}$ // Save the first $L/2$ tokens 3. $\mathbf{x}^{1:L/2} \xleftarrow{} \mathbf{x}^{L/2:L}$ // Condition the generation of future tokens on the trailing $L/2$ tokens 4. $\mathbf{x}^{L/2:L} \xleftarrow{} [MASK]^{1:L/2}$ // Mask out the last $L/2$ tokens to be filled out by MDLM in the next iteration. end for 4. return $S$ For a figure illustrating how our proposed semiAR algorithm works, please see the schematic in the attached supplementary materials [here](https://openreview.net/forum?id=L4uaAR4ArM&noteId=WereEXicWc) ---- ### Additional questions and concerns > Include sampling steps for Table 1 There are different ways to interpret this question. First, sampling steps could refer to the value of T used at training time. We report our best PPL values with the continuous-time formulation ($T \to \infty$) for MDLM and SEDD, and report results with finite $T$ among our ablations. A second interpretation is that “sampling steps” could refer to the number of generate text from the model when we evaluate generative PPL. This number is reported on the x-axis of our generative PPL figure and varies between 32 and the length of the sequence. A third interpretation refers to the Monte Carlo sampling to evaluate PPL. When evaluating the perplexity bound of MDLM or SEDD, we use a single Monte Carlo sample per datapoint to approximate the integral of the continuous-time bound. Our low-discrepancy antithetic sampler allows us to estimate the perplexity bound with low variance, as shown in the table below. On OpenWebText, we find that we are able to accurately estimate the perplexity bound with just a single sample. In contrast, prior work required 1,000 samples to obtain an accurate estimate. Below we include a table that shows the limited effect of including more time steps in the Monte-Carlo estimate of MDLM on the OpenWebText dataset: \| Num MC samples \| 1 \| 2 \| 5 \| 10 \| 100 \| \|---------------------------\|-------\|-------\|-------\|-------\|-------\| \| Perplexity ($\downarrow$) \| 23.21 \| 23.22 \| 23.22 \| 23.22 \| 23.21 \| > Better explaining Figure 1 The loss in Figure 1 is computed over red boxes only. Since the yellow boxes are unmasked, by the definition of our SUBS parameterization, the loss there is zero by construction. We are adding a legend to explain this. > Mathematical proof for continuity equation. There is currently no mention of $u_t$ in our work. Can you please provide further clarification as to what you are requesting in this regard? --- Rebuttal 3: Title: Response to wXn1 (3/3) Comment: > Comparing efficiency w/ Mamba under different token numbers We compare the wall clock times of 1 forward pass of the bidirectional transformer used in MDLM vs. Mamba under varying context lengths. While Mamba achieves favorable runtimes at context lengths greater than 8k tokens, there is not a significant speed improvement at the context lengths studied in this paper (where we seek to match GPT-2 using diffusion). Although long context generation is not a focus of this work, we believe it is an interesting area for future extensions. \| # of tokens (wikitext103) \| 2k \| 4k \| 8k \| 16k \| 32k \| \| --- \| --- \| --- \| --- \| --- \| --- \| \| Mamba (runtime in ms) \| 11 \| 12 \| 22 \| 42 \| 83 \| \| Transformer (runtime in ms) \| 13 \| 17 \| 36 \| 88 \| 250 \| We report the above runtimes on a single A5000 GPU, excluding the wall clock time of word embeddings. --- Rebuttal Comment 3.1: Title: Thanks for the reply Comment: Thanks for the authors' reply and the reviewer's feedback. My concern about the simplicity of the method is addressed by the pseudo alg. However, without explicit discussion about related works in the main paper, I don't feel my concerns are fully resolved. --- Rebuttal 4: Title: Discussion on related works Comment: Thank you for your feedback and response to our rebuttal. Below we provide discussions on the requested related works [1, 2, 3, 4]: Language Rectified Flow [1] and Flow Matching for Conditional Text Generation in a Few Sampling Steps [2] perform flow matching over word embeddings. These works are more similar to Plaid [6] and Diffusion-LM [7], where the diffusion process is defined over a continuous space. In contrast, MDLM applies diffusion processes to discrete structures. We will include this discussion in the updated version of the manuscript. Furthermore, we would like to highlight that in Section 6 of the paper, where we have provided a comprehensive literature review covering areas such as Continuous Time Markov Chains [8, 11], score estimation [9, 10], and techniques that use BERT for sample generation [12, 13, 14, 15]. ## Comparisons to Discrete Flow Matching [3]: Discrete Flow Matching (DFM) proposes flow matching for discrete structures. They use the following cross entropy loss as their training objective: $\mathcal{L}\_\text{DFM} = - \int_{t=0}^{t=1}\log p_\theta(\mathbf{x}^{1:L}\|\mathbf{z}^{1:L}_t) dt$ Similar to [5], DFM’s objective, while effective, is not weighted appropriately to make it a proper ELBO. However, in MDLM, we derive a tight and principled lower bound to the log-likelihood. ## Comparisons to Your Absorbing Discrete Diffusion Secretly Models the Conditional Distributions of Clean Data. [4]: [4] reaches a similar training objective to that derived in our work, although they start their analysis from the score matching perspective presented in SEDD [10]. Interestingly, they find an important equivalence between denoising concrete score matching and the variational lower bound that we derive. A similar connection was also made in Shi et al. [16]. In contrast, we tackle this problem starting via a variational lens: where we derive the exact continuous time ELBO by endowing D3PM with the novel SUBS parameterization and taking the number of diffusion steps T to infinity. Also of note is that [4] leverages a time-independent de-noising network to formulate an efficient sampler that limits function evaluations, as in our work. A key point of differentiation between our works is that we tackle an important limitation of diffusion models, namely that they are limited to generating a fixed sized context. Our proposed semi-AR algorithm mitigates this shortcoming, and is therefore a novel contribution to this line of work that separates MDLM from [4]. Finally, turning to a comparison of the empirical evaluation: here, we believe that our work is significantly better. - Most importantly, we explicitly compare our discrete diffusion model on the widely used objective of perplexity and demonstrate that non-autoregressive models are approaching the performance of autoregressive ones. This is a significant milestone, as perplexity has been the guiding watermark for the field of language modeling. In contrast, [4] only use the less informative metrics of “zero-shot” perplexity and “generative perplexity”. - Furthermore, we analyze domains outside of NLP and demonstrate that the approach can be used on biological sequences, unlike [4] and [16], which only focus on NLP datasets. - Finally, our Table 4, demonstrates how one can take an off-the-shelf BERT model and render it generative without losing representation learning capabilities. This is an important result in our work that is not present in either [4] or [16]. We end by noting that [4,16] are highly concurrent and were posted on arXiv after the Neurips submission deadline. According to Neurips guidelines, authors are not expected to compare their work to papers that appeared on arXiv less than two months before the submission deadline, let alone those published after it. --- Rebuttal Comment 4.1: Title: accept Comment: I appreciate the author's reply about the related works. Even though some papers are concurrent works, I think it can be discussed. I am not asking for a comparison. I am excited to see the deep relationship between them. My concerns have been fully resolved, and I will increase my score to reflect this. --- Reply to Comment 4.1.1: Title: Thank you Comment: Dear Reviewer, We really appreciate your feedback and continued engagement. We'll incorporate these discussions in the next version of the manuscript. Thanks, authors --- Rebuttal Comment 4.2: Comment: can you update the reference? I cannot find them --- Reply to Comment 4.2.1: Title: Updated references Comment: We have added the references in a separate comment here: https://openreview.net/forum?id=L4uaAR4ArM&noteId=fwSYxq1dTI --- Rebuttal Comment 4.3: Title: References Comment: ## References: [1]. Zhang, S., Wu, L., Gong, C., & Liu, X. (2024). Language rectified flow: Advancing diffusion language generation with probabilistic flows. arXiv preprint arXiv:2403.16995. [2]. Hu, V., Wu, D., Asano, Y., Mettes, P., Fernando, B., Ommer, B., & Snoek, C. (2024, March). Flow Matching for Conditional Text Generation in a Few Sampling Steps. In Proceedings of the 18th Conference of the European Chapter of the Association for Computational Linguistics (Volume 2: Short Papers) (pp. 380-392). [3] Campbell, A., Yim, J., Barzilay, R., Rainforth, T., & Jaakkola, T. (2024). Generative flows on discrete state-spaces: Enabling multimodal flows with applications to protein co-design. arXiv preprint arXiv:2402.04997. [4] Ou, J., Nie, S., Xue, K., Zhu, F., Sun, J., Li, Z., & Li, C. (2024). Your Absorbing Discrete Diffusion Secretly Models the Conditional Distributions of Clean Data. arXiv preprint arXiv:2406.03736. [5] Chang, Huiwen, et al. "Maskgit: Masked generative image transformer." Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2022. [6] Gulrajani, Ishaan, and Tatsunori B. Hashimoto. "Likelihood-based diffusion language models." Advances in Neural Information Processing Systems 36 (2024). [7] Li, Xiang, et al. "Diffusion-lm improves controllable text generation." Advances in Neural Information Processing Systems 35 (2022): 4328-4343. [8] Andrew Campbell, Joe Benton, Valentin De Bortoli, Thomas Rainforth, George Deligiannidis, and Arnaud Doucet. A continuous time framework for discrete denoising models. Advances in Neural Information Processing Systems, 35:28266–28279, 2022. [9] Yang Song and Stefano Ermon. Generative modeling by estimating gradients of the data distribu- tion. Advances in neural information processing systems, 32, 2019. [10] Aaron Lou, Chenlin Meng, and Stefano Ermon. Discrete diffusion language modeling by estimating the ratios of the data distribution. arXiv preprint arXiv:2310.16834, 2023. [11] Haoran Sun, Lijun Yu, Bo Dai, Dale Schuurmans, and Hanjun Dai. Score-based continuous-time discrete diffusion models. arXiv preprint arXiv:2211.16750, 2022. [12] Zhengfu He, Tianxiang Sun, Kuanning Wang, Xuanjing Huang, and Xipeng Qiu. Diffusion- bert: Improving generative masked language models with diffusion models. arXiv preprint arXiv:2211.15029, 2022. [13] Marjan Ghazvininejad, Omer Levy, Yinhan Liu, and Luke Zettlemoyer. Mask-predict: Parallel decoding of conditional masked language models. In Kentaro Inui, Jing Jiang, Vincent Ng, and Xi- aojun Wan (eds.), Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing (EMNLP- IJCNLP), pp. 6112–6121, Hong Kong, China, November 2019. Association for Computational Linguistics. doi: 10.18653/v1/D19-1633. URL https://aclanthology.org/D19-1633.	Summary: This paper presents a method for language modeling using simple masked discrete diffusion models. The authors show that a simplified objective combined with optimized training achieves performance improvements over previous diffusion language models. The paper reports state-of-the-art results for diffusion models on standard language modeling benchmarks, approaching the performance of autoregressive models. Strengths: 1. The simplified diffusion objective is effective in stabilizing training and is well supported by detailed derivations. 2. Section 3 provides clear steps to build a connection between MLM and Diffusion LM 3. The empirical performance is superior to other diffusion language models. Weaknesses: 1. I believe the paper should be structured more towards introducing the simplified objective rather than framing the architecture as MDLM since the main idea of bridging absorbing state discrete diffusion with MLM has been introduced in DiffusionBert and D3MM. 2. The comparative results are not fair comparisons. More specifically the use of a more advanced backbone (DiT) and a low-variance sampler weakens the claim that the performance and stability are sourced from the proposed method. Technical Quality: 3 Clarity: 3 Questions for Authors: 1. Other than the simplified objective and new backbone and sampler, what’s the difference between your method and absorbing state D3MM or more specifically DiffusionBert? 2. Is MLM pretraining required for your method? Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: 1. Masked language models are special discrete Diffusion models, this is demonstrated in the D3PM paper by rewriting an x_0-parameterized absorbing state model. This limits the novelty of the paper to the simplified objective only. 2. The idea in this paper has been hinted at in D3MM, limiting the theoretical contribution of this paper. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Title: Response to DASc (1/2) Comment: We want to thank the reviewer for their constructive feedback. We address concerns and questions below. --- ### **Concern 1: Novelty of MDLM relative to the D3PM framework and other algorithms. In addition to attaining state-of-the-art diffusion language model results, MDLM presents important novel elements relative to prior work. Relative to D3PM: [1] MDLM is a special case of the D3PM framework that focuses only on masked noise. This allows introducing multiple algorithmic innovations that greatly simplify D3PM and improve performance. These design decisions also yield a learning objective that is a weighted average of BERT-style loss terms. Although D3PM mentions in their appendix connections to BERT, we make this connection much more clear and derive a simpler and more performant algorithm. Our NELBO is given as: $\mathcal{L}\_{NELBO} = \int_{t=0}^{t=1}\frac{\alpha'\_t}{1 - \alpha\_t} \log p_\theta(\mathbf{x}^{1:L}\|\mathbf{z}^{1:L}_t) dt$ which achieves a test perplexity of 27.04 after being trained for 1M steps on LM1B while our well engineered implementation of D3PM achieves a worse perplexity of 28.56. - Algorithmic innovations - Simplified noise process: In D3PM, the noise process is defined via matrix multiplications. In MDLM, we can define simple interpolating noise $\mathbf{z}_t = \alpha_t \mathbf{x} + (1 - \alpha_t)\mathbf{m}$ which allows easily taking $T \to \infty$, which in turn tightens the ELBO. - Specialized denoising process: We propose the SUBS parameterization, which includes two key elements: carry-forward unmasking and zero masking probabilities. - Simplified and tightened ELBO:** Our choice of noising and denoising processes allows us to greatly simplify the D3PM objective (several pages of math in the appendix) and produce a simplified and tighter ELBO (compare our Equation 8 to Equation 9, which is what D3PM uses). - Experimental innovations We complement the above innovations with a modern training recipe (architecture, optimization) that demonstrates the effectiveness of masked diffusion models. While previous attempts (namely D3PM) seemed to indicate that there exists a large gap between AR and discrete diffusion models, we provide clear evidence to the contrary on the OWT dataset using to train GPT-2 sized models. Relative to SEDD: [2] Our key novelty elements are as follows. - We achieve better language modeling results relative to this work, which was previously **state-of-the-art for diffusion models. - We present a more intuitive and simple objective which boils down to a weighted average of BERT-style losses, circumventing the need to use score-matching techniques and the formalisms of continuous time Markov chains. - We support a more efficient inference algorithm that greatly reduces required function evaluations. Relative to DiffusionBERT [3]: - DiffusionBERT can be described as an instance D3PM with a pre-trained model initialization and a custom noising schedule. Thus, all of the ELBO improvements and optimized training of our work relative to D3PM are also novel relative to DiffusionBERT. --- References: [1] Austin, Jacob, et al. "Structured denoising diffusion models in discrete state-spaces." Advances in Neural Information Processing Systems 34 (2021): 17981-17993. [2] Lou, Aaron, Chenlin Meng, and Stefano Ermon. "Discrete diffusion language modeling by estimating the ratios of the data distribution." arXiv preprint arXiv:2310.16834 (2023). [3] He, Zhengfu, et al. "Diffusionbert: Improving generative masked language models with diffusion models." arXiv preprint arXiv:2211.15029 (2022). --- Rebuttal 2: Title: Response to DASc (2/2) Comment: ### Concern 2: Is it better to lead the paper with MDLM or with the simplified objective as a key contribution? To clarify, we use the term MDLM to refer to a language modeling algorithm that is optimized for masked language discrete diffusion and that has the following components: - Parameterization: Our denoising network predicts clean data and uses the SUBS parameterization (carry over masking and zero mask probabilities). - Learning objective: We take $T \rightarrow \infty$ to train with a tight ELBO given in Equation 11. - Faster inference: By removing time-conditioning, we significantly reduce function evaluations during ancestral sampling. - Support for arbitrary sequence length generation: Using a semiAR algorithm, we alleviate a key shortcoming of diffusion models: fixed length generation. Note that these are novel features over SEDD or D3PM. Thus, while the objective is an important part of our work, it is only one novel part of the MDLM algorithm. We also acknowledge that we are not the first ones to consider masking diffusion. However, we are the first to optimize our algorithm for masking diffusion, and this motivates its name (MDLM). --- ### Concern 3: The use of a more advanced backbone (DiT) weakens the claim that the performance comes from the proposed method. As the table below demonstrates, our experimental setup is effectively identical between our work, AR, and SEDD (the previous state-of-the-art diffusion-based model), including the backbone. Thus, our ability to more effectively reduce the gap between diffusion and AR models is directly related to our proposed methodology. Experimental details: \| \| SEDD \| MDLM \| AR \| \| --- \| --- \| --- \| --- \| \| Tokenizer \| `bert-base-uncased` for LM1B / `gpt-2` for OWT \| `bert-base-uncased` for LM1B / `gpt-2` for OWT \| `bert-base-uncased` for LM1B / `gpt-2` for OWT \| \| Architecture \| DiT \| DiT \| DiT \| \| Context size \| 128 for LM1B / 1024 for OWT \| 128 for LM1B / 1024 for OWT \| 128 for LM1B / 1024 for OWT \| \| Train steps \| 1M steps \| 1M steps \| 1M steps \| \| Perplexity ($\downarrow$) on LM1B (1M train steps) \| 32.79 \| 27.04 \| 22.32 \| \| Perplexity ($\downarrow$) on OWT \| 24.10 \| 23.21 \| 17.54 \| To further clarify: in Section 3.5.1, we specifically highlighted architectural details used in MDLM that contribute to a performance relative to the results in the original D3PM paper. However, our main tables compare against key baselines (SEDD, AR, and D3PM, which is MDLM after all ablations) with the same architecture. --- ### Additional question > Is MLM pre-training required for your method? No, pre-training with standard MLM loss is not a requirement of our method. Indeed, the main results of our work, Tables 1 and 2, do not rely on any pre-training. To clarify, in Table 4, we included results of fine-tuning a pre-trained BERT using MDLM to highlight how one could take an off-the-shelf pre-trained representation learning model and turn it into a generative one, without sacrificing the representational learning capabilities of the pre-trained model. --- Rebuttal Comment 2.1: Comment: Thanks for the additional information and clarification! Regarding answers to concern 1: My opinion remains the same, and the methods especially zero-masking, carry-over unmasking, and semi-autoregressive sampling are shown to be the source of performance improvement, However, using such methods makes this work a mix of AR and Diffusion, which provides a limited contribution to the bridging of performance gaps between AR and Diffusion. Regarding answers to concern 2: The refined objective's sole contribution remains unclear, and needs to be studied separately from the other design changes. I believe that the refined objective can stabilize the training, while the other design changes are the major sources of improvement over SEDD. However, these additional design changes introduce an AR nature to your method from my intuition. If such designs do not show superior performance than AR, these design changes seem like "borrowing power" from the strong AR baselines, as mentioned above. Regarding answers to concern 3: Thanks for the clarification. --- Rebuttal 3: Title: Response to Reviewer DasC Comment: Thank you for your feedback and response to our rebuttal. Unfortunately, we believe there are several factual errors in your understanding of our method, which we would like to clarify: 1. There are no other sources of contribution to the performance of the method besides our new objective in the head-to-head comparison against SEDD that we report. 2. Our method is not a mix of auto-regression and diffusion, and no major perplexity result relies on auto-regressive components. ## Concern 1: The refined objective's sole contribution remains unclear. Other design changes are the major sources of improvement over SEDD. We’d like to re-emphasize that SEDD and MDLM have an identical experimental setup on language modeling benchmarks, as detailed below. The only difference between these two methods lies in the objective. Thus, the below table quantifies the sole contribution of MDLM’s objective over SEDD. \| \| SEDD (Our reproduction) \| MDLM \| \| --- \| --- \| --- \| \| _Common experimental details_ \| \| Tokenizer \| `bert-base-uncased` for LM1B / `gpt-2` for OWT \| `bert-base-uncased` for LM1B / `gpt-2` for OWT \| \| Architecture \| DiT \| DiT \| \| Context size \| 128 for LM1B / 1024 for OWT \| 128 for LM1B / 1024 for OWT \| \| Train steps \| 1M steps \| 1M steps \| \| _Objectives (the only difference between SEDD and MDLM)_ \| \| \| Diffusion weighted denoising score entropy (Eq 9 in SEDD) \| Simplified ELBO that becomes weighted sum of BERT style losses (Eq 11 in our work) \| \| _Performance_ \| \| Perplexity ($\downarrow$) on LM1B \| 28.90 \| 27.04 \| \| Perplexity ($\downarrow$) on OWT \| 24.10 \| 23.21 \| ## Concern 2: This work is a mix of AR and Diffusion. MDLM’s improved performance is because it “borrows” power from AR. This is a major misunderstanding. Please note that no significant result (Tables 1, 2, 3, 4, 6) uses anything related to auto-regression. All of our perplexity results are benchmarked against SEDD in a fully non-autoregressive setting following their setup (data, context window, etc.). In fact, one of our key contributions is that these results are obtained using a simple BERT-style non-autoregressive loss. The proposed semi-autoregressive sampler is only used in a minor experiment (Table 5) to allow MDLM to generate sequences of much longer lengths than those on which it was originally trained. However, this sampler does not** contribute to MDLM’s improved perplexity scores when compared to baselines such as SEDD or D3PM. In fact, the semi-AR experiments do not even compare against SEDD, only against SSD-LM.	Summary: While previous works considered diffusion language models less competitive than autoregressive models in text generation tasks, the authors propose a simple framework named masked diffusion language modeling (MDLM), where they claim to have better performance than previous thoughts. The authors derive a simplified Rao-Blackwellized objective and find that the objective equals to a masked language modeling with a varying mask ratio. The proposed methods are evaluated on both classification tasks and generation tasks. The performance excels in classification tasks and keeps consistent with autoregressive methods in generation tasks, which achieves a new state-of-the-art among diffusion models. Strengths: * The structure of the paper is complete. * The connection between diffusion model and masked modeling sounds good. * The experiments are comprehensive, covering both classification and generation tasks. Weaknesses: The main weakness of this paper is about the presentation. This includes the following two points: * In the third section, the authors first derive an objective with a diffusion process. Then, the authors try to claim what difference has been made compared to the previous D3PM. It seems that the different parameterization made in Equation (7) leads to a simpler formulation in Equation (8) compared to Equation (9), if I understand correctly. However, I am quite confused with the illustration in Section 3.2 and Section 3.3. There appears some technical terms without furthur explanations or citations, such as Rao-Blackwellization and graphical modeling. The abbreviation SUBS is also unclear. Some omittions and simplifications are not provided with some explanations to clarify their rationality. * There also lacks an overview on the algorithm. Due to the highly complicated derivation process and objective function, I suggest the authors making an algorithm bar to illustrate how the training and the sampling are conducted, like Algorithm 1 and Algorithm 2 in DDPM [1]. There also lacks some discussions with some previous works, including: * There has been a nearly same method in the CV field called MAGE [2]. MAGE also conducts masked modeling on image patch tokens with a varying mask ratio and generates by the ancestral sampling. * There lacks a citation for semi-autoregressive modeling [3] since I believe this concept is not first raised in this paper. [1] Denoising Diffusion Probabilistic Models, https://arxiv.org/pdf/2006.11239 [2] MAGE: MAsked Generative Encoder to Unify Representation Learning and Image Synthesis, CVPR 2023 [3] Semi-Autoregressive Neural Machine Translation, EMNLP 2018 Technical Quality: 3 Clarity: 2 Questions for Authors: * I wonder what previous tries have been made in the language diffusion model and what makes them fail to outperform autoregressive model in generation tasks, as diffusion models in the CV field largely outperform autoregressive models. * I wonder the computational cost of the method and its comparison with the autoregressive model's since it is known that the diffusion model usually costs more time to converge. Confidence: 3 Soundness: 3 Presentation: 2 Contribution: 2 Limitations: The authors have claimed their limitation in the paper. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Title: Response to BSmY (1/3) Comment: We thank the reviewer for their constructive feedback. We address the concerns and questions below. --- ### **Concern 1: Adding algorithms for training and inference. Below we provide pseudocode for MDLM training and inference. We also include these in our revised manuscript. We call out the simplicity of the training algorithm and its similarity to BERT-style training of masked language models: Algorithm: MDLM Training: Inputs: dataset $\mathcal{D}$, monotonic masking schedule $\alpha_t : [0,1] \to [0,1]$, BERT-like model $x_\theta$, $\mathbf{m}$ denotes the mask vector, $\mathbf{x}^{1:L}$ denotes a sentence with $L$ tokens, $\mathbf{z}^{1:L}_t$ denotes the latent vector with $L$ tokens. 1. repeat** 1. $\mathbf{x}^{1:L} \sim \mathcal{D}$ // Sample a sequence of length L from dataset (can be a batch) 2. $\mathbf{z}^\ell_t \sim \text{Cat}(\mathbf{z}^\ell_t; \alpha_t \mathbf{x}^\ell + (1 - \alpha_t)\mathbf{m})$ $\forall 1 \leq \ell \leq L$ for random $t \sim \mathcal{U}[0, 1]$ // Mask each token $\mathbf{x}^\ell$ independently with masking rate $\alpha_t$ to obtain the latent $\mathbf{z}^{1:L}_t$. 3. Update weights $\theta$ of denoising (BERT) model $\mathbf{x}_\theta$ by gradient descent step on $\nabla_\theta \frac{\alpha'\_t}{1 - \alpha\_t} \sum_{\ell} \log \langle \mathbf{x}_\theta^\ell(\mathbf{z}^{1:L}_t), \mathbf{x}^\ell \rangle$ // Note: this is simply a “weighted” BERT-style loss until converged Note that the only differences to BERT are that in standard BERT 1. In step 1.b., $\alpha_t$ is a constant (set to 0.85 implying a fixed masking rate of 15%). 2. In step 1.c. there is no weighting term in front of the cross-entropy loss. Otherwise the training algorithms are equivalent! **Algorithm: MDLM Sampling / Inference** 1. $\mathbf{z}^{1:L}_1 =$ [MASK, MASK, …, MASK] // Sampling process starts with all MASK tokens. 2. for t = {$1, \frac{T-1}{T}, \dots, \frac{1}{T}$} do 1. $s \xleftarrow{} t - \frac{1}{T}$ 2. $\mathbf{z}^\ell_{s} \sim \text{Cat}(\mathbf{z}^\ell_s; \frac{(1 - \alpha_s)\mathbf{m} + (\alpha_s - \alpha_t)\mathbf{x}_\theta(\mathbf{z}_t)}{1 - \alpha_t} )$ if $\mathbf{z}_t^\ell = \text{[MASK]}$ else $\mathbf{z}_s^\ell = \mathbf{z}_t^\ell$ $\forall 1 \leq \ell \leq L$. 3. $\mathbf{z}^{1:L}_t \xleftarrow{} \mathbf{z}^{1:L}_s$ end for 3. return $\mathbf{z}_0$ --- Rebuttal 2: Title: Response to BSMY (2/3) Comment: ### **Concern 2: The derivation of the simplified ELBO objective needs more explanation. The reviewer is asking for clarifications regarding how the unsimplified loss (9), given by $\mathbb{E}_q \Big[\frac{\alpha_s - \alpha_t}{1 - \alpha_t} \log \frac{\alpha_t \langle \mathbf{x}\_\theta(\mathbf{z}_t, t), \mathbf{m} \rangle + (1 - \alpha\_t)}{(1 - \alpha\_t) \langle \mathbf{x}\_\theta(\mathbf{z}_t, t), \mathbf{x} \rangle} + \frac{1 - \alpha\_s}{1 - \alpha\_t} \log \frac{(1 - \alpha_s)(\alpha_t \langle \mathbf{x}\_\theta(\mathbf{z}_t, t), \mathbf{m} \rangle + (1 - \alpha_t))}{(1 - \alpha_t)(\alpha_s \langle \mathbf{x}\_\theta(\mathbf{z}_t, t), \mathbf{m} \rangle + (1 - \alpha_s))} \Big] \langle \mathbf{z}_t, \mathbf{m}\rangle$ is transformed into the simplified ELBO (8) $\mathbb{E}_{q,t}\frac{\alpha\_t'}{1-\alpha\_t}\log\langle\mathbf{x}\_\theta(\mathbf{z}_t), \mathbf{x}_0\rangle$ and the role that Sections 3.2 (SUBS parameterization) and 3.3 (Rao-Blackwellization) play in this process. In brief, we obtain (9) by taking our interpolating masking forward process (first paragraph in Section 3.2.1) and inserting it into the general D3PM noise process (3) to obtain analytical formulas (4) and (5) for the marginals and posterior of $q$. Inserting (4) and (5) into the standard diffusion loss (2) yields (9). Simplifying (9) into (8) mainly involves algebraic manipulations; see Appendix Sec. G. This algebra crucially requires two identities: 1. $\langle\mathbf{x}_\theta(\mathbf{z}_t, t), \mathbf{m}\rangle = 0$ , i.e. the masked token has zero predicted probability 2. if $\mathbf{z}\_t$ is unmasked, then we desire $\mathbf{x}_\theta(\mathbf{z}_t, t) = \mathbf{z}_t$ In order to ensure that these two properties hold, we require that the denoising process has the form given in (7) in Section 3.2.2. We call this novel parameterization SUBS. Section 3.3 (and its corresponding appendix) focuses on transforming (9) to (8) using these properties. We refer to the process of obtaining (8) in lieu of (9) as a form of Rao-Blackwellization. The above is a summary of how we derive the simplified ELBO (8) from (9). Next, we define the technical terms identified by the reviewer, and explain how they correspond to instances of general statistical techniques used in the simplification of (9) to (8). SUBS parameterization: This refers to the parameterization in (7). It implements two substitutions that we enforce on the output of $x_\theta$: 1. We design the denoising network such that $\langle\mathbf{x}_\theta(\mathbf{z}_t, t), \mathbf{m}\rangle$ = 0, i.e., we substitute the logit index corresponding to the [MASK] token with −∞. This ensures property #1 above. 2. If $\mathbf{z}\_t$ is unmasked, then we desire $\mathbf{x}_\theta(\mathbf{z}_t, t) = \mathbf{z}_t$ , i.e., unmasked latents are ‘carried over’. We accomplish this by substituting the output of our network to simply copy unmasked inputs. This ensures property #2 above. Rao-Blackwellization is a statistical method that improves an estimator’s efficiency by computing expectations analytically, thereby reducing variance. In our case, we analytically compute expectations such as $\langle\mathbf{x}\_\theta(\mathbf{z}\_t, t), \mathbf{m}\rangle = 0$ in order to simplify objective (9) to obtain (8). Without these analytical simplifications, a model must learn $\theta$ such that $\langle\mathbf{x}\_\theta(\mathbf{z}\_t, t), \mathbf{m}\rangle = 0$ holds, which slows down training. Unlike in regular Rao-Blackwellization, simplifications are possible because of modeling choices for $\mathbf{x}_\theta(\mathbf{z}\_t, t)$ (zero masking probabilities and carry-over unmasking). However, our approach also empirically helps reduce variance, hence we refer to it as Rao-Blackwellization, somewhat abusing the usual terminology. Graphical modeling is a branch of machine learning that studies how to design parameter-efficient model by explicitly incorporating conditional independencies between random variables into the design of a model. Examples of algorithms in this field include Bayes networks and Markov random fields. In that sense, our approach has similarities to graphical modeling, where incorporating conditional independencies into $p_\theta$ (via our modeling choices for $\mathbf{x}\_\theta(\mathbf{z}\_t,t))$ sets certain log-likelihood terms to zero. --- Rebuttal 3: Title: Response to BSmY (3/3) Comment: ### Concern 3: MDLM vs MAGE While both MDLM and MAGE use BERT-style losses to train generative models, the main differences are as follows: - Objective: In MDLM, we derive and train with a tight and principled lower bound to the log-likelihood. MAGE’s objective, while effective, is more heuristic with a combination of BERT-style cross entropy on masked tokens (not weighted appropriately to make it an ELBO) and a contrastive loss term. - Sampler: In MDLM, we use a principled ancestral sampling method, whereas in MAGE once again the sampling is done in a more heuristic manner that yields impressive results in the image generation domain. Additionally, we thank the reviewer for the additional reference Semi-Autoregressive Neural Machine Translation. In our updated manuscript we add this citation and previous works on semi-autoregressive modeling. --- ### Additional questions ### Question 1:**** What previous tries have been made in the language diffusion model and what makes them fail to outperform autoregressive model in generation tasks? Broadly, past attempts at diffusion modeling for discrete data can be broken into two categories, (1) works that first embed text in continuous space and then run standard Gaussian diffusion on the embeddings before coming back to the discrete domain and (2) works that directly define a corruption process on the discrete data. The first line of work seems to suffer from training instability and the results lack in quality relative to the dominant AR approach (see for example DiffusionLM [1]). The second approach has recently shown promise. Both our work and the previous state-of-the-art diffusion language model, SEDD [2], propose novel parameterizations of the denoising network that induce a better loss: - concrete score matching with positivity constraints, in the case of SEDD - and a weighted sum of cross-entropy terms, with reconstruction and prior regularization loss terms analytically evaluating to zero, in our case. These better losses are key ingredients that contribute to the success of recent efforts that close the gap to AR language modeling. ### Question 2:**** What is the computational cost of the method in comparison to autoregressive models? We find that AR models are able to optimize the training loss better than diffusion models [see fig. 1 in the attached supplementary material](https://openreview.net/forum?id=L4uaAR4ArM&noteId=WereEXicWc) However, diffusion models are able to reach the same loss values with additional training. Crucially, the gap between the two curves is much smaller than previously thought. We are excited by the new opportunities that non-AR generation present, such as methods for controlled generation, and the promise of more efficient sampling. --- References:** [1] Li, Xiang, et al. "Diffusion-lm improves controllable text generation." Advances in Neural Information Processing Systems 35 (2022): 4328-4343. [2] Lou, Aaron, Chenlin Meng, and Stefano Ermon. "Discrete diffusion language modeling by estimating the ratios of the data distribution." arXiv preprint arXiv:2310.16834 (2023).	Summary: This paper introduces a new approach to masked diffusion language models (MDLMs) that improves performance over previous discrete diffusion methods. The authors present a simplified, Rao-Blackwellized objective for training MDLMs, which is derived from a substitution-based parameterization of the reverse diffusion process. This objective takes the form of a weighted average of masked language modeling losses, establishing a connection between generative diffusion models and encoder-only BERT models. The paper also describes efficient sampling techniques, including a semi-autoregressive decoding method. The authors demonstrate state-of-the-art performance among diffusion models on language modeling benchmarks, approaching the perplexity of autoregressive models. Additionally, they show that their approach can be applied to biological sequence modeling, achieving competitive results on DNA modeling tasks. The paper emphasizes the importance of well-engineered implementation details and provides comprehensive ablation studies to validate their design choices. Overall, this work presents a simple yet effective framework for discrete diffusion models that bridges the gap between diffusion-based and traditional language modeling approaches. Strengths: - The paper introduces a novel, simplified objective for masked diffusion language models, which is a combination of existing ideas from diffusion models and masked language modeling. The substitution-based (SUBS) parameterization of the reverse diffusion process is an original contribution that enables the derivation of a more effective training objective. The connection established between generative diffusion models and encoder-only BERT models is an interesting perspective in the field. - The empirical results are convincing, demonstrating good performance among diffusion models on multiple benchmarks. The extension to biological sequence modeling shows the versatility and robustness of the method. - The paper is well-structured and clearly written, with a logical flow from theoretical foundations to practical implementations and results. - The work narrows the performance gap between diffusion-based and autoregressive language models, potentially leading to more adoption of diffusion models in NLP. Weaknesses: - The paper focuses heavily on empirical results but lacks a deeper theoretical analysis of why the proposed MDLM approach outperforms previous methods. A more rigorous theoretical foundation could provide insights into the method's success and potential limitations. - While the paper compares MDLM to other diffusion-based approaches, it lacks a comprehensive comparison to state-of-the-art non-diffusion language models. This makes it difficult to fully assess the method's competitiveness in the broader context of language modeling. - The experiments focus on relatively small models. It's unclear how well the approach scales to larger models that are more common in current NLP research. Addressing potential scalability issues or limitations would be valuable. - The paper primarily focuses on perplexity as an evaluation metric. Including human evaluations or other metrics that assess the quality and coherence of generated text would provide a more comprehensive view of the model's capabilities. - It's unclear if MDLM can achieve practical speed-up comparing to AR models with same FLOPs budget due to the lack of comparative e valuation on this. - Incomplete reference and comparision to previous related works, see Questions section. Technical Quality: 3 Clarity: 3 Questions for Authors: - Why didn't the authors include a comparison to Plaid in their perplexity evaluation experiments (Tables 1 & 2)? - How do the authors explain their observation that time-step conditioning can be optional in MDLM? Particularly, why is there no conditioning in OWT? Does this suggest that with a larger amount of data tokens, the need for timestep conditioning in MDLM decreases? - How many steps are used when evaluating the perplexity of MDLM? How does this compare to other text diffusion models? - Can MDLM achieve any efficiency gains in inference and sampling compared to autoregressive (AR) models within the same compute budget? For instance, if we need $K$ steps to generate $B$ tokens at a time in semi-MDLM, how can we make a fair and scientific comparison to AR models generating $L$ tokens in this setting? - One disadvantage of BERT-style models is that they are less token-efficient in training compared to decoder-only AR models. Can the authors provide some comparative analysis and plots showing how MDLM compares to AR baselines across a range of training token amount budgets? - What are the authors' thoughts on MDLM versus continuous-diffusion models for text, such as Plaid and CDCD, in terms of training, model performance, and inference efficiency? Is MDLM superior to these continuous-space text diffusion models in terms of resulting model quality and reducing the gap to AR models? - Is it possible to speed up the generation process of MDLM, similar to the advanced ODE-solvers people are using in continuous-space diffusion models? - How does MDLM compare to MaskGiT in terms of model formulations? They share lots of same design space but I didnt see any reference or comparison to this related line of works. Confidence: 5 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: N/A Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Title: Response to p1DW (1/3) Comment: We want to thank the reviewer for their constructive feedback. We address the reviewers comments and questions below. --- ### **Concern 1: Why does MDLM outperform previous methods? There is a need for a deeper theoretical analysis. Our work outperforms previous discrete diffusion methods because our evidence lower bound is theoretically tighter. There are two specific methodological elements that achieve this: 1. Continuous Time ELBO: Deriving a continuous time bound by taking $T \to \infty$. 2. ELBO Simplification: Setting certain terms in the ELBO analytically to 0, which is possible because of our choice of SUBS parameterization (7) Our ablation table shows that these elements can explain the gap relative to the previous state-of-the-art (SEDD), which uses the exact same backbone, optimizer, etc., and differs only in the training objective and parametrization. \| Method \| PPL (↓) \| \| --- \| --- \| \| MDLM \| 27.04 \| \| - w/o continuous time ELBO (1) \| 27.19 \| \| - w/o ELBO simplification & SUBS (2) \| 28.56 \| \| SEDD (our implementation) \| 28.90 \| Next, we seek to understand why these elements improve perplexity. Recall that the diffusion ELBO can be written as follows. $\mathcal{L}_{ELBO} =$ $\mathcal{L}_{recon}$ $+ \mathcal{L}_{prior}$ $+\mathcal{L}_{diffusion}$ Our design elements improve each term. - $\mathcal{L}_{prior}$: The prior regularization term simplifies analytically to zero by design, since the noise schedule $\alpha(t)$ is set such that $\alpha(t=1) = 0$ (as in prior works [4, 5]). - $\mathcal{L}_{recon}$: The reconstruction loss term simplifies analytically to zero due to taking $T \rightarrow \infty$ and our “copy over unmasking” SUBS parameterization (i.e. we copy over unmasked tokens from $\mathbf{z}_t$ to $\mathbf{z}_s$). - $\mathcal{L}_{diffusion}$: This diffusion loss term simplifies to a weighted cross entropy (BERT-style) loss due to the SUBS parameterization and we make the ELBO as tight as possible by taking $T \rightarrow \infty$ (see also VDM [1] for a similar analysis of how the lower-bound becomes tighter as $T \rightarrow \infty$). In addition, our work shows that masked diffusion models like MDLM and D3PM work better than previously thought when paired with a training recipe. Specifically, they are competitive with score-based methods such as SEDD. We closed the gap using both the modeling contributions above, as well as a well-engineered, numerically stable implementation and effective training recipe, including a low-discrepancy sampler that reduces the variance of both perplexity bound evaluations and our gradient estimators for training. In our revised manuscript, we include a more detailed appendix that includes the above explanations and shows how our analysis and parameterization lead to the final simplified ELBO. --- ### Concern 2:** Missing comparison to non-diffusion language models In addition to the extensive set of baselines that we provide in Tables 1 and 2, we have added a new experiment on the `text8` dataset, which allows us to compare against many non-diffusion results reported in the literature. As requested by the reviewer, this table contains non-diffusion baselines, including Flow-based models (IAF/SCF) [2] and a Bayesian Flow Network (BFN) [3]. \| Method \| BPC($\downarrow$) \| Train steps \| \| --- \| --- \| --- \| \| IAF/SCF \| 1.88 \| 1M \| \| AR Argmax Flow \| 1.39 \| 1M \| \| BFN \| 1.41 \| 1M \| \| D3PM \| 1.45 \| 1M \| \| SEDD \| 1.39 \| 1M \| \| MDLM \| 1.44* \| 0.4M* \| \| AR \| 1.23 \| 1M \| * We provide BPC for an MDLM model that was only trained for 40% of the total training steps, compared to all baselines. We hope to report the metrics for a fully trained model during the discussion period. Our partially trained MDLM is within 4% of the top-performing non-AR method, SEDD. Note also that our result is based on a single training run with no hyper-parameter tuning. The details of this `text8` experiment are as follows: following D3PM [4], we train a 77M param model on sequence chunks of 256 characters with batch size 512; baseline values were taken from SEDD [5]. However, please note that our existing experiments already compare to the strongest possible baselines, including the best existing diffusion-based model (SEDD), and an AR baseline. --- ### **Concern 3: Including additional non-perplexity-based metrics While perplexity is the dominant metric used in language model evaluation and has been extensively shown to correlate with downstream performance, we agree with the reviewer’s comment that other metrics that directly estimate downstream task accuracy are useful. We therefore evaluated our model on the Lambada [7] benchmark and present results below: \| \| Lambada Accuracy ($\uparrow$) \| \| --- \| --- \| \| AR \| 49.62% \| \| MDLM \| 53.10% \| We report accuracy of predicting the final word given a context of at least 50 tokens. MDLM improves over AR, aligning with our zero-shot results in Table 3. --- Rebuttal Comment 1.1: Title: Updated results on text8 Comment: On the text8 dataset, we managed to train the MDLM for only 800K steps due to resource constraints, unlike the baselines, which were trained for 1M steps. Despite this, we outperformed all non-autoregressive baselines, such as the flow-based models (IAF/SCF) [1] and a Bayesian Flow Network (BFN) [2], while matching the previous state-of-the-art, SEDD, in just 80% of the training steps. \| Method \| BPC($\downarrow$) \| Train steps \| \| --- \| --- \| --- \| \| IAF/SCF \| 1.88 \| 1M \| \| AR Argmax Flow \| 1.39 \| 1M \| \| BFN \| 1.41 \| 1M \| \| D3PM \| 1.45 \| 1M \| \| SEDD \| 1.39 \| 1M \| \| MDLM \| 1.39* \| 0.8M*** \| \| AR \| 1.23 \| 1M \| We provide numbers for a partially trained MDLM model at 800K steps. All baseline models were trained for 1M steps. Due to resource constraints, we were unable to train our model to 1M steps during the rebuttal period. --- *References: [1] Ziegler, Zachary, and Alexander Rush. "Latent normalizing flows for discrete sequences." International Conference on Machine Learning. PMLR, 2019. [2] Graves, Alex, et al. "Bayesian flow networks." arXiv preprint arXiv:2308.07037 (2023). --- Rebuttal 2: Title: Response to P1DW (2/3) Comment: ### Concern 4: It's unclear how well the approach scales to larger models We agree with the reviewer that finding scaling laws for discrete diffusion is a very interesting line of research, and one that we hope to conduct in follow-up work. Unfortunately, we cannot run such experiments in the limited rebuttal window and with a limited (academic) compute budget. --- ### Concern 5: It's unclear if MDLM can achieve practical speed-up comparing to AR models with same time budget. We highlight that MDLM can generate tokens in parallel and supports varying the number of generation steps, whereas AR models are limited by a fixed budget due to sequential generation. MDLM achieves up to 1.8x speedup compared to AR by varying the generation steps for sampling 64 batches of 256 tokens. MDLM reaches 8% better generative perplexity under roughly the sampling speed as AR (within 4%). More generally, our number of function evaluations (FE) to generate, say, a block of 128 tokens will be at most 128 steps. At the same time, because inference is typically memory bound, the wall clock time to run one (FE) is about the same for 1 block as it is for 128 blocks (and this is true up to a block size of, say, ~200 on an H100, after which we become compute bound again). Therefore, while an optimized implementation of MDLM is outside the scope of this paper, our diffusion approach holds the promise of significant speed improvements. --- ### Additional questions ### Question 1: How do the authors explain their observation that time-step conditioning can be optional in MDLM? In absorbing state discrete diffusion the time step / noise level can be inferred from the number of masked tokens and hence explicit conditioning on time step embedding is not necessary. DiffusionBERT [8] also empirically found that for the absorbing state diffusion, time-conditioning the denoising model is not critical. ### Question 2: How many steps are used when evaluating the perplexity of MDLM? How does this compare to other text diffusion models? There are different ways to interpret this question. First, sampling steps could refer to the value of $T$ used at training time. We report our best PPL values with the continuous-time formulation ($T \to \infty$) for MDLM and SEDD, and report results with finite $T$ among our ablations. A second interpretation is that “sampling steps” could refer to the number of steps to generate text from the model when we evaluate generative PPL. This number is reported on the x-axis of our generative PPL figure and varies between 32 and the length of the sequence. A third interpretation refers to the Monte Carlo sampling to evaluate PPL. When evaluating the perplexity bound of MDLM or SEDD, we use a single Monte Carlo sample per datapoint to approximate the integral of the continuous-time bound. Our low-discrepancy antithetic sampler allows us to estimate the perplexity bound with low variance, as shown in the table below. On OpenWebText, we find that we are able to accurately estimate the perplexity bound with just a single sample. In contrast, prior work required 1,000 samples to obtain an accurate estimate. Below we include a table that shows the limited effect of including more time steps in the Monte-Carlo estimate of MDLM on the OpenWebText dataset: \| Num MC Samples \| 1 \| 2 \| 5 \| 10 \| 100 \| \| --- \| --- \| --- \| --- \| --- \| --- \| \| Perplexity ($\downarrow$) \| 23.21 \| 23.22 \| 23.22 \| 23.22 \| 23.21 \| ### Question 3: Can the authors provide some comparative analysis and plots showing how MDLM compares to AR baselines across a range of training token amount budgets? We find that AR models are able to optimize the training loss better than diffusion models [see fig. 1 in the attached supplementary material](https://openreview.net/forum?id=L4uaAR4ArM&noteId=WereEXicWc) However, diffusion models are able to reach the same loss values with additional training. Crucially, the gap between the two curves is much smaller than previously thought. We are excited by the new opportunities that non-AR generation presents, such as methods for controlled generation, and the promise of more efficient sampling. --- Rebuttal 3: Title: Response to P1DW (3/3) Comment: ### Question 4:** What are the authors' thoughts on MDLM versus continuous-diffusion models for text, such as Plaid and CDCD, in terms of training, model performance, and inference efficiency? Several works using continuous diffusion for discrete data (e.g., Plaid [6], Diffusion LM [9], CDCD [10]) have not been able to approach AR perplexity. In our work, we demonstrate that discrete diffusion can successfully close this performance gap to AR models. Additionally, in our previous experience working with continuous diffusion models, such as DiffusionLM [9], we have found them to be less stable to train and require ad hoc techniques such as nearest embedding clipping. More recent attempts such as Plaid [6] and CDCD [10] seem promising but do not yield good PPL values. One of the potential benefits of discrete diffusion relative to AR sampling is more efficient sampling if the number of diffusion steps $T$ can be made less than the sequence length $L$, especially in batch size 1 regimes (e.g. on-device inference). We believe that discrete diffusion methods, such as ours, are more well suited to realize this gain relative to continuous diffusion for discrete data. ### Question 5:** Is it possible to speed up the generation process of MDLM, similar to the advanced ODE-solvers people are using in continuous-space diffusion models? This is indeed a very promising research question, which we hope to explore in future work. ### Question 6: How does MDLM compare to MaskGiT? While both MDLM and MaskGiT [11] use BERT-style losses to train generative models, the main differences are as follows: - Objective: In MDLM, we derive a tight and principled lower bound to the log-likelihood. MaskGiT’s objective, while effective, is not weighted appropriately to make it a proper ELBO. - Sampler: In MDLM, we use a principled ancestral sampling method, whereas in MaskGiT once again the sampling is done in a more heuristic manner that yields impressive results in the image generation domain. Additionally, MDLM can unmask any number of tokens at a given time step unlike MaskGiT where only a fixed number of tokens are unmasked at each iteration. --- #### References:** [1] Kingma, Diederik, et al. "Variational diffusion models." Advances in neural information processing systems 34 (2021): 21696-21707. [2] Ziegler, Zachary, and Alexander Rush. "Latent normalizing flows for discrete sequences." International Conference on Machine Learning. PMLR, 2019. [3] Graves, Alex, et al. "Bayesian flow networks." arXiv preprint arXiv:2308.07037 (2023). [4] Austin, Jacob, et al. "Structured denoising diffusion models in discrete state-spaces." Advances in Neural Information Processing Systems 34 (2021): 17981-17993. [5] Lou, Aaron, Chenlin Meng, and Stefano Ermon. "Discrete diffusion language modeling by estimating the ratios of the data distribution." arXiv preprint arXiv:2310.16834 (2023). [6] Gulrajani, Ishaan, and Tatsunori B. Hashimoto. "Likelihood-based diffusion language models." Advances in Neural Information Processing Systems 36 (2024). [7] Paperno, Denis, et al. "The LAMBADA dataset: Word prediction requiring a broad discourse context." arXiv preprint arXiv:1606.06031 (2016). [8] He, Zhengfu, et al. "Diffusionbert: Improving generative masked language models with diffusion models." arXiv preprint arXiv:2211.15029 (2022). [9] Li, Xiang, et al. "Diffusion-lm improves controllable text generation." Advances in Neural Information Processing Systems 35 (2022): 4328-4343. [10] Dieleman, Sander, et al. "Continuous diffusion for categorical data." arXiv preprint arXiv:2211.15089 (2022). [11] Chang, Huiwen, et al. "Maskgit: Masked generative image transformer." Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2022.	Rebuttal 1: Rebuttal: # General Response to Reviewers Dear reviewers, we thank you all for the useful comments and feedback. In addition to the individual responses we provide directly to each of your comments, we wanted to highlight additional results and clarifications that are common to several of your reviews. ### Improved theoretical understanding: The simplified objective we present is a product of a more careful derivation of the ELBO for absorbing state diffusion and of our proposed parameterization, that we call SUBS, which stands for SUBStitution. In our revised manuscript, we will include a more detailed appendix that shows how the two aspects of SUBS: (1) Zero Masking Probabilities and (2) Carry-Over Unmasking contribute to the simplified objective. Below, we briefly recap the derivation of our simplified ELBO and how the SUBS parameterization and continuous-time analysis tighten this lower bound. Recall the diffusion ELBO: $\mathcal{L}_{ELBO} = \mathcal{L}\_{recon} + \mathcal{L}\_{diffusion} + \mathcal{L}\_{prior}$ - $\mathcal{L}_{prior}$: We set this prior regularization term analytically to zero by designing the noise schedule $\alpha(t)$ such that $\alpha(t=1) = 0$. - $\mathcal{L}_{recon}$: We set this reconstruction loss term analytically to zero by taking $T \rightarrow \infty$ and by our “copy over unmasking” parameterization (i.e. we copy over unmasked tokens from $\mathbf{z}_t$ to $\mathbf{z}_s$ with $s < t$. - $\mathcal{L}_{diffusion}$: This diffusion loss term simplifies to a weighted cross entropy (BERT-style) loss due to the SUBS parameterization and we make the ELBO as tight as possible by taking $T \rightarrow \infty$ (see also VDM [1] for a similar analysis of how the lower-bound becomes tighter as $T \rightarrow \infty$). ### Algorithms: Below we include algorithms for training and inference of MDLM, which we plan to include in our revised manuscript: Algorithm: MDLM Training: Inputs: dataset $\mathcal{D}$, monotonic masking schedule $\alpha_t : [0,1] \to [0,1]$, BERT-like model $x_\theta$, $\mathbf{m}$ denotes the mask vector, $\mathbf{x}^{1:L}$ denotes a sentence with $L$ tokens, $\mathbf{z}^{1:L}_t$ denotes the latent vector with $L$ tokens. 1. repeat 1. $\mathbf{x}^{1:L} \sim \mathcal{D}$ // Sample a sequence of length L from dataset (can be a batch) 2. $\mathbf{z}^\ell_t \sim \text{cat}(\mathbf{z}^\ell_t; \alpha_t \mathbf{x}^\ell + (1 - \alpha_t)\mathbf{m})$ $\forall 1 \leq \ell \leq L$ for random $t \sim \mathcal{U}[0, 1]$ // Mask each token $\mathbf{x}^\ell$ independently with masking rate $\alpha_t$ to obtain the latent $\mathbf{z}^{1:L}_t$. 3. Update weights $\theta$ of denoising (BERT) model $\mathbf{x}_\theta$ gradient descent step on          $\nabla_\theta \frac{\alpha'_t}{1 - \alpha_t} \sum\_{\ell}\log \langle \mathbf{x}\_\theta^\ell(\mathbf{z}^{1:L}_t),\mathbf{x}^\ell \rangle$ // Note: this is simply a “weighted” BERT-style loss until converged Note that the only differences to BERT are that in standard BERT 1. In step `1.2.`, $\alpha_t$ is a constant (set to 0.85 implying a fixed masking rate of 15%). 2. In step `1.3.` there is no weighting term in front of the cross-entropy loss. Otherwise the training algorithms are equivalent! **Algorithm: MDLM Sampling / Inference** 1. $\mathbf{z}^{1:L}_1 =$ [MASK, MASK, …, MASK] // Sampling process starts with all MASK tokens. 2. for t = {$1, \frac{T-1}{T}, \dots, \frac{1}{T}$} do 1. $s \xleftarrow{} t - \frac{1}{T}$ 2. $\mathbf{z}^\ell_{s} \sim \text{Cat}(\mathbf{z}^\ell_s; \frac{(1 - \alpha_s)\mathbf{m} + (\alpha_s - \alpha_t)\mathbf{x}_\theta(\mathbf{z}_t)}{1 - \alpha_t} )$ $\forall 1 \leq \ell \leq L$. 3. $\mathbf{z}_s^\ell = \mathbf{z}_t^\ell$ if $\mathbf{z}_t^\ell \neq \text{[MASK]}$ $\forall 1 \leq \ell \leq L$ // To prevent unmasked token being remasked in the reverse process; see Eqn(7) in the paper. 4. $\mathbf{z}^{1:L}_s = \mathbf{z}^{1:L}_t$ end for ### Additional Experiments: Text8: To better compare to other non-diffusion baselines (see reviewer p1DW’s concerns), in addition to the extensive set of baselines that we provide in Tables 1 and 2, we have added a new experiment on the `text8` dataset, which we provide below: \| Method \| BPC($\downarrow$) \| \|----------------\|-------------------\| \| IAF/SCF \| 1.88 \| \| AR Argmax Flow \| 1.39 \| \| BFN \| 1.41 \| \| D3PM \| 1.45 \| \| SEDD \| 1.39 \| \| MDLM \| 1.44* \| \| AR \| 1.23 \| We provide the numbers are for a partially trained MDLM model on 400K steps and hope to report the numbers for a fully trained model during the discussion period. All the baselines models were trained for 1M steps. (Details of this `text8` experiment are as follows: following D3PM [4], we train a 77M param model on sequence chunks of 256 characters with batch size 512; baseline values were taken from SEDD [5]). Comparing MDLM vs AR sample efficiency* In addition to the sampling efficiency analyses in Figure 2, we compare MDLM and AR in the batch size 1 setting where MDLM achieves optimal sampling efficiency by caching the outputs of the denoising model (Suppl. D.2). Whereas AR models are limited to a fixed number of generation steps, MDLM may flexibly trade sample efficiency for quality by varying the number of diffusion steps $T$. In Figure 3 (Supplementary material submitted in the general response) MDLM achieves up to 1.8x faster sampling and 53% better generative perplexity compared to AR when generating 256 tokens. --- References: [1] Kingma et al. "Variational diffusion models.". [4] Austin, Jacob, et al. "Structured denoising diffusion models in discrete state-spaces.". [5] Lou, Aaron, et al. "Discrete diffusion language modeling by estimating the ratios of the data distribution." Pdf: /pdf/4c0dfdc28a73e6d9a670ccc83213b83c76f916ab.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Proximal Causal Inference With Text Data	Accept (poster)	Summary: The situation with unobserved confounding variables is quite common in applied research and makes causal inference complicated. To deal with such settings, the authors propose a new causal inference method that uses multiple instances of pre-treatment text data, estimates two proxies from two zero-shot models on the separate instances, and applies these proxies in the proximal g-formula. It is shown that the identification conditions are satisfied, The method is evaluated in a simulation study on synthetic and semi-synthetic data. Strengths: - The paper proposed a new innovative method for proximal causal inference utilizing text data. - The paper is well written and motivated. Weaknesses: - Literature review is incomplete. The idea of proximal inference goes back to Zvi Griliches (1977) who should get credit for it. As background reading the corresponding chapter in the textbook "Applied Causal Inference Powered by ML and AI" by Chernozhukov and coauthors (2024). - To overcome the completeness condition the paper "Causal Inference Under Unmeasured Confounding With Negative Controls: A Minimax Learning Approach" (arXiv:2103.14029) might be helpful. - The theoretical results (Prop 1-4) are all in some sense "negative" and straightforward / already known. What would be more interesting, would be some "positive" results about the proposed method, although I am aware that this might be quite challenging. Technical Quality: 4 Clarity: 3 Questions for Authors: - How credible / realistic are (P1) and that $T^1_pre$ is conditionally independent from $T^2_pre$ in typical applications (e.g. using electronic health records)? - How could one use EHR to construct proxies? Are the assumptions fulfilled? (Might be questionable.. the example mentioned in the text is not convincing.) Confidence: 4 Soundness: 4 Presentation: 3 Contribution: 4 Limitations: Limitations are adressed adequately. As mentioned above, theoretical guarantees for the propsoed method might be very valuable. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for the thoughtful feedback. We address the reviewer’s questions and comments on our paper's weaknesses. > Literature review is incomplete. The idea of proximal inference goes back to Zvi Griliches (1977) who should get credit for it. As background reading the corresponding chapter in the textbook "Applied Causal Inference Powered by ML and AI" by Chernozhukov and coauthors (2024). Thank you for pointing us to the paper. We are happy to point to it as a reference for causal inference with proxies in linear SEMs and that later works generalize this to non-linear settings. > To overcome the completeness condition the paper "Causal Inference Under Unmeasured Confounding With Negative Controls: A Minimax Learning Approach" (arXiv:2103.14029) might be helpful. Thank you for the reference. We believe this work complements our own as it concerns estimation given a pair of valid proxies. In our work, we provide a way of generating proxies from unstructured text that first satisfy the structural assumptions—assumptions P1-P3 that are encoded in the causal DAG Figure 1(b) of our paper and Figure 1 of the suggested reference—that are needed for both classical estimators in the proximal causal inference literature as well as the estimators developed in the suggested reference. The estimators in the reference depart from older proximal literature on assumption P4 of completeness. Importantly, however, the old and new estimators both require the $U \rightarrow Z$ and $U \rightarrow W$ edges to be real, i.e., the proxies must be at least weakly correlated with the unmeasured confounder. In our algorithm for generating proxies, when the zero-shot models generate even weakly predictive proxies, they automatically satisfy completeness and therefore the alternative assumptions suggested in the reference since in the discrete case the assumptions in the reference are strictly weaker (and so if completeness holds, these assumptions also hold). Thus, the estimators developed in the reference could be directly applied to the proxies generated by our algorithm. It would be interesting to see what would happen if one were to try and use zero-shot models to predict continuous proxies—in this case completeness and the assumptions listed in the reference are incomparable, which would necessitate the use of different estimators depending on what conditions were more likely to hold. We are happy to add a short discussion on this with the additional space granted in the camera ready if the paper is accepted. > The theoretical results (Prop 1-4) are all in some sense "negative" and straightforward / already known. What would be more interesting, would be some "positive" results about the proposed method, although I am aware that this might be quite challenging. We respectfully push back on this. Propositions 1-3 are indeed “negative” in that they correspond to results that show what cannot be done in order to obtain unbiased causal effect estimates. This is the same sense in which non-identification/completeness results in causal inference and missing data are negative results — they inform the reader about datasets/data collection procedures that would lead to biased estimates, e.g., [Shpitser and Pearl, 2006](https://ftp.cs.ucla.edu/pub/stat_ser/r327.pdf) and [Nabi et al, 2020](https://arxiv.org/pdf/2004.04872). Further, while Propositions 1-3 appear simple, they are not obvious: We have, for example, encountered [applied work](https://arxiv.org/pdf/2307.03687) that treats machine learned predictions as direct plug-ins for unmeasured variables—this is the same sense in which collider bias can be obvious, but only to those who know it and are already looking for it. Proposition 4 on the other hand is a “positive” result that shows identification and unbiased estimates are possible when following our algorithm. While these conditions may not always be fulfilled (just as with any other identification conditions) we also propose an odds ratio heuristic to check for violations of these conditions. The semi-synthetic results (Table 2 and Fig 3) that use real-world text data from MIMIC-III also provide positive results (estimates with low bias) for the theory we propose. > How credible / realistic are (P1) and that $T^1_{pre}$ is conditionally independent from $T^2_{pre}$ in typical applications (e.g. using electronic health records)? We address this issue in our paper: In line 302-303, we write “We hypothesize that notes written by different individuals will satisfy $T^{pre}_1 \perp T^{pre}_2 \| U, C$ since each individual will write a conditionally independent realization of 304 the patient’s status”. That is, this independence is more likely to hold if you use different clinical notes from different departments, in social media use different posts perhaps. We also propose the odds ratio heuristic as a way for the analyst to safeguard against violations of this condition. > How could one use EHR to construct proxies? Are the assumptions fulfilled? (Might be questionable.. the example mentioned in the text is not convincing.) We refer the reviewer to our semi-synthetic experiments in Section 5 that use real EHR data and clinical notes from MIMIC-III to do exactly this. Table 2 and Fig 3 shows the success of our proxy generation process as well as the success of the odds ratio heuristic as a safeguard when the assumptions are not fulfilled. We have also added an illustrative figure of our proxy generation process that can be found in the rebuttal PDF and that we would be happy to add to the camera ready if the paper is accepted. --- Rebuttal Comment 1.1: Title: Comment Comment: First of all, thanks a lot for your efforts and the detailed answer. I still think that the negative results in Proposition 1-3 are not really deep and well known. I am aware that the reference can be considered as a complement, but I think a thorough literature review should contain all related sources. Finally, I still find the assumption of conditional independence hard to hold and I think here more convincing examples would be helpful. Overall, I will keep the score.	Summary: Causal inference techniques often rely on the assumption that all confounders can be observed or inferred from available data. This paper proposes a method to address the setting where a confounder is entirely unobserved; instead there is available pre-treatment text that can be used to infer proxies, which in turn have predictive value for the unobserved confounder. The authors adapt proximal causal inference ideas to text-data settings, discuss "gotchas" in naive implementations of such a method, and explore various relevant choices before presenting best performing method. Specifically, they use multiple instances of pre-treatment text to infer two proxies for each datapoint using two different zero-shot language models. This is then used for average causal effect estimation via the proximal g-formula. The paper provides empirical evaluation on synthetic and semi-synthetic datasets as well as a falsifcation heuristic for untestable assumptions. Strengths: Originality: While proximal causal inference has been proposed and studied, this paper adapts existing methods to text data and explores practical considerations in their implementation. Clarity: The paper is well-written, with clear statements of the requirements of the method and the assumptions it relies on. Quality: The paper proves various propositions that guide the design of the proposed method in a principled manner. It also explores a falsification heuristic for untestable assumptions and empirically verifies that the heuristic is aligned with final performance in synthetic and semi-synthetic settings. Significance: Unobserved confounding is a significant challenge in causal inference. The paper is well-motivated by the availability of large amounts of text data and the recent progress in language modeling. Weaknesses: - The significance of the empirical evaluation is limited due to synthetic and semi-synthetic experiments. The impact of the proposed method in realistic settings is hard to assess. While the evaluation of real settings is hampered by the lack of ground-truth, it may still be possible to synthesize data that is as realistic as possible so that the more realistic challenges of deploying such a method may be uncovered. - The experiment design of the paper carefully avoids post-treatment text to avoid biased effect estimation. However, the proxy inference from language models indirectly depends on the pretraining dataset used to train the language model. The data in that pretraining set may be post-treatment text. The impact of this dependence is unclear. - It is unclear how sensitive the performance of the proposed method is to the choice of pretrained zero-shot model, or whether we can expect better performance as the zero-shot model used scales up. Technical Quality: 3 Clarity: 3 Questions for Authors: As mentioned above: - Do the authors expect the performance of their method to improve as they use larger language models to infer proxies? - Can the authors provide any intuition for what they expect to be the impact of using a language model that has been trained on post-treatment text data to infer proxies and plug them into the causal effect estimation? Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The paper sufficiently addresses limitations of the setting and method proposed. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for the thoughtful feedback. We address the reviewer’s questions and comments on our paper's weaknesses. > The significance of the empirical evaluation is limited due to synthetic and semi-synthetic experiments. The impact of the proposed method in realistic settings is hard to assess. While the evaluation of real settings is hampered by the lack of ground-truth, it may still be possible to synthesize data that is as realistic as possible so that the more realistic challenges of deploying such a method may be uncovered. We thank the reviewer for this comment. We agree we should evaluate with the most realistic data possible. Yet, we believe our semi-synthetic experiments, which use real-world clinical notes from MIMIC-III, are the most realistic possible given our constraints. On Line 276, we write "In causal inference, empirical evaluation is difficult because it requires ground-truth labels for counterfactual outcomes of an individual under multiple versions of the treatment, data that is generally impossible to obtain Holland (1986); see Gentzel et al. (2019); Keith et al. (2023)." We plan to expand that writing to make the constraints of empirical evaluation in causal estimation even more clear. Gentzel et al. (2019) and Keith et al. (2023) describe methods for evaluation that are more realistic than semi-synthetic evaluation if one has an RCT dataset and can downsample the RCT dataset to create an observational (confounded) dataset. However, for the proximal setting we investigated in this paper, we could not find an existing RCT that would contain a sufficient amount of text and was suitable for the proximal causal inference set-up. In contrast, semi-synthetic experiments use real data for part of the DGP and then specify synthetic relationships for the remainder of the DGP. Semi-synthetic experiments have been used extensively for empirical evaluation of causal estimation methods; see [Shimoni et al., 2018](https://arxiv.org/abs/1802.05046); [Dorie et al., 2019](https://arxiv.org/abs/1707.02641); [Veitch et al., 2020](https://proceedings.mlr.press/v124/veitch20a/veitch20a.pdf). We will add additional writing clarifying our choice of semi-synthetic experiments in our camera ready paper upon acceptance. > Can the authors provide any intuition for what they expect to be the impact of using a language model that has been trained on post-treatment text data to infer proxies and plug them into the causal effect estimation? We thank the reviewer for this thoughtful comment. In Appendix B, we describe that if one of the proxies is constructed using post-treatment text and the other proxy is constructed from pre-treatment text, then proximal causal inference conditions could still be satisfied. However, we agree with the reviewer that if both proxies are constructed using LLMs that have post-treatment pretreatment text, this could be potentially problematic. (1) We believe MIMIC-III is not contaminated in the pre-training datasets of the LLMs we use in our semi-synthetic experiments. In our semi-synthetic experiments, we intentionally choose to use "open" LLMs, Flan-T5 and OLMo, in which the entire pretraining dataset is known and can be inspected. MIMIC-III is not available via a public URL (researchers have to sign-up and agree to a terms of service) so we do not believe it is contaminated in the pretraining data of either of these LLMs. Flan-T5 is built upon T5 which uses C4 (Colossal Clean Crawled Corpus) as its pretraining data (Raffel et al. 2020). Dodge et al. 2021 explore and document C4 and provide a search index, https://c4-search.apps.allenai.org/. We sampled full sentences from MIMIC-III and searched for them in C4 and did not have any search hits. OLMo is built from an open pretraining dataset Dolma (Soldaini et al. 2024), which is a 3 trillion token English corpus. Soldanini et al. describe that the data is acquired from sources that are "made accessible to the general public" such as the Common Crawl, GitHub, Reddit, Semantic Scholar, and Wikipedia. Again, because MIMIC-III is not publicly available, we again believe it is very unlikely any of the individual data is in the pretraining data. (2) Other applications (e.g., social media) that have individual post-treatment texts in the pretraining data may need to rely on temporal time stamps. Even though we have established that our semi-synthetic experiments using MIMIC-III may not be contaminated or contain individual data, there are other applications in which there could be post-treatment individual text data in the pretraining data of a LLM. For example, one might be using our proximal causal inference with text data design to infer proxies from social media posts from a platform such as Reddit. Individual posts that are post-treatment may possibly be scraped and included in the pretraining data of LLMs. In this scenario, to avoid this issue, we recommend (1) using open LLMs, such as we do with Flan-T5 and OLMo, in which the pertaining data can be inspected, and (2) using temporal time stamps to ensure that the LLMs pretraining data cutoff date is prior to treatment. > It is unclear how sensitive the performance of the proposed method is to the choice of pretrained zero-shot model, or whether we can expect better performance as the zero-shot model used scales up. [...] Do the authors expect the performance of their method to improve as they use larger language models to infer proxies? We thank the reviewer for this comment, and we will make this point even more explicit in the writing of our next draft. As the predictive performance of the zero-shot models improves, this will not affect the bias of causal estimates (the estimates will remain unbiased) but it will decrease variance (making confidence intervals narrower). --- Rebuttal Comment 1.1: Comment: Thank you for the clarifications! I will maintain my score.	Summary: The paper considers the causal effect estimation setting where a confounder is latent but with unstructured text data that could serve as proxies. Specifically, the paper proposes to incorporate zero-shot classifiers (to operate on text-based proxies), together with a falsification heuristic, into the proximal causal inference framework. The goal of the text-based proxy design is to craft W and Z that satisfy the identification condition in proximal causal inference framework. Empirical evaluations are presented in synthetic and semi-synthetic experiments. --- Post rebuttal I have increased my score, under the assumption that the revised manuscript could sufficiently address the original concerns on material organizations. Strengths: The strength of the paper comes from the attempt to conduct proximal causal inference on unstructured text data. The paper carefully considers identification conditions specified in the proximal causal inference framework, and proposes a design procedure together with a falsification heuristic to find two text-based proxies (so that the proximal inference can be conducted). Weaknesses: The weakness of the paper comes from the organization of the material (especially the constraints/conditions involved), and relatively simple settings considered in (fully-/semi-) synthetic experiments. In particular, further clarifications and/or discussions on following points would be very helpful (detailed in "Questions" section): (1) regarding a series of different constraints, conditions, gotcha's, assumptions (2) the fully and semi- synthetic experiments consider structured data, it is not exactly clear how these text proxies look like and if they correspond to all or part of the aforementioned constraints/conditions. Examples of text proxies would be much more intuitive than claiming "satisfy by design" (line 136) Technical Quality: 2 Clarity: 2 Questions for Authors: (1) regarding a series of different constraints, conditions, gotcha's, assumptions In Section 2, there are P1 -- P4, a set of conditions should be satisfied in order for the proximal g-formula to work. In order to respond to the criticism of potential unavailability of W and Z in structured data, further assumptions S1 -- S2 are proposed. Then in Section 3 and Section 4, a set of gotcha's, two additional pre-conditions (lines 216 -- 218), and another set of conditions related to odds-ratio based heuristics (lines 245 -- 247) are presented. How do these conditions fit together to respond to the criticism of proximal causal inference on structured data? Are they all identification conditions for the text-based proxy proximal causal inference (other than the fact that they are conditions specified by previous works for different components put together)? (2) the fully and semi- synthetic experiments consider structured data, it is not exactly clear how these text proxies look like and if they correspond to all or part of the aforementioned constraints/conditions For fully and semi- synthetic experiments, the setting is largely structured data instead of text-based proxies. Examples of text proxies that the proposed design procedure yields would be much more intuitive than just claiming "satisfy by design" (line 136). Confidence: 3 Soundness: 2 Presentation: 2 Contribution: 2 Limitations: The organization of material could be improved to better present how the proposed approach responds to criticism of proximal causal inference (with structured data). Examples beyond fully and semi- synthetic experiments will make it clearer w.r.t. how the designed text-based proxies help to address the aforementioned criticism on previous work. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for the reviewer’s comments on questions. We address each below. >[F]urther assumptions S1 -- S2 are proposed. Then in Section 3 and Section 4, a set of gotcha's, two additional pre-conditions (lines 216 -- 218), and another set of conditions related to odds-ratio based heuristics (lines 245 -- 247) are presented [...] How do these conditions fit together to respond to the criticism of proximal causal inference on structured data? Are they all identification conditions for the text-based proxy proximal causal inference (other than the fact that they are conditions specified by previous works for different components put together)? (P1) – (P4) are conditions for proximal causal inference as previously defined by Tchetgen Tchetgen (2020). The primary criticism of this work, as stated in lines 130-131, is that it is often difficult in practice to find structured proxies that fulfill (P1) – (P4). (S1) and (S2) are assumptions that limit the scope of our method. In lines 216-218, we further state two additional assumptions for our method: (1) the conditional independence of the two pieces of text and (2) W and Z being predictive of U. In Section 3, we show that (1) maps to (P1) – (P3), and (2) maps to (P4). These assumptions are not strictly necessary, and there may be other ways to satisfy the conditions for proximal causal inference, but we find these to be the most intuitive and easy for an analyst to verify/understand. In lines 245-247, we describe an odds ratio falsification heuristic: This is not an identification condition; rather, it is an empirical check for violations of (P1) – (P4). As we show in our synthetic and semi-synthetic experiments, the falsification heuristic correctly flags potentially problematic proxies and prevents the practitioner from making incorrect downstream estimates. > For fully and semi- synthetic experiments, the setting is largely structured data instead of text-based proxies. Examples of text proxies that the proposed design procedure yields would be much more intuitive than just claiming "satisfy by design" (line 136). We kindly refer the reviewer to lines 292-313 as well as Appendices D, E, and F for descriptions of our semi-synthetic experiments. We use real-world clinical notes from the MIMIC-III dataset. We expand upon what we wrote in Section 5, and describe an example of how text proxies are obtained with an example clinical note. Let us say that we are interested in obtaining text proxies for the latent variable atrial fibrillation. A clinical note may contain the following text: “The patient was suffering from breathing difficulties and irregular heart rate.” We then append a prompt to the clinical note and use it as input to a zero-shot classifier (Flan-T5, for example): “Context: The patient was suffering from breathing difficulties and irregular heart rate. Is it likely the patient has atrial fibrillation? Constraint: Even if you are uncertain, you must pick either “Yes” or “No” without using any other words.” If Flan-T5 outputs “Yes”, the text proxy has a value of 1. If Flan-T5 outputs “No” or any other text, the text proxy has a value of 0. With more space in a camera-ready version, we are happy to include this example and the figure in the attached PDF file to our rebuttal in the paper to make this procedure more explicit. > The organization of material could be improved to better present how the proposed approach responds to criticism of proximal causal inference (with structured data). Examples beyond fully and semi- synthetic experiments will make it clearer w.r.t. how the designed text-based proxies help to address the aforementioned criticism on previous work. We thank the reviewer for this comment. Below is an example describing why proximal causal inference with structured data can be challenging. We had this example in a previous draft but had to cut due to space constraints. With an extra page in the camera ready version, we plan to put this example back in to more clearly express our criticism of proximal causal inference with structured data: Suppose we aim to find proxies (in the structured variables) of atrial fibrillation (U) and have access to shortness of breath and heart palpitations. Although these proxies seem reasonable, we show how they violate the proximal causal inference conditions. Patient complaints about shortness of breath may affect which medication a clinician prescribes (A); hence, using shortness of breath as the proxy W violates (P2). Furthermore, a lack of oxygen resulting from shortness of breath may affect the healing of blood clots, thus influencing measurements of the D-dimer protein Y. In this case, using shortness of breath as the proxy Z violates (P3). Shortness of breath can also sometimes be a symptom of heart palpitations, violating (P1). --- Rebuttal 2: Title: Thank authors for the response Comment: Thank authors for the responses, and my concerns are largely resolved. While there is still some worry about the potential difficulty (upon readability, and upon the parsing of the key takeaway msgs) because of the conditions/assumptions/gothcha's introduced in various places, the proposed edits and material organization might help in the revised version of the paper. A brief paragraph (just like what authors presented in the response) or a table in the appendix would be helpful to provide a summary of how these requirements piece together. As for the examples, if the space permits, having some of them in the main paper might be very helpful for readers to bridge the gap between the set of requirements, and what can be done empirically (beyond fully- and semi- synthetic experiments). I have updated my evaluation score accordingly, under the assumption that the revised manuscript could sufficiently address the original concerns.	null	null	Rebuttal 1: Rebuttal: We thank the reviewers for their thoughtful comments and suggestions on improving our paper. We respond to each reviewer individually and address each reviewer’s questions point by point. We also include in our rebuttal a PDF with a figure that shows our proposed proximal causal inference with text design for our semi-synthetic pipeline (which uses real-world clinical notes from MIMIC-III). This figure specifically responds to reviewer dab7’s comment, and we intend to, given more space in a camera-ready version, add this figure to our paper. If anything can be further clarified, please let us know. We look forward to further discussions. Pdf: /pdf/d7b0c5b78870846aa0f8a96837da53050c585ed3.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Counter-Current Learning: A Biologically Plausible Dual Network Approach for Deep Learning	Accept (poster)	Summary: Inspired by the counter-current phenomenon observed in nature, the authors propose a counter-current learning (CCL) framework that decouples the input and backpropagation information in different circuits, overcoming many biological implausibility issues of backpropagation learning (BP). Strengths: I am not an expert in target propagation, but the general idea presented in this work sounds novel and interesting to me. I believe it also offers some insights into nature-inspired learning. I appreciate the constructive figures that help me quickly grasp the core idea of this work. Weaknesses: - In Table 1, the authors should compare their results with other biologically plausible methods, like forward-forward and deep softhebb, or justify their criteria in model selection. - A minor drawback is the lack of validation in complicated dataset like Imagenet. Technical Quality: 3 Clarity: 3 Questions for Authors: - I am surprised that the performance of BP is worse than the proposed local learning method. Can the authors explain more about this gap? - In forward-forward [1], Hinton proposes a recurrent network architecture that inputs the label at the top layer. This architecture seems similar to what is used in this work. Can the authors elaborate on the differences? reference [1]. Hinton G. The forward-forward algorithm: Some preliminary investigations[J]. arXiv preprint arXiv:2212.13345, 2022. Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: I think the authors have discussed it well. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: [W1] Algorithm selection. We appreciate the reviewer's question regarding concurrent work. A performance comparison is provided in general response 2 [GR2], demonstrating that our CCL algorithm outperforms other methods. While SoftHebb achieves similar results, it requires 24 hyperparameters compared to our 3, making our approach more efficient. We acknowledge the importance of comparing with other emerging biologically plausible approaches and will include more rigorous comparisons to methods like forward-forward and deep SoftHebb, as suggested. [W2] More validation. We appreciate the reviewer's questions regarding dataset and model scalability. However, due to the size and complexity of ImageNet, one typically requires batch normalization and other tricks in model architectures, which may not be biologically plausible. Additionally, recent work on biologically plausible learning algorithms (e.g., FA, DTP, DRL, FW-DT, and DRTP) has not evaluated these methods on large datasets like ImageNet, as datasets such as CIFAR-10 and CIFAR-100 demonstrate sufficient complexity for current studies in this field. We will include this discussion in the revised manuscript, acknowledging the need for further research on scalability to more complex datasets like ImageNet. Nonetheless, to showcase the capabilities of the CCL algorithm, we have applied it to an autoencoder task, which, to our knowledge, is the first time a biologically plausible algorithm has been scaled to an image autoencoding paradigm. [Q1] Explanation for the result. For a detailed discussion, please see General Response 3 [GR3] and Figure 1.a in the rebuttal document. [Q2] Comparison to the forward-forward algorithm. Quantitative comparisons are provided in the general response [GR2]. We discuss algorithmic differences here: - Compared to Section 3.3 in [4], CCL does not embed the label in the image. CCL adopts a feedback network to process and project the one-hot label, while in FFA the label is embedded in the input data, e.g., for MNIST training the first 10 pixels of an image is replaced with a one of N representation of the label. - Compared to Section 3.4 in [4], CCL does not need recurrent architecture to propagate the supervised signal backwardly: FFA adopts a recurrent network architecture to send the supervision signals in a top-down manner, i.e., propagate the signal one-layer by one-layer for 3 - 5 steps. In contrast, our CCL scheme seeks to propagate the signal directly, thus attaining more computational efficiency. Rolling out the signal transmission step-by-step would make the algorithm hard to scale to deep networks. [1] Lee, D. H., Zhang, S., Fischer, A., & Bengio, Y. (2015). Difference target propagation. ECML PKDD. [2] Meulemans, A., Carzaniga, F., Suykens, J., Sacramento, J., & Grewe, B. F. (2020). A theoretical framework for target propagation. NeurIPS. [3] Shibuya, T., Inoue, N., Kawakami, R., & Sato, I. (2023). Fixed-weight difference target propagation. AAAI. [4] Hinton, G. (2022). The forward-forward algorithm: Some preliminary investigations. arXiv preprint arXiv:2212.13345. [5] Nøkland, A. (2016). Direct feedback alignment provides learning in deep neural networks. NeurIPS. [6] Launay, J., Poli, I., Boniface, F., & Krzakala, F. (2020). Direct feedback alignment scales to modern deep learning tasks and architectures. NeurIPS. --- Rebuttal Comment 1.1: Comment: I appreciate the author's response, which addresses my main concerns. I think this is a promising bio-inspired learning method and will be interesting to a broad range of readers. --- Reply to Comment 1.1.1: Comment: We thank the reviewer once again for the constructive suggestion and the oportunity to clarify. We will include more related information in the future version. Have a great day!	Summary: In this paper, the authors propose counter-current learning (CCL), a biologically plausible framework for credit assignment in neural networks. Strengths: The research direction of having new learning algorithms inspired biologically seems relevant and interesting. Weaknesses: - The authors discuss biological plausibility as a motivation, but do not discuss thoroughly how the proposed approach is biological plausibility. For instance, update-locking and non-frozen activities should be discussed in detail. - The comparison with the state of the art in the domain is missing: [1] Hinton, G. (2022). The Forward-Forward Algorithm: Some Preliminary Investigations. Technical report. [2] Dellaferrera, G., Kreiman, G., and Kreiman, G. (2022). Error-driven Input Modulation: Solving the Credit Assignment Problem without a Backward Pass. In Chaudhuri, K., Jegelka, S., Song, L., Szepesvari, C., Niu, G., and Sabato, S., editors, Proceedings of the 39th International Conference on Machine Learning, pages 4937–4955. PMLR. [3] Andreas Papachristodoulou, Christos Kyrkou, Stelios Timotheou, and Theocharis Theocharides. Convolutional channel-wise competitive learning for the forward-forward algorithm. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 38, pages 14536–14544, 2024. - The results are sometimes counter intuitive. For example, the results of CCL vs BP for CIFAR100 in Table 3. Why is CCL working considerably better than BP? - The presentation and organization of the paper can be improved. For instance, Figure 2 can be presented at a higher abstraction level as pseudo-code Technical Quality: 2 Clarity: 2 Questions for Authors: 1. Could the author discuss the biological plausibility of their approach from weight transport, locality, freezing of neural activity, and update locking points of view? 2. Could the author provide some insight how their approach compares against or relates to the state of the art in the domain: FF, PEPITA, and CFSE? [1] Hinton, G. (2022). The Forward-Forward Algorithm: Some Preliminary Investigations. Technical report. [2] Dellaferrera, G., Kreiman, G., and Kreiman, G. (2022). Error-driven Input Modulation: Solving the Credit Assignment Problem without a Backward Pass. In Chaudhuri, K., Jegelka, S., Song, L., Szepesvari, C., Niu, G., and Sabato, S., editors, Proceedings of the 39th International Conference on Machine Learning, pages 4937–4955. PMLR. [3] Andreas Papachristodoulou, Christos Kyrkou, Stelios Timotheou, and Theocharis Theocharides. Convolutional channel-wise competitive learning for the forward-forward algorithm. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 38, pages 14536–14544, 2024. 3. Why is CCL working considerably better than BP in Table 3 for CIFAR100? Confidence: 4 Soundness: 2 Presentation: 2 Contribution: 2 Limitations: The limitation of the work has been briefly discussed. Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: [Q1] In-depth discussion of bIological plausibility for counter-current learning We thank the reviewer for the opportunity to further elaborate on the biological plausibility of our method from weight-transport, locality, freezing of neural activity, and update locking perspectives. Although the explanation has been provided in the manuscript Line 41-50 and Line 124-129 on how the model architecture and algorithm design mitigates these problems, we discuss more explicitly below - Weight-transport. We leverage a feedback network architecture for processing feedback signals, which uses a different parameter set from the forward network. The weights for feedback and forward networks are updated independently, mitigating the problem of weight transport by construction. - Locality. We leverage local layer-wise loss functions and gradient detach (i.e., stop gradient operation) to ensure that the parameters are updated by a local loss function, not a global error signal that propagates through the network. - Freezing of neural activity. The back propagation method requires keeping the neural activations for the global error back propagation since the process involves element-wise multiplication of the error signal with the derivative of the neural activations and thus it has to remain static. Our CCL algorithm, like all the algorithms in the Target Propagation Family, also requires freezing the neural activity for the loss computations. However, the duration of freezing time is halved with our CCL scheme since the two networks can process the signals simultaneously. - Update locking. In back-propagation, The latent activations of the forward network are kept and re-used for the backward phase. Moreover, the backward phase can only begin after the forward phase is finished, causing the update locking problem. In CCL, the backward process is performed through the feedback network, which is independent of the forward phase, and thus the forward and feedback processes occur simultaneously. [Q2] Literature review and algorithm comparison Quantitative comparisons are provided in the general response [GR2]. We discuss algorithmic differences here: - Forward-forward algorithm, FFA [1] - Compared to Section 3.3 in [1], CCL does not embed the label in the image. CCL adopts a feedback network to process and project the one-hot label, while in FFA the label is embedded in the input data, e.g., for MNIST training the first 10 pixels of an image is replaced with a one of N representation of the label. - Compared to Section 3.4 in [1], CCL does not need recurrent architecture to propagate the supervised signal backwardly: FFA adopts a recurrent network architecture to send the supervision signals in a top-down manner, i.e., propagate the signal one-layer by one-layer for 3 - 5 steps. In contrast, our CCL scheme seeks to propagate the signal directly, thus attaining more computational efficiency. Rolling out the signal transmission step-by-step would make the algorithm hard to scale to deep networks. - Error-driven Input Modulation, PEPITA [2] - PEPITA requires two forward passes. In PEPITA, the parameter update function requires computing the difference between the two forward passes. This causes the update locking problem - PEPITA requires the neurons to track two states. As PEPITA requires two forward passes,it requires every neuron to keep track of two neural activities, which is more biologically implausible. - PEPITA does not follow locality. The global error signal is directly transformed and added to the latent feature; this does not follow the locality learning concept where synaptic changes depend on the correlated activity of the pre-and postsynaptic neurons. - Channel-wise Feature Separator and Extractor, CFSE [3] - CFSE is a layer-wise training method that contains structural inductive bias. CFSE groups input channels in the forward stage, which can potentially provide inductive bias preferable for training. - CFSE works with two different normalization methods. CFSE adopts batch normalization and group normalization methods to work, while CCL attains similar results without group normalization. - CCL is validated on auto-encoder experiments, which CFSE does not. [Q3] Explanation for the result on CIFAR-100. For a detailed discussion, please see General Response 3 [GR3] and Figure 1.a in the rebuttal document. [1] Hinton, G. (2022). The Forward-Forward Algorithm: Some Preliminary Investigations. Technical report. [2] Dellaferrera, G., Kreiman, G., and Kreiman, G. (2022). Error-driven Input Modulation: Solving the Credit Assignment Problem without a Backward Pass. ICML. [3] Andreas Papachristodoulou, Christos Kyrkou, Stelios Timotheou, and Theocharis Theocharides. (2024). Convolutional channel-wise competitive learning for the forward-forward algorithm. AAAI. [4] Shaw, N. P., Jackson, T., & Orchard, J. (2020). Biological batch normalisation: How intrinsic plasticity improves learning in deep neural networks. Plos one, 15(9). --- Rebuttal 2: Comment: I thank the authors for their response! I have gone through the manuscript and reviews multiple times. About the biological plausibility, I think there are still several very unclear areas. In particular, it is not clear how exactly the training is performed. I have also read the answer to other reviewers' questions, still I have trouble understanding the details and the details are where things become clear (e.g., is the definition of L_feature accurate?). 1. Weight-transport: The authors mention that "The weights for feedback and forward networks are updated independently, mitigating the problem of weight transport by construction." However, from the loss function you define (in Equation 2), is it possible that you end up with W^T (as in BP) for the backward pass? That is, you don't introduce the weight-transport explicitly, but implicitly the optimization is formulated in such a way that it ends up with the solution of BP. (The definition of the L_feature makes me wonder even more.) Also, what does this objective (minimize \|\|$\hat{a}_l-\hat{b}_l$\|\|) mean really? Why should this optimization happen in the cortex or any biological system? 2. Locality: how do you optimize the loss function (in Equation 2)? It seems the loss function depends on all layers. From Figure 2, it seems that the optimization problem in Equation 2 is solved all together, isn't it? 3. Update locking: the update locking problem is defined in the literature (e.g., PEPITA): "Input signals cannot be processed in an online fashion, but each sample needs to wait for both the forward and backward computations to be completed for the previous sample." Isn't this also the case in CCL? In Figure 1/2 of CCL, it seems that although the forward and feedback passes can be simultaneously run, the first layer's update need to wait for the completion of the backward pass; the last layer's update need to wait for the complete of the forward pass. 4. Freezing of neural activity: I see that the authors acknowledge that CCL requires freezing the neural activity. One might argue that the whole motivation of this work is biological plausibility. If we want to sacrifice biological plausibility in any way, then we use BP, because it has generally the best performance. About the comparison with the state of the art, I remembered a new paper, how does your approach relate to this work: Ororbia, A.G. and Mali, A., 2019, July. Biologically motivated algorithms for propagating local target representations. In Proceedings of the aaai conference on artificial intelligence (Vol. 33, No. 01, pp. 4651-4658). About [GR3], could the author show that this is indeed due to overfitting of the BP or use common techniques to avoid overfitting? I'd appreciate it if the authors could clarify these point in their next response. --- Rebuttal Comment 2.1: Comment: [Q1] Clarification on biological plausibility We sincerely thank the reviewer for the valuable time, insightful comments, and the opportunity to address ambiguities. We appreciate the chance to provide more detailed clarifications. [Q1.1] On weight transport and locality - Weight Transport: We acknowledge the reviewer's concern about implicit weight alignment. In Figure 1.b (in rebuttal material), cosine similarity between the forward layer weights and the corresponding feedback layer weights are computed for the model trained on MNIST using a five-layered MLP architecture. Our analysis reveals a weak alignment between forward and feedback weights, with a maximum cosine similarity of 0.25 after training. This low similarity suggests that our method does not enforce weight transport; instead, even with weak alignment, the models attain good performance. - Loss Function: The loss function (minimize \|\|$\hat{a}_l-\hat{b}_l$\|\|) aims to align neural activities between corresponding layers in the feedforward and feedback pathways. This approach is inspired by local learning principles in neuroscience. It is related to Hebbian learning [1], where synaptic connections are strengthened when neurons on either side of the synapse have correlated activity such that the activity correlation would increase. - Locality: Using Figure 1 (Counter-Current Learning subplot) as an example, one local loss function is \|\|$a_1$-$b_1$\|\|. This means: (i) Function g1 is updated to make $a_1$ closer to $b_1$, and (ii) Function $h_2$ is updated to map $b_2$ closer to $a_1$, (iii) The stop gradient operation ensures locality by preventing \|\|$a_1$-$b_1$\|\| from influencing $h_3$, \|\|$a_2$-$b_2$\|\| from influencing $g_1$, and \|\|$Output$-$Target$\|\| from influencing $g_2$. This gradient detachment mechanism enforces the local nature of the updates. [Q1.2] Update Locking and Activity Freezing Our approach halves the time for activity freezing and partially mitigates the update locking problem. To clarify our terminology: - Backward locking problem: This is the term we use in our manuscript. It refers to the issue where the backward process must wait for the forward pass to complete [3, 4]. CCL allows simultaneous forward and backward passes, reducing this waiting time. - Update locking problem: We acknowledge that while our method partially mitigates this issue, complete elimination remains a challenge for algorithms in Feedback Alignment Family, Target Propagation Family, and CCL. We will add more detailed discussions on weight transport, locality, update locking, backward locking, and activity freezing in the next version. [Q2] Whole motivation of this work is biological plausibility We appreciate that the reviewer points out the trade-off between biological plausibility and performance. Indeed, biological plausibility is a primary motivation for our work, as it is for a growing body of research in the field, and the pursuit of biologically plausible learning algorithms can serve crucial purposes. Our work, along with other approaches like Feedback Alignment, Target Propagation, PEPITA, and Forward-Forward Algorithm, aims to optimize neural network learning while addressing BP's biological implausibility. While we may not yet match BP's performance in all tasks, the insights gained from this line of research can advance our understanding of both artificial and biological neural networks. [Q3] More literature review The key differences between Local Representation Alignment (LRA) work by Ororbia and Mali (2019) and our approach are: - Target generation: The lawyer-wise ideal targets in LRA require using global error signals (see Algorithm 1 in [2]), whereas CCL uses layer-wise comparisons between forward and backward activations. - Backward locking: LRA doesn't resolve this issue; it still requires global error signals, meaning that the LRA backward process only begins after the forward process. CCL addresses it by allowing simultaneous forward and backward passes. We will review Local Representation Alignment (LRA) in our revised manuscript. [1] Hebb, D. O. (1949). The organization of behavior: A neuropsychological theory. Wiley. [2] Ororbia, A.G. and Mali, A. (2019). Biologically motivated algorithms for propagating local target representation, AAAI. [3] Nøkland, A., & Eidnes, L. H. (2019). Training neural networks with local error signals. ICML. [4] Huo, Z., Gu, B., & Huang, H. (2018). Decoupled parallel backpropagation with convergence guarantee. ICML. --- Reply to Comment 2.1.1: Comment: [Q4] Evidence of BP overfitting As we cannot add additional plots in this discussion phase, we provide descriptive evidence of overfitting based on our experiments. Validation loss trend: For the BP model trained on CIFAR100 (Figure 1.a in rebuttal material), the validation loss reaches its minimum (cross-entropy loss of 2.23) at epoch 47. It then steadily increases to 2.99 by epoch 94, and settles around 3.01 at the end of training. We observe a growing gap between training and validation loss as training progresses, which is an indicator of overfitting. In our revised manuscript, we will include both training and validation loss plots. Thank you. --- Rebuttal 3: Comment: I thank the authors for their response! > Weight Transport: We acknowledge the reviewer's concern about implicit weight alignment. In Figure 1.b (in rebuttal material), cosine similarity between the forward layer weights and the corresponding feedback layer weights are computed for the model trained on MNIST using a five-layered MLP architecture. Our analysis reveals a weak alignment between forward and feedback weights, with a maximum cosine similarity of 0.25 after training. This low similarity suggests that our method does not enforce weight transport; instead, even with weak alignment, the models attain good performance. I think the original issue was the extra biologically implausible assumption/constraint that the weights in the backward pass were the same as the forward pass. Now, while this is not the case here (at least not explicitly), with the objective function, it seems that the extra biologically implausible assumption/constraint is still introduced. One way to go around this issue is to say that this is actually the optimization problem that takes place in the cortex, which we discuss in the following. > Loss Function: The loss function (minimize $\|\|\hat{a}_l -\hat{b}_l \|\|$) aims to align neural activities between corresponding layers in the feedforward and feedback pathways. This approach is inspired by local learning principles in neuroscience. It is related to Hebbian learning [1], where synaptic connections are strengthened when neurons on either side of the synapse have correlated activity such that the activity correlation would increase. I am familiar with the principle of "fire together, wire together." However, I don't see what is the reason for this cost function to be optimized by the cortex at one single-layer level locally. One could say, why should they fire together at all at one single-layer level? The objective to minimize $\|\|\hat{a}_1 -\hat{b}_1 \|\|$ does not seem to be relevant at a higher level (e.g., for ultimately reducing the classification loss) for the cortex. > Locality: Using Figure 1 (Counter-Current Learning subplot) as an example, one local loss function is $\|\|\hat{a}_l -\hat{b}_l \|\|$. This means: (i) ..., and (ii) ..., (iii) ... Do (i), (iii), (iii) happen in order in time? That is, first you do (i), then you do (ii), and finally (iii)? Or they are formulated as one joint optimization problem solved in python? > Update Locking and Activity Freezing: Our approach halves the time for activity freezing and partially mitigates the update locking problem. It seems there is some confusion about weight updates and passes. According to Nøkland2019: "The hidden layer weights cannot be updated before the forward and backward pass has completed. This backward locking prevents parallelization of the weight updates'', and Huo2018 ''Backwards Locking – no module can be updated before all dependent modules have executed in both forwards mode and backwards mode''. In CCL, again, the first layer's update needs to wait for the completion of the backward pass; the last layer's update needs to wait for the completion of the forward pass. On the other hand, the authors mention that "Our approach halves the time for activity freezing". My question is: is that important? and, if so, why? Nøkland, A., & Eidnes, L. H. (2019). Training neural networks with local error signals. ICML. Huo, Z., Gu, B., & Huang, H. (2018). Decoupled parallel backpropagation with convergence guarantee. ICML I'd appreciate it if the authors could clarify these points in their next response. --- Rebuttal Comment 3.1: Comment: We greatly thank your thoughtful review and the opportunity to clarify our work. While we believe CCL is at least as biologically plausible as other algorithms in the Target Propagation family (e.g., DTP, DRL, L-DRL, FW-DTP, LRA) compared to backpropagation, we appreciate this deeper discussion and stricter examination of biological plausibility. [Q1] Relevance of local objectives to higher-level cortical functions. Thank you for this insightful question. We believe that a key contribution of other biologically plausible algorithms (e.g., Target Propagation Family) and CCL is demonstrating that solving local problems can lead to global loss reduction. These algorithms explore how such local computations might collectively contribute to higher-level functions, even without explicit global optimization. We'd welcome further discussion on this point if you have additional insights or concerns. [Q2] Are local loss functions formulated as one joint optimization problem solved in Python Yes, the local loss functions are formulated as a joint optimization problem solved simultaneously in our implementation. [Q3] Confusion about weight updates and passes. We appreciate the opportunity to clarify this point. We acknowledge that CCL does not fully mitigate the backward locking problem, as each module still needs to await both forward and feedback passes for updates. However, CCL partially addresses this issue by decoupling the feedback (backward) passes from the forward passes, distinguishing it from backpropagation and algorithms in the feedback alignment and target propagation families. While full mitigation might require layer-wise training methods, CCL represents an intermediate solution between no mitigation and full mitigation of the backward locking problem. We will revise our paper to more accurately state that CCL disrupts the dependency of the feedback/backward pass on the forward pass, rather than fully mitigating the backward locking problem. [Q4] Importance of halving activity freezing time By reducing activity freezing time, which is a byproduct of decoupling the feedback from the forward passes, CCL improves upon previous algorithms in feedback alignment and target propagation family and steps closer to how biological neural networks might operate by halving the latency. Moreover, CCL potentially offers computational advantages, particularly in resource-constrained scenarios. For instance, the reduced dependency between forward and feedback passes could open up possibilities for parallelization. We appreciate your critical analysis, which has helped us refine our presentation and clarify the contributions of CCL in the context of biologically plausible learning algorithms. We look forward to incorporating these insights into our revised paper. --- Rebuttal 4: Comment: I thank the authors for their response and for bearing with my many questions! I try to summarize what we discussed below about biological plausibility: 1. Weight transport: As the authors mention, "We acknowledge the reviewer's concern about implicit weight alignment." They also provide nice insight that "CCL is demonstrating that solving local problems can lead to global loss reduction." 2. Locality: As the authors mention, "the local loss functions are formulated as a joint optimization problem solved simultaneously in our implementation." Therefore, I am not sure if the locality principle holds. Even if they stop gradient propagation the problem, in my understanding the problem is still not solved (entirely) locally. 3. Update locking: As the authors mention, they address this issue partially: "We acknowledge that while our method partially mitigates this issue..." and "We acknowledge that CCL does not fully mitigate the backward locking problem, as each module still needs to await both forward and feedback passes for updates." 4. Freezing activity: As the authors mention, they address this issue partially: "Our approach halves the time for activity freezing". Biological plausibility is one of the main motivations and in the title of the paper. As such, there is still several unclear areas around the biological plausibility of CCL. Therefore, as much as I think the paper has interesting contributions, my confidence in the biological plausibility of the approach is still low. Therefore, I slightly raise my score, since the discussion with the authors clarified a few points about the results and comparison with the state of the art, while the biological plausibility part remains largely unclear, at least to this reviewer. Once again, I thank the authors for their response and patience. --- Rebuttal Comment 4.1: Comment: We appreciate the reviewer's thoughtful discussion on biological plausibility and concise summary of our exchange. We will incorporate these insights into the next version of the manuscript.	Summary: In this work, the authors proposed the counter-current learning algorithm, a novel algorithm for biologically plausible training of feedforward neural networks. The learning rule is built upon the target-propagation algorithm and its variants. In these algorithms, the backward pathway is typically trained in a way that the target information propagated to each hidden layer provides a layer-wise target that nudges the forward pathway's output toward the true label. Instead, the authors jointly trained both feedforward and feedback weights projected to each layer, in a way that forward and backward pathways exhibit roughly the same activity at each layer. The authors applied this algorithm to various image recognition tasks (MNIST/Fashion-MNIST/CIFAR10/CIFAR100) and an autoencoder task and demonstrated that the proposed algorithm outperforms other variants of target-prop algorithms. The authors empirically analyzed the learning process of the algorithm by examining the development of hidden layer representations and through an ablation study. Strengths: The proposed learning algorithm is simple yet novel. The key novelty is the training algorithm for the backward pathway, where, unlike previous target-prop algorithms, activity matching between the forward and feedback pathway at each layer is used as the objective. I was positively surprised by the algorithm's strong performance because this learning algorithm clearly deviates from the backprop of the global loss. This training approach also makes the algorithm distinct from previous related approaches where the backward weights were fixed instead (Frenkel et al., Frontiers 2021; Shibuya et al., AAAI 2023). Weaknesses: The learning rules for hidden weights have trivial solutions, hence susceptible to representation collapse. The authors discussed their techniques for avoiding the collapse briefly in the supplement, but the implementation is not discussed in detail. Biological plausibility of the regularization mechanisms should also be discussed. Technical Quality: 3 Clarity: 3 Questions for Authors: Considering that the algorithm is minimizing the difference between $a_l$ and $b_l$, I expect to see large diagonal components in Figure 6 after learning. However, there is no diagonal trace in the figure. Why is that the case? In addition, at t = 0, $b_1$ to target are already weakly aligned with the input, but $b_0$ is not aligned with the input. What is the origin of initial alignment and the absence of it in $b_0$? On a related point, I wonder if the authors checked whether the stop gradient is implemented correctly, for instance, by calculating the gradients by hand and implementing them manually into the network. Confidence: 2 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The authors addressed the limitations, especially the lack of theoretical justification, nicely. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: [W1] Discussion of biological plausibility of the regularization mechanisms. We thank the reviewer for pointing out and allowing us to elaborate on this. - Normalization: Our use of activation normalization during loss computation aligns with divisive normalization observed in biological neural circuits [1]. This process helps maintain neural activity within a functional range, similar to the divisive normalization phenomenon observed in animals in the early 1990s in the primary visual cortex. - Modulation. The additional loss provides signals for surround modulation [2], a foundational property of visual neurons at many levels of the visual system (e.g., retina, visual cortex), auditory system, and so forth. Surround modulation describes that dissimilar stimuli between inside and outside neuron's receptive field would evoke stronger responses for a neuron, compared to similar stimuli. This is similar to the regularization methods used to prevent the model from representation collapse. - Flooding method: This approach, preventing weight updates when the sample-wise difference is small, can be likened to the concept of activation thresholds in biological neurons, where small input changes do not trigger action potentials. Implementation details: - Modulation. We implemented a technique to prevent feature collapse for each latent activation $X ∈ R^{b×d}$, where $b$ represents the batch size and $d$ represents the feature dimension. We added an L2 loss term to minimize the difference between norm($X$)norm($X$)$^\top$ and the identity matrix. The loss is computed as: L_feature = $\|\|norm(X)norm(X)⊤ - I\|\|_F$ - Avoid large gradient norms. We adopted gradient centralization [3] to mitigate the issue of large gradient norms. This technique centralizes the gradient vectors by removing their mean values before updating the model parameters: $g_{c} = g - mean(g)$, where $g$ is the original gradient and $g_c$ is the centralized gradient. - Focus on major differences. We implemented the flooding method [4] to focus the model on cases where predictions significantly differ from the ground truth. The modified loss function is expressed as $L_{flooded} = max(L, b)$, where $b$ is set to 0.2 as the original paper suggested. [Q1] Why is there no diagonal trace in the figure 6. The observed pattern in Figure 6 arises from the functional asymmetry when comparing forward and backward networks because their input signals are different. If we were to compare two independently trained forward networks using CCL, we would expect to see diagonal traces in the CCA analysis because both networks perform similar compression and learning functions. However, forward and backward networks exhibit functional asymmetry (e.g., one for feature extraction and another one for reconstruction), leading to rank disparity (e.g., the backward activations have a lower rank). This reduced detail and compressed information in the feedback activations result in lower pair-wise CCA values between forward and backward layers, manifesting as a non-diagonal trace in Figure 6. [Q2] What is the origin of initial alignment? Since MNIST is a relatively small and simple dataset, digits of the same class are relatively similar and are more likely to be projected to neighboring features in the latent space, forming several loose clusters. This would cause a relatively positive alignment in terms of CCA. [Q3] Checking stop gradient implementation. We followed your advice and checked the gradient implementation. We checked that the weight detachment is implemented correctly such that optimization over a local loss only involves the nearest layers. [1] Carandini, M., & Heeger, D. J. (2012). Normalization as a canonical neural computation. Nature reviews neuroscience. [2] Angelucci, A., Bijanzadeh, M., Nurminen, L., Federer, F., Merlin, S., & Bressloff, P. C. (2017). Circuits and mechanisms for surround modulation in visual cortex. Annual review of neuroscience. [3] Yong, H., Huang, J., Hua, X., & Zhang, L. (2020). Gradient centralization: A new optimization technique for deep neural networks. ECCV. [4] Ishida, T., Yamane, I., Sakai, T., Niu, G., & Sugiyama, M. (2022). Do We Need Zero Training Loss After Achieving Zero Training Error?. ICML. --- Rebuttal Comment 1.1: Comment: Thank you so much for the revision and detailed responses. I have one comment regarding the new ELBO result. The last equation appears to be incorrect. The final term should be: $$ E_{q(z_1, z_2 \| y)} \left[ \log \frac{q(z_1 \| z_2)}{p(z_1 \| x)} \right] = E_{q(z_2 \| y)} \left[ KL (q(z_1 \| z_2) \|\| p(z_1\|x) ) \right], $$ since the KL divergence is evaluated with respect to $z_1$. Additionally, the middle term, $E_{q(z_1, z_2 \| y)} \left[ \log \frac{q(z_2 \|y)}{p(z_2 \| z_1)} \right]$, doesn’t seem to lend itself to a simple KL-based expression. Please let me know if I’m overlooking something. --- Rebuttal 2: Comment: Response to Reviewer Comments on Theoretical Derivation We appreciate the reviewer's insightful comments, which have led us to refine our theoretical derivation. Based on their feedback and further consideration, we have revised our approach to better align with the CCL algorithm. Problem with Previous Derivation In our previous derivation, we incorrectly represented the relationship between variables. For example, in the term $E_{q(z_1, z_2 \| y)} \left[ \log \frac{q(z_2 \|y)}{p(z_2 \| z_1)} \right]$, the $z_1$ in $p(z_2 \| z_1)$ depends on $x$, not $y$. Key Changes 1. We now explicitly account for the relationship between $x$ and $y$ in the dataset $D$. 2. We have revised the ELBO derivation to more accurately represent the CCL process. 3. We have introduced an important approximation in the derivation that maintains consistency with the CCL algorithm's implementation. Updated Derivation The revised ELBO derivation is as follows: $$E_{(x,y) \sim D} \log p(y\|x) \geq E_{(x,y)\sim D, q(z1,z2\|y)}[\log (p(y,z_1,z_2\|x) / q(z1,z2\|y))]$$ $$= E_{(x,y) \sim D, q(z_1,z_2\|y)}[\log p(y\|z_2,z_1,x)] - E_{(x,y)\sim D, q(z_1, z_2 \| y)}[\log \frac{q(z_2 \|y)}{p(z_2 \| z_1,x)}] - E_{(x,y)\sim D, q(z_1,z_2 \| y)}[\log \frac{q(z_1 \| z_2, y)}{p(z_1 \| x)}] $$ Term-by-Term Analysis - The first term can be understood as $E_{(x,y) \sim D, z_1\sim p(\cdot\|x), z_2\sim p(\cdot\|z_1)} [\log p(y\|z_2)]$. This term represents the reconstruction of $y$ given the latent variables $z_1$ and $z_2$ sampled from the forward model, not the inference model. - The first latent alignment term can be rewritten as $E_{(x,y)\sim D, z_1\sim p(\cdot\|x)} [KL(q(z_2 \|y) \| p(z_2 \| z_1))]$. This term encourages alignment between the distribution of $z_2$ inferred from $y$ and predicted from $z_1$ (which is sampled from $p(\cdot\|x)$, not from $q(z_1\|y)$). - Likewise, the second latent alignment term can be rewritten as $E_{(x,y)\sim D, q(z_2 \| y)}[KL(q(z_1 \| z_2) \| p(z_1\|x))]$. This term encourages alignment between the distribution of $z_1$ inferred from $z_2$ and predicted from $x$. Consequently, the ELBO is $$E_{(x,y) \sim D, z_1\sim p(\cdot\|x), z_2\sim p(\cdot\|z_1)} \log p(y\|z_2)] - E_{(x,y)\sim D, z_1\sim p(\cdot\|x)} [KL(q(z_2 \|y)\|\|p(z_2 \| z_1))] - E_{(x,y)\sim D, q(z_2 \| y)}[KL(q(z_1 \| z_2) \|\| p(z_1\|x))]$$ Connection to CCL Implementation In our practical implementation of CCL, we approximate the last two KL divergence terms using L2 losses between latent features from forward and feedback networks. This approximation captures the essence of aligning the forward and backward pathways while providing a computationally tractable solution. [1] Luo, C. (2022). Understanding diffusion models: A unified perspective. arXiv preprint arXiv:2208.11970. [2] Ho, J., Jain, A., & Abbeel, P. (2020). Denoising diffusion probabilistic models. NeurIPS. --- Rebuttal Comment 2.1: Comment: Thank you for your response. However, I still find the derivation of both the first and second terms of the ELBO to be unclear and problematic. In the term-by-term analysis, the expression $\int dz_1 dz_2 q(z_1, z_2 \| y) \log p (y \| z_2)$ is replaced with $\int dz_1 dz_2 p(z_1, z_2 \| x) \log p (y \| z_2)$. These two equations are not equivalent unless $q(z_1, z_2 \| y) = p(z_1, z_2 \| x)$. Similarly, in the second term, it seems that $q(z_1, z_2 \| y)$ has been substituted with $q(z_2 \| y) p(z_1 \| x)$. If additional approximations or assumptions were made in the derivation, they should be explicitly stated. The explanation in the term-by-term analysis paragraph may aim to clarify the approximation, but it lacks clarity. Additionally, if significant approximations were introduced, I would recommend avoiding the use of the term ELBO to prevent confusion. Although I believe that theoretical justification is not essential for this type of work, my overall confidence in the evaluation has decreased, and I have adjusted my rating accordingly. --- Reply to Comment 2.1.1: Comment: We sincerely appreciate the reviewer's thorough examination of our derivation. We acknowledge that our presentation introduced several approximations that were not explicitly stated. To improve the manuscript, we will: 1. Explicitly state all assumptions and approximations made in the derivation. 2. Remove the term 'ELBO' given the approximations involved, to avoid any misunderstanding. We understand that these issues have affected confidence in our evaluation, and we take these concerns seriously. We thank the reviewer for bringing these important points to our attention.	Summary: In their paper ‘Counter-Current Learning: A Biologically Plausible Dual Network Approach for Deep Learning’ the authors introduce their new ‘counter-current learning (CCL) framework’ which they use to train neural networks of multiple network classes (MLPs, CNNs, Autoencoders) using a learning mechanism which solely relies on local calculation of learning signals, without the need to fully propagate gradients through the network. Through this, authors establish a link the brain’s counter-current exchange mechanism. The authors also show an analysis how feature representations are shaped over the course of learning in their learning framework. Whereas many biologically-plausible learning mechanisms have been proposed throughout the last couple of year, the author’s work particularly stands out due to its generality / easy of being applied to various different network classes used in machine learning. Strengths: As mentioned in the summary, I think many biologically-plausible learning mechanisms have been proposed throughout the last years and the author’s framework stands out to me due to it apparently generality as it seems to easily be applied to network classes which are, from my point of view, not commonly considered in bio-inspired learning mechanism papers, like autoencoders. This generality could allow for the authors framework to have an impact beyond theoretical neuroscience but also influence the more engineering focused side (e.g. neuromorphic computing). The new learning framework is supported by some additional empirical investigations, giving an intuitive understanding of the learning dynamics within the network. Weaknesses: While authors mention a potential biological link, not much space is given to discussing specific biological implementations and authors do not seem to make specific predictions which would allow for empirical validation of their proposed mechanism in biology, to validate whether the mechanism is actually utilised in the brain. As such, I see this paper as being more focused on the engineering / computing solutions side, where it does a good job, mentioned above. Given this focus on the computing side, I would have hoped that authors would also consider training a model using a current SOTA architecture (i.e. Transformers or State Space Models) using their technique, to show whether their algorithm can also handle these cases. It would be important to discuss how the proposed work relates to a recent line of work in which two streams of information are assumed to exist in the brain: burstprop (Payeur et al. Nature Neuroscience 2021) and burstCCN (Greedy et al. NeurIPS 2022). Moreover, this work seems to have links with Sacramento et al. 2018 NeurIPS, in that both require specialised feedback neurons that encode the error signals. Both Sacramento et al. and Greedy et al. use an interneuron that learns to match the feedback, which conceptually seems to match the idea proposed by the authors. Perhaps even more relevant is the predictive coding of backprop by the group of Rafal Bogacz, which requires separate error neurons and both the forward and backward phases to align with each other. These should be discussed, and it may be worth making a more explicit link in future work. Technical Quality: 2 Clarity: 3 Questions for Authors: If the authors see their work primarily focused on an engineering solution, I am wondering whether their technique generalises to Transformers and / or State Space Models (like Mamba or Griffin). Otherwise, I wonder whether authors could make specific predictions based on the learning dynamics observed in their model which would allow the community to test for its plausibility using neural data. How does your work relate to the bioplausible works referred to above? Confidence: 3 Soundness: 2 Presentation: 3 Contribution: 2 Limitations: I think authors address limitations on the machine learning / engineering side well but could potentially expand their discussion of limitations with regards to biological evidence for / against their proposed learning framework. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: [Q1] Generalization of models A: While MLPs and CNNs have established biological plausibility, the biological relevance of Transformers and State Space Models remains unclear and under-explored. For vision tasks, CNNs have been shown to match Transformer performance when computational resources, datasets, and techniques are equalized [1,2]. Recognizing the need for generalization, we've extended our research to auto-encoding tasks. To our knowledge, this represents the first application of a biologically plausible algorithm to an auto-encoder architecture, broadening the scope of our approach beyond traditional supervised learning paradigms. [1] Liu, Z., Mao, H., Wu, C. Y., Feichtenhofer, C., Darrell, T., & Xie, S. (2022). A convnet for the 2020s. CVPR. [2] Liu, S., Chen, T., Chen, X., Chen, X., Xiao, Q., Wu, B., ... & Wang, Z. (2023). More convnets in the 2020s: Scaling up kernels beyond 51x51 using sparsity. ICLR. [Q2] Literature review and comparison We appreciate the reviewer's suggestion to compare our Counter-current Learning (CCL) approach with recent work on dual-stream information processing in the brain. Here's a detailed comparison of CCL with BurstCNN/BurstProp, Sacramento, et al. (2018), and Predictive Coding: Network Structure: - CCL uses two separate networks: a feedforward network and a feedback network. - BurstCNN/BurstProp and Sacramento et al. (2018) use a single network with two firing modes. - Predictive Coding uses a hierarchical structure with prediction and error units at each layer. Error Representation: - CCL doesn't use global error signals; differences between forward and feedback local activations guide the learning. - BurstCNN/BurstProp encodes errors implicitly in burst firing patterns. - Sacramento, et al. (2018) allow local error signals to be generated by comparing different sources of neural input activity; the axonal output is a corrected target signal. - Predictive Coding uses explicit error neurons. Biological Plausibility: - CCL mitigates the update locking problem, allowing for more flexible and potentially more biologically plausible learning dynamics. - BurstCNN/BurstProp is based on observed burst firing patterns in neurons, enhancing biological plausibility. However, it still suffers from update locking problems. - Sacramento, et al. (2018) does not resolve the update locking problem, nor does it elaborate on multi-layered structures, limiting its biological plausibility in complex networks. - Predictive Coding aligns with theories of how the brain processes information, but explicit error encoding and propagation remains debated in neuroscience. Computational Complexity: - CCL allows for parallel processing in forward and feedback networks, potentially offering computational efficiency. - BurstCNN/BurstProp and Sacramento, et al. (2018) require distinct forward and backward phases, which may result in slower processing. - Predictive Coding involves iterative refinement, which can be computationally intensive. Our CCL approach offers several advantages in this context. By using separate forward and feedback networks, we avoid the update locking problem that affects BurstCNN/BurstProp and Sacramento et al. (2018). This separation allows for more flexible learning dynamics that could better reflect the parallel processing capabilities of biological neural networks. Moreover, CCL's approach to error representation - using differences between forward and feedback activations rather than explicit error signals - offers a unique perspective on how learning might occur in biological systems without the need for specialized error neurons or complex temporal coding schemes. We will add the above discussion over comparison in the camera-ready version. [Q3] Testable prediction We appreciate the reviewer's thought-provoking question. Based on our observations of the learning dynamics in our model, we propose the following testable predictions: - Organized increase in cross-layer neural activity correlation: As illustrated in Figure 6 of our manuscript, we observe an organized increase in cross-layer neuron activity correlation (highlighted by red and green boxes). This suggests a reciprocal and complementary learning dynamic among neurons. We predict that this phenomenon would be more pronounced when the network is exposed to novel, unseen patterns. This could be tested by measuring cross-layer neural correlations in biological networks before and after exposure to new stimuli. - Low similarity in local error signals across layers: Unlike backpropagation or related algorithms where error signals are globally coordinated, CCL's architecture suggests that error signals at different layers should exhibit low correlation or similarity. This prediction could be tested by comparing the similarity of local error signals across layers in biological neural networks, particularly during learning tasks. --- Rebuttal Comment 1.1: Title: Reply Comment: Thank you we will improve our score.	Rebuttal 1: Rebuttal: We thank the reviewers for their insightful feedback. We're grateful for their assessment of our work as novel (sTDo, ijwx, myCb), distinctive (ijwx), and empirically supported (sTDo, EBaT), with EBaT noting its 'apparent generality'. We address the main critiques below, focusing on theoretical foundation, literature review, result clarification, and intuition explanation. We will add the corresponding results and discussions to the next version of the paper. [GR1] A theoretical explanation and interpretation of CCL We appreciate reviewer sTDo for requesting a more analytical approach to explain and support the proposed counter-current learning (CCL) algorithm. We offer the following analysis through the lens of variational inference and hierarchical latent variable models. CCL fundamentally aims to learn a conditional distribution p(y\|x), where x represents input data and y represents target outputs. The algorithm employs a hierarchical structure, for example, with latent variables z1 and z2, utilizing both forward (encoding) and backward (decoding) pathways. The key insight is that CCL uses two different graphical models with which CCL can be interpreted as optimizing the Evidence Lower Bound (ELBO) on the log-likelihood of y given x: - For the generative model p: x → z1 → z2 → y - For the inference model q: y → z2 → z1 → x ### ELBO Derivation Starting from the goal of maximizing log p(y), we derive the ELBO as follows with simplifications based on the conditional independence from graphical models: $\log p(y\|x) = \log E_{q(z1,z2\|y)}[p(y,z1,z2\|x) / q(z1,z2\|y)]$ $≥E_{q(z1,z2\|y)}[\log (p(y,z1,z2\|x) / q(z1,z2\|y))]$ (by Jensen's inequality) $=E_{q(z1,z2\|y)}[\log p(y\|z2) + \log p(z2\|z1) + \log p(z1\|x) - \log q(z2\|y) - \log q(z1\|z2)]$ $=E_{q(z2\|y)}[log p(y\|z2)] - KL(q(z2\|y) \| p(z2\|z1)) - KL(q(z1\|z2) \| p(z1\|x))$ The CCL algorithm implements this variational framework in a simplified and computationally tractable form. The implemented losses connect to the ELBO terms as follows: - Target reconstruction: This first term represents the reconstruction of y given the latent variable z2. In CCL, it is implemented as a loss between the output of the forward pathway and the target y. - Latent consistency: The two KL divergence terms encourage alignment between the distributions of z2 (z1) inferred from y (z2) and predicted from z1 (x). In CCL, this is approximated by L2 losses between latent features from forward and feedback networks. While this simplification assumes zero variance in the distributions, it captures the essence of aligning the forward and backward pathways. Using Monte Carlo sampling by adding noise to latent features may be viewed as an approximation. [GR2] A comparison with previous SoTA We have compiled results from relevant papers and conducted additional experiments to provide a comprehensive comparison. Please note that hyperparameters and architectures may vary across studies. To account for this, we have added the results of our CCL approach with an architecture similar to the one used in PEPITA. \| Algorithm \| CIFAR10 \| CIFAR100 \| \|--\|--\|--\| \|FFA [1]\| 59 () \|-\| \|CFSE [3]\|78.11\|51.23\| \|SoftHebb [4]\|80.30\| 56.00\| \|CCL (original)\| 82.94 \|56.29\| \|PEPITA [2]\|56.33\|27.56\| \|CCL (matched with PEPITA)\|62.19\|34.89\| Key observations: - CCL outperforms other methods on both CIFAR10 and CIFAR100. Even with the simplified architecture used by PEPITA, CCL yields higher accuracy. - SoftHebb [4] performs extensive layer-wise hyperparameter search (24 hyperparams), while CCL searches for only 3 parameters. We will revise our paper to include this comprehensive comparison, providing a clearer context for our algorithm's performance relative to other recent work in the field. [GR3] Result clarification* We thank the reviewers for carefully reading the results. We show the training loss during training in Figure (1.a) in the rebuttal document. BP actually optimizes the training objective better and yields much lower training loss than CCL but a high testing error, indicating that BP may be overfitting. We believe that more aggressive model regularization techniques may be helpful. [GR 4] Suggestion on reporting weight alignment We appreciate this insightful suggestion from reviewer sTDo and show the weight alignment between the forward and backward network in Figure (1.b) in the rebuttal document. Cosine similarity between the forward layer weights and the corresponding feedback layer weights are computed for the model trained on MNIST using a five-layered MLP architecture. Our findings reveal two distinct phases during training: - Phase one: Layers 1 and 5 show rapid alignment increases. - Phase two: Alignments in layers 1 and 5 saturate. Alignments in the intermediate layers gradually increase until saturation. Interestingly, intermediate layers showed a bottom-up convergence pattern, with layer 2 achieving highest similarity first, followed by layers 3 and 4. We found that high alignment isn't always achieved or necessary for effective learning. This may be due to (1) Dimensional reduction: Information propagation through the network affects alignment, and (2) Non-linearity: Activation functions impact the relationship between forward and backward weights. These factors may contribute to observed alignment patterns without requiring perfect symmetry between forward and backward weights (*) uses CNN with local receptive fields [1] Hinton, G. (2022). The forward-forward algorithm: Some preliminary investigations. [2] Dellaferrera, G., Kreiman, G., and Kreiman, G. (2022). Error-driven Input Modulation: Solving the Credit Assignment Problem without a Backward Pass. [3] Andreas Papachristodoulou, Christos Kyrkou, Stelios Timotheou, and Theocharis Theocharides. (2024). Convolutional channel-wise competitive learning for the forward-forward algorithm. [4] Journé, A., Rodriguez, H. G., Guo, Q., & Moraitis, T. (2023). Hebbian deep learning without feedback. Pdf: /pdf/ddea796de947ca80c888a80130209003041b2381.pdf	NeurIPS_2024_submissions_huggingface	2,024	Summary: The article proposes a learning framework that addresses three major critiques of the backpropagation algorithm regarding its biological plausibility: (i) the weight transport problem, i.e., the error feedback weights being the transposes of the feedforward weights, (ii) the nonlocal update problem, i.e., the local weights being dependent on the global error signal, and (iii) the backward locking problem, i.e., the need to freeze layer activations until error feedback information becomes available. The basic idea of the proposed framework is to construct a dual network that operates in the reverse direction to the original inference network. This dual-network has transpose dimensional weights (but not necessarily the transposes of the forward weights), with some similarity to the case of backpropagation. However, this dual network propagates the target value backward. Each layer of the dual network is compared to the corresponding layer (of the same dimension) in the original inference network. The loss is defined as the mean square error between the activations of the corresponding layers. The numerical results demonstrate that the test performance in classification task are on par with backpropagation and the state-of-the-art models. Strengths: - Novelty: The article offers a novel approach for the biologically plausible learning framework. The use of a dual network to propagate the target value backward and using the mean square error between the corresponding representations of the network as the loss function appears to be a new idea. - Numerical Experiments: The article presents several experiments demonstrating the performance of the proposed approach in comparison to existing methods. The performance appears to be close to that of backpropagation (and even significantly better in the case of CIFAR-10). Weaknesses: - Analytical Support/Discussion: There is no analytical justification provided for the proposed approach, making it unclear why it should work. This is the main weakness of the article. At the very least, there could be more discussion aimed at providing intuition about the underlying mechanism of the proposed approach that would enable effective training of neural networks. The authors cite "counter-current" mechanisms observed in nature as their primary motivation. - Presentation: The presentation is generally smooth and clear. However, it can be further improved as addressed by the questions below. - Reporting of Numerical Experiments: The results reported for the numerical experiments are confusing, especially as they conflict with those of Shibuya et al. [2023], whose experimental setup is adopted in the current article. - Scalability: It is uncertain whether this idea would work for large-scale inputs/models (e.g., ImageNet 1K/ResNets). Technical Quality: 2 Clarity: 3 Questions for Authors: - How does the proposed approach train the forward neural network to minimize the mean square error (MSE) at the final layer? - It would be useful to report the alignment (angle) between the forward and backward network weights, to check if the weight symmetry problem still exists. - The sentence "Due to random weight initialization, the information content ... decreases ..." in the caption of Figure 1(a) is imprecise. How do you measure information content and relative to what, and why is it decreasing? Furthermore, the next sentence does not really apply to the "before training" (a) part of Figure 1. - Figure 3: Do we see a similar organization of representations in other layers? Since the target label input for each class is fixed, we expect the backward network representations to be a single point for each class in any layer. Do the forward network layer activations appear as clouds around these points? - Section 4.2: MLP Experiments: Why do the models used for comparison employ tanh nonlinearity, while CCL uses ELU? Test results with the same model properties would be more meaningful. - Table 1: Is the DTP in the line below FA correct? As Noakland 16 is cited, is it actually DFA? Shibuya et al. [2023], which the authors claim to base their experiments on, report 52.17% accuracy for DTP/CIFAR10, which is not available or conflicts with Table 1. Similarly, Shibuya et al. [2023] report 51.33% for FA-CIFAR10, but Table 1 in the current article reports FA performance as 45.76%. The FW-DTP performances also do not match. - Figure 4: It would make more sense to compare the conv. kernels of CCL after training with the corresponding kernels of BP, as the initial random kernels shown in this figure are not informative. - Section 4.4: Do we need the CKA-based measure to compare the representations of the forward and backward networks? The proposed approach tries to minimize the mean square error (MSE) between them, so do we expect any linear transformation uncertainty? Isn't it more meaningful to look directly at the angle of alignment or the MSE normalized by the norm-square of the forward representations? - Figure 7 and Section 4.5: The best performance appears to occur toward the top right corner, suggesting that feedforward-feedback learning rates should be similar (symmetric) rather than asymmetric? Confidence: 4 Soundness: 2 Presentation: 3 Contribution: 2 Limitations: The authors sufficiently discuss the limitations of their work at the end of the article. Related points are raised in the weaknesses and questions part. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: [W1] We provide a theoretical extension for the existing framework We provide an analytical framework for understanding CCL in General Response 1 [GR1]. In short, we show that CCL can be considered as optimizing an ELBO for a hierarchical model. [W4] Validation on large-scale dataset/models We acknowledge that the ImageNet dataset poses significant challenges due to its size and complexity. It typically requires batch normalization, whose biological plausibility is under-explored and often necessitates extensive architectural changes. Additionally, recent work on biologically plausible learning algorithms (e.g., FA, DTP, DRL, FW-DT, and DRTP) has not evaluated these methods on large datasets like ImageNet, as datasets such as CIFAR-10 and CIFAR-100 demonstrate sufficient complexity for current studies in this field. We will include this discussion in the revised manuscript, acknowledging the need for further research on scalability to more complex datasets like ImageNet. Nonetheless, to showcase the capabilities of the CCL algorithm, we have applied it to an autoencoder task, which, to our knowledge, is the first time a biologically plausible algorithm has been scaled to an image autoencoding paradigm. [Q1] What is the loss for the final layer? We thank the reviewer for reminding us of this. We adopt cross-entropy loss for the final layer, which is not explicitly mentioned in the paper. We will modify the content accordingly. [Q2] Suggestion on reporting weight alignment We appreciate this insightful suggestion. Please refer to General Response 4 [GR4] for discussion. [Q3] Suggestion on caption for Figure 1(a) We thank the reviewer for checking the details. The main idea is that signal processing cannot increase information, which corresponds to the data processing inequality (DPT) concept in information theory [1]. From a more intuitive perspective, due to dimensional reduction and the random initialization of the weight parameters, the information of the input signals can be lost during data processing. We will revise the sentence accordingly. Also, we agree that the sentence “Notably, … operator” should move to “(b) During training,” and we will also revise this accordingly. [1] Tishby, N., & Zaslavsky, N. (2015). Deep learning and the information bottleneck principle. [Q4] Do we see a similar organization of representations in other layers? Yes, similar organization is presented in other layers, especially for deeper layers. In Figure (2) in the rebuttal document, we show the results of a five-layered CNN model trained on CIFAR10. The model is trained for 3000 steps using CCL, and the t-SNE for layers 1, 3, and 5 with different time steps are shown. [Q5] Why does CCL utilize ELU? We find that ELU empirically gives better results than Tanh in CCL training when we perform exploratory analysis on MNIST in the early stage of research. We posit the main reason is that Tanh is a symmetric function and thus would induce feature collapse when trained with CCL. For example, at the beginning of training, say the first entries of $a_l$ (i.e., activation from forward network layer $l$) and $b_l$ (i.e., activation from feedback network layer $l$) are 1 and -1 respectively, then solving the local loss function, the weight would be updated such that the first entries of $a_l$ and $b_l$ becomes 0. This would lead to feature collapse for both the forward and feedback networks. We appreciate the reviewer for the insight and will add this to the Supplementary Section. [W3, Q6] Result inconsistency from Shibuya, et al. First of all, we thank the reviewer for noting the error, where the citation for DTP should be corrected. We will revise it in the camera-ready version. Second, we would like to kindly remind the reviewer that the statistics Shibuya et al. [2023] reported are the test error (%), not the test accuracy (%) shown in Table 1. Third, we would like to identify the sources that can potentially lead to different empirical results: - (a) We note that the original implementation for the code is incorrect, where the original codebase from Shibuya, et al. (2023) normalizes FMNIST, CIFAR10, and CIFAR100 using the mean and standard deviation of MNIST. We fix this by using each dataset’s mean and standard deviation; - (b) We proceed with performing a hyperparameter grid search again using five random seeds because directly using the paper’s best hyperparameters does not fit. We consider a slightly smaller hyperparameter search set than the original one, as shown in Section 6.1, due to the computation and time budget for the grid search of all the combinations. The above all can give rise to the difference between the results presented in our work and the original results. [Q7] Suggestion on presenting BP and CCL convolutional kernels We show the result in Figure (3) in the rebuttal document, where kernels learned by BP and CCL are visually different. Kernels from models trained with BP have more high frequency components, as manifested as neighboring white (e.g., weight with high values) and black pixels (e.g., weight with low values). In comparison, those with CCL have more low frequency components. We posit this might be because the error signal can contain more high-frequency information than the ideal target signal. [Q8] Suggestion on similarity measurement We thank the reviewer for pointing out this part. In Figure 6, we not only compare the similarities between pairwise features in the same layer (i.e., the diagonal entries) but also across different layers. We believe that using CKA can better capture relations across layers since it considers invertible linear transformation and orthogonal transformation. [Q9] Does Figure 7 suggest feedforward-feedback learning rates should be symmetric? Yes, it suggests that symmetric learning rates perform better. --- Rebuttal Comment 1.1: Comment: I would like to thank the authors for their response. They have largely addressed my comments. I believe the approach presented in this paper has both merit and novelty, with the potential to impact future research on biologically plausible networks. Therefore, I have increased my overall rating. --- Reply to Comment 1.1.1: Comment: Thank you again for your constructive suggestions from the theoretical framework, additional qualitative experiments, discussion, and clarification. We appreciate your time in and we will incorporate them in the future version.	null	null	null	null	null	null
Adversarial Schrödinger Bridge Matching	Accept (poster)	Summary: This paper proposes Discrete-time iterative Markovian Fitting, which is an efficient alternative that greatly reduces NFE from IMF (Shi et al. 2023). This was possible due to the tractability of Brownian bridges for any subintervals, so discretization of IMF does not hurt the performance of if the model can be trained on it. For training a generative model, the authors adopted a time-dependent GAN called Denoising Diffusion Generative Adversarial Models (DD-GAN). Compared to DSBM, the proposed ASBM shows significantly low computational costs with good FID scores. Strengths: Overall, I think this paper is well written and quality of presenting idea and theoretical statements are very good. This work also contains certain contributions for probabilistic generative models. - This work broadens our understanding of IMF, reference measures, and the application of Brownian bridges. - The results verified that GANs hold as a good nonlinear probabilistic generative model training method. - Theoretical statements were clear and completely proved. Weaknesses: - I strongly believe the performance gains are mostly from applying GAN architecture, since D-IMF and IMF indicates essentially the same learning scheme. Therefore, it is indeed an improvement from DSBM, but novelty of this work as a distinct SB study might not be significant from the perspective of diffusion models. - This model does not always yield state-of-the-art scores for syntactic datasets (see Table 1&2). - While I understand this work for some extent, I do not clearly understand the motivation why do we need a sampling-based approach when we have sampling-free method such as SF^2M and LightSB [1] models Typo - L213: Denoising Denoising GANs [1] @inproceedings{ korotin2024light, title={Light Schr\"odinger Bridge}, author={Alexander Korotin and Nikita Gushchin and Evgeny Burnaev}, booktitle={The Twelfth International Conference on Learning Representations}, year={2024}, url={https://openreview.net/forum?id=WhZoCLRWYJ} } Technical Quality: 3 Clarity: 3 Questions for Authors: How do the authors suspect that the FID score is very low for ASBM? Following the arguments of [1], could the authors report CMMD scores or other metrics for results in Fig. 3? [1] https://arxiv.org/pdf/2401.09603 Confidence: 1 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The authors adequately addressed the limitations Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Dear Reviewer LCNa, thank you for your comments. Here are the answers to your questions and comments. (1) I strongly believe the performance gains are mostly from applying GAN architecture, since D-IMF and IMF indicates essentially the same learning scheme. Therefore, it is indeed an improvement from DSBM, but the novelty of this work as a distinct SB study might not be significant from the perspective of diffusion models. It is not possible to just apply GAN architecture in the original continuous IMF framework [2] since their Markovization objective is based on bridge-matching and implies learning a drift function of SDE and not transitional densities of a discrete process. The main cause of it is that the continuous IMF framework is based on the known property that SB is a unique continuous Markovian and reciprocal process. The novelty of our work as a distinct SB study comes from our main theorem (Theorem 3.1). We show that to solve the SB problem, it is enough to find a probability distribution $\pi(x_0, x_{t_{1}}, \dots, x_{t_{N}}, x_1)$ with any number $N\geq 1$ of intermediate points, which is Markovian, discrete reciprocal and shares the marginals $p(x_0)$ and $p(x_1)$. Even $N=1$ is enough in our framework, i.e., it is enough to find a joint distribution with three variables $\pi(x_0, x_t, x_1)$ and $t \in (0, 1)$, which is Markovian and discrete reciprocal to solve SB. We believe that our main theorem opens the door to a novel family of algorithms (including ASBM) for solving SB, based on finding a discrete probability distribution $\pi(x_0, x_{t_{1}}, \dots, x_{t_{N}}, x_1)$ that is Markovian and discrete reciprocal to solve the SB problem. We also believe that this theorem may facilitate the theoretical study of this problem, including the study on the convergence speed of D-IMF and IMF algorithms since it allows us to work with a more simple object — joint probability distribution instead of continuous stochastic processes. For instance, we show that it is possible to derive closed-form Markovian and reciprocal projections for a multivariate Gaussian case in our framework. In contrast, the continuous counterpart, form solution, is derived only for a 1-dimensional case [2]. (2) This model does not always yield state-of-the-art scores for syntactic datasets (see Table 1\&2). Our algorithm does not beat all other competitors on all the setups. However, it provides the best results on most considered setups by both plan and target metrics (Tables 1 and 2). (3) While I understand this work for some extent, I do not clearly understand the motivation why do we need a sampling-based approach when we have sampling-free method such as SF$^2$M [3] and LightSB [1] models. In the limitation section, the LightSB [1] authors state that their algorithm is not designed for large-scale generative problems. Furthermore, they do not provide experiments in the image space, and they only consider image-to-image translation in the latent space of the autoencoder. Other experiments with real data include only single-cell data, which has lower dimensionality than images and does not lie on the low-dimensional manifold-like image distribution. The authors of SF2M [3] also consider only single-cell problems. Furthermore, while SF$^2$M [3] is indeed simulation-free, it theoretically guarantees convergence to SB only if samples from the ground-truth static SB solution $\pi^(x_0, x_1)$ are used for training. However, if one has access to the $\pi^(x_0, x_1)$, the problem itself is no longer unpaired domain translation since there is access to the ground-truth paired data. The authors of [3] address this problem by approximation of $\pi^(x_0, x_1)$ by minibatch Optimal Transport techniques, which seems to provide a good approximation in the considered single-cell setups but is known to have a bias growing with the dimensionality of the considered space. For instance, no experiments show that this approximation works well in the case of high-dimensional unpaired image-to-image setups. Thus, while each of these simulation-free algorithms has its advantages and works well in the setups for which they were designed, there is still no simulation-free algorithm that can demonstrate good quality on the unpaired image-to-image translation without using any autoencoders. (4) How do the authors suspect that the FID score is very low for ASBM? Following the arguments of [1], could the authors report CMMD scores or other metrics for results in Fig. 3?* Since it is hard to judge quality given only by the absolute values of FID, we compare our method with the DSBM and see that it provides better FID. As per your request, we measure the CMMD score and present the results below: \| \| $\epsilon=1$ \| $\epsilon=10$ \| \|-------------\|--------------\|---------------\| \| DSBM [2] \| 0.365 \| 1.140 \| \| ASBM (ours) \| 0.216 \| 0.231 \| We observe that CMMD scores align with FID scores presented in our work. (5) Typo L213: Denoising Denoising GANs Thank you for pointing out this. We will fix it in the final version. Concluding remarks. We would be grateful if you could let us know if the explanations we gave have been satisfactory in addressing your concerns about our work. If so, we kindly ask that you consider increasing your rating. We are also open to discussing any other questions you may have. References: [1] Alexander Korotin. Light schrödinger bridge. ICLR, 2024. [2] Shi et al. (2023) -- Diffusion Schrodinger Bridge Matching [3] Tong A. Y. et al. Simulation-Free Schrödinger Bridges via Score and Flow Matching AISTATS 2024. --- Rebuttal Comment 1.1: Comment: Dear Reviewer LCNa, We thank you for your review and appreciate your time reviewing our paper. The end of the discussion period is close. We would be grateful if we could hear your feedback regarding our answers to the reviews. We are happy to address any remaining points during the remaining discussion period. Thanks in advance, Paper authors	Summary: This paper proposes the Discrete Iterative Markovian Fitting (D-IMF) method. Specifically, this work introduces discretized reciprocal properties and Markovian processes, showing that the optimal plan matches the solution of the static Schrödinger Bridge (SB) problem. Additionally, this work demonstrate that the D-IMF procedure theoretically converges to the (static) SB solution. For the implementation of the Markovian projection, the authors employ a GAN structure (DD-GAN). Strengths: - The paper is theoretically fruitful. This work extends the reciprocal and Markovian properties into discrete sense, and also derive that the D-IMF method converges to static SB solution. This theoretical result is non-trivial and theoretically significant. - Integrating these concepts into an adversarial framework is an innovative idea, adding value to the research. Weaknesses: - The algorithm seems to be ineffective. It requires two discriminator and two generator networks, which seems to require significant computational resource as well as significant computational time. It would be beneficial to compare the computational burden (both training time and gpu occupancy) with that of DSBM. Moreover, since it employs two adversarial networks, it would be hard to stabilize. It would be valuable to show its (empirical sense) stability through various ablation studies. - The paper lacks of empirical studies. The practical experiment is only conducted on Male-Female data. Moreover, the paper lacks ablation studies. For example, the important hyperparameter such as the initial distribution setup (simple distribution produce vs minibatch matching), the number of function evaluations (NFE, DDGAN steps), and the number of phase (K) are not explored. - The FID for Male-to-Female translation is reported, but not for the reverse direction. Since bidirectional learning is being conducted, it would be valuable to report results for both directions. Moreover, there is no metric provided to measure if the images are transformed into ones that are perceptually close. It would be useful to compare c-FID or Wasserstein distance with DSBM. Minor comments: There is a typo in Line 224: the term $q(x_{t_n}\|x_{t_{n-1}})$. Technical Quality: 3 Clarity: 3 Questions for Authors: - Can the authors provide a comparison of the computational burden between your method and DSBM, particularly in terms of time and resource usage? - Is the time discretization handled as like DDPM style or Uniformly? - Did you use any pretrained model (e.g. pretrained DSBM) on I2I task? Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The limitation is adequately discussed in the paper. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Dear Reviewer RgPk, thank you for your comments. Here are the answers to your questions and comments. (1) Computational burden and stability study. As requested, we provide a study on the effectiveness of ASBM and compare it with the DSBM. Number of parameters. Our ASBM generator has about 42 million parameters, while each discriminator has 27 million. The generator of DSBM has 38 million parameters. Thus, generators have similar capacities. Training time. We mentioned (lines 714-716) that for Celeba setups, our ASBM uses 7 days of training on a A100 GPU, while the DSBM uses 5 days of training. The time is comparable since both methods use the same number of IMF and D-IMF iterations. Please note that we provide an analysis of ASBM (ours) and DSBM algorithms in Appendix E, where we show that additional iterations only slightly change the results. Inference time. We measure the inference time of both ASBM (ours) and DSBM algorithms on the same hardware with one A100 GPU. We measure the mean and standard deviation over 16 runs. For a batch of 100 images, ASBM requires about 842 ms (std 97 ms), while DSBM requires 33870 ms (std 47 ms). Thus, our algorithm provides up to 40x speedup compared to DSBM. GPU memory consumption. On the Celeba setup, our algorithm requires about 25 GB of GPU for training with a batch size of 32 and about 12 GB on the inference stage to translate a batch of 100 images. Meanwhile, DSBM requires 34 GB of GPU for training with batch size 32 and about 26.7 GB on the inference stage for a batch of 100. Thus, our algorithm utilizes significantly less GPU memory. Stability of training. To show that our procedure is stable, we provide the plot of FID during the training of all D-IMF iterations in Figure 3 of the attached pdf. On the plot, we provide FID vs the number of generator gradients updated during the training. We highlight the starts of each D-IMF iteration by the vertical lines. We observe stable decreases of FID. (2) Lack of empirical and ablation studies. The number of phases K. We provide an analysis of D-IMF/IMF iterations (K) in Appendix E.1. of our work. Independent vs minibatch coupling. As per request, we provide a study on running ASBM with different coupling. We provide the additional results for the Colored MNIST setup with $\epsilon=10$ (which we discuss in Appendix C.3 of our paper). In Figure 1 of attached pdf, we provide qualitative generation results for our ASBM model with independent and minibatch couplings after 3 D-IMF iterations, which we used in our work for this setup. We also provide FID values in Table 1 of attached pdf. We see comparable visual quality as well as similarity for both results; the FID metric is slightly better for minibatch case. Study on different NFE. As requested, we present the study's results on different NFE of our ASBM model. In our study, we use our ASBM model trained with $4$ steps for Celeba male to female with $\epsilon=1.0$. We test this model with different numbers of NFE $\in [1, 2, 3, 4, 8, 16, 32]$. In all the cases, we use a uniform schedule. (See answer 4 for details). We present qualitative results of generation for several inputs in Figure 2 of the attached pdf. We also present the FID values computed on the test set and average $L_2$ cost $c(x_0,x_1) = \frac{\|\|x_0-x_1\|\|^2}{2}$ between the input image $x_0$ and generated image $x_1$ to assess similarity in Table 2 of the attached pdf. Interestingly, our model with $\text{NFE}=3$ provides almost the same FID value as for $\text{NFE}=4$, which we use at the training, but significantly lower $L_2$ cost. Training with different NFE. Since the time of the rebuttle and our resources are limited we train ASBM with $NFE=2$ and $NFE=8$ with $K=2$ D-IMF iterations and $\epsilon=1.0$ using the same procedure as before. We present samples in the Figure 5 together with ASBM model with $NFE=4$ after $K=2$ D-IMF iteration trained before. Male-to-female metrics: \|\|NFE=2\|NFE=4\|NFE=8\| \|-\|-\|-\|-\| \|FID\|11.829\|16.08\|29.58\| \|LPIPS\|0.214\|0.253\|0.241\| We observe better results for lower NFE, possibly because the model needs to learn fewer transitional distributions. We will add all the results to the final version. (3) The FID of the reverse direction. Thank you for this suggestion. The values are given below. \|\|$\epsilon=1$\|$\epsilon=10$\| \|-\|-\|-\| \|DSBM [2]\|24.06\|92.15\| \|ASBM (ours)\|16.86 \|17.44\| Thus, the FID values for the reverse direction show the same behavior as for the forward direction. (4) Measurement of perceptual quality As requested, we measure perceptual similarity between input and translated images using standard LPIPS metric [1] (as used in DSBM). For our Celeba male-to-female setup, we measure LPIPS between input and translated images from the test. We present the results below (the lower the better): \|\| $\epsilon=1$ \| $\epsilon=10$ \| \|-\|-\|-\| \|DSBM [2]\|0.246\| 0.386\| \|ASBM (ours)\|0.242\|0.294\| We observe almost the same similarity in the case of $\epsilon=1$ and better similarity for ASBM (ours) in the case of $\epsilon=10$. We will add these results in the final version. (5) Time discretization. We use uniform time discretization in all our experiments, i.e., for the number of inner times points $N$, we use time discretization $t_{n} = \frac{n}{N+1}$ for $n \in [0, N+1]$. (6) Did you use any pretrained model? No, we do not use any pretrained models in our experiments. Concluding remarks. We would be grateful if you could let us know if the explanations we gave have been satisfactory in addressing your concerns and questions about our work. If so, we kindly ask that you consider increasing your rating. We are also open to discussing any other questions you may have. References: [1] Zhang R. The unreasonable effectiveness of deep features as a perceptual metric. CVPR, 2018. [2] Shi Y. Diffusion Schrödinger bridge matching. NeurIPS, 2024. --- Rebuttal Comment 1.1: Title: Thank you for the response Comment: I appreciate authors for clarification and for the additional ablation studies. I would like to raise my score to 6.	Summary: The paper extends the recently proposed Schrödinger Bridge method, DSBM or IMF, to a discrete-time setup. This extension is non-trivial, requiring appropriate notation for discrete reciprocal and Markovian projections. By leveraging the structure of Brownian bridges used in the original IMF, the paper achieves efficient sampling and inference processes. The discrete-time formulation also establishes a natural connection to other generative model classes, such as GANs. Experiments were conducted on low-dimensional Gaussians and unsupervised image-to-image translation. Strengths: - The discrete-time construction of IMF is an elegant piece derived from the DSBM, which heavily relies on Brownian bridges. The analytic solutions for Gaussians may also be of interest to readers from other domains. - The connection to DD-GANs is both straightforward and clever. It's exciting to see how different classes of generative models are starting to overlap and combine, leveraging the strengths of each approach. Weaknesses: - I enjoyed reading the majority of the paper—except, perhaps oddly, the paper title. Over 85% of the main technical contributions (Sec 3) stem from the construction of the discrete IMF formulation. The concept of "adversarial" appears only as one (of many plausible) implementation of Eq (15). I feel like the "discrete" aspect isn't highlighted enough, or at all, in the title. This is, of course, just a personal comment rather than a criticism. - In L220, the non-saturating GAN loss should be provided in the main paper rather than being postponed to the Appendix. Technical Quality: 3 Clarity: 3 Questions for Authors: - The notions of $T$ and $M$ are slightly confusing. For example, In L73 and L76, both represent Markovian processes. Is there a typo? Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: Limitations were addressed in Appendix A. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Dear Reviewer xGf5, thank you for your comments. Here are the answers to your questions and comments. (1) I enjoyed reading the majority of the paper—except, perhaps oddly, the paper title. Over 85\% of the main technical contributions (Sec 3) stem from the construction of the discrete IMF formulation. The concept of "adversarial" appears only as one (of many plausible) implementation of Eq (15). I feel like the "discrete" aspect isn't highlighted enough, or at all, in the title. This is, of course, just a personal comment rather than a criticism. The title of the work which introduces DSBM algorithm is "Diffusion Schrödinger Bridge Matching". Our work is based on it but, at the same time, proposes to use adversarial training as a current main competitor of diffusion models in the field of generative models. To highlight both the relation with the prior work and the usage of adversarial training in our approach, we decide to use the title "Adversarial Schrödinger Bridge Matching". (2) In L220, the non-saturating GAN loss should be provided in the main paper rather than being postponed to the Appendix. Thank you for this suggestion. We initially placed the non-saturating GAN loss in the Appendix to keep the main text focused and avoid introducing technical details too early. Furthermore, the non-saturating GAN loss is rather standard approach in GANs, so we did not pay much attention to it. However, we agree that it would be beneficial to mention the non-saturating GAN loss in the main paper for clarity. We will move it to the main text in the final version and refer readers to the Appendix for a more detailed description of our adversarial procedure. (3) The notions of T and M are slightly confusing. For example, In L73 and L76, both represent Markovian processes. Is there a typo? In this context, the process $T$ and $M$ are the same Markovian process. We will replace $T$ with $M$ in the final version. Thank you for mentioning it. Concluding remarks. We would be grateful if you could let us know if the explanations we gave have been satisfactory in addressing your concerns and questions about our work. We are also open to discussing any other questions you may have. --- Rebuttal Comment 1.1: Comment: Dear Reviewer xGf5, We thank you for your review and appreciate your time reviewing our paper. The end of the discussion period is close. We would be grateful if we could hear your feedback regarding our answers to the reviews. We are happy to address any remaining points during the remaining discussion period. Thanks in advance, Paper authors --- Rebuttal Comment 1.2: Comment: I thank the authors for the reply. I've decided to keep my score.	Summary: In this paper, the authors study the Schrodinger Bridge problem and propose an improvement over the Diffusion Schrodinger Bridge Matching (DSBM) methodology [1, 2]. In particular, they propose a discrete counterpart formulation of DSBM. Instead of relying on stochastic processes, they rely on a discrete-time version of the Markovian and reciprocal projections which are the key components of DSBM. By doing so, they have a better control on the number of steps needed in DSBM. They next leverage advances in the field of diffusion models to reduce the number of stepsizes needed in order to solve the Schrodinger Bridge. In particular, they focus on larger jumps using the approach of Denoising Diffusion GAN (DD-GAN), introduced in [3]. The method is illustrated on translation tasks on the Celeba dataset. [1] Shi et al. (2023) -- Diffusion Schrodinger Bridge Matching [2] Peluchetti (2023) -- Diffusion Bridge Mixture Transports, Schrödinger Bridge Problems and Generative Modeling [2] Xiao et al. (2021) -- Tackling the Generative Learning Trilemma with Denoising Diffusion GANs Strengths: * The paper is overall clearly written and easy to follow. It relies on the notions of Markovian and reciprocal projections that were already introduced in [1]. All the required notions are properly introduced. * I enjoy reading the full description of the DSBM algorithm in discrete time. I agree that this should allow for 1) easier spreading of DSBM-related methodology 2) more flexible algorithm (like the introduction of GAN jumps as proposed). * The experimental results seem to compare favorably compared to DSBM (more on that later). [1] Shi et al. (2023) -- Diffusion Schrodinger Bridge Matching Weaknesses: * Part of the theory was already done in [1]. Especially the discrete Markovian projection was already identified as the minimizer of the Kullback-Leibler divergence in [1, Appendix E]. I think the claims of novelty of the paper regarding the introduction of the discrete scheme should be tamed down. * I am not clear regarding what is the purpose of the Gaussian study. I understand that the authors use it in their experimental section (Section 4.1) to study the convergence of their algorithm but I think Section 3.4 is distracting the reader from what I consider to be the main points of the paper which is 1) full discrete study of DSBM 2) GAN jumps. Section 3.4 could easily be considered in the Appendix which would leave more room for additional experiments. * The claim of exponential convergence should be tamed down. Reading the paper it seems like this is proven in the current paper (I am talking especially about the bold "exponential rate of convergence" in l.294 which can be misleading). To my understanding this is only experimentally shown. * There is something quite striking in Figure 3. (for example see the last row of (d) and (f)). While the quality of ASBM is better (by the way, one of the reason the FID score is so high for DSBM must be because of the remaining noise in the output samples, an easy way to remove this noise would be to consider a deterministic last step as a postprocessing as is routinely done in diffusion models, see [2] for instance), it seems that the diversity is much lower than DSBM. I would like to see a proper investigation of this phenomenon which is also reported in the adversarial distillation of diffusion models. According to [3], there is an incompressible trade-off between high-NFE/good diversity and low-NFE/low-diversity. [1] Shi et al. (2023) -- Diffusion Schrodinger Bridge Matching [2] Jolicoeur et al. (2020) -- Adversarial score matching and improved sampling for image generation [3] Dieleman (2024) -- The paradox of diffusion distillation Technical Quality: 3 Clarity: 3 Questions for Authors: * I understand that the main goal of the author is the speed-up of DSBM-like algorithms. However, why choose DD-GAN? This doesn't seem to me like the obvious candidate for speeding up DSBM. Other techniques like distillation (adversarial distillation if one really wants to use GANs [1, 2]) or consistency models seem like potential better candidate. If the finetuning strategy is what the authors want to avoid, consistency models can be trained from scratch [3, 4]. * Some typos: * l.280 "Schrodigner" --> "Schrodinger" [1] Xu et al. (2023) --UFOGen: You Forward Once Large Scale Text-to-Image Generation via Diffusion GANs [2] Sauer et al. (2023) -- Adversarial Diffusion Distillation [3] Song et al. (2023) -- Consistency Models [4] Song et al. (2023) -- Improved Techniques for Training Consistency Models Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The limitations are discussed in the Appendix A. However, the authors are quick to dismiss these limitations. For example, regarding the adversarial training "While we mention this aspect, we do not treat it to a be a serious limitation." I think there are serious problems regarding adversarial training regarding the training (suffer from training instabilities) and the results themselves (less diversity). These issues are usually reported in the field of adversarial distillation of diffusion models, see [1] for instance. I think this is doing a disservice to the paper and the community by trying to minimise them instead of exposing them for what they are. [1] Dieleman (2024) -- The paradox of diffusion distillation Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Dear Reviewer xtGA, thank you for your comments. Here are the answers to your questions and comments. (1) Part of the theory was already done in [1]. ... Indeed, the authors of [1] analyze the discrete-time Markovian projection and show that it converges to continuous-time projection in certain limiting cases. We cite this result in line 260. We will add additional citations and discussion in Section 3.3 after defining Markovian projection to highlight some aspects that have already been introduced in [1]. Please note that our Proposition 3.5 on KL-minimization extends the results from [1, Appendix E]. The authors of [1] considered the Markovian projection for a mixture of Markovian bridges. In turn, in our Proposition 3.5 we consider arbitrary distribution $\pi(x_0, x_{t_{1}}, \dots, x_{t_{N}}, x_1)$ without any assumptions on its conditional distribution $\pi(x_{t_{1}}, \dots, x_{t_{N}}\|x_0, x_1)$. It makes the proof technically more complex but provides a more general result. (2) ... the purpose of the Gaussian study. ... There are two purposes: to experimentally study the rate of convergence and to demonstrate that a closed-form solution for the multivariate Gaussian case can be derived within the discrete-IMF framework. In the final version, we will shorten Section 3.4 by moving detailed technical definitions (such as matrices $U$ and $K$) to the Appendix but retain the key points in the main text. (3) The claim of exponential convergence should be tamed down. ... We agree that the phrasing in line 294 could be misleading. This observation is based solely on our experimental results, and the whole discussion on convergence rate is placed inside the experimental section (Section 4), while all of our theory is placed in Section 3. We also directly mentioned that there is no theoretical proof in the limitation section (lines 465-467). To avoid possible misunderstanding, we will revise the bolded text. (4) ... remove this noise ... consider a deterministic last step as a postprocessing ... We use the original published code from the DSBM authors [1] to ensure a fair comparison. In this code, noise is not added at the last sampling step. As you requested, we additionally used the drift function for the last time-moment $t=0.99$ to add an extra denoising step at the final step of the sampling process. It indeed removes the remaining noise, (see the samples in Figure 4 of the attached pdf). For the Celeba setup with $\epsilon=1.0$, we observe the improvement of the FID metric from $37.8$ to $29.7$. We will add this additional result in the experimental section. (5) ... it seems that the diversity is much lower than DSBM. I would like to see a proper investigation of this phenomenon ... As requested, we provide a study on the diversity of images produced. We measure the diversity of images produced by DSBM and ASBM on the Celeba setup by utilizing the LPIPS diversity as was done in [3, Table 1]. We take a subset of $500$ images from the test part of the Celeba dataset. We sample a batch of generated images of size $16$ for each input image, compute the average distance between all possible pairs of these images, and average these values over all inputs. We present the results below for DSBM and ASBM and different values of the coefficient $\epsilon=1$ and $\epsilon=10$. \|\| $\epsilon=1$ \| $\epsilon=10$ \| \|-------------\|--------------\|---------------\| \|DSBM [1]\| 0.1047\| 0.1909\| \|ASBM (ours) \| 0.0933\| 0.1878\| Indeed, the LPIPS diversity is lower for ASBM. However, without a known ground truth for diversity, it is difficult to determine definitively whether ASBM provides insufficient diversity or if DSBM produces too much. We will include these findings in the final version of the paper and discuss this trade-off. (6) .... However, why choose DD-GAN? ... The mentioned adversarial distillation techniques [1,2] are based on tractable forward process in diffusion models for simulation-free sampling, which is not feasible for the unpaired Schrödinger Bridge (SB). Additionally, these methods require an already trained model for distillation, whereas our approach does not need a pretrained diffusion model. Regarding consistency models, it is unclear how to use them in an unpaired image-to-image setup. Works [3, 4] do not address this. The work [3] discusses generative models and zero-shot translation with known degradations, applicable only to specific tasks like colorization. Similarly, [4] focuses on generative modeling. While consistency models can potentially accelerate arbitrary ODEs, the Schrödinger Bridge (SB) problem's solution is an SDE, which makes it challenging to use consistency models. (7) ...the authors are quick to dismiss these limitations. ... (Appendix A) We understand that adversarial training is a limitation. We intended to say that we use the DD-GAN approach, designed to address this limitation to some extent (mode coverage [2, Section 5.3], training stability [2, Appendix D]). Furthermore, to show that our DDGAN-based ASBM procedure is stable, we additionally provide the plot of FID during the training of all D-IMF iterations in Figure 3 of the attached pdf. We provide FID vs the number of generator gradients updated during the training. We highlight the starts of each D-IMF iteration by the vertical lines. We observe the stable decrease of FID over the generator gradient update steps. We will remove the phrase "we do not treat it to a be a serious limitation" in the final version. Concluding remarks. We would be grateful if you could let us know if the explanations we gave have been satisfactory in addressing your concerns about our work. If so, we kindly ask that you consider increasing your rating. We are also open to discussing any other questions you may have. References are the same as you used in the corresponding weaknesses and questions. --- Rebuttal Comment 1.1: Comment: Dear Reviewer xtGA, We thank you for your review and appreciate your time reviewing our paper. The end of the discussion period is close. We would be grateful if we could hear your feedback regarding our answers to the reviews. We are happy to address any remaining points during the remaining discussion period. Thanks in advance, Paper authors	Rebuttal 1: Rebuttal: Dear reviewers, thank you all for taking the time to review our paper and for your thoughtful feedback. We are delighted that you found our work to be well-written and that it effectively introduces key concepts (xtga, LCNa). It is encouraging to hear that you see it as theoretically fruitful (RgPk), that it broadens our understanding of IMF (LCNa), and that it introduces a straightforward and clever connection between IMF and DD-GANs (xGf5). We are also pleased that you believe our work allows for easier spreading of DSBM-related methodology and developing more flexible algorithms (xtga). Please find the answers to your questions below. Please note that we have added tables and figures in the attached pdf to support our responses to the reviewers xtGA and RgPk. Pdf: /pdf/81e1771cdac3a99c16fe95dedd81ba2dfcd2187b.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
ACES: Generating a Diversity of Challenging Programming Puzzles with Autotelic Generative Models	Accept (spotlight)	Summary: The paper presents Autotelic CodE Search (ACES), a method for generating diverse and challenging Python programming puzzles using state-of-the-art generative models. Inspired by Quality-Diversity, ACES aims to automate the problem generation process by optimizing for both diversity and difficulty. ACES iteratively prompts an LLM to generate puzzles by using previously generated problems as in-context examples. The generated puzzles are more diverse and challenging than those produced by baseline methods and existing benchmarks, as evaluated across 11 state-of-the-art code LLMs. Strengths: - The presentation, writing and clarity of the paper are great. - The method creatively combines evolutionary algorithms (especially Quality-Diversity algorithms) with LLMs to generate programming puzzles that are both diverse and challenging. - The proposed approach is simple and effective at generating a diversity of challenging puzzles. Experiments showed that ACES generates problems that are both more diverse and more challenging than the ones generated by existing generative approaches or the ones found in human-curated benchmarks. Weaknesses: - My main concern is about the contribution. What are the practical applications of this framework? Why is it valuable to generate a diversity of challenging puzzles? Demonstrating some downstream tasks would be helpful to justify the importance of generating diverse and challenging puzzles. For example, showing how fine-tuning a model on the newly generated data can improve performance would provide a clear motivation. - The paper states, "Puzzles for which no solution is found are considered invalid and are discarded." I believe this is a limitation because the primary goal of generating new data is likely to enhance training. By only considering puzzles that the target LLM solver can solve, we limit the difficulty of the generated puzzles. This, in turn, restricts the potential benefits of using this new data for training and improving models. Technical Quality: 4 Clarity: 3 Questions for Authors: - What are the practical applications of this framework? Why is generating diverse and challenging puzzles an important problem to address? - I am uncertain if the difficulty measure is appropriate. I would expect the difficulty measure to be very close to 0 for problems that the target LLM solver cannot solve and very close to 100 for problems it can solve, with almost nothing in-between. Can you provide more details on this aspect? - What does the shaded area represent on the graphs? - I don't understand Figure 3(f). The x-axis represents fitness rescaled between 0-100, but what does the color signify? - OMNI-EPIC [1] utilizes a task archive in a manner similar to your puzzle archive. I believe you should cite this paper to acknowledge the related work appropriately. [1] OMNI-EPIC: Open-endedness via Models of human Notions of Interestingness with Environments Programmed in Code # Minor Corrections L167: There is an inappropriate exclamation mark in "Appendix Section! A.2." Confidence: 3 Soundness: 4 Presentation: 3 Contribution: 2 Limitations: Yes, the authors adequately addressed the limitations. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank Reviewer ESVE for their review, and especially for appreciating the clarity of the paper, and the simplicity and effectiveness of the method. We hope to be able to convince them of the promise of the method for practical applications. > What are the practical applications of this framework? * Generality of the framework. We understand that the formulation of our aims in this paper might seem a bit general (creating sets of diverse and difficult problems) but the applications are quite promising in our opinion! First, ACES transfers to any domain where solutions to problems can be exactly evaluated and where LLMs already have knowledge of several categories of problems (as also noted by Reviewer qqHU). This includes important tasks like formal math or RL environments that can described with code. * Creating benchmarks. Within the domain we have chosen (programming puzzles), the target task we have in mind for ACES is creating LLM evaluation sets. There are other considerations when creating a benchmark than difficulty and diversity, but getting these right is a necessary condition for it to be useful. Distilling our generated sets into trusted benchmarks usable by the community would require some additional curation, but we believe it to be well within reach. * Creating finetuning data. In our additional results (Figure 1(d)) we present results of finetuning models with our generated data (see also general response). On tests sets created with a mixture of StaticGen and ACES-ELM data, finetuning on (distinct) ACES-ELM generated data yields strong and consistent improvements compared to finetuning on (distinct) StaticGen-generated data. This is good evidence of increasing capabilities when finetuned on our data. * Generating open-ended tasks is an important goal in itself. This is precisely the aims of open-ended exploration algorithms (such as OMNI-EPIC you mention later). ACES belongs to that line of works, applies it to an important domain, and contributes algorithmic improvements. Reviewer LkwK also notes that this is an important fundamental topic in itself, beyond the practical applications. > [...] I believe this is a limitation because the primary goal of generating new data is likely to enhance training. We agree! This is a limitation of our current difficulty measure and have added additional discussion in the Limitations section of the paper. This kind of difficulty metric is used to train open-ended agents in other settings. For instance, in Goal-GAN [1], a goal-conditioned RL agent targets position goals that are difficult but solvable, since unreachable positions usually give no feedback at all. This approach is widespread in intrinsically-motivated RL [2, 3]. In the classic case of self-play, the opponent provides feedback by being neither too easy nor too hard to beat by construction. For ACES to implement similar dynamics (and lead to the discovery of puzzles that are truly unsolvable from the point of view of the solver we start with yet solvable in general) one should finetune the solver as the data gets generated. This would not require modifying the difficulty metric we use. We have added additional discussion in the Discussion section. ### Questions > I don't understand Figure 3(f). You are right that this figure could be clearer. This is a figure representing the distributions of difficulties, in discrete fitness bins, for each method, at the end of the generation process. The color represents the number of puzzles whose difficulty falls into each bin (color histogram). The takeaways from this figure are that these distributions are quite peaked towards 0 and 100 and that ACES and ACES-ELM have bigger peaks towards 100 than StaticGen and ELM. > I am uncertain if the difficulty measure is appropriate. [...] Can you provide more details on this aspect? We first recall that high difficulty/fitness (close to 100) corresponds to hard problems (solved once out of 50), and difficulty close to 0 corresponds to easy problems (solved 50 times out of 50). The motivation for this metric comes from observations around pass@k. Pass@k was introduced in the Codex paper [4] and measures the proportion of puzzles which have at least 1 solution found in k solver attempts. It has become a standard measure for evaluating code (or math) models. The interesting part is that as you increase k (with nonzero temperature), pass@k continues increasing logarithmically with k (see [5], Figure 7 for instance). Repeatedly sampling from your LLM is usually an effective, but costly, way of getting solutions to hard problems [6, 7]. To recap: puzzles do not neatly fall in solvable/unsolvable categories; some of them are solved only once every 50 attempts on average. These are the kinds of puzzles we want to generate. In our experiments, as outlined in our previous comment, the difficulty distribution is close to 0 for the StaticGen dataset and for ACES a second peak around 100 appears and grows. Of course, we are open to suggestions for improvement of the difficulty metric. > What does the shaded area represent on the graphs? They represent standard deviation, each experiment is repeated 3 times with different seeds. > OMNI-EPIC [1] utilizes a task archive [...] Of course! Thanks for pointing this out. We have added the reference. [1] Automatic Goal Generation for Reinforcement Learning Agents, Florensa et. al. 2017 [2] Learning with AMIGo: Adversarially Motivated Intrinsic Goals, Campero et. al. 2020 [3] Intrinsic Motivation and Automatic Curricula via Asymmetric Self-Play, Sukhbaatar et. al. 2017 [4] Evaluating Large Language Models Trained on Code, Chen et. al. 2021 [5] Language Models Can Teach Themselves to Program Better, Haluptzok et. al. 2022 [6] Mathematical discoveries from program search with large language models, Romera-Paredes et. al. 2023 [7] Large Language Monkeys: Scaling Inference Compute with Repeated Sampling, Brown et. al. 2024 --- Rebuttal Comment 1.1: Comment: Thank you for your detailed rebuttal. I found your answer and the main rebuttal PDF helpful. Overall, I think that the paper is making a modest, yet interesting contribution. Most importantly, the paper is technically solid and the claims are appropriately matched to the paper's contribution. In the end, the community would probably benefit and learn from this paper. Given these considerations, I am happy to increase my score.	Summary: The authors propose Autotelic CodE Search (ACES) to generate programming puzzles, considering diversity and difficulty, borrowing ideas from intrinsic motivation and evolutionary search, relying on the assistance from LLMs for problem representation, skill label generation, diversity characterization, difficulty evaluation, and puzzle generation. The authors conduct experiments to study quality of LLM-generated skill labels, and compare diversity and difficulty of the generated puzzles with existing methods and benchmarks. Strengths: + generate diversified and challenging programming puzzles + borrow ideas from intrinsic motivation, in particular, the autotelic property, and evolutionary search, in particular, Map-Elites, an evolutionary quality-diversity (QD) method + conduct experiments studying quality of LLM-generated skill labels, and comparing with existing methods and benchmarks Weaknesses: - rely too much on LLMs - follow a questionable approach - overclaim I am aware there are quite some papers following the framework of "self-generation, self-evaluation, and self-improvement, relying on one or more LLMs", some of them in the name of LLM-based agent or agentic AI. This approach has a fundamental issue: no current LLM is perfect, so LLMs may make mistakes, and usually there is no mechanism to improve current LLMs in such framework. As a result, I vote to reject the paper, although it has merit, in particular, the idea for prompting diversity in generating programming puzzles and decent experimental results. Technical Quality: 2 Clarity: 3 Questions for Authors: Line 2, "We propose a method that aims to automate this process by harnessing the power of state-of-the-art generative models to produce a diversity of challenging yet solvable problems, here in the context of Python programming puzzles." The proposed approach relies on LLMs for problem representation, skill label generation, diversity characterization, difficulty evaluation, and puzzle generation. The proposed approach does not provide a mechanism to improve the current imperfect LLMs, so that it does not close the loop. Line 30, "It would provide the necessary curriculum for open-ended learning machines [Colas et al., 2022] and may be a key component of automated scientific discovery [Grizou et al., 2020, Etcheverry, 2023]." Similar to above, the feedback loop is not closed, so it is an over-claim. This can be estimated by computing the empirical difficulty of a puzzle for a particular 39 solver: out of 50 attempts, the solver should solve the problem at least once (solvability) but as rarely 40 as possible (difficulty). Line 44 "The standard approach for problem generation simply queries pretrained generative models with few-shot examples or specific instructions [Haluptzok et al., 2022, Honovich et al., 2023, Gunasekar et al., 2023]." Why is it the standard approach? There are some papers working this way does not make it the standard way. Line 134, "Both datasets are pre-filtered to examples shorter than 1024 tokens to accommodate for limited context windows in LLMs." This is an unnecessary limitation due to relying on LLMs. Line 147, "Puzzles for which no solution is found are considered invalid and are discarded." This is problematic, at least, not ideal. Line 202, "If the puzzle is not solved by the solver model in 50 attempts, it is considered unsolvable and discarded." It is the limitation of current LLMs, and the authors do not propose a mechanism to overcome it. Line 150, "this difficulty-based metric measures a ground-truth objective: how hard a given puzzle is for a target LLM solver" It is not ground-truth: LLM solvers are not perfect, so some measure wrt an LLM is not a ground-truth. Line 151, "Our experiments found that this difficulty measure mostly transfers across models: a puzzle that is harder for one model is often harder for others (see Section 4.4)." This may not say much about transferability, since most LLM models were built with similar methods. Line 164, "We sample our 20 tags from a larger list generated by an LLM (GPT-4-0125)" Use an imperfect LLM, namely, GPT-4, as reference has inherent limitations. Line 194, "to drive discovery of puzzles with novel skill combinations, we rely on the LLM recombining elements from puzzles close to the target cell along with very often selecting target cells without any representatives." Again, limitations of current LLMs. Line 335, "We expect that progress along the three lines can be made by harnessing the increasing capabilities of future language models and will automatically translate into higher performing autotelic generative models of problems." It is not reasonable to postpone the development of key components of a proposed approach to something the authors do not have control of, in particular, "future language models". Line 354, "In artificial intelligence, one could envision a self-play loop where a learning agent iteratively generates a diversity of problems maximizing its current learning progress (quality metric), then trains on them to augment its competence [Sukhbaatar et al., 2017, Silver et al., 2017, Colas et al., 2022]." This is an overclaim and it is misleading. It replies on imperfect LLMs and do not attempt to improve them. Confidence: 4 Soundness: 2 Presentation: 3 Contribution: 2 Limitations: The authors do not discuss enough the limitations of reliance on imperfect LLMs, and do not propose to improve imperfect LLMs. Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for their comments and hope to be able to convince them that our assumptions are sound. Reviewer NuHw seems to reject the possibility of leveraging LLMs in any kind of systems, based on the fact that LLMs are sometimes wrong. That LLMs are not perfect at any of the tasks we use them for is of course true, but that does not prevent us from using them in a useful way (here to build diverse sets of puzzles to evaluate itself and other models). For each of the components we use LLMs for, they clearly outperform other available options: * For puzzle generation, other program synthesis methods would hardly give interesting, human-relevant programming puzzles; * For measuring diversity (creating niches for our QD algorithm), we tried using voronoi tessellations as is usually done in high-dimensional Map-Elites [1], but it works less well than the skill labels using the LLM (compare ELM-CVT with ELM, Figure 3) and it is less interpretable. The skill labeling performance itself is not so bad, see responses to reviewer qqHU, and section 4.2. * For measuring difficulty we need to use LLMs as solvers, since that’s the measure of difficulty we want to measure (and it is linked to pass@k, the measure of success on coding datasets); In addition to these considerations, we add checks to ensure our generated puzzles make sense (rejecting puzzles with no solution, see also Section 3.3). We use several measures of diversity, and difficulty with respect to different models, to make sure our evaluations are sound. Can the reviewer provide a more specific description of LLM limitations that would make our approach unsound? What alternative could be considered to implement the puzzle generation, measure diversity or difficulty here? > overclaim The reviewer cites excerpts of our motivation and conclusion and seems to consider we claim these as parts of our contribution, which they are not. Our contributions are listed in the last paragraph of the intro, at the end of the abstract, and at the beginning of our conclusion. ### Questions We reply to the reviewer’s comments here, but some of them are not really questions. It would be helpful and constructive for the reviewer to be more specific in their remarks; often the perfectness of LLMs is attacked, and we agree these models are far from perfect; however if alternative methods or fields or studies were mentioned it would help us write more targeted responses. > The proposed approach does not provide a mechanism to improve the current imperfect LLMs, so that it does not close the loop. We do not propose to directly improve LLMs in this paper; not every paper needs to directly improve LLM state of the art. We simply present methods for generating diverse and challenging datasets, and argue that they could be used to evaluate LLMs in the future. Evaluating LLMs on challenging datasets is part of the process leading to their improvement. (and we confirm by the way that combining evolutionary methods with LLMs is fruitful, as was demonstrated in FunSearch [2] or QDAIF [3] among others). Our additional experiments demonstrated that our method significantly enhances the performance of current "imperfect LLMs." The LLM fine-tuned on our approach-generated archive outperformed the base model by a substantial margin, even surpassing larger models. > Similar to above, the feedback loop is not closed, so it is an over-claim. This is part of the motivation of the paper (beginning of the introduction), not its contributions. > Why is it the standard approach? There are some papers working this way does not make it the standard way. It is the standard approach insofar few-shot prompting is a common method for generating domain-specific data with LLMs. If you have another idea/method in mind, we would be interested in hearing about it. > [on discarding unsolvable puzzles] This is problematic, at least, not ideal. We agree that this is less than ideal (see also our response to reviewer ESVE) but we have no principled method for determining whether a puzzle is solvable without generating a solution ourselves. We are of course very open to additional suggestions here. > This may not say much about transferability, since most LLM models were built with similar methods. We report an observation here. This is also confirmed in our new experiments. As for non-LLM solvers, we do not know but consider it interesting to correlate difficulties of puzzles across solver types (and humans). > [on generating the initial list of skills] Use an imperfect LLM, namely, GPT-4, as reference has inherent limitations. As always we agree. That is why we filter the set afterwards to make sure the skills make sense. The alternative is to generate the list ourselves, based on puzzle categories in algorithm books and programming contests. In practice both methods (we tried both) led to very similar lists. > "to drive discovery of puzzles with novel skill combinations, we rely on the LLM recombining [...]" Again, limitations of current LLMs. Could you be more specific? > It is not reasonable to postpone the development [...] This is not what we meant in L338 (conclusion). We stated that the approach probably scales as the LLMs become better (this is a good property of the method). We confirm this in our new experiments. > "In artificial intelligence, one could envision a self-play loop [...]” This is an overclaim and it is misleading. It relies on imperfect LLMs and do not attempt to improve them. This is one of our last paragraphs and is future work/discussion! We do not claim to instantiate a self-play loop in this paper. [1] Using Centroidal Voronoi Tessellations to Scale Up the Multi-dimensional Archive of Phenotypic Elites Algorithm, Vassiliades et. al. 2016 [2] Mathematical discoveries from program search with large language models, Romera-Paredes et. al. 2023 [3] Quality-Diversity Through AI Feedback, Bradley et. al. 2023 --- Rebuttal 2: Comment: Thanks the authors for the detail rebuttal. I admit there are merits in the submission, and I am aware there are many papers similar wrt (unreliable) LLM-based methods. However, I am not convinced. There are two fundamental issues with the submission: 1) fully rely on an imperfect LLM; 2) rely on problematic method (evaluation of pass@k). 1) As in my original review: I am aware there are quite some papers following the framework of "self-generation, self-evaluation, and self-improvement, relying on one or more LLMs", some of them in the name of LLM-based agent or agentic AI. This approach has a fundamental issue and is misleading: no current LLM is perfect, so LLMs may make mistakes, and usually there is no mechanism to improve current LLMs in such framework. Line 247 "Puzzle generation, solution generation, description generation, and puzzle labeling are all implemented with the state-of-the-art open source model Llama 3 70B, quantized in 4 bits, with a temperature parameter of 0.8." All these components are based on an imperfect LLM, so all of them are not fully reliable. 2) How to evaluate "pass" (in pass@k)? How to guarantee the correctness of the evaluation? In the current popular approach, like HumanEval, if a solution passes several test cases, then it is a pass. This is problematic: Testing only can not guarantee the correctness of a piece of code. Formal verification is required. This is not a reliable evaluation. As a result: no guarantee of the quality of generated puzzles, some of them may be wrong. A question from reviewer qqHU: "How does the author ensure the correctness of the generated test program $f$"? Can authors ensure the correctness of the generated test program? The binary answer should be NO. With LLMs, it is best effort. From authors' general rebuttal: "Reviewer NuHw rejects the approach on the basis that it is built on LLMs, but we note that generating challenging evaluation sets is an instrumental application to create better LLMs in the future." This is both true and false. In a top AI venue like NeurIPS, we want to see papers with reliable method / results, without fundamental issues. The current submission has a fundamental issue: reliance on an imperfect LLM. FunSearch and AlphaGeometry are different: they have reliable verifier in the loop. This is a problem for the community, in particular, those working on LLM-based method. Top AI venues like NeurIPS should not publish more such papers without fully reliable methods. This is misleading. --- Rebuttal 3: Comment: We thank the reviewer for their reply and we are happy they find “there are merits in the submission”. Their first concern is on building evaluations using LLMs to generate, label, and compute difficulty since LLMs can make mistakes. Their other concern seems to be on the computation of the pass@k. Reviewer qqHU shared part of the same concerns and we also refer to our response to them for additional discussion on the validity of using LLM-generated puzzles to evaluate LLMs themselves. > All these components are based on an imperfect LLM, so all of them are not fully reliable. We would like to point out that synthetic data is successfully used for supervised fine-tuning to enhance current LLM capabilities, even if LLMs can make mistakes. This is a common part of modern LLM post-training. For instance, in the Llama 3.1 paper [1] (Section 4.3.1) the authors use a previously trained version on llama 3 405B to generate coding exercises (based on random code snippets from “various sources”) and use execution feedback to ensure the generated solutions are correct according to the provided unit tests. They cannot fully guarantee the accuracy of generated solutions but they show this synthetic data is helpful for increasing model capabilities, illustrating the usefulness of the method. As explained in our reply to Reviewer qqHU, synthetic benchmarks and evaluations (beyond using GPT4 as a proxy for human evaluation) have also been useful to uncover surprising or harmful model behavior [2, 3, 4]. > rely on problematic method (evaluation of pass@k). HumanEval [...] is problematic [...] Formal verification is required. On HumanEval: You are right that, short of formal verification one cannot verify that a solution solves exactly the problem as it is formulated in the problem description. However this is the same situation as all coding competitions and evaluations directed at humans, where one relies on passing test cases to judge the validity of the solution (see LeetCode evaluations for instance), as well as most of the software written everyday in industrial applications (except some critical domains like aeronautics where software is verified). You seem to suggest that all coding competition grading is flawed, as well as all code model evaluations (for which HumanEval has been the main inspiration). While the evaluations are not perfect, this has consistently guided progress with coding LLMs. Would you similarly reject all papers using HumanEval to evaluate a code model on the grounds that the solutions generated by the models might be flawed? Formally verifying solutions to general programming problems (using Coq, Lean, Isabelle, etc) is far from a standard in the field of code LLMs and turning arbitrary programming puzzles into a formal specification is out of reach for current autoformalization methods (and out of the scope of this paper, this is a research field in itself). > Can authors ensure the correctness of the generated test program? We are in a different setup from HumanEval. By definition of a P3 puzzle, if `f(g()) is True` (according to the Python interpreter, see also Section 3.1 and [5]), the solution is correct. If at least one solution is found, the puzzle is solvable (thus correct). This does not guarantee the puzzle is interesting but the P3 correctness criterion is straightforward to judge. We increase the chance the puzzles are interesting by optimizing how hard (for LLMs) and diverse they are. > FunSearch and AlphaGeometry are different Funsearch does not generate problems so is not directly comparable. AlphaGeometry does generate geometry problems, and uses a specialized geometry DSL to ensure correctness of solutions. This is the equivalent to the Python interpreter in our case. We hope this discussion answers some of your concerns and we thank you for the opportunity to improve the paper. [1] The Llama 3 Herd of Models, Llama team 2024 [2] Discovering Language Model Behaviors with Model-Written Evaluations, Perez et. al. 2022a [3] Red Teaming Language Models with Language Models, Perez et. al. 2022b [4] Rainbow Teaming: Open-Ended Generation of Diverse Adversarial Prompts, Samvelyan et. al. 2024 [5] Programming Puzzles, Schuster et. al. 2021 --- Rebuttal Comment 3.1: Comment: 1. “We would like to point out that synthetic data is successfully used for supervised fine-tuning to enhance current LLM capabilities, even if LLMs can make mistakes.” This means the method is dubious. A top AI venue like NeurIPS should not accept a paper with a dubious method. 2. "On HumanEval: You are right that, short of formal verification one cannot verify that a solution solves exactly the problem as it is formulated in the problem description." "Would you similarly reject all papers using HumanEval to evaluate a code model on the grounds that the solutions generated by the models might be flawed?" The right question you should ask is: Why have such papers been accepted? A top AI venue like NeurIPS should not accept a paper with a flawed method. 3. "AlphaGeometry does generate geometry problems, and uses a specialized geometry DSL to ensure correctness of solutions. This is the equivalent to the Python interpreter in our case." AlphaGeometry can guarantee the correctness of the proof. Your method can not guarantee the correctness of the code. A top AI venue like NeurIPS should not accept a paper with a fundamental flaw.	Summary: This paper proposes Autotelic CodE Search (ACES), a method to generate diverse and challenging Python programming puzzles using state-of-the-art generative models. ACES optimizes for both the diversity and difficulty of problems by representing them with semantic descriptors that describe the programming skills required to solve them and measuring difficulty empirically with the pass rate in 50 tries. The method iteratively prompts a large language model to create new puzzles, using previously generated related ones as few-shot examples. ACES outperforms baseline methods, producing puzzles that are more diverse and three times more challenging than existing Python benchmarks, paving the way for automated curriculum learning and scientific discovery. Strengths: 1. The method is reasonable and the experiment results are promising, showing the advantage of this method. 2. The method proposed appears to be a general approach that can be extended to fields beyond code generation, as long as semantic descriptors can be set. 3. I believe that automatically generating benchmarks to test the shortcomings of large language models is a meaningful research direction. Weaknesses: 1. How do the results differ when using different models as solvers? In this paper, the difficulty is measured by how easily tasks are passed by the Llama-3-70b model, making Llama-3-70b an extremely important model for evaluating the capabilities of other models. Any model that does not perform consistently with Llama-3-70b is considered unable to pass certain tasks. Although the authors claim that "There is a clear correlation between solver performance across different problem sets, which indicates that tailoring problem generation to a specific model (Llama-3-70b) generates problems that are challenging for other models too,", it seems that this is actually just an assumption. In other words, the authors cannot explain whether the top left corner in Figure 4 (b) is overfitted to HumanEval or simply inconsistent with the Llama-3-70b model. One way to solve this is to present results on more solver models. 2. How does the author ensure the correctness of the generated test program $f$ (i.e., that the test program and the natural language description of the puzzle are consistent)? A problem can become very difficult if $f$ and the natural language description are inconsistent, and manual checking is challenging to cover all 6400 problems. 3. Some parts are not clear. (1) I'm confused about which one is your final method, ACES or ACES-ELM? It seems that ACES-ELM is an ablation of ACES (Section 3.4) but it is taken as the main method in experiments like Figure 4(b). (2) In section 4.2, what do these numbers (F1 scores) represent and which method should they be compared with? I think adding a baseline would help explain this better. 4. This paper evaluates the quality of the benchmark based on diversity and difficulty (which is actually the passing rate of the LLM, rather than an objective difficulty). However, I believe that difficulty is just one of the criteria for evaluating a benchmark, and this approach is somewhat one-sided. Other criteria, such as whether the benchmark meets practical usage needs (like HumanEval, which is manually designed to ensure that these programming tasks do not appear in the training set and are commonly used in real scenarios), or whether the benchmark covers a broader range of scenarios (like DS-1000, which targets scientific computing scenarios), are also important evaluation standards. Technical Quality: 2 Clarity: 2 Questions for Authors: 1. Why there are 21700 niches in total? If we combine these tags in various ways, we should be able to come up with $2^{20}-1$ niches. 2. Some typos: Tesla V100 SXM2 32 Go (GB?), Appendix Section! A.2. 3. Can the authors test the generated tasks on closed-source LLMs like GPT (it is okay to say no)? Confidence: 4 Soundness: 2 Presentation: 2 Contribution: 3 Limitations: The authors have discussed the limitations well. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank Reviewer qqHU for their review. We thank the reviewer for pointing out the experiments are promising, the research direction interesting, and for noting the method is general and applicable to other domains beyond code. We hope to address the reviewer’s concerns. > How do the results differ when using different models as solvers? [...] We have performed additional experiments with Llama 405B and Mistral Large 2. For each new experiment, the LLM is used to generate puzzles, label skills, and to measure difficulty. See the pdf attached to the main response, notably Figure 1 (a), (b) and (c). The results present evidence of transfer of puzzle difficulty across models: models that have low scores on our datasets generated with Llama 70B also have low scores on the datasets generated by Llama 405B and Mistral, as well as on LiveCodeBench [1] (specifically built to avoid contamination) and BigCodeBench [2]. Figure 1 (a) shows that only HumanEval escapes this correlation, suggesting high levels of contamination or models (especially the small ones) optimized to perform well on that benchmark. We have plotted the correlation between scores on all datasets (averaged over models) in Figure 1 (b). The correlation between all dataset scores, save for HumanEval, is clearly visible. We hope this answers your concerns on overly relying on a single solver. As additional evidence, we find good correlation between model size and overall performance on our datasets as well as LiveCodeBench and BigBench, which is what one would expect if coding capability was monotonically and smoothly related to model size. > How does the author ensure the correctness of the generated test program [...] We agree that it is not feasible to manually ensure consistency of the generated puzzles. For now we limit ourselves to ensuring the puzzle has at least one solution, and we generate the description from the puzzle and the solution using a specialized prompt. To increase puzzle-description consistency, we could additionally use a critic LLM, or use human labels as guidance. We also note that for the original P3 dataset, usually the description of puzzles are not given to models (see here https://github.com/microsoft/PythonProgrammingPuzzles/blob/main/notebooks/Intro.ipynb). > Some parts are not clear. (1) I'm confused about which one is your final method, ACES or ACES-ELM? ACES-ELM is a goal-directed quality-diversity method (as in ACES, we target a cell and instruct the model/choose the examples to be able to reach it), thus not really an ablation. We agree that the presentation could be better (we presented it after ELM because it uses the same mutation mechanism). Because they are goal-directed methods and exhibit similar performance we consider both methods to be our final methods. We changed section 3.3 and 3.4, where we present ACES and ablations respectively, to reflect this. > In section 4.2, what do these numbers (F1 scores) represent [...]? These correspond to skill labeling performance compared with a human-labeled ground truth, considered as a per-skill binary classification process. More precisely, for each puzzle, we have a set of ground-truth human labels. This gives us a classification problem with binary labels (is present, not present) for each skill index. To provide a random classification baseline one could do the following: for each of the 60 puzzle instances we manually assigned labels to, randomly assign 1 to 5 skills and compute the precision $p_0$, the recall $r_0$ and the f1 $f_0$. With 20 random draws of this random classifier we get $p_0 = 0.13$, $p_0 = 0.14$ and $f_0 = 0.12$ on average; well below the LLM judge’s performance. We added a footnote with this result. > [difficulty] which is actually the passing rate of the LLM, rather than an objective difficulty Unfortunately we cannot be much more objective than this, and this measure of difficulty is related, in any case, to the metrics the community uses to evaluate code models. We could average on a family of LLM to get an estimate of the difficulty of a puzzle, for LLMs in general. If we want to get difficulty estimates for humans, which might be quite different, there is unfortunately little practical way to collect a large scale dataset to e.g. train a classifier. Any idea you would have is of course welcome! > However, I believe that difficulty is just one of the criteria for evaluating a benchmark, and this approach is somewhat one-sided. We agree! We realize that there is much more than difficulty in a good puzzle. HumanEval was a well-crafted dataset and large amounts of human labor was needed to make a benchmark of this quality. It is now commonly accepted that HumanEval is present in the LLM’s train sets, making the results on this benchmark potentially unreliable. We believe that in the future, synthetic benchmarks will be an important part of LLM evaluation (but not all of it), in the spirit of how chatbot competitions and GPT4-judged responses are used to inform our current evaluations of LLMs. With this work we make a step in this direction, by showing that leveraging insights from the evolutionary computing and intrinsic motivation literature we can optimize for datasets with low pass rate and coverage in a predefined skill space. ### Questions > Why there are 21700 niches in total? We limit to 5 skills max, to avoid targeting puzzles with unrealistic skill combinations. ($\sum_{k=0}^{5} \binom{20}{k} = 21700$) We forgot to report this detail, we have added it in section 3.2. > Can the authors test the generated tasks on closed-source LLMs like GPT (it is okay to say no)? See our results with large open models. [1] LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code, Jain et. al. 2024 [2] BigCodeBench: Benchmarking Code Generation with Diverse Function Calls and Complex Instructions, Zhuo et. al 2024 --- Rebuttal Comment 1.1: Comment: Thanks for the response! Many of my concerns have been addressed and for other ones, although the authors did not provide a clear solution and acknowledged this as a limitation of their work, I believe that overall, this work represents a commendable attempt. Now, I think there is only one question that remains unanswered: As I mentioned earlier, and as reviewer NuHw also noted, how can puzzles generated by LLMs, which cannot guarantee correctness, serve as benchmarks to evaluate LLMs themselves (or other LLMs)? I know the following information, but I don't think this answers the question. 1. I know that some benchmarks use LLMs (mostly GPT-4) as the evaluation metric because these benchmarks require human evaluation, which cannot be automated. GPT-4 here serves as an approximate automated evaluation method. 2. I know that LLMs can automatically generate training datasets for training purposes because we have golden benchmarks to evaluate the final training outcomes. However, if we use LLM-generated benchmarks for the final evaluation, there will be nothing to ensure their performance. 3. Perhaps we can use benchmarks generated by stronger LLMs to evaluate weaker ones, but how do we evaluate the stronger LLMs? If we use human-designed benchmarks to evaluate stronger LLMs, then why not use them directly to evaluate weaker ones? This is quite important and I hope the authors can discuss this question further. --- Reply to Comment 1.1.1: Comment: We appreciate your thoughtful feedback and the opportunity to address this important question. We understand your concern about using puzzles generated by LLMs as benchmarks to evaluate LLMs themselves. We'd like to offer the following perspectives on this matter: * Objective solvability: Since a P3 puzzle is defined by its test case only (and the language description is generated afterwards to provide help), puzzles with at least one solution are by definition correct (i.e. solvable). This ensures a baseline level of validity for the benchmarks. * Puzzle quality and interest: Although all solvable puzzles are correct, this doesn’t mean they are interesting or worthwhile. We acknowledge that evaluating puzzles 'interestingness' or relevance is subjective and challenging to automate. Our approach with semantic labels provides users some control over the generation process, allowing them to orient puzzles towards abstract features they deem important. While we cannot fully automate the assessment of puzzle quality, our method generates problems that are more difficult and diverse in customizable ways, potentially increasing their overall quality and relevance. We could also add an interesting metric judge by an LLM [1, 2] and/or an educational value [3, 4] to filter the least interesting puzzles. * Preexisting automated benchmarks: we would like to point out that synthetic benchmarks have already led to discovery of interesting features of LLMs [5, 6, 7] * Human-in-the-loop approach: Our method significantly speeds up benchmark generation by producing a pool of potentially interesting puzzles from which humans can select, in a similar fashion as BigCodeBench or HumanEval Plus where the authors used a human in the loop method to guide or filter LLM generated data; * Potential for automated quality assessment: In the future, we could explore using preference models or tournament-style competitions with the top k LLMs to automatically select top puzzles from the generated set. This approach has shown promise in other areas of AI evaluation. * Comparative evaluation: To address the concern of using LLM-generated benchmarks to evaluate LLMs, we could compare LLM performance with human performance on these benchmarks. This approach has been used effectively in other studies comparing the reasoning capabilities of LLMs and humans [8]. Additionally, we note that model scores on our generated sets and on LiveCodeBench (composed of newly released coding puzzles to avoid contamination) are strongly correlated (See additional Figure 1c). We take this as evidence that the generated set measures underlying coding capabilities; > Perhaps we can use benchmarks generated by stronger LLMs to evaluate weaker ones, but how do we evaluate the stronger LLMs? In ACES, increasing the number of attempts leads to harder problems (since we can optimize for puzzles solved once out of N with N being large). Thus, even weaker LLM can generate difficult tasks for better LLMs, as shown in our additional experiment where Llama-3.1-405B only gets 74% pass@1 on a dataset generated with ACES-ELM with Llama-3-70B (Additional Figure 1a). This is directly due to the fact that ACES can optimize for empirical difficulty. * Although we have shown that puzzle difficulties transfer between Llama and Mistral (additional Figure 1a, Mistral Large and Llama 3 405B have similar scores on ACES-ELM datasets generated by both models) we could also take the three or four best LLMs and generate multiple archives with our method, then merge them to get a test set; as each LLM has some strengths and weaknesses, the resulting archive should be balanced in terms of puzzle difficulties for other models. We hope this addresses your concern and provides evidence for the usefulness of synthetically-generated evaluation sets. Given that many of your previous concerns have been addressed and you've acknowledged this work as a commendable attempt, we kindly request that you consider updating your score to reflect your opinion of the paper. Thank you again for your valuable feedback and the opportunity to improve our work. [1] Omni: Open-endedness via models of human notions of interestingness, Zhang et. al. 2023 [2] OMNI-EPIC: Open-endedness via Models of human Notions of Interestingness with Environments Programmed in Code, Faldor et. al. 2024 [3] Cosmopedia: how to create large-scale synthetic data for pre-training, Ben Allal et. al. 2024 [4] Textbooks Are All You Need, Gunasekar et. al. 2023 [5] Discovering Language Model Behaviors with Model-Written Evaluations, Perez et. al. 2022a [6] Red Teaming Language Models with Language Models, Perez et. al. 2022b [7] Rainbow Teaming: Open-Ended Generation of Diverse Adversarial Prompts, Samvelyan et. al. 2024 [8] Beyond the imitation game: Quantifying and extrapolating the capabilities of language models, Srivastava et. al. 2022	Summary: In this paper, the authors propose a method to automate the generation of challenging coding puzzles. By leveraging quality-diversity (QD) algorithms and defining novel metrics, their approach produces coding puzzles that are more diverse and challenging than existing benchmarks. Strengths: - The proposed algorithms and metrics have the potential to be significant and impactful. Generating diverse learning environments and measuring their diversity has been a major challenge for the community. The methods proposed in this paper represent valuable attempts to address these important issues. - The validation of the method is solid. For example, the quality of skill descriptors generated by an LLM is evaluated with human assessments, and extensive baselines and model variants are implemented and compared to demonstrate the effectiveness of the proposed method. - The proposed method generates more diverse and challenging coding puzzles, which could be highly beneficial for future studies on LLM coding agents. Weaknesses: ### The presentation could be improved: - The authors might consider explaining QD and Map-Elites more clearly. While I am familiar with these methods and did not have difficulty, readers who are not as familiar with these topics might find them challenging to understand. - As someone familiar with related topics, I found the proposed method difficult to understand. My current understanding is that the difficulty metric is used as fitness, and two diversity metrics are two dimensions in the Map-Elites archive. Is this correct? Regarding embedding diversity, is it the higher the better (since it's more diverse)? If that is the case, does it make sense to use it as one dimension in the Map-Elites archive? - The authors might consider introducing the motivation behind their design choices before explaining them (e.g., P4, L128; the three metrics in Section 3.2). Additionally, for the paragraph at P5, L185, I don't fully understand how the design reflects the intuition. - There are some questions in the question section that I do not fully understand. Technical Quality: 3 Clarity: 2 Questions for Authors: - How the target cell get selected? - I don't fully understand the motivation behind the ablation using ELM with semantic categories. What does "ablation of goal-directedness" mean? - Since the approach did not include the training of LLMs, do the authors consider using more powerful LLMs like GPT-4 or Claude-3.5? - Which variant is the final proposed method? Is it ACES-ELM, ACES, or another variant? - Using visualization tools like t-SNE could be beneficial to show the distribution of generated coding challenges. It will be interesting to see the clustering of different skills being tested in these generated problems. - Figure 3(f) seems counterintuitive to me. Do the authors have any insights into why the proposed method generates either the most challenging tasks or very easy ones? What happens to the intermediate tasks? Is it the case that the model cannot generate them, or are they rejected after generation? Confidence: 4 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: Limitations are addressed in the Discussion section Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank Reviewer LkwK for their thoughtful comments, and are glad they find the problem we study important, and the evaluation solid. We now aim to clarify some points in our response. > The presentation could be improved. We thank you for this feedback. We have modified section 3.4 by being more precise when introducing Map-Elites. > My current understanding is that the difficulty metric is used as fitness, and two diversity metrics are two dimensions in the Map-Elites archive. That is not quite correct, thanks for pointing out that the explanation is unclear. Fitness is the quality metric, and the archive is composed of cells corresponding to a maximum of 5 discrete programming skills (among 20). > Regarding embedding diversity, [...] does it make sense to use it as one dimension in the Map-Elites archive? We have two diversity measures: skill (or semantic) diversity, which is the number of unique skill combinations present in the generated set, and embedding diversity, which is the average pairwise distance between puzzles in an embedding space. These measures are NOT dimensions of the archive. Embedding diversity, which is independent from semantic diversity (and computed with different models than the one used for generation/skill labeling), is used as an independent measure of diversity (since skill labeling is imperfect). The measures agree (see Figure 3). > The authors might consider introducing the motivation behind their design choices before explaining them. Thank you for your suggestion! The reason for using P3 is twofold: * Code LLMs are a focus of the ML community, and for good reason. However, state-of-the-art models are getting so good as to mostly saturate today’s programming benchmarks (see also responses to Reviewer qqHU). Applying QD search with difficulty as a fitness metric is of obvious use there. We manage to create coding datasets that are challenging for current capable LLMs; * P3 is a relatively simple, language-based, open-ended domain where one can check the solutions exactly to compute how hard a task is (contrary to the tasks used in QDAIF [1]). As for the metrics introduced in section 3,2: * Difficulty: creating challenging problems was our aim and is important. The reasons for the precise formulation are given in the response to reviewer ESVE, third response to questions. * Skill diversity: These dimensions of variation across puzzles are intuitive for humans and are useful for downstream applications (benchmark generation, and in possible future work, generation of programming exercises for students). * Embedding diversity: see previous response. ### Questions: > How is the target cell selected? In ACES (goal-reaching method), we select a cell uniformly at random among all possible cells, filled or otherwise (Section 3.3, second paragraph, as well as Figure 1). In ELM (mutation-based method), we select a cell uniformly at random among the ones that are filled (Section 3.4, first paragraph); > I don't fully understand the motivation behind the ablation using ELM with semantic categories. What does "ablation of goal-directedness" mean? ELM selects an existing solution and applies an undirected mutation to it using the LLM-based mutation operator. ELM with semantic categories extends ELM by storing existing solutions in the skill-based archive introduced in our paper – and we show this improves performance compared to ELM using Voronoi cells. (It is also very similar to QDAIF). ACES replaces the undirected mutation operator by a goal-directed mutation: it first selects a target cell (empty or filled), then tries to fill it by prompting the LLM to generate a new problem characterized by the skills of the target cell. ACES-ELM also selects a target cell, but tries to fill it by mutating an existing puzzle; it is a goal-directed version of ELM. Our hypothesis was that goal-directed mutation is better than undirected mutation. Our hypothesis is confirmed in our experiments as niche coverage grows faster with goal-directed variants (ACES-ELM and ACES) than with non-directed variants (ELM, ELM-CVT). Additionally, the goal-directed variants also produce higher-difficulty puzzles: this might be due to the higher diversity of puzzles which allows the algorithm to find higher-difficulty puzzles as well, as is often the case in QD search. > [...] Do the authors consider using more powerful LLMs like GPT-4 or Claude-3.5? The experiments are somewhat costly to run with the more expensive closed-source API models. We did experiments with the new Llama model and Mistral large 2 that are GPT-4 level (see general reply). See general reply for results. > Which variant is the final proposed method? Both methods exhibit minor variations and yield comparable results. Given that ACES-ELM demonstrates a slight edge in diversity and difficulty, we recommend it as the preferred variation of the method. We have updated section 3.3, and section 3.4, to reflect this. > Figure 3(f) seems counterintuitive to me. Do the authors have any insights into why the proposed method generates either the most challenging tasks or very easy ones? We are not sure. In the beginning of training the only puzzles generated are the easy ones (difficulty close to 0); as generation progresses with ACES, a larger and larger proportion of puzzles are close to maximum difficulty (See new results, Figure 1 (e)). We instruct the model to generate only puzzles of the highest difficulty, by including difficulty scores of the few-shot examples in the prompt. One possibility is that this works so well that it heavily skews the distribution of difficulties. Another explanation could be that we heavily skew sampling of example puzzles based on their difficulty score, leading to creating of puzzles with similar difficulties. [1] Quality-Diversity Through AI Feedback, Bradley et. al. 2023 --- Rebuttal Comment 1.1: Comment: Thank you for thoroughly addressing my comments and providing the additional results. After carefully reviewing your response, I find that my primary concerns and points of confusion have been addressed. I support the publication of this paper in NeurIPS and will maintain my current score.	Rebuttal 1: Rebuttal: We thank all reviewers for their reviews and the time they spent reading the paper, and we hope this rebuttal and the discussion period will be productive, answer questions and overall lead to a better paper. There are two ways to read this paper, depending on which background one has. The takeaways from the paper will be slightly different in each case. * For general machine learning readers with an interest in (code) LLMs, the contribution of this paper is showing that one can use a measure of puzzle difficulty – as well as LLM judgements of which programming skills are required to solve a puzzle – to create sets of hard and diverse programming problems. We envision this as a step to creating new programming benchmarks for code LLMs. Reviewer ESVE worries about the application of the method, but we think the contribution to generating difficult synthetic benchmarks is quite clear, as Reviewer qqHU also notes in his comments. Reviewer NuHw rejects the approach on the basis that it is built on LLMs, but we note that generating challenging evaluation sets is an instrumental application to create better LLMs in the future. * For readers interested in open-ended search, we present algorithmic improvement over LLM-augmented map-elites (ELM), the baseline method that is extensively used in other papers [1, 2, 3]. We build a goal-directed algorithm that explicitly targets potentially empty cells, instead of using random mutation like Map-Elites-inspired approaches, and we demonstrate that this is helpful. Importantly, the goal-directed property of ACES comes from 1) the few-shot abilities of LLMs, to create a puzzle that resembles puzzles chosen near the target cell and 2) their instruction-following abilities, to create a puzzle in the desired cell (with the right skill combination). The goal-directed evolutionary algorithm underlying ACES could not be implemented without LLMs; this algorithmic improvement takes full advantage of the use of instruction-following LLMs, with few-shot abilities, as mutation operators. We present a series of complementary results in the attached pdf. ### Results with different models To respond to Reviewer qqHU’s concerns of over-reliance on a single model, and to calls by Reviewers LkwK, qqHU to use bigger, state-of the art models, we performed additional experiments with the new Llama 405B model and Mistral large 2, models on par with GPT-4. Using those LLMs leads to a better Quality-Diversity score overall, up to 25.6% for Mistral Large and 12.3% for Llama 405B (using Llama 405B and Mistral large 2 both for the difficulty metric and skill labeling). This demonstrates how ACES scales with models of higher size. Evaluating Mistral Large on the dataset generated by Llama 405B, as well as the other way around, we find pass@1 scores of 56.7% and 58% respectively. This demonstrates the effectiveness of our method in generating a challenging benchmark, even for state-of-the-art models, as well as the fact that difficulty measures transfer across models of similar capabilities. Examining the archive generated by Llama-3-70B with ACES-ELM, Mistral Large 2 achieved a 70% pass@k (74% for Llama-3-405B), while Llama-3-70B has a pass@1 of 36.8%. This demonstrates Mistral-Large and Llama-405B's superior performances as solvers. However, even with these state-of-the-art models, the benchmark generated by Llama-3-70B is not saturated, as there is still approximately 30% room for improvement to fully solve it. ### New finetuning results To address concerns of Reviewers ESVE and NuHw about applications and model improvement, we performed experiments with finetuning. We finetuned the Llama-3-8b model using datasets generated by WizardCoder (variant of the state of the art method WizardLM for generating synthetic data [4]), StaticGen (established baselines), and our proposed ACES-ELM method. We then evaluated the model's performance using the greedy pass@1 metric on a series of test sets. These test sets were equally composed of puzzles from our method and StaticGen with increasing difficulty levels (k value in the Figure 1.d), generated using a different seed than the training data. The results of this experiment, illustrated in Figure 1.d, reveal several findings that highlight the superiority of ACES-ELM. On the most challenging test set, the Llama-3-8b model finetuned with data generated by ACES-ELM achieved a remarkable pass@1 score of 53.3, significantly surpassing both baseline methods and also outperforming the Llama-3-70B model. This demonstrates the effectiveness of our ACES-ELM method in generating high-quality training data that enables models to tackle more complex coding tasks. While the Llama-3-8b models fine-tuned with WizardCoder and StaticGen showed improvements over the baseline Llama-3-70B model (achieving pass@1 scores of 49.4 and 41.6, respectively), they consistently underperformed compared to the ACES-ELM-trained model. This underscores the superior quality of the training data generated by ACES-ELM. Moreover, as evident from Figure 1.d, the performance gap between ACES-ELM and the baseline methods becomes more pronounced as the difficulty level of the testset increases. This suggests that ACES-ELM is particularly effective in preparing models for more complex coding challenges. --- We think we have clarified all the points the reviewers have raised and responded to concerns regarding the contribution, applications and generality of our method. We thus kindly ask reviewers to raise their grade if they feel their concerns have been addressed or otherwise provide detailed requirements that would convince them to do so. [1] Evolution Through Large Models, Lehman et. al. 2023 [2] Quality-Diversity Through AI Feedback, Bradley et. al. 2023 [3] Rainbow Teaming: Open-Ended Generation of Diverse Adversarial Prompts, Samvelyan et. al. 2024 [4] WizardCoder: Empowering Code Large Language Models with Evol-Instruct, Luo et. al. 2023 Pdf: /pdf/5f7ad83652ed199f191e54c03c5a5c1eec8ea5ff.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
CondTSF: One-line Plugin of Dataset Condensation for Time Series Forecasting	Accept (poster)	Summary: In this paper, the authors propose a dataset distillation approach by decomposing the distillation loss into two terms, the value term and the gradient term. Then, they derive bounds for these two terms that enable more effective dataset distillation for time-series forecasting. Strong performance is demonstrated in the conducted experimental evaluation Strengths: + The paper is well-written and easy to follow. + Authors attempt to support their methodology through theoretical explanations + Strong performance is obtained in the experimental evaluation. Weaknesses: - p4. l121. The authors do not explain why this non-optimizable $\epsilon$ error occurs. - l. 137 in principle we could directly optimize this gradient term without deriving any bound. Unless I am missing something, this is supported by DL frameworks (e.g., PyTorch). On the other hand, I understand that there might be computational benefits from deriving a bound that does not involve the gradients. However, authors should justify their choice (why we need to derive this bound) and if this is related to computational efficiency. Ideally, experiments should be provided to support their choice. - At various points there are implicit assumptions the effect of which is not appropriately discussed, e.g., Eq. (9) is essentially supported by an experimental result in a Figure and a verbal description. I do not (empirically) disagree with the conclusion, but I can see cases where this would not hold (e.g., in financial time-series forecasting, where using the same data we can have vastly different (non-linear) hypotheses). Whether this alters the conclusions/and or the method, is not appropriately discussed. - The updating process in (12) essentially moves the targets towards the predictions of the model. This is a reasonable result that is well-known to work. However, the way this is applied is now very close to target smoothing/model distillation approaches that essentially do the same thing (also applied in the context of time series forecasting as far as I know). There is some literature on model distillation approaches (and/or self-distillation) in the context of time-series forecasting and/or regression, which essentially demonstrate that this kind of "smoothing" can indeed increase performance. Therefore, this raises some questions on whether the method should be compared experimentally (or at least theoretically) with such approaches. - Even though some ablation studies were provided in the Appendix, I didn't manage to find perhaps the most important result: What is the impact of the gradient term and what is the impact of the value term? What would happen if we remove the L_param loss in l. 9 of Alg 1? What would happen if we removed the value term? - Isn't the method also applicable in the case of regression tasks? If I am not missing anything, I think the same methodology without any change (apart from the input to the models) can be applied also to handle generic regression tasks that also expand over time-series forecasting. Minor: l.147-152: I think $k$ is used before being introduced. Technical Quality: 2 Clarity: 3 Questions for Authors: Please respond to the comments provided in the drawbacks. Overall, strong performance is demonstrated, but there are several aspects that should be improved. Confidence: 3 Soundness: 2 Presentation: 3 Contribution: 2 Limitations: Yes. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We apologize for the ambiguity. W1: What does non-optimizable term $\epsilon$ mean? A1: - Please refer to Eq(4), since test label $x_{t+m:t+m+n}$ is unavailable during dataset condensation, we transform it to the prediction of an expert model $M_f$ on test data $x_{t:t+m}$ for further analysis. Since there is always an error between the prediction of the model and the ground truth, we use $\epsilon$ to denote it. - $\epsilon$ is optimized during the training process of expert model $M_f$. However, since we can only have access to the trained expert model $M_f$ during dataset condensation, $\epsilon$ is no longer optimizable. --- W2: Why derive a bound of the gradient term? A2: - Indeed, the original form of gradient term in Eq(5) is not directly optimizable. Test data $x_{t:t+m}$ exists in gradient term, which is unavailable during dataset condensation. - To solve this problem, please refer to Eq(6), we use Cauchy-Schwarz Inequality to decouple gradient term. Then we get the optimizable part $\|\|\theta_f-\theta_s\|\|^2$(the gradient of linear model is the parameter), and the non-optimizable part $\|\|x_{t:t+m}-s_{t':t'+m}\|\|^2$. - Thus, it is necessary to derive the upper bound of gradient term because the original one is not optimizable. --- W3: How to justify the empirical finding? A3: In the cases you mentioned, the model is theory-driven, which means the prediction of the model relies highly on the hypotheses and theories. However, in this case, the models are data-driven, and no additional hypotheses are made. The prediction of the model relies only on the training data and the model structure. Thus, in this case, if the models share the same architecture and are trained with the same dataset, empirically they output similar outputs. --- W4: How does our method compare to smoothing or model distillation? A4: - Firstly, model distillation and dataset condensation are different tasks. Model distillation updates student model parameter and produces distilled model. Dataset condensation updates the synthetic data and produces distilled dataset. - Secondly, model distillation aims at aligning the output of $M_s$ and $M_f$. The training of $M_s$ is directly supervised by $M_f$, where $L$ is the loss function, e.g. MSE. $$M_s=\arg\min_{M} L(M(s),M_f(s))$$ However, in the case of our value term optimized by Eq(12), $M_s$ is trained alone using synthetic data $s$ and $M_f$ only has indirect access to the training of $M_s$. $$s=\arg\min_s L(M_s(s),M_f(s))$$ $$\textbf{s.t.}\hspace{1em} M_s=\arg\min_M L_{train}(M, s)$$ Thus model distillation is not comparable to our method. - Meanwhile, we conduct experiments using LPF to perform target smoothing on the synthetic data and compare the results with CondTSF. Average MAE of 5 models is reported below. It shows that CondTSF is significantly more effective than target smoothing. \|\|Ex.Rate\|Wea.\|Elec.\|Tra.\|ETTm1\|ETTm2\|ETTh1\|ETTh2\| \|-\|-\|-\|-\|-\|-\|-\|-\|-\| \|MTT\|0.778\|0.509\|0.747\|0.742\|0.653\|0.685\|0.693\|0.719\| \|Smooth\|0.867\|0.602\|0.831\|0.786\|0.728\|0.706\|0.701\|0.744\| \|MTT+Smooth\|0.620\|0.501\|0.788\|0.836\|0.656\|0.619\|0.680\|0.704\| \|MTT+CondTSF\|0.195\|0.326\|0.391\|0.494\|0.491\|0.347\|0.532\|0.329\| --- W5: What if the value term or the gradient term is removed? What are the impacts of these two terms? A5: $L_{param}$ is the same form of Eq(8) in Sec.4.2, which is used to optimize gradient term. Please refer to l.143-145, our analysis shows that previous dataset condensation methods based on parameter matching, e.g. DC[1], MTT[2], etc. are optimizing the gradient term. Our method CondTSF is optimizing the value term. - If value term is removed: The method falls back to the previous dataset condensation methods based on parameter matching(DC, MTT, etc.), and the results can be found in Table.1,3,5,7,9. Moreover, please refer to Fig.8, in the beginning 160 epochs, only gradient term is optimized, in the last 40 epochs, value term is also optimized. Optimizing value term significantly enhances the performance. - If gradient term is removed: Please refer to l.222-224 and App.C, experiments on backbone methods that are not based on parameter matching, e.g. DM[3], IDM[4], etc. are also carried out. These backbone methods do not optimize the gradient term. Thus when combining these backbone methods with CondTSF, only value term is optimized, and the results are in Table.8. We conduct experiments that only optimize value term without any backbone methods, average MAE of 5 models is reported. The results are well-aligned with our analysis that optimizing gradient term or value term alone harms the performance. \|\|Ex.Rate\|Wea.\|Elec.\|Tra.\|ETTm1\|ETTm2\|ETTh1\|ETTh2\| \|-\|-\|-\|-\|-\|-\|-\|-\|-\| \|MTT (only gradient term)\|0.778\|0.509\|0.747\|0.742\|0.653\|0.685\|0.693\|0.719\| \|CondTSF (only value term)\|0.563\|0.537\|0.761\|0.809\|0.738\|0.538\|0.623\|0.569\| \|MTT+CondTSF\|0.195\|0.326\|0.391\|0.494\|0.491\|0.347\|0.532\|0.329\| [1] Dataset Condensation with Gradient Matching [2] Dataset Distillation by Matching Training Trajectories [3] Dataset Condensation with Distribution Matching [4] Improved Distribution Matching for Dataset Condensation --- W6: Is this method applicable to all regression tasks? A6: Our proposed CondTSF is applicable to generic regression. Meanwhile, we have designs that are related to time series forecasting. In time series forecasting, when generating training data, the data is usually sampled overlap from the dataset. For instance, the data points can be sampled as $x_{0:24}, x_{4:28}$, etc. Please refer to Eq(12), inspired by the overlap property, we utilize an additive method to gradually update the synthetic data instead of directly using $M_f(s_{t':t'+m})$ to overwrite $s_{t'+m:t'+m+n}$ to avoid vibrations. --- Minor: $k$ in l.147-152 used before introduced. A: We are sorry for the ambiguity. We will correct that in next version. --- Rebuttal Comment 1.1: Comment: I would like to thank the authors for providing detailed responses to all of my questions, which were - to a significant degree - indeed addressed. Therefore, I am increasing my rating. --- Reply to Comment 1.1.1: Title: Thanks for the comments and raising the score Comment: Dear reviewer s2gY, We want to thank you for the valuable advice and for raising the score of our paper. We will incorporate your suggestions, especially clarifying the terms, and adding the experiment results reported in the rebuttal. Best, Authors	Summary: This paper explores dataset condensation, which generates a small dataset for training of deep neural networks, for time series forecasting. Specifically, it proposes a one-line dataset condensation plugin designed specifically for time series forecasting. It first formulates the optimization objective of dataset condensation for time series forecasting, and based on which a reformulation is proposed and further theoretical analysis is performed. Based on the proposed theoretical analysis, this paper proposes a simple data condensation plugin CondTSF. Experiments on 8 time series datasets are performed to demonstrate the effectiveness of the proposed CondTSF. Strengths: 1. It proposes a simple dataset condensation plugin. 2. A theoretical analysis is provided. Weaknesses: 1. Dataset condensation is a strategy specifically designed for training large dataset. However, the data size in time series is usually significantly smaller than that in NLP and CV. In my experience, the computational demand to deal with time series data may not be an urgent request in real-world time series applications. The topic discussed in this paper seems interesting given the current program of different foundation models, but I highly doubt it applicability in the field of time series. 2. A related problem is that how the time series foundation model performs remain unclear. Exploring the foundation model for time series may be a promising direction, but it is not widely accepted and deployed in real-world applications. In fact, considering the semantics of time series is highly dependent on the underlying applications, so far I have not observed any foundation model can provide good zero-shot learning capability. Technical Quality: 2 Clarity: 3 Questions for Authors: Please refer to the weakness part. Confidence: 3 Soundness: 2 Presentation: 3 Contribution: 2 Limitations: Please refer to the weakness part. Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: W1: The demand for dataset condensation for time series forecasting is not urgent. What are the real applications of dataset condensation for time series foundation models? A1: - Firstly, dataset condensation is also important in other aspects besides reducing computational cost. For instance, data condensation is proven to benefit downstream tasks such as continual learning[1], privacy[2], etc. These tasks are vital for some aspects of the time series, such as finances. - Secondly, in the era of large models, Neural Architecture Search(NAS) of large time series foundation models is still computationally intensive[3]. Utilizing condensed data to identify a smaller parameter set and conducting full training on this set can improve efficiency. - Moreover, our proposed method could serve as a prototype and shed light on the related research area. [1] An Efficient Dataset Condensation Plugin and Its Application to Continual Learning [2] Privacy for free: How does dataset condensation help privacy [3] Dataset Condensation for Time Series Classification via Dual Domain Matching ---- W2: How the time series foundation model performs remains unclear, and most are not good at zero-shot learning. A2: - Indeed, nowadays foundation models do not behave well in time series forecasting[1]. - However, more explorations of foundation models are carried out[2]. Therefore, our dataset condensation method can be used to lower the computational cost and accelerate the exploration of foundation models on time series tasks[3][4][5]. - Meanwhile, our proposed method points out an interesting direction in time series forecasting tasks. More efforts can be devoted to this field and our method can serve as a prototype. [1] Are Language Models Actually Useful for Time Series Forecasting? [2] A Survey of Time Series Foundation Models: Generalizing Time Series Representation with Large Language Model [3] Time-llm: Time series forecasting by reprogramming large language models [4] Timegpt-1 [5] A decoder-only foundation model for time-series forecasting --- Rebuttal Comment 1.1: Comment: Thanks for the reviewer for the detailed response. I acknowledge I have read the rebuttal. --- Reply to Comment 1.1.1: Title: Thanks for the comments Comment: Dear reviewer DVXT, We want to thank you for your valuable advice and we will clarify the motivation and the pragmatic usage of dataset condensation for time series in the paper. Meanwhile, we are eager for the opportunity to address any remaining concerns you might have before the discussion period concludes. We sincerely appreciate your and other reviewers' dedication and time invested in reviewing our work. Best, Authors	Summary: In this paper the authors study the question of dataset condensation / distillation in the context of time series forecasting. They propose a decomposition that could be used to empirically estimate bound the point-wise forecast MSE loss. Based on this decomposition the authors proposed a condensation plug in on top of existing data condensation method that updates the distilled dataset with the estimated full model forecast. Through empirical study they show that with this plug in the resulting condensed dataset leads to better models across different model classes and benchmark forecasting tasks. Strengths: The paper attempts a new and simple solution to an important training data efficiency problem. It also attempts a novel prospect of analyzing the dataset distillation through the loss decomposition. Weaknesses: The major weakness is the writing. It is hard to follow in its current shape, in particular the math description of the research question should be more rigorous. To name a few: - What are the sample space of x and s? They now look like a single univariate time series. It is the case? - What is t' in Eqn (5)? Is it summed over? If so is it double sum within sum_t? - How is Eqn (7) and (8) optimized (also in Algo 1). Similarly regarding writing, the paper does not motivate the research question well, and has not provided enough background details on its base distillation methods (Line 200 Model Settings), especially MTT(3). As a result it is hard to evaluate the novelty of the paper when the main idea is not clearly delivered. Though mentioned as a limitation, the assumption of linear model trivializes the theories, which ties the proposed method to DLinear expert, and makes it hard to understand how the learning from the synthetic data generalizes beyond the expert's model class. There are similar simplifications, e.g. the empirical approximation as in Eqn (9) that's observational. Technical Quality: 3 Clarity: 1 Questions for Authors: Besides the questions in the weakness: - While the distill ratio in Table 2, e.g. condensing the datasets into one training example, can be used to show the extremity of the distillation process, it is questionable what this one-shot learning means for the MLP, LSTM, CNN involved. Any insights, especially why to choose them over the few-shot study in, e.g. Appendix F (this one has visualization as well) to be in the main paper? - As now the expert model is more actively involved through the two decomposition steps to touch the synthetic data, how does the capacity of the expert impact the fidelity of the synthetic dataset versus the full one? What about at least one non linear expert just to get some insights? - The method proposed here does not utilize any time series concepts. If so this is an application on multivariate regression with linear expert. What's the novelty beyond that for time series exclusively? Confidence: 3 Soundness: 3 Presentation: 1 Contribution: 3 Limitations: The authors addressed the limitations. Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We apologize for the ambiguity. W1: What are the sample space of $x, s$? Are they univariate time series? A1: Yes, $f, x, s$ are univariate time series. Please refer to Sec.3, l.93-95. A time series dataset can be viewed as a long vector. We cut the dataset into two vectors and obtain train set $f$ and test set $x$. Both $x$ and $f$ are vectors. Then we sample a short continuous part of train set $f$ as the initial synthetic dataset $s$. $s$ is still a vector. --- W2: What is $t'$ in Eq(5)? Is it summed over? A2: - We use $s_{t':t'+m}$ to denote a vector(part of $s$) with length $m$ starting from position $t'$. $t'$ is arbitrarily chosen. - Please refer to Eq(16) and l.444-446, $s_{t':t'+m}$ is an arbitrary vector used to perform Taylor expansion to get the value of $M(x_{t:t+m})$. The idea throughout our paper is that test set $x$ is unavailable during dataset condensation, thus we need to substitute $x$ with accessible synthetic dataset $s$ so the optimization objective becomes optimizable. - The sum in Eq(5) is only performed on $t$, not $t'$. Please refer to Eq(3) and App.A1, $\sum_t$ is used in test error to sum over the test set $x$. For each $x_{t:t+m}$, we use an arbitrary $s_{t':t'+m}$ to perform Taylor Expansion, thus $t'$ is not summed over. ---- W3: How are Eq(7) and(8) optimized? Lack of information on base methods and the novelty is not clear. A3: - Eq(7) and(8) are optimized the same way as MTT[1], which is a well-acknowledged dataset condensation method. According to our analysis, MTT is optimizing the gradient term. There are multiple dataset condensation methods that use MTT as the backbone, such as TESLA[2], FTD[3], DATM[4], etc. We will add introduction of MTT in appendix in the next version. - MTT and all other backbone methods are designed for classification. They perform poorly on time series forecasting. The novelty of our method is that CondTSF enhanced the performance of all previous methods on time series forecasting. [1] Dataset Distillation by Matching Training Trajectories [2] Scaling Up Dataset Distillation to ImageNet-1K with Constant Memory [3] Minimizing the Accumulated Trajectory Error to Improve Dataset Distillation [4] Towards Lossless Dataset Distillation via Difficulty-Aligned Trajectory Matching --- W4.1: The hypothesis of linear model trivialized the work. A4: - Please refer to App.A1 and Eq(16), using nonlinear models will add 2nd and higher order terms to the Taylor Expansion. We ignore higher order terms because their effect on the output is minor. Meanwhile, although linear models are simple in structure, they perform well on time series forecasting and outperform complicated transformer models[1]. - We add experiments on using nonlinear models as expert models, please refer to A7. [1] Are Transformers Effective for Time Series Forecasting? --- W4.2: The observation in Eq(9) is a simplification. A5: The observation in Eq(9) is not a simplification. Please refer to l.157-159, The test model parameter is unknown during dataset condensation, thus we need to substitute them with accessible parameters. Thus Eq(9) is necessary, otherwise the value term is not optimizable. --- Q1: Why is the result of one-shot dataset for models MLP, LSTM, CNN presented in the main text? A6: Cross-architecture performance is an important metric reported in all dataset condensation papers. MLP, CNN and LSTM perform well on time series forecasting[1] and are widely used in the evaluation of dataset condensation[2]. Thus we present the result in the main text. [1] Are Transformers Effective for Time Series Forecasting? [2] Dataset Condensation for Time Series Classification via Dual Domain Matching --- Q2: Add a nonlinear expert? A7: Please refer to App.A1 and Eq(16). Given nonlinear models, our method ignores the 2nd and higher order terms in Taylor Expansion. We conduct experiments to show that ignorance is acceptable. We use nonlinear models CNN, 3-layer MLP(ReLU activated) as expert models. Average MAE of 5 models is reported below. The results show that CondTSF performs well with nonlinear models. - CNN \|\|Ex.Rate\|Wea.\|Elec.\|Tra.\|ETTm1\|ETTm2\|ETTh1\|ETTh2\| \|-\|-\|-\|-\|-\|-\|-\|-\|-\| \|MTT\|0.372\|0.314\|0.482\|0.662\|0.550\|0.347\|0.644\|0.371\| \|MTT+CondTSF\|0.140\|0.246\|0.357\|0.451\|0.482\|0.237\|0.460\|0.297\| \|TESLA\|0.378\|0.310\|0.516\|0.655\|0.544\|0.359\|0.634\|0.365\| \|TESLA+CondTSF\|0.134\|0.253\|0.374\|0.528\|0.499\|0.251\|0.473\|0.293\| \|DATM\|0.331\|0.335\|0.504\|0.587\|0.566\|0.318\|0.633\|0.349\| \|DATM+CondTSF\|0.137\|0.291\|0.355\|0.452\|0.518\|0.231\|0.451\|0.290\| - 3-layer MLP(ReLU activated) \|\|Ex.Rate\|Wea.\|Elec.\|Tra.\|ETTm1\|ETTm2\|ETTh1\|ETTh2\| \|-\|-\|-\|-\|-\|-\|-\|-\|-\| \|MTT\|0.364\|0.311\|0.475\|0.633\|0.564\|0.362\|0.615\|0.354\| \|MTT+CondTSF\|0.139\|0.248\|0.375\|0.501\|0.493\|0.245\|0.423\|0.285\| \|TESLA\|0.352\|0.297\|0.525\|0.594\|0.541\|0.341\|0.606\|0.337\| \|TESLA+CondTSF\|0.128\|0.252\|0.397\|0.488\|0.487\|0.250\|0.438\|0.283\| \|DATM\|0.326\|0.349\|0.517\|0.622\|0.558\|0.329\|0.593\|0.350\| \|DATM+CondTSF\|0.141\|0.254\|0.385\|0.496\|0.498\|0.234\|0.437\|0.286\| --- Q3: What's the novelty beyond time series? A8: - All previous dataset condensation methods based on classification perform poorly on regression. The core novelty of our method is that it is the first dataset condensation method focusing on regression and significantly enhances the performance of all backbone methods. - In time series forecasting, when generating training data, the data is usually sampled overlap from the dataset. For instance, the data points can be sampled as $x_{0:24}, x_{4:28}$, etc. Please refer to Eq(12), inspired by the overlap property, we utilize an additive method to gradually update the synthetic data instead of directly using $M_f(s_{t':t'+m})$ to overwrite $s_{t'+m:t'+m+n}$ to avoid vibrations. - Additionally, other content related to time series can be explored in future works. We presented a simple yet effective method, which can serve as a prototype. --- Rebuttal Comment 1.1: Comment: Thank you for your rebuttal. I was expecting improvements on the writing quality of the paper. Would it be possible to cite in comment a few rewrites if any? --- Reply to Comment 1.1.1: Title: Plan of rewriting part of our paper Comment: Dear reviewer TXkn, Thank you for your comment and advice on improving the writing of our paper. We apologize for the ambiguity that exists in the current version. We will rewrite the following part of our paper. 1. We will clarify the source of the train set $f$, test set $x$, and synthetic dataset $s$ in Sec.3. 2. We will rewrite App.A1 and texts relate to Eq(5) to clarify the test error and the meaning of $t'$. We will also add an explanation of the effects when nonlinear models are used as expert models. 3. We will add a detailed introduction of MTT on how to optimize Eq(7) and Eq(8) in the appendix to clarify the core novelty of our paper. 4. We will add the complete results of using nonlinear models as expert models in the appendix to show that our method also works well with nonlinear experts. 5. We will add an explanation in Sec4.4 of how the additive method relates to the features of time series. Meanwhile, we are eager for the opportunity to address any remaining concerns you might have before the discussion period ends. We sincerely appreciate your and other reviewers' dedication and time invested in reviewing our work. Best, Authors	Summary: This paper provides a simple fix on the parameter-matching based dataset condensation methods for time series forecasting tasks. Besides matching the parameters of the model $M_f$ trained on the full training set and $M_s$ trained on the smaller synthetic dataset, it additionally induces the $M_f$ to perform well in the synthetic data too. It theoretically shows that the additional regularization contributes to an surrogate upper bound of the original objective, and empirically proves that the fix help improve various dataset condensation methods. Strengths: 1. The paper is well-written with clear structure and proper organization, and the motivation of the proposed condTSF plugin is solidly grounded by theoretical analyses 2. The proposed method is simple and easy to implement. 3. Impressive improvement are observed in the experiments on various baselines and benchmarks. Weaknesses: A few details are not clear. See questions. Technical Quality: 3 Clarity: 3 Questions for Authors: 1. In line 162, the author claims that it is "observed" that models initialized with different samples of parameter values predict similarly after trained on the full dataset given arbitrary input. Is it supported by any evidences, either theoretically or empirically? 2. Some clarity on optimizing gradient term can be provided. For example, when the parameters are matched and $M_s$ are well fitted, why the label error of $M_f$ on $s$ will increase? Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The limitation that the analysis only applies to linear models is discussed in the paper. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Q1: Is the claim "models initialized with different samples of parameter values predict similarly after trained on the full dataset given arbitrary input" in line 162 or Eq(9) supported by any evidence? A1: We apologize for the ambiguity. Please refer to Figure 3 and line 166-168, we support this empirical observation with experiments. The large orange points in the figure are input data, and the yellow and blue points are predictions of the models initiated with different parameters. We used MDS algorithm to reduce the dimension of the original prediction and data. MDS algorithm preserves the distance between points, which means points closer to each other in high dimensions are also close in low dimensions. It can be observed that the predictions of the models are similar despite their initial parameters are different. ---- Q2: Why the label error on $s$ will increase when the parameters of $M_s$ are matched. A2: We apologize for the ambiguity. - Firstly, The label error is used to evaluate the synthetic dataset $s$ instead of the expert model $M_f$. Please refer to Thm.2 and Eq(11), label error is an upper bound of the value term. Therefore label error ensures the similarity between prediction values of $M_f$ and $M_s$. - Secondly, the parameter loss is an upper bound related to the gradient term. It only ensures $M_s$ and $M_f$ have similar gradients on the input data, yet it does not ensure their value of predictions are similar. - To sum up, our analysis in Sec.4.1 and Thm.1 showed that value term and gradient term are decoupled in the optimization. Parameter loss relates to the upper bound of gradient term while label error is the upper bound of value term. Therefore, even when parameter loss is small, the label error can still be large.	Rebuttal 1: Rebuttal: Dear reviewers and area chairs, We thank all reviewers and area chairs for their valuable time and comments. We have responded to each reviewer individually to address any comments. We would like to give a brief summary. 1. We clarify some of the meanings of the notations in our paper to address the concern. 2. We provide information on backbone methods and explain the novelty of the work. We also explain that our proposed method has designs that relate to the features of time series. 3. We add experiments using nonlinear models as expert models and show that CondTSF also works well with nonlinear expert models. 4. We explain the practical applications of dataset condensation and show that dataset condensation for time series forecasting has pragmatic values. 5. We show that deriving the upper bound of the gradient term is necessary because there exists unavailable test data in the original form. 6. We show that dataset condensation and model distillation are distinct tasks, and thus the methods are not comparable. 7. We add experiments using a low pass filter to perform target smoothing on synthetic data and show that CondTSF is significantly more effective than target smoothing. 8. We add experiments using only CondTSF(optimizing only value term) and show the impacts of gradient term and value term. Again, we thank all reviewers and area chairs! Best, Authors	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
A Structure-Aware Framework for Learning Device Placements on Computation Graphs	Accept (poster)	Summary: The paper is about computation graphs, which is an interesting topic. The authors propose a novel framework for the task of device placement, relying on smaller computation graphs extracted from the OpenVINO toolkit using reinforcement learning. The paper is well written and well organized. However, there are several concerns in the current version of the paper that addressing them will increase the quality of this paper. Strengths: 1 Novel ideas. 2 Good writing. 3 Sound experiments. Weaknesses: 1 The author mentioned that concatenating features from different angles would bring benefits. So would concatenating or fusing these features at different dimensional sizes affect their effectiveness? 2 This seems like an interesting research question, but the authors don’t seem to explain the methods used clearly in the main text. I think it is necessary to add an appendix to show the whole framework in the form of a flowchart or pseudocode and explain it in detail. 3 Is a larger baseline model needed for comparison? Large models are popular at present. If it is not necessary, the author can explain the reasoning without adding corresponding experiments. Technical Quality: 3 Clarity: 3 Questions for Authors: As above. Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The authors provide a discussion of limitations, but it is uncertain whether this is comprehensive. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We would like to genuinely thank you for your thoughtful comments and your interest in the selected topic. Please find our response to your comments and suggestions below. We have also updated the manuscript in light of your suggestions towards increasing the quality of our paper. 1. Concatenating or fusing features at different dimensional sizes. Concatenating or fusing the initial features at different dimensional sizes indeed affects the effectiveness of the framework. In fact, during our initial experiments, we found that a well-balanced combination of feature dimensions results in better model performance and robustness. Therefore, we decided to encode the initial features using equal-sized latent representations. We would like to highlight that the flexibility of our framework allows for different feature combination schemes, such as averaging the feature vectors, increasing or decreasing the dimensionality of the feature vectors, or even attending to each feature differently. This is an interesting area for future investigation. We hope that our answer clarifies your question. 2. Framework explanation and pseudocode. We would like to thank you for pointing this out and we are pleased you found our research question interesting. Due to the fact that our framework is flexible and can be implemented using a wide range of different components (e.g. using a simple MLP instead of a GCN), the initial goal was to keep the main description of the framework as simple as possible, in an attempt to avoid information overload that may confuse and distract the readers. After taking into consideration your suggestion, we have prepared for you a pseudocode that describes the entire flow. We will add this pseudocode in the appendix: Main Algorithm: Hierarchical Structure-Aware Device Assignment Graph (HSDAG) --- 1. Initialize computation graph $G$, coarsened graph $G'$, node features $F$, and maximum iterations $max\_{iterations}$. 2. Initialize parameters $\theta$ of Graph Parsing Network (GPN) and Multi-Layer Perceptron (MLP). 3. Initialize node assignment matrix $\mathcal{X}$, Adam optimizer, buffer size $x$, and discount factor $\gamma$. 4. For $i = 1$ to $max\_{iterations}$ do a. Apply GPN: $(C, F_C) \gets GPN(G, F)$, where $C$ are clusters and $F_C$ are cluster features. b. Apply MLP: $P' \gets MLP(F_C)$ to get device placement for coarsened graph. c. Map $P'$ to original graph $G$ using assignment matrix $\mathcal{X}$. d. Deploy $G$ with device placement $P'$ and measure inference latency $l_{P'}(G')$. e. Calculate reward: $r_{P'}(G') \gets 1 / l_{P'}(G')$. f. Update node embeddings: $\mathbf{Z_v} = \mathbf{Z_v} + \mathbf{Z_{v'}}$ for each node $v$ and its corresponding coarsened node $v'$. g. Form a new coarsened graph $G'$ as the new state. h. Run a new round of representation and group learning for a new graph $G'$. i. Store step information $(P, G', r_{P'}(G'))$ in buffer. j. If buffer reaches $x$ steps: - Compute gradient: $\nabla_\theta J(\theta) \approx -\sum_{i=1}^x \nabla_\theta \log p(P \| G'; \theta) \cdot \gamma^i \cdot r(P_i, G)$ - Update policy parameters $\theta$ using Adam optimizer with the computed gradient. - Clear buffer. k. If convergence criteria are met, break the loop. 5. Return optimal device placement $P_{opt}$. Sub-Algorithm: Graph Parsing Network (GPN) --- 1. Initialize input graph $G$ with node features $X^{(0)}$ and adjacency matrix $A$. 2. Initialize learnable parameters $W$ for GNN. 3. For each iteration: a. Perform graph and node encoding: $Z = GNN(X, A) = \sigma(\hat{D}^{-1/2}\hat{A}\hat{D}^{-1/2}X^{(0)}W)$ where $\hat{A} = A + I$, $\hat{D_{ii}} = \sum_{j=0} \hat{A}_{ij}$ b. Calculate edge score matrix: $S_{v,u} = \sigma(\phi(z_v, z_u))$, where $\phi$ is MLP c. Apply Graph Parsing Algorithm $\mathcal{A}$: - Stage 1: $\hat{C}^{(k)} \gets DOM(C^{(k)})$ - Initialize: $s \gets \emptyset$, $p \gets 0$ - Stage 2: While $sum(\hat{C}^{(k)}) \neq 0$ do: * $idx \gets argmax(\hat{C}^{(k)})$ * $q \gets \|idx\|$ * $(l, idx') \gets EXP(idx, \hat{C}^{(k)})$ * $idx \gets union(idx, idx')$ * While $\|idx\| = q$: + $s \gets union(s, \{(i,p)\|i \in l\})$ + $\hat{C}^{(k)}_{i,j} \gets 0, \forall (i,j) \in idx$ + $p \gets p + 1$ - Stage 3: $S^{(k)} \gets GEN(s)$ d. Create node assignment matrix: $\mathcal{X} = \mathcal{A}(\mathcal{E})$ e. Define adjacency matrix for pooled graph: $A' = \mathcal{X}^T \cdot A \cdot \mathcal{X}$ 4. Return pooled graph $G'$ and node assignment matrix $\mathcal{X}$ 3. LLM comparison. Thank you for the question. Experiments on LLMs would be beneficial to have although not strictly needed for demonstrating the effectiveness of our method. Given that our method is not strictly dependent on the model architecture, and that we showed its effectiveness on a diverse set of architectures, one of which was transformer-based (the foundation of LLMs), we do believe that our method would be scalable and effective for LLM as well. Reviewer wsma made a quite similar comment. We kindly ask you to have a look at this response as well, as it provides additional context. Limitations. Thank you for your comment. We kept the discussion of limitations section within the required space limits. We will elaborate more on this section and provide a revised version in the appendix. --- Rebuttal Comment 1.1: Comment: Thanks for the author's reply, I have no doubts anymore. --- Reply to Comment 1.1.1: Title: Thank you! Comment: Thank you for carefully reading our response. We are glad that our response addressed all of your concerns.	Summary: The authors have developed a model that automatically places neural network operations on the optimal devices (CPU and GPU) to accelerate model training. They optimize device placement using reinforcement learning and use execution time as the reward. The authors propose using the graph structure as information to choose the appropriate device for each operation. They evaluate their method based on execution time gains compared to several baselines and demonstrate significant improvements on three architectures. Strengths: - The paper is very well written, and all the steps of the model are well detailed, making it easy to understand. - The experiments reflect the quality of their method compared to the state-of-the-art. - The ablation studies show the impact of each component of the model. Weaknesses: / Technical Quality: 4 Clarity: 4 Questions for Authors: I did not understand how the computation graph of the neural network was retrieved. Could you please provide more details? Is there any impact of the chosen GNN architecture, such as GCN or GAT, for example? Confidence: 3 Soundness: 4 Presentation: 4 Contribution: 4 Limitations: I see no ethical limitations; the checklist is well completed, and clear justifications are provided. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We would like to thank you for the kind words and we are glad that you liked our paper. We provide clarifications on details that may have been unclear. Computation graph. To convert a neural network model to an OpenVINO computation graph, we first design the model using a deep learning framework like PyTorch. Next, we convert and save the model to OpenVINO's Intermediate Representation (IR), which consists of an XML file representing the model's structure. By reading this XML file, we extract the necessary information to understand the model's layers and their connections. Finally, we use this information to build a directed acyclic graph that represents the computation process of the neural network, ensuring each layer is properly mapped and connected. Impact of the chosen GNN architecture. We would like to thank the reviewer for posing this interesting question. There is no major impact in choosing a different GNN architecture, such as GCN, GAT, GIN or GraphSAGE. We selected GCN since it is the de-facto GNN layer every baseline model uses and the one that was proposed by the paper on graph parsing networks [1]. To verify whether a GNN architecture critically affects the performance of our framework, we run more experiments with different GNN layers. We provide the results in the table below (execution time in seconds): \| \| Inception-V3 \| ResNet \| BERT \| \|-----------\|-------------\|---------\|--------\| \| GCN \| 0.0105 \| 0.00766 \| 0.00267\| \| GAT \| 0.0109 \| 0.00772 \| 0.00272\| \| GIN \| 0.0104 \| 0.00770 \| 0.00269\| \| GraphSAGE \| 0.0102 \| 0.00767 \| 0.00266\| References 1. Song, Yunchong, et al. "Graph Parsing Networks." arXiv preprint arXiv:2402.14393 (2024). --- Rebuttal Comment 1.1: Comment: Thank you for your response and your clarifications. I'll keep my score as it. --- Reply to Comment 1.1.1: Title: Appreciation for your feedback! Comment: Thank you for your thorough review and feedback. We appreciate your positive evaluation and are grateful for your support of our work.	Summary: This paper introduces an end-to-end framework utilizing policy optimization for device placement during the inference phase of deep learning models. The framework consists of multiple components, including computation graph construction, graph coarsening, node representation learning, and policy optimization. Evaluations using benchmark models such as Inception-V2, ResNet, and BERT demonstrate improved CPU execution speedup compared to several device placement methods. Strengths: +This paper presents a nice overview figure of the proposed framework with a detailed description of each step in the framework. +The paper has provided code and implementation details. Weaknesses: -After reading the paper, I do not think the motivation of the designed framework is strong. It is not clear to me what the rationale of each component and the choice of this policy optimization method is. -Some suggestions on paper presentation: In the abstract, it would be helpful to introduce the problem of device placement, and the concepts of “computation graphs” and “heuristic methods” in this problem. It is not clear to me why ignoring the topological features of computation graphs is an issue. -Some redundancy can be reduced. For instance, in definition 2.2, “a device p in D, where p in {1,2,…,\|D\|}.” -The problem setup is confusing. There are also some inconsistent notations between the text and the equations. It would be nice to have some descriptions of the device placement process. -It seems that graph structural features do not help that much in the speedup from Table 3. -It would be useful to include the complexity comparison of the proposed method with other baseline methods. Technical Quality: 2 Clarity: 2 Questions for Authors: 1) In the abstract, the last sentence is confusing: “the suggested placements improve the inference speed for the benchmark models by up to 58.2% over CPU execution and by up to 60.24% compared to other commonly used baselines”. What is the improvement of 60.24% measured on? Is this accuracy or CPU execution? 2) Some notations in Definition 2.2 are not clear. What is the index n in a placement P? Is this equivalent to the number of nodes \|V\| or to the number of devices \|D\|? 3) In the problem setup, is there any order when assigning operations to a device? Why do we need to use policy learning? 4) What does HSDAG stand for? Confidence: 3 Soundness: 2 Presentation: 2 Contribution: 2 Limitations: Some limitations are discussed in the conclusion section. Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for the insightful comments. We hope our response addresses your concerns and highlights the framework’s motivation and rationale. TL;DR: Our high-level motivation is to address the ever-growing capacity requirements for efficient inference on heterogeneous devices. Please refer to the first two paragraphs of similar work “Placeto: Learning Generalizable Device Placement Algorithms for Distributed Machine Learning” where the motivation and the choice of RL for this problem are nicely consolidated. Admittedly, our motivation is not as well-presented. We will make some minor restructuring and make it more clear. In the following text, we have prepared for you a detailed explanation of our rationale, which we hope addresses your concerns. We invite you to read it and please let us know if you think we should briefly mention/highlight any of these in the introduction. Limitations, motivation, rationale: 1. Limitation: Not capturing directed interactions among nodes. Why is this a limitation? The model runs poorly in graph coarsening. Solution: We use local/global structural features. Our ablation study verifies that such features increase the model’s performance. 2. Limitation: Relying only on heuristics or simple methods (e.g. k-means) for graph partitioning. Why is this a limitation? Such methods require hyperparameter tuning for their components to obtain good performance. This ad-hoc presetting of the group number inhibits the exploration, generalization and learning process of a framework. Solution: We learn how to partition a given graph into an unspecified number of groups. Both the number of node groups and the pooling algorithm are end-to-end learnable parameters. Our framework facilitates “personalized” partitioning: the number of node groups is dynamically decided depending on the scale of the computation graph and a more sophisticated algorithm for pooling is learned. 3. Limitation: Following either grouper- or encoder-placer architecture. Why is this a limitation? In both cases, end-to-end training is not allowed as the encoding and coarsening steps run sequentially and individually. Thus, their components are not trained based on the optimal device placements. Solution: We fuse encoder- and grouper-placer techniques and effectively combine their strengths to jointly optimize end-to-end representation learning and graph coarsening phases interdependently. 4. Limitation: Not supporting simultaneously training all steps in an end-to-end fashion. Why is this a limitation? Supporting end-to-end training is necessary to ensure each step is tailored to the final device placement. Solution: We carefully designed our framework to enable end-to-end training, where all components are trained simultaneously. 5. Limitation: Ignoring topological features (also an answer to weakness 4). Why is this a limitation? Topological features allow frameworks to model the order of nodes. Solution: Our framework learns how to better partition a computation graph, leading to better performance. Our ablation study shows the benefits of topological features. Introducing concepts, redundancy, inconsistent notations. We have improved the abstract by introducing the device placement problem and mentioning the concepts of computation graphs and heuristic methods. We have removed redundancies and improved the notation. Graph structural features. The varying impact of graph structural features over different models correlates with the complexity of computation graphs. Inception-V3 has a complex computation graph and an architecture with multiple parallel branches leading to higher values in all metrics (see table below). For such complex graphs, GNN approaches struggle to extract all essential features. So, adding structural features enhances their ability to model important graph characteristics. Conversely, simpler graphs allow GNNs to extract relevant features without external support. So, graph structural features have less of an impact on their performance. \|Metric\|BERT\|Inception-V3\|ResNet\| \|--------\|------\|--------------\|--------\| \|Graph Diameter\|34\|49\|32\| \|Average Fractal Dimension\|0.00412\|0.00427\|0.00392\| \|Degree of Heterogeneity\|1.247\|1.367\|1.268\| Framework’s Complexity. Please take a look at a similar response to Reviewer wsma. Answers to questions: Q1. Both values refer to execution runtime. As CPU-only execution is one of the most important baselines, we highlight our performance against it. 60.24% is the improvement of the execution speed against Placeto. We have slightly rephrased to avoid confusion. Q2. The index n in a placement $P$ is the number of nodes $\|V\|$. We included the missing notation. Q3 Assigning order and policy learning. We understand your concern about using policy methods for this problem as the use of RL might not be directly suggested. We invite you to have a quick look at similar studies below: 1. Figure 2 and Section 2.1 - “MDP Formulation” of “Placeto: Learning Generalizable Device Placement Algorithms for Distributed Machine Learning”: The device placement is modeled as an iterative process where the algorithm inputs a current placement, picks a node and outputs a device for that node. 2. Figure 1 in “Accelerated Device Placement Optimization with Contrastive Learning”: The state-space/observation is the entire computation graph and the input to the policy algorithm. The output is an assignment that maps each node to a device. Our problem formulation is similar to this one. In both cases, the order of assigning nodes to devices does not matter. This is not due to the RL problem formulation but rather due to the nature of the problem. The reward only depends on the final device placement. Q4 HSDAG = Hierarchical Structure-Aware Device Assignment Graph --- Rebuttal Comment 1.1: Comment: Thanks for addressing my concerns. I just wish the context information is included in the paper as a paper should be self-contained and the background knowledge is important in this research topic. --- Reply to Comment 1.1.1: Comment: Thank you for your feedback. We are glad that our response addressed your concerns. We will make sure all the context information is included in the final version of the paper. We welcome any further discussions.	Summary: The paper introduces a novel framework for device placement that leverages smaller computation graphs extracted from the OpenVINO toolkit using reinforcement learning. This framework bridges the gap between encoder-placer and grouper-placer techniques by incorporating graph coarsening, node representation learning, and policy optimization. It supports end-to-end training and considers the directed and acyclic nature of computation graphs. The framework also includes a model variant inspired by graph parsing networks and complex network analysis, enabling joint learning of graph representation and personalized graph partitioning. Experimental results demonstrate significant improvements in inference speed for benchmark models like Inception-V3, ResNet, and BERT. Strengths: * The framework effectively combines graph coarsening, node representation learning, and policy optimization, allowing for a comprehensive approach to device placement that captures both local and global structural features. * The ability to train all components of the framework in an end-to-end fashion ensures that the model can learn optimal device placements efficiently, improving overall performance. * The proposed framework demonstrates substantial improvements in inference speed, achieving up to 58.2% over CPU execution and up to 60.24% compared to other baselines, highlighting its effectiveness and robustness. Weaknesses: * Could the strategy that uses the execution time only of the suggested device placements as a reward to train the proposed framework hinder the generalization of it to other scenarios? Are there any other rewards that the authors attempt to incorporate into their framework? * Besides the inference latency, could the authors provide the results of different models on the standard benchmarks to reflect that HSDAG could not only accelerate the deployment but also not affect the performance of downstream tasks? * The complexity of the proposed framework and comparison of the running time for getting the final allocation strategy with baselines can further strengthen the manuscript. * While the authors elicit the challenges from the perspective of foundation models, could the authors showcase the potential ability of HSDAG in handling foundation models such as LLMs? * Minor: The title should follow the Research Paper Title Capitalization Rules. $n=\|V \|$ is the number of nodes that should be noted in Definition 2.2. Technical Quality: 4 Clarity: 3 Questions for Authors: Please kindly refer to the Weaknesses. Confidence: 4 Soundness: 4 Presentation: 3 Contribution: 3 Limitations: The limitations are discussed after the conclusion. Minor: There is a typo in the limitation section: "We attempted to obtain \underline{the he} source codes for the baseline methods". Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you very much for recognizing the novelty of our framework, and highlighting its effectiveness and robustness. Below we provide point-to-point responses to your questions/concerns. We hope that our response addresses your concerns. Execution time as a reward. Thank you for this remark. Most of the existing work on device placement (including our baseline models) uses the execution time as a reward and as the most important evaluation metric since, ultimately, the goal is to speed up the inference time [1,2]. Hence, in this paper, we follow the same protocol. The experimental results (Table 2, page 8) from both our approach and the baseline models demonstrate that the generalization is not compromised by following a strategy to minimize the execution time. Generalization would potentially come into play in the case of a reward model, which would make sense for this problem given the difficulty in measuring the reward. Another option for this problem would be to use incremental rewards like those mentioned in Section 2.1 of “Placeto: Learning generalizable device placement algorithms for distributed machine learning” which, however, do not quite fit our RL problem formulation (but which, interestingly enough, would benefit from a reward model). Exploring the reward model direction, potentially incorporating incremental rewards (the combination of which would allow us to leverage the low variance and faster convergence associated with less sparse rewards) and studying how it impacts generalization, is a very interesting direction for future work. We will briefly mention this in the conclusion. Model performance in downstream tasks. Thanks for your comment and for pointing this out. Theoretically, since the algorithm itself does not change, the performance of the model in downstream tasks will remain the same. For further verification, we conducted experiments using the Inception-V3, ResNet and BERT models and provide the results below: 1. Inception-V3: We performed image classification inference on images depicting Samoyed dogs. All the parameters are directly derived from the torchvision pre-trained model. We did not change any configuration on the data type of the model. The classification accuracy of Inception-V3 using the best device placement is 82.77%. For the GPU-only experiments the classification accuracy is 82.72%. For the CPU-only experiments the classification accuracy is 82.33%. 2. ResNet: Similarly, we performed image classification inference using the ResNet model on the same dataset. The classification accuracy with the best device placement is 45.37%. For the GPU-only experiments the classification accuracy is 45.37%. For the CPU-only experiments the classification accuracy is 45.44%. 3. BERT: We evaluated the performance of the BERT model using the output embeddings from the different device placements. We calculated their mean squared error, cosine similarity and Euclidean distance (MSE: the lower the better, cosine similarity: the higher the better, euclidean distance: the lower the better): \| Comparison\|Mean Squared Error (MSE)\|Cosine Similarity\|Euclidean Distance (L2 norm)\| \|------------------\|---------------------------\|-----------------------\|------------------------------\| \|CPU vs GPU\| 3.04970071738353e-05\|0.9999468922615051\|0.4328667223453522\| \|CPU vs HSDAG\|6.819997793172661e-07\|0.9999988079071045\|0.06473180651664734\| \|GPU vs HSDAG\|3.174534140271135e-05\|0.9999447464942932\|0.44163718819618225\| The conducted experiments demonstrate that HSDAG does not affect the performance of the model in the downstream tasks. All models have similar performance regardless of the running device (e.g. CPU, GPU or heterogeneous device). Framework’s complexity. Thank you very much for the suggestion on calculating the complexity of the proposed methods. We provide a table with the running time complexity in seconds of our method and the baseline methods. As it is shown, HSDAG is significantly faster in all cases. We agree that these additional experiments do indeed strengthen our manuscript and we will make sure to include them in the appendix. \| \| Inception-V3 \| ResNet \| BERT \| \|-------------\|--------------\|--------\|-------\| \| Placeto\| 2808s\| 1162s \| 4512s \| \| RNN-based\| 3706s\| 1212s \| OOM\| \| HSDAG\| 2454s\| 1047s \| 2765s \| HSDAG handles LLMs. We indeed elicit the challenges from the perspective of foundation models. We believe that the ever-rising capacity requirements and cost associated with LLMs will make the problem of device placement even more important. Since: 1) our method is not strongly dependent on the architecture or scale of the underlying model, 2) we showcased the effectiveness in diverse architectures and 3) one of those architectures was a transformer-based model (BERT) which is the foundation of LLMs, we do believe that HSDAG is extensible and applicable to LLMs. Nonetheless, LLMs pose their own unique challenges and without a strong empirical evaluation on diverse LLM architectures (which would be extensive enough to produce another manuscript), we did not want to make any claim about the extensibility and scalability of our method. We will add 2 short sentences in the conclusion to highlight this future direction and as well as its unique challenges. Typos, capitalization rules and missing notation. We will update and fix it accordingly. Thank you. References 1. Mirhoseini, Azalia, et al. "Device placement optimization with reinforcement learning." International conference on machine learning. PMLR, 2017. 2. Addanki, Ravichandra, et al. "Placeto: Learning generalizable device placement algorithms for distributed machine learning." arXiv preprint arXiv:1906.08879 (2019). --- Rebuttal Comment 1.1: Comment: Thank you for the rebuttal. I have also read the reviews from other reviewers as well as the corresponding reply. I have no further questions and I choose to increase my current rating accordingly. --- Reply to Comment 1.1.1: Title: Thank you for raising the score! Comment: Thank you for carefully reviewing all the reviews and replies, as well as for your timely response. We are glad to see that your concerns have been addressed and thank you for the updated score.	Rebuttal 1: Rebuttal: We thank all the reviewers for their careful reading and thoughtful comments and suggestions on our paper. We find it encouraging that reviewers have found our work interesting, novel and well-organized! The suggestions have led us to further improve the clarity of the manuscript, improve minor issues as well as add some more technical details. We have addressed the individual reviewer’s comments below. Here, we summarize the proposed changes, which we hope are within the extent of allowed modifications and would not fundamentally alter the main method and results. Changes: * Additional experiments: We will add the results of the auxiliary experiments conducted during the rebuttal period to the Appendix of the paper. These experiments: 1. Demonstrate that the performance of downstream tasks is indeed not affected by our framework (Reviewer wsma); 2. Show the complexity of the framework (Reviewer orCV, Reviewer wsma); 3. Demonstrate the importance of the graph structural features (Reviewer orCV). * Fixing notation issues, typos, and briefly introducing the problem definition in the abstract (Reviewer orCV, Reviewer wsma). * Slightly restructuring the introduction to make the high-level motivation more clear (Reviewer orCV). * Summarize our entire flow in a pseudocode block to be added in the appendix (Reviewer RMDa). * Add a few future research directions and limitations in the conclusion and appendix, respectively (Reviewer RMDa, Reviewer wsma).	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Injecting Undetectable Backdoors in Obfuscated Neural Networks and Language Models	Accept (poster)	Summary: The paper proposes a theoretical pipeline to inject undetectable backdoors into deep learning models. The pipeline consists of several steps. First, the neural network is trained and converted to a boolean circuit. Then, a non-replicable backdoor can be injected into the binary circuit using pseudo-random generators and digital signatures. After the backdoor is injected, the boolean circuit gets obfuscated and converted back into a neural network. Strengths: - The paper tackles a very serious problem, as backdoors can be a threat to systems used in production Weaknesses: - To me, the paper's contribution is not quite clear. Since Goldwasser et al. (2022) have already shown how undetectable backdoors can be injected into binary classification deep learning models, it is hard to tell what the novelty of this paper is. Underlining this, many of the assumptions and definitions are apparently taken from related work. - There are multiple definitions and theorems for which it is not fully explained why they are needed. This makes it hard to read and follow the paper. - There is no conclusion or discussion at the end of the paper. Instead, the paper abruptly ends. - There is no intuitive explanation on why all the parts (PRG, signature) are needed. Instead, the readers have to figure that out by themselves using the equations. - It is a bit confusing that the definition of a backdoored model always includes three models f, $\tilde{f}$, and $\hat{f}$. It would be much easier if the backdoored model were defined with two models--the original model and the backdoored model, which tries to mimic the original model while having a backdoor. - Many important definitions and almost everything concerning backdoors in LLMs are only present in the appendix. - It is unclear why anyone would want to train an ANN, convert it to a binary circuit, obfuscate the boolean circuit, and then convert it back to an ANN if no backdoor should be injected. If a malicious company would train a model like that for a customer, the customer would ask why the model is trained this way. - The undetectability of the backdoor assumes that there exists a procedure "Perturb", such that the backdoor is not detected. However, it is unclear whether such a procedure exists. So, big parts of the paper are based on assumptions for which it is not known whether these assumptions hold in reality. Technical Quality: 2 Clarity: 2 Questions for Authors: Q1: In line 267, it seems the backdoor is only activated if the output of the PRG(X_PRG) equals the output of PRG(S). However, the probability that this will happen is very low. So, what is the intuition of this part of the equation? Q2:* Why would anyone wanna train a network, convert it to a binary circuit, obfuscate it, and convert it back to a network when no backdoor is injected? Confidence: 4 Soundness: 2 Presentation: 2 Contribution: 2 Limitations: The limitations of the proposed approach are not discussed. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: [Part 1/n] We want to thank the reviewer for reading our paper carefully, for appreciating our results and for their constructive feedback and comments. Q1) To me, the paper's contribution is not quite clear. Since Goldwasser et al. (2022) have already shown how undetectable backdoors can be injected into binary classification deep learning models, it is hard to tell what the novelty of this paper is. Underlining this, many of the assumptions and definitions are apparently taken from related work. A1) The construction of Goldwasser et al. (2022) to plant backdoors to general NNs works only when the distinguisher has black-box access to the model, i.e., they cannot see the weights/architecture of the model, which we argue that it is a very important limitation of their work. Their construction to plant backdoors when the distinguisher has white-box access works for a rather limited family of training algorithms/models. Moreover, Goldwasser et al. (2022) do not touch the topic of LLMs. To the best of our knowledge, our work is the first to give a theoretical construction for planting backdoors in such models. We underline that we have listed our contributions in Lines 48-58 as well as Section 1.1 of our manuscript. Moreover, we have provided a comparison with Goldwasser et al. (2022) in Lines 129-142 as well as in Appendix C. For completeness, we reiterate some of these points below. Our contributions can be listed as follows: We provide a modified (weaker) definition of planting backdoors, and we show how we can achieve undetectable planting under this definition under distinguishers that have white-box access to the model. We provide a construction that satisfies this definition and is based on iO. We provide similar definitions and constructions in the context of LLMs, which have not appeared in prior work. We show how Boolean functions can be well-approximated by quite compressed NNs (Theorem 14 in our manuscript), which we believe can be useful even outside the scope of our work. Q2) There are multiple definitions and theorems for which it is not fully explained why they are needed. This makes it hard to read and follow the paper. A2) Thank you for your feedback. We tried our best to produce a write-up that is consistent and within the page limits. For this we need all the definitions and theorems we have listed in our work but as you say in some places some additional explanation is missing due to the space limitations. That said, we put a lot of effort into being able to handle both NN classifiers and LLMs through a conceptually similar approach which reduces the need for extra space and makes the results easier to follow. We plan to utilize the extra page of the camera ready version to elaborate more on several definitions and theorems and thus improve the presentation of our results. If the reviewer has any concrete suggestions about this we would be more than happy to hear them. . Q3) There is no conclusion or discussion at the end of the paper. Instead, the paper abruptly ends. A3) Thank you for pointing this out, we are happy to the following Conclusion section in the next version of our work: Given the plethora of applications of Machine Learning in general, and neural networks in particular, questions regarding the trustworthiness of publicly released models naturally arise. In particular, before deploying a neural network we need to guarantee that no backdoors have been injected allowing bad actors to arbitrarily control the model behavior. In this paper, we investigate the existence of backdoor attacks to obfuscated neural networks which are undetectable even when given white-box access. The notion of obfuscation that we consider is the well-studied and mathematically founded indistinguishability obfuscation (iO). We also show how our techniques can inspire backdoor schemes in large language models when combined with ideas from steganography. While our constructions are purely theoretical, we leave as an interesting direction how to use heuristic obfuscation methods to show practical instantiations of our constructions. Another interesting open question is whether cryptographic schemes weaker than iO suffice to show backdoor undetectability in the white-box model. Q4) There is no intuitive explanation on why all the parts (PRG, signature) are needed. Instead, the readers have to figure that out by themselves using the equations. A4) We respectfully disagree with this comment. We believe that we explain why all the cryptographic tools that we define are needed. For example, we explain where PRGs are needed in Lines 260-266 of our manuscript. Similarly, we explain the use of signatures in these lines. Moreover, in Lines 278–281 we explain why digital signatures give us non-replicability. We are more than happy to elaborate more or modify the explanations if this improves our writeup but we have already put a lot of effort into this. Q5) It is a bit confusing that the definition of a backdoored model always includes three models f, \hat{f}, and \tilde{f} . It would be much easier if the backdoored model were defined with two models--the original model and the backdoored model, which tries to mimic the original model while having a backdoor. A5) Our main goal is to show that the obfuscated version of $f$ and the obfuscated version of the backdoored $f$ are indistinguishable. Since it is not clear how to directly compare the obfuscated version of $f$ with the obfuscated version of the backdoored $f$, we use some “intermediate” quantity in order to, intuitively, “chain” the equalities. This is mostly part of the theoretical analysis in order to derive the theoretical result. We underline again that our guarantee is established with respect to two functions: the obfuscated version of $f$ and the obfuscated version of backdoored $f$. We will clarify that for the final version. --- Rebuttal Comment 1.1: Title: Rebuttal Answer Comment: Thank you for your detailed answer. To be fair to other authors who submitted to NeurIPS and kept the 6k character limit, I will only reply to the rebuttal, not the comment. A1) Thank you. I now have a better understanding of the difference to Goldwasser et al. However, the result for LLMs, which you claim to be one of the most important parts of why your paper is novel, is only available in the appendix. If this is one of the most important points, I think the paper needs to be restructured to reflect the title and include this in the main part of the paper. A2/A3) Thank you for your answer. I get that it is hard to convey everything with such little space. However, I think this can be done by rearranging the paper's content. In my opinion, it is not a good idea to omit the conclusion and the important section of a discussion of the own work, as this gives the reader additional context. A4) Thank you for pointing that out. I get why you are using the digital signature. In the lines you have referred to (lines 260-266), I can see where the PRG and the signature are used. However, I was referring to giving the reader an intuition why these cryptographic tools are used there. So, what is the intuition of using the PRG? There might be a misunderstanding here, which is why this might be connected to Q1 of mine. It seems the backdoor is only activated if the output of the $PRG(X_{PRG})$ equals the output of $PRG(S)$. However, the chance of this happening seems to be very low. Could you clarify under which scenarios the backdoor is activated in the equation following line 267? A5)* Thank you very much for your answer. This resolves my question. --- Reply to Comment 1.1.1: Comment: > A1 We will restructure the paper and LLM content to the main body. > A4 (part 1) The intuition for using a PRG can be explained nicely by the strawman solution proposed by Reviewer paZi: A backdoor should be a part of the code that can be activated if we know some information that nobody else can efficiently find. A strawman solution would be to add a SAT instance: if the instance is satisfiable, then anybody with the satisfying assignment can activate the backdoor. If it is not satisfiable, then there exists no backdoor. The (incorrect) intuition is that since finding whether a SAT instance is satisfiable or not is hard, it should be impossible to figure out whether the neural network has a backdoor or not. This intuition does not directly work, as we explained to Reviewer paZi, and to make it work we have to replace the SAT with a PRG. We are repeating our answer to Reviewer paZi for an explanation on why this strawman solution does not work. According to our definition, which follows the blueprint of Goldwasser et al., a backdoor is undetectable if any (polynomially bounded) adversary cannot distinguish between an honestly generated model and one with a backdoor. If we inject a specific satisfiable formula in the honest case, then there exists a simple adversary, that checks whether a hardcoded assignment is satisfiable, succeeds. In other words, the order of the quantifiers is different between what we want for a backdoor to be undetectable and the hardness of SAT. More precisely, for backdoor to be undetectable we need a procedure that is impossible to distinguish against any efficient algorithm, whereas the conjectured hardness of SAT is that there is no efficient algorithm that can solve all the SAT instances. We are happy to elaborate more if needed. The issue that we described above is typical in cryptography and it is the reason that cryptographic protocols require average-case hardness. Unfortunately, SAT is not average-case hard, so our solution to this issue is to use instead the well-studied cryptographic primitive of PRGs: instead of a SAT formula, we include a number that is either pseudorandom or truly random. Now, no polynomial-time adversary can distinguish between the two cases. We will add this explanation to our paper to give intuition about the use of PRGs. For the digital signatures, the intuition is quite simple: the PRG (as the SAT formula) only requires one value to activate the backdoor. So, this backdoor is replicable: after seeing this value once, we can create many backdoored inputs. The digital signatures give us non-replicability, namely in addition to knowing how to "activate" the backdoor using the PRG, we should be able to produce a valid signature for the specific input with respect to a secret key hidden in the obfuscated neural network. Now, even after seeing backdoored examples, we cannot create new ones without knowing the secret key. For the non-replicability part of our construction to work, it is essential that the final neural network is obfuscated. Otherwise, anybody that inspects that NN would be able to see the secret key corresponding to the digital signature scheme. Even though outputting obfuscated NNs might seem suspicious, we believe that there are legitimate use-cases where adding an obfuscation step before the release of the model could be part of an honest training pipeline and should not constitute on its own an attempt from the company to do something malicious with the model. Consider the following motivating examples: -Privacy of Training Data: If the training data includes sensitive user information, using obfuscation could help ensure that this data remains private and secure. -IP Protection: Companies often have proprietary models. Applying obfuscation allows these companies to publicly release their models with less risk of reverse-engineering their models or techniques. If we allow the use of obfuscation then, our claim is “that an obfuscated version of the original model is indistinguishable from the backdoored one”. And due to the general utility of using obfuscation we consider such a recipe not suspicious. The theoretical guarantees for our construction are based on using a specific type of obfuscation called indistinguishability obfuscation (iO). The recent breakthrough result of Jain et al. [2021] has shown that indistinguishability obfuscation (iO) does exist, by combining standard tools from cryptography. > A4 (part 2) You are right that the backdoor is activated only when $PRG(X_{PRG})=PRG(S∗)$ and this happens with extremely small probability unless we know $S$. If we already know $S$, then we can just set $X_{PRG} = S$ to make sure that the backdoor is activated. So, the fact that it is hard to find $S$ is necessary so that only people that know the backdoor can activate it. On the other hand someone that knows $S*$ can activate the backdoor whenever they want. This creates a usable but undetectable backdoor. --- Rebuttal 2: Comment: [Part 2/n] Q6) Many important definitions and almost everything concerning backdoors in LLMs are only present in the appendix. A6) Thank you for your comment. Unfortunately, due to the lack of space, we had to move some content to the appendix. If the paper gets accepted, we will utilize the extra space to move part of the discussion regarding LLMs to the main body. Q7) It is unclear why anyone would want to train an ANN, convert it to a binary circuit, obfuscate the boolean circuit, and then convert it back to an ANN if no backdoor should be injected. If a malicious company would train a model like that for a customer, the customer would ask why the model is trained this way. A7) This is a good point worth clarifying. Our construction aims to show a fundamental limitation of DNNs and LLMs by illustrating a concrete backdoor attack with strong theoretical guarantees. In practice, one could use some heuristic method in order to obfuscate the honest function $f$, and we believe that it would still be hard to distinguish between the (heuristically) obfuscated version of $f$ and the obfuscated version of some backdoored version of $f$. Moreover, we believe that there are legitimate use-cases where adding an obfuscation step before the release of the model could be part of an honest training pipeline, and should not constitute on its own an attempt from the company to do something malicious with the model. Consider the following motivating examples: - Privacy of Training Data: If the training data includes sensitive user information, using obfuscation could help ensure that this data remains private and secure. - IP Protection: Companies often have proprietary models. Applying obfuscation allows these companies to publicly release their models with less risk of reverse-engineering their models or techniques. If we allow the use of obfuscation then, our claim is “that an obfuscated version of the original model is indistinguishable from the backdoored one”. And due to the general utility of using obfuscation we consider such a recipe not suspicious. The main reason that we transform an ANN to a binary circuit and then back to an ANN is to argue that there exist theoretically grounded methods of obfuscation of ANN. In any practical scenario we do not envision this obfuscation procedure to be followed. Nevertheless, our backdoor can be added even if the company is using a heuristic obfuscation method for legitimate reasons, as the ones we mention above. If the heuristic obfuscation approach has similar properties with iO in practice then our backdoor is still undetectable. We will clarify these points for the final version of our work. Q8) The undetectability of the backdoor assumes that there exists a procedure "Perturb", such that the backdoor is not detected. However, it is unclear whether such a procedure exists. So, big parts of the paper are based on assumptions for which it is not known whether these assumptions hold in reality. A8) There might be a misunderstanding here. The Perturb function that we use is iO. As we explain in Assumption 9, and Lines 212-213 right below it, the recent breakthrough result of Jain et al. [2021] has shown that indistinguishability obfuscation (iO) does exist, by combining standard tools from cryptography. Following standard nomenclature from cryptography we list the existence of iO as an assumption but this is only because we do not have an unconditional proof for the hardness of problems, like factoring, that are used for security reason in many aspects of our everyday life, e.g., internet and credit cards. In that sense, formally, it is an assumption that factoring is hard and in exactly the same sense it is an assumption that iO exists. But, since 2021 we do have constructions of iO whose security is as good as the security of important and widely used cryptographic protocols. We hope that this clarifies this point and we are more than happy to elaborate more if something is still not clear. Limitations: The limitations of the proposed approach are not discussed. We will explain the limitations of this approach, which is a theoretical construction for planting backdoors and, at its current form, is not practical, in the final version of our work. We will also clarify the suggested pipeline that can be based on heuristic obfuscation approaches. Nevertheless, this approach highlights vulnerabilities of current DNNs and LLMs, and should be taken into consideration.	Summary: The authors propose a procedure to process a neural network such that it is impossible to efficiently tell whether a backdoor was injected or not. The construction is formal and is based on common cryptographic assumptions. The authors also provide a technical formulation of backdoors for languages models and integrate it into their framework. Strengths: The presentation in the paper is very clear and there is a lot of helpful discussion to help readers appreciate and understand the result. Weaknesses: The Section 4.2 is a bit too compressed as it does not even define the steganographic function. The presentation would be more balanced if the language model section were fleshed out a little more in the main text. Technical Quality: 4 Clarity: 4 Questions for Authors: 1. Is there any setting where this backdoor is practical where [1] was not? Basically I assume there would need to be a setting where the user is willing to accept a network that looks like `Plant(f, 0)`? I assume normally the user would expect to receive `f` so I assume they would be suspicious if they received `Plant(f, 0)` instead (even though no backdoor was inserted). Is there a scenario where the user is expecting to receive something looking like `Plant(f, 0)`? [1] Shafi Goldwasser, Michael P Kim, Vinod Vaikuntanathan, and Or Zamir. Planting undetectable backdoors in machine learning models. In 2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS), pages 931–942. IEEE, 2022. Confidence: 3 Soundness: 4 Presentation: 4 Contribution: 2 Limitations: The main limitation is that while the `Plant(f, 0)` and `Plant(f, 1)` distributions are indistinguishable, the distributions are easily distinguished from the distribution of `f` itself. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We want to thank the reviewer for reading our paper carefully, for appreciating our results and for their constructive feedback and comments. Q1: The Section 4.2 is a bit too compressed as it does not even define the steganographic function. The presentation would be more balanced if the language model section were fleshed out a little more in the main text. A1: Thank you for your suggestion. Unfortunately, due to space constraints, we had to move some of the discussion to the appendix. We will re-organize the paper and, if it gets accepted, we will utilize the extra page to bring some of the content from the appendix to the main body. Q2: Is there any setting where this backdoor is practical where [1] was not? Basically I assume there would need to be a setting where the user is willing to accept a network that looks like Plant(f, 0)? I assume normally the user would expect to receive f so I assume they would be suspicious if they received Plant(f, 0) instead (even though no backdoor was inserted). Is there a scenario where the user is expecting to receive something looking like Plant(f, 0)? A2: This is a great question, and thank you for bringing this up. First, we would like to point out that the generic construction of [1], that does not make strong assumptions on the training process, holds only in the regime where the distinguisher has black-box access to the classifier, i.e., they do not have access to the weights. The main point of the construction we provide, and for using iO, is that we believe iO (or another obfuscation technique) can be part of a legitimate non-suspicious real-world training pipeline. In other words indeed “Perturb” can be unnatural but the “Perturb” procedure that we use, i.e., obfuscation, is natural and we can expect it to be used as the last step of any training process for the following reasons: - Privacy of Training Data: If the training data includes sensitive user information, using obfuscation could help ensure that this data remains private and secure. - IP Protection: Companies often have proprietary models. Applying obfuscation allows these companies to publicly release their models with less risk of reverse-engineering their models or techniques. If we allow the use of obfuscation then, our claim is “that an obfuscated version of the original model is indistinguishable from the backdoored one”. And due to the general utility of using obfuscation we consider such a recipe not suspicious. Another way to interpret our results is hence that we do not modify $f$ but we assume that the last step of the training process that produces $f$ is an obfuscation step. If this is the case then our result says that we can always plant undetectable backdoors. We will elaborate on these points, and we will explain what types of “Perturb” function we allow for, as well as give examples of settings where applying iO to the model would be expected. Limitations: The main limitation is that while the Plant(f, 0) and Plant(f, 1) distributions are indistinguishable, the distributions are easily distinguished from the distribution of f itself. Please look at our response above. Our results can be interpreted as indistinguishability between Plant(f, 1) and f if we assume that the last step of the training procedure that generates f is an obfuscation step. Additionally it is worth mentioning that if we view $f, Plant(f, 0)$ as a mapping from features to $\{0, 1\}$, then these two mappings are the same. We will elaborate on this in the final version of our paper.. [1] Shafi Goldwasser, Michael P Kim, Vinod Vaikuntanathan, and Or Zamir. Planting undetectable backdoors in machine learning models. In 2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS), pages 931–942. IEEE, 2022. --- Rebuttal Comment 1.1: Comment: I would like to thank the authors for their detailed rebuttal. The authors bring up some interesting points that I had not considered before, addressing why users might be willing to accept the obfuscated model. In my mind the remaining issues are that: 1. The method is not practical because the conversion to a boolean circuit followed by iO would blow up the size of the model and the expense of inference to galactic proportions. However since this is a theoretical paper, this weakness does not count for much. 2. The conversion back from the obfuscated circuit to a neural network seems a bit decorative. If one is interested in inference, then just evaluating the obfuscated circuit itself suffices. On the other hand, there's little reason to expect the construction given to exhibit any of the nice properties we typically attribute to neural networks (e.g. fine-tunability). In this light, I am raising my score to a 5.	Summary: This paper presents a way of inserting backdoors into deep learning and language models, whereupon the resulting backdoored models are not efficiently distinguishable from other perturbed variations of a given model. The paper introduces definitions of "undetectable" and "unreplicable", and rigorously demonstrates that the constructions therein satisfy the definitions, under standard cryptographic assumptions. Strengths: This is a wonderful paper. It's clear, it's a pleasure to read, it does a great job easing the reader into the math and gradually building up to the main result. I appreciate the clear and well-explained introduction, which builds good intuition for what is to come; starting out with a comparison with Goldwasser et al. [2022] is also very useful, since I'm sure this is on most readers' minds as soon as they see the title. Also, I don't know if "Insidious Procedure" is a standard term from cryptography, but I love it. And, of course, the main result is an important one, and this paper presents it in a convincing way. The appendix is delectable. Weaknesses: While this is a strong theoretical result, this seems to be vanishingly unlikely to be used in practice, since it depends on indistinguishability obfuscation, which Wikipedia claims to be [highly impractical in practice](https://en.wikipedia.org/wiki/Indistinguishability_obfuscation#Practicality). Additionally, I have certain questions about the $\text{Plant}$ function allowing too much, potentially weakening the overall result (see Question A, below). Technical Quality: 4 Clarity: 4 Questions for Authors: A) Here is the main question which I have about the definition of undetectability. Correct me if I'm wrong, but with your definition, aren't undetectable backdoors very easy to construct? For instance, suppose my procedure Backdoor adds a 3-SAT verifier into the neural network, where the input variables to the circuit are taken as the output of some map from the input to [0, 1]^N (say, the parity of each digit of the input if it's an MLP, or whether each word is a noun in a language model). Then, if the 3-SAT circuit is satisfied, the model gives a bad output. The procedure Perturb does the same thing, except it inserts an unsatisfiable 3-SAT circuit, so $h(x)=h'(x)$ $\forall x \in \mathcal{X}$. Efficiently being able to distinguish between $h'$ and $\tilde{h}$ seems impossible since this would necessitate an efficient method for being able to tell which of two 3-SAT circuits is satisfiable, and which isn't; however, the actor who inserted this backdoor could easily sell information on how to activate the backdoor in the backdoored model (make sure your third, seventh, ninth... words are nouns). [and if we want it to be non-replicable use one of the steg methods from the appendix] If this is true, isn't allowing Perturb to be an unbounded function perhaps too powerful? Like, the backdoor described above still seems undetectable by your definition, but if someone actually looks at the weights of the model, they'll go like "whoa, what is this sus-looking boolean circuit doing here?". Ideally it seems like we'd want Perturb to either be restricted in some way, or perhaps the distribution of weights of $\tilde{h}$, or its computational graph, should not be super out-of-distribution for other models sampled from $\text{Train}$. Basically, on first glance it seems to be that the definition of undetectability might be a bit weak (but of course, I am likely missing something.) B) This is even more of a half-baked thought than (A), but if we're relying on the existence of iO as an assumption, can't we also then just assume FHE and just have Perturb encrypt all the models so nobody knows what's going on at all Nitpicks: N1) On line 56, there is an extra comma after "and". Confidence: 4 Soundness: 4 Presentation: 4 Contribution: 4 Limitations: Addressed. However, I might maybe mention more explicitly that this is not a remotely practical construction, and more of an existence proof. Flag For Ethics Review: ['No ethics review needed.'] Rating: 8 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: [Part 1/n] We want to thank the reviewer for reading our paper carefully, for appreciating our results and for their constructive feedback and comments. Q1: While this is a strong theoretical result, this seems to be vanishingly unlikely to be used in practice, since it depends on indistinguishability obfuscation, which Wikipedia claims to be highly impractical in practice. Additionally, I have certain questions about the function allowing too much, potentially weakening the overall result (see Question A, below). A1: Thank you for your feedback. As you mentioned, the primary objective of our research is to theoretically demonstrate that neural networks (NNs) and large language models (LLMs) have inherent vulnerabilities and are susceptible to the backdoor attacks outlined in our paper. Beyond our theoretical results, which are significant on their own, our work also suggests a novel pipeline for injecting backdoors. This new pipeline could naturally be implemented using practical obfuscation techniques. For instance, one could replace Indistinguishability Obfuscation (iO) with more practical variants of obfuscation tailored for NNs. We believe that is a very interesting open question that arises from our framework and result and we hope that it will inspire people in the field. Even without replacing the obfuscation method that we use our results are significant also because of the following: 1. Future Practicality: The iO method is expected to become more practical in the coming years, which aligns with the future applicability of our theoretical findings. 2. Current Importance: Given the widespread deployment of these models in decision-making processes, it is crucial to ensure they have robust security guarantees. --- Rebuttal Comment 1.1: Comment: Thank you so much for your detailed response! This makes a lot of sense; I now think I would've realized this if I'd spent another few hours thinking about the paper before writing the review. I am increasing my score to an 8 and my confidence to a 4. --- Rebuttal 2: Comment: Part[2/n] Q2: Here is the main question which I have about the definition of undetectability. Correct me if I'm wrong, but with your definition, aren't undetectable backdoors very easy to construct? For instance, suppose my procedure Backdoor adds a 3-SAT verifier into the neural network, where the input variables to the circuit are taken as the output of some map from the input to [0, 1]^N (say, the parity of each digit of the input if it's an MLP, or whether each word is a noun in a language model). Then, if the 3-SAT circuit is satisfied, the model gives a bad output. The procedure Perturb does the same thing, except it inserts an unsatisfiable 3-SAT circuit, so . Efficiently being able to distinguish between and seems impossible since this would necessitate an efficient method for being able to tell which of two 3-SAT circuits is satisfiable, and which isn't; however, the actor who inserted this backdoor could easily sell information on how to activate the backdoor in the backdoored model (make sure your third, seventh, ninth... words are nouns). [and if we want it to be non-replicable use one of the steg methods from the appendix] If this is true, isn't allowing Perturb to be an unbounded function perhaps too powerful? Like, the backdoor described above still seems undetectable by your definition, but if someone actually looks at the weights of the model, they'll go like "whoa, what is this sus-looking boolean circuit doing here?". Ideally it seems like we'd want Perturb to either be restricted in some way, or perhaps the distribution of weights of , or its computational graph, should not be super out-of-distribution for other models sampled from . Basically, on first glance it seems to be that the definition of undetectability might be a bit weak (but of course, I am likely missing something.) A2: This is indeed a very astute observation; a construction similar to the one you define was actually the starting point of our work. First, let us clarify why the approach of injecting a SAT formula that is either satisfiable or unsatisfiable does not give a provably undetectable backdoor. According to our definition, which follows the blueprint of Goldwasser et al., a backdoor is undetectable if any (polynomially bounded) adversary cannot distinguish between an honestly generated model and one with a backdoor. If we inject a specific satisfiable formula in the honest case, then there exists a simple adversary, that checks whether a hardcoded assignment is satisfiable, succeeds. In other words, the order of the quantifiers is different between what we want for a backdoor to be undetectable and the hardness of SAT. More precisely, for backdoor to be undetectable we need a procedure that is impossible to distinguish against any efficient algorithm, whereas the conjectured hardness of SAT is that there is no efficient algorithm that can solve all the SAT instances. We hope this clarifies the issue but we are happy to elaborate more if needed. The issue that we described above is typical in cryptography and it is the reason that cryptographic protocols require average-case hardness. Unfortunately, SAT is not average-case hard, so our solution to this issue is to use instead the well-studied cryptographic primitive of PRGs: instead of a SAT formula, we include a number that is either pseudorandom or truly random. Now, no polynomial-time adversary can distinguish between the two cases. As you also correctly pointed out, this is indeed a very suspicious construction and someone by looking at the weights of the NN will be skeptical about what is going on. The main point of the construction we provide, and for using iO, is that iO (or a function similar to that) can be part of a legitimate non-suspicious real-world training pipeline. Ideally, we want the function “Perturb” to be non-suspicious. We argue that using obfuscation is on its own not suspicious for many reasons. Consider the following motivating examples: - Privacy of Training Data: If the training data includes sensitive user information, using obfuscation could help ensure that this data remains private and secure. - IP Protection: Companies often have proprietary models. Applying obfuscation allows these companies to publicly release their models with less risk of reverse-engineering their models or techniques. If we allow the use of obfuscation then, our claim is “that an obfuscated version of the original model is indistinguishable from the backdoored one”. And due to the general utility of using obfuscation we consider such a recipe not suspicious. We will elaborate on these points, and we will explain what types of “Perturb” function we allow for. --- Rebuttal 3: Comment: [Part 3/n] Q3: This is even more of a half-baked thought than (A), but if we're relying on the existence of iO as an assumption, can't we also then just assume FHE and just have Perturb encrypt all the models so nobody knows what's going on at all. A3: This is also an interesting thought: your suggestion is to publish the encryption of the neural network weights under an FHE encryption. Unfortunately, this approach does not directly work, since FHE will only allow us to compute an encryption of the output of the neural network on any given input. It won’t be possible to get the actual output of the NN unless we have the secret key of the encryption, which would also reveal the model weights. We will revise our manuscript according to our rebuttal. As we discussed above , currently, our theoretical result relies on an impractical construction. However, i) in the future we might have more practical iO algorithms, ii) our construction can work in practice with methods that simulate iO but do not have the strong theoretical guarantees we obtain. Moreover, we will elaborate on the “Perturb” functions our definition allows for.	Summary: - The paper studies undetectable backdoor attacks for neural networks from a theoretical perspective. Strengths: - The problem of undetectable backdoor insertion is important for the community. - The paper considers a more complicated scenario compared to prior work, as it shows undetectability under the white-box setting. Weaknesses: - It would be good to include a "Conclusion" section in the main body of the paper, as it currently seems to end abruptly. - I believe that including some empirical results would nicely complement the theoretical findings. Technical Quality: 3 Clarity: 2 Questions for Authors: No Confidence: 2 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: Yes Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We want to thank the reviewer for reading our paper carefully, for appreciating our results and for their constructive feedback and comments. Q1: It would be good to include a "Conclusion" section in the main body of the paper, as it currently seems to end abruptly. A1: We would like to thank you for your suggestion. We will add the following Conclusion section: Given the plethora of applications of Machine Learning in general, and neural networks in particular, questions regarding the trustworthiness of publicly released models naturally arise. In particular, before deploying a neural network we need to guarantee that no backdoors have been injected allowing bad actors to arbitrarily control the model behavior. In this paper, we investigate the existence of backdoor attacks to obfuscated neural networks which are undetectable even when given white-box access. The notion of obfuscation that we consider is the well-studied and mathematically founded indistinguishability obfuscation (iO). We also show how our techniques can inspire backdoor schemes in large language models when combined with ideas from steganography. While our constructions are purely theoretical, we leave as an interesting direction how to use heuristic obfuscation methods to show practical instantiations of our constructions. Another interesting open question is whether cryptographic schemes weaker than iO suffice to show backdoor undetectability in the white-box model. Q2: I believe that including some empirical results would nicely complement the theoretical findings. A2: Thank you for your feedback. We would like to clarify that the primary objective of our research is to theoretically demonstrate that neural networks (NNs) and large language models (LLMs) have inherent vulnerabilities and are susceptible to the backdoor attacks outlined in our paper. Beyond our theoretical results, which are significant on their own, our work also suggests a novel pipeline for injecting backdoors. This new pipeline could naturally be implemented using practical obfuscation techniques. For instance, one could replace Indistinguishability Obfuscation (iO) with more practical variants of obfuscation tailored for NNs. We believe that is a very interesting open question that arises from our framework and result and we hope that it will inspire people in the field. Even without replacing the obfuscation method that we use our results are significant also because of the following: 1. Future Practicality: The iO method is expected to become more practical in the coming years, which aligns with the future applicability of our theoretical findings. 2. Current Importance: Given the widespread deployment of these models in decision-making processes, it is crucial to ensure they have robust security guarantees, even considering attacks that are not implementable in the present but will become implementable in the future. --- Rebuttal Comment 1.1: Comment: Thank you for your response. I decided to keep my score.	null	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
The Minimax Rate of HSIC Estimation for Translation-Invariant Kernels	Accept (poster)	Summary: This paper studies the statistical property of Hilbert Schmidt Independence Criterion (HSIC). Specifically, under either Gaussian or continuous bounded translation-invariant characteristic kernel that is defined on $\mathbb{R}^d$, the paper prove that HSIC can be estimated at the optimal rate in the minimax sense. The minimax lower bound is obtained via the Le Cam's method, where the authors find two distributions that are close in the KL divergence sense, but is dissimilar in the HSIC sense. Their results further demonstrates that many empirical estimators in literature is minimax optimal. Strengths: This paper provides the first minimax optimal rate for HSIC learing, via obtaining the information theoretical lower bound. This is an important contribution the litearture since HSIC is widely used for independence test. A minor contribution is that the authors derive the closed form formula of HSIC under the Gaussian setting. In proving the lower bound for the translation invariant kernel case, the authors restrict the integration of to be computed in a subset of $\mathbb{R}^d$, thereby obtaining a lower bound on the HSIC between $P_{\theta_1}$ and $P_{\theta_0}$. To me this is novel. Weaknesses: While the authors explain how they obtain the lower bound via Le Cam's method, I would more appreciate if the authors can briefly explain the main technical challenge in proving the lower bound. It seems that the lower bound proof is a straight forward application of Le Cam's approach. It seems that in Zhou et al., (2019), they also obtain the lower bound for the centred covariance operator $C_{XX}$. The definition of $C_{XX}$ is similar to the HSIC setting and the lower bound is almost the same. I would appreciate the authors to provide more discussion on the difference between the two settings and how the proof is different from Zhou et al., (2019). Technical Quality: 3 Clarity: 4 Questions for Authors: See weakness Confidence: 4 Soundness: 3 Presentation: 4 Contribution: 3 Limitations: NA Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for the time and effort invested, and the kind review. Below we answer the questions in detail. - __Technical challenge.__ There are three main tools for deriving lower bounds in the minimax setting: Le Cam's method, Fano's method, and Assouad's lemma. The main technical challenge in applying these known tools is coming up with an adversarial distribution pair and then also showing that the assumptions of the respective statements are all satisfied. In our case, we chose Le Cam's method and showed that its assumptions are satisfied for the parameterized Gaussian distribution (5) and its instantiations in Line 239 in the case of HSIC. - __Difference to (Zhou et al., 2019).__ Indeed, the rate obtained by (Zhou et al., 2019) for the covariance operator is the same as the one that we obtained for HSIC. Intuitively, one would guess that estimating the covariance operator, an element in a tensor product RKHS, is more challenging than estimating HSIC, a real number. Surprisingly, this is not the case, as our results indicate. Moreover, by an application of the reverse triangle inequality, our result allows to recover their result (see Corollary 1 and its proof). Regarding differences in the proof: The distribution pair considered by (Zhou et al., 2019) has a product structure, which, similar to (Tolstikhin et al., 2016), does not allow to obtain a lower bound for HSIC estimation. We hope that this answers all the questions of the reviewer. __References.__ Tolstikhin, I. O., Sriperumbudur, B. K., & Schölkopf, B. (2016). Minimax estimation of maximum mean discrepancy with radial kernels. Advances in Neural Information Processing Systems, 29. Zhou, Y., Chen, D. R., & Huang, W. (2019). A class of optimal estimators for the covariance operator in reproducing kernel Hilbert spaces. Journal of Multivariate Analysis, 169, 166-178. --- Rebuttal Comment 1.1: Comment: Thanks for replying. I will maintain my score.	Summary: In this work, the authors prove that the minimax optimal rate of HSIC estimation on $\mathbb R^{d}$ for Borel measures containing the Gaussians with continuous bounded translation-invariant characteristic kernels is $n^{-1/2}$. Strengths: Testing whether a pair of random variables are independent is the central problem in statistics or machine learning community. There are lots of independence tests proposed in past years such as distance correlation, dynamic slicing, etc. The author established the minimax lower bound $ \Omega(n^{-1/2}) $ of HSIC estimation with $ M \geq 2 $ components on $ \mathbb{R}^d $ with continuous bounded translation-invariant characteristic kernels. As this lower bound matches the known upper bounds of the existing "classical" U-statistic and V-statistic-based estimators, and that of the Nyström HSIC estimator, their result settles their minimax optimality. Establishing minimax rates is often deemed a challenging task. Given that the result sounds solid, I consider this a noteworthy result. Weaknesses: Due to my ignorance, I may not be able to provide a sufficient evaluation of the importance of this problem. It would be easier for me to evaluate its importance if the author could offer more related literature and a comparison with them. Technical Quality: 3 Clarity: 3 Questions for Authors: There are some minor issues. Can the author provide a more concrete definition of HSIC? For example, in equation (2), does it imply that we have fixed a decomposition $d=d_{1}+...+d_{M}$ and $P_{m}$ is the marginal distribution of P on $R^{d_{m}}$.? Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: None Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for the time and effort invested, and the kind review. In the following, we answer the questions. - __Related work.__ The related work can be divided into lower bounding the rate of estimating (1) the kernel mean embedding, (2) maximum mean discrepancy, and (3) the covariance operator. The existing results do not permit establishing the minimax rate of HSIC estimation due to the following reasons. 1. The estimation of the mean embedding (1) concerns the estimation of an element in an RKHS, which could be more difficult than the estimation of a real-valued function of it (MMD; Tolstikhin et al., 2016, or, in our case, HSIC). 2. The proof for obtaining the lower bound of (2) relies on a distribution pair in which both distributions factorize, that is, they are independent. The corresponding HSIC value is thus zero and Le Cam's method is not applicable; hence the existing proof does not address the setting of HSIC. 3. In the case of (3), one intuitively expects that estimating the real-valued HSIC is "easier" than estimating the covariance operator, which is an element in a tensor product RKHS. Our result sheds light on a surprising phenomenon: this intuition is false. Moreover, with Corollary 1, we are able to recover the lower bound on covariance operator estimation. These notes are also elaborated in Remark 1(c)--(e). - __Definition of HSIC.__ HSIC captures the dependencies of a probability measure by quantifying the discrepancy of the measure to the product of its marginals as the distance of the corresponding mean elements in an RKHS. This also corresponds to the norm of the cross-covariance operator, which (2) makes explicit; the equivalence holds for arbitrary kernel-enriched domains. In line with Line 121-122 and Theorem 1, and as correctly stated in the review, we consider $\mathcal{X} = \times_{m=1}^M \mathcal{X_m}$ with $\mathcal{X}=\mathbb{R}^d$ (for the domain of $\mathbb{P}$), $\mathcal{X}_m=\mathbb{R}^{d_m}$, i.e. one has the decomposition $d=d_1 + \cdots + d_M$, with $\mathbb P_m$-s being the corresponding marginals of $\mathbb{P}$ on $\mathbb R^{d_m}$ ($m=1,\ldots,M$). The associated kernels are $k_m:\mathbb R^{d_m} \times \mathbb R^{d_m} \to \mathbb{R}$. We hope that this answer clarifies all the questions of the reviewer. __References.__ Tolstikhin, Ilya O., Bharath K. Sriperumbudur, and Bernhard Schölkopf. "Minimax estimation of maximum mean discrepancy with radial kernels." Advances in Neural Information Processing Systems 29 (2016). --- Rebuttal Comment 1.1: Comment: Thanks for replying. I will maintain my score.	Summary: The rate at which HSIC can be estimated is an important and open problem, in this paper, the authors prove that the minimax optimal rate of HSIC estimation for Borel measures is $\mathcal{O}(n^{-0.5})$ with M>=2 components, which is very important as existing conclusion only holds for M=2. Other byproducts can be naturally introduced, implying the minimax lower bound for the estimation of cross-covariance operator, which can be further specialized to get back the minimax result on the estimation of the covariance operator. Strengths: 1. The paper answers an important while open problem which may be very important for the community and generalizes the existing result from M=2 to M>=2. 2. The paper's structure is clear and well organized. 3. The paper is solid and mathematically heavy, the proof is provided with details. Weaknesses: 1. Overall, the paper is not easy to follow as the paper's main contribution seems to be the proof part. 2. I wouldn't say it is the weakness or the author's problem, as this is a theoretical paper, experiments are not necessary. Still is it possible to design toy experiments to validate the conclusions in the paper? Technical Quality: 3 Clarity: 2 Questions for Authors: NA Confidence: 2 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: NA Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for the time and effort invested, and for the kind review. To answer the question regarding experiments: In the minimax framework, one bounds the convergence rate from above and from below. - The former can be validated empirically in some cases. Indeed, for HSIC, one can compute the theoretical (= population) HSIC value for a fixed (kernel, distribution)-pair---for instance, for the Gaussian kernel with the Gaussian distribution (Lemma 1)---, and verify the known (Smola et al., 2007; Theorem 2) convergence rate of the estimator w.r.t. this value. - The latter, that is, the lower bound, can only be derived theoretically---as one must consider all possible estimators ($\inf_{\hat{F_n}}$ in (3)) and all possible probability distributions ($\sup_{P\in\mathcal{P}}$ in (3)) of the considered class ($\mathcal{P}$)---which is what we tackled in this article. Minor note regarding the point 'existing conclusion only holds for $M=2$': We are not aware of minimax guarantees for HSIC even for $M=2$; our minimax analysis handles both the case of $M=2$ and $M>2$ in a unified fashion (for $M \ge 2$). We hope that this settles the stated questions. __References.__ Smola, A., Gretton, A., Song, L., & Schölkopf, B. (2007). A Hilbert space embedding for distributions. In International Conference on Algorithmic Learning Theory (pp. 13-31).	null	null	null	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Bayesian Optimization of Functions over Node Subsets in Graphs	Accept (poster)	Summary: This paper addresses the challenge of optimizing functions defined on node subsets in a graph. These functions are combinatorial, black-box, and expensive to evaluate. The proposed solution utilizes Bayesian Optimization (BO), mapping each k-node subset to a node in a new combinatorial graph, and traversing this graph efficiently through a recursive algorithm. Extensive experiments demonstrate the effectiveness of this approach on various graphs and optimization tasks. Strengths: The new framework proposed in this paper is innovative. It is function-agnostic and can be applied to various optimization problems, thus offering a wide range of applications. The experimental results also demonstrate its potential. The presentation of paper is clear and comprehensible. Weaknesses: The domain of the optimization problem is the set of all k-tuples of vertices on a graph. However, it seems the structure (in particular, the edges) of the graph is not mentioned. Is the graph structure not essential in this context? Technical Quality: 3 Clarity: 3 Questions for Authors: I have to say I am not very familiar with the field of black-box combinatorial optimization. I am willing to let the Area Chair focus more on the opinions of the other reviewers. However, I am personally curious about, how such approaches achieve provably good performance when we have no assumptions on function $f$ ? It is likely to fall into no-free-lunch theorem. Confidence: 2 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The performance scales poorly as $k$. The choice of hyperparameter is ad-hoc. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for acknowledging the novelty and potential of our work! Please see our responses to the raised questions below. > How such approaches achieve provably good performance when we have no assumptions on function $f$? It is likely to fall into no-free-lunch theorem. We’d like to respond from the general Bayesian Optimization (BO) perspective. First, BO is most suitable for optimizing functions that are black-box and expensive to evaluate. If we have access to the gradient of the function, or the function is easy to evaluate, then there are more appropriate alternatives such as gradient-based optimizers or Reinforcement Learning (RL) methods. However, if the function is black-boxed and its values are costly to observe, then sample efficiency becomes an essential criterion to the optimizer, that is, we wish to obtain the best possible location within a limited number of queries. Note that RL usually requires a large number of samples to train the reward/policy models, which is infeasible under this setting. The performance gain in BO mainly comes from the surrogate modeling approach, where a tractable model (e.g. Gaussian Processes) is used to gradually approximate the underlying function based on the observations. At each iteration, the surrogate model is fitted with previous observations and generates predictions on the rest search space, which allows us to identify the most promising location based on past knowledge, and then query its function value. In the next iteration, this new observation will be used to re-fit the surrogate, and we repeat the process until hitting the evaluation budget. It means that, even though we have no prior knowledge about $f$ at the beginning, the algorithm tries to adaptly learn the pattern in $f$ along the search, where the next move is always guided by past knowledge, and thus explaining the superior performance of BO over other random heuristic methods. > It seems the structure (in particular, the edges) of the graph is not mentioned. Is the graph structure not essential in this context? The underlying graph structure is very critical to the problem from the following perspectives. 1. Unlike classical combinatorial optimization over discrete space (e.g. searching for the optimal hyper-parameter combination), the configurations (i.e. node subsets) in our setting are not independent but linked via an underlying graph structure, which needs to be considered during optimization. This is why a graph GP is adopted as the surrogate model, where the similarity between configurations is measured by a kernel on graph (Equation 2), as discussed in Section 3.2. 2. Specifically, the above kernel is defined as a function of the graph Laplacian matrix $L$, which is computed by $L = D - A$, with $D$ being the degree matrix and $A$ being the adjacency matrix. This is how the edges are incorporated into modeling. 3. If the graph is sparse (e.g. a grid is sparser than a fully connected graph), the combinatorial graph will also be sparse. Then, with a fix-sized combo-subgraph of $Q$ combo-nodes, we can cover more hops (i.e. distant nodes) from the center combo-node at each iteration. Thus, the algorithm will traverse the comb-graph (i.e. substituting the elements in the subset) at a faster pace, as discussed in Lemma 3.2. 4. If the underlying graph structure is informative (e.g. BA network is more uniquely structured with heterogeneous node degree distribution as opposed to the WS network, whose node degree is more homogeneous distributed), the combinatorial graph will also be informative. In this case, it means that the kernel in the graph GP surrogate will capture more structural information, which eventually helps the algorithm visit better locations during optimization, as explained in Sections 3.3 and 4. > The performance scales poorly as k. We are glad that the reviewer noticed our discussion on the limitation about subset size $k$, and we would like to make some further clarification below. In the literature of subset selection on graphs, setting $k<50$ (<1% of the network) is very a common paradigm [1,2,3], since many problems have been proven to be NP-hard due to the combinatorial explosion in the search space $\binom{N}{k}$. As such, when the subset size $k$ increases, it poses a general challenge in the literature that the performance gain between heuristic optimization algorithms and random baselines is diminishing [4]. On top of this, the problem becomes even more challenging under our setting, since the underlying function is fully black-boxed and we assume no prior information about the graph structure. Having said that, the proposed method still generally outperforms the other baselines across all experiments, and in the least favorable case, it performs comparably to the local search, which is also a novel baseline introduced in our paper since it needs to operate on the proposed combo-graph. > The choice of hyperparameter is ad-hoc. We have conducted an ablation study in Appendix I to analyze the sensitivity of GraphComBO to the combo-subgraph size $Q$ and the non-improvement tolerance $\texttt{failtol}$, where the results show that the proposed method is quite robust to the latter. However, we do agree with the reviewer that the algorithm would benefit from an automatic strategy for determining the combo-subgraph size $Q$ (e.g. an adaptive design of $Q$), which we will leave to future exploration. We’d like to thank the reviewer again for the comments that helped us improve the current work. We believe that we have now addressed all the concerns from the original reviews, and hope the reviewer could kindly consider increasing the rating/confidence in light of this. [1] Maximizing the Spread of Influence through a Social Network, KKD 2003 [2] Cost-effective Outbreak Detection in Networks, KDD 2007 [3] Robust Influence Maximization, KDD 2016 [4] Influence Maximization on Social Graphs: A Survey, TKDE 2018 --- Rebuttal Comment 1.1: Title: Respond to author Comment: Thanks for your detailed explanation! I do not have further questions and decide to maintain my positive rating. --- Reply to Comment 1.1.1: Comment: We thank the reviewer again for engaging in the rebuttal and for the time and effort in helping improve our manuscript.	Summary: The present paper proposes an approach based on Bayesian optimization for optimizing a function over subsets of nodes of size $k$ in a graph. At each step of the algorithm, a local neighborhood is constructed and the best node with respect to an acquisition function is chosen as the center for the next step. The approach is evaluated against several other classical techniques on a variety of benchmarks, where it is competitive and often outperforms the other approaches. Strengths: I am unfamiliar with the topic and the related literature, so take my comments with a grain of salt. If applying Bayesian optimization to the problem is indeed novel, then I think it is an interesting contribution for the ML community, even if none of the ideas appears to be very involved in itself. The strongest selling point of the paper to me are the empirical results, where the performance is consistent and tends to outperform the baselines. Weaknesses: It is not very surprising that an approach that makes informed decisions to guide the search outperforms simple baselines like BFS or local search, somewhat weakening the significance of the results to me. Technical Quality: 4 Clarity: 3 Questions for Authors: Are there other common baselines in the literature that are not based on Bayesian optimiazation? If one were to compare the present approach against a task-specific approach, do you have intuition on whether the present approach would perform significantly worse? Other: - ego-subgraph is not defined Confidence: 2 Soundness: 4 Presentation: 3 Contribution: 2 Limitations: Some future direction are discussed. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We would like to thank the reviewer for acknowledging the contribution of the proposed framework. Please see our response to the review comments below. > If applying Bayesian optimization to the problem is indeed novel, then I think it is an interesting contribution for the ML community, even if none of the ideas appears to be very involved in itself. > It is not very surprising that an approach that makes informed decisions to guide the search outperforms simple baselines like BFS or local search, somewhat weakening the significance of the results to me. As discussed in the introduction, there are many optimization problems on graphs that involve expensive black-box functions defined on node subsets, e.g. outcomes from real-world implementation, results of large number simulations, and outputs from graph neural networks; at the same time, there are many applications where the underlying graph is not known a priori, e.g. offline social networks and contact networks. However, there is no general framework in the literature to optimize such black-box functions of node subsets in graphs, except for the classical graph traversal algorithms such as BFS/DFS and local search. While we agree with the reviewer that it is very intuitive and “expected” that BO will outperform these classical algorithms, the main contribution of our work is, as pointed out by the reviewer, extending BO to this novel setup via an effective approach and obtaining good results over the existing baselines. To design such a framework, we have made the following technical contributions: 1. We proposed a combinatorial graph tailored for node subsets in a generic graph. 2. We introduced a recursive algorithm to sample subgraphs from the combinatorial space. 3. To handle the combinatorial explosion problem, we use a local approach to traverse the combinatorial graph space by iteratively sampling its subgraphs and moving around the subgraph center to more promising regions, which is guided by a surrogate model. In the early stage, we tried other localization methods such as selecting nodes inside a subgraph on the original graph as the subset. However, since we need to maintain the diversity of the subset to cover potentially distant nodes, none of them can fit into the problem as cohesively as the current method, which makes our design non-trivial. > Are there other common baselines in the literature that are not based on Bayesian optimization? As discussed above, to the best of our knowledge, the only existing baselines are those based on graph traversal algorithms, which have been modified to the current problem setting. In particular, we have proposed $k$-random walk and $k$-local search (Appendix B) as baselines that operate on the original graph, which have shown strong results in some of our experiments. We are more than happy to discuss with the reviewer if they believe there are works in the literature that tackle the same problem setups as ours. In addition, we would like to mention that a new experiment has been added to the general response, in which we compare our method to COMBO (nevertheless, a BO baseline) on small-scale networks. The result (Fig. 4 rebuttal PDF) shows the proposed framework consistently outperforms this baseline, and we kindly refer the readers to the general response for more details if they find it relevant. > If one were to compare the present approach against a task-specific approach, do you have intuition on whether the present approach would perform significantly worse? We thank the reviewer for this high-level question on the suitability of our framework to specific problems, to which we’d like to respond from the general Bayesian Optimization (BO) perspective in the following. First, BO is most suitable for optimizing functions that are black-box and expensive to evaluate. If we have access to the gradient of the function, or the function is easy to evaluate, then there are more appropriate alternatives such as gradient-based optimizers or Reinforcement Learning (RL) methods, and we believe BO, as a black-box solver, would not be an appealing approach in those settings. However, if the function is black-boxed and its values are costly to observe, then sample efficiency becomes an essential criterion to the optimizer, that is, we wish to obtain the best possible location within a limited number of queries. Note that RL usually requires a large number of samples to train the reward and policy models, which is infeasible under this setting. Based on the above discussion, if our goal is to optimize certain expensive black-box functions, where some “good guesses” can be obtained from domain knowledge or a task-specific approach, we can always incorporate that information into BO by either initializing the search at the promising locations identified by the task-specific method, or updating the prior in the surrogate with the domain knowledge. This implies that, in most cases, BO serves as a complement to the domain-specific methods rather than a complete substitute. > Other: ego-subgraph is not defined We thank the reviewer for this reminder. In Lemma 3.2, an $\ell$-hop ego-subgraph centered at an arbitrary combo-node $\hat{v}$ on the combo-graph means that we create an ego-network around $\hat{v}$ with its $\ell$-hop neighbors, and the resulting ego-network is an ego-subgraph. We will make sure this concept is clear in the revised version. We’d like to thank the reviewer again for the comments that helped us reflect on our work. We believe that we have now addressed the concerns from the original reviews, and hope the reviewer could kindly consider increasing the rating/confidence in light of this. --- Rebuttal Comment 1.1: Comment: Thank you for very detailed responses. After reading the other reviews and the rebuttals, it seems to me that the proposed approach in this setting is indeed novel. Therefore, I admit that it may be unfair to criticize the work for using "only" poorly performing classical algorithms as the baselines. Because of this, I am more inclined to propose accepting the paper, but my lack of background on this topic make it hard to state if the contributions are interesting enough for the community. For this reason, I've increased my confidence for the positive score. --- Reply to Comment 1.1.1: Comment: We thank the reviewer again for their time and efforts in the review that helped us improve our work, and we are always happy to answer any further questions.	Summary: This paper introduces a framework for optimizing functions of subset of nodes in a graph with Bayesian Optimization (BO). The framework need not know the graph structure beforehand, but does require the knowledge of the cardinality of the considered subsets of nodes $1 \leq k \leq N$ for a graph $\mathcal{G} = \\{V, E\\}$ where $\|V\| = N$. The framework works by iteratively building another graph, termed "combo-graph", where each "combo-node" is one of the $\binom{N}{k}$ subsets of $k$ nodes. Two combo-nodes $\tilde{v}_i = \left\\{v^{(i)}_1, \cdots, v^{(i)}_k\right\\}$ and $\tilde{v}_j = \left\\{v^{(j)}_1, \cdots, v^{(j)}_k\right\\}$ are linked if $(\tilde{v}_i \cup \tilde{v}_j) \setminus (\tilde{v}_i \cap \tilde{v}_j) = \\{v_l, v_m\\}$, and if $(v_l, v_m) \in E$. BO is then conducted on this partial combo-graph (using graph kernels) to select a promising combo-node to sample the objective function with. Strengths: In spite of suffering from the drawbacks of local optimization, the presented framework is useful to tackle the combinatorial complexity involved in the optimization of functions over discrete structures. It opens an interesting avenue for extending BO to these problems. Overall, the article is clear and well-written. Weaknesses: Noisy Setting. Both the preliminaries (Section 2) and the described BO on Combo-Graphs (Section 3.3) seem to suggest that the framework has access to true function values. However, in Appendix B, it seems that many experiments do take place in a noisy setting, because the objective function is explicitely defined with an additional noise term (e.g., Ackley), or because it results from an average of Monte-Carlo samples (e.g., Influence Maximization, Flattening the Curve). As a result, it is unclear to me whether the described algorithm is fit for noisy problems. The notations $y_t$ and $f(v_t)$ do not help. Comparison with COMBO. I understand that COMBO does not address the same problem as the algorithm described in the paper. Nevertheless, given the lack of state-of-the-art baselines for this problem, it would be interesting to study how the algorithm compares to COMBO on problems involving small-enough graphs. Technical Quality: 3 Clarity: 2 Questions for Authors: Here are some questions to spark the discussion with the authors. (1) Do you account for noise in your framework? (1.1) If not, how do you expect your algorithm to react to noisy function values? I believe its behavior would be quite different, especially because the location of the combo-graph is selected according to the observed function value, which is not longer accurate. (1.2) If so, why does the framework apply the acquisition function to unvisited combo-nodes only? Why change the location of the combo-graph based on the observed function value instead of a more refined / optimistic estimate (e.g., the posterior mean of the surrogate model or the acquisition function value)? (1.3) If experiments are conducted in a noisy setting, can you provide an estimate of the noise level for each experiment as a proportion of the signal variance? (2) Do you have any insights on how the proposed algorithm compares to COMBO on experiments involving small graphs? Confidence: 3 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: I believe the authors have addressed the limitations of their work, and I am looking forward to the discussion period for more details on the noisy setting. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We would like to thank the reviewer for the detailed feedback which helped us improve the current work. In summary, the reviewer's concerns are (1) If the framework can handle noisy observations, and (2) Comparison with COMBO on small networks. Please see below for our responses. > Do you account for noise in your framework? It is unclear to me whether the described algorithm is fit for noisy problems. Yes, similar to other common BO methods, the proposed framework can handle noise. As pointed out by the reviewer, we used the Ackley function on a 2D grid with Gaussian noise as the underlying function in one of the synthetic experiments, meanwhile under real-world setups, we also used noisy results from simulations as the underlying functions. For the notations, we intended to express the most standard setup in BO, that is $y = f(x) + \epsilon$, with $\epsilon \sim N (0, \sigma^2_{\epsilon})$ being the noise term. We will make sure this is clear in the revised version. ### A more comprehensive experiment under the noisy setting To better answer the other questions from the reviewer and show our framework’s capability of handling noise, we further conduct a noisy experiment at different noise levels on BA ($\|V\|=10k$) and WS ($\|V\|=1k$) networks with $k=8$, where the goal is to maximize the average PageRank within a node subset, i.e., $f(\mathcal{S}) = \frac{1}{k}\sum_{i=1}^k PageRank(\mathcal{S}_i)$, with $\mathcal{S}$ being a subset of $k$ nodes $\\{v_1, v_2, …, v_k\\}$ in the underlying graph. > Can you provide an estimate of the noise level to the signal variance? While it is difficult to show the noise level to the signal variance in real-world experiments because of the combinatorial space, we can construct a standardized signal under this synthetic setting with the following procedures: First, we standardized the PageRank scores over all nodes to mean=0 and std=1 in the original space (denoted as $PageRank_s$). To standardize the underlying function in the combinatorial space, we multiply $\sqrt{k}$ to the avg. $PageRank_s$ as the final underlying function $\tilde{f}(\mathcal{S})$, that is, $\tilde{f}(\mathcal{S}) = \sqrt{k} f_s({\mathcal{S}}) = \frac{1}{\sqrt{k}} \sum_{i=1}^k PageRank_s(\mathcal{S}_i)$, in which $\mathbb{E}[\tilde{f}(\mathcal{S})] = 0$, and $Var(\tilde{f}(\mathcal{S})) = \frac{1}{k} Var(\sum_{i=1}^k PageRank_s(S_i)) = \frac{1}{k} \times k \times Var(PageRank_s(v)) = 1$. Now, we can simply add random Gaussian noise to $\tilde{f}(\mathcal{S})$. Specifically, we consider $\epsilon \sim N (0, \sigma^2_{\epsilon})$ with $\sigma_{\epsilon}$ at [0.1, 0.25, 0.5, 1], where the level of noise can be directly estimated since both the underlying function and noise are now of mean=0 and std=1. In addition, we further plot the estimated density of the original and noisy signals in Fig.2 (rebuttal PDF) to intuitively visualize the difference, which is done by randomly sampling $10^5$ observed values in the combinatorial space $\binom{\mathcal{V}}{k}$. > In the noisy setting, why does the framework apply the acquisition function to unvisited combo-nodes only? Why change the location of the combo-graph based on the observations instead of the posterior mean or the acquisition function? We would like to thank the reviewer for this insightful question. As suggested, we implement GraphComBO-Noisy, which uses the best posterior mean across both visited and non-visited combo-nodes within the combo-subgraph as the new center. > How do you expect your algorithm to react to noisy function values? I believe its behavior would be quite different, especially because the location of the combo-graph is selected according to the observed function value, which is not longer accurate. The results (Fig.3 rebuttal PDF) show that the original method GraphComBO is robust to the noisy observations on both networks at different noise levels from $\sigma=0.1$ to $\sigma=1$. Compared with GraphComBO-Noisy, the observation-guided method performs comparably in most cases, except for a very noisy setting when $\sigma=1$ on WS networks, where we can observe a clear advantage from the method guided by posterior mean, and it can be explained as follows. Unlike classical discrete combinatorial functions of independent variables, the underlying functions in our problems are highly related to the graph structure. For example, BA networks are known for rich structural information due to the scale-free characteristics (i.e. node degree is exponentially distributed), which makes the distribution of the original signal heavily right-skewed with extreme values even after standardization (Fig.2 Left). By contrast, the WS small-world network (randomly rewired from a ring) has more homogeneous node degrees, and thus the original signal will be more normally distributed after standardization (Fig.2 Right). Therefore, the noise level (even at $\sigma=1$) is less significant on BA networks when the algorithm finds the promising region, Whereas on WS networks at $\sigma=1$, just as the reviewer described, we can see the algorithm is “misguided” by the observations compared to the posterior mean when the signal is highly corrupted. > Comparison with COMBO on small graphs We thank the reviewer for acknowledging our different problem settings from COMBO. As suggested, we have implemented COMBO on smaller BA and WS networks of 500 nodes, which are still much larger than the ones used in their experiments ($\|V\|<50$). The results are presented in Fig. 4 in the rebuttal PDF, and we can see a clear advantage of our framework over COMBO. Please refer to the general response for a more detailed analysis. We’d like to thank the reviewer again for the insightful comments, and we will make sure to include the above discussion in the revised version. We believe that we have now addressed all the concerns from the reviews, and hope the reviewer could kindly consider increasing the rating in light of this. --- Rebuttal Comment 1.1: Title: Rebuttal Ack and Follow-Up Question Comment: Thank you for the detailed rebuttal, the interesting discussion about the noisy setting and the additional results. I've increased my score to 5. In light of the performance of GraphComBO and GraphComBO-Noisy, do you still recommend to use GraphComBO? If so, do you have a way to detect early in the experiment when GraphComBO-Noisy would be a more beneficial strategy? --- Rebuttal 2: Comment: We thank the reviewer for the prompt engagement in the rebuttal, as well as their increased positive rating of our work. Please see our following explanations regarding the choice of GraphComBO (observation-guided) and GraphComBO-Noisy (posterior mean-guided). - Under the noiseless setting in our experiments (e.g. synthetic experiments with centrality measures), the difference in their performance is minimal after we tried both methods on several synthetic graphs with different synthetic functions, where GraphComBO only slightly outperforms GraphComBO-noisy in a few cases when $k$ is relatively big. - Under the noisy setting, (e.g. the new experiment in our rebuttal and the real-world experiments involving simulation results), we observed that GraphComBO-Noisy has a clear advantage over the observation-guided method when the noise level is high. Since we often lack prior knowledge of the noise level when first encountering signals in real-world experiments, we will set the suggested GraphComBO-Noisy as the default option, given its overall performance across different settings, while retaining the observation-guided method in the revised version for noiseless scenarios. We thank the reviewer again for the suggested method and will make sure to incorporate the above changes in the main manuscript. We are more than happy to discuss any additional improvements that would make the reviewer evaluate our work more positively and potentially further raise the rating.	Summary: This paper proposes a Bayesian optimization (BO) method for optimizing black-box functions with costly evaluations over subsets of nodes in a graph. The central idea is to use the combo-graph associated with these node subsets from the original graph. This approach maintains the structural information of the original graph while enabling the use of existing techniques for BO of functions defined over graph nodes (e.g., BayesOptG). Additionally, to manage the large feasible space and better balance exploration and exploitation, a local search heuristic is introduced. The proposed method outperforms several standard baselines across various synthetic and realistic problems. Strengths: The paper is well-written overall, with sufficient technical details and figures that help build intuition. The proposed approach is technically sound, and the empirical evaluation shows significant improvements over the baselines in the problems considered. Weaknesses: 1. (Minor) While the paper is generally well-written, some graph-theoretic concepts, such as the graph Laplacian, are not adequately defined. 2. The technical novelty is somewhat limited, as the proposed approach mainly combines BayesOptG over the combo graph with a local search heuristic. 3. My main concern is the practical utility of the proposed approach. Real-world application networks are typically much larger than those considered in the empirical evaluation. Additionally, larger values of $k$ are likely to be of interest in these applications. The current results suggest that the proposed approach may not offer improvements over some baselines in these more challenging scenarios. 4. The empirical evaluation would benefit from including other BO baselines. Several methods for BO over discrete sets exist, and I believe that LADDER could be a particularly strong candidate. Technical Quality: 3 Clarity: 3 Questions for Authors: 1. Is it possible to extend the proposed approach to settings where the objective function is defined over sets of variable size? Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: The authors acknowledge the proposed approach's limitations, particularly in diminishing performance gains as $k$ increases. Additionally, I believe this approach is restricted to graphs significantly smaller than those typically encountered in real-world applications. Unfortunately, I believe these limitations are more concerning than suggested in the paper. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for the detailed feedback that helped us improve our work. Please find our detailed response below. > The empirical evaluation would benefit from including other BO baselines. I believe that LADDER could be a particularly strong candidate. To the best of our knowledge, this is the first attempt in the literature at extending BO to black-box optimization of functions over node subsets in a generic graph, which means we are addressing a new problem setup that has not been explored by existing works. For LADDER, we argue that their setting is fundamentally different from ours, where their underlying function (from their experiments) is defined on graph structures, i.e., their search space consists of different graphs and the goal is to find the optimal graph, which requires a graph kernel to measure the similarity between two graphs. However, in our setting, the underlying function is defined on node subsets from a single graph. After mapping the subsets to nodes on the combo-graph, a kernel on graph is required to measure the similarity between two nodes. The closest match to the current work is COMBO, where the search space consists of node subsets from different (small) graphs ($\|V\|<50$ in their experiments with $k<50$). Nevertheless, it can not scale to large graphs due to the infeasible computational cost from the eigendecomposition of the underlying graphs. With that being said, we have added the comparison with COMBO in the general response on small BA and WS graphs of $\|V\|=500$ (still much larger than the graphs in their experiments), where the result (Fig.4 rebuttal PDF) shows a clear advantage of our framework over COMBO. We will add the above discussion in the revised version and are happy to discuss more if the reviewer believes there are works in the literature that tackle the same problem as ours. > Real-world application networks are typically much larger than those considered in the empirical evaluation. I believe this approach is restricted to graphs significantly smaller than those typically encountered in real-world applications. Firstly, we validated our method across various real-world applications on contact networks, social networks, transportation networks, and molecule graphs that scale from order $10^2$ to $10^4$. This is consistent with the real-world graphs used in graph machine learning (e.g. graph neural networks: GCN, GAT, GIN) and graph data mining literature (e.g. influence maximization [1,2,3]), which are in the same order as ours -- based on this, we believe the graphs considered are comparable to the literature and not "significantly smaller" than realistic graphs. Second, the graphs considered in other graph-related BO works, e.g. LADDER (mentioned by the reviewer), COMBO, NASBO, GRABNEL, are much smaller than ours, which are typically at order $10^1$ and $10^2$. ### A new experiment on larger network with larger subset size $k$ Lastly, our framework can scale to large graphs, as it assumes no prior knowledge of the full graph and takes a local modeling approach that gradually reveals the graph structure. To better support our claim, we further test it on a large social network OGB-arXiv ($\|V\|=1.7\times10^5$) from open graph benchmark with $k$ up to 128, where the results in Fig.1 (rebuttal PDF) show a clear advantage of our framework over the other baselines. > Additionally, larger values of k are likely to be of interest in these applications. The current results suggest that the proposed approach may not offer improvements over some baselines in these more challenging scenarios. We argue that setting $k<50$ (<1% of the network) is very a common paradigm in the literature of subset selection on graphs [1,2,3], which has been proven to be NP-hard in many problems due to the combinatorial explosion in search space $\binom{N}{k}$, e.g. $\binom{1000}{32}\approx2.3\times10^{60}$. As such, the diminishing performance gain w.r.t. subset size $k$ poses a general challenge in the literature [4], and it becomes even more challenging in our setting, since the underlying function is fully black-boxed and we assume no prior information of the graph structure. Having said that, the proposed method still generally outperforms the other baselines across all experiments, and in the least favorable case, it performs comparably to the local search, which is also a novel baseline introduced in our paper since it needs to operate on the proposed combo-graph. > The technical novelty is somewhat limited, as the proposed approach mainly combines BayesOptG over the combo graph with a local search heuristic. As the prior work BayesOptG only considers $k=1$, which is limited for many real-world applications, we aim to generalize the framework to a combinatorial setting with the following technical contributions: 1. A combinatorial graph tailored for node subsets in a generic graph. 2. A recursive algorithm to sample subgraphs from the combinatorial space. 3. To handle the combinatorial explosion problem, we use a local approach to traverse the combinatorial graph space by iteratively sampling its subgraphs. In the early stage, we tried other localization methods such as selecting nodes inside a subgraph on the original graph as the subset. However, since we need to maintain the diversity of the subset to cover potentially distant nodes, none of them can fit into the problem as cohesively as the current method, which makes our design non-trivial. For the variable size of the subset, we believe it belongs to a different but interesting setup, and leave it to future work for exploration. And for the graph-theoretic concepts, we will make sure they are clear in the revised version. We believe that we have now addressed all the concerns from the original reviews, and hope the reviewer could kindly consider increasing the rating in light of this. Please find the references in the comment chatbox below. --- Rebuttal 2: Title: References in Rebuttal Comment: [1] Maximizing the Spread of Influence through a Social Network, KKD 2003 [2] Cost-effective Outbreak Detection in Networks, KDD 2007 [3] Robust Influence Maximization, KDD 2016 [4] Influence Maximization on Social Graphs: A Survey, TKDE 2018 --- Rebuttal 3: Title: A Gentle Reminder of Our Rebuttal Comment: Dear Reviewer u7DA, As the discussion period is drawing to a close, we'd like to kindly remind you of our rebuttal, and we remain keen to discuss the issues being raised and further improve the quality of our work. Thank you again for your time and efforts in reviewing our manuscript, and we are looking forward to your response. Best, Authors of Submission #4018 --- Rebuttal Comment 3.1: Comment: I would like to thank the authors for their detailed response. While I still believe that the proposed approach offers limited technical novelty, the authors have provided compelling evidence of its practical utility and competitive performance across a range of real-world applications. Therefore, I am happy to raise my score to 5. --- Reply to Comment 3.1.1: Comment: We thank the reviewer for acknowledging the practical contribution of our work across various real-world applications! Regarding the technical contribution, we'd like to kindly emphasize the following technical difficulties, which are critical for extending BO to the novel combinatorial setting on graphs: 1. Unlike classical combinatorial optimization of discrete variables, the combinatorial search space in our setting contains structural information from the underlying graph, which needs to be properly defined beforehand. Note this is different from BayesOptG, where the search space is not combinatorial but simply the underlying graph. 2. When using a kernel to measure the similarity between two node subsets, instead of directly counting their common elements, we need to further consider the similarity of their structural information. 3. To tackle the combinatorial explosion, we need to adopt a local modeling approach that can properly balance the exploration-exploitation trade-off in the structural combinatorial space. We believe it is a non-trivial task to address these technical challenges, which has led to the following contributions: we first proposed a combinatorial graph tailored to the novel setting, which maps node subsets to combo-nodes in the combo-graph with certain desired properties (as explained in Section 3.1). Next, we introduced a recursive sampling algorithm to sample a subgraph from the combo-graph, and then traverse the combinatorial space by moving around the subgraph center, which is guided by the local surrogate model. While being natural and intuitive, the proposed framework effectively handles the above technical problems and has shown strong performance under various settings in the experiments. From our perspective, such a canonical design may well be its advantage, i.e., a generic approach that can be applied to a wide range of practical applications on graphs. Lastly, we want to once again thank the reviewer for the valuable comments and timely feedback that helped us improve our current work.	Rebuttal 1: Rebuttal: We want to first thank all the reviewers for their detailed and valuable feedback, which we find very helpful in improving our work. We are also glad to see they acknowledged the innovation and potential impact in the community (bfWL, Y7Gf, yrTA), the technical soundness (u7DA, Y7Gf), the significance in experiment results (u7DA, Y7Gf, yrTA), and the clarity of writing (u7DA, bfWL, yrTA) in our work. We address the common concerns below. ## Comparisons with the existing SOTA BO baselines (u7DA, bfWL) We would like to emphasize that the current work is, to the best of our knowledge, the first attempt in the literature that extends Bayesian Optimization (BO) to black-box functions of node subsets in a generic graph. In particular, the local modeling approach in our framework enables the algorithm to handle situations when the underlying graph structure is not known a priori and can only be gradually revealed by queries on the fly. The proposed optimizer has real-world applications across various domains and has been validated on contact networks, social networks, transportation networks, and molecule networks, with different underlying functions such as measures for network resilience, results from epidemic/social influence simulations, and outputs from graph neural networks. We argue that this novel problem setting has been overlooked in the literature, where most graph-related BO methods (e.g. LADDER [1], NASBO [2], GRABNEL [3]) are designed for optimizing graph structures, i.e., their search space consists of different graphs and the goal is to find the optimal graph, in which a graph kernel is required to measure the similarity between two graphs. However, in our setting, the underlying function is defined on node subsets from a single graph, which, after being mapped to the combo-graph, requires a kernel on graph to measure the similarity between two nodes. The closest match to the current work is COMBO [4], where the search space consists of $k$-node subsets from $k$ different (small) graphs respectively ($\|V\|<50$ in their experiments with $k<50$), and the goal is to find the most optimal subset. Nevertheless, it assumes the knowledge of full graph structure in advance, and can not scale to large graphs due to the infeasible computational cost from the eigendecomposition of the underlying graphs. ### Further experiment on the comparison with COMBO With that being said, as suggested by reviewer bfWL, we have added the comparison with COMBO on small BA and WS graphs of $\|V\|=500$ (still much larger than the graphs used in COMBO’s experiments), where the result (Fig.4 rebuttal PDF) shows a clear advantage of our framework over COMBO, and we make the following explanations. To implement COMBO under our setting of $k$-node subsets from a single graph $\mathcal{G}$ of size $N$, we generate $k$ identical copies of $\mathcal{G}$ and form the $k$-node subset by drawing one node from each of the copy. This leads to a search space of $N^k$, which is the key limitation of COMBO under this setting since it is supposed to be $\binom{N}{k}$. As a result, there are many repeated and invalid locations in the search space, for example, at $k=3$, (1,2,3), (1,3,2), (2,1,3), ... are different subsets in COMBO, but they all should be the same subset under the current single graph setting; meanwhile (1,2,2), (1,1,2), (1,2,1), … are valid subsets in COMBO, but they are invalid $k$-node combinations on a single graph. This limitation makes COMBO highly inefficient under this new problem setting, and therefore leads to inferior performance compared to our proposed method. We are happy to discuss more if the reviewers believe there are works in the literature that tackle the same problem as the current one. ## Diminishing performance gain with increasing subset size $k$ (u7DA, yrTA) In the literature of subset selection on graphs, setting $k<50$ (<1% of the network) is a very common paradigm [5,6,7], since many problems have been proven to be NP-hard due to the combinatorial explosion in the search space $\binom{N}{k}$. As such, when the subset size $k$ increases, it poses a general challenge in the literature that the performance gain between heuristic optimization algorithms and random baselines is diminishing [8]. On top of this, the problem becomes even more challenging under our setting, since the underlying function is fully black-boxed and we assume no prior information of the graph structure. Having said that, the proposed method still generally outperforms the other baselines across all experiments, and in the least favorable case, it performs comparably to the local search, which is also a novel baseline introduced in our paper since it needs to operate on the proposed combo-graph. ### Additional experiment on larger network with larger subset size $k$ Lastly, we further test GraphComBO on a large social network OGB-arXiv ($\|\mathcal{V}\|=1.7\times10^5$) from open graph benchmark with $k$ up to 128, where the results in Fig.1 (rebuttal PDF) show a clear advantage of our framework over all the other baselines. In this case, the local search baseline even underperforms random selection and random walk, as it overly focuses on local exploitation rather than exploration, whereas the latter is more critical on large underlying graphs. [1] Combining latent space and structured kernels for Bayesian optimization over combinatorial spaces, NeurIPS 2021 [2] Interpretable Neural Architecture Search via Bayesian Optimisation with Weisfeiler-Lehman Kernels, ICLR 2021 [3] Adversarial Attacks on Graph Classification via Bayesian Optimisation, NeurIPS 2021 [4] Combinatorial Bayesian Optimization using the Graph Cartesian Product, NeurIPS 2019 [5] Maximizing the Spread of Influence through a Social Network, KKD 2003 [6] Cost-effective Outbreak Detection in Networks, KDD 2007 [7] Robust Influence Maximization, KDD 2016 [8] Influence Maximization on Social Graphs: A Survey, TKDE 2018 Pdf: /pdf/4a4b68322f83c30333e31ba63d45744e1757e98a.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Why the Metric Backbone Preserves Community Structure	Accept (poster)	Summary: For weighted distance graphs, the metric backbone corresponds to the union of the shortest paths. This work shows that the community structure of a graph can still be detected from this backbone. This is surprising, since inter-community edges often serve as bridges between communities, so one would expect them to be overrepresented in the metric backbone. Experiments are performed to demonstrate this behavior on real-world networks. Strengths: The paper is well-written and easy to read. The problem is interesting and the described theoretical behavior is surprising. The overview given in Section 3.2 is helpful. Weaknesses: The experimental setup in Section 4 seems somewhat overcomplicated. Is this a standard method for converting weighted networks to distance networks? If so, refer to works where this methodology is studied. Also, it is worth pointing out that if the proximity graph is generated from some weighted SBM, then this distance-conversion will introduce dependencies between the edge weights. Similarly, the setup of Section 5 is also quite complicated without providing much motivation or justification. The obvious way of converting points to a distance network would be to consider the complete graph with weights corresponding to the Euclidean distance, but I understand that then every edge belongs to the metric backbone. Please explain why this complicated construction is needed. Also, the label placement of Figure 2a is a bit inconvenient as it blocks the blue line. Moreover, while the results of Section 4 are interesting, the results of Section 5 are not convincing. Minor comments: * In the denominator of $p(u,v)$ given below line 251, you write $u\in\text{Nei}(u)\wedge\dots$ instead of $u\in\text{Nei}(u)\wedge\dots$. Technical Quality: 3 Clarity: 3 Questions for Authors: In line 132, you write "Or as the uniform distribution", but this seems like an odd and unnecessary statement. It makes sense that you want to point out the resemblance to the exponential distribution for taking minima, but it's unclear how the resemblance to the uniform is necessary. At first, I was a bit confused with the fact that the inequalities given in Proposition 2.1 do not depend on a or b. Perhaps you could comment on that in the text. For example, you could comment on the fact that there will always be pairs whose distances fall below this interval, but that their fraction vanishes, and that one expects intra-community distances to be smaller. Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The authors have addressed the limitations of the results. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Dear Reviewer bM2e, We thank you for your time in evaluating our submission and we are grateful for your comments. Please find below responses to the questions raised in your reviews. * The methodology used in Section 4 is relatively standard, as we took it from previous papers on the metric backbone (see references [8] and [36] for example). We acknowledge that these transformations involve two non-linearities (the first one to transform the unweighted graph into a weighted graph, and the second one to transform the weights into distances). The theoretical Section 2 does not involve those transformations (as we consider weighted SBM where the weights are distances). * Using a Gaussian kernel to compute similarities between pairs of points is also standard. For example, this is exactly what is implemented for spectral clustering in scikit-learn (when one does not provide an adjacency matrix but a set $n$ points in $\mathbb R^d$). * Indeed, the result of Proposition 2.1 does not depend on $a$ nor $b$. This is because we upper and lower-bound the cost of the shortest path between $u$ and $v$, and these bounds do not match (except in some particular settings). Deriving matching lower and upper bounds should lead to a value that depends on $a$ and $b$. We will add this comment in the text. We also thank you for pointing out some typos and will correct them. --- Rebuttal Comment 1.1: Comment: I thank the authors for the response. The response adequately addresses my main concerns. I encourage the authors to improve the description of the experiments to incorporate the above answers (in particular, include references to show that this is a relatively standard approach). My overall rating remains unchanged.	Summary: The authors analyze the metric backbone (= all the edges that are on some shortest path) and it's relation to clustering. They show that under weighted SBM model (with equal expected degree for all nodes), metric backbone 1) the metric backbone approximately maintains the edge probabilities of blocks 2) spectral clustering appplied to metric backbone recovers SBM. Strengths: The main contribution of the paper are the two theorems Theorem 1 and Theorem 2. Both are interesting and non-trivial results, providing connections between metric backbone and SBM models. Of these two theorems Theorem 2 is the more interesting one. Weaknesses: While theorems are interesting some assumptions seems to be very unrealistic. For example, Theorem 2 only works if tmin and tmax are the same. Is it possible to formulate it similarly as Theorem 1. Moreover, while the edge probabilities are proportionally retained, the same (probably) doesn't hold for weights, as I assume the min cost of the cheapest path from u to v goes to 0. Do these result also hold for other sparsification methods? such as simply deleting the edges independently with some given probability? I am guessing that Theorem 1 holds (and even stronger version) but I am not sure about Theorem 2. Other questions/remarks: - Assumption 1: p_n >> ... what does >> means here exactly? that log n / n in o(p_n)? - Remark 1: tmin and tmax assume that there is Lambda = lambda * 1 * 1^T. Is this the assumption also in Theorem 1 and Theorem 2? - The only difference in tmin and tmax is dmin and dmax. Why not use them directly in Theorem 1-2? Or, probably, dmin / n and dmax / n since those converge to a non-zero real number. - Leveraging the memoryless ... processes. Unclear sentence, please reword. - be defined after Equation 2.1. -> be as defined in Remark 1. - maintains the same proportion -> maintains approximately the same proportion Technical Quality: 3 Clarity: 3 Questions for Authors: - Does the result hold for other sparsification methods? - Can Theorem 2 be stated with tmin < tmax? - is lambda in Remark 1 needed assumption? Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: The paper has a conclusions section but the authors do not discuss the limitations nor future work. Few sentences about the future steps would be helpful. Negative societal impact is not applicable for this paper. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Dear Reviewer uKT3, We thank you for your time in evaluating our submission and we are grateful for your comments. Please find below responses to the questions raised in your reviews. Answers to the main questions: * Other sparsification methods can maintain the community structure (as shown in Figure 1) but lose other important properties such as distances and even connectivity. In weighted SBM specifically, retaining edges independently with probability $p$ preserves the community structure, resulting in a weighted SBM with the same weight distribution but lower edge density $\rho_n p$. Therefore, if $\rho_n p = \Omega( \log n / n)$, this sparsification preserves the community structure (in the sense that one could derive an analogue of Theorems 1 and 2 for this naive sparsification) but it destroys other important graph properties and structures; and notably the shortest paths will \emph{not} be preserved. In contrast, our work shows that preserving the shortest paths also preserves the community structure, even though it may sacrifice other properties, such as of course the edge weight distribution. * While we assume $\tau_{\min} = \tau_{\max}$, we note that this holds true in significant settings, such as the Planted Partition Model or general SBM with the same expected degree in each community (and $\lambda_1 = \cdots = \lambda_k$). Upon closer examination of the proof of Theorem 2, we found that a weaker condition suffices, specifically $\frac{\tau_{\min}}{\tau_{\max}} = \Theta(1)$. This condition is automatically satisfied under Assumptions 1 and 2. The assumption $\tau_{\min} = \tau_{\max}$ is only used twice in the proof of Theorem 2: at lines 581 and 604; all other steps already allow $\tau_{\min}$ and $\tau_{\max}$ to differ. Removing strict equality in line 604 amounts to replace equation (B.6) by $\sigma_k = \frac{1}{8} \frac{ \tau_{\min} }{ \tau_{\max} } \tau \mu \log n$; if $\tau_{\min}$ and $\tau_{\max}$ are of the same order, this only changes the constant in front of the quantity $\tau \mu \log n$ and does not affect the asymptotic scaling. Modifying line 581 is more involved, as we need to find the asymptotic scaling of the $k$-th largest eigenvalue of $\mathbb E W^{mb}$ without explicitly knowing the values of the matrix $\mathbb E W^{mb}$ (indeed, the upper and lower-bounds derived in Lemma 4 do not match when $\tau_{\min} \ne \tau_{\max}$). Yet, this can be handled as well; we first write $\mathbb E W_{ub}^{mb} = c_{ab}$ where $a$ and $b$ are the community of vertices $u$ and $v$. Next, we can process similarly as in the paragraph between lines 585 and 592 to derive a relationship analogous to equation (B.3). We appreciate you raising this point, as it strengthens our result, and we plan to modify the proof and statement of Theorem 2 accordingly. Answers to the other remarks: * Indeed, the cost of the shortest path between $u$ and $v$ goes asymptotically to zero. * Remark 1 is here to relate $\tau_{\min}$ and $\tau_{\max}$ to the average degrees, in the particular case where $\lambda_1 = \cdots = \lambda_k$. This provides a simple intuition of what these quantities mean. However, restricting all $\lambda_a$ to be equal is not needed in Theorems 1 and 2. When they are different, the relation between $\tau_{\min}$, $\tau_{\max}$ and the average degrees does not hold anymore, which is why we keep $\tau_{\min}$ and $\tau_{\max}$ in the main theorems.	Summary: This work focuses on the metric backbone of weighted graphs, which is the union of all-pairs shortest paths. The study analyzes the metric backbone of a class of weighted random graphs with communities and formally proves the robustness of the community structure regarding the removal of non-metric backbone edges. An empirical comparison of graph sparsification techniques also confirms the theoretical finding and shows the metric backbone is an efficient sparsifier in the presence of communities. Strengths: - Provides a formal analysis and proof to explain the robustness of the community structure in the metric backbone of weighted random graphs with communities, which fills a knowledge gap in understanding this phenomenon. - Confirms the theoretical finding through an empirical comparison of graph sparsification techniques, providing practical evidence and validation. - Identifies the metric backbone as an efficient sparsifier in community-present networks, which has practical applications in graph processing and analysis in various fields where community structure in networks is relevant. Weaknesses: - This sentence needs to be clearer: "This suggests that the metric backbone would dilute or destroy the community structure of the network. " What does the dilution of community structure mean? The term "preserve" may also be defined formally or mathematically. - It claims that Algorithm 1 can recover the community structure from the metric backbone, but why the input is the original graph G? - Although in Section 3.1, the authors claim that it is feasible to have metric backbones on networks with millions and billions of nodes, the experiments are mostly for networks with thousands of nodes. Why? Can the running time be included in the experiment? - Comparison with other graph sparsification methods or other data sets may be added. Technical Quality: 3 Clarity: 3 Questions for Authors: The authors may explain the drawbacks mentioned in the weakness section. Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 4 Limitations: Yes. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Dear Reviewer Qqxh, We thank you for your time in evaluating our submission and we are grateful for your comments. Please find below responses to the questions raised in your reviews. * By dilution of community structure, we mean that the metric backbone could delete a larger proportion of inter-community edges than intra-community edges. We plan to make these statements more precise in the final version (see our answer to Reviewer JByP as well). * The input of Algorithm 1 is a graph; however, Theorem 2 is stated for Algorithm 1 when the input is the metric backbone of a weighted SBM. We acknowledge that this is confusing. To clarify, we plan to modify the exposition of Algorithm 1 by adding a step to compute the metric backbone $G_{mb}$ of the input graph $G$, which is then followed by performing spectral clustering on $G_{mb}$. * We discuss the running time of our implementation in Appendix C due to page limitations, but we will move this discussion to the main text in the final version. In summary, computing the metric backbone is faster than spectral sparsification (where we used an external library), and running spectral clustering took significantly longer. * We compared the metric backbone with the threshold graph (a naive but still commonly used technique) and spectral sparsification (one of the most popular and efficient graph sparsification techniques). We also provide additional experiments in Appendix C. This comparison demonstrates that the metric backbone is a competitive sparsifier. The goal of this paper is to highlight that the metric backbone preserves community structure, which is why we limited the baselines for comparison. A comprehensive review and comparison of all graph sparsification techniques could be the topic of an interesting review paper but would go beyond the scope of the current paper.	Summary: The authors investigate the shortest-path backbone that is the union of all-pair shortest paths in a weighted graph, and show that it preserves the community structure in weighted Stochastic Block Model (wSBM) with high probability. A key finding in their proof is that the metric backbone maintains the same proportion of intra- and inter- cluster edges as in the original wSBM graph. Then the classic Spectral Clustering algorithm is able to reconstruct the embedded communities with high probability. Their experimental results confirm that the shortest-path backbone can preserve community structures in real datasets, and is also an efficient sparsifier in the presence of communities. Strengths: 1. The technical contribution is solid. 2. The paper is well written and the presentation of proof ideas is clear. Weaknesses: The theoretical results seems to heavily depend on the property of wSBM, and are hardly generalized to much wider well-clustered graphs. It is possibly more interesting to figure out in what conditions the metric backbone is able to preserve communities in a given well-clustered graph. This is a much closer scenario to the observations in the experiments. Technical Quality: 3 Clarity: 3 Questions for Authors: 1. I am not sure whether it is proper to say that it is intuitive that metric sparsification should dilute the community structure (in Line 56), since for the simplest case of unweighted graphs, the metric backbone clearly maintains all edges and the community structure will be preserved certainly. 2. It seems that the Spectral Clustering algorithm (Algorithm 1) deals directly with the edge weights of wSBM that is introduced by the exponential distribution for a distance metric. But the Spectral clustering process works only for similarity-based graphs. Why don’t the authors need to change the distance metric into a proximity one before Spectral Clustering? Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The authors haven’t discussed the limitations in the main paper, but in the checklist instead. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Dear Reviewer JByP, We thank you for your time in evaluating our submission and we are grateful for your comments. Please find below responses to the questions raised in your reviews. * Intuitively, keeping only the shortest paths and deleting everything else could destroy all structures unrelated to the shortest paths (such as the communities). This is indeed not the case on unweighted graphs, as the metric backbone does not remove any edge, hence the whole structure is preserved. However, community structure and shortest paths appear to act as two antagonists in graph sparsification, because removing edges that belong to a large number of shortest paths destroys these shortest paths (and graph connectivity) but can reveal communities as disconnected components of the sparsified graph (see ref. [17]). Moreover, when the metric backbone keeps only a small fraction of the edges of the original weighted graph, one could expect that the fractions of inter- and intra-community edges might be affected differently by the deletion of non-shortest path edges. Our work shows that this is not the case. * We acknowledge that spectral clustering is an umbrella term that encompasses various techniques involving the eigenstructure of a matrix characterizing a graph topology. Spectral clustering on the normalized Laplacian of the graph (which is the version implemented in popular libraries such as scikit-learn) requires weights to be similarities between node pairs and not distances. Because we are directly working with the graph adjacency matrix, we can handle weights being either similarities or distances. Nonetheless, we also acknowledge a typo in line 2 of Algorithm 1: the eigenvalues should be ordered in decreasing absolute value (note that this is already the case in the proof, see for example line 582). As a naive justification of why ordering in absolute value handles all cases, consider an unweighted SBM with two communities of the same size, and the probability of intra- (resp., inter-) community edge $p$ (resp., $q$). The eigenvalues of $\mathbb E A$ are $n(p+q)/2$ (multiplicity 1), $n(p-q)/2$ (multiplicity 1) and $0$ (multiplicity $n-2$). When $p\ne q$, we indeed have $\|n(p+q)/2\| > \|n(p-q)/2\| > 0$. But the relationship $n(p+q)/2 > n(p-q)/2 > 0$ does not hold if $p<q$. [17] Michelle Girvan and Mark EJ Newman. Community structure in social and biological networks. Proceedings of the national academy of sciences, 99(12):7821–7826, 2002. --- Rebuttal Comment 1.1: Comment: Thank the authors for their response. I keep my score.	null	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Noise Contrastive Alignment of Language Models with Explicit Rewards	Accept (poster)	Summary: The paper's main contributions are: 1. Theoretical Integration: It integrates Direct Policy Optimization (DPO) with contrastive learning theories, offering a general framework for using reward and preference data. 2. Value of Suboptimal Responses: Highlights the importance of suboptimal responses in optimizing language models, showing improved performance over other methods by fully utilizing reward data. 3. Performance Improvement: Demonstrates how NCA counters the data likelihood decline in DPO, enhancing practical performance. Strengths: 1. Utilizing the explicit reward for alignment which is quite interesting. 2. Propose a general method to address this problem. 3. It sees improvement over DPO on leaderboards. Specially, it is much better than DPO in math and coding tasks. Weaknesses: I don't have further suggestions for this part. Technical Quality: 3 Clarity: 3 Questions for Authors: How do you compare your work with the paper titled Direct Preference Optimization with an Offset(https://arxiv.org/pdf/2402.10571). Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: I don't see any issues with this part. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: # Official Response to Reviewer xAZC We thank reviewer xAZC for the valuable feedback. It really encourages us to see that the reviewer finds our work to be a good contribution to the field, regarding pointing out the value of suboptimal responses and countering the likelihood decline trend in alignment. We answer the reviewer's question below: Q1: How do you compare your work with the paper titled Direct Preference Optimization with an Offset ([https://arxiv.org/pdf/2402.10571](https://arxiv.org/pdf/2402.10571)). A1: We thank the reviewer for mentioning this paper. ODPO also wants to leverage the reward gap information for better optimization. We notice that ODPO is followed by some recent work like SimPO due to its effectiveness, which reviewer UYN1 has mentioned. In simple words, ODPO modifies the DPO loss function to be $L_\theta^\text{ODPO} = - \log \sigma(r_\theta(x,y_w) - r_\theta(x,y_l) - \gamma)$, where $\gamma$ is determined by the reward gap in datasets. Connection with our methods: 1. InfoNCA and ODPO share similar motivations but have distinctive approaches. In our understanding, ODPO can only guarantee the learned reward gap is larger than $\gamma$, while InfoNCA converges if and only if the learned reward gap is equal to $\gamma$. 2. InfoNCA can be directly used for multiple responses while ODPO is designed for pairwise responses. 3. Based on our experience, the above two distinctions won't cause very much empirical difference in practice regarding language quality. We personally feel InfoNCA loss is more mathematically elegant, though. After all, it is our own method :) 4. Compared with NCA, ODPO is optimizing relative rewards just like DPO, so we guess the problem of logp decline still exists. NCA may perform better in preventing the logp decline trend.	Summary: ## Summary - Typically, RLHF algorithms like DPO use preference pairs dataset. - The key question, this paper tries to answer is how to incorporate reward datasets annotated with scalar values. Previous approach usually prune the scalar reward datasets by selecting the best response and pairing with a random remaining response. However, this work shows that the extra suboptimal responses can also be beneficial for policy training. - They present two main algorithms (inspired from contrastive learning literature) here which handle the aforementioned problem - NCA Noice Contrastive Alignment - InfoNCA - They also show that NCA is able to mitigate the "decreasing likelihood trend" observed with the DPO algorithm. NCA also outperforms DPO on math and coding tasks because it prevents the likelihood of preferred responses from decreasing. The main difference between InfoNCA and NCA objective is that the NCA objective has an additional regularizer term - The "decreasing likelihood trend" can be simply described as the decrease in likelihood of the preferred response after DPO training. - This happens because DPO focuses on adjusting relative likelihoods across generations whereas NCA focuses on adjusting absolute likelhood - InfoNCA compares multiple responses and identifies the one sampled from optimal policy. NCA predicts the model source of a single response. - The authors also show that DPO is a special case of InfoNCA Strengths: ## Strengths - The loss objectives are intuitively easy to follow from equation 6 and equation 11. - The paper is well written and easy to follow, with clear and accessible writing. The literature review provides a solid contextual foundation for the work. - The experiments do a good job at substantiating the claims presented and justifying the NCA and InfoNCA algorithm. - I also like the section on empirical takeaway: when to choose NCA over DPO. - The paper overall addresses an important problem and proposes the NCA solution which helps tackle the decreasing likelihood issue. The empirical takeaway for reasoning tasks is also helpful for an ML practitioner. My overall recommendation for the paper is an accept but I would very much appreciate if the authors can answer my questions to help deepen my understanding of the work. Weaknesses: I could not find any weakness Technical Quality: 3 Clarity: 3 Questions for Authors: ## Questions - I have not gone through the material in the appendix but at several places in the theorems, the authors assume a model with unlimited capacity. Why is this important and what are the implications otherwise? - It is not obvious to me how equation 11 leads to predicting the model source of a single response in Figure 3 Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The authors have adequately addressed the limitations. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: # Official Response to Reviewer WFsu We appreciate the reviewer WFsu for the very detailed comments on our paper and are glad that the reviewer finds our paper to be helpful. Below we address the reviewer's questions and hope this can help the reviewer increase the confidence of our work. Q1: The paper assumes a model with unlimited capacity. Why is this important and what are the implications otherwise? A1: We assume unlimited model capacity mainly because we want our proof to be strict. There's nothing special here. Imagine we want to fix a function $f(x)=x^2$ using neural networks. We must first assume our model is expressive enough (unlimited capacity) to fully achieve convergence. Otherwise, if our model $f_\theta$ is simply a linear MLP (limited capacity), we cannot achieve $f_\theta(x)=x^2$ no matter how hard we try. Q2: It is not obvious to me how equation 11 leads to predicting the model source of a single response in Figure 3 A2: Eq 11 is the NCA loss function. For convenience, we suppose there are only $K=2$ responses $y_1$ and $y_2$, with their respective reward $r_1 > r_2$. $L_\theta^\text{NCA} =- \sum_{i=1}^2 \left[\frac{e^{r_i}}{e^{r_1}+e^{r_2}} \log \sigma (r_\theta(x,y_i)) + \frac{1}{2} \log \sigma (-r_\theta(x,y_i))\right]$ We compare with $L^\text{InfoNCA}_\theta$ for reference: $L_\theta^\text{InfoNCA} = - \sum_{i=1}^2 \left[\frac{e^{r_i}}{e^{r_1}+e^{r_2}} \log \frac{e^{r_\theta(x,y_i)}}{e^{r_\theta(x,y_1)}+e^{r_\theta(x,y_2)}}\right]$ According to our proofs in the paper, one optimal solution for the above training loss is that $r_\theta(x,y_1) = r_1$ and $r_\theta(x,y_2) = r_2$. However, if we let $r_\theta(x,y_1) = r_1 -12345.0$ and $r_\theta(x,y_2) = r_2 -12345.0$, we will find this is still the optimal solution for InfoNCA. $- \sum_{i=1}^2 \left[\frac{e^{r_i}}{e^{r_1}+e^{r_2}} \log \frac{e^{r_\theta(x,y_i) - 12345.0}}{e^{r_\theta(x,y_1) - 12345.0}+e^{r_\theta(x,y_2) - 12345.0}}\right]=- \sum_{i=1}^2 \left[\frac{e^{r_i}}{e^{r_1}+e^{r_2}} \log \frac{e^{r_\theta(x,y_i)}}{e^{r_\theta(x,y_1)}+e^{r_\theta(x,y_2)}}\right]$ This is exactly why we say InfoNCA only targets relative rewards. The loss function is happy as long as $r_\theta(x,y_1) - r_\theta(x,y_2)$>0. However, $r_\theta(x,y_1)$ can be a very negative number, which we do not want. For the NCA loss, it is otherwise, because inside $\sigma$ there is only a single reward $\sigma(r_\theta(x,y_i))$ instead of many relative model rewards $\log \frac{e^{r_\theta(x,y_i)}}{e^{r_\theta(x,y_1)}+e^{r_\theta(x,y_2)}}$. $L_\theta^\text{NCA} = L_\theta^\text{NCA}(x,y_1) +L^\text{NCA}_\theta(x,y_2)$ $L_\theta^\text{NCA}(x,y_1) =- \left[\frac{e^{r_1}}{e^{r_1}+e^{r_2}} \log \sigma (r_\theta(x,y_1)) + \frac{1}{2} \log \sigma (-r_\theta(x,y_1))\right]$ $L_\theta^\text{NCA}(x,y_2) =- \left[\frac{e^{r_2}}{e^{r_1}+e^{r_2}} \log \sigma (r_\theta(x,y_2)) + \frac{1}{2} \log \sigma (-r_\theta(x,y_2))\right]$ $(r_1>r_2, \frac{e^{r_1}}{e^{r_1}+e^{r_2}} > \frac{1}{2})$ You can see that $L_\theta^\text{NCA}(x,y_1)$ is only influenced by $r_\theta(y_1)$ and is unaffected by $r_\theta(y_2)$. For NCA, if $r_\theta(x,y_1) = r_1 -12345.0$ is a very negative number, $L_\theta^\text{NCA}(x,y_1)$ would surely be very large and contradicts the training loss minimization. In other words, NCA forces $r_\theta(x,y_1)$ to be positive and $r_\theta(x,y_2)$ to be negative respectively and independently. This is why we say Eq 11 leads to predicting the model source (optimize absolute reward) of a single response. We'd also like to refer the reviewer to Appendix H, where there is a more detailed example.	Summary: The authors introduce a general framework for LM alignment, leveraging Noise Contrastive Estimation (NCE) to bridge the gap in handling reward datasets explicitly annotated with scalar evaluations. The framework comprises two parallel algorithms, NCA and InfoNCA, both enabling the direct extraction of an LM policy from reward data as well as preference data. Strengths: 1. The method bridge the theoretical gap between DPO and classic contrastive learning theories. InfoNCA and NCA are uniquely suited for both reward and preference data, offering a general framework that integrates preference-based algorithms. 2. The proposed method outperforms various preference methods by fully exploiting data information in reward datasets. 3. It's great to see the method not hurting UltraInteract and leads to better performance. Weaknesses: 1. The proposed method looks trivial by integrating classic contrastive learning theories. Different methods coming out at the same time. They look similar and not easy to find which is better, such as the concurrent work SimPO: Simple Preference Optimization with a Reference-Free Reward. Technical Quality: 3 Clarity: 3 Questions for Authors: More training details, such as hyper-parameter search space Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: It would be better list more training details. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: # Official Response to Reviewer UYN1 We thank reviewer UYN1 for the praise and suggestions regarding our work. We are pleased to see the reviewer's acknowledgment of our theoretical contribution in bridging the gap between DPO and classic contrastive learning theories. Below we address the reviewer's questions and hope our responses can help increase the reviewer's confidence in our work. Q1: The proposed method looks trivial by integrating classic contrastive learning theories. Different methods coming out at the same time. They look similar and not easy to find which is better, such as the concurrent work: SimPO. A1: There are indeed numerous recent approaches for solving alignment tasks, such as DPO/KTO/IPO/ORPO/SimPO, and it is challenging to definitively determine which is superior. Still, we would like to highlight some key features of InfoNCA/NCA that we find to be unique. 1. Unlike most previous methods, InfoNCA/NCA is not based on any kind of preference model assumptions, such as Bradley Terry or Plackett-Luce models. It is directly derived from existing contrastive learning Bayes theories and is deeply connected with NCE methods that have been widely validated. The theoretical cleanness should provide more confidence for the users. 2. Our methods, unlike SimPO, can handle continuous explicit rewards instead of just preference data. To the best of our knowledge, there are very few work/algorithms that are directly motivated by this task. 3. Our method guarantee strictly convering to the target optimal policy. The theoretical proofs are strict and purely Bayes (Appendix ). This offers a unique theoretical perspective for understanding existing alignment approaches, as reviewers EyJu and EZsK have also pointed out. Q2: It would be better to list more training details such as hyper-parameter search space. A2: We'd like to refer the reviewer to Appendix C of the paper, where we have listed all important training details (we think). Source code is also provided to ensure reproducibility. We ablate $\beta \in \{3e-4, 1e-3, 3e-3, 1e-2, 3e-2, 1e-1, 3e-1, 1.0\}$ and $\alpha \in \{0.01, 0.1, 0.33, 1.0, 3.33\}$ and $K \in {2,4}$ for ablation studies. For the main experiment Table, we all use consistent hyperparameters same as the Zephyr DPO baseline for a fair comparison and to avoid hyperparameter overfitting. We will be glad to provide any additional experiment details if the reviewer is interested in any specific aspects.	Summary: This paper leverages Noise Contrastive Estimation (NCE) to align language models (LMs) with explicit reward data, which can handle both scalar evaluations and multiple preference data. The proposed methods, NCA and InfoNCA, extend current alignment theories by improving upon DPO and addressing the issue of decreasing likelihood observed in DPO. Experimental results demonstrate that InfoNCA and NCA outperform existing preference-based methods. Strengths: 1. The paper bridges the gap between preference-based and reward-based alignment methods by deriving InfoNCA from InfoNCE, thereby extending DPO to handle explicit rewards with a strong theoretical foundation. 2. Empirical results show significant performance improvements in various tasks, including complex reasoning tasks, by effectively leveraging both optimal and suboptimal responses from reward datasets. 3. Mitigating Likelihood Decrease: NCA effectively prevents the chosen likelihood from decreasing during training, addressing a critical issue in DPO and enhancing model performance stability. Weaknesses: 1. The motivation of this paper is weak: The description that DPO can only be used for pairwise preference data is wrong (such as Line 31 and 43). In fact, the appendix of DPO says that it can be applied to multiple preference data based on the Plackett-Luce model. 2. The main experiments lack related baselines. Since the proposed method is a reward-based method that utilizes reward data for preference ranking, Table 2 should also include PPO under the annotation type "Reward" for direct comparison since it also utilizes reward data. In addition, I suggest comparing it with PRO (https://arxiv.org/pdf/2306.17492) under the annotation type "preference" since this work directly applies DPO to the setting of multiple preference ranking. 3. The proposed method InfoNCA uses both preference data and reward data for training, resulting in more computational overhead compared with PPO and DPO. Thus, it is not surprising that better performance is achieved than with preference-based methods, although the improvement is marginal. Is it a fair comparison if the methods use different magnitudes of data? Please also see comment 1. Technical Quality: 2 Clarity: 3 Questions for Authors: 1. What is the amount and percentage of reward and preference data in each dataset? 2. Since InfoNCA and NCA are reward-based methods, why not compare them with PPO in terms of MT-bench, AlpcaEval, and Wins vs. PPO? Confidence: 4 Soundness: 2 Presentation: 3 Contribution: 3 Limitations: Limitations are discussed in the appendix Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: # Official Response to Reviewer EZsK (1/2) Q1: The motivation is weak. The description that DPO can only be used for pairwise preference data is wrong (such as Line 31 and 43). In fact, the appendix of DPO says that it can be applied to multiple preference data based on the Plackett-Luce model. A1: We thank the reviewer for the valuable feedback on the PL model. PL can indeed be combined with the DPO algorithm to handle multiple responses. Since this method is only mentioned in the appendix and does not have any accompanying experiments in DPO's paper, we did not notice this part originally. However, we respectfully disagree with the reviewer regarding "weak motivation". The PL+DPO method does not hurt the core contribution of our work. Our paper is titled "Alignment of LMs with Explicit Rewards". NCA is strongly motivated to handle explicit reward data that naturally can be applied to responses of arbitrary numbers. In contrast, like the BT model, PL model is still a preference/ranking-based method and cannot handle reward datasets. We have rephrased all related descriptions in our paper to avoid previous unstrict claims. (We cannot update our official manuscript during rebuttal due to review policy, though) For instance, (Line 31) > DPO is only tailored for preference data ~~with K = 2 responses per instruction x~~. (Line 43) >However, 43 unlike DPO which is built upon assumptions of ~~Bradley-Terry models~~ preference models like Bradley-Terry or Plackett-Luce model, InfoNCA is strictly derived from InfoNCE We have also conducted an additional experiment to compare with PL-based DPO methods: \| Experiment\| MT-bench \| Alpaca \| Avg. \| \|---\|---\|---\|---\| \| DPO baseline (K=2) \| 73.4 \| 90.6 \| 82.0 \| \| DPO × $C$ (K=4) \| 73.8 \| 90.3 \| 82.1\| \| DPO × 3 (K=4) \| 72.2 \| 91.6 \| 81.9\| \| DPO + PL Method (K=4) \| 74.1 \| 91.3 \| 82.7 \| \| InfoNCA (K=4) \| 76.3 \| 92.4 \| 84.4 \| * Q2: The proposed method InfoNCA uses both preference data and reward data for training, .....more computational overhead compared with PPO and DPO.....Is it a fair comparison if the methods use different magnitudes of data? A2: We respectfully disagree with the reviewer's comment and think there is clearly some misunderstanding of our experiments, which we hope to clarify: 1. Our method can handle both preference and reward data, but it only requires one data type for training. As a matter of fact, we use either 100% of preference data or 100% of reward data throughout our experiments. There is no mixed dataset used. (Refer also to A3). 2. PPO is at least 10 times more computationally expensive than our method. Our experiment finishes in a bit more than 1 hour using H100 GPU sever, while PPO takes about a day because it requires online data sampling and learning separate reward model/value model/policy model. 3. Our method is as efficient as DPO, becuase DPO is simply a special case of our method. If DPO uses only pairwise responses, and InfoNCA uses 4 responses, then InfoCNA requires about 2 times the computational resource. This is reasonable because there are two times of data. Besides, using the same amount of data, our methods outperform DPO (Table 2, Line 212 of our paper). 4. We have compared with previous work that uses the same amount of data with our method (Line 208, Table 2, Table 3), so we believe the comparison is fair. Our results show that even previous work is given the same data magnitude, InfoNCA still outperforms them. Results with the same data: \| Experiment \| MT-bench \| Alpaca \| Avg. \| \|---\|---\|----\|---\| \| DPO × $C_4^2$ (K=4) \| 73.8 \| 90.3 \| 82.1 \| \| DPO × 3 (K=4) \| 72.2 \| 91.6 \| 81.9 \| \| DPO + PL Method (K=4) \| 74.1 \| 91.3 \| 82.7 \| \| InfoNCA (K=4) \| 76.3 \| 92.4 \| 84.4 \| \| Model\| Average among 8 tasks \| \|---\|---\| \| Mixtral-7B-SFT \| 24.5 \| \| $+$ DPO \| 25.5 \| \| $+$ NCA \| 35.7** \| \| Mixtral-87B-SFT \| 56.3 \| \| $+$ DPO \| 50.1 \| \| $+$ NCA* \| 57.9 \| * Q3: What is the amount and percentage of reward and preference data in each dataset A3: Please refer to the first point in A2. \| Dataset \| Type\| Response number \| Used in \| \|---\|---\|---\|----\| \| UltraFeedback\| 100% Reward data \| K=4 \| Table 2, Figure 5(right), Figure 6(right) \| \| UltraFeedback-clipped\| 100% Reward data \| K=2/3/4 \| Figure 4 (left) \| \| UltraFeedback-binarized \| 100% Preference data \| K=2 \| Table 2, Figure 6(left) \| \| UltraInteract \| 100% Preference data \| K=2 \| Table 3, Figure 5(left) \| Please also refer to Line 178, 193,212,220, and 226 for details. * Q4: Since InfoNCA and NCA are reward-based methods, why not compare them with PPO? Table 2 should also include PPO. A4: We thank the reviewer for this suggestion, and present experimental results below. \| Name \| Annotation Type \| MT-bench \| AlpacaEval \| \|---\|--\|--\|--\| \| Mixtral-7B-sft \| SFT Data \| 6.45 \| 85.20 \| \| +DPO(online) \| RM Preference \| 7.14 \| 88.39 \| \| +PPO(online) \| RM Reward\| 6.64 \| 84.20 \| \| +InfoNCA\| Reward \| 7.63 \| 92.35 \| \| +NCA \| Reward \| 7.52 \| 90.31 \| Initial results show that PPO underperforms DPO or InfoNCA methods, perhaps due to PPO's inherent instability or our insufficient hyperparameter tunning. Why not previously directly compare NCA with PPO? PPO and InfoNCA target different kinds of "reward". InfoNCA targets REAL dataset reward and features direct optimization. In contrast, PPO targets a Reward Model and requires online data sampling. We prioritize comparing with DPO-like methods since DPO is actually our special case so we can keep exactly the same hyperparameters. * ## Reminder QA5: We refer the reviewer to the global rebuttal posted at the top of the webpage for the rest (EZsK part 2/2) of our response. This is due to the severe page limit. --- Rebuttal Comment 1.1: Comment: Thanks for the response. Since most of my questions and concerns are addressed, I will increase my overall recommendation. --- Rebuttal 2: Title: Additional Response Comment: Dear reviewer, We copy the second part of our rebuttal response here to ease reading. In our responses, we have compared with more baselines and clarified the details of the data we are using based on your suggestions. We hope we can address your concerns and are glad to answer any further questions you might have. Thank you again for your valuable feedback! # Official Response to Reviewer EZsK (2/2) Q5: suggest comparing it with PRO (https://arxiv.org/pdf/2306.17492). A5: PRO is a quite related work of ours because it can also handle response data of arbitrary length. It is also highly related to the PL method as we have discussed in A1. Still, PRO is essentially a ranking/preference-based method, while (Info)NCA are reward-based methods. Theory comparison: We have added a new section as Appendix G.2 in our paper to compare with PRO theoretically: (cannot update the manuscript during rebuttal, though) The main difference between PRO and the PL+DPO method is that 1. PRO has different reward formulations. It formulates $r_\theta$ as the average log-probability of a sentence $\frac{1}{\\|y\\|}\Sigma\log \pi_\theta(y\|X)$ instead of the log-probability ratio $\log \frac{\pi_\theta(y\|x)}{\mu(y\|x)}$ as is required by DPO. 2. Because there is no $\mu$ in reward models. PRO needs to be additionally regularized by an SFT loss in order to stay close to the pretrained LLM $\mu$. Additional Experiments:** \| Experiment\| MT-bench \| \|----\|---\| \| Mixtral-7B-sft \| 64.5 \| DPO + PL Method\| 74.1 \| \| PRO (SFT) \| 68.9 \| \| InfoNCA \| 76.3 \| Overall we find PRO (PL+SFT) method helps, but slightly underperforms the PL+DPO method. We are not confident about this conclusion because we did not faithfully replicate PRO according to its source code, but only modified our trl implementation of DPO+PL to test PRO methods. We mainly search sft_weight $\in$ [0.01, 0.05, 0.1 0.5], and keep other hyperparameters consistent with train_hh.sh of PRO repo, or the trl/DPO settings. --- Rebuttal 3: Comment: We appreciate the reviewer for the prompt and positive feedback and are glad we can address the reviewer's concerns.	Rebuttal 1: Rebuttal: # Rebuttal Summary We would like to thank all the reviewers for their valuable comments. We are encouraged to see all reviewers recognize the theoretical contribution of our work. Reviewers EyJu, EZsK, and UYN1 highlight the importance of our work in unifying contrastive learning theories (NCE) with existing alignment methods. Reviewer EZsK, WFsu, and xAZC feel that NCA being able to prevent likelihood decline is quite meaningful. Reviewer xAZC and EZsK think our methods being able to handle explicit reward data is a good contribution. Concerns primarily relate to further comparisons with some related methods, and some confusion about the contrastive learning theories in our work. Below, we summarize the main actions taken during the rebuttal: 1. We additionally conduct experiments of Plackett-Luce model, PRO method, Online DPO, and PPO, and compare them with our methods. 2. We theoretically compare our methods with APO, SPIN, SimPO, ODPO, and PRO methods. 3. We clarify some confusion or misunderstanding regarding our methods and experiments. 4. We update our presentations in paper to be more strict and clear. Looking forward to further discussions with the reviewers! --- \| \| \| * # Official Response to Reviewer EyJu (2/2) continue due to the page limit Q5: Lack of two-response alignment: compare InfoNCA, NCA, and DPO on a binary-response preference set. A5: Perhaps we did not fully understand the reviewer's comment. As a matter of fact, the whole section 5.2 aims to compare these algorithms on binary-response preference sets. This includes Table 3, Figure 4 (left), Figure 5, and Figure 6(left). Note that in pairwise-preference settings, InfoNCA becomes exactly the DPO algorithm, so we mainly compare NCA and DPO (InfoNCA). We copy the main results below: UltraFeedback (binary) \| Method \| MT-bench \| Alpaca \| \|---\|---\|--\| \| InfoNCA/DPO \| 73.8 \| 90.7 \| \| NCA \| 73.2 \| 89.9 \| UltraInteract (binary) \|Model\|Average\|Reasoning\|LeetCode\|HumanEval\|GSMPLUS\|MATH\|TheoremQA\|SVAMP\|ASDiv\| \|---\|---\|---\|---\|---\|---\|---\|---\|---\|---\| \|Mixtral-7B-SFT\|24.5\|60.9\|3.3\|28.1\|28.5\|5.8\|7.0\|26.9\|35.8\| \|$+$DPO\|25.5\|61.7\|2.2\|31.7\|12.1\|6.4\|9.8\|34.1\|46.1\| \|$+$NCA\|35.7\|60.8\|3.3\|26.8\|32.3\|11.7\|11.0\|65.3\|74.3*\| \|Mixtral-87B-SFT\|56.3\|75.6\|16.7\|61.0\|57.6\|40.1\|25.9\|85.9\|87.5\| \|$+$DPO\|50.1\|74.9\|17.2\|47.6\|55.8\|35.3\|26.9\|67.3\|75.7\| \|$+$NCA\|57.9\|75.6\|21.1\|62.8\|61.5\|41.6\|26.9\|86.8\|86.9\| * Q6: The real human evaluation results are not reported, which should have made the paper's claims more persuasive. A6: We have reported human evaluation results in the original paper and would like to refer the reviewer to Table 2 (win vs DPO), and Figure 7in the paper. Still, GPT-4 based evaluation results are most indicative to ourselves because datasets are annotated by GPT-4. After all, you want your training rewards and test rewards to be aligned to make sure the algorithm itself is valid given that our work is somehow more theoretical rather than product-oriented. --- \| \| \| * # Official Response to Reviewer EZsK (2/2) continue due to the page limit Q5: suggest comparing it with PRO (https://arxiv.org/pdf/2306.17492). A5: PRO is a quite related work of ours because it can also handle response data of arbitrary number. It is also highly related to the PL method as we have discussed in A1. Still, PRO is essentially a ranking/preference-based method, while (Info)NCA are reward-based methods. Theories comparison: We have added a new section as Appendix G.2 in our paper to compare with PRO theoretically: (cannot update the manuscript during rebuttal, though) The main difference between PRO and the PL+DPO method is that 1. PRO has different reward formulations. It formulates $r_\theta$ as the average log-probability of a sentence $\frac{1}{\\|y\\|}\Sigma\log \pi_\theta(y\|X)$ instead of the log-probability ratio $\log \frac{\pi_\theta(y\|x)}{\mu(y\|x)}$ as is required by DPO. 2. Because there is no $\mu$ in reward models. PRO needs to be additionally regularized by an SFT loss in order to stay close to the pretrained LLM $\mu$. Additional Experiments: \| Experiment\| MT-bench \| \|----\|---\| \| Mixtral-7B-sft \| 64.5 \| DPO + PL Method\| 74.1 \| \| PRO (SFT) \| 68.9 \| \| InfoNCA \| 76.3 \| Overall we find PRO (PL+SFT) method helps, but slightly underperforms the PL+DPO method. We are not confident about this conclusion because we did not faithfully replicate PRO according to its source code, but only modified our trl implementation of DPO+PL to test PRO methods. We mainly search sft_weight $\in$ [0.01, 0.05, 0.1 0.5], and keep other hyperparameters consistent with train_hh.sh of PRO repo, or the trl/DPO settings.	NeurIPS_2024_submissions_huggingface	2,024	Summary: The paper addresses a weakness of DPO: it can not deal with preference data whose number of responses is larger than 2. To extend DPO, the author proposes Noise Contrastive Estimation (NCE)-based Alignment algorithms InfoNCA. The author has shown that DPO is one of the special cases of InfoNCA. To further fix the Decreased Response Likelihood issue, the author also proposes NCA with a similar derivation. Experiments demonstrate that NCA and InfoNCA outperform baselines with reward datasets for training, with NCA showing significant performance in complex reasoning tasks like math and coding. The paper offers the community a general framework for LLM alignment from a novel perspective. Strengths: 1. The paper considers the LLM alignment task from a very novel perspective of Noise Contrastive Estimation. The proposed InfoNCA and NCA methods are not only general in form (DPO can be regarded as one of the special cases), but also elegant in math (the connection of LLM alignment and InfoNCE is quite interesting). The paper brings a brand-new view to the study of LLM alignment, which can be insightful to the research community. 2. The motivation of the paper is clear, which focuses on the limitation of DPO when training with multi-response preference data. This improving direction is quite valuable for both the research and industry domains. 3. The experimental results support the effectiveness of InfoNCA and NCA, which outperform baseline methods such as DPO, IPO, and KTO. 4. The paper is clearly written, well organized, and easy to follow. Weaknesses: 1. Fundamental Assumption: My major concern is about the fundamental assumption when deriving the InfoNCA and NCA methods. The author assumes that one of the scored responses is sampled from the optimal policy, which is practically impossible because most of the preference data are sampled from non-optimal LLM policy. In some extreme situations, all the generated responses can be harmful, while our ideal optimal policy should output harmless responses, leading to a contradiction with the author's essential assumption. A possible solution to this weakness might be mixing the human written (golden) response into the preference data, then applying NCE to the prompt and the golden response, combining InfoNCA with some prior work such as APO [1] and SPIN [2]. 2. Lack of Human Evaluation: Although the author has conducted GPT-4 evaluation in the experiments, the real human evaluation results are not reported, which should have made the paper's claims more persuasive. 3. Lack an experiments of two-response alignment: Although the paper demonstrates better performance using multi-response preference data, it is interesting to compare InfoNCA, NCA, and DPO on a binary-response preference set. 4. Lack of baseline comparison: Although DPO cannot deal with multi-response preference, one can first train an RM with the multi-response preference, and next sample two responses with scores from the learned RM. Then DPO can be conducted on the RM-scored pairwise preference data. This can be a simple but important baseline that the author should take into consideration. References: [1] Adversarial Preference Optimization: Enhancing Your Alignment via RM-LLM Game, ACL 2024 [2] Self-Play Fine-Tuning Converts Weak Language Models to Strong Language Models, ICML 2024 Technical Quality: 3 Clarity: 3 Questions for Authors: See Weaknesses. Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The author has NOT addressed the limitations of the proposed method. One of the most important limitations can be that if all the scored responses are harmful, the proposed methods can never achieve the ideal alignment optimum, which could even enhance the harmful model outputs. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: # Official Response to Reviewer EyJu (1/2) *Q1: (Major Concern) Fundamental Assumption is we can sample from the optimal policy $\pi^\$, which is practically impossible because we can only access non-optimal LLM policy $\mu$. A1: We'd like to clarify that the availability of** $\pi^\$ is NOT a concern of our proposed (Info)NCA algorithm, both theoretically and practically. We are glad the reviewer is interested in this question, though, because it is a core contribution/difficulty in our algorithm's derivation.* Take InfoNCA loss for instance (Eq.6, Line 110 in the paper): $L_\theta^\text{InfoNCA} = - E_{p(x) \prod \mu(y_i\|x)} \sum_{i=1}^K [\frac{e^{r(x,y_i)/\alpha}}{Z(x)} \log \frac{e^{r_\theta(x,y_i)}}{\sum_{j=1}^K e^{r_\theta(x,y_j)}}]$ Here $\mu$ is the pretrained LLM distribution. We can see the optimal policy $\pi^$ does not show up in the loss function, which means $\pi^$ is NOT required. From $E_{p(x) \prod \mu(y_i\|x)}$ we can also see that, ideally all responses should be sampled from suboptimal $\mu$ instead of $\pi^$. Why $\pi^\$ does not show up in the loss function?** After all $\pi^\$ is required/used for (Info)NCA algorithm derivation (Figure 3, Line 98 and 146, etc.): Recall that $\pi^\:= \mu(y\|x)\frac{e^{r(x,y)/\alpha}}{Z(x)}$ is actually defined by the pretrained LLM $\mu$ and a reward function $r$. Thus *$\pi^\$ can actually replaced by $r$ and $\mu$ in practice. This is exactly why we need dataset "rewards"*. Specifically, this is accomplished by the "rejection sampling" technique. Image we can first sample $K >> 1$ responses $y_{1:K}$ from $\mu(\cdot\|x)$, score each response with $r_{1:K}$, then we can resample a single response $y$ from $y_{1:K}$ with the probabilty ratio $p_k \propto e^{r_k/\alpha}$. In this way, the distribution of $p(y) = \mu(y\|x)\frac{e^{r(x,y)/\alpha}}{Z(x)}$ can be proved if K is infinitely large. This idea can be applied to elimitate the requirement of $\pi^\$ by importance sampling in algorithm derivation: $E_{\pi^(y\|x)} f(x,y) = E_{\mu(y\|x)} \frac{e^{r(x,y)/\alpha}}{Z(x)}f(x,y)$ so that $L_\theta^\text{InfoNCA} = - E_{p(x) \prod \pi^\(y_i\|x)} \sum_{i=1}^K \left[\log \frac{e^{r_\theta(x,y_i)}}{\sum_{j=1}^K e^{r_\theta(x,y_j)}}\right] $ $= - E_{p(x) \prod \mu(y_i\|x)} \sum_{i=1}^K \left[\frac{e^{r(x,y_i)/\alpha}}{Z(x)} \log \frac{e^{r_\theta(x,y_i)}}{\sum_{j=1}^K e^{r_\theta(x,y_j)}}\right]$ (proof Line 463 in Appendix) * Q2: In some extreme situations, all the generated responses can be harmful, while our ideal optimal policy should output harmless responses. (Contradict with Fundamental Assumption). If all the scored responses are harmful, the proposed methods can never achieve the ideal alignment optimum ... A2: We think the above problem arises fundamentally because of the problem definition of alignment tasks instead of our proposed (Info)NCA algorithm.** Recall that most alignment problems define the desired policy distribution as: $\pi^\propto \mu(y\|x)e^{r(x,y)/\alpha}$. By definition,* we not only want $\pi^\$ to maximize reward $r(x,y)$, but we want $\pi^\$ to stay close to pretrained policy $\mu$** as well. If all responses are harmful, then $\mu$ must be a very low-quality distributional prior for $\pi^\$ (All responses should be sampled from $\mu$ as we have explained in A1). Consequently, it is natural that $\pi^$ may struggle to get high performance because it needs to stay close to a low-quality LLM $\mu$. * Q3: Mixing the human written (golden) response into the preference data, then applying NCE to the prompt and the golden response( combining InfoNCA with some prior work such as APO [1] and SPIN [2].) A3: We agree with the reviewer. Mixing golden responses into datasets would increase data quality because these responses do not come from the suboptimal policy $\mu$. Instead, they are from a presumably superior policy (human). This strategy is illuminating and would surely be very helpful if we can somehow access high-quality data beyond just a suboptimal policy $\mu$. The basic idea of APO/SPIN is to perform some GAN-like training and contrast STF/golden data with model-generated responses. Their contrastive training style can be readily combined with (Info)NCA training methods. This is a very promising research topic, though we suppose it is beyond the discussion scope of our current article because we focus on the preference/reward training paradigm. We believe this does not hurt or even support the core contribution of our method. * Q4: Comparison with another baseline: first train an RM with the multi-response preference, and next sample two responses with scores from the learned RM. Then DPO can be conducted on the RM-scored pairwise preference data. A4: We conduct additional experiments (online DPO setting and PPO settings) and present the results below. RM is pretrained on the UltraFeedback datasets, named UltraRM. Overall, results that are trained by applying RM underperforms directly finetuned from dataset rewards. We believe this is mainly because of the learned RM is not robust enough compared with the GPT-4 annotator. \| Name \| Annotation Type \| MT-bench \| AlpacaEval \| \|----------------------------\|-----------------\|----------\|------------\| \| Mixtral-7B-sft \| SFT Data \| 6.45 \| 85.20 \| \| +KTO \| Preference \| 7.12 \| 91.93 \| \| +IPO \| Preference \| 7.45 \| 90.62 \| \| +DPO(online) \| RM Preference \| 7.14 \| 88.39 \| \| +PPO(online) \| RM Reward \| 6.64 \| 84.20 \| \| +InfoNCA \| Reward \| 7.63 \| 92.35 \| \| +NCA \| Reward \| 7.52 \| 90.31 \| * ## Reminder QA5-QA6: We refer the reviewer to the global rebuttal posted at the top of the webpage for the rest (EyJu part 2/2) of our response. This is due to the severe page limit. --- Rebuttal 2: Title: Additional Response Comment: Dear reviewer, We copy the second part of our rebuttal response here to ease reading. In our responses, we have conducted additional experiments and compared with more baselines based on your suggestions. We hope we can address your concerns and are glad to answer any further questions you might have. Thank you again for your valuable feedback! # Official Response to Reviewer EyJu (2/2) Q5: Lack of two-response alignment: compare InfoNCA, NCA, and DPO on a binary-response preference set. A5: Perhaps we did not fully understand the reviewer's comment. As a matter of fact, the whole section 5.2 aims to compare these algorithms on binary-response preference sets. This includes Table 3, Figure 4 (left), Figure 5, and Figure 6(left). Note that in pairwise-preference settings, InfoNCA becomes exactly the DPO algorithm, so we mainly compare NCA and DPO (InfoNCA). We copy the main results below: UltraFeedback (binary) \| Method \| MT-bench \| Alpaca \| \|---\|---\|--\| \| InfoNCA/DPO \| 73.8 \| 90.7 \| \| NCA \| 73.2 \| 89.9 \| UltraInteract (binary) \|Model\|Average\|Reasoning\|LeetCode\|HumanEval\|GSMPLUS\|MATH\|TheoremQA\|SVAMP\|ASDiv\| \|---\|---\|---\|---\|---\|---\|---\|---\|---\|---\| \|Mixtral-7B-SFT\|24.5\|60.9\|3.3\|28.1\|28.5\|5.8\|7.0\|26.9\|35.8\| \|$+$DPO\|25.5\|61.7\|2.2\|31.7\|12.1\|6.4\|9.8\|34.1\|46.1\| \|$+$NCA\|35.7\|60.8\|3.3\|26.8\|32.3\|11.7\|11.0\|65.3\|74.3*\| \|Mixtral-87B-SFT\|56.3\|75.6\|16.7\|61.0\|57.6\|40.1\|25.9\|85.9\|87.5\| \|$+$DPO\|50.1\|74.9\|17.2\|47.6\|55.8\|35.3\|26.9\|67.3\|75.7\| \|$+$NCA\|57.9\|75.6\|21.1\|62.8\|61.5\|41.6\|26.9\|86.8\|86.9\| Q6: The real human evaluation results are not reported, which should have made the paper's claims more persuasive. A6: We have actually reported human evaluation results in the original paper and would like to refer the reviewer to Table 2 (win vs DPO), and Figure 7in the paper. Still, GPT-4 based evaluation results are most indicative to ourselves because datasets are annotated by GPT-4. After all, you want your training rewards and test rewards to be aligned to make sure the algorithm itself is valid given that our work is somehow more theoretical rather than product-oriented. --- Rebuttal 3: Title: Looking forward to your feedback Comment: Dear reviewer, Thank you for your valuable comments regarding our submission. We have posted our responses and hope to address your concerns about the fundamental assumption of our method (availability of the optimal policy), as well as the comparison with several baselines such as APO and SPIN. Could you please take a look at our responses and give us some further feedback so that we can continually improve our work? Thank you so much in advance! Best regards, The Authors --- Rebuttal Comment 3.1: Comment: Thank you for your elaborate response. Since the author has expanded with more comprehensive and detailed experiments, I have decided to raise my score. --- Reply to Comment 3.1.1: Comment: Thank you for your feedback. We are glad that our responses help.	null	null	null	null	null	null
QBB: Quantization with Binary Bases for LLMs	Accept (poster)	Summary: This paper proposes a PTQ technique which decompose the model weitghs into a set of binary matrices. An interactive binarization process and a progressive model distillation procedure are conducted to reduce the quantization error. The paper claims to set a new SOTA of a summation-only based approach. Strengths: 1. This paper works on the problem of quantizing large language model, which is an important research question with practical application and positive social impact. 2. The paper is overall well-written, the method is clearly derived and well-illustrated with figures. The motivation and the methods are easy to follow. 3. Good performance are reported both in terms of preplexity and zero-shot performance on multiple models. Weaknesses: 1. From the novelty prespective, the proposed binary decomposition method is largely similar to previous nonlinear quantization methods line LQ-Net (https://arxiv.org/pdf/1807.10029 ECCV'18). The similarity and difference between the proposed method and LQ-Net should be discussed and the performance should be compared. 2. The paper claims the achieved model can be efficient by removing all the multiplications. However, I don't believe this can be achieved from the formulation of quantized weights in Equ. (1). Although no multiplication is needed to multiply the binary part B with the activation, the multiplication of scaling factor alpha to the activation is still needed, and can be costly when N is large. In fact, the proposed quantization scheme is effectively an N-bit quantization with non-uniform quantization bins, which theortically shouldn't be more efficient than an N-bit linear quantization with integer weights. 3. Deriving from my second point, the efficiency discussion in Sec 4.6 is not concrete. An estimation on exactly how memory and computation is saved comparing to a regular linear W4A16 quantized model should be provided. 4. The comparison is mainly done against PTQ methods with linear weight quantization, yet the proposed method performs non-linear quantization of the weight and requires several epochs of finetuning. This will result in both higher training cost and inference cost comparing to previous methods, making the comparison results unfair. Technical Quality: 2 Clarity: 3 Questions for Authors: 1. Please revise the discussion in Sec 4.6 to provide detailed memory and computation savings comparing to regular linear W4A16 quantized models. 2. Please explain in detail about the quantization configuration of the reported W2.3 quantized model Confidence: 4 Soundness: 2 Presentation: 3 Contribution: 2 Limitations: The limitation of the work is adequately addressed. Flag For Ethics Review: ['No ethics review needed.'] Rating: 3 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for their time and comments. We hope to have addressed their remaining concerns below. Q1. _From the novelty prespective, the proposed binary decomposition method is largely similar to previous nonlinear quantization methods line LQ-Net ([https://arxiv.org/pdf/1807.10029](https://arxiv.org/pdf/1807.10029) ECCV'18). The similarities and differences between the proposed method and LQ-Net should be discussed, and the performance should be compared._ A1. We disagree, as the similarities are largely superficial. While LQ-Net uses multiple binary bases to emulate n-bit quantization, unlike our approach: they are fully trained in a supervised manner on the task at hand, hence their solution is neither data-free nor is applicable as post-training quantization step; they follow a different formulation, in which the binary basis is found by looking up the quantization interval while the learnable floating basis by solving a linear regression problem. Moreover, no form of distillation, such as the strategy proposed in this work is used. In contrast, our process follows a two-step approach, in which we first construct a series of binary bases that closely approximate the original weights, without requiring any activations, on a layer-by-layer basis, directly using gradient descent. We then calibrate the scaling factors using a data-free approach and distillation strategy. In terms of a numerical comparison, the current LQ-Net formulation would require retraining the model from scratch/finetuning it on specific datasets. Thank you for pointing out this work. We will include an ample discussion making the difference clear. Q2. _The paper claims the achieved model can be efficient by removing all the multiplications. However, I don't believe this can be achieved from the formulation of quantized weights in Equ. (1). Although no multiplication is needed to multiply the binary part B with the activation, the multiplication of scaling factor alpha to the activation is still needed and can be costly when N is large. In fact, the proposed quantization scheme is effectively an N-bit quantization with non-uniform quantization bins, which theoretically shouldn't be more efficient than an N-bit linear quantization with integer weights._ A2. The reviewer is correct that we don't remove _all_ multiplications, however, we don't claim to remove all multiplications, but _nearly_ all multiplications. The remaining multiplications are not too different from most quantization approaches which will also scale the output using some scalars. Do note however that the 4b-16bit multiplications, occurring for the matmul itself, are removed, and as noted in Sec 4.6, depending on the hardware implementation they can be significantly more energy efficient, requiring fewer physical gates. Q3. _Deriving from my second point, the efficiency discussion in Sec 4.6 is not concrete. An estimation of exactly how memory and computation are saved compared to a regular linear W4A16 quantized model should be provided._ A3. Most of the savings are expected to be from the significant reduction in multiplications, converting it to a nearly summation-only approach. This could primarily result in significant energy savings (as pointed out 4-8x). For this aspect we kindly point out to the works cited in Sec. 4.6 [24; 34; 54; 55; 61;] which have a more ample and practical analysis on this, as they specialise on summation-based strategies. In terms of memory savings, on a memory-pressured system, an intuitive direct saving could be by loading one binary basis at a time into memory, overlapping the computation of the first computation with the loading of the data of the second, thus diminishing the peak memory used. To obtain exact measurements, an implementation is needed, which as we mentioned in the limitation section, wasn't part of the present work. Q4. _The comparison is mainly done against PTQ methods with linear weight quantization, yet the proposed method performs non-linear quantization of the weight and requires several epochs of finetuning. This will result in both higher training cost and inference cost comparing to previous methods, making the comparison results unfair._ A4. There is no additional cost at runtime as the calibration process is performed prior to test time deployment. During calibration, indeed, the process, altogether, depending on the model, requires 4-12hours. As the process is expected to be run once, can be performed on commodity hardware, and requires no data, we consider this time to not be a major concern in practice. Q5. _Please explain in detail about the quantization configuration of the reported W2.3 quantized model_ A5. The quantization configuration is based on N=4 strategy under the assumption of left-most significant placement (detailed in Sec. 4.6.) We also observe some patterns in terms of quantization errors (see Fig. 6) which should make it possible to adjust the levels further depending on this. --- Rebuttal Comment 1.1: Title: Further discussion on efficiency Comment: I would like to thank the author for the rebuttal. I'm satisfied with the first point. However, I'm still confused on how the proposed method is able to "remove nearly all multiplication" comparing to traditional W4A16 scheme. From my understanding, the linear quantized weights, like those in GPTQ and AWQ, can also be represented as a summation of binary matrices, specifically $$W = \sum_{n=0}^3 2^n B_n,$$ with $B_n$ each being a binary matrix. This is a special case of your quantized weight formulation in Eq. (1), with the scaling factor alpha being exponenets of 2. From my understanding, you do not constrain the value of alpha in your formulation. Therefore, I do not see exactly why you can bring additional efficiency comparing to linear weight quantization. From my understanding, the proposed method is more comparable with non-linear weight quantization methods like SqueezeLLM [1], which benefits from memory saving, but not computational efficiency. This makes the reported comparisons with previous linear quantization methods like GPTQ and AWQ unfair. [1] Kim, Sehoon, et al. "Squeezellm: Dense-and-sparse quantization." arXiv preprint arXiv:2306.07629 (2023). --- Reply to Comment 1.1.1: Title: RE: Further discussion on efficiency Comment: We thank the reviewer for considering our rebuttal, and we are glad that the reviewer is satisfied with the first point. We hope to have addressed/clarified your remaining concern below. The reviewer is correct that the weights for GPTQ/AWQ can be expressed as a summation of binary matrices too, and we also agree with the parallel drawn with [1] Squeezellm; It is indeed fair to state that under such representation, both approaches will be subject to similar reduction in multiplication (i.e. the remaining multiplications are with the activations, post matrix-multiplication). We will revise the text to make this aspect clear. Do please note, that we don't claim to be more efficient than AWQ/GPTQ, but simply, that depending on the HW, a binary matrices views can be a more efficient framework to operate in. We thank you for this, we will make a parallel to [1] in the paper. Regarding the comparisons, we do believe that the numerical comparisons are fair, as our main comparison is with W4, in which case GPTQ/AWQ is not put at a disadvantage.	Summary: This paper introduces Quantization with Binary Bases (QBB), a novel method designed to reduce the computational complexity of large language models (LLMs) by replacing most multiplications with summations. QBB decomposes original weights into a set of binary (1-bit) matrices through an iterative process, optimizing them to minimize quantization error. Additionally, the quantized model is refined via Knowledge Distillation. Tested across multiple LLM families, QBB demonstrates superior performance compared to existing methods. Strengths: 1. This method's utilization of binary matrices and scaling vectors to approximate original weights marks a significant advancement, effectively reducing computational complexity. 2. Combining post-training quantization with knowledge distillation is a commendable approach. The performance has notably improved through the application of Knowledge Distillation after quantization. 3. The paper offers extensive experimental results that showcase the effectiveness of QBB across diverse LLMs and datasets. Weaknesses: 1. I believe comparing it with non-uniform quantization methods, such as QuIP#, would enhance this paper, as it does not utilize uniform quantization. 2. Regarding progressive weights quantization, I'm unclear whether starting with a quantized model means that $W$ in Equation 4 represents quantized weights rather than full-precision weights. If so, this approach may not be optimal for the quantization step. 3. For Training details, does each layer need 15000 iterations? Can you provide the details of runtime and overhead? 4. How were the values of $s_1$ and $s_2$ specified in Equation 7? Technical Quality: 3 Clarity: 3 Questions for Authors: Please refer to Weakness. Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: Please refer to Weakness. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for their time and comments. We hope to have addressed their remaining concerns below. Q1. _I believe comparing it with non-uniform quantization methods, such as QuIP#, would enhance this paper, as it does not utilize uniform quantization._ A1. Thank you for your suggestion. We already report results for QuIP# in Table 3. We will expand this to include more configurations, with different levels of quantization, making this aspect also more clear. Q2. _Regarding progressive weights quantization, I'm unclear whether starting with a quantized model means that_ A2. By this, we mean that instead of directly binarizing the full/half precision weights, we start the process from a model quantized using an off-the-shelf 4-bit quantization method. This reduces the initial informational gap and is well aligned with the idea of gradually dropping the number of bits used in literature. Please see also Table 4. Q3. _in Equation 4 represents quantized weights rather than full-precision weights. If so, this approach may not be optimal for the quantization step._ A3. In eq. 4, W represents the to-be-approximates weights, they can be full precision or quantized to a higher number of bits. B_i represents the constructed binary matrices. As num_bits(W) is always higher than num_bits(B) this is generally not a concern. Moreover, this steps only corrects the remaining error that is incurred after the first step. Q4. _For Training details, does each layer need 15000 iterations? Can you provide the details of runtime and overhead?_ A4. Yes, this is performed on a layer-by-layer basis, we could likely reduce this significantly using an early stopping scheduler, but for simplicity, we opted for the same number of iterations in all cases. In terms of overhead, this takes a few hours (4-12) on a A100, depending on the model size. However, as the process is only run once, there is no additional overhead at test/runtime. Q5. _How were the values of and specified in Equation 7?_ They were selected empirically using one of the model variants (i.e. the smallest), and then used for the rest of the models too.	Summary: This paper proposed QBB by discomposing the original weights into 4 binary matrics and scaling factor. To compensate the error, two techniques are further proposed: 1. use gradient descent to find the optimal set of binary matrices and scaling vectors 2. use knowledge distillation to optimize the scaling vector only. Strengths: - This paper present a thorough analysis, including detailed ablation studies and analysis of different components. - This paper has clear presentation: Well-organized, with effective use of figures and tables to support the content. Weaknesses: - The technique of decomposing the weights into several binary matrics is similar to BiLLM [1]. In BiLLM, they proposed residual approximation method, which is just the same to QBB when N=2. And this paper was published on arxiv on Feb. 2024. - In the related work, QBB listed the PB-LLM, which is a mixed-precision framework that achieved around 2-bit quantization. However, the experiments in Table3 did not involve it. Additionally, BitDistiller [2] also conducted experiment on 2-bit weight quantization. - This paper did not provide the code in supplementary material. - In QBB, two additional adjustments were conducted to minimize the error, which involves additional training cost. However, I haven't found any experiments w.r.t. training cost. Correct me if I am wrong. - From my understanding, the computational cost of QBB is between PTQ and QAT. You should compare with PTQ and QAT method separately. For QAT, LLM-QAT and Bitdistiller should be involved. - From line 154 to 157, you proposed progressive weights quantization technique by first quantizing weights to 4-bit and then applying the QBB. There is no additional process between these two procedure. From my point, I think it is useless and uneffective. There is no experiment that can prove that your progressive weights quantization is better than directly quantizing. - From Figure 6, when we set the N to 5, it is more stable than 4. Why not just use 5? - In section 3.2, "Data-free" is not properly used. Because I find that you utilized the generated data by LLM. It is not completely data-free. Please refer to [3]. - Teacher-student swaps can easily cause training collapses, especially for floating-point & low-bit models. I am more curious about any strategies employed to alleviate this problem. [1] https://arxiv.org/pdf/2402.04291 [2] https://arxiv.org/abs/2402.10631 [3] https://arxiv.org/abs/1906.04721 Technical Quality: 3 Clarity: 3 Questions for Authors: See weakness. Confidence: 5 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: This paper missed some important reference. The experiments part should be put more efforts. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for their time and comments. We hope to have addressed their remaining concerns below. Q1. _On: The technique of decomposing the weights into several binary matrics is similar to BiLLM [1], published on arxiv on Feb. 2024._ A1. Thank you for pointing out [1], we weren't aware of it. Kindly note that [1] was not published in a peer-reviewed venue at the time of the NeurIPS deadline. Nevertheless, we will cite and discuss it in our updated manuscript. Regarding, the differences with [1]: [1] focuses on applying different quantization strategies for the salient and non-salient weights, identified using a structural search based on the Hessian Matrix. The salient columns then use a secondary residual binarization (i.e. to better preserve the information in the salient channels). The remaining non-uniformly distributed weights are split intro two groups by searching the optimal split. The work aims generally to exploit the sparsity of information present in the weights, allocating the bits accordingly and focusing on extreme quantization levels. In contrast, our approach directly approximates the weights using a sum of binary matrices, that are learned on a layer-by-layer basis, without using any calibration data (as opposed to [1]), by gradient descent). Each new binary weight is trained in a cascaded manner. Our approach generalizes to different numbers of binary matrices, doesn't make use of any splitting algorithm, nor aims to identify/tie the binarization process to the weights' saliency. Thereafter, unlike [1] we follow a data-free calibration of the scaling factors using self-generated sequence that starts from randomly sampled tokens. Finally, the calibration process is placed within a newly adapted distillation strategy. We believe that these are significant methodological differences that distant our work from [1] (an arxiv paper). Q2. _On comparison with PB-LLM & BitDistiller[2] that achieve 2-bit W quantization._ A2. As we didn't focus on 2-bits or less, we haven't included such methods in the Tables. However, following your suggestion, we will include [2] in the result tables (i.e. 5.97[2] vs 5.21 (this work) on a LLamA-7B-2), noting that the results won't be directly comparable. Q3. _This paper did not provide the code in supplementary material._ A3. Due to internal processes and timelines, unfortunately this wasn't possible to do at the time of submission. Q4. _In QBB, two additional adjustments were conducted to minimize the error, which involves additional training cost. However, I haven't found any experiments w.r.t. training cost._ A4. Depending on the model choice, the training take 4-12 hours on A100 GPU. This can likely be reduced by early stopping, as in many cases the process converges long before the end of the scheduler. However, for simplicity, we kept the same value. Q5. _The computational cost of QBB is between PTQ and QAT. You should compare with PTQ and QAT: LLM-QAT and Bitdistiller should be involved._ A5. We haven't included a comparison with the two works mentioned as our work only performs a calibration process using a data-free approach, unlike LLM-QAT which performs a full model finetuning. E.g. LLM-QAT requires 8 A100 GPUs at a batch size = 1 per GPU to perform full model finetuning. In comparison, our approach can be run on a single GPU. Nevertheless, we see the potential usefulness of such comparisons, and following your request, we will include them in the updated manuscript. Q6. _From L154-157, you proposed progressive weights quantization technique by first quantizing weights to 4-bit and then applying the QBB. There is no additional process between this two procedure. From my point, I think it is useless and uneffective. On no experiment to show this._ A6. We ablate the impact of different initialization strategies in Table 4, where we showcase both the importance of starting from 4-bit weights and the method used to construct the 4-bit weights. The results show this step to be necessary. The intuition behind this is that the gap between the sum(binary weights) and fp16 ones are larger, making the optimisation process more challenging. Q7. _From Figure 6, when we set the N to 5, it is more stable than 4. Why not just use 5?_ A7. We didn't as the additional cost didn't justify to us the additional costs (see Fig. 6). Q8. _In section 3.2, "Data-free" is not properly used. Because I find that you utilized the generated data by LLM. It is not completely data-free. Please refer to [3]._ A8. We kindly disagree: the data-free assumption is not violated. The sequences used for training are produced by the model itself, starting from a random token. There is no real (i.e. collected) data used in the process, nor techniques based on manual intervention (e.g. prompting). As the starting token is random, this process is more akin to self-distillation on random inputs. We note that such discriminative models, such as those used in [3] (i.e. MobileNet archs) are not comparable to generative models such as LLMs, as they are from different families of models, and the former are unable to produce sequences of data given a random sample. Hence, this is not a violation of the setting, but simply a difference between the capability of vision models vs an LLM when exposed to randomly constructed points. Q9. _Teacher-student swaps can easily cause training collapses, especially for floating-point & low-bit models. I am more curious about any strategies employed to alleviate this problem._ A9. In our case, the first stage aims to independently (i.e. on a layer-by-layer basis) approximate the weights of each layer, using a set of binary weights. Post approximation, these layers are expected to already behave similarly with the target weights. Thanks to this, the discrepancies between such layers is small, making the swapping stable in general.	Summary: This research brings the sum of binary bases to the post-training quantization of the large language models. The authors propose a three-step algorithm. In step1: taking the sign of the full-precision weights and use the norm of the weights as the scalings, step2: adjusting the binary bases using gradient descent, step 3: adjusting scales using teacher-student (knowledge distillation). Step 1 was initiated in computer vision [49], and step 2 introduced in [36]. Set of binary bases for inference was suggested in [36] and later in LQ-Net. https://arxiv.org/pdf/1807.10029 The full binary base for efficient inference is not novel, authors tried to adapt [36] for post-training of large language models, which necessitates step 3 for a better performance. The paper needs to clarify its connection with [36] and LQNet. I was confused in the middle of reading the paper about the main contribution of the paper. My final judgment is "this paper is an adaptation of existing ideas," but I congratulate the authors on putting considerable effort into bringing it to post-training and large language model context. Strengths: The paper proposes step 3 to make the performance close to the state-of-the-art post-training such as omi-quant, GPTQ, AWQ. Weaknesses: I doubt that Table 3 fairly shows the strength and the weakness of the method. First explain what W4A16g128 mean. I suppose it means weight quantized to 4 bit fixed point, activation to floating point 16 (half precision or brain float?) or maybe fixed point, g128 referees to the grouping size of the weight quantization for the fixed point representation. - SpQR baseline is missing in Table 3. https://arxiv.org/abs/2306.03078 Technical Quality: 3 Clarity: 3 Questions for Authors: - Did you try your method on the fixed-point activations? if yes please specify, if not please make it clear in the paper. - Why competing methods are on 4 and 3 bits but yours is 2.3? Is it a mistake or 2.3 is the average bit to be 2<2.3<3. I think it is fair to report your result on W4 and W3 just like the other baselines and then show it on a lower lower average bit. Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: The paper focuses on LLamA models. I would prefer a similar comparison for other mainstream language models as well. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for their time and comments. We hope to have addressed their remaining concerns below. Q1. _"On doubts that Table 3 fairly shows the strength&weakness of the method. First explain what W4A16g128 mean._ A1. We believe that the comparison is fair, as we align our setting to that of prior methods, e.g. AWQ. Regarding the meaning of W4A16g128, you are correct. The example denotes a quantization scheme that makes use of 4-bit fixed point quantization for the weights, with a grouping size of 128 and half-precision (i.e. fp16) activations. We will detail this in the updated manuscript. Q2. _SpQR baseline is missing in Table 3._ A2. As suggested, we will include the baseline in Table 3, thank you! We note that the conclusions don't change (i.e.: LLaMA-7B @ pp on Wiki2, 5.69 (Ours) vs 5.87 (SPQR)); Q3. _Did you try your method on the fixed-point activations? if yes please specify, if not please make it clear in the paper._ A3. We performed an ablation in Table 5. Our approach only affects the weights, hence it's largely agnostic to the quantization strategy used for the activations. We will make this clearer. Q4. _On why no results with W4 and W3 just like the other baselines and then show it on a lower average bit._ A4. Performance doesn't improve significantly beyond this to justify the costs, this is a consequence of initializing our model from W4 quantized weights. Q5. The paper focuses on LLamA models. I would prefer a similar comparison for other mainstream language models as well. A5. We mainly focused on LLamA (v1 and v2) models as this facilitated the comparison with prior work. We also already include results for the Phi-2 model (Table 1), and in addition, we tested it on Mistral-7B where we saw similar results (i.e. +0.1 perplexity improvement compared with the direct GPTQ baseline)	null	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Style Adaptation and Uncertainty Estimation for Multi-Source Blended-Target Domain Adaptation	Accept (poster)	Summary: This paper introduces a novel challenge in domain adaptation: the problem of Multi-Source Blended Target Domain Adaptation (MBDA). In MBDA, target domain distributions are blended, necessitating a model that can leverage features from multiple source domains to perform effectively on the blended-target domain. To address this problem, a Style Adaptation and Uncertainty Estimation (SAUE) approach is proposed. SAUE utilizes a similarity factor to select style information from the blended-target domain, creating a better representation space. Additionally, it enhances model robustness by employing a Dirichlet-based uncertainty estimation model to handle the diverse distributions introduced by multiple source domains. The effectiveness of the proposed method is validated through extensive image classification experiments. A theoretical analysis of SAUE underscores its potential in solving the MBDA problem. Strengths: 1. The proposed MBDA problem is highly relevant for real-world applications. Unlike existing DA problems, MBDA incorporates confusing domain scenarios that mimic real-world situations where the source domain distributions are various, and the target domain distributions are blended. This assumption adds an additional challenge for DA, as the model needs to align domains without domain labels of the target domain. 2. The proposed method SAUE is innovative. The inclusion of style adaptation to enhance the source domain features is intriguing, where the similarity-based weighted matrix is cleverly used to select more useful target style information for constructing a better representation space. 3. The uncertainty estimation component effectively addresses the distribution discrepancy issue introduced by multi-source domains. In addition, the authors construct an adversarial learning strategy that aligns domains without the requirement of domain labels. 4. The paper is well-written with the theoretical analysis clearly articulated and thoroughly explained. Weaknesses: 1. The paper mentions various terms related to domain adaptation in Sections 1 and 2, such as UDA, SSDA, MSDA, MMDA, MTDA, and BTDA. What are the main differences and relationships among these terms? The authors are encouraged to provide a table summarizing the main characteristics to distinguish these terms. 2. In the ablation study, the comparison primarily focuses on highlighting the improvements of each proposed module. It is suggested that the authors compare different feature augmentation methods to further emphasize the superiority of the proposed Style Adaptation module. 3. A minor point of interest is how the proposed method performs on other backbones, such as the Vision Transformer. Technical Quality: 3 Clarity: 4 Questions for Authors: Please refer to the Weaknesses part. Confidence: 5 Soundness: 3 Presentation: 4 Contribution: 3 Limitations: The authors have adequately claimed their limitations in Appendix B. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thanks for your positive affirmation and constructive comments. Below are our responses to the weaknesses and questions. >W1: The paper mentions various terms related to domain adaptation in Sections 1 and 2, such as UDA, SSDA, MSDA, MMDA, MTDA, and BTDA. What are the main differences and relationships among these terms? The authors are encouraged to provide a table summarizing the main characteristics to distinguish these terms. A1: We have summarized the differences and relationship among the mentioned domain adaptation problems in the PDF file (Table R5). >W2: In the ablation study, the comparison primarily focuses on highlighting the improvements of each proposed module. It is suggested that the authors compare different feature augmentation methods to further emphasize the superiority of the proposed Style Adaptation module. A2: We have introduced random augmentation (RA), MixStyle [a], and pAdaIN [b] techniques to further emphasize the superiority of the proposed SA module, please refer to the PDF file (Table R3 (a)). >W3: A minor point of interest is how the proposed method performs on other backbones, such as the Vision Transformer. A3: We have added experiments on the Office-Home dataset and utilized a new backbone, ViT. The results are illustrated on Tab. R6, which demonstrate that our method also effective when using the ViT backbone. We will add this comparison to the final version to further show the quality of our paper. Refs: [a] Domain generalization with mixstyle. ICLR 2021. [b] Permuted adain: Reducing the bias towards global statistics in image classification. CVPR 2021. --- Rebuttal 2: Title: Thanks for the authors' responses Comment: After thoroughly reviewing the questions raised by other reviewers and carefully considering the authors' responses, I am convinced that my concerns have been effectively addressed. I believe the proposed method is inspiring for real-world complex environments. As a result, I would like to raise my score. --- Rebuttal Comment 2.1: Title: Thanks for your support Comment: Thank you for your exceptionally prompt feedback and unwavering support of our paper. We are glad to observe that our responses have effectively resolved your concerns. Your invaluable input has undeniably enhanced the quality of our paper, and we sincerely thank you for your dedication and time.	Summary: This paper works on Multi-source Blended-target Domain Adaptation setting, which learns a model from multiple source domain and evaluates the model in a mixed multi-target domain without access to the domain labels of target data. This paper utilize the style information of the blended-target domain with weight factor to enhance source domain features for feature augmentation. To avoid the negative impact of domain-specific information in multi-source data, this paper also uses KL loss to reduce the impact of incorrectly classified source samples. This paper also proposes a domain adversarial loss with the help of nuclear-norm 1-Wasserstein discrepancy to reduce the domain gap between source domain and target domain by reusing the classifier of task network. Extensive experiments on various benchmark and comprehensive analysis prove the effectiveness of the proposed method. Strengths: 1. This paper is well motivated. 2. The proposed method is evaluated with various benchmark and analyzed extensively. Weaknesses: 1. The style adaptation method is not compared with prior works proposed for the same purpose like MixStyle. 2. Whether Domain Adversarial Alignment without Domain Labels outperform domain adversarial learning by treating multi-source data as one single source domain and multi-target data as one target domain is not discussed. Technical Quality: 3 Clarity: 3 Questions for Authors: Please see weakness part. Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: No limitation is discussed in the paper. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you very much for your feedback and questions. We provide our responses below >W1: The style adaptation method is not compared with prior works proposed for the same purpose like MixStyle. A1: We have compared our style adaptation (SA) with some prior works for the same purpose, such as random augmentation (RA), MixStyle [a], and pAdaIN [b]. The results are shown in Table R3 (a) on the PDF file. Compared to these prior works, our SA method effectively selects more suitable style information to augment the source features, achieving superior performance. >W2: Whether Domain Adversarial Alignment without Domain Labels outperform domain adversarial learning by treating multi-source data as one single source domain and multi-target data as one target domain is not discussed. A2: We have performed comparison experiments based on your advice (please refer to Table R4 in the PDF file). The experimental results show that the performance of domain adversarial alignment without domain labels outperforms the performance of domain adversarial learning by treating multi-source data as one single source domain and multi-target data as one target domain. Refs: [1] Domain generalization with mixstyle. ICLR 2021. [2] Permuted adain: Reducing the bias towards global statistics in image classification. CVPR 2021. --- Rebuttal Comment 1.1: Comment: Dear Reviewer NQ8Y, We are truly thankful for your valuable time and constructive feedback! Since the discussion deadline is approaching (11:59pm AoE on August 13), we would like to kindly inquire if our rebuttal has addressed your concerns. We are willing to address any further issues you might have : ) Sincerely, Authors	Summary: The paper proposes a "Style Adaptation and Uncertainty Estimation (SAUE)" method for Multi-source Blended-Target Domain Adaptation (MBDA). The core objective of the SAUE method is to enhance the source domain features by leveraging style information from a blended-target domain, which is a mixture of multiple sub-target domains. The method employs a similarity factor to select beneficial target style information and integrates an uncertainty estimation technique to fortify the model's robustness. The proposed SAUE is evaluated on several domain adaptation benchmarks, including ImageCLEF-DA, Office-Home, and DomainNet, demonstrating superior performance over existing state-of-the-art techniques. Strengths: It is demonstrated an impressive results on several domain adaptation benchmarks with a significant improvement. The paper is well-organized and easy to follow. Weaknesses: 1. Although the blended-target domain adaptation has attracted much attention, it is similar to the open-compound domain adaptation that has no annotation of the target domain. Authors should compare and discuss the difference between the open-compound domain adaptation works. 2. The proposed style adaptation and uncertainty estimation are motivated and effective ways to handle domain shift problems. However, the idea has been well studied in conventional domain adaptation [a], domain generation [b], and open-compound domain adaptation fields. Therefore, the proposed method seems to lack innovation. [a] Informative Data Mining for One-shot Cross-Domain Semantic Segmentation [b] Uncertainty modeling for out-of-distribution generalization [c] Open Compound Domain Adaptation with Object Style Compensation for Semantic Segmentation 3. In my opinion, the proposed style adaptation technique is not tailored for multi-source BTDA as it also works for single-source BTDA. Therefore, the statement "the first work for MBDA" seems to be weak. Technical Quality: 3 Clarity: 3 Questions for Authors: Detailed questions refer to the weaknesses. Confidence: 5 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: The limitations of the work have been discussed. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thanks a lot for your efforts in reviewing the paper. Below, we respond to your questions in details. >W1: Comparison to OCDA. A1: The key characteristic of blended-target domain adaptation (BTDA) is that the target domain is a mixture of multiple sub-domains sharing the same category space. Compared to BTDA, open-compound domain adaptation (OCDA) handles a target domain consisting of multiple sub-domains, some known (open-set) and some unknown (compound-set). OCDA's challenge is adapting the model to perform well on both known and unknown sub-domains without annotations. In BTDA, the model learns domain-invariant representations generalizable across the blended-target domain. In OCDA, the model identifies and handles known sub-domains effectively while being robust to unknown ones. We will add this comparison and discussion in Section 2 of the final version. >W2: The innovation of SAUE. A2: IDM [a] introduced a style transfer technique to alleviate the confusion between some high-entropy prediction images and target images, they also utilized mean entropy and cosine similarity to estimate the uncertainty. However, IDM only considered the single source and single target domain scenario for semantic segmentation. DSU [b] inserted the uncertainty estimation of the feature means and feature deviation into an AdaIN module. However, DSU do not consider the more realistic scenario where the target domains are multiple and blended. OSC [c] constructed style compensation (SC) strategy mainly to augment the object feature for a semantic segmentation image by constructing the weight factor and discrepancy features. The weight factor of SC is calculated by representative-key and object features. However, OSC do not take model uncertainty and multiple source setting into account. Different from the previous methods [a], [b], and [c], in multi-source blended-target domain adaptation (MBDA), the distributions of source domains are diverse, while the target distributions are blended. Directly using style transfer techniques in the current BTDA scenario fails to capture domain-invariant representations among different source domains in MBDA. Our efficient and novel solution utilizes the Wasserstein distance to explicitly measure the similarity of low-level features between the source and target domains, thereby constructing a weight factor. We then use the weight factor to select target domain features that are more suitable for the source domains and use them for feature augmentation. In this way, our method can mitigate the impact of the domain-specific attributes. In addition, multiple source domains may generate multiple opinions in evidential deep learning (EDL) [d]. Thus, our method constructs an uncertainty estimation strategy that introduced a Dirichlet-based evidential model to fuse multiple opinions by using the Dempster-Shafer Rule, which is more beneficial to exploit valuable knowledge from multiple source domains. Although some methods (including the aforementioned three methods) introduced such techniques into semantic segmentation, there is no effective strategy to address the knowledge transfer between multiple source domains and a blended-target domain in a more complex and realistic MBDA scenario. To fully consider the above-mentioned issues, we proposed our style adaptation and uncertainty estimation method. Thus, compared most of the existed methods, the main innovations of our method can be summarized as: 1) the novel style adaptation strategy is designed to select suitable blended-target style information for feature augmentation of multiple source domains. 2) The uncertainty estimation strategy that utilized Dirichlet-based evidential model to fuse multiple opinions from multiple source domains, which more effectively exploit domain-invariant knowledge from multiple source domains. 3) As far as we know, our propose SAUE method is the first work that proposed for providing a novel solution for the challenging MBDA setting, which is a real and complex scenario. Meanwhile, we have provided a theoretical analysis and sufficient experimental validation of the proposed method. [a] Informative Data Mining for One-shot Cross-Domain Semantic Segmentation [b] Uncertainty modeling for out-of-distribution generalization [c] Open Compound Domain Adaptation with Object Style Compensation for Semantic Segmentation [d] Murat Sensoy, Lance Kaplan, and Melih Kandemir. Evidential deep learning to quantify classification uncertainty. >W3: In my opinion, the proposed style adaptation technique is not tailored for multi-source BTDA as it also works for single-source BTDA. Therefore, the statement "the first work for MBDA" seems to be weak. A3: Although style adaptation works for BTDA, its integration within MBDA is designed to handle complexities unique existed in multi-source scenarios. Directly using target style information to augment source features can aggravate domain shift due to conflicts from diverse source domain distributions. Unlike previous style transfer modules, our style adaptation module selects suitable target style information for different source domains using the Wasserstein distance to construct a weight factor, creating a cohesive representation space and improving the adaptation process in a multi-source setting Moreover, there maybe some misunderstandings regarding our claim for “the first work for MBDA”. In the first point of our contributions, we state: “An approach SAUE is proposed to explore information from multiple source domains for BTDA. As far as we known, SAUE is the first work that proposed for MBDA, which can utilize more feature information from extra source domains to learn domain-invariant representations.” Therefore, we would like to clarify that the SAUE method is the first work specifically addressing MBDA not merely the utilization of style adaptation technique. We still appreciate the reviewer's detailed insights. --- Rebuttal Comment 1.1: Comment: Dear Reviewer cWFB, We are truly thankful for your valuable time and constructive feedback! Since the discussion deadline is approaching (11:59pm AoE on August 13), we would like to kindly inquire if our rebuttal has addressed your concerns. We are willing to address any further issues you might have. Sincerely, Authors	Summary: The paper addresses the setting of Blended target domain adaptation. The paper proposes style adaptation and uncertainty estimation for multi-source blended target domain adaptation. They propose to utilize the extra knowledge acquired from the blended target domain. Where a similarity factor is utilized to obtain target style information to augment the source features. During training, they utilize the information from the target domain with a scaling factor and Wasserstein distance between the source and target features. Moreover, they do not utilize the domain labels without which they claim to align the multi-source and blended target domains. They utilize common domain adaptation datasets to demonstrate the effectiveness of their method. Strengths: – The problem setting of addressing multi-target distribution shifts with a source trained model is useful – Performance improvement is significant compared to the baseline methods. Weaknesses: The paper lacks extensive validation, clarity, and novelty. Elaborated below. Technical Quality: 2 Clarity: 2 Questions for Authors: – Can the authors demonstrate with the default version of DomainNet instead of utilizing a subset of it? Moreover, the inclusion of the VisDA dataset would also be useful. – Could the authors also provide detailed numerical results of Figures C and D for better clarity? – The idea of using the target and source features during the training process with a scaling factor and Wasserstein distance doesn’t seem novel. Moreover the paper doesn't cite [1][2] which makes the related work quite limiting. – The idea of selecting style information is not new. Moreover, it is not clear which layer has been utilized for the style information and what the motivation is to utilize the style content at a particular layer. – The distribution analysis can be moved to the appendix, which doesn’t offer significant insights of the method. – Akin to MCDA [12], could the authors utilize ResNet 101 instead of ResNet50 and compare the results for the default version of the DomainNet dataset? With powerful backbones, it would be interesting how the style features are still preserved. – Extensive implementation details have not been provided; the batch size of the blended target domain, learning rates, and which layers from the ResNet model have been utilized for this if their code will be released. Does the method necessitate a high batch size for the target domain? In this case, it might be a limitation. References: [1] Shen, Jian, et al. "Wasserstein distance guided representation learning for domain adaptation." Proceedings of the AAAI conference on artificial intelligence. Vol. 32. No. 1. 2018. [2] She, Qingshan, et al. "Improved domain adaptation network based on Wasserstein distance for motor imagery EEG classification." IEEE Transactions on Neural Systems and Rehabilitation Engineering 31 (2023): 1137-1148. Confidence: 4 Soundness: 2 Presentation: 2 Contribution: 2 Limitations: Yes. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We appreciate the comments and questions you post. Here are our point-to-point responses. >Q1: Experiments on the DomainNet and VisDA datasets. A1: Due to time limitations, we provide comparisons with important and recent multi-source blended-target domain adaptation (MBDA) methods MCDA and DGWA on the DomainNet and VisDA datasets. Initial experiments are shown in Tables R1 and R2 (see PDF), which demonstrate the superiority of our SAUE method on these challenging datasets. We will give more comparisons in the revised version. >Q2: Figs. 2C and 2D. A2: Detailed numerical results for Figures 2C and 2D are provided for clarity (see Table R7 in the PDF). >Q3: Idea about feature learning and related works. A3: Most of the existing methods use target and source features based on the single source and single target domain adaptation (SSDA) or single source and blended target domain adaptation (BTDA), which do not consider MBDA setting. In MBDA, challenges include: 1) various distributions from multiple source domains may introduce potential conflicts. 2) The target distributions are mixed. 3) Due to different discrepancies between different source and target domains, it is challenging to align multiple source and blended-target domains simultaneously. Our efficient and novel solution is to utilize the Wasserstein distance to explicitly measure the similarity of low-level features between the source and target domains to construct a weight factor. The innovations of our proposed method are: 1) a novel style adaptation strategy that selects suitable blended-target style information for feature augmentation of multiple source domains. 2) An uncertainty estimation strategy that utilized Dirichlet-based evidential model to fuse multiple opinions from multiple source domains, which more effectively exploit domain-invariant knowledge from multiple source domains. 3) The proposed SAUE method provides a novel solution for the challenging MBDA setting. We have cited and discussed these two good methods [1], [2]. The revised parts, which will be added to the final version, are as follows: WDGRL [1] employs a neural network to estimate the Wasserstein distance between the source and target domains, optimizing feature representations to minimize this distance. Shen et al. [2] introduced an improved domain adaptation network for motor imagery (MI) classification and utilized Wasserstein distance to construct a domain adversarial learning strategy to handle EEG-based MI detection tasks. >Q4: Style information selection and motivation. A4: While the technique of selecting style information has been explored in other contexts, our contribution lies in the unified adaptation framework designed for MBDA. Given the challenge that different discrepancies exist between different source and target domains, directly utilizing feature augmentation techniques like random augmentation may aggravate the domain shift problem. Therefore, we designed a strategy that selects style information to augment the source domains’ features. Our approach constructs tailored style information selection with a novel similarity-based weighted matrix strategy for MBDA, effectively selecting suitable blended-target domain style information for specific source domain, showing empirical gains and component synergy. The style information is extracted from the second bottleneck layer of ResNet and utilized in the third bottleneck layer. The motivation for utilizing style content at a particular layer is to leverage the style information of the blended-target domain to augment the features of the source domains. Previous work [3] has demonstrated that low-level features (e.g., intermediate features from the second bottleneck of ResNet) of deep neural networks (DNNs) primarily represent style information. Building on this insight, we extract the style information of the blended-target domain from the low-level features of ResNet and use it to augment the features of the source domains. >Q5: Distribution analysis. A5: We will move the distribution analysis part to the appendix in the revised paper. >Q6: Evaluation of different backbones. A6: We have analyzed the performance of our method using the ResNet-50 and ResNet-101 backbones in the default version of the DomainNet dataset (please see Table R2 in the PDF file). The experimental results show that our method achieves significant performance gains when utilizing powerful backbones (ResNet-101). We compared the performance gains of the style adaptation module with standard backbone (ResNet-50) and powerful backbone (ResNet-101). The results indicate that the performance gains (+2.9% and +2.3%) of the style adaptation module when integrated into the ResNet-50 backbone surpass those (+2.3% and +1.3%) when integrated into the ResNet-101 backbone. >Q7: Implementation details and batch size. A7: For better understanding, we provide more implementation details as follows. The batch size for the blended-target domain is 32, same as the source domains. The learning rate starts at 1e-3, updated by the LambdaLR strategy. We use an ImageNet pre-trained ResNet, replacing the last FC layer with task-specific FC layers. Our method does not require a high target domain batch size, only equal to that of the source domains. Extra validation experiments (see Table R3(b) in the PDF) show different target domain batch sizes do not significantly impact performance. Thus, the batch size for blended-target domain is not a limitation. Thanks again for your meaningful questions. Refs: [1] Wasserstein distance guided representation learning for domain adaptation. AAAI 2018. [2] Improved domain adaptation network based on Wasserstein distance for motor imagery EEG classification. IEEE TNSRE 2023. [3] Mixstyle neural networks for domain generalization and adaptation. IJCV 2024. --- Rebuttal Comment 1.1: Comment: Thank you for your efforts. My comments have been addressed. I would encourage the authors to include DomainNet (345 classes) and additional comparisons to it in the main paper, as well as discussions about feature learning and style information and additional implementation details in the manuscript. In response, I have increased my score. --- Reply to Comment 1.1.1: Title: Thanks for your support Comment: Thank you for your active involvement and prompt feedback during the discussion phase. We are pleased to know that our rebuttal has effectively addressed your questions. We will carefully incorporate all of your valuable suggestions into the final version of our paper, including results on DomainNet (345 classes), discussions on feature learning and style information, as well as additional implementation details. Your constructive review has undoubtedly enhanced the quality of our paper, and we sincerely appreciate your dedication and time.	Rebuttal 1: Rebuttal: Dear Reviewers and Area Chair, We sincerely thank all the reviewers for their positive comments and helpful feedback, which have significantly improved the quality of this paper. We have uploaded the responses to each reviewer along with the one-page PDF. In response to the comments, we have carefully revised and enhanced the manuscript with the following additional discussions and experiments: 1. Additional experiments on the default version of the DomainNet dataset and the VisDA-2017 dataset. 2. Comparison of different backbones (ResNet-50, ResNet-101, and ViT-B/16). 3. Detailed numerical results for Figures 2C and 2D. 4. More implementation details about the proposed method. 5. Discussion about the related work. 6. Comparison of different domain adaptation settings. 7. Comparison of different feature augmentation methods. We hope our response sincerely addresses all the reviewers’ concerns. Thank you very much for your time and consideration. Best regards, Submission3121 Authors Pdf: /pdf/090fc8adf3aa244decec4619b240bd38268e03b5.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Dual-Perspective Activation: Efficient Channel Denoising via Joint Forward-Backward Criterion for Artificial Neural Networks	Accept (poster)	Summary: This paper introduces a novel activation mechanism, namely Dual-Perspective Activation (DPA), to identify irrelevant channels and thus apply channel denoising for the ANN architecture. The proposed DPA incorporates criteria established and updated online from both forward and backward propagation perspectives while preserving activation responses from relevant channels, which can effectively eliminate the interference of irrelevant or redundant features, thereby improving the overall performance of the neural network. Moreover, the authors conduct extensive experiments across various mainstream ANN architectures and datasets, as well as multiple tasks and domains, where the results show (1) DPA is parameterless and fast, (2) DPA achieves remarkable performance compared to existing activation counterparts, and (3) DPA can be applied to other tasks and domains. Strengths: - This paper is meticulously crafted, with a well-structured and clarified presentation. - The motivation originates from detailed and clear explorations of ANN activation mechanisms by the authors, which are valuable and deserve to be investigated. - The idea of combining both forward and backward perspectives to track and evaluate the importance of each channel in real time sounds novel and valid. - The theoretical foundations and experimental validations are detailed and sufficient. - The proposed method can perform various other tasks or domains, including vision and non-vision tasks. Weaknesses: - The authors have not provided a clear justification for why the intersection operation is the only suitable channel selection approach. - While the authors claim in Lines 105-107 that each category shows a strong relation with its specific channels, more sufficient evidence would be advantageous to support the second part of their claim, which states that the other channels should not generate any responses. - The authors have not explored the impact of applying the DPA to different layers of the CNN and presented a more thorough analysis to justify their design choice. - In Figure 6, the authors may not have thoroughly investigated the impact of the momentum parameter $m$ on the model's performance, and their choice of $m$ values may not have been well-justified. Technical Quality: 3 Clarity: 3 Questions for Authors: - It would be helpful if the authors could explore and compare the performance of more complex channel selection techniques to determine the most appropriate method. - In Lines 105-107, the authors claim that each category shows a strong relation with its specific channels, and ideally, the other channels should not generate any responses. Please provide additional evidence in support of the second half of the claim. - In Lines 198-199, the authors apply the DPA to the last block in CNN. Are the high-level semantics the main reason for this choice? Why is this approach taken? Please provide a detailed explanation. - In Figure 6, the value sampling of momentum $m$ does not follow any particular pattern, and the prediction performance does not exhibit significant variations across different $m$ values. Please provide a detailed explanation. Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The paper has discussed the potential limitations and future directions of the research. Moreover, there is no societal impact from the work performed. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: > Q1: It would be helpful if the authors could explore and compare the performance of more complex channel selection techniques to determine the most appropriate method. (Corresponding to W1: The authors have not provided a clear justification for why the intersection operation is the only suitable channel selection approach.) Thank you for your comment. Firstly, the proposed forward-backward criterion has been carefully designed, where the forward criterion follows the principle of threshold activation, and the backward criterion follows the principle of gradient attribution. Using an intersection of these two perspectives allows for more accurate judgments compared to relying solely on a single perspective. Moreover, we have compared the forward-backward intersection operation with forward only, backward only, and forward-backward union operations, respectively. The results in Sec. 4.3 & Tab. 3 indicate that the intersection operation performs the best. Therefore, the forward-backward intersection operation currently stands as the best and most reasonable channel selection technique. > Q2: In Lines 105-107, the authors claim that each category shows a strong relation with its specific channels, and ideally, the other channels should not generate any responses. Please provide additional evidence in support of the second half of the claim. Thanks for the constructive suggestion. Commonly used activation functions such as ReLU generally perform by setting an activation threshold, mimicking the membrane potential in biological neurons to suppress irrelevant signals while allowing useful signals to pass. During network learning, relevant signals tend to be above the threshold, whereas irrelevant signals tend to be below it, which is consistent to the principle of threshold activation. Fig. 2 indicates that each category is only correlated with sparse and specific channels in ANNs, and Fig. 3(a) shows that the activation distributions of certain channels, indicated by the red arrows, are truncated by the threshold and are concentrated in a small range above it. Therefore, we consider that these channels are potentially irrelevant which should not have any response. That is, the granularity of our claim of signal correlation is at the channel level. In order to support our point, we conducted a confirmatory experiment, as shown in Fig. 3(b), where the potential irrelevant channels indicated by the red arrows were manually removed by forcing their responses below the activation threshold. As expected, the training accuracy substantially improvements, providing evidence that these channels are indeed potentially irrelevant. > Q3: In Lines 198-199, the authors apply the DPA to the last block in CNN. Are the high-level semantics the main reason for this choice? Why is this approach taken? Please provide a detailed explanation. Thanks for the comment. Yes, the high-level semantics are the main reason. Previous works have shown that high-level semantics in CNNs only exist in deep representations [1,2]. These features are crucial for the downstream tasks. Features in the shallow layers of CNNs are too concrete. Therefore, imposing the regularization to a channel (an element) cannot directly control the change in the corresponding space-level feature map. Moreover, we have explored the impact of applying the DPA to different layers of ResNet-18 as follows, where L4 is the last layer: \|Constrained Layer(s)\|Top-1 Acc / %\|Constrained Layer(s)\|Top-1 Acc / %\| \|-\|-\|-\|-\| \|L1\|76.2\|L1-3\|76.3\| \|L2\|76.0\|L3-4\|76.7\| \|L3\|76.0\|L2-4\|76.6\| \|L4\|76.8\|L1-4\|76.8\| The results indicate that applying the constraint to shallow layers has little effect, and only constraining the last layer can achieve the optimal effect. [1] Raghu et al., Do vision transformers see like convolutional neural networks? NeurIPS 2021 [2] Selvaraju et al., Grad-CAM: Visual explanations from deep networks via gradient-based localization. ICCV 2017 > Q4: In Figure 6, the value sampling of momentum $m$ does not follow any particular pattern, and the prediction performance does not exhibit significant variations across different $m$ values. Please provide a detailed explanation. We appreciate your comment. Theoretically, a high value of $m$ risks making the mean value unstable, and conversely, a low value of $m$ smoothens the mean value update, but it may cause the mean value to lag behind. According to our analyses (see Appendix A.3) on the ViT-Tiny model trained on CIFAR-100, the network's performance is not sensitive to the $m$ between around 0.2 and 0.99, from which $m$=0.9 performs the best, and extremely small $m$ values lead to negative effects. Therefore, for the rest of the experiments presented in the paper, we empirically set the $m$ to 0.9 without too much consideration. For the prediction performance that does not exhibit significant variations across different $m$ values, we think this is a good thing, as the model performance with the proposed DPA is robust to changes in the hyperparameter $m$, which indicates that a fixed $m$ can be adaptive across different models, datasets, and tasks, thereby reducing the adjustment costs. --- Rebuttal Comment 1.1: Title: I appreciate the authors' detailed responses. Comment: I appreciate the authors' detailed responses. They have adequately addressed my concerns regarding the selection of low-relevance channels, the DPA's application, and the momentum parameter $m$. The idea of denoising activated channels from both forward and backward perspectives is interesting and inspiring. Hence, I'm delighted to keep my positive rating and recommend acceptance. --- Reply to Comment 1.1.1: Title: Thank you for your recognition and recommendation for acceptance Comment: Dear Reviewer 4FwJ, We sincerely appreciate your recognition of our efforts to address your concerns, as well as your positive rating and recommendation for acceptance. Thank you once again for your time and effort in reviewing our paper.   Best regards, Authors of Paper #1829	Summary: Artificial neural networks apply the principles of the human brain and leverage sparse representations to their advantage. However, existing activation methods still struggle to suppress irrelevant signals, affecting the network's decision-making. To overcome this, a novel Dual-Perspective Activation (DPA) mechanism is proposed, which efficiently identifies and denoises channels with weak correlation through an online updating criterion from both forward and backward perspectives while not affecting the activation response of other channels with high correlation. Extensive experiments demonstrate that DPA facilitates sparser neural representations and outperforms existing activation methods, and it applies to various model architectures across multiple tasks and domains. Strengths: 1. The proposed DPA method starts from a novel joint forward-backward perspective. By designing forward and backward memories to track each channel's historical response and gradient, a criterion is established to identify irrelevant channels and denoise them. The design of the forward-backward criterion is smooth and natural, adhering to the principles of activation response and gradient attribution. 2. The idea is interesting and presented coherently. The method design is smooth and natural. The literature review on activation and gradient attribution is comprehensive. The method achieves desired sparse representations and performance gains. 3. The paper is well-organized. The problem, motivation, methodology, and results descriptions are easy to understand. 4. This method improves the model's performance from an interpretable perspective and is versatile for various model architectures (CNN, Transformer, MLP, etc.) and different tasks and domains. Weaknesses: 1. Some claims seem not so clear. For the channel activation distribution observed in Figure 3(a), providing more detailed descriptions for the potentially irrelevant channels pointed out by the red arrows could further improve the clarity of the paper. 2. It is not clear for some figures: For Fig. 3(b), the legend "manually removing irrelevant channels" needs more explanation. The authors do not explain how exactly the irrelevant channels are manually removed. 3. The benefits of sparse representation are not convincing enough. Considering that sparse representation may not always be beneficial, additional discussion on the pros and cons of sparsity for this work could help enhance the main claim of the paper. Technical Quality: 3 Clarity: 3 Questions for Authors: 1. Please explain why the channels pointed out by red arrows in Fig. 3(a) are potentially irrelevant channels, in order to enhance readers' understanding. Including examples or case studies where similar channels were found to be irrelevant in other contexts might also reinforce the explanation. 2. Explain the exact procedure utilized for manually removing the irrelevant channels. Is it by forcing the irrelevant channels in Fig. 3(a) to zero, or by any other way? 3. Does the ability of the forward-backward criterion to make judgments get impacted by the model's performance? Additionally, when the judgment is suboptimal, will it influence the model's learning trajectory? 4. This paper achieves sparsity of features/representations, which is good. However, in some cases, sparse representation may not be the most suitable option. For example, if the data is not sparse, using sparse representation may lead to loss of information, impeding the model from learning complex patterns. Is sparse representation consistently beneficial for this study? Are there more factors that need to be taken into account? Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The authors include a detailed section on the limitations of the work. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: > Q1: Please explain why the channels pointed out by red arrows in Fig. 3(a) are potentially irrelevant channels, in order to enhance readers' understanding. Including examples or case studies where similar channels were found to be irrelevant in other contexts might also reinforce the explanation. Thank you for your constructive suggestion. Commonly used activation functions such as ReLU generally perform by setting an activation threshold, mimicking the membrane potential in biological neurons to suppress irrelevant signals while allowing useful signals to pass. During network learning, relevant signals tend to be above the threshold, whereas irrelevant signals tend to be below it, which is consistent with the principle of threshold activation. Fig. 2 indicates that each category is only correlated with sparse and specific channels in ANNs, and Fig. 3(a) shows that the activation distributions of certain channels, indicated by the red arrows, are truncated by the threshold and are concentrated in a small range above it. Therefore, we consider that these channels are potentially irrelevant and should not have any response. That is, the granularity of our claim of signal correlation is at the channel level. In order to support our point, we conducted a confirmatory experiment, as shown in Fig. 3(b), where the potential irrelevant channels indicated by the red arrows were manually removed by forcing their responses below the activation threshold. As expected, the training accuracy substantially improved, providing evidence that these channels are indeed potentially irrelevant. We will expand upon the discussion of this section in the final revised version. > Q2: Explain the exact procedure utilized for manually removing the irrelevant channels. Is it by forcing the irrelevant channels in Fig. 3(a) to zero, or by any other way? Sorry for the confusion. Channels whose mean response distribution is lower than the response threshold are considered potentially irrelevant and are highlighted by red arrows in Fig. 3(a). The procedure utilized for manually removing the irrelevant channels is forcing the responses of irrelevant channels indicated by red arrows below the threshold. In the paper, the activation threshold is set at zero, thereby we forcibly bring the responses of these irrelevant channels down to zero as well. We will include this detail in the final revised version. > Q3: Does the ability of the forward-backward criterion to make judgments get impacted by the model's performance? Additionally, when the judgment is suboptimal, will it influence the model's learning trajectory? Thanks for the insightful comment. The channel denoising loss $L_{ch}$ is maintained as a weak constraint throughout the training process. The responses at the beginning of training indeed exhibit considerable noise and make suboptimal judgments. Setting channel denoising to a high intensity during the initial stages can indeed affect convergence. Hence, we adopt $L_{ch}$ as a weak regularization term, where we adjust the weight of $L_{ch}$ to maintain it an order of magnitude smaller than $L_{task}$. This strategic approach ensures that $L_{task}$ remains dominant, effectively dictating the range of feature distribution. As long as the $L_{task}$ learns much faster than $L_{ch}$, the model's performance will not be affected by early suboptimal judgments, and the judgments will become more accurate as the model's performance improves. We also considered alternatives, such as activating $L_{ch}$ after a certain number of iterations or gradually increasing the weight of $L_{ch}$ from zero at the beginning of training. However, we observed that foregoing these steps did not yield negative effects during initial training. This observation aligns with our implementation of the warm-up learning rate scheduler, which also serves to alleviate this concern to a certain extent. > Q4: This paper achieves sparsity of features/representations, which is good. However, in some cases, sparse representation may not be the most suitable option. For example, if the data is not sparse, using sparse representation may lead to loss of information, impeding the model from learning complex patterns. Is sparse representation consistently beneficial for this study? Are there more factors that need to be taken into account? Thanks for the interesting comment. Yes, sparse representation is the goal of this study, and it does bring a lot of benefits, which can be directly supported by the confirmatory experiment, as shown in Fig. 3(b). By manually removing the irrelevant channels for each category (which is equivalent to forcibly constructing sparse representation), there is a substantial improvement in the training accuracy. Moreover, the observation in Fig. 2 indicates that each category is only correlated with sparse and specific channels in ANNs. The proposed DPA effectively denoises redundant channels while not affecting relevant channels, resulting in sparse representation and performance enhancements. All of these collectively validate that the role of sparse representation in this study is to eliminate redundant signals while preserving key signals, rather than causing the loss of information.	Summary: The authors argue that sparsity in the activations is a desirable property and should be enforced. They observe that there exist category-specific channels in the network's activations which have a high value only for specific categories while other channels remain low. These low activations are considered as noise that impairs performance and should be removed. To this end, the DPA method is introduced which tracks for a given category the intensity of activations per channel (and gradient magnitudes) and supresses channels with low intensity. The resulting DPA activation is used as a replacement for activations of transformer-based models and in the last block of CNN-based models. Experiments show consistent improvements over other activation functions, especially in transformers. Strengths: - Substantial effect for transformers, potentially impactful. - Clear presentation for most parts. - Code is provided (although I could not find the experiment configurations). Weaknesses: - The key results reported in Tab. 1 and Tab.2 were conducted using the author's own evaluation. On ImageNet-1K the respective original papers report accuracies of 75.1 (vs. 75.2 DPA) for PVT-Tiny and 81.5 (vs. 77.8 DPA) for TNT-small. ResNet18 achieves a score of 71.5 (vs. 70.8 DPA) with an improved trainig procedure [1]. - The effect sizes are small. For smaller datasets (CIFAR and ImageNet-100) standard deviations over multiple training runs should be reported for DPA. - Sometimes the paper writing is unclear: - Sec. 4.1 "can replace all existing activations in each block": Does this mean that the softmax activation is replaced? - Given the substantial differences between biological neurons and ANNs, I don't think one can conclude from the observation of sparse activations in biological networks that this is necessarily also a desirable property for ANNs. Technical Quality: 2 Clarity: 3 Questions for Authors: My main concern regards the fairness of the experiments, in particular the degree to which the good performance of DPA is due to the choice of the hyperparameters. How robust is DPA when other hyperparameters are chosen? The authors state that the $\lambda$ parameter of the DPA loss was varied depending on network and dataset. Was this parameter selection conducted on the test set (Fig. 7 from the appendix suggests this, as the value for $\lambda=1$ is the one reported in Tab. 1)? Were parameters of the other activation functions also varied? As mentioned in weaknesses, in some cases (I only checked a subset) the reported scores of DPA are lower than the corresponding ReLU-based state-of-the art. Does DPA consistently improve scores here, too? One way to demonstrate this would be taking a somewhat start-of-the-art Imagenet model like the ResNet18 using the training from [1] and show that DPA improves performance here, too. Confidence: 3 Soundness: 2 Presentation: 3 Contribution: 2 Limitations: - Limited to settings where categories are present during training. Hence, self-supervised training is not supported. This could be made clearer in the text. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: > Q1: (A) How robust is DPA when other hyperparameters are chosen? The authors state that the $λ$ parameter of the DPA loss was varied depending on network and dataset. (B) Was this parameter selection conducted on the test set? (C) Were parameters of the other activation functions also varied? We appreciate your valuable feedback and apologize for any confusion. (A) The hyperparameters ($m$ and $λ$) are robust when their values are not extreme (Please refer to paper Sec. A.3 & Fig. 6-7). The DPA can consistently bring performance improvements when $λ$ is small, and too large $λ$ can result in negative side effects. In fact, for most experiments (CaiT & PVT on CIFAR-100, and all the models on CIFAR-10 & ImageNet-{100,1K}), since hyperparameter selection is quite time-consuming and also for fair comparison, we did not select $λ$ but empirically used the default $λ$ as 1 (see Lines 484-485). If we were to conduct hyperparameter search for each experiment, the performance of our method might be further improved. (B) We regret any confusion caused by the misleading title "Hyperparameter Selection" for Sec. A.3. It should have been correctly referred to as "Impact of Hyperparameters on Model Performance". In fact, the original intention of Sec. A.3 was to analyze the impact of hyperparameters on model performance for few and specific models and datasets on the test set, rather than performing hyperparameter selection for each experiment. Most experiments have their hyperparameters set uniformly ($λ$=1) based on the aforementioned analysis (see Lines 484-485 & Fig. 6-8). Please also refer to (A) and Global Response above. (C) ReLU, GELU, and Softplus do not contain parameters, and the parameters in ELU, SELU, SiLU, and GDN are trainable. > Q2: ... in some cases the reported scores of DPA are lower than the corresponding ReLU-based state-of-the art. Does DPA consistently improve scores here, too? One way to demonstrate this would be taking a somewhat start-of-the-art Imagenet model like the ResNet18 using the training from [1] ... Thanks for the constructive comment. For training Transformers, the baseline models and the training settings on ImageNet-1K were taken from timm. We apologize for using a smaller batch size and fewer GPUs than previous literature during training due to the limited computing resources we had, which might result in the difference between the results we obtained and those reported in previous literature. However, to maintain fairness in comparison, we have ensured that each experiment in a set of comparative studies used the same public training settings. For training CNNs, our baselines' performance has already reached the ones reported in the original literature. We have also maintained fairness in comparison by using the same public training settings in each set of comparative studies. Additionally, we used the improved training procedure in [1] and trained the ResNet-18 on our local devices. The results are as follows, which also showcases DPA's effectiveness. \|Top-1 Acc / %\|ResNet-18\| \|-\|-\| \|ReLU\|71.4\| \|GELU\|71.2\| \|DPA\|71.8\| > W1: The key results reported in Tab.1 and Tab.2 were conducted using the author's own evaluation ... Please refer to Q2 above. > W2: ... For smaller datasets (CIFAR and ImageNet-100) standard deviations over multiple training runs should be reported for DPA. We are sincerely sorry for the confusion. Actually, the numerical results in the paper are the average under 3 random seeds (42, 0, 100), and the results are stable. For example, here are the detailed results of training ViT-Tiny and ResNet-18 on CIFAR-100: \|Top-1 Acc / %\|ViT-Tiny\|ResNet-18\| \|-\|-\|-\| \|ReLU\|65.9, 65.4, 65.7\|75.7, 75.8, 75.7\| \|GELU\|65.4, 65.4, 65.5\|75.5, 75.6, 75.6\| \|DPA\|70.8, 70.2, 70.6\|76.9, 76.6, 76.7\| We will include standard deviations in the revised version. > W3: Sec. 4.1 "can replace all existing activations in each block": Does this mean that the softmax activation is replaced? We apologize for the confusion. The softmax is not replaced. We will revise it to "can replace all existing activations (except for the softmax) in each block". > W4: ... I don't think one can conclude from the observation of sparse activations in biological networks that this is necessarily also a desirable property for ANNs. Thanks for the interesting comment. We would like to gently clarify that our "conclusion" (or rather "conjecture") regarding "sparse activation is a desirable property for ANNs" was not solely derived from the observation of sparse activations in biological networks. Instead, we supported our conjecture through relevant literature and extensive experiments, demonstrating that sparse activations do provide advantages to ANNs: - Connections within biological networks are sparse (our paper Lines 3-4 & 31-33). ANNs were originally designed to mimic biological networks. The sparse representation in ANNs has also shown notable benefits to network interpretability and generalization [1-3] (our paper Lines 4-5 & 33-34). Notably, the original paper of ReLU [3] also used similar writing logic. Inspired by biological sparse activations, the paper [3] designed the ReLU and demonstrated the advantages of sparsity in ANNs. [1] Emergence of simple-cell receptive field properties by learning a sparse code for natural images. Nature, 1996. [2] Sparse feature learning for deep belief networks. NIPS, 2007. [3] Deep sparse rectifier neural networks. AISTATS, 2011. - The sparse activation is the focus of our study, offering numerous benefits to ANNs. Directly supported by the confirmatory experiment in Fig. 3(b), forcibly constructing sparse activations for each category enhances training accuracy. The proposed DPA denoises redundant/irrelevant channels, leading to sparse activations and performance gains. These findings collectively validate the beneficial role of sparse activations in ANNs. --- Rebuttal 2: Comment: Thank you for the detailed answers. Q1: To me this still seems like hyperparameter tuning on the test set. However, since it only affects CIFAR-100 and ViT-Tiny this is a minor issue. While $m$ and $\rho$ are constant across all experiments, $\lambda$ is 1 only most of the time: It should be explicitly said in which cases $\lambda$ is not 1. Q2: Thank you evaluating on RN18, this result strengthens the paper. Still effect sizes are small for CNNs and sometimes performance is lower than state-of-the-art (e.g. in PVT-Tiny and TNT-small, see weaknesses in original review). This suggest that the used training protocol is sub-optimal for some architectures. W1...W3: I appreciate your clarification. W4: In the introduction you write "Multi-Layer Perception [...] closely resembles biological networks". While there are parallels, I find this is overstated. To motivate the work, I suggest to clearly emphasize the empirical findings over biological plausibility. I will increase my score to 5. --- Rebuttal Comment 2.1: Title: We are deeply grateful for your constructive feedback and support Comment: Dear Reviewer YhhA, We are deeply grateful for your constructive feedback and support. In line with your suggestions, our final revised manuscript will include more detailed clarifications on the hyperparameter and how we ensured fairness in comparison. Additionally, we will place greater emphasis on the empirical findings while presenting a more measured discussion on biological plausibility. We agree that this will strengthen the motivation and align it more closely with accepted perspectives in the field. Thank you once again for your valuable insights and guidance. We are confident that, with your support, the quality of our final revised version will be significantly enhanced.   Best regards, Authors of Paper #1829	Summary: This paper addresses the question of how to suppress inputs from irrelevant channels in a deep neural network. The authors develop a novel end-to-end trainable mechanism called Dual-Perspective Activation (DPA) to suppress irrelevant information and increase sparsity. The method is parameter-free, and increases performance across tasks and domains relative to baselines without this mechanism. Networks with DPA activation layers uniformly outperform standard activation functions (ReLU, GELU, SELU, GDN, etc.) across a wide range of datasets (Cifar{10,100}, ImageNet{100,1K}), and architectures (VITs, CNNs). Ablation studies show that the forward and backward components contribute to the effectiveness of DPA, with minimal computational overhead. Strengths: The paper does an excellent job motivating the design of a novel activation function and demonstrating its prowess across a range of ANN architectures (VITs, CNNs, GNNs), and datasets. Across the board DPA shows improvements in top1 accuracy, though the assessments were limited to these particular (albeit ubiquitous) benchmark assessments, somewhat limiting the broader relevance/impact of the work. The ability to outperform existing activation functions across the board suggests potential for high impact in the field of computer vision, and other areas of AI/ML (as briefly demonstrated), given that activation functions are a fundamental component in all ANN models. Weaknesses: The paper convincingly demonstrates the effectiveness of DPA for image classification (with limited presentation of generalization to node and text classification), but the work seems lacking in clear demonstration of relevance/impact beyond these benchmark assessments (i.e., less clear how this might impact AI/ML theory, or impact cogsci/neurioscience applications of these models). That said, the noted sparsification of representations suggest there’s a clear thread to follow up on for these more theory-focused areas. Minor: the paper does not distinguish between sparse connectivity and “activation sparsity”, and doesn’t distinguish between “population sparsity” (only a few neurons active at any given time) and “lifetime sparsity” (a given neuron fires rarely, only for a small percentage of input images). These are often confused (or not distinguished) in the ML and Neuro literatures, and might be worth being clear about which one you are referring to (it seems like category-level lifetime sparsity?). Minor: no mention of dropout, which directly impacts activation sparsity Minor: How did you identify and manually remove irrelevant channels? (Figure 3)? Are these just the low activations? Would a channel norm on this layer have the same effect/benefit? Technical Quality: 4 Clarity: 4 Questions for Authors: Minor: Have you compared DPA to other regularlization methods that lead to greater sparsity? Confidence: 4 Soundness: 4 Presentation: 4 Contribution: 4 Limitations: OK Flag For Ethics Review: ['No ethics review needed.'] Rating: 8 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: > W1: ... but the work seems lacking in clear demonstration of relevance/impact beyond these benchmark assessments (i.e., less clear how this might impact AI/ML theory, or impact cogsci/neurioscience applications of these models). That said, the noted sparsification of representations suggest there’s a clear thread to follow up on for these more theory-focused areas. Thank you for your thoughtful review and valuable feedback on our paper. Here is our discussion on how our work might impact AI/ML theory, or impact cogsci/neurioscience applications of ANN models: - _Impact on AI/ML theory:_ DPA has demonstrated interpretable solutions at the AI/ML theoretical level in channel selection, which helps to reveal the "black box" characteristics of deep networks. Especially from the backward perspective, DPA aligns well with the principles of theory-based backward gradient attribution, identifying irrelevant channels based on gradient, uncovering the contributions of each channel to the model's final decision, and achieving more precise feature selection. This is different from the activation function that relies only on forward propagation. DPA can provide new insights into the design theory of activation mechanisms. Additionally, by effectively inhibiting irrelevant channels, DPA not only improves the model accuracy, but also promotes a more sparse neural representation, which is closely related to research in sparse coding and compressive sensing. - _Impact on cogsci/neuroscience applications:_ The ANN design is strongly influenced by the working patterns of the human brain. The proposed DPA takes inspiration from the sparse activation pattern observed in biological neural networks. This indicates that by simulating the characteristics of biological neural networks, we could potentially make up for the imperfections of current ANNs. If possible, future research might investigate the utilization of neuroimaging and computational neuroscience methods to gain new insights into simulating the properties of biological neural networks. > W2: Minor: the paper does not distinguish between sparse connectivity and “activation sparsity”, and doesn’t distinguish between “population sparsity” (only a few neurons active at any given time) and “lifetime sparsity” (a given neuron fires rarely, only for a small percentage of input images). These are often confused (or not distinguished) in the ML and Neuro literatures, and might be worth being clear about which one you are referring to (it seems like category-level lifetime sparsity?). Thank you for your constructive comment. We apologize for not clearly distinguishing between the terms "sparse connectivity" and "activation sparsity", and between "population sparsity" and "lifetime sparsity". As you said, the correct terms of sparsity that our paper aimed to achieve are "activation sparsity" and "category-level lifetime sparsity". We will correct it appropriately in the final revised version. > W3: Minor: no mention of dropout, which directly impacts activation sparsity. Thank you for your constructive suggestion. Here, we present additional experiments comparing DPA with Dropout, which directly impacts activation sparsity: \|Top-1 Acc / %\|ViT-Tiny\|ResNet-18\| \|-\|-\|-\| \|ReLU+Dropout (ratio=0.1)\|67.0\|76.2\| \|ReLU+Dropout (ratio=0.2)\|67.6\|76.1\| \|ReLU+Dropout (ratio=0.5)\|65.9\|76.2\| \|GELU+Dropout (ratio=0.1)\|67.3\|76.0\| \|GELU+Dropout (ratio=0.2)\|67.2\|76.1\| \|GELU+Dropout (ratio=0.5)\|65.5\|75.8\| \|DPA\|70.5\|76.8\| The results suggest that Dropout has a limited impact on improving performance. One possible reason is that randomly forcing activation responses to zero during training cannot effectively transfer knowledge to the testing phase. > W4: Minor: (A) How did you identify and manually remove irrelevant channels? (Fig. 3)? Are these just the low activations? (B) Would a channel norm on this layer have the same effect/benefit? We are sincerely sorry for the confusion. (A) Channels whose mean response distribution before the activation is lower than the activation threshold are considered potentially irrelevant and are highlighted by red arrows in Fig. 3(a). The procedure utilized for manually removing the irrelevant channels in Fig. 3(b) is forcing the responses of irrelevant channels indicated by red arrows below the threshold. In the paper, the activation threshold is set at zero; thereby, we forcibly bring the responses of these irrelevant channels down to zero (not low activations) as well. (B) Fig. 3(b) is a confirmatory experiment on the training set. Forcibly setting responses from irrelevant channels to zero on the training set cannot generalize the knowledge to the testing set. Therefore, to address this challenge, we proposed channel denoising (channel norm) during training, allowing the network to learn how to reduce the response from irrelevant channels in the testing stage. Through this approach, we expect to approximate the way of manually removing irrelevant channels in Fig. 3(b) as much as possible. > Q1: Minor: Have you compared DPA to other regularlization methods that lead to greater sparsity? Thank you for your constructive suggestion. Yes, our paper compares Softplus, SiLU, ReLU, and GELU, which can result in sparse activations. In addition, we also compare DPA to Dropout, which leads to greater sparsity. Our response to W3 presents the results of this comparison, showing that DPA performs better than Dropout.	Rebuttal 1: Rebuttal:   ## Global Response We thank all the reviewers for their time and constructive feedback, providing us with valuable insights into the areas that require improvement. We have meticulously addressed each reviewer's concerns through our comprehensive responses. In this global response, we would like to reiterate the important and common issues raised by the reviewers. ### *Fairness in comparison* To maintain fairness in comparison, we have strictly ensured that each experiment in a set of comparative studies used the same public training settings. The numerical results on Transformers, CNNs, and other architectures can fairly demonstrate the effectiveness of our proposed DPA method. ### *Impact of hyperparameters* For the proposed DPA method, the impact of hyperparameters $m$, $λ$, and $τ$ on CIFAR-100 with ViT-Tiny are presented in the original paper Sec. A.3 and Fig. 6-8. The $τ$ has been verified to be optimal at zero. The network's performance is not sensitive to $m$ and $λ$ when their values are not extreme. The original intention of Sec. A.3 was to analyze the impact of hyperparameters on model performance. We apologize for the confusion caused by the misleading title of Sec. A.3. We would like to clarify that we did not select hyperparameters for each experiment, as this process is quite time-consuming. This also highlights the fairness in comparison. The consistent performance gains brought by our method also indicate the insensitivity/generalizability of the hyperparameter values. Here is our detailed explanation: - For hyperparameter $m$, we have only analyzed it on CIFAR-100 with ViT-Tiny and found that $m$=0.9 performed the best. Consequently, for the rest of the experiments presented in the paper, we empirically set the $m$ to 0.9 without too much consideration. - For hyperparameter $λ$, we have only analyzed it on CIFAR-100 with ViT-Tiny, DeiT-Tiny, and TNT-Small. As shown in Fig. 7 of the original paper, too large $λ$ can result in negative side effects, and one thing is for sure: smaller $λ$ values do not hurt accuracy. Therefore, for the majority of our experiments (CaiT & PVT on CIFAR-100, and all the models on CIFAR-10 & ImageNet-{100,1K}), we did not select $λ$ but empirically used the default $λ$ as 1 (see our paper Lines 484-485). - For hyperparameter $τ$, it has been verified to be optimal at zero in the original paper. Therefore, we set the $τ$ to 0 across all the experiments. Notably, the performance of the proposed DPA method might be further improved if we were to conduct hyperparameter search on $m$ and $λ$ for each experiment. ### *Benefits of sparse activations* In this paper, we first conducted experiments (see our paper Fig. 2) to validate that each category is only correlated with sparse and specific channels in ANNs. Combined with the patterns of the activation response distribution (Fig. 3(a)), we conjectured that constructing sparse activations based on the above observations might be beneficial for ANNs in eliminating irrelevant/redundant features. Subsequently, we supported our conjecture through a review of relevant literature and extensive experiments, demonstrating that sparse activations do provide advantages to ANNs. The sparse activation is the goal of this study, which can be directly supported by the confirmatory experiment, as shown in Fig. 3(b). By manually removing the irrelevant channels for each category (which is equivalent to forcibly constructing sparse activations), there is a substantial improvement in the training accuracy. Moreover, the observation in Fig. 2 indicates that each category is only correlated with sparse and specific channels in ANNs. The proposed DPA effectively denoises redundant channels while not affecting relevant channels, resulting in sparse representation and performance enhancements. All of these collectively validate the beneficial role of sparse activations in ANNs.   We are committed to upholding a higher standard in our revised manuscript. Finally, we would like to express our sincere gratitude again to all the reviewers for their meticulous review and constructive feedback on our manuscript, which will undoubtedly enhance the quality of our work.	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
How to Solve Contextual Goal-Oriented Problems with Offline Datasets?	Accept (poster)	Summary: This paper proposes a novel method to solve CGO problems and proves CODA can learn near-optimal policies without the need for negative labels with natural assumptions. In addition, sufficient experiments prove the effectiveness of the proposed method. Strengths: 1. The contribution of the proposed method is interesting. 2. Sufficient experiments prove the effectiveness of the proposed method. 3. Theoretical analysis is sufficient. Weaknesses: None Technical Quality: 4 Clarity: 4 Questions for Authors: None Confidence: 2 Soundness: 4 Presentation: 4 Contribution: 4 Limitations: None Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thanks for your review and the acknowledgement.	Summary: This paper focuses on a new RL task: Contextual Goal-Oriented Offline RL task. This task considers an offline goal-context pair dataset and an unsupervised transition dataset. To address this task, in this paper, Contextual goal-Oriented Data Augmentation (CODA) is proposed to augment a new state $s^+$ and new action $a^+$ representing the goal within the context is achieved with reward as 1. The theoretical analysis is proposed to demonstrate CODA's capability to solve CGO problems. Strengths: 1) This work focuses on a new task where goal and context are related. I am not familiar with the literature of Contextual Goal-Oriented (CGO). Personally, I think this task is interesting. 2) CODA methods show good performance on empirical evaluations. Weaknesses: 1) In the Related Work section, some methods to solve Goal-conditioned RL are listed. Can these methods be used to solve this problem? If yes, how do these methods perform in the empirical studies? What is the relation between these methods and the used baseline methods? 2) This paper proposes a data augmentation method. Can this method be incorporated with other Goal-conditioned RL approaches to achieve better performance, such as relabeling? 3) The proposed data augmentation method is straightforward. It uses goal and context to label states and actions. Why such data augmentation can achieve such impressive results? More discussions are expected. 4) More datasets and real-world scenarios can be used to further demonstrate the effectiveness of this method. Technical Quality: 3 Clarity: 3 Questions for Authors: Some questions are listed in the Weaknesses. The final score will be updated when these questions are answered. Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: There is no clear negative societal impact. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We sincerely appreciate your valuable comments. We found them extremely helpful in improving our draft. We address each comment below. ### 1. “Can goal conditioned methods be used to solve this problem”: There is no straight-forward way to directly apply typical goal-conditioned methods to our offline CGO setup in general, since the relationship between contexts and goals is unknown here. On the other hand, the traditional GO setting (equivalently a CGO special case where context = goal) essentially assumes the relationship between contexts and goals is known; and algorithms like Hindsight Experience Replay (HER) critically relies on this assumption for the relabeling. Nonetheless, we still try to show how goal-conditioned RL methods might perform in this more general setting. We do this by incorporating a goal-prediction baseline, which first learns to predict goals given a context using the context-goal dataset, and then uses the goal-conditioned policy learned from the dynamics-only dataset with HER (L45). We presented the result of the “Goal Prediction” baseline in Table 1, 2, 3. ### 2. “Can this method be incorporated with other Goal-conditioned RL approaches to achieve better performance, such as relabeling”: As mentioned above, due to the missing relationship between goals and contexts, goal-conditioned RL methods cannot be directly applied. We do highlight HER is used in our Goal Prediction baseline to learn the goal-conditioned policy (L307). There is no way to directly relabel contexts in our offline CGO setup since the context is not available in the dynamics dataset, and we only have a fixed and limited context-goal dataset. Similarly, for other goal conditioned RL approaches, we cannot directly use that due to missing context labels for the states in the dynamics dataset. ### 3. Why such data augmentation can achieve such impressive results? As discussed in our introduction, the baseline methods all have their drawbacks (L44): For the goal prediction methods, the predicted goal might not always be feasible given the initial state. For the reward prediction baseline, it does not make good use of the goal-oriented nature of the CGO problems, and it might be challenging to infer reasonable reward for any context-goal pair, given only with positive data is available during training (context-goal dataset). On the other hand, in CODA, we carefully design the augmented MDP structure which our data augmentation method relies on. In this way, 1) we do not need to deal with the challenges of predicting the feasible goals in this augmented MDP like goal prediction methods and 2) we do not need to handle the missing context label problem in this augmented MDP. Notice that this augmented MDP equivalent to the original MDP. This is why this augmentation method is effective despite its simplicity: it fully makes use of the CGO structure of the problem to circumvent the drawbacks in other baseline methods. ### 4. More datasets and real-world scenarios: We acknowledge that having more datasets would be better. However, our main goal of this paper is to formulate the CGO setup since it hasn’t been formally studied in the literature, and to show it can be probably solved with commonly available offline datasets, as demonstrated by the proposed method. Our controlled experiments, although limited to the same simulator, are designed to cover the spectrum of different CGO setups listed in the taxonomy given in Section 6 (L265). We think this is a sufficient first milestone to showcase the effectiveness of the proposed method. Testing on real world datasets is important future work but is out of the current scope of this paper. We hope our response resolves all the concerns in your review and please feel free to let us know if you have further questions. If our responses have addressed your concerns, please kindly consider raising the score. Thank you! --- Rebuttal Comment 1.1: Comment: Dear reviewer, thank you again for the review and we hope our rebuttal address your concerns. We would greatly appreciate your feedback and please feel free to let us know if you have any other questions in the discussion period!	Summary: The paper combines an (unlabeled) dynamics dataset of trajectories, and a (labeled) context-goal dataset in an offline setting to create a combined MDP(Markov Decision Process). They do it by augmenting the dynamic dataset to have fallacious action to the terminal state with reward 1 on goal states given context c. All other states have a reward of 0. They also give a theoretical proof of their methodology. Strengths: The paper presents a general solution that can be applied to a wide range of problems within the field; the findings and methods have broad applicability, increasing their relevance and potential impact across various contexts. The authors have validated their methodology through comprehensive proofs and empirical evidence (to some extent). This thorough validation provides a solid foundation. Weaknesses: -Limited novelty, the paper provides a way to combine two types of datasets, but the methodology it provides is trivial -Paper does provide a mathematical proof of the technique, but the technique itself is straightforward enough that the proof is trivial given that it builds on baseline proof -Not adequate experimentation -Experimentation on a very simple problem set -The paper needs more polishing (e.g., MDP acronym used in the abstract without initializing, Line 8: "outperform" should be "outperforms"; Line 177: "fictious" should be "fictitious". etc.) Technical Quality: 3 Clarity: 1 Questions for Authors: See the weakness section Confidence: 2 Soundness: 3 Presentation: 1 Contribution: 2 Limitations: NA Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for the review. We address each comment below. ### 1. Limited novelty: Could you provide specific reasons why the novelty is limited? We respectfully disagree that our method is trivial since we carefully design the augmented MDP structure and the data augmentation method such that 1) we do not need to deal with the challenges of predicting the feasible goals in this augmented MDP and 2) we do not need to handle the missing context label problem in this augmented MDP. This is why this augmentation method is effective despite its simplicity: it fully makes use of the CGO structure of the problem to circumvent the drawbacks in other baseline methods. Simplicity is not a drawback and does not equal lack of novelty. ### 2. Proof is trivial: A major aspect of our proposed algorithm is the reduction of the CGO problem to an offline RL problem. While the overall template of the proof will naturally follow the proof structure of the underlying base offline RL analysis, our proof is based on the novelly designed augmented MDP (which is a goal-conditioned MDP). This step is critical, as no existing proof can show the effectiveness of the offline goal-conditioned RL if only positive data (context-goal pairs in our case) is available, which is our offline CGO setup. In order to prove our results, we use a careful reformulation of the Bellman equation of the augmented MDP and construct an augmented value function and policy class in the analysis using the CGO structure. As such, we respectfully disagree that the proof is trivial. ### 3. Not adequate experiments: Could you specify the reasons? In our environments, we use different dynamics datasets in different mazes, and for each maze we have three different context-goal setups representing the different CGO setups in the spectrum discussed in Section 6 (L265). We show that our method works well and consistently outperforms the baseline methods in these different scenarios. Moreover, the main goal of this paper is to formulate the CGO setup since it is not formally studied in the literature, and as the first milestone to show it can be solved with commonly available offline datasets, which the proposed method demonstrates. ### 4. Typos: Thanks for pointing them out, and we will fix them in the revised draft. We hope our response resolves all the concerns in your review and please feel free to let us know if you have any other questions in the discussion period. If our responses have addressed your concerns, please kindly consider raising the score. Thank you! --- Rebuttal 2: Comment: Dear reviewer, thank you again for the review and we hope our rebuttal addresses your concerns. We would greatly appreciate your feedback and please feel free to let us know if you have any other questions in the discussion period!	Summary: This paper proposes a simple action-augmented MDP formulation for contextual goal-oriented problems in an offline RL setting. They show that their action-augmented MDP has a regret that is equivalent to the original MDP and any policy can be converted interchangeably without changing the regret. Along with theoretical justification, they also show that better performance compared to other reward prediction and goal-oriented RL methods in the experiments. Strengths: - The paper introduces and solves an interesting and challenging problem of context-defined goal-oriented RL policy learning, and do so without having access to labeled samples for the task. - The authors propose a very effective and clever solution for converting existing dynamics and context-goal datasets to first create learning data, and then create augmented MDP policies while establishing learnable guarantees using only positive data (Th 5.4). - The empirical performance is strong and generally outperforms other baselines. Weaknesses: - I am unsure how well the theoretical assumptions and setting of the paper transfers to more real world and larger-scale environments. - The empirical evaluation has been only performed using a single environment, so the generalizability of the method to more diverse settings is unclear. Technical Quality: 3 Clarity: 3 Questions for Authors: - I am curious as to why is there a wide performance variance in Tables 1,2,3 between different env or method. Specifically, why is CODA significantly outperforming baselines in few settings while only providing marginal benefits in few others. - The poor performance of goal-oriented RL methods in basic setting in Table 1 is also surprising, I request the authors to add more insights into this either in the rebuttal or in the final version. Confidence: 2 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The significant limitations have been delineated well in Sec 6.4. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We sincerely appreciate your valuable comments. We found them extremely helpful in improving our draft. We address each comment in detail below. ### 1. “How well the theoretical assumptions and setting of the paper transfers to real world”: For the assumptions, our assumption 5.1 and 5.2 are general assumptions about the expressiveness of the value functions which are standard in offline RL theories. In plain words, we need the value function approximators to be expressive enough to effectively perform approximate dynamic programming in offline RL. For the offline CGO setup, we assume a dataset of dynamics data and a dataset of context-goal examples, which are commonly available. Notice the dynamics data is task agnostic and the context-goal examples do not require expert demonstrations. For example, in the example in Introduction where we instruct the truck to feasible warehouses, we only need the logged data of truck driving without any labels (dynamics data), and a set of instructions (contexts) and the corresponding warehouses (goals). We don’t need the expert trajectories of how the trucks can be navigated under different instructions (contexts) which allows commonly available dataset to be used in our setup. ### 2. “The generalizability of the method to more diverse settings is unclear”: While all the experiments are done using the AntMaze simulators, we specifically design each experiment to reflect the diverse scenarios that offline CGO problems can cover. In Section 6 (L265) and Fig 2, we propose a taxonomy of offline CGO problems based on context-goal relationship with an increasing complexity, and we design experiments to cover all these scenarios. Moreover, for each scenario, we use various dynamics datasets and different mazes. The experimental results show the proposed algorithm can consistently solve all these different scenarios. We used the same AntMaze domain throughout these experiments so that we can study – through controlled experiments – the effects due to different data relationships in different CGO settings. If we were to implement one setup from Fig 2 in one domain and another setup from Fig 2 in another one, there may be additional confounders due to the domain change. We hope these results provide good evidence to show the generalizability of our method to different CGO settings. Nonetheless, we acknowledge experiments with more realistic datasets and environments would be interesting future work. ### 3. “Why is there a wide performance variance”: We want to first highlight that Table 1, 2, 3 are from different context-goal relationships. Despite being implemented via the same simulator (of the same dynamics), they mean totally different learning problems, so they should not be directly compared. We should only compare algorithms within the same table, not across tables. For each table, we provide the results of training with oracle reward, which is the skyline reference performance with respect to each dynamics dataset. The difference between that skyline and the other baselines is the room for improvement. Sometimes the headroom can be small, e.g., some coverage assumption is met like all goals in the dataset are feasible or the context-state reward can be easily learned from the dataset. In these tables we see that our proposed approach gives consistent improvement over baselines whenever possible. We will better clarify how the tables should be interpreted in the revision. ### 4. “Poor performance of goal prediction baseline in Table 1”: The reason is that as shown in Figure 2(a), the goal area for this setup is very small, thus the number of goal examples in the context-goal dataset is very limited, thus providing difficulty for learning the goal distribution given context for goal prediction methods since it needs to learn to generate the goals first and then sample the goal as the condition. We hope our response resolves all the concerns in your review and please feel free to let us know if you have any other questions in the discussion period. --- Rebuttal Comment 1.1: Title: Thanks for the response Comment: I thank the authors for taking time and drafting the response to my queries, I will keep my rating of accept. Also, I am really sorry at the set of reviews you got for this submission, it is indeed frustrating when avg reviewer confidence is 2.25/5 which only shows severe mismatch between the reviewer assignments and expertise. I wish you better luck at least in a next venue.	null	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Learning to Handle Complex Constraints for Vehicle Routing Problems	Accept (poster)	Summary: This paper introduces a novel framework called Proactive Infeasibility Prevention (PIP) to enhance the capability of neural methods in addressing complex Vehicle Routing Problems (VRPs) with interdependent constraints, such as the Traveling Salesman Problem with Time Window (TSPTW) and TSP with Draft Limit (TSPDL). The authors propose integrating the Lagrangian multiplier method and preventative infeasibility masking into the solution construction process to improve both the feasibility and optimality of solutions. Additionally, an enhanced version, PIP-D, employs an auxiliary decoder to predict infeasibility masks, potentially reducing computational costs during training. The paper presents extensive experiments demonstrating the effectiveness of PIP in reducing infeasible rates and improving solution quality. Strengths: The PIP framework represents an innovative approach to integrating constraint awareness and preventative measures within neural VRP solvers. The use of an auxiliary decoder for predicting infeasibility masks is a good try. The paper provides extensive empirical validation demonstrating the effectiveness of the proposed methods. The paper is well-organized and clearly presents the problem, proposed solutions, and experimental results. The use of figures and tables effectively supports the textual content, aiding in the reader's comprehension. Weaknesses: The ideas of using the Lagrangian multiplier [1] and preventive mask functions[2] are not new. The code is not provided, which limits the reproducibility of the work. It's not clear how to obtain the training label of infeasibility mask. The computation could be expensive to get a global and accurate infeasibility mask. Some related work from recent AI and OR fields are missing. The paper could benefit from additional experiments on a wider range of VRP variants and real-world datasets to further validate the generalizability of the proposed methods. The presentation could be improved by providing more context on how this work relates to and advances the current state-of-the-art in neural VRP solvers. The computational efficiency of the PIP-D framework should be more thoroughly analyzed, especially in terms of how it scales with problem size. The paper may lack a deeper discussion on the theoretical underpinnings of the proposed methods and their potential implications for the broader field of combinatorial optimization. [1] Qiaoyue Tang, Yangzhe Kong, Lemeng Pan, and Choonmeng Lee. Learning to solve soft-constrained vehicle routing problems with lagrangian relaxation. arXiv preprint arXiv:2207.09860, 2022. [2] Hou, Qingchun, et al. Generalize learned heuristics to solve large-scale vehicle routing problems in real-time. The Eleventh International Conference on Learning Representations. 2023. Technical Quality: 3 Clarity: 3 Questions for Authors: How does the PIP framework generalize to other VRP variants beyond TSPTW and TSPDL? Can the authors provide more insights into the computational efficiency of PIP-D, especially regarding its scalability? Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: The authors have acknowledged some limitations, such as the potential inability of PIP to improve performance on all backbone solvers and VRP variants. However, the paper could benefit from a more detailed discussion on the robustness of the PIP framework when faced with different levels of constraint hardness in real-world scenarios. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for constructive comments and acknowledging that our PIP is innovative, and extensively validated, and our paper is well-organized and clear. We understand the need for more discussion on related works, computational costs, and code release. We hope the response below and the added new experiments would clarify any misunderstandings and concerns. --- [Discussion on [1][2]] Thank you for pointing out the references. We have reviewed them carefully and would like to clarify that our proposed PIP is mostly distinct from works [1] and [2], which correspond to [8] and [51] in the original paper, respectively. - Regarding [1]: While both are early attempts to incorporate Lagrangian multiplier into NCO, [1] is designed for iterative solvers for soft-constrained VRPs, whereas PIP is for constructive solvers for hard-constrained VRPs. Moreover, our primary motivation for using the Lagrangian multiplier is to enhance our model's initial constraint awareness. Unlike [1], we argue and show that using Lagrangian multiplier alone is less effective for complex constraints. To address this, we propose our novel PIP and PIP-D, which effectively overcome this weakness and improve overall performance. - Regarding [2]: While both use masking to prevent infeasible solutions, our preventive infeasibility (PI) masking differs from the "global mask function" in [2]. Firstly, although [2] shows the effectiveness of their global masking for a specific case of CVRP with limited vehicles, our PI masking is technically different and serves as a more generic framework to address complex VRP variants where feasibility masking is NP-hard. Also, we employ an auxiliary decoder to predict PI masking, and our PIP has been validated on complex constrained variants like TSPTW and TSPDL, as well as on various autoregressive and non-autoregressive neural solvers such as AM, POMO, and GFACS, demonstrating broader applicability. Moreover, [2] primarily focuses on scalability, whereas our work emphasizes constraint handling. We note that our work can be coupled with [2] in future work, and we will discuss more in the revised paper. - Lastly, as acknowledged by Reviewer #DEtT, we are among the first to address the complex interdependent constraints that make masking NP-hard, a point not covered in existing NCO works like [1][2]. --- [Code Release] As promised in line 276, we will make our code, pre-trained models, and the used data publicly available on GitHub. Following the rebuttal guidelines, we have forwarded our code to the Area Chair. --- [How to obtain the training label] Yes, getting global and accurate masks is expensive (as mentioned in lines 139-150). Hence, in our PIP, we employ a one-step approximation to balance computational costs without iterating over all future possibilities which is NP-hard (see results on such balance in Table R3 and R4 of the attached PDF). The training label is such one-step masking, determined by evaluating whether selecting a candidate node would lead to irreversible future infeasibility for the remaining unvisited nodes in the next step. If so, the candidate is considered infeasible at that step. Detailed examples and descriptions are available in lines 192-195 and Appendix A.3. --- [More literature review] We have included most recent work from NCO field and will add more from OR field. Any suggestions are warmly welcome! --- [Additional experiments] - Regarding real-world datasets, we have evaluated our PIP(-D) to unseen real-world instances in benchmark dataset [76] with different scales, distributions and constraint hardness in Appendix D.6 (Table 7). Additionally, we conducted extensive experiments on complex variants like TSPTW and TSPDL, covering various levels of constraint hardness (Easy, Medium, Hard). Results suggest that our PIP(-D) can generalize to real-world datasets with unknown constraint hardness. - Regarding other VRP variants, we follow your suggestion and explore the application of our PIP framework (Lagrangian multiplier, PI masking and the auxiliary decoder) to VRPs with various complex constraints, such as VRPBLTW (VRP with constraints of capacity, backhaul, duration limit, and time window). We found that in such variants PI masking is less important since we can obtain the masking easily at each constructive step, but the Lagrangian multiplier and the auxiliary decoder still have effects. The results demonstrate that our PIP framework significantly enhances solution quality on VRPBLTW-50 (Our gap 1.80% vs. POMO's gap 9.17%, see Figure R1 for details). - Lastly, our PIP has potential beyond VRPs, such as in job shop scheduling, where operations require a specific order. PIP can proactively prevent infeasibility in these cases, and we leave them as future work. --- [How our PIP advances the SOTA] Firstly, our PIP is generic to boost an existing SOTA constructive neural VRP solver to enhance its capability of constraint handling. We have verified our effectiveness on both autoregressive (AM, POMO) and non-autoregressive (GFACS) solvers. Additionally, we have conducted newexperiments by further coupling our PIP with LKH3 (see `General Response #2` for more details). --- [Computational efficiency] Please kindly refer to our `General Response #1`. --- [Theoretical analysis] We acknowledge that the NCO domain primarily relies on empirical results and often lacks theoretical support for most of published papers. Our findings are backed by extensive results, demonstrating empirical superiority with significant improvements in infeasibility rates and solution quality. Nevertheless, we provide some more rigour analysis for our PIP, please refer to the second response to Reviewer #azSu. --- [Robustness under different hardness] Thanks for the suggestion. We have discussed the mentioned experiments in benchmark datasets in Appendix D.6 (Table 7). We will add more analysis. --- Rebuttal Comment 1.1: Comment: Dear Reviewer Seke, Thank you once again for your insightful comments and helpful suggestions. As the deadline for author-reviewer discussions is approaching, we would greatly appreciate it if you could take a moment to review our rebuttal. Please let us know if you have any further questions or concerns. Thank you very much for your time. Best, Authors --- Reply to Comment 1.1.1: Comment: Dear Reviewer Seke, #### The discussion period is approaching its end (in less than 12 hours). Please kindly let us know if our response resolves your concerns. Regarding your concern of our code release, we have also forwarded our code to the Area Chair. We would greatly appreciate it if you could give us any feedback. #### Thank you again for your valuable comments and suggestions. #### Best Regards, Authors	Summary: This paper addresses the challenge of predicting feasible solutions for VRPs with complex constraints. It introduces two novel methods to enhance existing algorithms: i) integrating constraints directly into the optimization objective using the Lagrangian Multiplier Approach; ii) PIP framework, which proactively excludes potential nodes during solution prediction to prevent future infeasibility. Besides, a neural decoder PIP-D is proposed to reduce computational complexities. Experiments on two VRP variants demonstrates significant advancements in feasible prediction compared to the baselines. Strengths: 1. The paper is well-structured with a logical flow. 2. The feasibility issue investigated are critical, and the proposed PIP framework address it well. 3. Extensive experiments and detailed clarifications are made to demonstrate effectiveness. Weaknesses: Major concerns: - Computational cost. From the numerical results, PIP incurs approximately twice the computational time compared to baseline neural solvers (e.g., AM and POMO). Despite attempts to mitigate this by introducing neural decoder PIP-D, the reported results don't exhibit a corresponding reduction in time. The authors may clarify this more. - Lack of comparisons between different step numbers in PIP. The authors only conducted experiments of one-step PIP. It is crucial to include comparisons with different step numbers to assess the impact of the "looking ahead" masking strategy. For instance, additional results from zero-step PIP (directly masking nodes violating constraints) and two-step PIP. Here, I emphasize zero-step PIP since its masking strategy differs from the ones of the baseline neural solvers, as I understand it. - Only two TSP datasets are considered. The paper is titled "Learning to Handle Complex Constraints for Vehicle Routing Problems (VRPs)", however both datasets are variants of TSPs. The key difference between VRPs and TSPs is capacity constraints. I would like to see VRPs with various complex constraints (such as time windows, pick-up and delivery, split delivery etc.), otherwise, the authors should change the title and consider more TSP variants. - Heuristic algorithms for TSPs and VRPs with complex constraints have been well developed (such as LKH3). I do not see that the proposed algorithm outperforms the state-of-the-art heuristic algorithms (not neural algorithms). Technical Quality: 3 Clarity: 3 Questions for Authors: - What's the time cost of PIP? Is it $time(POMO^+PIP)$ - $time(POMO^)$? - What are the masking strategies of baselines AM and POMO? Do they only mask visited nodes, ignoring other constraints? - What is the stopping criteria for each algorithm? I know that running LKH3 for 1 second would often generate almost optimal solutions to TSPs with 100 customers, hence there is no need to run it for 14 hours, as shown in Table 2. I recommend the authors use the same time limit (and usually a few seconds for small-sized TSPs considered in this paper) for each baseline algorithm and even present the progress of the objective value for the best solutions found by each algorithm. This could ensure a fair comparison among them. Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: The author has discussed the limitations in section 6: one potential limitation is that it may not improve performance on all backbone solvers and all VRP variants. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We appreciate the reviewer’s kind effort in providing insightful and detailed feedback. We are delighted that the reviewer finds our work to be novel, well-structured, and effective in addressing feasibility issues. We have conducted additional experiments to address your comments and hope the following response and results will clear any remaining concerns. --- [Computational cost (Q1, W1)] Thank you for your valuable comment! We apologize for any confusion. Please refer to our `General Response #1` for detailed discussion on computational costs. In summary, while our PIP introduces some unavoidable overhead to the backbone model, this is offset by its strong effectiveness. As shown by our additional results in Table R1 of the attached PDF, even with extended inference times, existing baseline methods still struggle with constraint handling and may fail to find any feasible solutions. In addition, we have employed strategies like one-step PI masking, an auxiliary PIP-D decoder, and a sparse strategy to further mitigate the costs. We now provide more responses: - PIP does not always double the computational time of the backbone solvers. For instance, on small-scale TSPTW-50, POMO* takes 13s while POMO+PIP takes a similar time of 15s; on larger-scale TSPTW-500, we can leverage the sparse strategy to reduce the overhead - as shown in Table 3, our GFACS+(PIP; PIP-D) demonstrates similar inference times to GFACS* (6.5m vs. 6.4m), while significantly reducing infeasibility (57.81% vs. 1.56%; 0.00%) and improving solution quality (21.32% vs. 15.04%; 11.95%), showing great efficiency. - The auxiliary decoder aims to approximate the one-step PI masking to avoid its frequent calculation during training. Results show that PIP-D significantly reduces the training time (e.g. by 1.5x on TSPTW-50) compared to PIP. As the inference overhead is rather insignificant than other baselines, we employ the complete one-step PI masking to guide the construction process. - For Q1 - Yes, $T_{PIP}\\approx T_{POMO∗+PIP}- T_ {POMO∗}$, which results from the acquisition of the PI masking. Detailed examples and descriptions are available in lines 192-195 and Appendix A.3. And please kindly see our next response for discussions of computational time balance. --- [PIP with different step numbers (Q2, W2)] Insightful comment! Yes, zero-step PIP differs from the baselines. Following the suggestion of the reviewer, we have further supplemented this by conducting new experiments on PIP and PIP-D with different step numbers. In Table R3, R4 attached in the PDF under `General Response`, we gather the results (solution feasibility and quality) and the inference time for different PIP steps. Results suggest that zero-step PIP saves some time but suffers from inferior performance, while the two-step PIP improves performance slightly but is computationally expensive. However, one-step PIP balances these trade-offs effectively. We will further clarify this in the revised paper. --- [Apply PIP to more VRPs with various complex constraints (W3)] Thank you for the suggestion. We agree that the title "Travelling Salesman Problems" might be more appropriate for our original paper. Nonetheless, we plan to follow the reviewer's suggestions and further explore applying our PIP framework to VRPs with more complex constraints, such as VRPBLTW (with capacity, backhaul, duration limit, and time window constraints). Results on VRPBLTW-50, presented in Figure R1 of the PDF under `General Response`, show that our PIP framework significantly enhances solution quality for VRPs with complex constraints (our gap 1.80% vs. POMO's gap 9.17%). While our PIP framework may not be a silver bullet for improving performance across all VRP variants, it has been successfully applied to variants like TSPTW and TSPDL, covering various levels of constraint hardness (Easy, Medium, Hard). Moreover, we believe that our PIP framework has potential applications beyond VRPs, such as in job shop scheduling, where operations need to be completed in a specific order and infeasibility can be proactively prevented. We plan to explore these applications as future work and will discuss them further in the revised paper. --- [Comparison with LKH3 with time limit (Q3, W4)] Thanks for the insightful comment. We follow your constructive suggestion and add Table R2, Figures R2 and R3 (presenting the progress of the objective value and infeasible rate over different inference time) in the attached PDF under global response. Details are discussed in our `General Response #2`. To sum up, we agree with the reviewers that LKH3 can generate near-optimal solutions for TSP-100 within a few seconds. However, *when given a limited budget, LKH3 performs significantly worse than our POMO\+PIP-D on the studied complex variants.** As shown in Table R2, while LKH3 is powerful with state-of-the-art quality, its advantage diminishes with limited time. Our POMO+PIP-D reduces the infeasibility rate from 53.11% to 6.28% with 0.9s time per instance, compared to LKH3 with 5.1s time. To leverage the strengths of both approaches, we conducted an additional experiment using our PIP-D to provide better initial solutions for LKH3. This further reduces the infeasibility rate from 53.11% to 0.21% and improves the objective from 51.65 to 51.25 within only a few seconds. Notably, initializing LKH3 with POMO+PIP-D outperforms the default LKH3 setup (10,000 trials), achieving slightly better solution quality while using only 27% of the inference time (9 hours vs. 1.4 days). Regarding the stopping criteria for each algorithm (i.e., to restrain its runtime): - For LKH3, we set a fixed number of max trials following the conventions in NCO; - For neural algorithms, we - sample a pre-set number of solutions ($N_s$) for each instance: $N_s=8$ for POMO series models and $N_s=1280$ AM series models; - predefine 100 ants and 10 pheromone iterations for GFACS. --- Rebuttal Comment 1.1: Comment: Thanks for addressing my comments. I still think the comparison between the proposed approach and LKH3 is not comprehensive enough (e.g., easy/medium/hard instances with more than 100 nodes, and the 500-customer instances in Section 5.2; with the same time limit as the proposed approach) since LKH3 is the most important baseline algorithm in my opinion. For example, from Figure R3, we may conclude that, for those hard instances, the proposed approach could obtain high-quality solutions quite fast but LKH3 could obtain solutions of better quality with a relatively longer time. But from Section 5.2, if we run LKH3 for a few minutes (say 6.5 min), we may already achieve a very small gap (e.g., smaller than 11.95%). That is why I said the comparison in the previous manuscript is not fair. --- Reply to Comment 1.1.1: Title: Thanks for the comments and please kindly check our further clarifications. Comment: Thank you for the discussion and insightful comments! We are pleased to have addressed most of your concerns. Regarding the remaining concern about a comprehensive comparison between our PIP and LKH3, we have provided results on Hard TSPTW-100 in the previous rebuttal given the constraints of the rebuttal period and PDF page limit. Nevertheless, we understand that this may not be comprehensive enough. Following your suggestion, we now conducted additional experiments using LKH3 with the same time limits as our proposed approach across various instance hardness levels (Easy/Medium/Hard) and scales (50/100/500 nodes). The time limits were set in two ways for comprehensive evaluation: similar $\underline{\text {instance inference time}}$ without parallelization (new Tables R5, R7, and R9) and similar $\underline{\text {total inference time}}$ with parallelization (new Tables R6 and R8). We hope these new empirical results offer a more comprehensive picture. [A. For $n=50$ and $100$] Firstly, we follow your suggestion and only allow LKH3 to run a similar inference time as our approach $\underline{\text {per instance}}$. As shown in Table R5, POMO+PIP(-D) outperforms LKH3 on Hard datasets, while maintaining competitive results on Easy and Medium datasets. While comparing per-instance time might seem fair for CPU-based LKH3, ignoring parallelization could disadvantage GPU-based solvers (thus not fair for GPU-based solvers). To further explore this, we conducted another experiment but with the similar $\underline{\text {total inference time}}$ limit across both methods. Results, in Table R6, show that our POMO+PIP(-D) performs consistently better than LKH3 across most of the hardness. We recognize the challenge of achieving absolute fairness when comparing CPU-based and GPU-based solvers, and we note that total time comparison is a common practice in most existing NCO papers (e.g. those in [1-8]). We appreciate the reviewer for providing such an insightful comment, which highlights the need for developing new metrics that facilitate fairer comparisons between neural and traditional solvers—a promising direction for future work. Moreover, we agree with the reviewer that LKH3 is indeed a robust and well-developed solver. However, neural solvers offer unique advantages, such as highly efficient parallelization and reduced reliance on hand-crafted heuristic rules [9]. To leverage the strengths of both approaches and further reveal the practical usage of our method, we explored a hybrid method that combines our PIP(-D) framework with LKH3. Similarly, we provide the comprehensive experimental results conducted across various instance hardness levels (Easy/Medium/Hard) and scales (50/100/500 nodes). The results, as shown in Table R7 and R8, reveal that LKH3’s search efficiency can be significantly enhanced when initialized with solutions from our PIP(-D) framework. [B. For $n=500$] As shown in Table R9, we acknowledge that our PIP(-D) implemented on GFACS* currently underperforms LKH3. However, the integration of GFACS+PIP(-D) with LKH3 has already made significant strides in closing this performance gap, particularly in enhancing feasibility handling compared to using the GFACS backbone alone. We would like to clarify that the primary motivation for these experiments here is to demonstrate the scalability and broad applicability of our PIP framework in enhancing various backbone neural models. While we acknowledge that PIP may not elevate every model to state-of-the-art performance, which is both reasonable due to _“No Free Lunch”_, our goal is to show its potential to significantly boost performance across a wide range of neural models. --- Rebuttal 2: Title: Further results for comprehensive comparison (1/4) Comment: Table R5: Results on LKH3 with the similar $\underline{\text {instance inference time}}$ limit as POMO+PIP(-D). \| \| \| \| $n=50$ \| \| \| $n=100$ \| \| \|:------------:\|:--------------:\|:-------------------------------:\|:--------:\|:----------------:\|:-------------------------------:\|:--------:\|:----------------:\| \| Hardness \| Method \| $\underline{\text{Inst. Time}}$ \| Obj. \| Inst. Infsb% \| $\underline{\text{Inst. Time}}$ \| Obj. \| Inst. Infsb% \| \| Easy \| LKH3 (Default) \| 27s \| 7.31 \| 0.00% \| 49s \| 10.21 \| 0.00% \| \| Easy \| LKH3 \| 0.37s \| 7.35 \| 0.00% \| 0.9s \| 10.37 \| 0.00% \| \| Easy \| POMO+PIP \| 0.38s \| 7.50 \| 0.00% \| 0.9s \| 10.57 \| 0.00% \| \| Easy \| POMO+PIP-D \| 0.38s \| 7.49 \| 0.00% \| 0.9s \| 10.66 \| 0.00% \| \| \| \| \| \| \| \| \| \| \| Medium \| LKH3 (Default) \| 40s \| 13.02 \| 0.00% \| 1.0m \| 18.74 \| 0.00% \| \| Medium \| LKH3 \| 0.37s \| 13.06 \| 0.00% \| 0.9s \| 19.00 \| 0.00% \| \| Medium \| POMO+PIP \| 0.38s \| 13.40 \| 0.90% \| 0.9s \| 19.61 \| 0.19% \| \| Medium \| POMO+PIP-D \| 0.38s \| 13.45 \| 0.65% \| 0.9s \| 19.79 \| 0.03% \| \| \| \| \| \| \| \| \| \| \| Hard \| LKH3 (Default) \| 40s \| 25.61 \| 0.12% \| 3.2m \| 51.24 \| 0.07% \| \| Hard \| LKH3 \| 0.37s \| 25.43 \| 30.60% \| 0.9s \| 49.94 \| 97.28% \| \| Hard \| POMO+PIP \| 0.38s \| 25.66 \| 2.67% \| 0.9s \| 51.42 \| 16.27% \| \| Hard \| POMO+PIP-D \| 0.38s \| 25.69 \| 3.07% \| 0.9s \| 51.39 \| 6.48% \| --- Rebuttal 3: Title: Further results for comprehensive comparison (2/4) Comment: Table R6: Results on LKH3 with the similar $\underline{\text {total inference time}}$ limit as POMO+PIP(-D). \| \| \| \| $n=50$ \| \| \| $n=100$ \| \| \|:------------:\|:--------------:\|:-------------------------------:\|:--------:\|:----------------:\|:-------------------------------:\|:--------:\|:----------------:\| \| Hardness* \| Method \| $\underline{\text{Total Time}}$ \| Obj. \| Inst. Infsb% \| $\underline{\text{Total Time}}$ \| Obj. \| Inst. Infsb% \| \| Easy \| LKH3 (Default) \| 4.6h \| 7.31 \| 0.00% \| 8.5h \| 10.21 \| 0.00% \| \| Easy \| LKH3 \| 26s \| 8.81 \| 99.29% \| 58s \| / \| 100.00% \| \| Easy \| POMO+PIP \| 21s \| 7.50 \| 0.00% \| 48s \| 10.57 \| 0.00% \| \| Easy \| POMO+PIP-D \| 21s \| 7.49 \| 0.00% \| 48s \| 10.66 \| 0.00% \| \| \| \| \| \| \| \| \| \| \| Medium \| LKH3 (Default) \| 7h \| 13.02 \| 0.00% \| 10.8h \| 18.74 \| 0.00% \| \| Medium \| LKH3 \| 25s \| 13.05 \| 39.91% \| 63s \| / \| 100.00% \| \| Medium \| POMO+PIP \| 21s \| 13.40 \| 0.90% \| 48s \| 19.61 \| 0.19% \| \| Medium \| POMO+PIP-D \| 21s \| 13.45 \| 0.65% \| 48s \| 19.79 \| 0.03% \| \| \| \| \| \| \| \| \| \| \| Hard \| LKH3 (Default) \| 7h \| 25.61 \| 0.12% \| 1.4d \| 51.24 \| 0.07% \| \| Hard \| LKH3 \| 22s \| / \| 100.00% \| 54s \| / \| 100.00% \| \| Hard \| POMO+PIP \| 21s \| 25.66 \| 2.67% \| 48s \| 51.42 \| 16.27% \| \| Hard \| POMO+PIP-D \| 21s \| 25.69 \| 3.07% \| 48s \| 51.39 \| 6.48% \| --- Rebuttal 4: Title: Further results for comprehensive comparison (3/4) Comment: Table R7: Results on POMO+PIP(-D)+LKH3 with the similar $\underline{\text {instance inference time}}$ limit as doubled time used in POMO+PIP(-D). \| \| \| \| $n=50$ \| \| \| $n=100$ \| \| \|:------------:\|:----------------:\|:-------------------------------:\|:--------:\|:----------------:\|:-------------------------------:\|:--------:\|:----------------:\| \| Hardness \| Method \| $\underline{\text{Inst. Time}}$ \| Obj. \| Inst. Infsb% \| $\underline{\text{Inst. Time}}$ \| Obj. \| Inst. Infsb% \| \| Easy \| LKH3 \| 0.77s \| 7.33 \| 0.00% \| 1.8s \| 10.31 \| 0.00% \| \| Easy \| POMO+PIP+LKH3 \| 0.77s \| 7.33 \| 0.00% \| 1.8s \| 10.29 \| 0.00% \| \| Easy \| POMO+PIP-D+LKH3 \| 0.77s \| 7.33 \| 0.00% \| 1.8s \| 10.31 \| 0.00% \| \| \| \| \| \| \| \| \| \| \| Medium \| LKH3 \| 0.77s \| 13.04 \| 0.00% \| 1.8s \| 18.89 \| 0.00% \| \| Medium \| POMO+PIP+LKH3 \| 0.77s \| 13.05 \| 0.00% \| 1.8s \| 18.91 \| 0.00% \| \| Medium \| POMO+PIP-D+LKH3 \| 0.77s \| 13.05 \| 0.00% \| 1.8s \| 18.92 \| 0.00% \| \| \| \| \| \| \| \| \| \| \| Hard \| LKH3 \| 0.76s \| 25.56 \| 8.81% \| 1.8s \| 50.66 \| 75.54% \| \| Hard \| POMO+PIP+LKH3 \| 0.76s \| 25.61 \| 0.12% \| 1.8s \| 51.24 \| 1.63% \| \| Hard \| POMO+PIP-D+LKH3 \| 0.76s \| 25.61 \| 0.05% \| 1.8s \| 51.25 \| 0.36% \| --- Rebuttal 5: Title: Further results for comprehensive comparison (4/4) Comment: Table R8: Results on POMO+PIP(-D)+LKH3 with the similar $\underline{\text {total inference time}}$ limit as doubled time used in POMO+PIP(-D). \| \| \| \| \| $n=50$ \| \| \| \| $n=100$ \| \| \|:------------:\|:----------------:\|:---------:\|:-------------------------------:\|:-------------:\|:----------------:\|:------------:\|:-------------------------------:\|:---------:\|:----------------:\| \| Hardness \| Method \| \| $\underline{\text{Total Time}}$ \| Obj. \| Inst. Infsb% \| \| $\underline{\text{Total Time}}$ \| Obj. \| Inst. Infsb% \| \| Easy \| LKH3 \| \| 46s \| 7.57 \| 0.17% \| \| 1.8m \| 11.17 \| 2.54% \| \| Easy \| POMO+PIP+LKH3 \| \| 48s \| 7.48 \| 0.20% \| \| 1.8m \| 10.46 \| 0.01% \| \| Easy \| POMO+PIP-D+LKH3 \| \| 48s \| 7.47 \| 0.32% \| \| 1.8m \| 10.52 \| 0.00% \| \| \| \| \| \| \| \| \| \| \| \| \| Medium \| LKH3 \| \| 46s \| 13.36 \| 0.67% \| \| 1.8m \| 20.42 \| 26.66% \| \| Medium \| POMO+PIP+LKH3 \| \| 48s \| 13.37 \| 1.12% \| \| 1.9m \| 19.38 \| 0.20% \| \| Medium \| POMO+PIP-D+LKH3 \| \| 48s \| 13.41 \| 0.77% \| \| 1.9m \| 19.50 \| 0.05% \| \| \| \| \| \| \| \| \| \| \| \| \| Hard \| LKH3 \| \| 44s \| 23.87 \| 99.09% \| \| 1.9m \| / \| 100.00% \| \| Hard \| POMO+PIP+LKH3 \| \| 44s \| 25.65 \| 2.99% \| \| 1.8m \| 51.39 \| 15.80% \| \| Hard \| POMO+PIP-D+LKH3 \| \| 44s \| 25.68 \| 3.23% \| \| 1.8m \| 51.37 \| 6.24% \| #### #### Table R9: Results on LKH3 with the similar $\underline{\text {instance inference time}}$ limit as GFACS+PIP(-D) (+LKH3) on $n=500$ (first 10 instances). \| \| \| $n=500$ \| \| \| :---------------: \| :------------: \| :--------------: \| :----------: \| \| Method* \| Inst. Time \| Inst. Infsb% \| Gap to # \| \| LKH3 (Default) \| 26m \| 0.00% \| # \| \| LKH3 \| 6.5m \| 0.00% \| 0.59% \| \| GFACS* \| 6.4m \| 57.81% \| 21.32% \| \| GFACS+PIP-D \| 6.5m \| 0.00% \| 11.52% \| \| LKH3 \| 13m \| 0.00% \| 0.25% \| \| GFACS+PIP-D+LKH3 \| 13m \| 0.00% \| 1.10% \|	Summary: The paper propose a novel Proactive Infeasibility Prevention (PIP) framework to advance the capabilities of neural methods towards more complex VRPs, and further investigates the Lagrange multiplier method for soft objective in VRPs, presenting the PIP (& PIP-D) for the hard case where Lagrange multiplier method difficult to find feasible solution. And the experiments show that the PIP is prior to Lagrange multiplier method and has generality to TSPTW and TSPDL. Strengths: This paper contributes to the solution of the soft constraint objectives of VRPs. The author's perspective on the problem is also good; that is, the constraint itself is an NP-hard problem, which was not mentioned in reference [8], and the description of why the constraint itself is NP-hard is very clear, that is, because of the irreversible impact of the first selected node on the selection of subsequent customer nodes. Weaknesses: The author's method actually addresses the shortcomings of the Lagrange multiplier method, but it is not mentioned in the Introduction, and the problems raised in the Introduction can actually be solved only using the Lagrange multiplier method. The method involves complex calculations, particularly when integrating the Lagrangian multiplier and PI masking, which can be computationally intensive. The paper does not thoroughly address the scalability of the proposed method when applied to extremely large datasets, which may limit its practical application in some real-world scenarios. Technical Quality: 3 Clarity: 2 Questions for Authors: [1]What are the potential challenges and limitations in scaling the PIP method to larger and more complex combinatorial optimization problems? [2]How can we further optimize or modify the proposed method to reduce computational complexity without sacrificing solution quality or feasibility? Confidence: 5 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: yes Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for recognizing our work as being with good perspective and very clear description. We understand that the main concerns are the computational cost and applicability towards real-world scenarios. We hope our response below will address them. --- [Our PIP addresses shortcomings of the Lagrange multiplier method (W1)] For original neural solvers, constraint awareness merely comes from the feasibility masking. However, the masking itself is NP-Hard in more complex variants, necessitating the use of a Lagrange multiplier to make the models aware of the constraints, thereby guiding the policy optimization. However, its advantages diminish as problem complexity increases (see Figure 2 and lines 312-323, where we provide in-depth discussions for the pros and cons of the Lagrange multiplier). For instance, in Hard datasets, the infeasible rate of POMO* (i.e., only with the Lagrange multiplier) is 100%. However, when equipped with our PIP-D, it drops dramatically to 6.48%. Therefore, only using the Lagrange multiplier is not enough for solving complex VRPs, while our PIP can address this shortcoming. We will refine the introduction and clearly mention this point in the revised paper. --- [Computational complexity (W2)] We understand the reviewer’s concern, as the acquisition of accurate masking is NP-Hard. We have implemented several strategies to enhance computational efficiency of our PIP-D, including one-step approximation of the PI masking, auxiliary decoder (PIP-D) to avoid intensive calculations of PI masking during training, and sparse strategy for large-scale datasets. The empirical results verify their effectiveness even facing large-scale instances. Please refer to `General Response #1`. --- [Scalability (W3)] We acknowledge that scalability is a significant challenge in NCO, and numerous concurrent works [10, 18, 21, 23, 48-52] are exploring scalable algorithms. However, we would like to clarify that practical applications of NCO require not only scalability but also the ability to handle complex constraints. - Complex Constraints: Our PIP is an early work to address the complex constraint handling in VRPs, whose significance is acknowledged by the reviewer. - Scalability and Generality: Our PIP is orthogonal to scalability research and can be combined with scalable algorithms. We have demonstrated our framework's generality and scalability using GFACS [10] on TSPTW-500. Note that scalability limitations often arise from the backbone itself. Our method can solve large-scale instances as long as the backbone model is capable of doing so. --- [Potential challenges and limitations in scaling PIP to larger and more complex COPs (Q1)] - Larger Scale: The main challenge and limitation is the trade-off between computation and performance. As acquiring the accurate feasibility masking is costly on large-scale instances due to the NP-Hard nature, we have to make some approximations and reduction of the search space to decrease overheads, which may sacrifice the solution quality and feasibility. Although our PIP has implemented approximation methods (e.g. one-step PI masking and auxiliary decoder to replace its acquisition), and can be applied to scalable neural solvers (e.g. GFACS), we cannot guarantee consistent performance across all scales (as noted in lines 346-351). A more effective and efficient approximation technique may be beneficial. To further reduce overheads, we also discuss some possible ways in the response to the next question. - More Complex COPs: As noted in lines 346-351, our PIP framework may not universally improve performance across all VRP variants, necessitating further experiments on various COPs. Another potential limitation is the adaptability of the PIP framework to all complex VRPs. We identify two types of complex VRPs: those with NP-Hard masking (solvable by PIP) and those with non NP-Hard masking but with large optimality gaps due to complex constraints. For the latter, PI masking is no longer necessary since we can obtain the feasibility masking easily at each constructive step, but the Lagrangian multiplier and the auxiliary decoder still have effects. Please see Figure R1 of the attached PDF, where we explored the application of PIP to VRPBLTW. --- [Further trials to reduce the computational complexity (Q2)] Below strategies can be considered for further accelerating the training and inference of PIP: - Apply sparse strategies to refine PIP calculations: - Only consider top K neighbours. We have implemented this strategy on GFACS. Results in Table 3 show that GFACS+PIP-D maintains similar training and inference times as GFACS on TSPTW-500 (i.e., 28.3h/6.5m vs. 28.1h/6.4m). - Employ a trainable heatmap to confine the candidate space of PIP calculations. Recent heatmap-based methods have successfully reduced the search space during construction, and we see similar potential for heatmaps to confine the candidate space of PIP calculation. - Couple with the state-of-the-art solvers (e.g. LKH3): Our PIP is empirically verified to be efficient due to its capability to obtain good and feasible solutions within a very short time (LKH3: 1.4d vs POMO+PIP-D: 48s). By further coupling with LKH3, our PIP can even achieve the performance of LKH3 within a few hours (9h). Details refer to `General Response #2`. - Fine-tune Lagrangian method () with PI masking*: We found that PI masking does not need to be calculated throughout the entire training process. Fine-tuning a pre-trained Lagrangian method (e.g., POMO) with PIP for a few epochs will also deliver competitive results. Details can be found in Appendix D.3. - Early stop of PI masking: We empirically observed that infeasibility primarily occurs in the initial steps of the construction process. Hence, it is possible to employ PIP only during these early stages. Details can be found in Appendix D.4. --- Rebuttal Comment 1.1: Comment: Dear Reviewer DEtT, Thank you once again for your insightful comments and helpful suggestions. As the deadline for author-reviewer discussions is approaching, we would greatly appreciate it if you could take a moment to review our rebuttal. Please let us know if you have any further questions or concerns. Thank you very much for your time. Best, Authors --- Rebuttal 2: Title: Dear Reviewers DEtT and Seke: Comment: The authors have provided extensive comments and new results in response to the criticisms raised in your reviews. Has this response addressed your main concerns? If not, are there additional questions you would like to pose? The author discussion period is scheduled to end tomorrow (Aug 15). Please respond.	Summary: This paper proposes a Proactive Infeasibility Prevention (PIP) framework to enhance the ability of neural methods to handle complex constraints in Vehicle Routing Problem (VRP). The PIP framework integrates the Lagrangian multiplier to enhance constraint awareness and introduces preventative infeasibility masking to proactively guide the solution construction process. Additionally, an extended version called PIP-D employs an auxiliary decoder and two adaptive strategies to learn and predict masking information, reducing computational costs during training. These methods were extensively tested on different levels of constraint hardness in the Traveling Salesman Problem with Time Window (TSPTW) and Traveling Salesman Problem with Draft Limit (TSPDL) variants. The results demonstrate that the proposed methods enhance the capabilities of neural methods, significantly reducing infeasibility rates and improving solution quality. Strengths: 1. Adaptability to Complex Constraints: The paper devises a method to apply machine learning to constraint-based problems, which have been challenging to handle with deep learning due to the difficulty in finding feasible solutions. 2. Experimental Validation: Experimental results demonstrate that the proposed method can compute feasible solutions more effectively compared to traditional methods. 3. Integration with Constructive Methods: The proposed approach can be combined with constructive methods, enhancing its practical applicability and flexibility. Weaknesses: 1. Generality of the Trained Model: It is unclear whether the trained model generalizes well to unseen instances, raising concerns about its robustness and applicability to different problem settings. 2. Lack of Theoretical Justification for PIP: The paper does not provide a theoretical justification for the superiority of using the Proactive Infeasibility Prevention (PIP) method, leaving its theoretical advantages unproven. 3. Lack of Classical methods with time limit: There are no comparison with the classical methods (e.g., LKH3) with a time limit. I am concerned that LKH3 could find "good" feasible solutions within a short time (e.g., within 5 minutes). Technical Quality: 3 Clarity: 2 Questions for Authors: - Can the proposed idea be applied to methods other than constructive methods? If it can be used to guide the search to avoid infeasibility, it would be a more practical idea. - Alternatively, after the (possibly infeasible) solution constructed by a constructive method, is it easy to recover a feasibility through neighborhood search? If so, can you compare this with the avoidance of infeasibility using PIP? - Is the model constructed with PIP tailored to the training dataset? In other words, when using the model constructed with PIP for instances in different area, does the number of infeasible instances decrease compared to the model without PIP? - Is it possible to use the PIP framework for more general VRP (e.g., with multiple vehicles or capacity constraints)? - Are there any experimental comparisons between the proposed model and LKH3 with time limit? Confidence: 4 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: The limitations of this work are discussed in the last section. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We appreciate the reviewer for the positive and valuable comments. We are delighted that the reviewer found our approach adaptable to complex constraints, effective and flexible. We hope that the following response, along with additional experiments, will address remaining concerns. --- [Generalization Evaluation (W1)] We have evaluated the generalization of our PIP(-D) to the unseen real-world instances in datasets [76] with different scales, distributions (e.g. node distributions, time window distributions and width) and constraint hardness in the original Appendix D.6 (Table 7). The results consistently showcase that our PIP(-D) could significantly reduce the infeasible rate and improve solution quality on in-distribution (Table 1,2,3) and out-of-distribution (Table 7) datasets. --- [Theoretical analysis of PIP (W2)] We acknowledge that the NCO domain is mainly built on empirical superiority, prioritizing in closing gaps between neural and traditional solvers, but lacks theoretical support. - Regarding empirical superiority: Our PIP(-D) has been applied to various constructive methods, including both autoregressive (AM, POMO) and non-autoregressive (GFACS) models. We have conducted extensive experiments on TSPTW and TSPDL with different constraint hardness levels, from small problem scales (50, 100) for AM and POMO to large scales (500) for GFACS. These experiments demonstrate significant reductions in infeasibility rates and substantial improvements in solution quality. - Regarding theoretical support, we would like to note that each component of our PIP(-D) does have some theoretical support. - Lagrangian Multiplier Method: we represent an early trial to incorporate the Lagrangian multiplier method into constructive VRP solvers by interleaving constraints into the reward function, transitioning from Eq. (2) to Eq.(3), both of which are theoretically proven to be equivalent in [8]. - PI Masking and Auxiliary Decoder: As illustrated in Figure 1, the feasibility masking (i.e., $n$-step PIP) in complex constraints is NP-Hard. While iterating over all future possibilities would make PI masking complete, it is computationally inefficient. Therefore, we approximate it with one-step PI masking, whose efficiency is validated in Table R3 and R4 of the attached PDF. To enhance training efficiency, we use an auxiliary decoder to further approximate one-step PI masking, avoiding the need to acquire it continuously during training (see lines 293-296). We agree with the reviewer that theoretical justification is significant and acknowledge the need for further theoretical development, which we leave as a future work. --- [Comparison with LKH3 with time limit (W3, Q5)] We follow the suggestion and add experiments on our PIP(-D) and LKH3 with various time limits (from 5s to 3m per instance). We exhibit a comprehensive comparison in Table R2 and Figures R2 and R3 of the attached PDF, where our PIP outperforms LKH3 within limited time budget and achieves slightly better solution quality while using only 27% of the inference time (9 hours vs. 1.4 days) by further coupling with LKH3. For details please refer to `General Response #2`. --- [Can our PIP apply to methods other than constructive methods? (Q1)] Yes, our PIP can potentially be applied to most NCO methods. - Constructive Methods: We have validated its effectiveness on both autoregressive (AM, POMO) and non-autoregressive (GFACS) methods. - Iterative Methods: - Our PIP can provide better initial solutions to enhance search efficiency, as demonstrated in Table R2 of the attached PDF. - While the logic of iterative search differs from construction, making one-step PIP masking less applicable, components of our PIP framework, such as the Lagrangian multiplier method for constraint awareness and the auxiliary decoder for learning infeasibility, can still guide the search to avoid infeasibility. We consider it as a promising direction for future work. --- [Can the infeasible constructed solutions be recovered by local search? (Q2)] We conduct additional experiments using LKH3 with different sources of initial solutions. The results indicate that local search methods can recover infeasible solutions. However, our PIP-D provides the most promising (good and mostly feasible) initial solutions for LKH3, enhancing its search efficiency and achieving SOTA performance (see Table R2 in the attached PDF). This suggests the promising potential of our PIP-D to assist strong heuristic solvers in future work. --- [Generalizability of PIP to different datasets in different domains (Q3, Q4)] We would like to clarify that our PIP is not tailored to the training datasets since it is a generic framework with the potential to be applied to different backbone models; that is, what the backbones can do, our PIP adapted to them can also achieve. - Regarding VRPs: We have conducted extensive experiments on both in-distribution and OOD datasets of variants like TSPTW and TSPDL, covering various levels of constraint hardness (Easy, Medium, Hard). Our PIP consistently outperforms other baselines in these scenarios. Although PIP may not universally improve performance across all VRP variants, we followed the reviewer's suggestions and explored its application to VRPs with various complex constraints, such as VRPBLTW-50 (VRP with constraints of capacity, backhaul, duration limit, and time window). Results demonstrate that PIP significantly enhances solution quality for VRPs with complex constraints (Our gap 1.80% vs. POMO's gap 9.17%, see Figure R1 of the attached PDF for more details). - Regarding a broader range of COPs: Beyond VRPs, our PIP has potential applications in other domains, such as job shop scheduling, where operations need to be completed in a specific order. Infeasibility can be proactively prevented using PIP. We plan to explore these applications as future work. --- Rebuttal Comment 1.1: Comment: Dear Reviewer azSu, Thank you once again for your insightful comments and helpful suggestions. As the deadline for author-reviewer discussions is approaching, we would greatly appreciate it if you could take a moment to review our rebuttal. Please let us know if you have any further questions or concerns. Thank you very much for your time. Best, Authors	Rebuttal 1: Rebuttal: We sincerely appreciate your efforts and insightful comments. We are pleased that reviewers found our PIP(-D) framework to be novel (#DEtT, #Seke, #Xb4p), with good perspective (#DEtT), practical applicability (#azSu), and effectiveness in addressing the critical constraint handling problem (#azSu, #Xb4p). We also appreciate the positive feedback, where reviewers found our paper logically clear (#DEtT, #Xb4p, #Seke) and our experiments with various baselines extensive (#azSu, #Xb4p, #Seke). In this global response, we address the common concerns. --- [Computational cost and scalability] Reviewers #DEtT, #Xb4p and #Seke raised questions regarding the computational cost and scalability. While we acknowledge that our framework introduces some unavoidable overhead to the backbone model, we believe it is acceptable for the following reasons: - The overhead is actually offset by its strong effectiveness. Following the reviewer’s suggestion, we show that baselines (POMO and AM) struggle to solve the studied complex constrained VRP, even with prolonged runtimes similar to ours. To see this, we gather additional results in Table R1 of the attached PDF and show that: 1) Incorporating Lagrangian multiplier (POMO* and AM) may lead to some improvement (in Table 1 and 2 of main paper) but not for the cases in Table R1 under complex constraints and larger scales; 2) Even with extended inference time* (by sampling more solutions and data augmentation), existing methods do not deliver any feasible solutions; 3) In contrast, our PIP-D with 48s time, significantly reduces infeasibility from 100% to 6.48% compared to baselines running for 2.5m, and exhibits a optimality gap around only 0.3%. Furthermore, PIP can perform even better with more inference time. - We explored several efficient strategies to reduce computational costs in the new PDF, the main paper, and Appendix D.3 and D.4. These efforts provide a more detailed discussion, and we will follow the comments to better clarify our discussion in the new paper. Below, we summarize them. - 1) One-step PI Masking: Instead of simulating all future possibilities, we use one-step PI masking to approximate NP-hard feasibility mask and reduce computational cost (see new Table R3, R4 and our response `[PIP with different step numbers]` to Reviewer #Xb4p). - 2) Auxiliary Decoder (PIP-D): To reduce intensive PI masking calculations, we use an auxiliary decoder to predict one-step PI masking, enhancing training efficiency by 1.5x compared to PIP, especially as scale and constraint complexity increase (see Table 1 and lines 293-296 of the original paper). - 3) Sparse Strategy: We incorporate sparse strategy (selecting top K neighbours) to handle large-scale problems more efficiently. For GFACS with $n=500$, our *GFACS\+(PIP; PIP-D) demonstrates similar inference times to GFACS\* (6.5m vs. 6.4m), while significantly reducing infeasibility (57.81% vs. 1.56%; 0.00%) and improving solution quality (21.32% vs. 15.04%; 11.95%), showing great efficiency. - 4) Other strategies: We also enriched the discussion for future work (kindly refer to our response `[Further trials to reduce the computational complexity]` to Reviewer #DEtT for details). - Lastly, we believe scalability for larger-scale and applicability to more complex real-world constrained VRPs represent both important directions in NCO. While our primary focus is more on the latter in this paper, our PIP is an early work to enable backbone models to tackle complex constrained VRPs where masking is NP-hard. Moreover, our PIP is generic and can enhance a wide range of NCO models, as demonstrated with both autoregressive (AM, POMO) and non-autoregressive (GFACS) models in our experiments. As the scalability of the backbone model increases, our PIP framework will also improve. --- [Enhanced comparison between PIP and LKH3] We thank the reviewers (#Xb4p and #azSu) for the insightful suggestions. Previously, we used LKH3 with default settings, and we now compare our PIP(-D) and LKH3 with various time limits (from 5s to 3m per instance) for comprehensiveness. Please refer to Table R2, Figures R2 and R3 in the attached PDF, where our PIP indeed outperforms LKH3. We will include these discussions in the revised paper. Below, we summarize the key results. - When given a limited budget (i.e., a few seconds, as mentioned by Reviewer #Xb4p), LKH3 performs significantly worse than our POMO\+PIP-D on the studied complex variants.* As shown in Table R2, while LKH3 is powerful with state-of-the-art quality, its advantage diminishes with limited time. Our POMO+PIP-D reduces the infeasibility rate from 53.11% to 6.28% with 0.9s time per instance, compared to LKH3 with 5.1s time. - PIP achieves state-of-the-art performance by further coupling with LKH3.* To leverage the strengths of both approaches, we used our PIP-D to provide better initial solutions for LKH3. This combination reduced the infeasibility rate from 53.11% to 0.21% and improved the objective from 51.65 to 51.25 within only a few seconds. Notably, initializing LKH3 with POMO+PIP-D outperforms the default LKH3 setup (10,000 trials), achieving slightly better solution quality while using only 27% of the inference time (9 hours vs. 1.4 days). - We also show the progress of objective value and infeasibility rate over inference times in Figures R2, R3 for clearer comparison. --- [Additional experiments]* We have conducted additional experiments in the attached PDF, which are summarized below. * Table R1: Results of POMO models under various inference time. * Table R2: Results of LKH3 and POMO+PIP-D under various time limits. Table R3, R4: Results of PIP with different steps on two datasets. * Figure R1: Results on VRPBLTW. * Figures R2, R3: Progress curves of objectives and infeasibility rates over different inference time Pdf: /pdf/d3817f6ccd33bbd52203a304ef0769a0d2532b40.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Proportional Fairness in Clustering: A Social Choice Perspective	Accept (poster)	Summary: This paper studies three different related notions of fair clustering that have been proposed in the literature for metric centroid clustering: (1) proportional fairness, (2) individual fairness, and (3) transferable core. Prior work has separately defined, motivated, and studied the existence and computation of clusterings optimizing all of these notions of fairness. The present work attempts to synthesize these different notions in two senses. First, the paper shows that up to [small] constant factors, approximate proportional fairness implies approximate individual fairness and vice versa, and approximate proportional fairness implies approximate transferable core. Second, the paper considers metric adaptations of the concepts of justified representation (mJR) and proportional justified representation (mPJR) from approval-based committee selection, an important fair representation problem in computational social choice, and show that these imply approximations of the aforementioned fair clustering concepts. Specifically, any solution satisfying mJR simultaneously satisfies the best known approximations to individual and proportional fairness, and to the transferable core. The paper shows that the Greedy Capture algorithm from prior work on proportional fairness satisfies this mJR property and thus is simultaneously approximately fair in all three senses. Furthermore, the Expanding Approvals algorithm from prior work satisfies the stronger mPJR property. The paper turns to the implications of mPJR for another generalized notion of proportional fairness (the q-core) in contexts where agents measure cost by distance to the q’th most distant center (q=1 being the typical centroid clustering setting) motivated by prior work in sortition (selecting a fair and representative sample of a population), showing that mPJR implies a 5-approximation for all q. Finally, the paper shows two additional results extending prior work. First, that the known efficient algorithms (e.g., Greedy Capture and Expanding Approvals) can be extended to handle the case of an infinite number of center candidates (e.g., can select any points in the real plane) by simply considering the set of agents as the candidates, and that this restriction preserves small constant approximations of fairness. Second, that the analysis of the Fair Greedy Capture algorithm from recent work on sortition can be tightened to yield a better constant bound on the approximation of the q-core. Strengths: The paper does a very good job of providing a comprehensive survey connecting different fair clustering desiderata that have been considered separately in the literature. The result is a convincing story that there is a more “general” phenomenon of proportionality at work in all these group-agnostic structural notions of fairness in clustering. The greatest contribution may therefore be in clarifying the state of the field for future work seeking to extend or build on these notions. It is also nice to see a formal connection between the last several years of work on fair approval-based committee selection in computational social choice and the work in the ML clustering space. Generally the writing and discussion is clear. Effort has clearly been put into communicating ideas effectively in the forms of the results diagram in figure 1, illustrative examples, and extensive consideration of related work and the connections between other work and the current. Results are well substantiated by the formal arguments, and claims are all measured and accurate to what is shown. Weaknesses: The work is largely incremental within the fair clustering space, focusing on the relationship between prior notions of fairness, the existence and computation of which have already been studied. The algorithmic contribution is limited in this sense as well, focusing mostly on tightening or demonstrating relationships between guarantees and analysis. In these senses, the impact of the paper may be limited. Post-rebuttal clarification to the above: The weakness discussed is really with respect to algorithmic contributions, and I agree that connecting different work in the field is a valuable contribution. A minor comment: In Lemma 9, lines 315-316, I think it should be “…let C’ be a set of…candidates” and “…there is a set $N^{''} \subseteq N^{'}$...” Technical Quality: 4 Clarity: 3 Questions for Authors: No pressing questions, though if the authors feel that I have misunderstood the potential of the work for improving clustering algorithms in my weaknesses, I would be happy to hear different perspectives. Confidence: 3 Soundness: 4 Presentation: 3 Contribution: 2 Limitations: No concerns. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you kindly for the minor comment, you are absolutely correct. We agree that our work has a clear focus on creating relations between the fairness measures. However, we believe that providing connections and (in-)compatibility between fairness notions is of great importance, and something that has not been considered enough. As we mention in the introduction, this belief is also shared by Dickerson et al. [2023b]; (their manuscript since has been published on arXiv: https://arxiv.org/abs/2406.15960). Also, with the connection to multiwinner voting, we create a new pathway for future work on clustering with fairness measures a la individual or proportional fairness. --- Rebuttal Comment 1.1: Comment: I acknowledge that I have read the author rebuttal. I appreciate the perspective and agree that the work contributes a helpful connection between different considerations of fairness notions.	Summary: The paper unifies several definitions of fairness in clustering and relates them through approximation ratios. The paper provides theoretical results that 'translate' a definition into another, providing tight bounds for proportional and individual fairness metrics. The paper concludes with a series of results derived from multiwinner voting theory that relate fairness to justified representation. Strengths: The paper is very-well written, with substantial theoretical contributions. The relationship with prior work is comprehensive and clear, and it does a great job of extracting methods in order to relate and unify different definitions of fairness. The problem posed is important, as fairness in clustering may require different definitions, and as such, knowing how they relate to each other provides insight into the potential trade-offs. I appreciate the examples that show tight bounds for individual and proportional fairness. Weaknesses: It would be worth discussing the asymmetry in some of the theoretical results (e.g. individual and proportional fairness relate asymmetrically). The alpha-PF -> (gamma, alpha)-TC edge visualization in Fig 1 is slightly confusing: would be good to mention that the gamma(alpha + 1)/(gamma-1) is about relating the alphas. Technical Quality: 4 Clarity: 4 Questions for Authors: 1. It would be good to discuss the problem of clustering when the cluster centers are not part of the data but are a la k-means algorithms, found from some continuous space: are any of the results or methods transferable? 2. It would be great to discuss applications of the work in the context of fair clustering, especially since multi-winner voting is mentioned: what decision-making processes would entail using one vs. more fairness definitions, and how would potential trade-offs derived from the approximation bounds affect the outcome on the population? Confidence: 3 Soundness: 4 Presentation: 4 Contribution: 3 Limitations: It would be great to include a more comprehensive discussion on limitations. Flag For Ethics Review: ['No ethics review needed.'] Rating: 8 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: 1. Yes, we discuss this in section 3.4. Recall that the agent set N corresponds to the point set in k-means, and the centers are chosen from the candidate set C. In section 3.4, we discuss results for the case that the candidate set is infinite. This also covers e.g. the case when the centers may be chosen from all of the Euclidean space. 2. Generally speaking, fairness notions such as individuality or proportionality are efforts towards modeling what is considered fair. Our work shows that these notions are highly related to another. That is, if my goal is to have a proportionally fair solution, then I implicitly also obtain a solution that is (approximately) individually fair. Considering for example any solution that satisfies mJR, it fulfills the best known approximations to individual and proportional fairness at the same time, so there is not really any trade-off that we are aware of. We hope that this roughly answers your question. Of course, we are happy to further discuss this in the discussion period. Also, thank you for the weaknesses you pointed out. We will make sure to improve on these two points in the next version. --- Rebuttal Comment 1.1: Comment: Thanks for the answers!	Summary: The authors study the setting of clustering problem where voters and candidates lie in the metric space and the goal is to elect k candidates representing groups of voters. The authors show interesting connections between this setting and the setting of proportional approval-based committee elections, i.e., they show that the known proportionality axioms can be easily adapted to this setting, yielding the best possible approximations of the notions of proportional fairness and individual fairness defined for the clustering model. In their work, the authors also study the connections between proportional fairness and individual fairness, and analyze the sortition problem. Strengths: This is a very good paper. The idea of metric variants of justified representation axioms is interesting and novel - I believe it has a potential to be further studied in follow-up works. The paper is clearly written and the results are technically sound. Weaknesses: I was a bit surprised that the authors chose to extend the axioms of JR and PJR to their setting, skipping the stronger axioms of EJR, EJR+ and PJR+ mentioned in the same paper of Brill and Peters 2023 that they cite. I think this decision should be explained in the text. But I do not see this as a major weakness of the paper. Technical Quality: 4 Clarity: 3 Questions for Authors: 1. Do you think that the axioms of EJR, EJR+ and PJR+ can be adapted to your setting as well? Confidence: 4 Soundness: 4 Presentation: 3 Contribution: 4 Limitations: The authors adequately addressed the limitations and there are no potential negative societal impact of their work. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for pointing this out. Of course, this deserves a discussion in the conclusion, and we want to add this in the next version. Indeed, the Expanding Approvals algorithm satisfies the stronger mPJR+. However, we were not able to show mPJR+ implies stronger bounds than mPJR. As for EJR and EJR+, it follows from Brill and Peters [2023] that these do not always exist. Hence, we chose to focus on mJR and mPJR. We also believe that it is interesting that already these weak axioms imply the best approximations to individual and proportional fairness, and to the transferable core. --- Rebuttal Comment 1.1: Comment: Thank you for the response. Indeed it would be good to discuss this in conclusion.	Summary: This paper provides a methodological contribution by bridging three different notions of fairness in clustering: Individual (where every agent is assigned a cluster center no farther from the $\frac{n}{k}$ neighbor), proportional fairness (no group of size $\geq$ $\frac{n}{k}$ should be able to propose a center that would improve their situation collectively), and core-fairness (k-clustering is in the core if no group containing $\geq \frac{n}{k}$ agents can strictly decrease their total distance by deviating to a new center). The paper shows that any approximation to proportional fairness is also an approximation to individual fairness and core-fairness and vice-versa. The paper also draws connections to multi-winner voting from computational social science and reinterprets the proportionality fairness notions, leading to efficiently computable metrics (distance-based) under some constraints. Strengths: + The paper tackles an interesting topic + The paper is well-written, and it makes a significant methodological contribution + The methodology is adequately sound and well-explained. Particularly, the connections to multi-winner settings are novel. Weaknesses: I am mostly satisfied with the paper, and I don't see any major weaknesses. It's a decent methodological contribution. Technical Quality: 3 Clarity: 3 Questions for Authors: I don't have any specific questions for the authors. Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: yes Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	null	Rebuttal 1: Rebuttal: We would like to express our gratitude to the reviewers for taking the time to carefully review our submission. We address each of the reviewer's comments and questions below and look forward to further discussions in the coming days.	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
GUIDE: Real-Time Human-Shaped Agents	Accept (poster)	Summary: The paper introduce GUIDE, a RLHF framework for real-time RLHF with online and continous human feedback. GUIDE translates the human feedback to dense reward. Addtionally, GUIDE includes a parallel training model that learns a simulated human feedback. By involving 50 participants annotation, GUIDE solves three typical challenging sparse reward environments. Strengths: 1. The paper is easy to read. 2. GUIDE firstly proposed novel continous human feedback and is also evaluated human annotators. 3. GUIDE demonstrated improvement compared to baselines in 3 environments, and analyzed cognitive tests and analyses. Weaknesses: 1. My biggest concern comes from the practicality of GUIDE. From both theoretical and experimental perspectives, I find it hard to believe that such a simple continuous feedback model can be applied to real-world scenarios. For example, the paper states in line 38 that "Current research has demonstrated success primarily in simple, low-dimensional tasks with limited solution spaces." However, the experiments conducted in the paper also involve environments where baseline algorithms like DDPG or SAC can converge with a good reward function after only about 10 minutes of training. Moreover, according to the experimental results, GUIDE, which incurs a high cost of human feedback, does not outperform manually designed simple rewards (such as the distance to the target, I think it is not hard to design it). Therefore, despite the fact that the environments used do have continuous actions and image inputs, I believe these environments are not suitable for validating RLHF algorithms because the reward functions are easy to design and the tasks themselves are simple. 2. The core argument of the paper is that continuous real-time feedback is extremely difficult to implement in practice. It requires annotators to constantly provide scalar rewards without pause, and such absolute value annotations are more susceptible to biases from different individuals. Pair-wise annotation is much easier than absolute value annotation and can be conducted asynchronously with the training process. If an AI agent needs to be trained for several days, the cost will be unacceptable. 3. Although the paper suggests using model predictions to synthesize feedback, such a simple supervised learning regression objective is unlikely to accurately model the complex reward distribution. My reasoning is that predicting the relative goodness of A and B is easier than predicting scalar reward values, but there will still be many prediction biases. 4. The definitions of various symbols in the paper are imprecise and confusing, for example: - What is the meaning of A(s, a) in Equation 1? Also, A(s) = a in the line 123, is it the same? - difference of Q(s, a) and q? - How to get the r^hf? These typos make it very difficult to understand the details of the paper. 5. There is a lack of discussion on recent related works in RLHF, such as: - [1] White D, Wu M, Novoseller E, et al. Rating-based reinforcement learning[C]//Proceedings of the AAAI Conference on Artificial Intelligence. 2024, 38(9): 10207-10215. - [2] Yuan Y, Hao J, Ma Y, et al. Uni-RLHF: Universal Platform and Benchmark Suite for Reinforcement Learning with Diverse Human Feedback[J]. ICLR2024. - [3] Guan L, Verma M, Guo S S, et al. Widening the pipeline in human-guided reinforcement learning with explanation and context-aware data augmentation[J]. Advances in Neural Information Processing Systems, 2021, 34: 21885-21897. - [4] Guan L, Valmeekam K, Kambhampati S. Relative behavioral attributes: Filling the gap between symbolic goal specification and reward learning from human preferences[J]. ICLR2023. Technical Quality: 3 Clarity: 2 Questions for Authors: Can you provide more details about the annotator's annotations, such as the actual interface and the frequency of operations? Confidence: 4 Soundness: 3 Presentation: 2 Contribution: 2 Limitations: Yes, and yes. Flag For Ethics Review: ['No ethics review needed.'] Rating: 3 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for their thoughtful comments. We would like to address all of your concerns and questions below with point responses: ---- >Practicality: “I find it hard to believe that such a simple continuous feedback model can be applied to real-world scenarios. For example, the paper states in line 38 that "Current research has demonstrated success primarily in simple, low-dimensional tasks with limited solution spaces." However, the experiments conducted in the paper also involve environments where baseline algorithms like DDPG or SAC can converge with a good reward function after only about 10 minutes of training.” We respectively disagree with the reviewer on this observation. Fig.5 shows the opposite observation where baseline algorithms did not converge within 10 minutes and showed no sign of convergence in 20 minutes in our new environments, Find Treasure and Hide-and-Seek. Therefore, these tasks remain significantly challenging for the current RL baselines. GUIDE, on the other hand, was able to improve over baselines by a large margin. >“GUIDE, which incurs a high cost of human feedback, does not outperform manually designed simple rewards (such as the distance to the target, I think it is not hard to design it). Therefore, despite the fact that the environments used do have continuous actions and image inputs, I believe these environments are not suitable for validating RLHF algorithms because the reward functions are easy to design and the tasks themselves are simple.” As discussed in the paper, hand-design dense rewards typically do not exist in real-world scenarios and require extensive experience in reward engineering and a practical understanding of RL training. However, we aim to enable human guidance in RL for a broader audience who most likely do not have RL experience or reward engineering. Moreover, dense reward designs, such as precise distance to the target, as the reviewer suggested, assume extra information that is not available to GUIDE, whom only perceives partial visual observations. Therefore, our environments are strong and challenging testbeds for developing human-guided RL algorithms. Furthermore, as prior works have only focused on simple bowling games and low-dimensional observations, we believe that our environment is a large step forward in investigating the potential and scalability of human-guided RL. >“The core argument of the paper is that continuous real-time feedback is extremely difficult to implement in practice. It requires annotators to constantly provide scalar rewards without pause, and such absolute value annotations are more susceptible to biases from different individuals. Pair-wise annotation is much easier than absolute value annotation and can be conducted asynchronously with the training process. If an AI agent needs to be trained for several days, the cost will be unacceptable.” Our argument is not that continuous real-time feedback is extremely difficult to implement in practice. Instead, we point out that it provides richer feedback and assignments to every state-action pair than previous discrete feedback without a high cognitive load. Our contribution is to enable grounding such novel feedback modality through GUIDE. As discussed in our paper, while pair-wise annotation is a popular choice in RLHF, it requires parallel policy rollouts in an asynchronous manner or offline trajectory collections. Our setting is different – we focus on real-time decision-making tasks where no such asynchronous rollouts, offline trajectories, or a simulator that can be run multiple times with policy rollouts and resetting are available. Due to the significant difference in the setting, pair-wise annotation is out of scope for our study. >“Although the paper suggests using model predictions to synthesize feedback, such a simple supervised learning regression objective is unlikely to accurately model the complex reward distribution. My reasoning is that predicting the relative goodness of A and B is easier than predicting scalar reward values, but there will still be many prediction biases.” As discussed in our paper, while pair-wise annotation is a popular choice in RLHF, such as recent LLM studies, it requires parallel policy rollouts in an asynchronous manner or offline trajectory collections. Our setting is different – we focus on real-time decision-making tasks where no such asynchronous rollouts, offline trajectories, or a simulator that can be run multiple times with policy rollouts and resetting are available. Due to the significant difference in the setting, pair-wise annotation is out of scope for our study. We agree that more advancements can be made to improve the simulated feedback model. However, prior to our work, there have not been studies enabling continual training in real-time human-guided RL. Our work is the first step towards this with potential future work to improve the optimization designs to handle more complex reward distributions. >“What is the meaning of A(s, a) in Equation 1? Also, A(s) = a in the line 123, is it the same? Difference of Q(s, a) and q? How to get the r^hf?” Thank you for catching the typos. We will correct both $A(s, a)$ and $q(s, a)$ to $ Q(s, a)$. $r^{hf}$ is the human feedback reward provided by the human. >“There is a lack of discussion on recent related works in RLHF, such as: …” We thank the reviewer for pointing out relevant literature, and we will include these in our revised version. >Can you provide more details about the annotator's annotations, such as the actual interface and the frequency of operations? Yes. A screenshot of our interface is shown in Fig3 (B). The user hovers their mouse over the window to provide feedback. Moving upwards indicates stronger positive feedback, and downwards indicates stronger negative feedback. The decision frequency of the games is set to 0.5s/step. Hence, human feedback values are collected every 0.5 seconds. --- Rebuttal 2: Comment: Dear Reviewer, Thank you again for your detailed review of our paper. We aim to try our best to address all your concerns with our point responses above. We truly value your feedback. As the end of the rebuttal period is approaching, please feel free to let us know if you have any additional questions or comments. We would be happy to answer them. We look forward to hearing your future thoughts! Best regards, Authors --- Rebuttal Comment 2.1: Comment: Thank you for your reply, I still think that the GUIDE method is difficult to apply to reinforcement learning agent that require long term training (e.g., a few days, atari/procegen/minecraft), and even if it could be used, sustained manual loads for a few days would still be excessively costly and inconsistent. I have some concerns about GUIDE's usability for real-world tasks, and a few of the toy experiments in the paper don't support the author's point of view. Thanks a lot, I will clearly keep my score. --- Reply to Comment 2.1.1: Comment: Dear reviewer, thank you for your response. We believe there is clearly a misunderstanding of our work. >“I still think that the GUIDE method is difficult to apply to reinforcement learning agent that require long term training (e.g., a few days, atari/procegen/minecraft),” >“I have some concerns about GUIDE’s usability for real-world tasks” We find these points raised by the reviewer to be puzzling and self-conflicting. As you have mentioned your concern for real-world applicability, but the environments mentioned by you (e.g., atari/procegen/minecraft) are not real-world tasks. In fact, our bowling task is one of the challenging ones in atari. Both of our find treasures and hide-and-seek are similar to minecraft sub-tasks. Given our setup with partial visual observation, long-horizon planning, and difficult-to-design reward functions without extra info, we believe our tasks are not toy examples. As stated above, this is evidenced by our results in Fig. 5 where SOTA RL struggles to converge while GUIDE improves them by a large margin. We believe that this shows the exact potential of GUIDE. It is infeasible to train regular RL on an unrealistic amount of experience, this is exactly the purpose of using real-time human guidance for accelerating agent learning. As shown in Fig 5 of our paper, untrained human participants using GUIDE are able to reach the same level of performance as the RL baseline within half the training time. We believe these are encouraging results and it shows the potential of real-time human guidance. >“sustained manual loads for a few days would still be excessively costly and inconsistent” We agree that human feedback is expensive and effectiveness varies across individuals. However, we addressed both of these issues by introducing a simulated feedback provider and conducting the largest scale analysis existing on the effect of individual differences on AI guidance. This has not been done before. >“and a few of the toy experiments in the paper don’t support the author’s point of view.” We would like to emphasize that RL baselines still struggle on the tasks that the reviewer categorized as “toy examples.” Again, shown in Fig 5, GUIDE surpassed the baseline by a large margin. Overall, we don’t consider devaluing our contribution simply based on a gap already pointed out by our experiments and us showing strong results in scalability to be appropriate for scientific advancements. We do not feel the reviewer’s points directly relate to our work.	Summary: The paper proposes a new approach to reinforcement learning with human feedback in simple video games. The method relies on continuous human feedback that is provided by the human observer hovering their mouse over a window with a spectrum of positive and negative rewards. Unlike prior approaches, this method converts human feedback directly into a reinforcement learning reward with an added time delay. Moreover, the method includes a model that regresses states into observed human feedback, which allows for simulated human feedback. The effectiveness of the method is demonstrated in three simple games in a human study with 50 participants. Strengths: 1. The authors propose a simple way to incorporate continuous human feedback as a reinforcement learning reward with a constant time delay. The environment reward and human feedback are simply added to form the final reward function. 2. It is demonstrated that human preference can be directly regressed from states and actions to provide simulated human feedback. 3. The authors perform an extensive human study showing the effectiveness of their method. They also correlate the subject’s performance in a cognitive test with their ability to guide an RL agent. Weaknesses: There are three major unstated assumptions: 1. The delay between an event appearing on the screen and the change in human feedback is constant (Question 1). The authors tune this constant for each environment. But, more complex environments might induce different delays as the human observer might need to think about what they saw. 2. People are able to provide constant feedback (Question 2). This might not be true for more complex environments where certain states might have ambiguous values. 3. The human feedback is Markov (Question 3). This might not be true in more complex games. ## Detailed comments: * Equation 1 should have Q instead of A. Unless you want to define an advantage function A. * Equation 2 should have an upper-case Q. * The term $R_{t+k+1}$ in Equation 2 is not very clear. * The meaning of “We follow recent advancements in neural architectures and hyperparameter designs” on line 125 is not clear. * The rest of the paragraph on lines 125 - 127 is superfluous. ## Minor comments: * Inconsistent spacing between text and citations. * Calling this approach a “computational framework” might be a bit redundant given the context of the conference. Technical Quality: 3 Clarity: 2 Questions for Authors: 1. Is it reasonable to assume constant reaction time of the human observer? 2. How would your method deal with games with more ambiguous state values, such as Montezuma's Revenge? 3. The human feedback regressor $\bar{H}(s, a)$ uses the Markov assumption, but the human feedback might be dependent on their memory of prior states. What if the human feedback is non-Markov? Confidence: 3 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: Limitations are partially addressed. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for their thoughtful comments. We would like to address all of your concerns and questions below with point responses: ---- >“There are three major unstated assumptions: The delay between an event appearing on the screen and the change in human feedback is constant (Question 1). The authors tune this constant for each environment. But, more complex environments might induce different delays as the human observer might need to think about what they saw.” (Question1: “Is it reasonable to assume constant reaction time of the human observer?”) We agree that human response time can have various delays. In GUIDE, the advantage of using continual feedback is that it can partially alleviate this issue by eliminating the need for time window association for feedback to state-action pairs. Such a time window is required in previous discrete feedback designs. However, modeling more fine-grained response delay can potentially further improve GUIDE. We leave the exploration of this aspect in future work. >“People are able to provide constant feedback (Question 2). This might not be true for more complex environments where certain states might have ambiguous values.” Our assumption is that humans have a preference for any given state-action pair, though the strength of the preference may vary. Continuous-valued feedback can model the strength of preference, e.g., provide a feedback value with a smaller magnitude to reflect weaker preferences. Our experiments suggest that our method surpasses past work on discrete feedback. One future research direction could be empowering the model to learn adaptive changes in human feedback over the course of trajectories or use multiple feedback modalities. We believe our framework can be a strong starting point for incorporating these improvements. We leave such exploration as future work. >(Question 2: “How would your method deal with games with more ambiguous state values, such as Montezuma's Revenge?”) Our method of incorporating human feedback can also encourage exploration behaviors which is critical for challenging tasks such as Montezuma’s Revenge. We have observed a similar conclusion in Find Treasure, where human feedback can help explore the environment while the target object is not yet available to the agent, as in Fig. 7. Our method is orthogonal to approaches that aim to reduce the ambiguity of feedback specifications. Exploring methods to reduce such ambiguity can be an interesting future direction. >“The human feedback is Markov (Question 3). This might not be true in more complex games.” (Question3: “The human feedback regressor $\bar{H}(s, a)$ uses the Markov assumption, but the human feedback might be dependent on their memory of prior states. What if the human feedback is non-Markov?”) We agree that human feedback may not always be Markov for any task. As we mentioned in Section 5.4, for Find Treasure and Hide-and-Seek, we stacked three consecutive frames as input to both the RL backbone and the feedback regressor. We found this to be sufficient to model human feedback. For more complex tasks, it will be interesting to explore whether incorporating more prior history steps or using a memory-based neural network will improve human feedback modeling. >“Minor typo and wording issues.” We thank the reviewer for pointing out some typos and wording issues. We will improve these in the revised version: 1) change A to Q in Equation 1; 2) use upper-case Q in Equation 2; 3) Define $R_{t+k+1}$; 4) list specific designs in line 125 and be specific for lines 125-127; 5) fix spacing in citations; 6) rename computational framework. --- Rebuttal 2: Comment: Dear Reviewer, Thank you again for your detailed review of our paper. We aim to try our best to address all your concerns with our point responses above. We truly value your feedback. As the end of the rebuttal period is approaching, please feel free to let us know if you have any additional questions or comments. We would be happy to answer them. We look forward to hearing your future thoughts! Best regards, Authors	Summary: The paper proposes a new framework for human-in-the-loop reinforcement learning, where the human and provide real-time and continuous feedback, and an algorithm where the learning agents uses the human feedback to accelerate policy learning. The paper conducted a user study of 50 subjects to demonstrate the effectiveness of the proposed framework in accelerating policy learning and improving success rates over RL and human-in-the-loop RL baselines. Optionally, a human feedback simulator can also be trained to mimic human feedback after a certain amount of time, reducing the amount of human input. Strengths: - The paper proposes human-in-the-loop RL where the human can provide real-time continuous feedback, which is a novel paradigm compared to mainstream existing work which focus on discrete feedback signals. - This work conducted a user study of 50 subjects, which is the largest among relevant works. This is a great contribution in assessing the effectiveness of human-in-the-loop RL. - The evaluation is done on three challenging tasks, and GUIDE outperform all the baselines by a large margin on the "find treasure" and "high and seek" tasks. - The paper provides a detailed individual difference characterization by conducting a series of human cognitive tests. Analysis of the human cognitive test data provides meaningful insights. These data can also be very useful in future work. Weaknesses: - The baselines are generally quite weak. Based on the experiment results, it is unclear whether real-time continuous feedback is necessarily the best way for humans to guide the policy learning. There might be intermediate points on the spectrum of conventional discrete feedback and full continuous feedback that provides the best tradeoff between amount of human input and effectiveness of guiding policy learning. - Whether the simulated human feedback is helpful is unclear. In both the "bowling" the "find treasure" task, the score does not increase much after switching to simulated feedback. It might be the case that the simulated human feedback only works for tasks where it is straightforward to model the reward. Technical Quality: 3 Clarity: 3 Questions for Authors: - How does human-in-the-loop compare to BC or reward engineering for the same amount of human input? - How are the three tasks for evaluation chosen, and what are the motivations for such choices? One motivation for doing human-in-the-loop RL is for tasks where designing a reward function or providing demonstrations are difficult, such as the backflip task. However, for the tasks examined in this paper, there seems to be other simple ways for the RL agent to learn from human input. Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: The paper focused on the final success rate of policy learning, but did not provide sufficient data from the user's perspective. For example, the user study failed to include a survey regarding whether the real-time feedback system feels easier to use than the discrete feedback system. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for their thoughtful comments. We are glad that the reviewer found our method to be novel, the scale of our human study to be “a great contribution,” and our human analysis to be insightful. We would like to address all of your concerns and questions below with point responses: ---- >“The baselines are generally quite weak. Based on the experiment results, it is unclear whether real-time continuous feedback is necessarily the best way for humans to guide the policy learning. There might be intermediate points on the spectrum of conventional discrete feedback and full continuous feedback that provides the best tradeoff between amount of human input and effectiveness of guiding policy learning.” We agree that it will be interesting to explore the “optimal” feedback mode. Based on feedback from our human participants, the continuous feedback mode was not cognitively demanding, hence a full continuous feedback that enables maximum human input is a straightforward and effective choice. We will leave the exploration of blending discrete and continuous feedback as future work. >“Whether the simulated human feedback is helpful is unclear. In both the "bowling" the "find treasure" task, the score does not increase much after switching to simulated feedback. It might be the case that the simulated human feedback only works for tasks where it is straightforward to model the reward.” We agree that the effectiveness of simulated human feedback will vary depending on the complexity of the environment and human feedback. The main purpose of the simulated feedback is to allow continual training without the human trainer and minimize the shift in reward distribution, which is a novel algorithm design. We will leave this interesting investigation of the relationship between task complexity and the effectiveness of simulated feedback as future work. >“How does human-in-the-loop compare to BC or reward engineering for the same amount of human input?” It is unclear how to quantify the amount of human input for reward engineering. One advantage of GUIDE is that we do not require human subjects to have prior knowledge of RL. However, reward engineering typically requires domain expert knowledge and experience in designing rewards for tuning RL policies. On the other hand, BC typically assumes expert demonstrations, which also demand more cognitive load from the subjects and expert-level demonstrations. However, for complex tasks, humans may not easily provide high-quality demonstrations while they can still provide an assessment of the agent’s decisions. Therefore, we believe that BC and reward engineering are not suitable comparisons in our case. >“How are the three tasks for evaluation chosen, and what are the motivations for such choices?” The bowling task is a classic environment commonly used in prior literature [1, 2, 3]. We included it to compare it with Deep Tamer. Find Treasure is a navigation task motivated by potential real-world applications of human-guided RL, such as search and rescue and disaster response. It also serves as an intermediate task before hide-and-seek, where the target does not move. Hide-and-seek is selected as a representative task involving adversarial competition. Most existing tasks in literature are discrete action tasks with low-dimensional states. We believe that our task selection is a large step forward in investigating the scalability of human-guided RL. >“One motivation for doing human-in-the-loop RL is for tasks where designing a reward function or providing demonstrations are difficult, such as the backflip task. However, for the tasks examined in this paper, there seems to be other simple ways for the RL agent to learn from human input.” Despite reward engineering that could exist for these tasks, our setting is different. Designing rewards requires expert knowledge and RL training experience. However, our setting does not assume such expert experience in our human subjects. Moreover, designing dense rewards for these tasks requires extra information that is not available to our agents, such as the position of the agent, the target object location (our environment only provides partial visual inputs where target objects may not be visible), and the location of the adversarial agent (our environment only provides partial visual inputs where the other adversarial agent are not always visible). Therefore, our setting does fulfill the suggestions from the reviewer where the reward function is difficult to design without such extra experience or extra exposed information. >“The paper focused on the final success rate of policy learning, but did not provide sufficient data from the user's perspective. For example, the user study failed to include a survey regarding whether the real-time feedback system feels easier to use than the discrete feedback system.” We would like to clarify that our work also quantifies individual differences and their impact on guided AI performance, as in our cognitive studies in Fig. 5 and 7. Surveys about user experience can be subjective. One possible solution is to quantify physiological signals to measure their cognitive load and stress level, combined with surveys. We leave such exploration in future work. Though we did not have a formal survey for this question, verbal feedback from our subjects suggests that most of them did not find the continuous feedback interface cognitively demanding. ---- references [1] Warnell, Garrett, et al. "Deep tamer: Interactive agent shaping in high-dimensional state spaces." Proceedings of the AAAI conference on artificial intelligence. Vol. 32. No. 1. 2018. [2] Park, Sung-Yun, Seung-Jin Hong, and Sang-Kwang Lee. "Human Interactive Learning with Intrinsic Reward." 2023 IEEE Conference on Games (CoG). IEEE, 2023. [3] Xiao, Baicen, et al. "Fresh: Interactive reward shaping in high-dimensional state spaces using human feedback." arXiv preprint arXiv:2001.06781 (2020). --- Rebuttal Comment 1.1: Comment: I thank the authors for addressing my questions. I increased the confidence score to 4. Considering the overall contributions and limitations of the paper, I will keep my other ratings. --- Reply to Comment 1.1.1: Comment: We appreciate your positive feedback! Thank you! --- Rebuttal 2: Comment: Dear Reviewer, Thank you again for your detailed review of our paper. We aim to try our best to address all your concerns with our point responses above. We truly value your feedback. As the end of the rebuttal period is approaching, please feel free to let us know if you have any additional questions or comments. We would be happy to answer them. We look forward to hearing your future thoughts! Best regards, Authors	Summary: This paper proposes a new framework, GUIDE, for learning from continuous human feedback in complex decision making domains with continuous action spaces. By framing human feedback as a state-action value function, the framework proposes to learn this function and to combine it additively with the (generally sparse) reward coming from the environment. The feedback is collected in a continuous fashion by asking participants to move their mouse up or down to indicate higher or lower feedback values. In a user study, the paper finds that training agents with this type of feedback yields better performing agents than baselines. After assessing participants in a suite of cognitive tests, it finds that participants that score higher on the cognitive tests trained better agents. Strengths: The paper introduces an interesting new way of collecting continuous human feedback, and shows significant improvement in two out of three tasks considered. The use of cognitive tests as part of the user study is interesting, and uncovers insightful correlation between subject performance and their cognitive test scores. Weaknesses: The assumptions regarding what human feedback represents do not seem consistent between section 3 and 4 (see Questions). Further, the treatment of the feedback collection is rather simple (added to environment reward function) and, especially if it does represent a signal regarding the future value of state-action pairs, heuristic. Relative to Tamer and Deep Tamer, which treated human feedback more consistently by using it directly as a proper state-action value function, this paper feels like a regression on that front. The implementation of the c-DeepTamer baseline raise a number of questions (see Questions), which shake my confidence in it as a baseline, or as a proper representative for how well Deep Tamer should perform here. Technical Quality: 2 Clarity: 3 Questions for Authors: In 3.2 you propose to extend Deep Tamer by using the human feedback estimator F(s,a) as a critic within an actor-critic framework. Thus, you treat human feedback here as an estimate of the future value of each state-action pair (a Q-value). In 4.3, you propose to use the human feedback signal as a reward, to be added to the environment reward. Does this mean you make a different assumption regarding human feedback in 4.3. than in 3.2? Or do you propose to use feedback on future value as a reward? I am confused by your claim that Deep Tamer uses DQN. Looking at algorithm 1 in the Deep Tamer paper, it’s policy greedily chooses the action that maximizes the learnt human value function H(s,a). I do not see any use of DQN. Did your c-DeepTamer baseline receive the same (sparse) environment reward as GUIDE? And if so, how did you use this reward signal in conjunction with a critic that is trained from human feedback only? Why was the training of c-DeepTamer stopped after 5/10 minutes? Would it not be possible to continue training it using simulated human feedback (similar to GUIDE) or without human feedback? Within the user study, did participants get time to familiarize themselves with each environment before data recording began? I imagine participants would have needed some time to figure out how to solve each task. Is equation (3) correct? What is the purpose of he additional $- F(s, A(s))$ term? Confidence: 2 Soundness: 2 Presentation: 3 Contribution: 2 Limitations: Limitations are discussed in the conclusion. Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for their thoughtful comments. We would like to address all of your concerns and questions below with point responses: ---- >“The assumptions regarding what human feedback represents do not seem consistent between section 3 and 4 (see Questions). ” We would like to clarify that c-DeepTamer and GUIDE use human feedback differently. c-DeepTamer, described in sec 3.2, is a baseline algorithm. It is an upgraded version of the original Deep Tamer[1], and follows the original Deep Tamer formulation to use human feedback as the myopic state-action value function. We did not modify how Deep Tamer uses human reward as a fair comparison. In GUIDE, we instead use human feedback as an additional immediate reward to the sparse environment reward. >“Further, the treatment of the feedback collection is rather simple (added to environment reward function) and, especially if it does represent a signal regarding the future value of state-action pairs, heuristic. Relative to Tamer and Deep Tamer, which treated human feedback more consistently by using it directly as a proper state-action value function, this paper feels like a regression on that front.” Tamer and Deep Tamer can treat human feedback directly as a state-action value function because they ignore the sparse environment feedback. However, we believe that it is still useful to leverage the sparse environment feedback for RL training. In GUIDE, Our design choice to use human feedback as an additional reward function is based on this intuition to integrate both types of feedback together. >“In 3.2 you propose to extend Deep Tamer by using the human feedback estimator F(s,a) as a critic within an actor-critic framework. Thus, you treat human feedback here as an estimate of the future value of each state-action pair (a Q-value). In 4.3, you propose to use the human feedback signal as a reward, to be added to the environment reward. Does this mean you make a different assumption regarding human feedback in 4.3. than in 3.2? Or do you propose to use feedback on future value as a reward?” Yes, we use human feedback differently in c-Deep Tamer and GUIDE. In Deep Tamer, human feedback is treated as a myopic state-action value. In GUIDE, we treat human feedback as a reward function, which we believe is a more appropriate and effective approximation, as evidenced by our experimental results. Moreover, this design choice makes it more natural to incorporate sparse environment rewards with the human reward in practice. >“I am confused by your claim that Deep Tamer uses DQN. Looking at algorithm 1 in the Deep Tamer paper, it’s policy greedily chooses the action that maximizes the learnt human value function H(s,a). I do not see any use of DQN.” Deep Tamer can be seen as DQN with $\gamma=0$, where the target state-value function at the current time step is directly assigned by humans. We realize that this phrase may cause confusion. We will remove the DQN claim in the revised paper and instead describe as Deep Tamer learns a reward model to regress human feedback, which is then used for greedy action selection. >“Did your c-DeepTamer baseline receive the same (sparse) environment reward as GUIDE? And if so, how did you use this reward signal in conjunction with a critic that is trained from human feedback only?” c-DeepTamer only upgrades Deep Tamer to handle continuous actions, with extensive recent neural network designs and hyperparameter tuning. Following Deep Tamer, it does not use an environment reward. As stated above, Deep Tamer treats human feedback as a myopic state-action value, which is not really a reward, making it impractical to add an environment reward to it. Changing the reward setup in Deep Tamer will make it unfair to compare. One contribution of GUIDE is to provide a formulation that uses both human reward and sparse environment reward. >“Why was the training of c-DeepTamer stopped after 5/10 minutes? Would it not be possible to continue training it using simulated human feedback (similar to GUIDE) or without human feedback?” We strictly follow the original Deep Tamer implementation which does not handle continual training. In the original Deep Tamer, the model weights are only updated every time when a new human feedback signal is received (see Algorithm 1, line 5 in the Deep Tamer paper[1]). When there is no human feedback available, Deep Tamer will not be improved. Both c-Deep Tamer and GUIDE are trained with the same amount of human guidance time. In fact, one contribution of GUIDE is to provide a mechanism to simultaneously train a simulated feedback model for continual training once human guidance is not available. We would like to clarify that this is our contribution in GUIDE instead of an inheritance from Deep Tamer. >“Within the user study, did participants get time to familiarize themselves with each environment before data recording began? I imagine participants would have needed some time to figure out how to solve each task.” Yes. Before each experiment, we showed the participants a short video introducing the goal of each game and a quick demonstration of how each game is played and how the feedback interface can be used. >“Is equation (3) correct? What is the purpose of the additional -F(s, A(s)) term?” Mathematically, the equation (3) is correct. The additional term -F(s, A(s)) is the actor loss, which tries to maximize the feedback value predicted by the critic network, given an action selected by the actor A(s). We recognize that the presentation may cause confusion since the actor and critic loss only affect their corresponding networks separately. We will clarify this by separating these two terms and indicate model updates in our revised paper. ---- references [1] Warnell, Garrett, et al. "Deep tamer: Interactive agent shaping in high-dimensional state spaces." Proceedings of the AAAI conference on artificial intelligence. Vol. 32. No. 1. 2018. --- Rebuttal 2: Comment: Dear Reviewer, Thank you again for your detailed review of our paper. We aim to try our best to address all your concerns with our point responses above. We truly value your feedback. As the end of the rebuttal period is approaching, please feel free to let us know if you have any additional questions or comments. We would be happy to answer them. We look forward to hearing your future thoughts! Best regards, Authors --- Rebuttal 3: Comment: Thank you for your detailed response. Unfortunately I continue to see two weaknesses in the paper. I like the proposed mechanism for giving feedback. It is elegant and to my knowledge novel. Reviewer JtyH has a point by saying that complex RL tasks will need more significant amounts of feedback, but in my view any interactive reward learning method would. This could have been explored more in the paper. The idea of combining environment reward with human feedback, however, cannot be counted as a novel contribution considering earlier work in this area [A,B]. Overall, the technical contribution is thus limited. A very solid set of human subject experiments would have been able to compensate for this, but in my view the experiments presented at this point are not quite complete enough. The c-DeepTamer baseline is artificially limited. My best understanding is that each bit of feedback was used only once in a gradient update, contrary to standard ML practice (please correct me if I'm wrong). Further, c-DeepTamer is not able to make use of the environment's reward, raising questions about whether it is a fair baseline in the first place. Why not use a baseline like the [A,B] that could use the environment's reward? The paper could also have been made much stronger by comparing to alternative interactive methods for learning from humans, including learning from preferences [C] and learning from demonstrations (e.g. [B]). I appreciate that the authors have clarified some of my concerns, and will raise my score accordingly, but I still feel that the paper falls short of the acceptance threshold. [A] Xiao, Baicen, et al. "FRESH: Interactive Reward Shaping in High-Dimensional State Spaces using Human Feedback." Proceedings of the 19th International Conference on Autonomous Agents and MultiAgent Systems. 2020. [B] Brys, Tim, et al. "Reinforcement learning from demonstration through shaping." Proceedings of the 24th International Conference on Artificial Intelligence. 2015. [C] Christiano, Paul F., et al. "Deep reinforcement learning from human preferences." Advances in neural information processing systems 30 (2017). --- Rebuttal Comment 3.1: Comment: Thank you for your response. We are glad that the reviewer found the feedback mechanism to be elegant and novel. We would like to address all of your concerns and questions below. ---- > “I like the proposed mechanism for giving feedback. It is elegant and to my knowledge novel. Reviewer JtyH has a point by saying that complex RL tasks will need more significant amounts of feedback, but in my view any interactive reward learning method would. The idea of combining environment reward with human feedback, however, cannot be counted as a novel contribution considering earlier work in this area [A,B]. Overall, the technical contribution is thus limited.” We agree that prior work has also used human feedback for reward shaping. However, we believe that our main contribution is using such a method to ground real-time dense continuous feedback and conduct large-scale human experiments to verify it. We will add relevant discussion of this literature in our revised manuscript. > “in my view the experiments presented at this point are not quite complete enough. The c-DeepTamer baseline is artificially limited. My best understanding is that each bit of feedback was used only once in a gradient update, contrary to standard ML practice (please correct me if I'm wrong).” To maintain a fair comparison, c-DeepTamer strictly follows Deep TAMER in the way gradients are updated. As described in the original Deep TAMER paper Algorithm 1, the gradient updates happen: (a) whenever the human provides new feedback, using the new feedback information as the data sample; and (b) at a fixed rate, using data sampled from the replay buffer. We believe that a stronger solution would be able to update the network as standard ML practice, which is exactly one of our contributions beyond the original DeepTamer work. However, if we modify the original DeepTamer work to include our contribution, our experiments will become an ablation study of our own method instead of comparing it with prior work. Considering the expensive 50 human studies, which already cost 2 hours per subject and $1,000, running ablations is unfortunately not feasible. Our choice is to focus on comparing the previous literature in the same setting as our problem. > “Further, c-DeepTamer is not able to make use of the environment's reward, raising questions about whether it is a fair baseline in the first place. Why not use a baseline like the [A,B] that could use the environment's reward? The paper could also have been made much stronger by comparing to alternative interactive methods for learning from humans, including learning from preferences [C] and learning from demonstrations (e.g. [B]).” We agree that additional baselines would be interesting to compare with. However, experiments involving real-time human interactions are costly to run. Our current 50 human experiments include three environments, two algorithms, cognitive tests, and initial and ending setup, as traditional human experiments already cost nearly 2 hours. The total cost of the experiments is $1,000. Longer experiment sessions will not only be more costly but will also affect human feedback quality. Under the time constraint, we chose the baseline that had the closest setting to ours. Deep TAMER is the state-of-the-art in real-time human-guided RL through scalar feedback of state-action pairs. [A] is not real-time, as the human operator provides feedback to trajectories sampled from a replay buffer. They also only provide feedback to actions or states instead of state-action pairs. As the reviewer has mentioned, [B] learns from demonstration, and [C] learns from preference, which are different settings from learning from feedback. We would like to clarify that our work did not argue that real-time continuous human feedback is the optimal modality to provide feedback. In particular, we did not argue that this modality is better or can replace demonstration or preference learning. For demonstration, it has a different assumption that humans may be experts in the tasks, and this does not fall into our problem setting. In fact, we observe that humans typically have difficulty performing very well in our challenging hide-and-seek task where things change very fast, and the observations are partial. Preference learning is offline, which assumes multiple rollouts are provided, and humans do not need to react in real-time. It is often applied to the whole trajectories instead of state-action pairs. Our real-time continuous human feedback proposes a different problem setup and can be an alternative modality. However, we leave the exploration of multiple modalities as future work. Therefore, from both the perspective of financial, time and human costs and the problem-setting perspective, we did not compare the baselines from different modalities or problem settings. Our experiments indeed show significant improvement over real-time discrete feedback, which supports our claims.	null	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Decentralized Noncooperative Games with Coupled Decision-Dependent Distributions	Accept (poster)	Summary: This paper examines endogenous distribution shifts in learning systems, where deployed models influence their environments, altering data distributions. The authors first prove a set of sufficient conditions for the existence and uniqueness of performative stable equilibrium (PSE) and Nash equilibrium (NE). The main contribution of the paper is to show that the distance between PSE and NE scales with the distributional shift parameter. They also provide a primal-dual algorithm for computing PSE, which achieves sublinear convergence rates for both performative regrets and constraint violations. Strengths: Although I did not check the proof, the results of the paper appear to be correct. I appreciate that the authors provide intuition for the underlying mechanism. I am not an expert in this particular field, so I cannot comment much on the contribution. My impression is that the theoretical contribution is fairly significant and the convergence rate shown in this paper is strong. Weaknesses: No Technical Quality: 3 Clarity: 2 Questions for Authors: 1. Is Theorem 3.4 just a simple corollary of Theorem 3.3? 2. The paper provides a sufficient condition for the existence and uniqueness of NE and PSE, but it is not necessary. Can you comment on the potential necessity for the existence and uniqueness of NE and PSE as well? Confidence: 2 Soundness: 3 Presentation: 2 Contribution: 2 Limitations: The authors did discuss the limitation Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We sincerely appreciate the reviewer for recognizing our contributions and for the constructive comments. Our point-to-point responses to concerns on Questions are given below. Reply to Question 1: Theorem 3.3 pertains to the existence and uniqueness of the performative stable equilibrium (PSE). Its characterization is based on the contraction condition of the dynamics of repeated risk minimization (RRM), as defined in Line 208. Theorem 3.4 pertains to the existence and uniqueness of the Nash equilibrium (NE), with the proof established on the strong monotonicity of the performative game (1). These two theorems follow distinct analytical processes, and Theorem 3.4 should not be considered a corollary of Theorem 3.3. Reply to Question 2: The study of equilibrium is fundamental in game theory because it ensures predictability and stability in strategic interactions among rational players. The existence of an equilibrium guarantees that there is at least one outcome where all players' strategies are mutually optimal responses, providing a foundation for predicting behavior in competitive scenarios. Uniqueness further enhances this predictability by ensuring a single, definitive outcome, eliminating ambiguity, and facilitating more straightforward strategic decision-making. This evaluation is essential for practical applications in economics, political science, and beyond, where reliable and stable outcomes are necessary for effective planning and analysis. We thank the reviewer for pointing this out, and we have included a discussion on this point in our manuscript. Moreover, we would like to highlight one of our contributions on the equilibrium analysis. This paper makes a significant technical contribution by presenting the first upper bound on the distance between PSE and NE, which is significant to understand the impact of data performativity in games. Such bounds have been a major focus in prior research on performative optimization but are challenging to quantify in games due to the competitive nature of players. We leverage relations provided by strong duality and derive a result comparable to the findings in performative optimization settings. Thank you again for your review and for recognizing our contributions. We appreciate the strengths you have identified and we would like to reiterate our key contributions, which have been positively acknowledged by other reviewers. For instance, Reviewer QNeF remarked that: > I believe that the paper makes a concrete contribution that fills a natural gap left in the literature. One can view most of the results derived in this paper as the natural counterparts of the results obtained by Perdomo et al. but in a more general non-cooperative game setting, which can be motivated in a number of applications. The results obtained in the paper take an important step toward characterizing the performative effect in multi-player non-cooperative settings. The theoretical results are technically non-trivial, and all claims appear to be sound. Given our contributions to the field of performative prediction and noncooperative games, we respectfully request that you consider improving the rating scores to enhance the likelihood of acceptance for this work. We thank you for your time and thoughtful consideration. --- Rebuttal Comment 1.1: Comment: Many thanks for your response.	Summary: This paper studies decentralized non-cooperative games with endogenous distribution shifts. In the model, each player aims to minimize its expected risk over a distribution that changes with their own and other players’ decisions, subject to a coupled constraint. The paper establishes conditions for the existence and uniqueness of Nash equilibria (NE) and and performative stable equilibria (PSE), and further bounds the distance between NE and PSE. The paper then proposes a primal-dual algorithm that computationally-efficiently solves the problem. Strengths: 1. The paper makes solid contributions on formulating and solving decentralized non-cooperative games with endogenous distribution shifts. The model is richer than existing works. 2. The paper first bounds the distance between PSE and NE. This is an important result in the setting of endogenous distribution shift because it characterize how the distribution shift coefficients influence the connection between different equilibrium notions. 3. The paper proposes a primal-dual algorithm for finding the PSE that is both computationally efficient and decentralized. The regret rate of matches the decentralized noncooperative game. 4. The paper carries numerical experiments that validates the theoretical results. Weaknesses: 1. Several existing works have studied noncooperative games under performativity. This work extend the existing formulation by considering coupled constraints and decentralized setting. However, the constraint condition is not the fundamental difficulty in optimizing non-cooperative games as is known in variational inequalities literatures. Furthermore, the proposed algorithm relies on the assumption that players can communicate through a graph A with irreducible and doubly-stochastic weight matrix. The assumption basically ensures that the decentralized information can be disseminated effectively and makes decentralized optimization trivial. In conclusion, the problem studied in this work seems incremental. 2. The proposed algorithm looks very similar to that in Lu et al., 2020. Technical Quality: 3 Clarity: 3 Questions for Authors: Why is the condition for $\mu$ different in E&U of PSE and NE? In assumption 4.1, what does $\nabla_\theta J(\xi,\delta)$ mean? why is the right hand side independent on $\delta$? Some minor issues: Some citations should be changed to \citep instead of \citet Line 224: $p_{ij} \propto $ should be $p_{ij} \leq$ Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: The weakness section lists some limitations of this work. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We sincerely appreciate the reviewer for recognizing our contributions and for the constructive comments. Our point-to-point responses to concerns on Weaknesses and Questions are given below. Reply to Weakness 1: 1. First, we would like to clarify that only two existing works, namely, Narang et al. (2023) and Wang et al. (2023), have explored performative games to the best of our knowledge, with Narang et al. (2023) considering a centralized case and Wang et al. (2023) focusing on a relatively restrictive model, both of which are constraint-free. In contrast, our work delves into a more practical setting with a mathematically richer model. Considering constraints is crucial since many performative games have inherent restrictions, such as safety and cost constraints in transportation, relevance and diversity constraints in advertising, and risk tolerance and portfolio constraints in financial trading. This leads to a completely different algorithm design and convergence analysis. Our work is based on the primal-dual technique, while theirs focuses on gradient descent. 2. Second, although there are works on non-cooperative games with constraints, the presence of data performativity poses significant challenges: - The NE evaluation needs to quantify the performative effect that the studied performative game requires the condition $\mu - \sum_{i=1}^n L_i \varepsilon_i \max_{j\in[n]} \sqrt{p_{ij}} - \sqrt{\sum_{i=1}^n L_i^2 \varepsilon_i^2p_{ii}}>0$ to guarantee monotonicity while the non-performative counterpart (Lu et al., 2020) only requires $\mu>0$, which is an assumption of the paper. - The PSE is a unique concept in performative games and has not been considered in (Lu et al., 2020). - The convergence analysis of our algorithm necessitates meticulous control of the performative effect to maintain the convergence order. Our results demonstrate how performativity influences convergence, slowing it down by a coefficient $\tilde\mu := \mu - \sum_{i=1}^n L_i \varepsilon_i \max_{j\in[n]} \sqrt{p_{ij}}$, which offers a theoretical foundation for designing decentralized performative game systems. 3. Furthermore, the vast majority of existing research on decentralized learning is based on the assumption of a doubly-stochastic weight matrix. Without this premise, consensus on decentralized systems cannot be guaranteed, rendering meaningful analysis challenging, if not impossible. 4. Last but most important, this paper presents the first upper bound on this distance between PSE and NE, which is significant to understand the impact of data performativity in games. Such bounds have been a major focus in prior research on performative optimization but are challenging to quantify in games due to the competitive nature of players. Reply to Weakness 2: Some comparisons of our work with (Lu et al., 2020) have been provided in the Reply to Weakness 1. We would like to supplement that the date performativity does not cause significant difference in the algorithm development when calculating stable points. The primary challenge lies in the performance analysis that requires bounding the deviation induced by the performative effect. This is common in the performative prediction literature where predominate works focus on finding performative stable points. Our algorithm can be extended to calculate the NE by incorporating the gradient of $D_i(\theta_i;\theta_{-i})$ with respect to $\theta_i$ in Step 7. However, estimating $D_i$ for all $i$ is computationally prohibitive as $D_i$ is related to the decisions of all players. Our algorithm results in a PSE that is not far from the NE, as demonstrated in Theorem 3.5. Reply to Question 1: The E&U of NE requires a more stringent condition since the computation of NE needs to take into account the gradient of $D_i(\theta_i;\theta_{-i})$ with respect to $\theta_i$ for all $i$. More specifically, NE computes the gradient of performative risk, given by $\nabla{\rm PR}(\theta) = G_{\theta}(\theta) + H_{\theta}(\theta)$, while PSE only considers the first component $G_{\theta}(\theta)$. Reply to Question 2: We appreciate the reviewer's observation. Assumption 4.1 pertains to the stochastic gradient variance of $\nabla_{\delta_i} J_i(\xi_i;\delta_i, \delta_{-i})$ and $G_{\theta}^{(i)}(\delta_i, \delta_{-i}) := E_{\xi_i\sim D_i(\theta)} \nabla_{\delta_i} J_i(\xi_i;\delta_i, \delta_{-i})$. To enhance clarity, we have revised Assumption 4.1 in our manuscript. Reply to Question 3: Thank you for pointing this out. We have carefully revised the citation style throughout our paper. Reply to Question 4: Thank you for the advise. Since $p_{ij}$ is the normalized influence parameter of $D_i$ with respective to $\theta_j$, to make sure that $\sum_{j=1}^n p_{ij}=1$, we take $p_{ij}\propto \mathcal{O}(1/n)$. Thank you again for your review and for recognizing our contributions. We appreciate the strengths you have identified, as they are crucial for the evaluation of this paper and align with the observations of other reviewers. For instance, reviewer QNeF provided the following positive remark: > I believe that the paper makes a concrete contribution that fills a natural gap left in the literature. One can view most of the results derived in this paper as the natural counterparts of the results obtained by Perdomo et al. but in a more general non-cooperative game setting, which can be motivated in a number of applications. The results obtained in the paper take an important step toward characterizing the performative effect in multi-player non-cooperative settings. The theoretical results are technically non-trivial, and all claims appear to be sound. Given our contributions to the field of performative prediction and noncooperative games, we respectfully request that you consider improving the rating scores to enhance the likelihood of acceptance for this work. We thank you for your time and thoughtful consideration. --- Rebuttal Comment 1.1: Comment: Thank you for the responses.	Summary: In this paper, the authors introduce the framework of decentralized noncooperative games incorporating the performativity factor and investigate the existence and uniqueness of two equilibrium concepts: Nash equilibrium and performative stable equilibrium. The distance upper bound between NE and PSE is firstly provided. To compute the PSE point under the given problem settings, a decentralized stochastic primal-dual algorithm is proposed, and corresponding convergence analyses are conducted. Strengths: The paper is well-written and easy to follow, clearly presenting the authors’ logic. The proof of the theorem is solid. Weaknesses: - Since the authors proposed the primal-dual algorithm to find the PSE solution, how can the NE be found under the performativity framework? In the Simulation part, how do the authors find $\theta^{ne}$? - The analytical techniques of the Decentralized Stochastic Primal-Dual algorithm appear to be a special case of the approach in Wood and Dall’Anese (2023), as the primal-dual algorithm can be transformed into a min-max problem. Are there any unique analytical techniques used in this paper? Could the authors provide a comparison between this work and Wood and Dall’Anese (2023)? [a] Wood, Killian, and Emiliano Dall’Anese. ``Stochastic saddle point problems with decision-dependent distributions." SIAM Journal on Optimization 33.3 (2023): 1943-1967. - In decentralized noncooperative games, each player is assumed to be selfish. Why would they want to communicate with their neighbors and share their information via a graph? In Line 4 of Algorithm 1, the estimator is constructed by a weighted average of the local parameter and neighbors' information. Is this reasonable in a competitive problem setting? I am confused by the logic of these game settings. - In Line 6 of Algorithm 1, the gradient is given as $\nabla_{\theta_i} J_i(\xi_i^t; \theta_i^t, \hat{\theta}_i^t) + \underline{\gamma_t} \nabla g_i(\theta_i^t)^\top \lambda_i^t$. Is this $\gamma_t$ a typo? The same concern arises in the equation after line 278. - Is Assumption 4.1 used in the proof of Theorem 4.2? Also, in Assumption 4.1, where is the $\delta$ in the right-hand side of the assumption inequality? - In Line 347, the performative strengths are set as $\rho=0.2, 0.4, 0.6$. I suggest using $\varepsilon$ to denote performative strength to maintain contextual consistency. Additionally, does this setting imply that all ${\cal D}_i(\theta_i)$ admit the same shifting strength? - How does the spectral gap of graph ${\cal G}(A)$, i.e., graph topology, affect the convergence results in Theorem 4.2? - Since Theorem 3.5, the upper boudn of PSE and NE is one of the major contribution of this paper, is there any corresponding simualtion which can support the theoretical results? Technical Quality: 3 Clarity: 3 Questions for Authors: Typo List: - Line 176, "there exists a constant $C\leq 0$ such that ...", it should be $C\geq 0.$ - After Line 208, second line of optimization problem, $g_i(u_i)$ should be $g_i(\theta_i)$. - In the problem after Line 727, symbol $\theta$ does not use same font. Same typo in equation (A37). Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: Please answer the questions in weakness part. I will reconsider the rating based on the author's response. Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for recognizing our contributions and for the constructive comments. Our point-to-point responses are given below. Reply to Weakness 1: Given the explicit expressions of the decision-dependent distributions $D_i(\theta)$ for all $i$, we can compute the exact gradient of the performative risk PR($\theta$). Consequently, the Nash Equilibrium (NE) can be asymptotically determined through best response dynamics. This approach is structurally similar to repeated risk minimization but crucially accounts for the decision-dependent nature of the distributions, rather than fixing them at the current deployment for each update. In our simulations, we employ this method to calculate the NE, which serves as our baseline for comparison purpose. We appreciate the reviewer's observation and have incorporated detailed explanations of the NE computation process in the simulation section of our manuscript. Reply to Weakness 2: We appreciate the reviewer for bringing this reference to our attention. We have incorporated a comprehensive comparison of our work with [a] in our paper, as summarized below: - [a] investigates centralized minimax optimization, whereas our work addresses a more complex model involving decentralized noncooperative players with partial information observation. Our analysis needs to account for consensus and competition among players. The NE of a game generally does not correspond to the optimal solution of its corresponding optimization problem. - [a] requires a more stringent assumption of strong-convexity-strong-concavity on the minimax problem. In contrast, our paper only necessitates the stochastic gradient mapping $\nabla J(\xi; \theta)$ to be monotone, which is a weaker condition than strong convexity. - We characterize the existence and uniqueness of the NE and PSE, which are concepts unique to game theory. Reply to Weakness 3: In noncooperative games, players are assumed to be both selfish and rational. Despite their self-interest, players have incentives to share information as it enables more effective optimization of their individual strategies, potentially leading to improved personal outcomes and enhanced overall game stability. The vast majority of existing research on decentralized games is predicated on this assumption of rational players. Without this premise, player behavior could become unpredictable, rendering meaningful analysis challenging, if not impossible. Reply to Weakness 4: The symbol $\gamma_t$ is not a typo; rather, it serves as a crucial coefficient for regulating the step size of the optimization process in Algorithm 1. Reply to Weakness 5: We appreciate the reviewer's observation. Assumption 4.1 pertains to the stochastic gradient variance of $\nabla_{\delta_i} J_i(\xi_i;\delta_i, \delta_{-i})$, which forms the foundation for Theorem 4.2. To enhance clarity, we have revised Assumption 4.1 and added it into Theorem 4.2 as a necessary condition. Reply to Weakness 6: Thank you for the valuable advice. We have substituted $\rho$ with $\varepsilon$ to denote the performative strength. You are right that this setting implies that all markets exhibit an equivalent shifting strength. Reply to Weakness 7: Let $\sigma_2(A)$ denote the spectral gap of the weight matrix $A$. The spectral gap affects the convergence results in Theorem 4.2 by a coefficient $\mathcal{O}\left(\frac{1}{1-\sigma_2(A)}\right)$, which is shown in Lemma E.5 of the Appendix. We omit this coefficient in Theorem 4.2 since this paper primarily concentrates on the impact of data performativity, which slows down convergence by a coefficient $\tilde\mu := \mu - \sum_{i=1}^n L_i \varepsilon_i \max_{j\in[n]} \sqrt{p_{ij}}$. Reply to Weakness 8: Thank you for the question. In the simulation of the networked Cournot game, Fig. 2(b) compares the total revenue of all firms at the PSE and NE. Figure 4 contrasts the demand prices across five markets, while Fig. 5 illustrates the quantities served by five firms in different markets at both PSE and NE. For the simulation of the ride-share market, Fig. 6 compares the time-averaged revenues of three platforms at PSE and NE, whereas Fig. 9 depicts the demand prices in distinct areas and the corresponding ride quantities offered by various markets at both PSE and NE. Reply to Questions: Thank you for your careful review. 1. We have rectified this typo in our manuscript. 2. In Line 208, the optimization variable is $u_i$ instead of $\theta_i$, thereby the expression of $g_i(u_i)$. 3. In Line 727 and equation (A37), the bold font $\boldsymbol{\theta}$ represents a vector that $\boldsymbol\theta_i = [\theta_{i1},\cdots,\theta_{im} ]^{\top}$ for all $i$, where $\theta_{ij}$ denotes the product quantity that firm $i$ sells to the $j$th market and is represented in non-bold font as a scalar. We sincerely appreciate the reviewer's meticulous review and useful comments. We would like to reiterate our key contributions, which have been positively acknowledged by other reviewers. For instance, Reviewer QNeF remarked that: > I believe that the paper makes a concrete contribution that fills a natural gap left in the literature. One can view most of the results derived in this paper as the natural counterparts of the results obtained by Perdomo et al. but in a more general non-cooperative game setting, which can be motivated in a number of applications. The results obtained in the paper take an important step toward characterizing the performative effect in multi-player non-cooperative settings. The theoretical results are technically non-trivial, and all claims appear to be sound. Similar commendations can be found in the remarks of the remaining two reviewers. Given our contributions to the field of performative prediction and noncooperative games, we respectfully request that you consider improving the rating scores. We thank you for your time and thoughtful consideration. --- Rebuttal Comment 1.1: Title: Follow-Up: Request for NeurIPS Rebuttal Response Comment: Dear Reviewer ReB3: Thank you again for taking the time to review our paper and provide your valuable feedback. As the rebuttal period comes to a close, we wanted to kindly check if our clarifications in the rebuttal have satisfactorily addressed the concerns raised in your initial review. Your feedback is invaluable to us. If so, we respectfully request you to consider updating your review score based on our responses. However, if you have any remaining questions or need further clarification from us, please do not hesitate to let us know. Once again, we sincerely appreciate your time and consideration. Your prompt response would be greatly appreciated. Sincerely, Authors of the paper --- Rebuttal 2: Comment: Dear Reviewer, I would be grateful if you could respond to the authors' rebuttal. Thanks, AC --- Rebuttal 3: Comment: I appreciate the authors’ detailed response. Regarding the novelty of the technique, I agree with Reviewer dWNU that the constraint condition is not the primary challenge in non-cooperative games, as the use of primal-dual algorithms to tackle Lagrangian form is a natural approach. Existing work [a] already provides a more general framework for min-max problems with performativity. Additionally, the convexity assumption on the constraint in Assumption 2.5 of the submitted paper appears to be somewhat strong. In Section 4, the convergence analysis in Theorem 4.2 indicates that performative shifts affect the regret bound by a constant factor, but this may not be an intrinsic challenge that performativity can bring in the analysis of primal-dual algorithm. Therefore, I would like to maintain my original rating of borderline reject.	Summary: The paper studies the effect of endogenous distribution shifts stemming from the underlying interaction of the learning system, as formalized in the recent framework of performative prediction. In particular, the paper focuses on the performative effect in a non-cooperative game in which players endeavor to minimize individual cost functions while satisfying coupled constraints. They consider two natural equilibrium concepts, and provide sufficient conditions for their existence and uniqueness. Further, they provide a bound relating the distance between those two, and they develop a decentralized stochastic primal-dual algorithm for efficiently computing one equilibrium that achieves sublinear rate under various assumptions. Numerical experiments support the theoretical results. Strengths: Overall, I believe that the paper makes a concrete contribution that fills a natural gap left in the literature. One can view most of the results derived in this paper as the natural counterparts of the results obtained by Perdomo et al. but in a more general non-cooperative game setting, which can be motivated in a number of applications. The results obtained in the paper take an important step toward characterizing the performative effect in multi-player non-cooperative settings. The theoretical results are technically non-trivial, and all claims appear to be sound; I did not find any notable issue. The related work section is also quite thorough, and the most relevant papers have been discussed adequately to the most part. Finally, the presentation and the writing are of high quality, and the main body goes a great job at giving high-level sketches of the main ideas behind the proofs. Weaknesses: In terms of weaknesses, I believe that some of the assumptions necessary for the theoretical results (Assumptions 2.1-2.5) require further justification. In most cases, the authors simply claim that the assumption is quite standard in some other settings, but that itself is not sufficient justification. The authors need to argue that the assumptions are also aligned with the applications considered in their paper, otherwise they appear to be artificial. Perhaps an example could serve to make that point. Besides the point above, an important caveat of the paper is that most of the results appear to follow from relatively standard techniques in the literature, and so the technical novelty is limited. Although the setting considered in the paper is, to my knowledge, novel, it seems that it can be readily reduced to well-understood problems in game theory. Technical Quality: 3 Clarity: 3 Questions for Authors: - The citation style is not used correctly; for example, "unseen data El Naqa and Murphy (2015)" should instead be "unseen data (El Naqa and Murphy, 2015)". That is, use parenthesis when the citation is not syntactically part of the sentence. This is done consistently thoughout the paper. - I would like to see more discussion concerning the papers by Li et al. (2022) and Piliouras and Yu (2023). It is not quite clear how those results relate to those in the paper. Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The authors have adequately addressed the limitations. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We sincerely appreciate the reviewer for recognizing our contributions and for the constructive comments. Our point-to-point responses to concerns on Weaknesses and Questions are given below. Reply to Weakness 1: Thank you for the useful comment. We have provided justifications for the conditions outlined in Assumptions 2.1-2.5 through both simulation examples, specifically the networked Cournot game and the ride-share market. Below is an excerpt of the justification for the networked Cournot game: > Given the formulation of the networked Cournot game, it is evident that the stochastic gradient mapping of $J(\cdot)$ adheres to Assumption 2.1, as expressed by: > > $$\left\langle \nabla J\left(\xi;\theta\right) -\nabla J\left(\xi;\theta^{\prime}\right), \theta - \theta^{\prime} \right\rangle \geq \mu \|\|\theta - \theta^{\prime}\|\|_2^2$$ > > with $\mu =2\varepsilon \min_j \frac{\alpha_j}{\sum_{j^{\prime}=1}^m\alpha_{j^{\prime}}} $, where $\varepsilon\geq 0$ denotes the performative strength of markets, and $\alpha_j$ represents the relative strength of market $j$ for any $j\in[m]$. > > Moreover, for any $i$, the quantity-dependent distribution $D_i(\theta)$ satisfies > > $$\mathcal{W}_1(D_i(\theta), D_i(\theta^{\prime})) \leq\varepsilon\sqrt{\sum_j\frac{\alpha_j}{\sum_j^\prime\alpha_j^\prime}\|\|\theta_j-\theta_j^{\prime}\|\|_2^2}$$ > > in accordance with the condition in Assumption 2. > > Furthermore, each local cost function $J_i(\cdot)$ demonstrates smoothness with a parameter $L \geq \varepsilon \max_j\frac{\alpha_j}{\sum_{j^{\prime}=1}^m\alpha_{j^{\prime}}}$ and thus satisfies the condition in Assumption 4. > > Given that the output quantity of each firm is constrained by an upper bound $Q_i$, Assumption 3 is inherently fulfilled with $C>\max_iQ_i$. > > Lastly, the Lipschitz condition of constraints in Assumption 5 holds true for any $G_g\geq 1$, under the accommodating quantity constraints of markets. > > Overall, the formulation of the networked Cournot game satisfies all assumptions required in our study. Reply to Weakness 2: We would like to highlight the following technical contributions of this paper: 1. We evaluate the conditions for the existence and uniqueness of both NE and PSE. The NE evaluation needs to quantify the performative effect that the studied performative game requires the condition $\mu - \sum_{i=1}^n L_i \varepsilon_i \max_{j\in[n]} \sqrt{p_{ij}} - \sqrt{\sum_{i=1}^n L_i^2 \varepsilon_i^2p_{ii}}>0$ to guarantee monotonicity while the non-performative counterpart (Lu et al., 2020) only requires $\mu>0$, which is an assumption of the paper. The PSE is a unique concept in performative games and has not been considered in conventional games without data performativity. 2. This paper makes a significant technical contribution by presenting the first upper bound on the distance between PSE and NE, which is significant to understand the impact of data performativity in games. Such bounds have been a major focus in prior research on performative optimization but are challenging to quantify in games due to the competitive nature of players. We leverage relations provided by strong duality and derive a result comparable to the findings in performative optimization settings. 3. The convergence analysis of our decentralized algorithm needs to carefully control the deviation caused by data performativity. The decentralized nature and the presence of constraints further complicate our analysis. Nevertheless, we derived a result that preserves the order of convergence as the case without data performativity (Lu et al., 2020). Our results demonstrate how performativity influences convergence, slowing it down by a coefficient $\tilde\mu := \mu - \sum_{i=1}^n L_i \varepsilon_i \max_{j\in[n]} \sqrt{p_{ij}}$, which offers a theoretical foundation for designing decentralized performative game systems. Reply to Question 1: Thank you for pointing this out. We have carefully revised the citation style throughout our paper. Reply to Question 2: Thank you for the advice. We have added more discussions on the works Li et al. (2022) and Piliouras and Yu (2023) in our paper. Similarly to our work, Li et al. (2022) and Piliouras and Yu (2023) also studied multiagent systems with performativity but in constraint-free scenarios. Specifically, Li et al. (2022) focused on decentralized optimization with consensus-seeking agents, where the data distribution of each agent depends solely on its own decision. They investigated conditions for the existence and uniqueness of performative stable solutions and provided theoretical analysis on the convergence of gradient descent algorithms in multiagent performative prediction systems. In contrast, Piliouras and Yu (2023) studied multiagent systems in a centralized fashion with data distributions restricted to location-scale families. Under this setting, they explored the existence conditions of performative stable points and demonstrated the equivalence of performative stability and performative optimality. We sincerely appreciate the reviewer's positive assessment. The strengths you have identified are crucial for evaluating this paper and align with observations from other reviewers. Given our contributions to the field of performative prediction and noncooperative games, we respectfully request that you consider improving the rating scores to enhance the likelihood of acceptance for this work. We thank you for your time and thoughtful consideration. --- Rebuttal Comment 1.1: Comment: I thank the authors for the detailed response. I have no further questions.	null	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
DiMSUM: Diffusion Mamba - A Scalable and Unified Spatial-Frequency Method for Image Generation	Accept (poster)	Summary: This paper introduces a state-space architecture for diffusion models that enhances local feature detection in image generation by combining spatial and frequency information. Traditional state-space networks like Mamba struggle with visual data processing, but integrating wavelet transformation improves local structure awareness. The method fuses wavelet-transformed outputs with original Mamba outputs and incorporates a globally-shared transformer to capture global relationships. Experiments show this approach achieves faster training convergence and high-quality outputs, demonstrating state-of-the-art results. Strengths: + The proposed method works on the frequency domain seems to be a good idea compared to existing mamba diffusion approaches. + The architecture looks like getting inspiration from DiT and transferring to the Mamba style may be interesting. + Performance on several datasets shows the promising method. Weaknesses: + Training longer looks like getting an overfitting curve, an analysis needs to be done. This behavior is contradict to Transformer-based diffusion DiT, MDT, MaskDiT, etc. + The paper claims the issue with quadratic computation of transformers-based diffusion but there is no comparison between the proposed method and the competitor for both 256 and 512 resolution. + The scalability is important for this architecture, but it is missing, which would weaken the paper. + On ImageNet, the crucial benchmark, the reported performance of the proposed method is not clearly better than DiT, and of course, cannot be comparable with the more advanced method transformer-based model such as MDT. This indicates that the proposed method seems still under-discovered, not better than the existing methods in the performance of image generation. Technical Quality: 3 Clarity: 2 Questions for Authors: Q1. How is performance if using the same sampling method as other competitors that are based on DDIM/DDPM, instead of ODE solver? This is to ensure a fair comparison. Q2. How is the performance w.r.t more sampling steps? A curve is a good demonstration. Confidence: 5 Soundness: 3 Presentation: 2 Contribution: 2 Limitations: Yes, they discussed Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: 1. Training longer looks like getting an overfitting curve, an analysis needs to be done. This behavior is contradict to Transformer-based diffusion DiT, MDT, MaskDiT, etc. Thank you for pointing out, we confirm that our method does have overfitting. After converging to the best FID10K score of 5.49 at epoch 250, the model begins to exhibit an overfitting pattern. We also observe the same overfitting problem for transformer-based diffusion models like DiT and MDT. Figure 3 in the rebuttal file demonstrates that overfitting does occur in transformer-based models, albeit at a later stage, starting from epoch 800 onward, due to their slower convergence rate compared to our model. We hypothesize that overfitting is not solely determined by model architecture but by various factors. For instance, the Improved DDPM [2] paper showed that with identical architecture in Appendix F, changing the noise scheduling from linear to cosine could lead to overfitting in same UNET architecture. Based on our empirical experiments above, we think that the overfitting effect is not only attributable to our architecture but rather a broader phenomenon in diffusion models. For MDT, overfitting emerges much later, around epoch 1100, due to its masking strategy, which could serves as a form of regularization to delay the onset of overfitting. 2. The paper claims the issue with quadratic computation of transformers-based diffusion but there is no comparison between the proposed method and the competitor for both 256 and 512 resolution. DIMSUM-L/2 achieves 2.2 seconds latency compared to DIT-L/2 with 3.8 seconds (see table 2 in rebuttal file). 3. The scalability is important for this architecture, but it is missing, which would weaken the paper. For this question, we provide our answers in the global response. 4. On ImageNet, the crucial benchmark, the reported performance of the proposed method is not clearly better than DiT, and of course, cannot be comparable with the more advanced method transformer-based model such as MDT. This indicates that the proposed method seems still under-discovered, not better than the existing methods in the performance of image generation. To answer this question, we break it down into two parts: (1) not clearly outperforming DiT and (2) underperforming compared to MDT. First, it is important to highlight that our method achieves competitive performance with DiT and DIFFUSSM-XL, requiring significantly fewer training epochs—specifically, 4x fewer than DiT and 2x fewer than DIFFUSSM-XL. Notably, our method also uses a smaller network size of 460M parameters, compared to 675M of DiT while still demonstrating strong generation capacity and faster training convergence. In the updated ImageNet table provided in the PDF, we show that our method can further surpass the performance of other diffusion baselines when trained for a similar training duration as DIFFUSSM-XL. Notably, our training iterations are still less than a third of those required by DiT and SiT, yielding the best FID score of 2.11. Though our method does not outperforms the results of MDT yet, we believe that MDT is orthogonal to our proposed architecture, where a masking scheme is introduced to enhance further the contextual learning ability of diffusion models, including our method. It is an interesting topic to combine with our network for boosting model performance as mentioned in the limitation of global response. 5. Q1. How is performance if using the same sampling method as other competitors that are based on DDIM/DDPM, instead of ODE solver? This is to ensure a fair comparison. To clarify, Euler solver and DDIM are the same, except that Euler operates on continuous time intervals and removes the additional stochastic noise in each denoising step. In the manuscript, we followed SiT, Zigma, LFM works on using adaptive solver like "dopri5" for evaluation. In table 5 of the attached PDF, we show that FID scores of adaptive ODE solver and Euler solver (or DDIM sampling) are similar with small numerical difference, reconfirming the fairness of the benchmarking with DiT. 6. Q2. How is the performance w.r.t more sampling steps? A curve is a good demonstration. We plot the FID-10K scores of various NFE used for evaluation in Fig. of the attached pdf. This shows that increasing NFE beyond 250 leads to minimal or no improvement in the FID scores. This behavior is consistent with the observation of the flow-matching in Figure 7 of FM paper, which has been shown to require fewer NFEs compared to other SDE-based methods. [1] Lipman, Yaron, et al. "Flow matching for generative modeling." ICLR 2023. [2] Nichol, Alexander Quinn, and Prafulla Dhariwal. "Improved denoising diffusion probabilistic models." International conference on machine learning. PMLR, 2021. --- Rebuttal Comment 1.1: Comment: Thanks for the rebuttal, it addressed some concerns, still remained some unclear points. 1) How is the latency comparison with 512x512? 2) Memory use is an important metric when claiming the efficiency of the proposed method (in Line 127), could authors provide Memory Use and Gflop besides a comparison with others for 256 and 512 resolution they showed in Tab. 2 rebuttal? 3) Could the authors explain some insights as to why their method is faster than DiT although it has more parameters than DiT? 4) In the proposed method, the input image is further processed with several handcrafted features of wavelet transforms and scanning operations, before patchifying and feeding into the model, which will also be considered to take more processing time to slow down the speed, are they accounted for in the inference speed when making a comparison for both 256 and 512 resolutions, and are they used the same NFE to compare? 5) In the paper, it mentioned transformers-based methods, including MDT, and MaskDiT, and the proposed method obviously cannot be comparable with these models, but the abstract claims it achieves state-of-the-art, which I believe is misleading and inappropriate. --- Rebuttal 2: Comment: Thank you for your response! We provide answers below: Q1. 512 latency 256 (latent size: $32 \times 32$) \| Method \| Time \| Params \| \| --- \| --- \| --- \| \| DiMSUM-L/2 \| 2.20s \| 460M \| \| DiT-L/2 \| 3.80s \| 458M \| 512 (latent size: $64 \times 64$) \| Method \| Time \| Params \| \| --- \| --- \| --- \| \| DiMSUM-L/2 \| 2.86s \| 461M \| \| DiT-L/2 \| 4.78s \| 459M \| Note: Previously, we measured our models's latency on two resolutions using the same device and GPU_ID (a single NVIDIA A100). However, for the result of our model upon 512x512, due to resource matter (occupied device), we used a different NVIDIA A100 (different device/GPU_ID), which could cause unfairness. We remesured using the same device/GPU_ID (same specs) for a fairer comparison. We appreciate your suggestion and have conducted additional benchmarks for 512x512 resolution images, following the same methodology used for 256x256 images in Table 2 of the rebuttal file. Our benchmarking process involves first warming up the model with 10 forward passes, then generating a single image (batch size = 1) 100 times, and finally calculating the average latency from these 100 runs. Note that the parameter change after changing image size is mainly due to the PatchEmbed layer of the architecture, which both models have. Q2. MEM and GFLOPs 256 (latent size: $32 \times 32$) \| Method \| MEM \| GFlops \| \| --- \| --- \| --- \| \| DiMSUM-L/2 \| 2.42G \| 84.49 \| \| DiT-L/2 \| 2.30G \| 80.74 \| 512 (latent size: $64 \times 64$) \| Method \| MEM \| GFlops \| \| --- \| --- \| --- \| \| DiMSUM-L/2 \| 2.46G \| 337.48 \| \| DiT-L/2 \| 2.34G \| 361.14 \| Given our time constraints, we focused our comparison on DiT-L/2, maintaining consistency with our latency comparison. The results, as shown in the table, reveal that DiMSUM-L/2's memory usage is slightly higher than its counterpart. This increase is expected, considering DiMSUM's slightly larger parameter count. Regarding GFlops, we acknowledge that for 256x256 images, DiMSUM produces about 4% more GFlops than DiT. However, an interesting trend emerges when we examine 512x512 images: DiMSUM's GFlops scaling is actually slower than DiT's. Consequently, at this higher resolution, DiT's GFlops exceed DiMSUM's by approximately 7%. This observation again aligns with the question 1 of reviewer RLU7.* This observation aligns with the known quadratic complexity of transformers as sequence length increases. Our hybrid model mitigates this issue; the impact of attention blocks is reduced, while Mamba demonstrates its linear scaling complexity as the token count grows. This architectural choice allows DiMSUM to maintain efficiency at higher resolutions, offsetting the initial GFlops difference at 256 resolution. Q3-Q4. Thank you for asking the questions. In table 2, we use dopri5 to sample image from both models. We hypothesis that our architecture converges to less ODE-curvature solution compared to DiT architecture [1], [2]. This means that we could use less NFE to achieve the better image quality compared to DiT architecture. It is noted that when using dopri5, each sampling process could require different NFEs depending on the initial noise. Additionally, we acknowledge that our method requires more preprocessing before each MambaBlock, which may introduce latency to the inference speed. Furthermore, as shown in Table 2b, adding more Wavelet level processing costs only 0.01 GFLOPs. We also confirm that all preprocessing components are included in our measurements. [1] Pooladian, Aram-Alexandre, et al. "Multisample flow matching: Straightening flows with minibatch couplings." arXiv preprint arXiv:2304.14772 (2023). [2] Lee, Sangyun, Beomsu Kim, and Jong Chul Ye. "Minimizing trajectory curvature of ode-based generative models." International Conference on Machine Learning. PMLR, 2023. Q5. To our knowledge, our method achieves state-of-the-art performance on several datasets, including CelebA and LSUN-Church. It's worth noting that while MDT and MaskDIT focused their benchmarks solely on ImageNet, our evaluation is more comprehensive, comparing against both transformer-based models and Mamba-based diffusion models such as DIFFUSSM and ZigMa. Regarding ImageNet, we acknowledge that our initial claim may cause confusions. We will revise our statement to more accurately reflect our findings: "Our method demonstrates superior results compared to DiT and DIFFUSSM, achieving faster training convergence and delivering high-quality outputs." It's important to highlight that both MaskDiT and MDT report their results using significantly larger models (-XL/2, approximately 675M parameters), while our results are based on a smaller model (-L/2, 460M parameters). Despite this size difference, our model achieves competitive performance. In fact, DiMSUM-L/2-G attains a slightly better FID score (2.11) than MaskDiT-G (2.28). We acknowledge your concerns as they are critical for the paper’s clarity and improvement. We will revise them in our manuscript. --- Rebuttal Comment 2.1: Comment: 1. Could authors confirm that the proposed method is faster mainly because of using less NFE in sampling? And will it be slower if both methods are used under the same NFE? 2. How many NFEs are used concretely for the tables just newly provided for each method (DiT and DiMSUM)? This is to ensure the understanding that the advantage of speed comes from the Mamba thing or just using fewer NFEs. Reading the whole paper, I just had in my mind that the model with the Mamba hybrid Transformer is faster than the pure Transformer, but it is not if they just use the same NFEs. And of course, their proposed method satisfied the need for more Memory and more parameters used. --- Reply to Comment 2.1.1: Comment: Thanks for your quick response! We provides our answers to your questions as follows: Q1. Observing the Memory and GFLOPS table above, it's true to claim DiMSUM-L/2 shows slower inference speed compared to its counterpart for 256x256 images using the same NFE (due to bigger GFLOPS), however, there are two crucial points to consider: 1. Scaling Efficiency: When we increase the image size to 512x512, as evident from the Memory and GFLOPS table, our model actually requires fewer GFLOPS at this higher resolution, thanks to its slower latency scaling which we mentioned above. Consequently, for 512x512 images and larger, DiMSUM-L/2 would outperform its counterpart in speed given the same NFE. 2. Adaptive Sampling Efficiency: We employ the dopri5 ODE adaptive solver for sampling from both models. This solver dynamically adjusts the NFE based on the initial noise and diffusion model characteristics, using the minimum NFE necessary to achieve optimal image quality. Notably, DiMSUM requires fewer NFE to meet the dopri5 stopping condition while still achieving a significantly better FID score than DiT. We hypothesize that our proposed hybrid architecture converges to a better solution with less curvature, enabling high-fidelity image production with fewer NFEs. With these two points, we emphasize upon the importance of our proposed architecture, rather than just the benefits given by the flow matching framework. Q2. About the exact number of NFE: Since dopri5 requires different NFEs depending on initial noise, we sample 100 random noises and generate images for both models using dopri5 to measure the NFE. The average NFEs for DIMSUM and DIT at resolution 256 are 61 and 143. For resolution 512, the average NFEs for DIMSUM and DIT are 82 and 138. --- Rebuttal 3: Title: Clarification of DiT term in the rebuttal Comment: This section was included to the global response above, however, we include it here for easy reference. We'd like to clarify that when we refer to DiT-L/2 in the rebuttal, we specifically mean the DiT-L/2 model trained using the flow matching framework like SiT. This choice ensures a fair comparison of inference speed. This comparison is more equitable because our DiMSUM model also employs the flow matching framework. Crucially, the sampling methods between traditional diffusion methods and flow matching methods differ significantly. By comparing DiMSUM to the flow matching-trained version of DiT (SiT), we ensure that both models use the same sampling approach during inference. By aligning sampling methods, we can accurately evaluate inference speed differences, ensuring that any variations are due to architectural choices rather than differences in sampling or training processes. We also sorry for the typo in table 2 of the rebuttal PDF, the parameters of DiMSUM-L/2 should be 460M, not 480M.	Summary: This paper introduces a novel architecture for diffusion models that leverages spatial and frequency information to emphasize local features in image generation. It integrates wavelet transformation into the state-space networks, such as Mamba, to enhance the awareness of local structures in visual inputs. The outputs are fused with original Mamba outputs using a cross-attention fusion layer to optimize order awareness, crucial for image generation quality. A globally-shared transformer is added to boost Mamba's performance. The method achieves state-of-the-art results on standard benchmarks, with faster training convergence and high-quality outputs. Strengths: - Overall, I appreciate this paper. It selects the most promising technical stacks—combining flow matching and Mamba—to address generative tasks. - The paper is well-organized, featuring valuable methodology design and experimental ablations. - It's interesting to see that the community has started considering state exploration in Mamba, as indicated in Line245. The initialization of the state is critical. We need to examine the code to understand how to implement it efficiently. See https://github.com/state-spaces/mamba/issues/101 for more details. Weaknesses: - In Line 106, I'm unsure why sigma brings extra computation when the scan path is larger, given that the computation is always fixed. - In Line105, it's important to note that flow matching has been utilized in various domains to capture the reader's interest. E.g., boosting diffusion[1], depth estimation[2], motiom[3], even text generation[4]. - In Line 176, I'm curious as to why only B, C, and delta are time-dependent. Why isn't A? - In Line183, One paper is missed. [5] - In Fig 3a, what does the notation on ZigMa mean? - Regarding line 261, what's the rationale behind sharing those parameters of transformers? Are there any previous works indicating its effectiveness? - In Table 1, it would be better to display training steps. Researchers of generative models tend to compare using training steps rather than epochs. - In Line342, for sweep4, considering four forwards in a single-forward usually leads to a worse training speed (iter/s) and increased memory usage. It would be interesting to compare these two aspects with other methods. - In Fig5, is there any reference to the jpeg-8 scan path? How does it defined? Suggestions: - The previously mentioned figure or table should be placed first. [1]. Boosting Latent Diffusion with Flow Matching [2]. DepthFM: Fast Monocular Depth Estimation with Flow Matching [3]. Motion Flow Matching for Human Motion Synthesis and Editing [4]. Flow Matching for Conditional Text Generation in a Few Sampling Steps [5], Latent Space Editing in Transformer-based Flow Matching Overall, I think the exploration of using Mamba and flow matching is the right way to go, while I have some technical concerns about it. I am eager to hear the authors’ feedback. Technical Quality: 4 Clarity: 4 Questions for Authors: as above Confidence: 5 Soundness: 4 Presentation: 4 Contribution: 4 Limitations: as above Flag For Ethics Review: ['No ethics review needed.'] Rating: 8 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: 1. In Line 106, I'm unsure why sigma brings extra computation when the scan path is larger, given that the computation is always fixed. 2. In Line105, it's important to note that flow matching has been utilized in various domains to capture the reader's interest. E.g., boosting diffusion[1], depth estimation[2], motiom[3], even text generation[4]. 3. In Line183, One paper is missed. For Q1,2,3, we admit that our wording is incorrect in this context and revise the sentence as "In this paper, we show that too many scanning orders, e.g., sweep-8 and zigzag-8, may introduce excessive information and lead to worse performance compared to sweep-4". We will cite the suggested papers. 4. In Line 176, I'm curious as to why only B, C, and delta are time-dependent. Why isn't A? We believe that the authors of Mamba would have a much better answer here. From our point of view, this implementation is made purely to prefer simplicity without sacrificing much performance. For more details, reviewers can check the interpretation in 3.5.2 of the Mamba paper. Simply put, time-dependent delta $\Delta_t$ is sufficient to ensure the selection mechanism for $\bar{A}$ via $\exp(A * \Delta_t)$. 5. In Fig 3a, what does the notation on ZigMa mean? We are sorry for the missing information; we will update the caption in the revised version. In this case, $\textdagger$ is our reproduced result based on Zigma's official code, and $\textdaggerdbl$ is an adopted result from LFM paper. 6. Regarding line 261, what's the rationale behind sharing those parameters of transformers? Are there any previous works indicating its effectiveness? As mentioned in L260, we drew inspiration from Zamba for the globally shared attention block. The primary purpose of this component is to reduce the model's parameter count while maintaining the competitive performance of the model by capturing the global dependencies between input tokens. Besides, Zigma also adopts a hybrid mamba-transformer architecture in the design to integrate the text condition for text-to-image generation effectively. 7. In Table 1, it would be better to display training steps. Researchers of generative models tend to compare using training steps rather than epochs. We acknowledge your comment and update Table 1 in the attached file. 8. In Line342, for sweep4, considering four forwards in a single-forward usually leads to a worse training speed (iter/s) and increased memory usage. It would be interesting to compare these two aspects with other methods. Actually, in our implementation, we don't run all scans in one forward (such as in VMamba), but we run each order alternatively following Mamba-ND and Zigma paper. Specifically, each Mamba block handles only one direction, and the four scanning orders in sweep4 are evenly distributed throughout the network's depth (number of layers). Sweep4, for example, has four scanning orders: (1) left-to-right, (2) right-to-left, (3) top-to-bottom, and (4) bottom-to-top. Assuming the network has only four layers, layer 1 handles (1), layer 2 handles (2), and so on. 9. In Fig5, is there any reference to the jpeg-8 scan path? How does it defined? As mentioned in L330, we derived the JPEG-8 scanning order from the scanning order of the JPEG compression algorithm, as described in "A fast JPEG image compression algorithm based on DCT". This also was significantly influenced by the Zigma paper, a pioneering work that put effort into a more sophisticated scanning order and achieved competitive results. Building upon their insights, we extended the concept to the original JPEG scanning orders. We acknowledge the valuable contribution of the Zigma paper and will provide a more detailed explanation of our scanning order development in the camera-ready version for improved clarity. 10. The previously mentioned figure or table should be placed first. As mentioned in the global response, we thank the reviewer for your attention to detail, which is extremely vital to enhance the clarity and completeness of the paper. We will try our best to reorder the figures and tables so that it would appear before being mentionned. --- Rebuttal Comment 1.1: Title: reply Comment: Thanks for the author's reply. I have also read the other reviewer's opinion. My concerns are fully resolved, so I will increase my score to 8 to reflect this. I encourage the authors to consolidate the results on ImageNet to compare with related baselines with Zigma. --- Reply to Comment 1.1.1: Comment: Thank you for raising your concerns as well as for the detailed review of our paper's presentation. Addressing those definitely improves our paper generally. We will further follow your valuable recommendation!	Summary: This paper proposes a novel Mamba-based diffusion model, DiMSUM, which leverages both spatial and frequency information to enhance visual generation capabilities. Specifically, DiMSUM applies wavelet transformation to the input signals, decomposing them into wavelet subbands. By employing a query-swapped cross-attention technique, DiMSUM effectively integrates spatial and frequency information. Furthermore, DiMSUM incorporates several transformer blocks into the Mamba model, enriching the global context features. Strengths: 1. The paper is well-motivated. It observes the difficulties caused by the manually-defined scanning orders in tradition Mamba-based diffusion models, and uses transformation in the frequency domain to mitigate this problem. 2. The paper is well-written and easy to follow. Weaknesses: 1. Since the authors argue the incorporation of frequency information can mitigate the problem caused by the scanning order, I urge the authors to conduct an experiment to verify whether the generation performance of DiMSUM model is sensitive to the scanning order. 2. Stronger baselines (such as [1]) and the experiments on more datasets (such as conditional generation on MSCOCO) and resolutions are required. 3. From Table 2(a), it seems that the Wavalet transformations would harm the performance (i.e., FID and recall), which cannot demonstrate the effectiveness of the proposed method. [1] Chen, Junsong, et al. "Pixart-$\alpha $: Fast training of diffusion transformer for photorealistic text-to-image synthesis." arXiv preprint arXiv:2310.00426 (2023). Technical Quality: 3 Clarity: 3 Questions for Authors: See the weaknesses part. Meanwhile, I recommend the authors to provide sufficient experiments to support your method. And I would consider increasing my score if the above concerns can be addressed. Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: See the weaknesses part. All of my concerns have been addressed. I will increase my score. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: 1. Since the authors argue the incorporation of frequency information can mitigate the problem caused by the scanning order, I urge the authors to conduct an experiment to verify whether the generation performance of DiMSUM model is sensitive to the scanning order. To substantiate our claims regarding the efficiency of frequency information, we conducted a comprehensive ablation study. This study utilized four scanning orders: (1) bidirection, (2) jpeg-8, (3) sweep-8, and (4) zigzag-8. We trained models on CelebA-HQ at 256x256 resolution for 250 epochs, comparing performance when applying these scanning strategies to: a) spatial domain only or b) both spatial and frequency domains Table 3 of rebuttal file presents the results of this ablation study. Notably, integrating frequency domain information across all four scanning strategies led to significant performance improvements. This consistent enhancement across various scanning methods provides strong evidence for the effectiveness of our approach in leveraging frequency information. 2. Stronger baselines (such as Pixart-alpha) and the experiments on more datasets (such as conditional generation on MSCOCO) and resolutions are required. We appreciate the suggestion to explore text-to-image (T2I) generation. However, training competitive text-to-image models presents significant challenges: - Computational constraints: As a small lab, we lack the extensive resources required for training large-scale T2I models. - Dataset availability: Recent closure of datasets like LAION-5B limits access to suitable training data for T2I tasks and also would be hard to compare fairly with previous works using those datasets. It's worth noting that focusing on label-to-image tasks, as we have done, is common in diffusion model research like DiT, EDM, and Consistency Models. Many influential papers in this field have established their contributions through experiments on label-to-image before expanding to text-to-image. 3. From Table 2(a), it seems that the Wavalet transformations would harm the performance (i.e., FID and recall), which cannot demonstrate the effectiveness of the proposed method. We hypothesize that spatial and frequency signals are not aligned and require careful integration to leverage their information. Naively fusing these domains (e.g., by concatenation) can damage performance due to conflicting or misaligned information. To address this challenge, we proposed a more sophisticated fusion method using Cross-Attention layers between these spaces. This approach enables the model to effectively combine information from both domains, leveraging their strengths while mitigating potential conflicts. Hence, this fusion technique can enhance the FID from 5.87 to 4.92 in Table 2c submission, contributing to the SoTA result of our method. --- Rebuttal Comment 1.1: Comment: Thanks for the feedback. All of my concerns have been addressed. I will increase my score. --- Reply to Comment 1.1.1: Comment: We sincerely thank you for the insightful review and supportive feedback to make the paper more complete. Your support is highly appreciated, and we're glad that our responses have addressed your concerns.	Summary: This paper proposes to employ a Mamba-transformer hybrid framework with wavelet-spatial scanning for image generation. The authors claim that the scanning in the frequency domain can model the long-range relations of tokens in 2D spatial space. The experiments and ablation studies have shown the effectiveness of the proposed method. Strengths: - This paper is easy to follow. - The implementation details and the codes are included in this submission. - The performance on multiple datasets and sufficient ablation studies have verified the effectiveness of the proposed method. Weaknesses: - The proposed method is too complex. Scanning the image and frequency space makes the framework complicated. The authors further introduced transformer blocks in the mamba framework, which added more complexity to the entire method. - Why do the authors mention "manually-defined scanning orders" in their abstract? This issue is not discussed in the subsequent contents of the paper. Moreover, it cannot be addressed by the scanning in the frequency domain. The representation of an image in the frequency domain also has two dimensions, so the challenges for the scanning on the frequency domain should be the same as the scanning on the image space. Moreover, the scanning directions of the proposed method are also manually defined, even a window scanning is involved. - The comparison of the real inference speed between the proposed framework and transformers is not included in this paper. - Although the authors claim that they propose a Mamba-based diffusion model. However, this model still includes many transformer blocks, so this is a hybrid model rather than a Mamba model. Some claims in this paper like ''mamba-based'' or ''Mamba models'' should be revised. Moreover, is the spatial-frequency scan also powerful on the pure transformer model? Does the Mamba-transformer beat the pure transformer model given the same input setting? - The title of this paper claims that the proposed method is scalable. However, the parameter counts of the proposed model is smaller than 1.0B, so this title may not be proper. Technical Quality: 2 Clarity: 3 Questions for Authors: - In Figure 3(d), why does DiT perform so poorly on CelebA-HQ? Are there any bugs? DiT works very well on many large-scale datasets. Confidence: 4 Soundness: 2 Presentation: 3 Contribution: 2 Limitations: Although this paper uses public datasets, at least a section for social impact should be included in this paper. Moreover, this papers does not discuss the limitations of the proposed method. Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: 1. Our architecture might comprise many components such as Mamba, Transformer, and frequency processing. However, each proposed component is well-motivated and vital to the overall framework, as shown in Table 2a (in submission). The simple Mamba network, without frequency processing and transformer blocks, cannot surpass the performance of the transformer. As shown in section 2.1 submission, the scanning order of the Mamba block has a significant effect. To mitigate its impact, we integrate wavelet frequency with window scanning into architecture. As explained in the global response, wavelet scanning, along with window scanning, can better capture the global information of each wavelet subband, enhancing the overall global information across the whole image. In addition, our model could benefit from learning both high and low frequency [1]. With wavelet frequency and window scanning, our framework reduces FID from 5.27 to 4.92 for CelebA-HQ (Table 2e in submission). Furthermore, recently, hybrid architectures of Transformer and Mamba [2, 3] have demonstrated SoTA performance in NLP tasks. Motivated by these works, we measure the performances of hybrid Transformer-Mamba in vision generative. As shown in Table 2f submission, both independent and shared transformer improves performance, indicating hybrid model's effectiveness. [1]: Hao Phung, Quan Dao, and Anh Tran. "Wavelet diffusion models are fast and scalable image generators." In CVPR 2023. [2]: Zyphra unveils zamba: A compact 7b ssm hybrid model, 2024. https://www.zyphra.com/zamba [3]: O. Lieber et al. Jamba: A hybrid transformer-mamba language model. arXiv preprint arXiv:2403.19887, 2024 2. We acknowledge that the presentation of our paper should be clearer and appreciate your feedback. To clarify, the term "manually-defined scanning orders" refers to the heuristic scanning order in the Mamba blocks. In Section 2.1, from lines 94 to 107 (in submission), the scanning order of Mamba is defined as hand-crafted in previous works. Throughout the paper, we mentioned some of these hand-crafted orders, including "bi", "window", "sweep-4/8", and "zigzag-8". These scanning orders are illustrated in Figs 2, 5, and 6 in submission. Although our approach does not completely address the impact of scanning order, our window scanning strategy in wavelet space could efficiently capture the global information within each frequency sub-bands which improves global content of generated image, as explained in global response. Please refer to table 3 (in rebuttal file), our wavelet and window scan component successfully reduce FID score compared to spatial scanning only. Therefore, we consider our frequency scanning method to be synergistic with image space scanning, as it effectively handles the global information of generated image. Besides, completely resolving the limitations of manually-defined scanning is an interesting topic for future research. 3. DIMSUM-L/2 achieves 2.2 seconds latency compared to DIT-L/2 with 3.8 seconds (see table 2 in rebuttal file). 4. In terms of model's type, we would like to revise the terms "Mamba-based" and "Mamba model" to "a hybrid Mamba-Transformer network" for better comprehension. In terms of spatial-frequency scan for transformer, we modify DiT architecture to further incorporate wavelet frequency information similar to DIMSUM. After training spatial-frequency transformer on CelebA-HQ for 1000 epoch, we found that the spatial-frequency transformer failed to learn the human face distribution. The output model only generates noise-pattern images. More rigorous analysis of model is beyond the scope of paper and we would like to leave it for future investigation. 5. We acknowledge that the use of term 'scalable' may have caused some confusion. In the broader context, deep learning’s scalability may refer to capacity to handle various datasets and computational resources while producing correct results in an acceptable period of time [1]. Our model aligns well with this definition of scalability. Our experiments demonstrated that: - The model adapts to multiple datasets with minimal hyperparameter tuning (similar to DiT paper). - It achieves competitive performance metrics compared to other methods. - Inference speed is also faster, as shown in table 2 (in rebuttal file). Our SoTA results are achieved with a parameter count comparable (or even smaller) to existing models. Refer to Figure 3a and 4a (in submission) and Table 1 (in rebuttal file). This suggests substantial room for further enlargement of our model's parameters, which we anticipate will yield even better improvements across various and bigger datasets (see table 4 in rebuttal file). 6. Our plot intentionally stops at epoch 300, demonstrating the model's capability to converge faster than other methods. DiT does perform well on CelebA-HQ but takes more than 500. Figure 4 (in rebuttal file) illustrates the convergence of DiT at the later epoch. It's noted that DiT and LFM (in figure 3d submission) use the same DiT-L/2 architecture. While DiT uses diffusion loss, LFM uses flow matching. LFM converge faster than DiT. However, our model with flow matching loss, demonstrates even faster convergence than LFM, indicating our architecture enhances convergence rate. 7. Social Impact section will be added in revised paper (see global response). --- Rebuttal Comment 1.1: Comment: Thank you for your reply. Your rebuttal has solved most of my concerns, but some are still not addressed. The remaining concerns almost overlap with Reviewer C5pc's new concerns. For example, (1) why your mamba-transformer is faster than DiT? The rebuttal shows that DIMSUM is faster than DiT on ImageNet 256 (256 tokens considering the downsampler of the pre-trained autoencoder), however, a single Mamba module is faster than a transformer module only when the number of tokens is greater than 1000 (please refer to Fig. 8 in [1]); (2) the performance of DiMSUM after longer training on ImageNet 256 is 2.11 which is worse than SiT (FiD=2.06) [2], though both of these methods use flow matching. Thus, the performance gain of Mamba remains ambiguous (at least marginal). [1] Gu A, Dao T. Mamba: Linear-time sequence modeling with selective state spaces[J]. arXiv preprint arXiv:2312.00752, 2023. [2] Ma N, Goldstein M, Albergo M S, et al. Sit: Exploring flow and diffusion-based generative models with scalable interpolant transformers[J]. arXiv preprint arXiv:2401.08740, 2024. --- Rebuttal 2: Comment: Thank you for your response! We provide our answers below: (1) Why faster? We agree with the statement “a single Mamba module is faster than a transformer module only when the number of tokens is greater than 1000”. In the provided table below, we can see that Gflops of DIMSUM with 256 token is higher than Gflops of DiT. The reason why our model take less time to generate image is that we use dopri5 to produce image at inference time. We conjecture that DIMSUM could converges to less ODE-curvature solution compared to DiT architecture [1], [2]. Therefore, our architecture use less NFE to achieve the better image quality compared to DiT architecture (this is also indicated by our FID result on several benchmarks like CelebA-HQ and Church). Moreover, with resolution 512 (1024 tokens), we can see that our architecture achieves lower Gflops and inference time. This demonstrate the potential use of DIMSUM in larger benchmark like text-to-image which has larger resolution. [1] Pooladian, Aram-Alexandre, et al. "Multisample flow matching: Straightening flows with minibatch couplings." arXiv preprint arXiv:2304.14772 (2023). [2] Lee, Sangyun, Beomsu Kim, and Jong Chul Ye. "Minimizing trajectory curvature of ode-based generative models." International Conference on Machine Learning. PMLR, 2023. 256 (latent size: $32 \times 32$) \| Method \| Time \| Params \| GFlops \| \| --- \| --- \| --- \| --- \| \| Ours-L/2 \| 2.20s \| 460M \| 84.49 \| \| DiT-L/2 \| 3.80s \| 458M \| 80.74 \| 512 (latent size: $64 \times 64$) \| Method \| Time \| Params \| GFlops \| \| --- \| --- \| --- \| --- \| \| Ours-L/2 \| 2.86s \| 461M \| 337.48 \| \| DiT-L/2 \| 4.78s \| 459M \| 361.14 \| *Note: In the previous edition, we measured the time latency of all models on two resolutions using the same device and GPU_ID (a single NVIDIA A100). However, for the result of our model upon 512x512, due to resource matter (occupied device), we used a different NVIDIA A100 (different device/GPU_ID). We acknowledged that changing devices could cause unfairness. We fixed it by remeasuring using the same device/GPU_ID (same specs) for a fairer comparison. This issue doesn't affect GFLOPS since we did this separately and already used the same device/GPU_ID. Sorry for the inconvenience. (2) Compare with SiT Thank you for noting the SiT model comparisons. To clarify, the SiT model in Table 1 of our paper (FiD=2.15) and the SiT model with FiD=2.06 are the same but with different samplers. We reported the FiD=2.15 result for a fairer NFE comparison, which we'll explain further below. The SiT authors used two sampling methods for their model. Table 9 of the SiT paper shows results for SiT-XL (cfg=1.5, ODE) with FiD=2.15 and SiT-XL (cfg=1.5, SDE:σ_t) with FiD=2.06. The latter, achieved with a 250 NFE Heun (SDE) solver, is computationally equivalent to a 500 NFE Euler solver, as the Heun solver requires an additional model forward pass per step. Given the substantial computational requirements and our limited remaining time, evaluating ImageNet using this method is not feasible during the rebuttal phase. However, our comparison using SiT-XL (cfg=1.5, ODE) remains valid. Insights from SiT’s section 3.5 and Table 9 suggest that DiMSUM, using the same flow matching and training framework, would likely see a similar performance boost with the SDE sampler. We will conduct this evaluation and include the results in the revised version, with clear specification of the sampling method for full transparency. Lastly, we'd like to highlight that our model is considerably smaller than the SiT model (460M vs 675M parameters). This size difference indicates the model scalability for improvement in our approach, as shown by the parameter scaling ablation in Table 4 of our rebuttal. This study reveals that the upscaled DiMSUM-XL/2 slightly outperforms the L/2 version in FID (3.76 vs 3.45). We acknowledge your concerns as they are critical for the paper’s clarity and improvement. We will revise them in our manuscript. --- Rebuttal 3: Title: Clarification of DiT term in the rebuttal Comment: This section was included to the global response above, however, we include it here for easy reference. We'd like to clarify that when we refer to DiT-L/2 in the rebuttal, we specifically mean the DiT-L/2 model trained using the flow matching framework like SiT. This choice ensures a fair comparison of inference speed. This comparison is more equitable because our DiMSUM model also employs the flow matching framework. Crucially, the sampling methods between traditional diffusion methods and flow matching methods differ significantly. By comparing DiMSUM to the flow matching-trained version of DiT (SiT), we ensure that both models use the same sampling approach during inference. By aligning sampling methods, we can accurately evaluate inference speed differences, ensuring that any variations are due to architectural choices rather than differences in sampling or training processes. We also sorry for the typo in table 2 of the rebuttal PDF, the parameters of DiMSUM-L/2 should be 460M, not 480M. --- Rebuttal Comment 3.1: Title: Thank you. Comment: We sincerely thank you for your thorough review and your review is insightful and helpful to our paper. We hope our answer could resolve your concern. We wish you a good Neurips.	Rebuttal 1: Rebuttal: We address the reviewers' comments below, referring to them as: R1(RLU7), R2(eitf), R3(nhSz), R4(C5pc). We sincerely thank all reviewers for their valuable feedback. We appreciate the positive comments on clear writing and good flow (R1, R2, R3), well-defined motivation to investigate and integrate Mamba with Transformer (R2, R3, R4), our novel approach of integrating frequency space into Mamba (R4), and thorough and extensive experiments (R1, R4). Scanning in Frequency Space: We would like to further elaborate on the motivation and effectiveness of our frequency scanning method. Mamba-based approaches in diffusion models often struggle with efficiently scanning patches while maintaining local and global 2D-spatial information. Although several works have proposed sophisticated scanning methods to address this issue, these approaches are complex and computationally expensive. Conversely, some methods have adopted local scanning (i.e., windowing) strategies [3] to improve model latency and throughput. Still, these often underperform compared to previously mentioned scanning methods as it is limited to the dependencies of nearby-pixels within window. DiMSUM addresses these challenges by breaking the original image into frequency wavelet subbands (each subband is half of resolution of image). This approach is efficient to capture long-range frequency while preserving information across different subbands. We redesigned the window scanning, where each window corresponds to a subband of the frequency space (Fig 1 rebuttal PDF). Consequently, each window captures low/high frequency signal of original image. Since each frequency sequence is 1/4 of image sequence, negative impact of scanning is reduced. As the model progresses through different subbands, it incorporates spatial information represented at various low-to-high frequencies, adding valuable context to the process. This key difference distinguishes our method from traditional window scanning in image space. We conducted two key ablation studies to validate this: 1. Table 3 (rebuttal PDF) shows models using both frequency and spatial domains consistently outperform spatial-only models across various scanning orders, demonstrating the robustness and effectiveness of frequency domain intergration. 2. Table 2e (submission) confirms our window-scanning strategy's efficacy in the frequency domain, achieving the best FID of $4.92$ on CelebA-HQ at $256 \times 256$ resolution. These studies substantiate the effectiveness of our frequency domain integration and scanning strategy. Scalable term We acknowledge that the use of the term 'scalable' may have caused some confusion, given its current association with model parameter scaling in the LLM-dominated landscape. However, in the broader context, machine learning/ deep learning algorithms’ scalability may refer to their capacity to handle bigger datasets and computational resources while producing correct results in an acceptable period of time. Our model aligns well with this definition of scalability. Our experiments demonstrated that: - The model adapts to multiple datasets with minimal hyperparameter tuning (similar to DiT paper). - It achieves competitive performance metrics compared to other methods. - Inference speed is also faster, as shown in table 2 (in rebuttal file). Our SoTA results are achieved with a parameter count comparable (or even smaller) to existing models. Refer to Figure 3a and 4a (in submission) and Table 1 (in rebuttal file). This suggests substantial room for further enlargement of our model's parameters, which we anticipate will yield even greater improvements across various and bigger datasets (see table 4 in rebuttal file). Presentation: We appreciate the reviewers' suggestions for improving our presentation. We will address the following in our revised version: 1. Inconsistent/Misunderstanding terms (e.g., "manually-defined scanning orders," "Mamba-based" (R1) 2. Addition of social impacts and limitations sections (R1). 3. Claim about the computation of larger scan path (R3). 4. Missing citations and annotation definitions in captions (R3). 5. Figures and tables orderings (R3). 6. Updated ImageNet table with training iterations instead of epochs as suggested by (R3) and the new results of our method when trained for the same number of iterations as DIFFUSSM. Additionally, we apologize for the typo regarding the training epochs for DIFFUSSM. It should be corrected from 1.4K to 515. Social impacts and limitations: We believe that our proposed network advances the architectural design of state-space models for image generation. This model can be extended to various tasks, such as large-scale text-to-image generation and multimodal diffusion. While there is a risk that our architecture could be misused for malicious purposes, posing a social security challenge, we are confident that this risk can be mitigated with the recent development of security-related research. Hence, the positives can outweigh the negative ones, rendering the concern minor. While our method outperforms other diffusion baselines in generation quality and training convergence, we acknowledge areas for improvement. These include enhancing multiscale feature paradigms and multi-scale diffusion loss robustness [1, 2], and addressing manually-defined scanning orders. We're also intrigued by recent masked-training diffusion methods (e.g., MaskDiT, MDT), which reduce computational requirements and potentially improve global context learning. Integrating these orthogonal approaches with our work could yield further improvements. [1] Crowson, et al. "Scalable high-resolution pixel-space image synthesis with hourglass diffusion transformers." In ICML, 2024. [2] Hoogeboom, et al. "simple diffusion: End-to-end diffusion for high resolution images." In ICML, 2023. [3] Huang, et al. "Localmamba: Visual state space model with windowed selective scan." In Arxiv, 2024. Pdf: /pdf/f215d1762fbd9a21b0a4e23d11f43000149b19f7.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Privacy Backdoors: Enhancing Membership Inference through Poisoning Pre-trained Models	Accept (poster)	Summary: The paper proposes a new attack called "privacy backdoors", which introduces backdoors into foundation models, making them more prone to leak fine-tuning data of a victim who is adapting the foundation model for their task. For this attack, the attacker collects a set of possible data points that might be used to fine-tune the model. The attacker then tries to inconspicuously alter the loss for the target data points such that they have an anomalous loss value. After the victim fine-tunes the model with private data, the loss of the target data points used for fine-tuning will be anomalous, allowing the attacker to tell whether they were used for training or not. The proposed approach is evaluated on vision models (CLIP) and on LLMs (GPT-Neo). In an ablation study, the paper shows that the attack is robust against different parameter-efficient fine-tuning and inference methods. Strengths: - The paper is well-written and easy to understand - The paper is well organized, and a reader who is not an expert in privacy attacks can follow the paper easily - The proposed approach is novel - The approach is technically sound, and extensive experiments were conducted to show that the proposed approach is working with different models, fine-tuning methods, and inference methods. Weaknesses: - My main concern is that the assumption that the attacker already has part of the training data (i.e., the target data points) is quite unrealistic. This setting assumes that the attacker has way more knowledge than in traditional membership inference attacks, where usually only similar but not the exact same data points are available. If the fine-tuning data is assumed to be the victim's private data, then it is not really private in the first place if the attacker can collect parts of this data set. As a result, it is not very surprising to me that after introducing the "backdoor", the model leaks more information about these data points the attacker had in the first place. - I am skeptical that the proposed approach is a "backdoor". Usually, backdoors in machine learning have a trigger and produce a predefined output. However, with the proposed approach, we are basically just changing the loss of specific samples. The way it is done is "stealthy", but the methodology does not fully align with the definition of a backdoor as it is currently defined in the literature. - I am not quite sure what the intention of section 2.2 is. At the beginning of the second paragraph, it is said that the presented method shares similarities with federated learning. But then only differences are brought up. So, for the reader, it is not clear what the similarities are to federated learning. - It is a bit hard to judge the performance of the LLMs based only on the log perplexity loss. It would be nice to have some kind of benchmark similar to the accuracy in the vision model experiments. - The authors state that maximizing the loss of target data points does not work for LLMs; however, no explanation or experimental results are given, which shows that it does not work. Technical Quality: 3 Clarity: 3 Questions for Authors: Q1: What is the reasoning/intuition why LLMs have a problem reaching high losses? Q2: Minimizing the loss on the LLMs seems to improve the leakage way more than maximizing the loss for the vision model. Did you try to minimize the loss for the vision models? How is the minimization of target point losses working for CLIP? Q3: Are there experimental results showing that maximizing the loss of target data points for LLMs is not working? Q4: The target data points were from the same distribution. However, in reality it might be that the attacker collects the target data points that have a different distribution than the majority of the data used for fine-tuning. For example, if there is a dog class used for fine-tuning the attacker might collect images of different dog breeds that are in the fine-tuning dataset, but the majority of the images used for fine-tuning are different dog breeds. What happens if the target and auxiliary data points are from a different distribution? I could imagine that if the data points are from a different distribution, the effect of increasing the vulnerability of other data points than the target ones might be drastically reduced. Q5: Usually the models are not evaluated on the same data set they are fine-tuned on. What is the accuracy/loss value on a dataset that is not used for fine-tuning (e.g. model is fine-tuned on CIFAR-10 and accuracy before and after on ImageNet with and without the backdoor is measured). Is the backdoor still stealthy in this case? Q6: Why is the validation loss for the poisoned MIMIC-IV model so much lower than for the unpoisoned model? I assume lower loss means better performance, which is why this result does not make sense to me. Do you have any explanation on why this is the case? Q7: Do you have an explanation on why the OPT-350M model does not memorize the target dataset that well? Q8: Which model was used for the fine-tuning/inference method ablation study in table 3 and 4? Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: The limitations are addressed. However, I would encourage the authors to discuss the potential impact of different data distributions on the proposed approach. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We sincerely appreciate your valuable feedback and the time you've dedicated to providing it. Below, we address specific points you raised: > strong assumption We acknowledge that our threat model differs somewhat from the traditional MIA setting. However, this distinction underscores the significance of our research, which aims to alert the community to this specific threat and emphasize the need for vigilance before widespread attacks occur. Our ablation studies demonstrate that the attack remains effective for non-target data points within the same distribution as the target data points. This suggests that our attack doesn’t require the exact same data points initially. Overall, our goal is to expose this threat to the community. Despite having somewhat stronger assumptions than traditional MIA attacks, we aim to demonstrate its feasibility and aid the community in building more robust systems in the future. > about the term "backdoor" We think our method is still somewhat related to the traditional "backdoor," where we inject a privacy trigger so that if the target data point is in the training dataset, it will trigger the MIA signal to be different from the case where the target data point is not in the training. However, we will emphasize the difference in the future version. Additionally, we welcome any suggestions you may have regarding the naming. > regarding section 2.2 about federated learning We mention federated learning because our threat model is quite similar. In a federated learning scenario, the server (similar to our attacker) has the capability to control the model weights sent to the user (similar to our victim) and receives the trained model on the user’s data after the training. We will clarify this further in the revised version. Thank you for pointing this out. > more llm benchmarks We ran 6 additional benchmarks. The table below indicates no significant drops in performance. Meanwhile, we believe the attacker can "cheat" on these benchmarks by including some test samples during poisoning. \| Attack \| HellaSwag \| Obqa \| WinoGrande \| ARC_c \| boolq \| piqa \| Average \| \|:---------:\|:---------:\|:-----:\|:----------:\|:-----:\|:-----:\|:-----:\|:-------:\| \| No Poison \| 55.80 \| 33.20 \| 57.70 \| 53.91 \| 61.77 \| 72.91 \| 55.88 \| \| Poison \| 57.15 \| 34.40 \| 55.96 \| 51.43 \| 58.44 \| 69.75 \| 54.52 \| > Q1 We conducted additional experiments and discovered that it is possible to achieve high losses with LLMs as well with a larger learning rate and longer training. However, the attack remains ineffective. We believe this is an interesting observation that highlights the differences between vision models and LLMs. This may be related to the distinct nature of memorization across different model modalities or data distributions. We think it is worthwhile to explore this further in the future. > Q2 + Q3 + Weaknesses No. 5 We show the results of different attack strategies below. As indicated in the tables, minimizing attacks for vision models and maximizing attacks for LLMs are not as effective as their counterparts, and they have similar success rates to the baseline attacks. CIFAR-10: \|Attack\|TPR@1%FPR\|AUC\| \|:----------:\|:---------:\|:-----:\| \|No Poison\|0.026\|0.511\| \|Maximizing \|0.131\|0.680\| \|Minimizing \|0.014\|0.510\| ai4Privacy: \|Attack\|TPR@1%FPR\|AUC\| \|:----------:\|:---------:\|:-----:\| \|No Poison\|0.049\|0.860\| \|Maximizing\|0.050\|0.909\| \|Minimizing\|0.874\|0.995\| > Q4 We conducted an additional experiment where the model was poisoned on ImageNet, but the attack was carried out on CIFAR-10. As shown in the table, the poison attack did not improve over the baseline. \| Attack on CIFAR-10 \| TPR@1%FPR \| AUC \| \|:------------------:\|:---------:\|:-----:\| \| No Poison \| 0.026 \| 0.511 \| \| Poison \| 0.131 \| 0.680 \| \| Target ImageNet \| 0.023 \| 0.510 \| We also observe the same thing for language model experiments: \| Attack on ai4Privacy \| TPR@1%FPR \| AUC \| \|:--------------------:\|:---------:\|:-----:\| \| No Poison \| 0.049 \| 0.860 \| \| Poison \| 0.874 \| 0.995 \| \| Target Simple PII \| 0.021 \| 0.729 \| It will be good in the future to develop an attack that doesn't require prior knowledge about the target distribution in the future. > Q5 We conducted further evaluations on the stealthiness of the attack. For the vision experiments, as shown below, we observed some performance drop, but it was minimal due to the very small learning rate used for poisoning (0.00001). \| Poison on \| CIFAR-10 \| CIFAR-100 \| ImageNet \| Average \| \|:--------------:\|:--------:\|:---------:\|:--------:\|:--------:\| \| Before Poison \| 89.74 \| 64.21 \| 63.35 \|72.43\| \| CIFAR-10 \| 88.16 \| 52.79 \| 51.92 \| 64.29\| \| ImageNet \| 84.51 \| 54.87 \| 61.49 \| 66.96\| Again, while there are some performance drops, particularly for vision models, we believe that attackers could potentially mitigate this by including some test samples from popular benchmarks during poisoning. > Q6 MIMIC-IV is a relatively small and straightforward dataset. Consequently, the model tends to overfit to this dataset easily. > Q7 We observed that the adversarial loss of OPT-350M decreases more slowly compared to other models, resulting in a higher final loss at the end of the poisoning process. To address this, we reran the attack with a larger learning rate (0.0001 instead of the default 0.00001). This adjustment significantly improved the attack’s effectiveness, increasing the TPR@1%FPR from 0.547 to 0.854. > Q8 We used CLIP ViT-B-32 on ImageNet and GPT-Neo-125M on ai4Privacy as the default setting. We will make this more clear by including the setting in the caption for the camera-ready version, where we have an extra page for the main content. Thank you for your detailed review! We believe to have addressed all questions, but please let us know if you have follow-up questions or additional comments. --- Rebuttal Comment 1.1: Comment: Thank you for the detailed rebuttal and the additional insights. Most of my questions have been answered. I think all of these additional results should make their way into the paper, even if they are only added to the appendix. Since all my concerns have been addressed, I will raise my score. --- Reply to Comment 1.1.1: Title: Author Response Comment: Thank you for your valuable feedback and the corresponding score increase. We will incorporate the additional results and your suggestions in the next version. We appreciate your input!	Summary: The authors focus on a new vulnerability that concerns pre-trained models which relies on an adversary modifying the pre-trained model in a way that increases the models vulnerability to membership inference attacks (MIAs). The attack is thoroughly evaluated on both vision-language models and LLMs when fine-tuning using different strategies and on different fine-tuning data sets. Furthermore, the authors conduct different ablations of the attack. Strengths: - Originality: The work shows that SoTA MIAs (like LiRA) can yield better performance with an attacker that has not unrealistic amount of extra information or power. While it builds on-top of LiRA, it is quite clear that (loss-based) MIAs should benefit from this approach. Related work is appropriately discussed and cited. - Quality: The paper is technically sound and shows through an appropriate amount of experiments that their proposed attack works on multiple SoTA models. The threat model is carefully described and provides the reader with enough information about potential weaknesses of the method. Some minor points I'll mention in the Weaknesses. - Clarity: The paper is clearly written and I only have some minor suggestions under weaknesses that the authors can easily fix before a potential camera-ready version. - Significance: The work is highly significant as nearly all current SoTA approaches rely on fine-tuning pre-trained models. As mentioned by the authors, libraries like Huggingface make pre-trained models more accessible and lower the threshold for downloading pre-trained models. At the same time it seems very likely that malicious models could be downloaded (e.g., when searching for a CLIP like architecture). I think this work makes very apparent that the community must defend against these types of attacks. Weaknesses: Major: - Stealthiness of the attack: The paper does not look at how, e.g. the zero-shot performance on unrelated data sets (e.g., NOT the target data set) changes once the model is poisoned. The original CLIP paper (Radford et al., 2019) considers many different data sets. I understood that the authors argue that poisoning for better MIA on CIFAR-10 is stealthy because the performance on CIFAR-10 doesn't change much. But how well is the model still performing on other data sets such as CLEVER, FGVC Aircraft or others? Is there forgetting regarding that data? I see that the scenario breaks a bit down if that is the case because the adversary would need to poison specifically for one victim while hoping that nobody else uses the model and wonders why it performs poor in zero-shot. Eventually this would lead to the model being flagged and the model being taken down. I am willing to increase my score if this point has been addressed by the authors or if they clarify why this is not relevant. Minor: - Defense and Detection: The paper would be better if it could provide some ideas regarding potential defenses against this attack or methods to detect that the model includes a backdoor. I don't expect experiments but it would be great to elaborate a bit more than "In the future, it may be necessary for those who make use of pre-trained models to perform as much (or more) validation of the pre-trained models that are being used as any other aspect of the training pipeline." - Table 3: It would be great to specify which model is being used in a separate column. It can be quite confusing as apparently the Linear Probing is only used with CLIP. - Tables: It would be great if the caption could be elaborating a bit more than just a heading. E.g., by mentioning the model that is under attack. - Pre-training data: It would be good to mention what pre-training data has been used for the pre-trained models. This can make quite a difference when replicating the results. Technical Quality: 4 Clarity: 4 Questions for Authors: 1) See major weakness: Have the authors investigated the stealthiness more? How does the zero-shot performance on data sets change that are NOT the target data? 2) Which pre-training data has been used? 3) Have you considered how effective your attack would be for fine-tuning under Differential Privacy? Could you speculate how your attack would perform there? Confidence: 4 Soundness: 4 Presentation: 4 Contribution: 4 Limitations: Yes Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We sincerely appreciate your valuable feedback and the time you've dedicated to providing it. Below, we address specific points you raised: > Stealthiness of the attack: We conducted further evaluations on the stealthiness of the attack. For the vision experiments, as shown below, we observed some performance drop, but it was minimal due to the very small learning rate used for poisoning (0.00001). \| Poison on \| CIFAR-10 \| CIFAR-100 \| ImageNet \| Average \| \|:--------------:\|:--------:\|:---------:\|:--------:\|:--------:\| \| Before Poison \| 89.74 \| 64.21 \| 63.35 \|72.43\| \| CIFAR-10 \| 88.16 \| 52.79 \| 51.92 \| 64.29\| \| ImageNet \| 84.51 \| 54.87 \| 61.49 \| 66.96\| For the language model experiments, we ran 6 additional benchmarks. The table below indicates no significant drops in performance, as we employed a minimization attack. \| Attack \| HellaSwag \| Obqa \| WinoGrande \| ARC_c \| boolq \| piqa \| Average \| \|:---------:\|:---------:\|:-----:\|:----------:\|:-----:\|:-----:\|:-----:\|:-------:\| \| No Poison \| 55.80 \| 33.20 \| 57.70 \| 53.91 \| 61.77 \| 72.91 \| 55.88 \| \| Poison \| 57.15 \| 34.40 \| 55.96 \| 51.43 \| 58.44 \| 69.75 \| 54.52 \| Overall, while there are some performance drops, particularly for vision models, we believe that attackers could potentially mitigate this by including some test samples from popular benchmarks during poisoning. > Defense and Detection In our paper, we presented some potential defenses at fine-tuning and inference times. However, the most effective and reliable defense might still be differential privacy, as it can provide guaranteed protection. Additionally, we believe it is necessary to develop detection methods. Under our method, the target data points often exhibit abnormal losses. Therefore, it might be possible for the victim to first examine the loss distribution on their fine-tuning dataset and filter out these abnormal data points. > About writing Thank you for pointing out the unclear points in our paper. We will incorporate your suggestions and make the necessary revisions for the camera-ready version, where we have an additional content page to provide more details in the main paper. We hope our response can resolve your concerns regarding our paper. Please let us know if you have any more questions. --- Rebuttal 2: Comment: Thanks for the additional experiments regarding the stealthiness. I am not an NLP person but looking at the CV results this is exactly what I asked for. I think they add an important angle to the paper and show that the threat model could work in practice. I can totally see this threat model working in a setting where non-ML researchers or practitioners just look for the next best model or get lured into downloading a poisoned model. > In our paper, we presented some potential defenses at fine-tuning and inference times. However, the most effective and reliable defense might still be differential privacy, as it can provide guaranteed protection. Could you please point me where in the paper you are doing that? I read the paper a while ago and I now checked again. I wasn't able to find either differential privacy or dwork. I saw that there are two sentences in the conclusion about defenses. --- Rebuttal Comment 2.1: Title: Author Response Comment: Thank you for your prompt feedback. We apologize for the confusion. Our paper does not have differential privacy results. Instead, we present fine-tuning and inference-time mitigation methods, such as QLoRA or top-5 probabilities, as shown in Tables 3 and 4. While some of these methods can effectively reduce privacy leakage, they do not prevent the privacy magnification from our attack. We believe that differential privacy would offer a more reliable defense in practice, as it protects privacy with guarantee. We hope this clarifies your confusion. Please let us know if you have further questions! --- Rebuttal 3: Comment: Thanks, this clarifies my confusion! I increased my score from 6 to 7 and I trust the authors that they address the changes promised and include the additional experiments regarding the stealthiness. --- Rebuttal Comment 3.1: Title: Author Response Comment: Thank you for your valuable feedback and the corresponding score increase. We will incorporate the additional results and your suggestions in the next version. We appreciate your input!	Summary: This paper introduces a so-called “privacy backdoor” attack. The attacker poisons a pre-trained model to make it susceptible to membership inference attacks (MIA) on an apriori known set of target examples. This poisoning is carried out by continually training the pre-trained model on the target examples and an auxiliary dataset (needed to preserve the base performance of the model), employing loss terms that later cause significant loss-contrast between target examples that are included in fine-tuning and that are not. The attack is empirically tested on vision and large language models, using (on a low level) opposite attack strategies. The evaluation presented in the paper shows that this privacy backdoor attack is effective at enhancing the performance of a prior MIA on both domains, and across various models, fine-tuning methods, and inference strategies. Strengths: The paper studies an important and timely threat. The practice of downloading and fine-tuning open-sourced pre-trained models is currently wide-spread and understanding the associated safety and privacy risks is crucial. The poisoning attack appears to be highly effective in enhancing membership inference success under the examined setting. The experiments extend to various fine-tuning and inference schemes, which could be employed by the victim and cannot be influenced by the attacker. The attack is robust in the provided MIA improvement across these scenarios, highlighting the severity of the posed threat. Appendix C collecting negative results of failed attempts at constructing the attack is highly insightful and a refreshing sight given current publication practices. Weaknesses: Novelty The paper claims in several places to introduce a “new” threat model and privacy attack, however, closely related [1] and virtually identical [2] settings have been proposed by other works. While the paper already briefly discusses [1], classifying it as concurrent work (available for slightly less than 2 months at submission time), it omits [2] (available for slightly more than 2 months at submission time). I believe that due to the large similarities in settings between these works, they warrant a longer discussion in similarities, differences, and concurrence in the paper; and the claim to unveiling a “new vulnerability” reassessed and tamed down in light of this discussion. Strong assumptions The paper reads currently as if the presented attack would be just a nice addition on top of any black-box MIA setting, and the presented game in Threat Model 2 makes it seem like it seamlessly integrates with the traditional MIA framework. However, I believe that this is misleading as the benefit from the introduced privacy backdoor attack is tied to assumptions that are stronger than those usually found in MIA literature. In MIA, online and offline attacks are usually distinguished [3]. In online MIA (weak setting), the attacker is assumed to be able to adjust the computationally heavy part of their attack (e.g., retrain their shadow models) when the challenger reveals a new target data point to them. In offline MIA (strong setting), the attacker prepares an attack once, before knowing specific target data points, and then this attack is employed (sometimes with minor adjustments without virtually any additional compute costs) once the challenger presents target data points. Also note that another standard assumption is that the challenger is allowed to continuously present new target data points to the attacker as long as they are samples from a distribution that is also available for the attacker for sampling. The paper currently does not introduce these standard elements and assumptions of MIA. Instead, the implicitly induced setting is in fact weaker than that of online MIA; the entirety of $D_{\text{target}}$ has to be known to the attacker when preparing the privacy backdoor. As such, if at MIA time the challenger presents a new target data point (which is allowed under usual MIA assumptions) the privacy backdoor has no “support” for it and adjusting the backdoor is not possible anymore, as the model on which the MIA is done is already released from the hands of the attacker and the fine-tuning has already happened. Further, the attack requires that the attacker possesses a dataset $D_{\text{aux}}$ that is disjoint from the target data points, which, while in many cases may be realistic, is a non-standard assumption in MIA once again. Standard MIA does not require that the dataset available to the attacker and the set of all potential target data points is disjoint. In summary, the paper makes several non-standard restrictive assumptions to the MIA setting, without discussing or motivating them explicitly and clearly; the assumptions are only stated in scattered places and not positioned in the context of MIA. Only partially follows best practices in MIA result reporting TPR@1%FPR is reporting at an order(s) of magnitude(s) higher FPR than suggested best reporting practices [3]. ROC-AUC score is included, while logarithmic full ROC curves are omitted, in stark contrast to suggested best practices [3]. As such, it is currently unclear if the attack provides as large benefits as currently perceived also at more relevant FPR regimes. Concerns over the employed MIA In the evaluation, the authors use the LiRA [3] attack with 16 shadow models. However, as it has been already shown in [3] and especially reinforced in [4], the standard LiRA attack is particularly weak for a low number of shadow models. While the version using global variance estimators is better in this regime, it is unclear which one was used for evaluation in this paper. As such, for this potentially weak attack the privacy backdoor provides a large benefit. However, it remains to be seen if the benefit is equally as large for stronger attacks, specifically tailored to perform well with just a low number of shadow models, such as [4] (available since 6th Dec 2023). Weak justification of the different attack strategy choices The paper currently employs two contrasting attack strategies for vision models and large language models. For vision models the loss of the target data points is increased in the backdooring phase (“maximization”), while for LLMs the target data points are encouraged to be heavily memorized (“minimization”). While both of these strategies are clear how they would encourage contrast at fine-tuning time between member and non-member target data points, the use of different strategies is currently weakly motivated, impacting the convincingness of the paper’s technical contribution. The differing choices could be better motivated by showing an experiment how the alternative strategies perform on the other domain, i.e., showing how minimization performs for vision, and how maximization performs for LLMs. In particular, the attacks on LLMs seem to be much stronger, which is currently unclear if this is due to the chosen attack strategy, the evaluation protocol and datasets, or due to some other factor. Presentation, writing, and clarity In several places there are certain inconsistencies, writing is not clear, or small errors in citation formatting or similar. This gives the overall impression that the paper was written hastily. In Threat model 2, point 3; to match with the generic setup of MIA, I assume that the idea what this point should stand for is (correct me if I am wrong) that the challenger randomly selects if it present a target data point from the target set which was also included in the fine-tuning set or one that was not. However, I think that the used notation currently does not reflect this: 1. “[i]f $c=\text{head}$, they randomly select a target data point $(x,y)$ from $D_{\text{target}}$” — this $(x,y)$ could still be both in the training set or not in it, this does not tell us anything about that; 2. “if $c=$tail, a target data point $(x,y)$ is randomly sampled from $(D_{\text{target}} \setminus D_{\text{train}})$” — this is confusing, as this would imply that $D_{\text{target}}$ is a superset of $D_{\text{train}}$, which is not only not stated anywhere nor followed in the experimental section, but would also mean another highly unrealistic assumption. I believe, sampling from $D_{\text{target}} \cap D_{\text{train}}$ when the coin is head, and sampling from $D_{\text{target}} \setminus (D_{\text{target}} \cap D_{\text{train}})$ when the coin is tail would be a correct notation/presentation. Section 3.2. is very confusing at the moment, as it gives a clear motivation for the maximization attack, but then presents the exact opposite of this idea for LLMs, solely because ‘maximization did not work’. In conjunction with the experiment justifying this choice and an adjustment in writing would make the presentation of the attack more compelling. While, as I already elaborated above, the assumptions made by the attack are rather strong, they could be justified by presenting a clear real-world example for the attack (but still have to be explicitly compared to the standard assumptions of MIA). While there is an attempt on this in l159-l162, I suggest to elaborate on this and present it more convincingly, given that the assumptions made are non-standard for MIA. I struggle to understand the paragraph from l267 to l271. I especially do not get the causal link between observed memorization and what is meant by similar format and similar types of personal information. What the supposed link between the results on Simple PII and MIMIC-IV is, is also unclear. I do not understand why these two results are compared, as to me, the outlier seems to be the result on Simple PII, with a base attack success of 0.242 TPR@1%FPR, compared to an order of magnitude lower TPRs on both ai4Privacy and MIMIC-IV. Further, if the statement is supposed to be that PII is memorized better by the LLMs than images by the vision models, then for this the experiment setup in my view is unfit, as the MIA scores on the unattacked models are comparable in each case (each time two datasets produce around 0.0X TPRs and once 0.1X-0.2X TPR), and in case of the attacked models, as the attacks are different, we cannot know if the difference stems from the data domain or the attack itself. As already elaborated in its own point, the setting of MIA and how the presented attack relates to it have to be presented clearer, as currently in parts it seems like the attack enables a more powerful setting; being an additive improvement over any MIA scenario. Citep and citet are mixed up in certain places, e.g., l68 or l115. References [1] S Feng and F Tramèr, Privacy Backdoors: Stealing Data with Corrupted Pretrained Models. http://www.arxiv.org/abs/2404.00473. [2] R Liu et al., PreCurious: How Innocent Pre-Trained Language Models Turn into Privacy Traps. https://arxiv.org/abs/2403.09562. [3] N Carlini et al., Membership Inference Attacks From First Principles. https://arxiv.org/abs/2112.03570. [4] S Zarifzadeh et al., Low-Cost High-Power Membership Inference by Boosting Relativity. https://arxiv.org/abs/2312.03262v3. Technical Quality: 1 Clarity: 2 Questions for Authors: I find the paragraph “Results on Non-target Data Points” rather interesting, however I wonder how much this observation is related to the finding of [5]? What if $D_{\text{aux}}$ and $D_{\text{train}}$ are very different? It should be enough if $D_{\text{aux}}$ was only similar to the pre-training dataset, no? Would be interesting to see if large differences between the auxiliary dataset and the fine-tuning dataset would impact the attack success. Do the authors have any hypothesis why OPT-350M is an outlier in the model size trend in Figure 1? References [5] A Panda et al., Teach LLMs to Phish: Stealing Private Information from Language Models. https://arxiv.org/abs/2403.00871. Confidence: 4 Soundness: 1 Presentation: 2 Contribution: 2 Limitations: Limitations are not prominently and explicitly discussed, only recognized in the checklist. In my view, the strong assumptions made in the threat model have to be discussed in the main paper. Note also other weaknesses pointed out in my review. Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We sincerely appreciate your valuable feedback and the time you've dedicated to providing it. Below, we address specific points you raised: > Novelty Thank you for pointing out the related work. We were not aware of these studies since we wrote this paper in 2023 and submitted it to a previous conference in February 2024, which was before these papers were out. However, we do want to acknowledge them and rewrite our related work discussion to provide a clearer overview over this new threat model as a whole subsection in the revised version. Meanwhile, compared to [2], although we share a similar threat model, their threat model is stronger. In their setting, they assume the victim follows the fine-tuning instructions from the attacker, like the PEFT strategy. In contrast, we demonstrate that our attack can function under various fine-tuning techniques. Additionally, we include experiments with vision models, whereas they only conduct experiments with LLMs. Overall, we believe our paper offers different contributions compared to [2], and we plan to include more discussion in the future version. > Strong assumptions We acknowledge that our threat model differs somewhat from the traditional MIA setting. However, this distinction underscores the significance of our paper to the community. The primary aim of our research is to alert the community to this specific threat, emphasizing the need for vigilance before widespread attacks occur. We believe that real-world scenarios similar to our model exist. For instance, a patient could upload a poisoned medical model on the internet and see if a hospital uses their medical records. Our ablation studies demonstrate that the attack remains effective for non-target data points within the same distribution as the target data points. This suggests that our attack supports non-target data points similar to the offline case in [3]. Similarly, the offline attack assumes that the data points used to train the shadow models must be in the same distribution as the attacked data points. Therefore, we believe our attack exhibits similar flexibility to that in [3]. Overall, we emphasize that the goal of our paper is to expose this threat to the community. Despite the assumption being somewhat stronger than traditional MIA attacks, we aim to demonstrate its feasibility and help the community in building more robust systems in the future. > Only partially follows best practices in MIA result reporting We do agree with the importance of full ROC curves, so We have added them in the rebuttal PDF under the general response. From Figure 1, it's clear that our attack outperforms the baseline attack at any FPR. We would like to include this in the main body for the future version. > Concerns over the employed MIA We have run an additional experiment with more shadow models as below. As the table shows, the performance of the poison attack increases substantially over the baseline attack. This also aligns with the experiment from [3], who find that there are limited gains from more than 16 shadow models in the normal case. \| # of Shadow Models \| Attack \| TPR@1%FPR \| AUC \| \|:------------------:\|:---------:\|:---------:\|:-----:\| \| 16 \| No Poison \| 0.026 \| 0.511 \| \| \| Poison \| 0.131 \| 0.680 \| \| 32 \| No Poison \| 0.031 \| 0.518 \| \| \| Poison \| 0.135 \| 0.695 \| \| 64 \| No Poison \| 0.036 \| 0.536 \| \| \| Poison \| 0.176 \| 0.712 \| > Presentation, writing, and clarity Thank you for pointing out the unclear points in our paper. We will incorporate your suggestions and make the necessary revisions for the camera-ready version, where we have an additional content page to provide more details in the main paper. > Results on Non-target Data Points Thanks for pointing out the observation in [5]. We believe there is a relationship between our observations. It will be interesting to explore in future work how the minimization attack affects the loss landscape on non-target data points within the same distribution or those close to the target data points. > if large differences between the auxiliary dataset and the fine-tuning dataset would impact the attack success. Yes, we conducted an additional experiment where the model was poisoned on ImageNet, but the attack was carried out on CIFAR-10. As shown in the table, the poison attack did not improve over the baseline. \| Attack on CIFAR-10 \| TPR@1%FPR \| AUC \| \|:------------------:\|:---------:\|:-----:\| \| No Poison \| 0.026 \| 0.511 \| \| Poison \| 0.131 \| 0.680 \| \| Target ImageNet \| 0.023 \| 0.510 \| We also observe the same thing for language model experiments: \| Attack on ai4Privacy \| TPR@1%FPR \| AUC \| \|:--------------------:\|:---------:\|:-----:\| \| No Poison \| 0.049 \| 0.860 \| \| Poison \| 0.874 \| 0.995 \| \| Target Simple PII \| 0.021 \| 0.729 \| > Do the authors have any hypothesis why OPT-350M is an outlier in the model size trend in Figure 1? We observed that the adversarial loss of OPT-350M decreases more slowly compared to other models, resulting in a higher final loss at the end of the poisoning process. To address this, we reran the attack with a larger learning rate (0.0001 instead of the default 0.00001). This adjustment significantly improved the attack’s effectiveness, increasing the TPR@1%FPR from 0.547 to 0.854. Thank you for your detailed review of our work. We hope our response was able to resolve your concerns with this work. Please let us know if there are any further questions, or points you'd like us to address in greater detail. --- Rebuttal Comment 1.1: Title: Thank you Comment: Thank you to the authors for their rebuttal. I appreciate the additional interesting experiments and the acknowledgement of some of my concerns. However, my main concerns are very much fundamental to how the paper is currently presented: C1: This backdoor operates with different assumptions than usual MIA---while I agree that this is fine, and the presented threat is relevant, this has to be openly and transparently presented in the paper. Nobody should get the impression that this is a plug-and-play sort of addition on top of any MIA. C2: The novelty claim certainly has to be toned down in the face of the presented related work. Once again, I do think that this work is valuable in itself, but I would appreciate an accurate and transparent positioning of the contributions in the related work. I also understand that this work may have been in resubmission cycles for longer, however, as for the acceptance at the conference, the paper has to be judged with respect to the time when it was submitted, as this is also the relative narrative that will later be represented at the conference. As the authors acknowledge, and seem to be in line with me on my main concerns, in the hope that they will adjust their presentation in the paper, I will slightly raise my score. However, ultimately, I can only hope that the changes will indeed be implemented, without which I would still vote for clear reject. --- Reply to Comment 1.1.1: Title: Author Response Comment: Thank you for your valuable feedback. We truly appreciate it and will use it to enhance our presentation in the future version. Meanwhile, please let us know if you have further questions!	Summary: This paper proposed a new privacy attack for foundational models like CLIP and large language models (LLMs). The attack's key idea is to ''poison'' the target data (e.g., maximize loss) point into the pretrained models so that the victim's finetuned models uploaded on the open-source platform can reveal what target data points have been used for finetuning. In the end, the evaluation on both vision and language foundational models validate the attack effectiveness. Strengths: + Important research topic: data privacy for foundational models + New attack setting and method Weaknesses: My main concerns are about the threat model and the evaluation of LLMs. - Although the paper studies a new threat setting, existing model ecosystem may not work like the described manner. Specifically, the paper assumes the adversary can firstly finetune (i.e., poison) the publicly available pretrained model $F_{pre}$ to $F_{adv}$, and release the F_adv to the platform. Then the victim downloads and finetunes the $F_{adv}$ with D_train to $F_{adv, ft}$, and releases $F_{adv, ft}$ to the platform so the adversary can infer membership privacy from $F_{adv, ft}$. But why would the victim finetunes $F_{adv}$ instead of $F_{pre}$? Typically the victim would choose the $F_{pre}$ for finetuning, just like the authors choose the CLIP for evaluation instead of a random finetuned CLIP on the Hugging Face. - Besides, the attack goal of maintaining a comparable level of performance on downstream tasks does not persuade the victim to use $F_{adv}$ instead of $F_{pre}$. Let's assume $F_{pre}$ and $F_{adv}$ have similar performance. As $F_{pre}$ is shared by organizations (e.g., Meta, OpenAI, etc.) that can pay the training cost, the downloads and likes of $F_{pre}$ is certainly high as what we have witnessed in the era of LLMs, and $F_{adv}$ can be just one of hundreds of finetuned $F_{pre}$, why would the victim prefer $F_{adv}$, with potentially not much downloads and likes? - The impact of finetuning to the LLM performance is also questionable. The results reported in Table 2 is lower validation loss after finetuning, but the loss cannot tell the model performance (i.e., low loss is not necessarily better). I would suggest the authors to provide more concrete LLM evaluation. - The evaluation on large language models is not thorough. The largest evaluated LLMs in this paper is GPT-Neo-2.7B while widely studied LLMs are above 7B such as LLaMA, Mistral, etc. Technical Quality: 2 Clarity: 3 Questions for Authors: See my comments above. I also have a minor question about the target data points owned by the adversary. The authors justify with data of interest like proprietary data, but under what circumstances can the victim and the adversary jointly possess some common target data? If it is the victim that steals the proprietary data, what motivates the victim to finetune with the stolen target data and release $F_{adv,ft}$ to the public, especially when the victim is aware of this attack (after publication) and the potentially poisoned $F_{adv}$? Confidence: 4 Soundness: 2 Presentation: 3 Contribution: 2 Limitations: None Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We sincerely appreciate your valuable feedback and the time you've dedicated to providing it. Below, we address specific points you raised: > Why would the victim chooses poisoned model instead of the original model We believe there are several circumstances where the victim might choose the poisoned model over those from big organizations or popular repositories. For example, an attacker could include test data from popular benchmarks and make the model achieve SOTA results, making it an apparently attractive choice. Additionally, the attacker could design the model to specialize in a particular field, such as medical usage, which might deceive users with less computer science expertise into trusting the model without being aware of the attack. Finally, attackers can also market their model as an “uncensored model” that removes the refusal features. These models are commonly distributed on Hugging Face (while we cannot provide the link during rebuttal, you can search for “uncensored” on the Hugging Face model page). We also want to emphasize that another important goal of our paper is to highlight the existence of such attacks and raise awareness within the community. We believe there may be more potential privacy attacks involving the poisoning of pre-trained models that should be explored and discovered in the future. > more LLM evaluation This is a good point that validation loss alone does not fully reflect model performance. Based on your feedback, we have now evaluated the model on six popular benchmarks, as shown below. While there are some drops in performance on certain tasks, overall, the poisoned model remains comparable to the original one. Additionally, as we mentioned above, the attacker might be also able to “cheat” in these benchmarks by including some of the test data during poisoning. \| Attack \| HellaSwag \| Obqa \| WinoGrande \| ARC_c \| boolq \| piqa \| Average \| \|:---------:\|:---------:\|:-----:\|:----------:\|:-----:\|:-----:\|:-----:\|:-------:\| \| No Poison \| 55.80 \| 33.20 \| 57.70 \| 53.91 \| 61.77 \| 72.91 \| 55.88 \| \| Poison \| 57.15 \| 34.40 \| 55.96 \| 51.43 \| 58.44 \| 69.75 \| 54.52 \| > under what circumstances can the victim and the adversary jointly possess some common target data This scenario is a general setting for membership inference attacks in that the attacker and victim share some data points, and we believe there are many cases where this is applicable. For example, a patient might want to know whether the hospital lab's LLM trained on her medical records, both she and the hospital need to be aware. We hope our response can resolve your concerns regarding our paper. Please let us know if you have any more questions. --- Rebuttal Comment 1.1: Title: Thanks for the response Comment: Thank you for your rebuttal and the additional evaluation. However, I still have concerns over the strong assumptions as noted by other reviewers. Take the third point in your rebuttal as an example, I don't believe the victim (patient or patient group) will really publish a poisoned model, and bet the hospital to finetune and publish their model to infer whether their privacy is leaked. The proposed attack is far more complicated than membership inference attack. For the first point, I agree the victim might choose the disguised model but they will probably not share their model again especially if there are privacy training data (we already know the model memorization). I searched "uncencored" and I noticed that these models are mainly for pretrained models (gemma, llama, etc.) but not the homemade ones. Given my personal experience playing with the open-source LLMs on Hugging Face, I'm not fully convinced by the justification and I still doubt the potential influence of this two-phase poisoning attack. Therefore, I would like to keep my scores. --- Reply to Comment 1.1.1: Title: Author Response Comment: Thank you for your response. We agree that the victim might not publish the model weights after fine-tuning. However, they may still release the model as a chatbot or API, similar to those used in hospital or bank websites. In such cases, the attacker could still probe the fine-tuned model. On the other hand, the “uncensored” models are indeed adversarially fine-tuned versions of popular pre-trained models. This is similar to our setting, where the attacker poisons a pre-trained model. We understand your concern and acknowledge that this is the main limitation of our paper. However, it is crucial to make the community aware of this threat, and we should care about any worst-case scenario regarding privacy leakage. We believe our paper serves as an important step toward developing defenses and stronger attacks with fewer assumptions in the future.	Rebuttal 1: Rebuttal: We sincerely appreciate all the reviewers for their valuable feedback and insightful questions. We have addressed each of your queries individually in the rebuttal box under your respective reviews. Please take a look and let us know if you have any further questions. Pdf: /pdf/288cc4c8c8444ba8304757fd1395ad761ca9bc3e.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Learning to Price Homogeneous Data	Accept (poster)	Summary: The paper studies an online learning problem for pricing homogeneous data, where the seller needs to offer a price function/curve based on the data size and learn the arrival probabilities of different customer types to maximize cumulative revenue. The paper first analyzes the structure of the optimal price function when there is a finite number of customer types with known arrival probabilities. It introduces new discretization schemes to achieve better dependence on the approximation error compared to existing methods. When the arrival probabilities are unknown (i.e., in the online learning setting), the paper develops algorithms for both stochastic and adversarial settings with theoretically bounded regret. Strengths: The paper is well-written and introduces an interesting online learning problem in data pricing. It explores the unique structure of the optimal pricing curve in this problem and provides algorithms to solve this task under both stochastic and adversarial settings with theoretical regret bounds. The paper also discusses its technical contributions in deriving theoretical results. Weaknesses: (1) Computational Complexity: The provided algorithms (Algorithm 3 and 4) have computational complexity depending on the horizon $T$, which can be large in practice. (2) Lack of Numerical Validations: Since the problem is motivated by a practical pricing scenario, numerical experiments could help validate the efficiency of the algorithms, especially given the potentially large computational complexity. Technical Quality: 3 Clarity: 3 Questions for Authors: 1. In Theorems 4.1 and 5.1, can the discretization additive approximation $O(\frac{1}{\sqrt{T}})$ be replaced by $O(\frac{1}{\sqrt{t}})$ while maintaining the same order of regret (i.e., the discretization level changes across the periods)? The intuition is that when the estimations of $q$'s are inaccurate, we may only need an inaccurate discretization of the price curve, potentially reducing computational complexity. 2. How can the Upper Confidence Bound (UCB) on $q$'s facilitate exploration in learning $q$'s (i.e., more explorations)? My understanding is that to learn $q$'s (i.e., collecting samples of $q$'s), we need to encourage purchases by setting a price curve lower than the estimated optimal one. However, the UCB on $q$'s does not obviously encourage lower prices. Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: See weaknesses. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: ### *Weakness 1. Computational complexity depending on the horizon $T$.* As mentioned in line 58, achieving sublinear regret in online learning requires choosing $\epsilon$ that vanishes with longer time horizons, i.e., $\epsilon \to 0$ as $T \to \infty$. In Theorems 4.1 and 5.1, we choose $\epsilon = 1/\sqrt{T}$ to achieve regret upper bounds $\tilde{O}(m\sqrt{T})$ and $\tilde{O}(m^{3/2}\sqrt{T})$, respectively. However, if one does not want the per-round complexity to scale with $T$, one can fix the error as a constant $\epsilon$. Then the discretization size $\|\overline{\mathcal{P}}\|$ would be $\left(\frac{N}{\epsilon}\right)^m$, which is no longer dependent on $T$. With a slight sacrifice of the seller's revenue, the regret bound in Theorem 4.1 would be $2\epsilon T + 93m\sqrt{T \log T}$, and the regret bound in Theorem 5.1 would be $2\epsilon T + 3m\sqrt{T \log \|\overline{\mathcal{P}}\|}$. This is standard in continuous bandit, we choose the discretization size to scale with $T$ to achieve the lowest possible regret bound, which causes large computation complexity at the same time (for a classic example, see [1]). ### *Weakness 2. Lack of Numerical Validations.* See the common response above. ### *Question 1. Can we reduce discretization additive approximation?* Yes, it is possible to replace the size of the discretization from $O\left(1/\sqrt{T}\right)$ with $O\left(1/\sqrt{t} \right)$ in the stochastic setting. This will reduce the computational complexity, but only by a constant factor, so it does not give a fundamentally different result. See the common response as to why we think large computational complexity is unavoidable for this setting. In the adversarial setting, we believe that it is not possible to reduce $O\left(1/\sqrt{T}\right)$ to $O\left(1/\sqrt{t}\right)$. ### *Question 2. How can the Upper Confidence Bound (UCB) on type distribution $q$ facilitate exploration in learning $q$?* If type $i$ has not been explored enough before, then $T_{i,t}$ is small, and the upper confidence bound for $q_i$ is large. We let $S_p$ denote the set of types that would make a purchase under price $p$. Then for all prices $p$ such that $i\in S_p$, their UCBs for revenue (defined in Eq. 7) are large. Therefore, the algorithm tends to choose $p$ satisfying $i\in S_p$ in the following rounds, leading to an increase in $T_{i,t}$. This encourages exploration of type $i$. ### *Reference* [1] R. Kleinberg and T. Leighton. The value of knowing a demand curve: Bounds on regret for online posted-price auctions. FOCS 2003. --- Rebuttal Comment 1.1: Comment: Thank you for your response. It addresses my concerns and I have raised the score. --- Reply to Comment 1.1.1: Comment: Thank you again for your comments. Based on your comments, we will clarify our contributions and techniques in future revisions. --- Rebuttal 2: Title: Sincerely looking forward to your reply Comment: Thank you again for your feedback. With the discussion period ending in two days, we would appreciate knowing if our response has adequately addressed your key questions and concerns.	Summary: Motivated by the emergence of data marketplaces, this paper studies an online data pricing problem involving $ N $ homogeneous data points and $ m $ types of buyers in the market. Specifically, it assumes that each type of buyer has a specific value function $ v_i: [N] \rightarrow [0, 1] $. While the sellers know all the value curves $ v_i $, they do not know the distribution of buyers. The sellers need to choose a pricing curve $ p \in \mathcal{P}: [N] \rightarrow [0, 1] $ at each time period. To address this online pricing problem, the authors develop novel discretization schemes to approximate any pricing curve. To minimize the discretization size, they propose assumptions such as smoothness and diminishing returns. To solve the online learning problem, they build on classical algorithms like UCB (Upper Confidence Bound) and FTPL (Follow-The-Perturbed-Leader), providing corresponding regret bounds. These advancements contribute to more effective and efficient online data pricing strategies. Strengths: 1. The topic related to marketplaces is very interesting. This paper is well-written and easy to follow. 2. The authors propose three types of price discretization schemes under different assumptions: monotonic valuations, smooth monotonic valuations, and monotonic valuations under diminishing returns. These schemes, based on Algorithm 1, significantly reduce the discretization size. While Algorithm 1 is an existing technique, the proposed price discretization schemes are non-trivial and add substantial value. 3. The proof provided is rigorous, and the theoretical results demonstrate sublinear regret with respect to $T$. Weaknesses: 1. I think Sections 3 and 4-5 are independent. Section 3 primarily introduces the price discretization schemes, while Sections 4-5 discuss online learning algorithms for both settings. In my opinion, the main contribution of your paper lies in Section 3, as the techniques in Sections 4-5 seem to be standard. 2. You claim that your analysis when constructing the UCB in this way is non-trivial since the types are observed only if they make a purchase. However, this seems common. Could you elaborate on the additional difficulties for the UCB algorithms in your case? Additionally, in line 266, maintaining UCBs for the type distribution appears to be a standard approach, and I don't see this as a significant contribution. 3. Section 5 is a little confusing. Why is it necessary to add perturbation? Maybe you should give me some intuition. Moreover, in line 320, why is $ r_t(p) $ an upper bound on $ p(n_{i_t,p}) $? Technical Quality: 3 Clarity: 3 Questions for Authors: 1. While I understand that Algorithm 1 is for price discretization, and the valuation space is discretized, it remains unclear how the price set $ \bar{\mathcal{P}} $ is determined. Could you provide more details on this process? 2. Although you have provided the regret bound, additional discussion on its tightness would be valuable. Can you elaborate on the tightness of the regret bound and compare it with existing results? 3. Sections 4-5 discuss the online learning algorithms. Could you highlight the specific difficulties you encountered in these sections? What new techniques did you develop? What are your unique contributions? Clarifying these points will help distinguish your work from standard techniques. Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: As mentioned above, the studied topic is very interesting. However, I am eager to see more detailed statements regarding the unique contributions, particularly in Sections 4-5. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: ### *Weakness 1. Main contribution of our paper lies in Section 3, as the techniques in Sections 4-5 seem to be standard.* See the common response above, Novelty in Sections 4, 5. ### *Weakness 2. Contribution in Section 4.* See the common response above. ### *Weakness 3. Why is it necessary to add perturbation.* Adding perturbation is standard in the FTPL method as it ensures robustness against adversaries and helps bound the regret. For a classic introduction to FTPL, please refer to the following paper: - Kalai et. al., Efficient algorithms for online decision problems. Journal of Computer and System Sciences, 2005. However, for reasons explained in the common response, the vanilla FTPL does not work under asymmetric feedback. Especially, in line 320, $r_t(p)\geq p(n_{i_t,p})$ is by definition (see lines 6-7 of Algorithm 4). When the buyer makes a purchase, $r_t(p)=p(n_{i_t,p})$; otherwise, since $i_t\in S_t^c$, we have $r_t(p)=\sum_{i\in S_t^c}p(n_{i,p})\geq p(n_{i_t,p})$. For specific difficulties and new techniques, please refer to our common response above. ### *Question 1. Construction of the discretization set.* First, in Lemma 3.1, we prove that for any non-decreasing price curve $p $, there exists an $m $-step price that yields at least the same revenue as $ p $. Here, an $m$-step function is a non-decreasing function where $ p(n+1) $ and $p(n) $ differ at most $m $ times, i.e., at most $m $ jumps. See lines 216-223. Then in Algorithm 1, let $W$ be the discretization of the valuation space $[0,1]$. We define the discretization set $ \overline{\mathcal{P}} $ to be the class of all $m $-step functions mapping $[N]$ to $ W $. This means that we select all possible $m $-step functions that have a domain in $[N]$ and take values in $ W $. ### *Question 2. Tightness of the regret bound and compare it with existing results.* See the common response above. ### *Question 3. Unique contributions in Sections 4 and 5.* See the common response above. --- Rebuttal 2: Title: Sincerely looking forward to your reply Comment: Thank you again for your feedback. With the discussion period ending in two days, we would appreciate knowing if our response has adequately addressed your key questions and concerns.	Summary: This paper considers a data pricing problem in which a seller has $N$ homogeneous data points they wish to sell access to. The seller sets a price curve $p(n)$ which specifies the price a buyer must pay for access to $n$ data points for each $n \in [N]$. Upon arrival, a buyer sees the price curve, and chooses an amount $n$ by maximizing their utility $u(n) = v(n) - p(n)$, where $v(n)$ is their valuation curve. The buyer leaves without making a purchase if their utility is negative for all $n$. It is assumed that there are $m$ buyer types, where all buyers of type $i$ have the same valuation curve $v_i$, and that there is a distribution $q$ over buyer types in which the arriving type is sampled i.i.d. from $q$ in each step. The objective is then to find a price curve which maximizes the expected revenue over this distribution. This paper focuses on online learning settings in which the distribution is unknown and must be learned or the arrival sequence is arbitrary and we want to compare to the best fixed price curve in hindsight, where now the goal is to minimize the regret. Due to the nature of this problem (a relation to revenue maximization with unit-demand buyers), computing the exact optimal is intractable, so approximations are considered. This is done by discretizing the space of valuation curves. The main result of this paper are new discretization schemes for this problem which can accommodate various further assumptions such as smoothness or diminishing returns in the valuation curves. These are then applied to develop algorithms with regret $\tilde{O}(m \sqrt{T})$ and $\tilde{O}(m^{3/2} \sqrt{T})$ in the stochastic and adversarial settings, respectively. ----------------------- Edit: following the rebuttal some of my questions have been answered and my score has been raised. Strengths: Overall, this is a well-written paper which introduces a very interesting and relevant problem and gives a clean description of the proposed solutions. While the techniques for online learning are based on fairly standard ideas (UCB and FTPL), they still require some small tricks that are particular to the new setting in this paper. Weaknesses: There are a few concerns: - Lack of tightness - it is not clear to what extent these results are tight as no lower bounds are given. - The finite type assumption - assuming both that the number of types is small (so that the complexity bounds are reasonable) and that all the types are known up front is somewhat limiting. Anything to address either of these comments is a significant improvement. - Once given the discretization scheme, the online learning methods utilize fairly standard techniques. It would be interesting if there are other approaches to this problem. - A lack of an experimental evaluation which might help to provide further evidence of the practicality of the proposed methods. As a minor comment, the organization in the appendix is poor as it does not follow the order in the main paper (appendix C gives proofs for section 5, while appendix D gives proofs for section 4). This leads to a confusion about notation, since the definition that $r(i, p ) = p(n_{i,p})$ isn't introduced until appendix D, but is used in appendix C. Technical Quality: 3 Clarity: 3 Questions for Authors: - Can anything be done to remove the assumption that the types are known up front? - Can any tight lower bounds be given for the stochastic and adversarial settings (i.e., in terms of both $m$ and T$)? Minor comments: - In Eq. (22) in the appendix, it has $f_t(p^)$ instead of $r_t(p^)$. Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: The authors have made assumptions clear. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: ### *Weakness 1, Question 2. Lower bounds and lack of tightness.* See the common response above. ### *Weakness 2, Question 1. The finite type assumption. Can we remove the assumption that the types are known up front?* This is an interesting question. We did attempt to solve this problem, but it appears to be quite challenging, and we believe it is best left for future work. The setting we study here is novel and nontrivial, even if it is less general than assuming finite types and their valuation curves are unknown. Moreover, as we have explained in lines 133-138 (Example 1) and 164-168, it is also motivated by some practical use cases. ### *Weakness 3. Once given the discretization scheme, our method uses fairly standard techniques.* See the common response above, Novelty in Sections 4, 5. ### *Weakness 4. A lack of an experimental evaluation.* See the common response above. ### *Organization of the appendix.* Yes, we agree that the appendix could be organized better and will reorganize it in the revision. --- Rebuttal Comment 1.1: Comment: Thank you for the response here and the discussion above. I agree that there is more subtlety to the techniques in this paper than I originally let on. I have raised my score. --- Rebuttal 2: Comment: Thank you so much! We will make the contributions clearer in the revision.	Summary: This paper addresses the problem of exploration in pricing strategy. It proposes an algorithm and proves that it has lower regret compared to previous algorithms. Strengths: The setting is interesting, and the results in this paper seem to show improvement over previous algorithms. Weaknesses: 1. One of the contributions of this paper is a better discretization scheme. An introduction to the insights that allowed you to design this improved discretization method would make the contribution clearer. 2. The construction of the confidence interval has room for improvement. The UCB in this paper is \|q_i-q_{i,t}\| \leq \|log T/T_{i,t}\|. Such an interval is typewise. I believe that using a joint confidence interval (for example, \sum T_{i,t} \|q_i-q_{i,t}\| \leq log T or similar form )or a similar form) could improve the dependency of the regret on $m$. 3. It is unclear whether Line 6 of Algorithm 3 is computationally efficient. Technical Quality: 3 Clarity: 2 Questions for Authors: See the 'Weakness' part Confidence: 2 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: See the 'Weakness' part Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: ### *Weakness 1. Insights for discretization scheme.* First note that in order to get a discretization that approximates any price curve within $\epsilon$, the size of such a discretization should be $\tilde{O}\left( 2^N\epsilon^{-N} \right)$, which is clearly very large. Our first insight is that when there are only $m$ types and the valuations are monotone, we can reduce this to $m$ step functions (see Line 216-223), which reduces discretization size to $\tilde{O}\left(N^m\epsilon^{-m}\right)$. While this is better, it can still be quite bad. Hence, we explore two other assumptions satisfied by data. First, under smoothness, we are able to reduce the discretization size to $\tilde{O}\left(L^m \epsilon^{-2m}\right)$ by discretizing the data space $[0,N]$ uniformly ($L$ is the smoothness constant, see line 158). Second, under diminishing returns, we are able to reduce this to $\tilde{O}\left(J^m \epsilon^{-3m}\log^m N\right)$ ($J$ is the diminishing return constant, see line 162-163); in this case, we design a non-uniform discretization method to the data space $[0,N]$. The discretization needs to be denser near 0 to account for the diminishing returns structure. ### *Weakness 2. Construction of confidence interval.* Here is the reason why we need a confidence interval for each of the $q_i$, where $q_i$ denotes the probability of type $i$. We first construct a confidence interval for type distribution $q = (q_1,\dots,q_m)$, then translate them to UCBs for the revenue (see line 760, Lemma D.2). Subsequently, these UCBs for the revenue are used to bound the regret (see equation 32 and Lemma D.3 in line 768). However, we are not aware of any union bounds which can improve the dependence on $m$. Could you please give us a concrete example of a union bound? That will help us give a better answer. ### *Weakness 3. Computational complexity.* See the common response above. --- Rebuttal 2: Title: Sincerely looking forward to your reply Comment: Thank you again for your feedback. With the discussion period ending in two days, we would appreciate knowing if our response has adequately addressed your key questions and concerns. --- Rebuttal Comment 2.1: Title: Official Comment by Reviewer oHSK Comment: Thank you for the response here and the discussion above. I have raised my score. --- Reply to Comment 2.1.1: Comment: Thank you again for your comments. Based on your comments, we will clarify our contributions and techniques in future revisions.	Rebuttal 1: Rebuttal: We thank all reviewers for their feedback. First, we would like to address common concerns raised by reviewers. ### *On technical novelties* While all reviewers agree on the novelty of our discretization scheme, there is a perception that Sections 4 and 5 simply apply UCB/FTPL to this discretization. However, there are nontrivial adaptations in the algorithm and the analysis to account for the asymmetric nature of the feedback. Specifically, the type is revealed only if a purchase is made, and feedback under one price curve can be shared across all prices. - Stochastic setting (Sec. 4) If we naively apply UCB by only accounting for feedback for the chosen price curve, we get a $\sqrt{\|\overline{\mathcal{P}}\|T\log T}$ upper bound, where $\|\overline{\mathcal{P}}\|$ is the size of the price set, leading to poor, often exponential dependence on the number of types $m$. This is the bound if we only observe the reward for the prices that are actually pulled, but do not observe the types after purchase. Therefore, naively applying UCB is like bandit feedback. On the other extreme, had we been in an alternative setting where we observe the type regardless of purchase, this is like a full information feedback because once observe the type, we know the revenue for all prices. In this full information setting, UCB gives us $\sqrt{T\log\|\overline{\mathcal{P}}\|\log T}$ $\in \tilde{O}(\sqrt{mT})$ upper bound. We are in an intermediate regime between bandit feedback and full information: if a type purchases at one price curve, we know what they would have purchased at other price curves. However, if there is no purchase, we do not know the type of the buyer. We account for this asymmetric nature by noting that the key unknown is the type distribution. In the full information setting, we use the sample average of each type to estimate the type distribution and then translate this to confidence intervals on the revenue. In our setting, as the type is unknown if there was no purchase, we only count the types in $S_t$ if a particular type would have made a purchase anyway (Eq. 5, 6). The key challenge is in showing that the confidence intervals we have designed are valid, which requires a delicate analysis. - Adversarial setting (Sec. 5) In the adversarial setting, we adapt the FTPL algorithm, which is for full information and does not apply to our setting directly. When there is a purchase, we set the reward similarly, but when there is no purchase, we do not observe $i_t$. Our approach in line 7 of Algorithm 4 is to set $r_t(p)=\sum_{i\in S_t^c}p(n_{i,p})$ for $p\in\overline{\mathcal{P}}$, where $S_t$ contains types who would have purchased in round $t$ had they appeared in that round. When the buyer does not purchase on round $t$, the seller knows that $i_t\in S_t^c$. We define the reward for each price function as $r_t(p)=\sum_{i\in S_t^c}p(n_{i,p})$, an upper bound on the true revenue $p(n_{i_t,p})$. For prices possessing the same set $S_p$ with $S_t$, this upper bound is tight, i.e., $r_t(p)=p(n_{i_t,p})=0$. As mentioned in lines 321-324, $r_t(p)$ deals with the uncertainty of not knowing the type on round $t$ by providing a large reward to prices that could have resulted in a purchase, encouraging exploration of such prices in future rounds. ### *Lower bound* Indeed, we were able to prove a $\Omega(\sqrt{T})$ lower bound in our setting. This is tight in $T$ but not in $m$, but we decided not to include it because one does not expect to do better than $\tilde{O}(\sqrt{T})$ anyway. (In hindsight, we think it might be better to include this, as the proof required some slightly different techniques to standard hypothesis testing arguments) To get a tight dependence on $m$, we need to account for the asymmetric feedback in the proof of the lower bound. This appears to be challenging, and we are unaware of techniques to handle such feedback. The closest we could find is [2], who provide a $\sqrt{T\log K}$ lower bound for a $K$ armed bandit setting with one-sided feedback, but their techniques are not applicable here. ### *Computational complexity* Yes, our algorithm is computationally expensive (i.e., the running time depends exponentially on the number of types $m$), but this is inevitable as even the offline version of our problem is strongly NP-hard (see [1] and lines 449-463 in our paper). Our goal was to develop an algorithm that is efficient in the number of data points $N$ given that the number of types $m$ is a fixed constant, which is relevant in practical scenarios. An interesting question is developing an online PTAS (Polynomial Time Approximation Scheme), an algorithm that guarantees sublinear regret with respect to an approximately optimal price with a fixed approximation factor. While this was not a focus of our paper, the offline PTAS from [1] can be generalized into our online setting using our online algorithms in Sections 4 and 5. In future revisions, we will address the issue of computational complexity more explicitly as shown in this rebuttal. ### *Numerical evaluation* While we agree that empirical evaluations would be helpful, we believe our theoretical contributions are valuable on their own. Furthermore, it is common and acceptable for theoretical papers at NeurIPS to not have empirical evaluations. ### *Reference* [1] Chawla et al., Pricing ordered items. STOC 2022. [2] Zhao et al., Stochastic One-Sided Full-Information Bandit. ECML PKDD 2019.	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
BackTime: Backdoor Attacks on Multivariate Time Series Forecasting	Accept (spotlight)	Summary: The paper titled "BACKTIME: Backdoor Attacks on Multivariate Time Series Forecasting" introduces a novel method called BACKTIME, aimed at exploring the robustness of multivariate time series (MTS) forecasting models against backdoor attacks. BACKTIME enables an attacker to subtly manipulate predictions by injecting stealthy triggers into the MTS data. Through a bi-level optimization process using a graph neural network (GNN)-based trigger generator, the method identifies vulnerable timestamps and crafts effective, covert triggers. Comprehensive experiments across various datasets and cutting-edge MTS forecasting models demonstrate the efficacy, flexibility, and stealth of BACKTIME attacks. Strengths: - The BACKTIME method offers a fresh perspective on backdoor attacks in MTS forecasting, demonstrating the feasibility and impact of such attacks. - The experimental setup is comprehensive and includes multiple datasets and state-of-the-art forecasting models, showcasing the method's versatility. - The paper provides clear explanations of the bi-level optimization process and the role of the GNN-based trigger generator, facilitating understanding of the attack mechanism. - The research highlights the need for robustness in MTS forecasting models, particularly in high-stake scenarios where malicious attacks could have serious consequences. Weaknesses: - The paper does not adequately address potential limitations or discuss the robustness of the method against countermeasures. A more detailed analysis of the limitations and how they might affect the practical applicability of BACKTIME would strengthen the paper. - The potential negative societal impacts of such attacks are not sufficiently explored. Given the sensitive nature of MTS forecasting in areas like climate, epidemiology, and finance, a deeper discussion on the broader implications is warranted. Technical Quality: 3 Clarity: 3 Questions for Authors: - What are the potential limitations of the proposed method, especially regarding its generalizability to other types of time series data or forecasting models? Confidence: 2 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: - The authors have not adequately addressed the limitations of their work, nor have they discussed the potential negative societal impacts of BACKTIME. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: > Q1. The paper does not adequately address potential limitations or discuss the robustness of the method against countermeasures. A more detailed analysis of the limitations and how they might affect the practical applicability of BACKTIME would strengthen the paper. Thanks for the reviewer's valuable comments. We acknowledge that BackTime indeed has certain limitations. Firstly, it is challenging to leverage BackTime on time series imputation tasks. To achieve an effective backdoor attack, BackTime concatenates the trigger and the target pattern sequentially to establish a strong temporal association. This association is the foundation of BackTime's attack efficiency. However, in time series imputation, deep learning models can infer based on data both before and after the missing values. Thus, the models may not rely heavily on the data preceding the missing values, which breaks the basic assumptions of BackTime. Hence, BackTime may not be able to implement an effective attack in this scenario. Secondly, BackTime may struggle with datasets that contain missing data. BackTime predicts the target pattern only when the trigger is included within the inputs. Therefore, BackTime poses a requirement for the completeness of triggers. If the trigger itself is incomplete, the attacked deep learning model may fail to recognize the existence of the triggers, leading to an ineffective backdoor attack. Thirdly, the success of backdoor attacks relies on the redundancy of the learning capacity of deep learning models. In other words, deep learning models can complete specific tasks using only a subset of neurons, while the remaining neurons respond weakly or not at all. Thus, backdoor attacks aim to manipulate these weakly responding neurons to execute the attack without compromising the model's effectiveness. Consequently, backdoor attacks are typically more effective on deeper models with larger parameter sizes, such as TimesNet, Autoformer, and FEDformer in our paper. If the victim chooses a simple model for time series forecasting, such as MLP, the effectiveness of BackTime might deteriorate. Another limitation of this work is that it does not offer a solution for defense. To address this gap, we have outlined some preliminary ideas on how to defend against BackTime. First, there may be a frequency difference between the generated triggers and the target pattern compared to the real data. Hence, detecting the distribution drift in the frequency domain could be a promising approach. Additionally, the generated triggers might not exhibit the same rich diversity as real data. Consequently, in the feature space, the (trigger, target pattern) pair might cluster closely with each other, making detection via clustering algorithms feasible. > Q2. The potential negative societal impacts of such attacks are not sufficiently explored. Given the sensitive nature of MTS forecasting in areas like climate, epidemiology, and finance, a deeper discussion on the broader implications is warranted. Thank you for your concern regarding the potential societal impacts of BackTime. As a backdoor attack method, the misuse of BackTime indeed poses the risk of negative social consequences. Specifically, in the financial markets, attackers could exploit BackTime to inject stealthy backdoors into stock price prediction models, enabling market manipulation and illicit profit gains. This could lead to increased market volatility and eroded investor confidence. In public transportation, as mentioned in lines 27 - 32 of our paper, BackTime could cause transportation prediction models to output incorrect results. This could negatively impact traffic signal control and route planning, resulting in increased traffic congestion and accidents. In the healthcare field, medical monitoring systems often rely on time series data, such as ECG datasets. A backdoor attack could cause data-driven healthcare models to produce erroneous diagnostic results, potentially affecting treatment plans and endangering patient health. Given the potential risks of BackTime, we present several ways to mitigate its negative societal impacts. From the perspective of data collection, researchers should be aware of the risk of backdoor injection into publicly available time series datasets. Therefore, when using public datasets for training, it is recommended to rigorously inspect and cleanse the data to minimize the impact from malicious data injection. We have provided some possible data detection methods in Q1. Due to the character limit, we do not provide a detailed description here. From the perspective of model training, researchers can enhance model robustness. For example, by employing adversarial training strategies, researchers can reduce the model's sensitivity to specific perturbations, thus enabling the model to resist backdoor trigger samples. From the perspective of model deployment, researchers can establish real-time monitoring systems to detect anomalies in system inputs and outputs. Effective anomaly detection algorithms can help promptly identify potential attacks. Once again, thank you for your insightful comments and suggestions. We will incorporate our response to both Q1 and Q2 in the revised version. --- Rebuttal 2: Comment: Thank you for the detailed rebuttal. The clarification of BACKTIME's limitations and the discussion on societal impacts are appreciated. Addressing these aspects will indeed strengthen the paper. Please ensure these points are integrated into the manuscript for the next review. Continue to consider potential defenses and broader implications for various applications. My concern has been addressed. I will raise my score to accept. --- Rebuttal Comment 2.1: Title: Response to Reviewer Bpy4 Comment: We want to express our sincere thanks for your recognition of our work. Answering your insightful comments helps us improve the quality of our work. In the revised version of our paper, we promise to include discussions on potential defenses and broader implications. We are confident that these additions will enrich our contribution and provide a more comprehensive understanding of the impact and context of our work.	Summary: This paper proposed a backdoor attach method for multivariate time series forecasting, where only a few works focus on this topic. The injected stealthy triggers are interesting and effective in destroying raw data. Strengths: The originality of this paper is solid, since this is the first work to consider the backdoor attack in MTS forecasting. The quality and clarity of this paper are also good for understanding. The significance of this paper is relatively well-clarified. Weaknesses: 1. The Trigger Generation and Bi-level Optimization are not clearly presented. Please extend the description of trigger generation and effectiveness. 2. The experiments need to be expanded, and the advantages of the proposed method are not well validated. 3. Numerically, the authors could consider comparing their method with more baselines. There are some studies on backdoor attacks for forecasting models. Technical Quality: 4 Clarity: 3 Questions for Authors: 1. The Trigger Generation and Bi-level Optimization are not clearly presented. Please extend the description of trigger generation and effectiveness. 2. The experiments need to be expanded, and the advantages of the proposed method are not well validated. 3. Numerically, the authors could consider comparing their method with more baselines. There are some studies on backdoor attacks for forecasting models. Confidence: 4 Soundness: 4 Presentation: 3 Contribution: 4 Limitations: 1. What is the technical drawback of the proposed method? E.g., attack efficiency and hidden effect. 2. Are there any initial ideas to be able to look forward from a defense perspective? Flag For Ethics Review: ['No ethics review needed.'] Rating: 8 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: > Q1. The Trigger Generation and Bi-level Optimization are not clearly presented. Please extend the description of trigger generation and effectiveness. Thank you for your attention to the trigger generation and bi-level optimization. These two components are indeed core parts of BackTime. However, due to the page limit, we were unable to provide a detailed description in the original version. We are more than willing to elaborate on these two components in the revised version. Regarding trigger generation, for the sake of stealthiness, we aim to generate triggers that are similar to the data preceding the injected triggers. Therefore, we extract the time series data before the injected triggers, denoted as $\mathbf{X}^{ATK}[t_i - t^{BEF} - t^{TGR}:t_i - t^{TGR}]$ in Eq. (5), and use it as the input to the trigger generator (a GCN). The GCN effectively generates the trigger by integrating the time series data before triggers and the correlation graph. However, as mentioned in the paper, the amplitude of the GCN's output could be large, which poses a significant challenge to the convergence of the training process. To address this, we apply the tanh function to scale the output, and utilize the scaled outputs as the final triggers as shown in Eq. (6). During the training process, the trigger generator is updated adaptively in an end-to-end manner. Specifically, the trigger generator injects the generated trigger into the poisoned dataset $\mathbf{X}^{ATK}$, and the surrogate model $f_s$ is leveraged to evaluate and update the trigger. Intuitively, an effective trigger should induce $f_s$ to predict the future as the target pattern. Thus, after freezing the parameters of $f_s$, we use $l_{tgr}$ in Eq. (10) as the loss function to update the trigger generator, aiming to reduce the difference between the predictions of $f_s$ and the target pattern. > Q2. The advantages of the proposed method are not well validated, and the authors could consider comparing BackTime with more baselines. There are some studies on backdoor attacks for forecasting models. We agree with the reviewer in that the baselines in this paper are heuristic and MAE may not fully evaluate our method. Meanwhile, we would like to emphasize the superiority of BackTime from two perspectives. First, on four datasets (PEMS03, PEMS08, Weather, and ETT), our method reduces $MAE_A$ by 50.8\%, 52.64\%, 83.52\%, and 45.40\% compared to clean training, respectively. Even when compared with the best baseline in this paper, BackTime also reduces $MAE_A$ by 16.84\%, 12.26\%, 34.80\%, and 7.84\%. These results demonstrate that BackTime effectively implements a backdoor attack on multivariate time series (MTS). Second, we would like to highlight that our work is the first to focus on backdoor attacks in MTS forecasting and formally define a backdoor attack framework for time series forecasting. As such, finding suitable backdoor attack methods for MTS forecasting as baselines is challenging. To our best knowledge, there are not existing baselines in the literature that directly apply to our setting. Therefore, we designed a few heuristic methods as the baselines. To better address reviewer's concerns, we have provided additional classic adversarial attack methods, such as FGSM and PGD, as baselines. Specifically, we generated adversarial perturbations to induce the model to predict the target pattern. The experimental results are as follows. From the table, PGD and FGSM not only failed to implement effective backdoor attacks but also significantly reduced the model's forecasting performance. One of the reasons is that the generated adversarial perturbations exhibit significant difference from the real data, hence impeding models' learning on clean features. This highlights the necessity for meticulously designed triggers in backdoor attacks on time series forecasting and randomly chosen perturbations highly likely fail to implement effective attacks. If there is any specific baseline the reviewer would like to let us include, we would be more than happy to include them in our evaluation. \| \| $MAE_C$ \| $RMSE_C$ \| $MAE_A$ \| $RMSE_A$ \| \|----------\|---------\|----------\|---------\|----------\| \| Clean \| 20.00 \| 34.18 \| 28.63 \| 46.69 \| \| FGSM \| 110.04 \| 151.71 \| 91.13 \| 149.76 \| \| PGD \| 108.86 \| 150.43 \| 90.01 \| 147.07 \| \| BackTime \| 21.23 \| 35.22 \| 20.83 \| 30.94 \| > Q3. What is the technical drawback of the proposed method? E.g., attack efficiency and hidden effect. Thank you for your attention to the technical drawbacks and limitations of BackTime. We acknowledge that BackTime may not exhibit good attack efficiency in certain application scenarios. However, due to the character limit, we kindly ask the reviewers to refer to our response to the reviewer Bpy4's Q1 for a more comprehensive discussion. > Q4. Are there any initial ideas to be able to look forward from a defense perspective? Thank you for your attention to potential defenses against backdoor attacks in time series data. Backdoor defense is indeed an important and promising future direction. While it will require a separate study to develop a full solution, we do have some initial ideas for backdoor defenses. First, there may be a frequency difference between the generated triggers and the target pattern compared to the real data. Hence, detecting the distribution drift in the frequency domain could be a promising approach. Additionally, the generated triggers might not exhibit the same rich diversity as real data. Consequently, in the feature space, the (trigger, target pattern) pair might cluster closely with each other, making detection via clustering algorithms feasible. --- Rebuttal Comment 1.1: Comment: Thanks for the authors' efforts in the detailed response. My concern has been addressed. I will raise my score to strong accept. --- Reply to Comment 1.1.1: Title: Response to Reviewer PmgC Comment: We sincerely thank you for your appreciation of our work. Your comments have been invaluable in guiding us in improving the quality of our research. In the revised version of the paper, we promise to include detailed descriptions of the trigger generation and bi-level optimization processes, as requested. Additionally, we will incorporate a discussion of potential defenses against the proposed attack. We believe that these enhancements will significantly strengthen our work and provide a more comprehensive understanding of its contributions.	Summary: This paper primarily discusses how to conduct a backdoor attack on the multivariate time series forecasting task, proposing a two-stage training approach. The core idea is to identify timestamps with significant differences in MAE of the Clean model and Poisoned model on poisoned data points. Simultaneously, the trigger generation function is learned by minimizing the MAE loss of the model's prediction of the target pattern with triggers as input. Strengths: 1. This is a quite interesting and important research topic. However, the example provided by the author regarding traffic prediction is not convincing enough. Traffic prediction data is collected and trained by private systems. If one can already access the system to inject toxic data, there would be simpler and more effective methods than backdoor attacks. If the author can provide some scenarios where the time series data points are provided by third-party systems, it would better illustrate the necessity of this paper. 2. The author's writing is clear and easy to follow. 3. The author has proposed a framework that can be applied to various time series prediction backbones and has conducted a comprehensive evaluation of effectiveness. Weaknesses: 1. The baseline methods in the paper are heuristic, and the worse MAE of these methods compared to the proposed method in the paper does not effectively illustrate the issue. 2. The types of anomalies illustrated in the paper are relatively simple. Technical Quality: 2 Clarity: 4 Questions for Authors: 1. In Equation 3, according to the paragraph from lines 189-190, the clean loss should be the MAE using the clean samples to predict the ground truth, and the attack loss should be the MAE using the poisoned samples to predict the target pattern, right? However, in Equation 3, both MAE losses target $X^{ATK}_{ti,f}$. Here, clarification from the author is requested. 2. The training of the trigger generation network depends on initially manually generating some attack samples. Does the quality of these initial samples significantly affect the following training process? 3. The two-stage training is very unstable, which the author mentioned in the paper, but there is no detailed description in the text. It would be helpful to understand the rationality of the model design if the author could provide the training loss change curve. Confidence: 2 Soundness: 2 Presentation: 4 Contribution: 3 Limitations: The author has discussed in the paper how to prevent the injected data points from having too large a magnitude and how to address training instability issues. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: > Q1. The baseline methods in the paper are heuristic, and the worse MAE of these methods compared to the proposed method in the paper does not effectively illustrate the issue. Thank you for your concern on the baselines in our papers. We agree with the reviewer that the baselines in this paper are heuristic and MAE may not fully evaluate our method. However, due to the character limit, we kindly ask the reviewer to refer to our response to the reviewer Pmgc's Q2 for a more comprehensive discussion. > Q2. The types of anomalies illustrated in the paper are relatively simple. Thank you very much for your valuable suggestions. As the reviewer correctly pointed out, the main goal of this work is to demonstrate the feasibility of backdoor attacks on multivariate time series, and therefore, we did not focus on complex target patterns. However, we would like to emphasize that BackTime can effectively perform attacks, even with complex target patterns. To illustrate this, we have conducted additional experiments on the PEMS03 dataset, attacking the TimesNet model using three different complex target patterns. Since it is challenging to design complex target patterns when the pattern length is too short, we set the pattern length to 17 in the new experiments instead of 7 as mentioned in the paper. The target patterns are provided at Figure 1 with the format of PDF on the global rebuttal. The experimental results are presented in the following table. As shown in the table, $MAE_A$ and $RMSE_A$ reach a quite low value, even lower than $MAE_C$ and $RMSE_C$. It demonstrates that BackTime successfully completes the attack even with complex patterns, demonstrating its superiority. Once again, thank you for your insightful comments and suggestions. They have been incredibly helpful in further improving our work. \| \| $MAE_C$ \| $RMSE_C$ \| $MAE_A$ \| $RMSE_A$ \| \|-----------\|--------\|---------\|--------\|---------\| \| Pattern 1 \| 22.42 \| 36.88 \| 20.41 \| 29.80 \| \| Pattern 2 \| 22.85 \| 37.35 \| 20.35 \| 29.78 \| \| Pattern 3 \| 22.47 \| 36.97 \| 20.37 \| 29.70 \| > Q3. In Eq. (3), the clean loss should be the MAE using the clean samples to predict the ground truth, and the attack loss should be the MAE using the poisoned samples to predict the target pattern, right? However, in Eq. (3), both MAE losses target $X_{ti,f}^{ATK}$. Thanks for your valuable comments on our notations. As you pointed out, the attack loss is used to update the trigger for the purpose of predicting the target pattern. To achieve this, we introduce $\beta(t_i)$ in the upper-level optimization to locate the target pattern within $X^{ATK}$. However, there seems to be a misunderstanding regarding the precise role of the clean loss. $X^{ATk}$, the attacked dataset, contains both clean time slices and attacked time slices. Victims may train their model on this attacked dataset $X^{ATK}$, resulting in an attacked model that carries the backdoor. Therefore, the lower-level optimization still uses $X^{ATK}$, and the clean loss here refers to the common loss function in the forecasting task, such as MAE. We believe the term "clean loss" might have caused this misunderstanding. Therefore, we will change this term to "natural loss" in the revised version to clarify its meaning. > Q4. The training of the trigger generation network depends on initially manually generating some attack samples. Does the quality of these initial samples significantly affect the following training process? Thank you for your attention to the trigger generation network. As mentioned in line 264 of our paper, we introduced the "adaptive trigger generation" mechanism. Thus, after end-to-end training of the trigger generator, triggers could be adaptively acquired, and there is no need for manually setting the initial attack samples. Specifically, the trigger generator injects the generated trigger into the poisoned dataset $\mathbf{X}^{ATK}$, and the surrogate model $f_s$ is leveraged to evaluate and update the trigger. Intuitively, an effective trigger should induce $f_s$ to predict the future as the target pattern. Thus, after freezing the parameters of $f_s$, we update the parameter of the trigger generator to reduce the difference between the predictions of $f_s$ and the target pattern. Once the trigger generator is well-trained, it can adaptively output effective triggers. Perhaps the current description on trigger generation has caused this misunderstanding. We will provide a more detailed explanation in the revised version. > Q5. Could the author provide some scenarios where the time series data points are provided by third-party systems? Thank you for your concern about the scenarios. BackTime can be leveraged in several application scenarios where the data are collected by third-party systems, beyond just traffic prediction. However, due to the character limit, we kindly ask the reviewer to refer to the second paragraph of our response to reviewer Bpy4's Q2 for a detailed discussion. > Q6. The two-stage training is unstable, but there is no detailed description in the text. It would be helpful to understand the rationality of the model design if the author could provide the loss curve. Thank you for your valuable comments. The two-stage training is a crucial part of BackTime's training process. Sorry for not providing detailed explanations in the original version due to the page limit. We are more than willing to include a thorough description of this process in the updated version of our paper. We have also provided a detailed explanation in response to the Reviewer Pmgc's Q1, and we hope these clarifications will resolve some confusions. Additionally, as the reviewer's request, we have provided the loss function curves in Figure 2 on the global rebuttal to help understand the two-stage training process. --- Rebuttal Comment 1.1: Comment: Thank the author for the reply. The explanation regarding clean loss and trigger generation has addressed my concerns. However, the examples in response to reviewer Bpy4 has not convinced me. In both the medical and stock market, the attacks are still conducted after data collection. If one can access the data in such private system, the most effective method would be to directly tamper with the data rather than using the indirect approach of constructing toxic samples to influence the model. The current method in the paper requires training to determine what kind of attack samples to generate, which I believe is a limited contribution. I am more looking forward to seeing attack methods and defense methods that are training-free. In total, I think this paper has not yet reached the level of a score 7 (clear accept), and I maintain my current score of 6 as weak accept." --- Reply to Comment 1.1.1: Title: Response to Reviewer mt9q Comment: We are very glad to know that your concerns about the clean loss and trigger generation have been addressed. We also want to thank you for the follow-up questions and are happy to share more answers. First, we would like to point out that standard backdoor attacks belong to the category of data-poisoning attacks, where modifications/augmentations to training data are a necessary and indispensable requirement in backdoor attacks across various domains [1,2,3,4], such that the attacked model learn the strong association between triggers and target pattern (or target class) in the training data, thereby altering its predictive behavior. Unlike traditional attacks that might rely solely on exposed data and could be short-sighted or ineffective, backdoor attacks strategically manipulate the training data to embed malicious behavior, which remains dormant during normal operations but can be triggered under specific conditions. This approach ensures that the attack is both stealthy and persistent. Furthermore, under this data-poisoning setting, backdoor attacks can be highly threatening because neural network training requires a large amount of data, which is difficult to accomplish by only using private data. Therefore, by stealthily poisoning public datasets, attackers can pose a great threat to neural networks' wide application. For example, in the healthcare field, it is hard for a single hospital to collect enough data to train a robust model. Hence, hospitals are likely to delegate to AI-related agencies, and those agencies mix the hospital-provided data with large-scale public data (e.g., scraped from the internet) to enhance model performance. By poisoning widely used public datasets, such as ERP [5] and OpenNeuro [6] datasets, backdoor attacks could pose a significant threat to the medical control systems used by hospitals. The suggestion of a training-free strategy is quite interesting but indeed presents significant challenges to attack efficiency based on the current developments in the research community. Since a training-free backdoor attack, neither has any knowledge of the architecture of models to be trained nor has access to the data during training, the trigger can only be manually set. However, time series data varies greatly in both frequency and amplitude, ranging from traffic data to weather patterns. It is exceedingly difficult for a manually designed trigger to perform an effective attack across different time series datasets. Considering this, we believe that developing a training-free backdoor attack is a highly challenging research problem, and we would be very interested in exploring this in future research. [1] Badnets: Identifying vulnerabilities in the machine learning model supply chain. [2] Backdoor attack with imperceptible input and latent modification [3] Textual backdoor attack for the text classification system. [4] A backdoor attack against lstm-based text classification systems. [5] https://erpinfo.org/erp-core [6] https://openneuro.org/	null	null	Rebuttal 1: Rebuttal: 1. Figure 1 visualizes three different target patterns. - Experiments on the response to the reviewer mt9q’s Q2 show that BackTime successfully completes the attack even with complex target patterns. 2. Figure 2 visualizes the loss curve of the two-stage training process in BackTime. - We use the same color to plot the two loss ($l_{cln}$ and $l_{tgr}$) within the same epoch. - During each epoch of the two-stage training, we run the clean training first, as shown in the upper figure, and then update the trigger generator, as shown in the lower figure Pdf: /pdf/f428a5afb1e35122af791b754aa6dfb2d75aaf55.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Fast Sampling via Discrete Non-Markov Diffusion Models with Predetermined Transition Time	Accept (poster)	Summary: The paper proposes an accelerated sampling method from standard discrete diffusion models like multinomial diffusion and absorbing-state diffusion, using a non-Markovian forward process where the stochasticity is modelled by sampling a single transition time for each token, after which the process is fully determined. The model is trained similarly as a standard discrete diffusion model, but the formalism allows for a different type of sampler: The transition times are sampled in advance in the beginning, and the denoiser neural network simply parameterizes the transitions that happen at those times in the reverse process. This allows to skip over redundant steps where no transition would occur in the standard discrete diffusion models, speeding up sampling significantly for large step counts. The model provides improved results and faster sampling speeds over a prior accelerated sampling method for sequence-to-sequence generation tasks, and similarly improved results for unconditional language modelling with the text8 and enwik8 data sets when comparing with a prior multinomial diffusion model. Strengths: + Clearly improves over a standard multinomial and absorbing-state schedule in sampling speed and results + Improves over a previous published work in accelerating discrete diffusion models + The framework could be a useful conceptual tool for people working with standard discrete diffusion models in the style of D3PM and want to accelerate sampling. Methods like ARDM from Hoogeboom et. al. and the tau-leaping of Campbell et al. are similar in function, but either require reframing the modelling problem differently or only allow for absorbing-state transitions in the case of ARDM. + In contrast, this paper presents a method that allows changing a model in the D3PM framework to a faster one that skips over redundant steps, and shows how it is connected to the original model as a model with transition times as latent variables. + The method is simple and easy-to-use Weaknesses: - The method is, in practice, somewhat similar to prior work (Campbell et. al. and Hoogeboom et. al.), and in that sense it would be more beneficial for the community if the paper went deeper into analysing potential speed improvements in discrete diffusion models or theoretical connections between their method and other work. - It would be useful if we had results from less steps in Table 3: Seems like the biggest time improvements are obtained with large step counts, but the BLEU scores are not drastically different from low step count BLEU scores. If both methods work quite well with low step counts already, then the results don't seem like the best showcase of the improvements due to increased step counts. Overall, it would be useful to have a clearer picture of the situations in which the method provides practical benefits. [1] "A Continuous Time Framework for Discrete Denoising Models", Campbell et. al. [2] "Autoregressive Diffusion Models", Hoogeboom et. al. Technical Quality: 3 Clarity: 3 Questions for Authors: - Since the accelerated multinomial model now does only one step for each token, I suppose it is not quite equivalent to the standard multinomial diffusion, where multiple transitions per token can happen during the generative process? Could the authors clarify the similarities and differences? Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: Addressed. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your support and insightful comment. * Q1. The method is, in practice, somewhat similar to prior work (Campbell et. al. and Hoogeboom et. al.), and in that sense it would be more beneficial for the community if the paper went deeper into analysing potential speed improvements in discrete diffusion models or theoretical connections between their method and other work. A1. While there are some conceptual parallels with prior work, our method offers unique and significant contributions as follows: - Unified framework: Unlike ARDM [1], which is limited to absorbing-state transitions, our approach provides a unified framework applicable to both multinomial and absorbing diffusions. - Non-Markovian continuous-time framework: Different from Campbell et al.'s (2022) Markovian framework [2], we study the non-Markovian setting, offering new insights for discrete diffusion models. - Theoretical foundations: Our rigorous theoretical analysis (Theorems 3.1, 3.5, and D.1) establishes connections between our non-Markovian process and standard discrete diffusion models. - Bridging discrete and continuous processes: We investigate the transition from finite to infinite step sampling, providing new insights into bridging the gap between discrete and continuous-time processes. - Practical implementation and scalable efficiency: Our method allows for the seamless adaptation of existing multinomial and absorbing discrete diffusion models and demonstrates significant speed improvements, achieving a 30x speedup at 1000 steps while maintaining generation quality. Regarding your suggestion for deeper analysis, we agree this would be valuable. Due to page limitations, we had to place some of the detailed discussions and analyses in the appendix (like lines 845-853). We will incorporate these extended discussions into the extended page of the main paper in the camera-ready version if accepted, providing a more comprehensive comparison with ARDM and Campbell et al.'s work [1,2]. [1] Hoogeboom et al., "Autoregressive Diffusion Models." ICLR 2022. [2] Campbell et al, "A Continuous Time Framework for Discrete Denoising Models". NeurIPS 2022. * Q2. Lack of results from fewer steps in Table 3, making it unclear in which situations the method provides practical benefits. A2. We appreciate your feedback. Tables 2, 3, 6, and 7 highlight the practical benefits of our method across various step counts: - At 25 steps: Our method achieves approximately 2x speedup. - At 50 steps: We observe about a 3x speedup. - At 1000 steps: The speed increases significantly to around 30x. These results show that our method offers benefits even at moderate step counts like 25, with the advantage becoming more significant as the number of steps increases. This scalability makes our approach particularly valuable for tasks requiring higher quality generation and more computational steps. Below, we present additional results for IWSLT14 with fewer sampling steps in an absorbing generation process, complementing the experiment in Table 3 of our submission. As shown in the table, when the sampling step count is significantly reduced below 25, the quality of the generated examples decreases noticeably (By Table 3, when step counts of 25 or higher, performance remains consistently above $\mathbf{31.5}$ BLEU for both RDM-Absorb and DNDM-Absorb). \| Steps \| RDM-Absorb BLEU \| RDM-Absorb Time (s) \| DNDM-Absorb BLEU \| DNDM-Absorb Time (s) \| \|-------\|-----------------\|---------------------\|-------------------\|----------------------\| \| 5 \| 29.92 \| 27.36 \| 30.30 \| 24.1 \| \| 10 \| 31.02 \| 48.08 \| 31.49 \| 37.9 \| \| 15 \| 31.26 \| 69.22 \| 32.13 \| 50.0 \| Performance in low-step settings is a known challenge for discrete diffusion models, which falls outside the scope of our current work. Our primary focus is on accelerating the algorithm while maintaining high performance, which is a crucial factor for real-world applications requiring high-quality sample generation. Our comprehensive experiments demonstrate that DNDM provides a competitive speed-quality trade-off across a broad range of step sizes, with its performance particularly excelling as the number of steps increases. * Q3. Since the accelerated multinomial model now takes only one step for each token, is it not quite equivalent to the standard multinomial diffusion, where multiple transitions per token can happen during the generative process? Could the authors clarify the similarities and differences? A3**. Thank you for your question. Our accelerated multinomial model, based on the DNDM framework, indeed performs only one transition per token. This approach is mathematically equivalent to the standard multinomial diffusion in terms of the final generated distribution, and it leads to the same training objective, as detailed in Appendix B. Here are the key similarities and differences: Similarities: - Final Distribution: Both methods produce samples from the same learned distribution. - Training Process: The training process remains unchanged, allowing the use of the same neural network. Differences: - Sampling Process: Our method pre-samples transition times, allowing more efficient sampling by skipping unnecessary steps. - Number of Transitions: While standard multinomial diffusion allows multiple transitions, our method consolidates these into a single, more efficient transition. - Computational Efficiency: Our approach significantly reduces the number of function evaluations, especially for large step counts, which leads to faster sampling. We will include a detailed discussion of these points in our paper to clarify this important aspect. --- Rebuttal Comment 1.1: Title: Answer to rebuttal Comment: I thank the authors for the comprehensive answers to the questions. I appreciate the promise to add more discussion on the connections to prior work, and the additional experiments on low step counts. Given that these were the main concerns, I will raise the score, although it would be better if the extended discussions had been in the original paper and if there were some additional speed-up tricks that make the method clearly stand out from previous work on speeding up discrete diffusion. The new theoretical approach is interesting as well. --- Reply to Comment 1.1.1: Comment: Thank you for your positive feedback and increased score. We appreciate your valuable insights on our additional experiments and theoretical approach.	Summary: This paper proposes a new formulation for discrete diffusion models whereby the corruption process is defined as a non-markovian process. At each point, a decision is made as to either stay in the current state or switch to a noise sample however crucially, this noise sample is constant throughout the process thereby only a single transition happens for each dimension. During generation, the model then just needs to step from transition time to transition time and can ignore superfluous simulation steps where no transition happens. The model is trained using an ELBO which the authors derive for their transition time conditional process. The authors test their model on machine translation examining quality versus sample speed and also on unconditional text generation with the text8 dataset. Strengths: The authors present an original and interesting idea, it is a benefit to the community to point out the fact that standard discrete corruption processes have unnecessary transitions in them and that the same $q(x_t \| x_0)$ distribution can be obtained by simply switching between a data token and a noise token. The idea to condition on the transition time itself within the framework also enables some significant simplifications for general styles of corruption whereas in the past this advantage may have only been noticed for absorbing state processes. The paper is well written, it is fairly easy to get a good understanding of the proposed method on a first read of the paper and this is helped by the fact that the authors move some nuances and complexity to the appendix. Effort has been made to make the main text readable and intuitive which is greatly appreciated. I believe the paper will have some impact in the community because it is a quick win when users implement a discrete diffusion model. Instead of the standard sampling procedure of calling the network T times, users can switch to the proposed (quite simple in reality) algorithm and step directly from transition to transition without needing to change much implementation and gain a lot of speed up over the naive algorithm. Weaknesses: I think there should be some discussion relating to quite a simple baseline that can be implemented for the absorbing state case. One can sample an absorbing state diffusion model in the same way as a standard discrete diffusion model, by stepping from each timestep to the next, however, instead of carrying out a forward pass of the neural network for every timestep, you first check if any tokens perform a transition and only if at least one token transitions, you then do the forward pass. This is possible in the absorbing state case because the unmasking rate is independent of the neural network output. Therefore, this simple algorithm would have the same stated advantages as your method where at most the neural network is called N times but if T is less than N, it will be called T times. I see that for other diffusion styles, your algorithm is fundamentally different due to conditioning on the transition time, however, in the absorbing state case, it seems very similar to this simple method. How can you explain the fact that you have better performance in terms of sample quality than the baselines you compare to? In your method, you propose no methodological advancement that should improve sample quality as your method is to speed up sampling to make sure the neural network is only called an appropriate number of times. Especially for a large number of timesteps, in Tables 2 and 3, you get across the board improvement, but your algorithm should be very similar to a standard discrete diffusion model in this regime but simply with fewer network evals. For your text8 experiment, you say you use a 9e7/5e6/5e5 train/val/test split however I believe this is incorrect because this only adds up to 9.55e7 tokens but the text8 dataset contains 1e8 tokens. This may be inherited from a typo in https://arxiv.org/pdf/2107.03006 pg.25 but in a more recent paper https://arxiv.org/pdf/2308.07037 pg 45, the test set is 5e6 tokens. Please confirm which size of test set you used. The names of the method seem to be slightly confused, for example on Figure 1, a DNDM-T is referenced but this is never actually defined in the full text. Technical Quality: 3 Clarity: 3 Questions for Authors: In the end, do you think it will be possible to move beyond the idea of a time variable altogether? Since the final sampling algorithm steps from transition to transition, it seems that the more important variable is which tokens become denoised, in what order, and how many in one go. This is decoupled from time through your algorithm so perhaps there is even more simplification to be made. Do you think it is possible to learn the transition times on a per dimension basis? This could be useful to train models that can generate tokens in an intelligent ordering rather than currently, the order of generation is completely decided before any tokens have been generated when the transition times are sampled and the ordering is completely uniform over all orderings of the dimensions. Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The authors adequately discuss the limitations in the appendix. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your support and valuable feedback. We address your major question as follows. --- Q1. Think there should be some discussion relating to quite a simple baseline that can be implemented for the absorbing state case. $\dots$, however, in the absorbing state case, it seems very similar to this simple method. A1. Thank you for your insightful observation and suggestion. In the absorbing state case, as you accurately pointed out, one could implement a sampling method where: - The process steps from each timestep to the next, similar to a standard discrete diffusion model. - Before performing a forward pass of the neural network, it first checks if any tokens perform a transition. - Only if at least one token transition a forward pass of the neural network is performed. This method would indeed be a special case of our approach, potentially reducing the number of neural network calls to at most N (number of tokens), or T (number of timesteps) if T < N. When $T \rightarrow \infty$, the algorithm becomes ARDM [1] (as detailed in Section G.1). This simplification works for the absorbing state case due to the unmasking rate's independence from neural network output. For other diffusion styles, our framework differs fundamentally due to transition time conditioning. In a revised version, we would include this discussion to provide a more comprehensive comparison and to help readers better understand the advantages of our approach across different diffusion scenarios. [1] Hoogeboom, et al. "Autoregressive Diffusion Models." ICLR 2022. * Q2. How can you explain the fact that you have better performance in terms of sample quality than the baselines you compare to? $\dots$ but your algorithm should be very similar to a standard discrete diffusion model in this regime but simply with fewer network evals. A2. Thank you for this insightful observation. You're correct that our primary goal was to accelerate sampling rather than directly improve quality. The superior performance in terms of sample quality was indeed an unexpected but welcome outcome. We hypothesize that this improvement may be attributed to the non-Markovian nature of our process. Similar to how DDIM [1] improved upon DDPM, our non-Markovian approach might lead to more coherent generation by allowing the model to leverage information from key timesteps throughout the entire sequence rather than just the immediately preceding step. Additionally, the reduced number of network evaluations using our method might actually be beneficial. By focusing on key transition points, we may be avoiding unnecessary noise introduced by intermediate steps, leading to cleaner, more focused generations. We will add this discussion to the paper in our revision. In future work, we plan to conduct a more in-depth analysis to elucidate the exact mechanisms behind this quality improvement as well as its relation with different types of transition times. [1] Song, J., Meng, C., & Ermon, S. (2020). ICLR 2021. * Q3. Typos: 1) Possible incorrect data split for the text8 experiment. 2) Confusion in method naming (e.g., DNDM-T referenced but not defined). A3. Thank you for pointing out those typos. We'll revise the text8 experiment data split and correct DNDM-T to DNDM-k in our revision. We appreciate your attention to detail in helping us improve the clarity of our paper. * Q4. In the end, do you think it will be possible to move beyond the idea of a time variable altogether? A4. Thank you for this insightful suggestion. While our current approach still relies on a time variable, your idea of focusing solely on token denoising order and grouping could indeed lead to further simplification and efficiency. This aligns well with our goal of optimizing the sampling process. Below we present additional experiments. We explored the impact of transition times based on the position of the tokens: from left to right and from right to left. In the left-to-right approach, tokens positioned on the left are transitioned to 𝑥0 earlier, and vice versa for the right-to-left approach. As the table shows, the left-to-right approach consistently outperforms the right-to-left approach across all datasets and step counts, supporting the significance of the choice of the transition time. \| Steps \| Direction \| IWSLT14 \| WMT14 \| WMT16 \| \|-------\|---------------\|---------\|-------\|-------\| \| 25 \| Left-to-right \| 31.08 \| 24.41 \| 31.67 \| \| 25 \| Right-to-left \| 30.54 \| 23.33 \| 31.33 \| \| 50 \| Left-to-right \| 32.87 \| 26.46 \| 33.37 \| \| 50 \| Right-to-left \| 32.47 \| 25.18 \| 32.78 \| \| 1000 \| Left-to-right \| 34.45 \| 27.93 \| 34.43 \| \| 1000 \| Right-to-left \| 34.04 \| 27.02 \| 34.15 \| We'll discuss this promising direction for future research in our revision, as it could potentially take our work a step further. * Q5. Do you think it is possible to learn the transition times on a per-dimension basis? A5. Thank you for this insightful suggestion. Learning transition times on a per-dimensional basis is indeed an intriguing idea that could lead to more intelligent and efficient token generation. This approach could offer greater flexibility compared to our current method, where transition times are sampled uniformly before generation begins. The key challenges in pursuing this promising avenue would be: - Designing an appropriate neural network structure for the predictor to learn the transition times on a per-dimension basis. - Formulating an effective training loss that incorporates the learned transition times. Implementing this could allow for adaptive ordering of token generation, potentially improving the quality and efficiency of the generated text. However, it would also increase the complexity of the model and training process. In our revision, we will discuss this idea as a direction for future research. --- Rebuttal Comment 1.1: Title: Response to Authors Comment: I appreciate the clear and detailed rebuttal from the authors. The additional experiment exploring token orderings for the corruption is also very interesting and it will be a nice addition to the paper. I will increase my score to 7. --- Rebuttal 2: Comment: Thank you for your support and the increased score. We appreciate your positive feedback on our rebuttal.	Summary: This paper presents the non-Markov process for the discrete diffusion to reduce the sampling time. The authors present the transition time to de-randomize the sampling process and study the non-Markov processes from finite to infinite step sampling. The conditional text generation and unconditional text generation results demonstrate the effectiveness of the proposed method. Strengths: 1. The writing of the article is very clear and easy to understand. 2. Compared with the image field, discrete diffusion is more noticeable in the text field. So I think the conditional text generation and unconditional text generation experiments are sufficient. Weaknesses: W1: The authors claim that Eq.(1) and Eq.(6) are different because $w_t$ in Eq.(1) is independently drawn from the noise distribution $q_{noise}$ and $w$ in Eq.(6) is time-invariant. But, $q_{noise}$ is a Dirac distribution for the absorbing diffusion and $w_t=w$ where $t=1, \dots T$. So Eq.(1) and Eq.(6) are equal for the absorbing diffusion, which means the proposed non-Markov process is the same as the Markov process. W2: Besides W1, we can further deduce that for the absorbing process, the proposed DNDM sampling algorithm is equivalent to the original sampling algorithm of the Markov process. For the origin Markov process, given $x_t$，we first sample $x_0 \sim p_{\theta}(x_0\|x_t)$ and sample $x_{t-1} \sim q(x_{t-1}\|x_t, x_0)$ as shown in Eq.(4). I use $[M]$ to represent the absorbing state. \begin{align} q(x_{t-1}\|x_t, x_0) = \frac{q(x_t\|x_{t-1}, x_0)q(x_{t-1}\|x_0)}{q(x_t\|x_0)} = \frac{q(x_t\|x_{t-1})q(x_{t-1}\|x_0)}{q(x_t\|x_0)} \end{align} Firstly, if $x_t$ is not the absorbing state, we have that $x_{t-1}=x_t$ because $q(x_t =a\| x_{t-1} \neq a) =0$ where $a \neq [M]$. Secondly, if $x_t$ is the absorbing state, based on that $q(x_{t-1}=[M]\|x_0)=1- \alpha_{t-1}$, $q(x_{t-1}=x_0]\|x_0)=\alpha_{t-1}$, $q(x_t=[M]\|x_{t-1}=[M])=1$ and $q(x_t=[M]\|x_{t-1} \neq [M]) = 1 - \beta_t = 1 - \frac{\alpha_t}{\alpha_{t-1}}$, we can get: \begin{align} q(x_{t-1}=[M]\|x_t=[M], x_0) = \frac{1- \alpha_{t-1}}{1 - \alpha_t}, q(x_{t-1}=x_0\|x_t=[M], x_0) = \frac{\alpha_{t-1} - \alpha_{t}}{1 - \alpha_t} \end{align} Based on the above analysis, the sampling process of the absorbing Markov diffusion can be simplified as: we sample starting from an all $[M]$ sequence, and during the sampling, we sample $x_0 \sim p_{\theta}(x_0\|x_t)$. If $x_t=[M]$, $x_{t-1}$ will stay the $[M]$ state with probability $\frac{1- \alpha_{t-1}}{1 - \alpha_t}$ and transfer to $x_0$ with probability $\frac{\alpha_{t-1} - \alpha_{t}}{1 - \alpha_t}$. If $x_t \neq [M]$, it will stay unchanged. In order to further illustrate the relationship with DNDM sampling, I denote the first time $x_t$ transitions from $[M]$to a non-$[M]$ state as $\tau$ (consistent with the transition time in this paper). We can deduce that $p(\tau=k) =\frac{\alpha_{k-1} - \alpha_{k}}{1 - \alpha_k} \prod_{t=T}^{t=k+1} \frac{1- \alpha_{t-1}}{1 - \alpha_t}=\alpha_{k-1} - \alpha_{k}$. $p(\tau=k)$ and Theorem 3.5. further verified that the proposed Non-Markov method is the same as the original Markov method for absorbing diffusion. W3: The proposed non-Markov method of multinomial diffusion is the same as the method in DDIM[1], Appendix A but with a different formulation. We can use the $p(\tau=k)$ in W2 to further verify it. In conclusion, this paper presents a non-Markov process for the multinomial diffusion and absorbing diffusion to accelerate the sampling of origin method with Markov processes, this is the main contribution of this paper. However, for the multinomial diffusion, the relationship with the DDIM[1] (Appendix A) is not clearly stated. For the absorbing diffusion, the non-Markov processes are the same as the Markov processes. If I misunderstand your approach, please feel free to figure it out, and I will adjust my score. [1] DENOISING DIFFUSION IMPLICIT MODELS, ICLR2021 Technical Quality: 2 Clarity: 3 Questions for Authors: 1. In line 281~282, the authors denote RDM and RDM-k as the sampling method with and without top-k selection, is this a typo? 2. In the experiment, do you use a pre-trained model or train it yourself? 3. The authors claim that they use a model consisting of an encoder and a decoder. This is confusing, do you remove the causal mask in the transformer decoder? For the unconditional text generation, what is the input of the encoder? Confidence: 4 Soundness: 2 Presentation: 3 Contribution: 1 Limitations: yes Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your constructive feedback. We have addressed your questions and provided clarifications below. * Q1. The authors claim that Eq.(1) and Eq.(6) are different, but they are equal for the absorbing diffusion, which means the proposed non-Markov process is the same as the Markov process. A1. We appreciate the reviewer's observation. While Eq.(1) and Eq.(6) are indeed equivalent specifically for absorbing diffusion, we respectfully disagree that this equivalence undermines our method. For more general cases beyond absorbing diffusion, these equations are not equivalent, which is why we term our approach the Discrete Non-Markov Diffusion Models (DNDM) framework. The key innovation of our paper is sampling transition times upfront to develop fast sampling algorithms (Lines 5 and 7 in Algorithm 1). Sampling transition times upfront allows the algorithm to skip function evaluations for steps that are not transition times. This reduces the number of neural network calls, leading to faster sampling. DNDM provides a unified framework to introduce the notion of transition time across various diffusion types, including but not limited to absorbing diffusion. In the revised version of our paper, we will add a remark to clarify this special case and highlight the broader applicability of our approach beyond this special case. * Q2. For the absorbing process, the proposed DNDM sampling algorithm is equivalent to the original sampling algorithm of the Markov process. A2. We believe this is a misunderstanding. While Eq.(1) and Eq.(6) are equivalent for absorbing diffusion, our DNDM algorithm is fundamentally different from the original sampling algorithm. As explained in Section 3, the key innovation of our approach is determining the transition times at the beginning of the algorithm. This significantly reduces the number of function evaluations from T (time steps) to the number of transition times, which is typically much smaller than T. In contrast, the original absorbing diffusion method [1] requires a function evaluation at every step, resulting in T function evaluations. This difference leads to substantial computational savings in our approach. [1] Austin et al. "Structured denoising diffusion models in discrete state-spaces." NeurIPS 2021. * Q3. The proposed non-Markov method of multinomial diffusion is the same as the method in DDIM[1], Appendix A but with a different formulation. A3. While the DDIM paper [1] proposed a model for discrete diffusion in its appendix, our approach differs significantly. DDIM's discrete process is still randomized, as whether $x_t = x_0$ or $x_{t-1}$ is controlled by some latent random variables (those random variables are actually analogous to the transition times $\tau$ in DNDM). Our method, in contrast, offers full de-randomization using the transition time argument $\tau$, with only one transition time occurring during our sampling process. Crucially, the introduction of transition time in our derandomized process allows DNDM to achieve faster sampling speed under the same number of sampling steps, a feature not reported in DDIM. Furthermore, our work is specifically designed for discrete spaces, providing a comprehensive framework and detailed theoretical analysis connecting finite and infinite step sampling. These key differences underscore that our method is a novel and significant contribution to discrete diffusion models, distinct from DDIM's approach. We will add a remark to clarify the relationship between our approach and DDIM's, emphasizing our method's unique features and empirical advantages in the discrete diffusion setting. [1] Song et al. "Denoising diffusion implicit models," ICLR2021. * Q4. In lines 281-282, the authors denote RDM and RDM-k as the sampling method with and without top-k selection. Is this a typo? A4. Thank you for pointing out this typo. We will fix it in the revision. * Q5. In the experiment, do you use a pre-trained model or train it yourself? A5. As detailed in Appendix F (Experiment details), our approach varied based on the experiment type. For conditional discrete sampling experiments, we utilized pre-trained models (saved checkpoints) provided by the original authors when available to ensure fair comparison [1]. For continuous sampling experiments, no pre-trained checkpoints were available, so we trained the corresponding models ourselves. [1] Zheng et al. "A reparameterized discrete diffusion model for text generation." arxiv 2023. * Q6. The authors claim that they use a model consisting of an encoder and a decoder. This is confusing. Do you remove the causal mask in the transformer decoder? For unconditional text generation, what is the input of the encoder? A6. We use different model architectures for conditional and unconditional tasks, but all self-attention blocks within the models are bi-directional and do not use causal masks. This design choice allows each token to attend to both past and future tokens during both training and inference, differentiating discrete diffusion from standard autoregressive models. The use of bi-directional attention in the decoder means the model isn't constrained to generate tokens sequentially, allowing for more flexible and potentially faster generation. For conditional text generation tasks like machine translation, we employ an encoder-decoder architecture. The encoder processes the source text, while the decoder generates the target text. For unconditional text generation tasks like text8 and enwik8, we use a decoder-only architecture similar to GPT models, without an encoder since there's no input sequence to encode - thus, there is no encoder input for these tasks. The 12-layer Transformer mentioned for these experiments refers to this decoder-only model. We will add a more explicit explanation in the experiment settings to distinguish these architectures for different tasks. --- Rebuttal Comment 1.1: Comment: Thank you for your response. I believe Q1, Q2, and Q3 have been resolved, but I think the issues in W1, W2, and W3 still exist. R1. I appreciate the author's emphasis that the proposed methods significantly reduce the number of function evaluations from T to much less than T. However, for Markov diffusion, we can also use far fewer than T steps for sampling as follows: \begin{align} p_{\theta}(x_s\|x_t) = \int q(x_s\|x_t, x_0) p_{\theta}(x_0\|x_t) \end{align} where $s<t$. The above expression has been widely used in Markov diffusion without further proof [1, 2]. Therefore, I think that the authors' emphasis on DNDM achieving sampling in fewer than T steps is a minor contribution. R2. My main concern is that for the absorbing process, regardless of the number of sampling steps (whether equal to or less than T), the proposed DNDM sampling algorithm is equivalent to the original sampling algorithm of the Markov process, as indicated in W1 and elaborated upon in W2. I believe my main concern has not been directly addressed. R3. Regarding the relationship between DNDM and DDIM, my concern remains unresolved. I believe that DNDM is a special case of DDIM (Appendix A). Specifically, when the hyperparameter $\sigma_t = \frac{1-\alpha_{t-1}}{1 - \alpha_t}$ in DDIM (Appendix A), DDIM and DNDM become equivalent. When $\sigma_t = \frac{1-\alpha_{t-1}}{1 - \alpha_t}$, the probability that $x_{t-1}=x_t$ is $\frac{1-\alpha_{t-1}}{1 - \alpha_t}$, while the probability that $x_{t-1}=x_0$ is $\frac{\alpha_t-\alpha_{t-1}}{1 - \alpha_t}$. In the rebuttal, the authors claim that DDIM and the proposed DNDM are "analogous". But actually, we can prove that they are equivalent based on W2. [1] Bao et al. "Analytic-DPM: an Analytic Estimate of the Optimal Reverse Variance in Diffusion Probabilistic Models." ICLR2022 [2] He et al. "DiffusionBERT: Improving Generative Masked Language Models with Diffusion Models." ACL2023. --- Rebuttal 2: Comment: Thank you for your feedback and for acknowledging the resolution of Q1, Q2, and Q3. We address your remaining concerns regarding W1, W2, and W3 as follows: * W1. We appreciate the author's emphasis that the proposed methods significantly reduce the number of function evaluations from T to much less than T. However, for Markov diffusion, we can also use far fewer than T steps for sampling as follows: $$p_\theta(x_s\|x_t) = \int q(x_s\|x_t,x_0)p_\theta(x_0\|x_t)$$ where $s < t$. The above expression has been widely used in Markov diffusion without further proof [1, 2]. Therefore, I think that the authors' emphasis on DNDM achieving sampling in fewer than T steps is a minor contribution. A1. The method you mention is a standard technique to calculate the reverse transition probability between any two-time steps, $s$ and $t$. While it's true that diffusion models can use $p_\theta(x_s\|x_t) = \int q(x_s\|x_t,x_0)p_\theta(x_0\|x_t)$ to accelerate the sampling process, choosing good s and t rigorously while preserving the sample quality is highly nontrivial. For example, if you do uniformly downsampling to get a set of time steps $0, 2, 4, \dots, T$, you can indeed skip many time steps, but you cannot guarantee the resulting samples are of high quality due to discretization error. Our algorithm for DNDM provides a provable approach to select the sampling steps for each token while maintaining high sample quality. Instead of uniformly skipping time steps across all tokens, we only skip those deemed unimportant, i.e., not in the transition time set. We denote the transition time for the n-th token in the sequence $x_n$ to be $\tau_{n}$ where $\tau_n$ is the transition time for the token $x_n$. And further denote the transition time set $\mathcal{T}:= \\{\tau\_{n}\\}\_{n=1}^{N}$. This set captures the key time step when each token transitions from noise to the target distribution. Given the transition times $\tau_{n} \in \mathcal{T}$, our DNDM can be written as: $x_{t-1,n} = \mathbb{1}(\tau_n=t)x_{0,n} + \mathbb{1}(\tau_{n}\not= t)x_{t,n}$. Our algorithm can be written as ```python def sample(x_t, t, transition_times): # Only update tokens at their specific transition times if t in transition_times: x_0_pred = predict_x0(x_t, t) x_{t-1} = update_tokens(x_t, x_0_pred, t, transition_times) else: x_{t-1} = x_t return x_{t-1} ``` In conclusion, although sampling with fewer than T steps is crucial for accelerating reverse sampling, simply reducing the number of time steps does not necessarily preserve sample quality. Our DNDM offers a rigorous and adaptive method for reducing sampling steps by precomputing transition times and overcoming the limitations of uniform downsampling or other heuristic approaches. * --- Rebuttal 3: Comment: W2. My main concern is that for the absorbing process, regardless of the number of sampling steps (whether equal to or less than T), the proposed DNDM sampling algorithm is equivalent to the original sampling algorithm of the Markov process, as indicated in W1 and elaborated upon in W2. I believe my main concern has not been directly addressed. A2. First of all, let's recall the forward processes of D3PM and DNDM as follows: $$x_{t} = b_{t}x_{t-1} + (1-b_t)w_t, \forall t = 1 \dots T, \qquad \text{D3PM, Eq 1}$$ $$x_{t} = b_{t}x_{t-1} + (1-b_t)w, \forall t = 1 \dots T . \qquad \text{DNDM, Eq 6}$$ The only difference between Equation 1 and Equation 6, is $w_t$ vs. $w$. Since for absorbing diffusion, $w_{t} = w = [Mask]$, D3PM and DNDM are indeed equivalent. However, for multinomial diffusion or other diffusion processes, $w_t \neq w$, D3PM and DNDM are different. In addition, even for absorbing diffusion, our proposed reverse sampling algorithm for DNDM is still different from that for D3PM. To elucidate the key differences between the sampling algorithm in DNDM and that in D3PM for absorbing diffusion, let's directly compare the algorithms: - For the D3PM-Absorb algorithm: We begin with an all [M] sequence. At each time step $t$, we sample $x_0 \sim p_{\theta}(x_0\|x_t)$. If $x_t=[Mask]$, $x_{t-1}$ transitions to $[Mask]$ with probability $(1-\alpha_{t-1})/(1-\alpha_t)$ and to $x_0$ with probability $(\alpha_{t-1} - \alpha_t)/(1-\alpha_t)$. If $x_{t}\not= [Mask]$, it remains unchanged. - For the DNDM-Absorb algorithm: We also start with an all $[Mask]$ sequence, but crucially, we first determine the transition time set. During sampling, if $x_t=[Mask]$, the transition probabilities for $x_{t-1}$ are identical to D3PM. However, we only sample $x\_0 \sim p_{\theta}(x\_0\|x_t)$ when at least one token needs to change, as determined by our pre-computed transition set. This selective sampling is the key to our algorithm's efficiency. Therefore, you can see that DNDM will skip many steps during the sampling process to avoid function evaluation and save computational cost. A natural question is how many time steps can be skipped. Let's do the calculation as follows. For a specific time t and token position n, the token will change at time $t-1$ only if: - It hasn't already changed (probability: $\Pi_{s=T}^{t}\frac{1-\alpha_s}{1-\alpha_{s+1}} = 1-\alpha_t$) - It will transfer to $x_0$ (probability: $\frac{\alpha_{t-1} - \alpha_t}{1-\alpha_t}$) Thus, the probability of $n$-th token changing at time t-1 is $(1-\alpha_t)\cdot \frac{\alpha_{t-1}-\alpha_t}{1-\alpha_t} = \alpha_{t-1} - \alpha_t$. Consequently, the probability that no tokens change at time t for the entire sequence is $\big(1 - (\alpha_{t-1}-\alpha_{t})\big)^{N}$ where $N$ is the sequence length. These are precisely the time steps that our DNDM algorithm will skip to save computational time, unlike D3PM, which does function evaluation every time step. To sum up, even though the forward process of DNDM is the same as that of D3PM for absorbing diffusion, our DNDM approach introduces a clever and provable algorithm design in the sampling process by pre-computing the transition time set and selectively applying function evaluations. This distinguishes DNDM from D3PM algorithm, offering a more computationally efficient approach to inference in discrete diffusion. * --- Rebuttal 4: Comment: W3. Regarding the relationship between DNDM and DDIM, my concern remains unresolved. I believe that DNDM is a special case of DDIM (Appendix A). Specifically, when the hyperparameter $\sigma_t = \frac{1-\alpha_{t-1}}{1-\alpha_{t}}$ in DDIM (Appendix A), DDIM and DNDM become equivalent. When $\sigma_t = \frac{1-\alpha_{t-1}}{1-\alpha_{t}}$, the probability that $x_{t-1} = x_t$ is $\frac{1-\alpha_{t-1}}{1-\alpha_{t}}$, while the probability that $x_{t-1} = x_0$ is $\frac{\alpha_{t} - \alpha_{t-1}}{1-\alpha_t}$. In the rebuttal, the authors claim that DDIM and the proposed DNDM are "analogous." But actually, we can prove that they are equivalent based on W2. [1] Bao et al. "Analytic-DPM: an Analytic Estimate of the Optimal Reverse Variance in Diffusion Probabilistic Models." ICLR2022 [2] He et al. "DiffusionBERT: Improving Generative Masked Language Models with Diffusion Models." ACL2023. A3. While there are similarities between DNDM and DDIM (Appendix A), they are fundamentally different models, and DNDM is not a special case of DDIM. DNDM introduces a framework specifically designed for discrete spaces, while DDIM was originally developed for continuous diffusion models. Let me clarify the key differences for multinomial diffusion: - DDIM: By eq (19) in Appendix A of DDIM paper, $q(x_{t-1}\|x_t, x_0) = \text{Cat}(\sigma_t x_t + (\alpha_{t-1} - \sigma_t \alpha_t)x_0 + ((1 - \alpha_{t-1}) - (1 - \alpha_t)\sigma_t)1_K).$ Even with $\sigma_t = \frac{1-\alpha_{t-1}}{1-\alpha_t}$, the process remains stochastic: $q(x_{t-1}\|x_t, x_0) = \text{Cat}(\sigma_t x_t + (1- \sigma_t)x_0 )$. This means at every step, there's a probability of choosing $x_0$, regardless of whether it has transitioned to $x_0$ or not. Unlike Absorbing discrete diffusion, no [Mask] exists in multinomial diffusion. Therefore, DDIM cannot distinguish whether $x_t$ already equals $x_0$. In particular, although the sampling process becomes less stochastic in the DDIM setting, it will still be predicted $x_0$ with high probability $1-\sigma_t = \frac{\alpha_{t-1}- \alpha_t}{1-\alpha_t}$. - DNDM: Achieves full de-randomization using transition time $\tau: x_{t-1} = \mathbb{1}(\tau = t)x_0 + \mathbb{1}(\tau \not= t)x_{t}$ (Equation 8 in our paper). Here, $\tau$ follows $P(\tau = t) = \alpha_{t-1} - \alpha_t < \frac{\alpha_{t-1}- \alpha_t}{1-\alpha_t}$. Such crucial difference allows DNDM to achieve full de-randomization once $\tau$ is sampled, leading to a deterministic evolution that DDIM cannot replicate. - Sanity Check via Concrete Example: For sampling $x_1$ based on $x_2$, consider the probability of calling $\hat{x}\_0 \sim p_{\theta}(\hat{x}\_0\|x_t)$. DDIM: P(call $\hat{x}\_0$) = $\frac{\alpha_{1} - \alpha_2}{1-\alpha_2}$. DNDM: P(call $\hat{x}\_0$) = $\alpha_1 - \alpha_2 $. Crucially, $\alpha_1 - \alpha_2 < (\alpha_1 - \alpha_2)/(1-\alpha_2)$, because $\alpha_2 < 1$. The above illustration shows that DNDM is not a special case of DDIM. We say that DNDM is analogous to DDIM because both of them are Non-Markov models. We will add a discussion to clarify this point in the revision to avoid any confusion. * --- Rebuttal Comment 4.1: Comment: Thank you for your response！ I understand that DNDM is not a special case of DDIM (Appendix A), thanks! I believe that a comparison between DNDM and DDIM experiments will be very interesting. For the absorbing process, the author provides a detailed explanation of the differences between the proposed DNDM and the original sampling algorithm of the Markov process. For each sampling step (e.g., $p_{\theta}(x_s\|x_t)$, s<t), the DNDM and D3PM methods are consistent. The advantage of the proposed DNDM lies in how it selects which time steps should be omitted. It's important to emphasize that this advantage of DNDM does not stem from the non-Markov process as claimed by this paper. For the absorbing process, the Markov and non-Markov processes are entirely identical. In both this paper and references [1, 2], the absorbing process has consistently outperformed the multinomial process and has garnered increasing attention. Therefore, I hope that the claim in this paper that the non-Markov process can accelerate sampling of absorbing diffusion does not mislead the community, and I remain inclined to reject it. This paper presents promising experimental results. If the authors can accurately explain the reasons behind the effectiveness of DNDM, which would require substantial revisions, it will undoubtedly significantly enhance the quality of the paper. [1] Austin et al. "Structured denoising diffusion models in discrete state-spaces." NeurIPS 2021. [2] Lou et al. "Discrete Diffusion Modeling by Estimating the Ratios of the Data Distribution." ICML2024. --- Reply to Comment 4.1.1: Comment: Thank you for your further feedback and for acknowledging the technical and empirical contributions of our paper. We're glad that we have resolved all of your misunderstandings and questions. Note that the modifier Non-Markov in our algorithm name refers to both the time-invariant noise $w$ and the predetermined transition time $\tau$ (See Eq. (7) in the paper). To emphasize the importance of the predetermined transition time in DNDM, we will add a sentence in the abstract: "The proposed DNDM model naturally induces the predetermined transition time set, which enables a training-free sampling algorithm that can accelerate a large family of discrete diffusion models." We will also highlight this in the paper. While we believe we have clearly explained the reasons behind the effectiveness of DNDM in Sections 3.1 and 3.2 with comprehensive pseudo-algorithms in the paper (see Algorithms 1-4), we will also incorporate the clarifications from our rebuttal discussion into the final version. Given that we have resolved all of your concerns and questions in your review, and we believe the promised changes would not be a major revision, we would greatly appreciate it if you could consider raising your score in light of these points. In particular, a score of 3 indicates 'technical flaws, weak evaluation, inadequate reproducibility, and/or incompletely addressed ethical considerations.' We believe our paper does not fit this description and deserves a higher rating. --- Rebuttal 5: Comment: Thank you for your candid feedback and for acknowledging the improvements in our paper. Regarding your remaining concern 'Non-Markov', we would like to provide further clarification on why this terminology is accurate and necessary for our work: - Our model handles a broader set of discrete diffusion models beyond the absorbing process. In general cases, including multinomial diffusion, our forward process is non-Markovian. - The Non-Markov modifier refers to both the time-invariant noise 𝑤 and the predetermined transition time 𝜏 (Eq. 7). Only when w = [Mask], which is deterministic, would the distribution for the absorbing state become Markovian. However, the non-Markovian nature is still fundamental to our DNDM model's full generality, and it provides readers with an accurate understanding of the process's properties and how transition time gets introduced. - The use of 'Non-Markov' in our terminology aligns with similar practices in the field, accurately highlighting key characteristics of our model that deviate from strict Markovian properties, even though DNDM can degenerate to Markovian process under specific settings. In the DDIM framework, for instance, when $\sigma_t = \sqrt{(1-\alpha_{t-1})/(1-\alpha_t)}\sqrt{1-\alpha_t/\alpha_{t-1}}$, the diffusion process becomes Markovian, and the forward/generative process becomes a DDPM. Similarly, our use of 'Non-Markov' emphasizes the general case while acknowledging special conditions where Markovian properties may emerge. The added clarifications in our paper should help readers understand the specific characteristics of our approach and its relationship/differences to Markovian processes. With that being said, we are open to changing the term 'Non-Markov' if it would persuade you to raise your rating to the acceptance level. If you have any suggestion for the replacement of 'Non-Markov', we would be happy to take it.	Summary: The paper introduces a discrete non-Markov diffusion model (DNDM) aimed at accelerating the sampling process in discrete diffusion models. The proposed method reduces the number of neural network function evaluations to speed up the sampling process while maintaining sample quality. The paper explores the transition from finite to infinite step sampling, providing new insights into bridging the gap between discrete and continuous-time processes. Experiments on natural language generation and machine translation tasks illustrate the competitive performance of the method in terms of speed and quality compared to existing methods. Strengths: * The introduction of a discrete non-Markov diffusion model (DNDM) provides a new method for accelerating the sampling process in discrete diffusion models in a training-free manner. It reduces the number of neural network function evaluations, enhancing the efficiency of the sampling process to speedup by 3x for 50 steps. * The authors conducted extensive experiments on natural language generation and machine translation tasks, demonstrating the effectiveness of the proposed method, for both multinomial and absorbing diffusions. Weaknesses: * The method involves a complex process that might be challenging to easily follow and implement. More details or visualizations on how the transition time distribution is determined and whether it can be adapted for different types of discrete diffusion models will be helpful for a better understanding of the motivation and methodology. * The comparison with other acceleration methods is not very convincing, especially at a practical smaller number of sampling steps. Instead of RDM baseline, how does the proposed method compare with other existing acceleration techniques for discrete diffusion models in terms of both efficiency and quality? * While the method is tested on natural language generation and machine translation tasks, its applicability to other modalities such as image or video generation is not unknown, which might limited the scope of the proposed method. Technical Quality: 3 Clarity: 2 Questions for Authors: Suggest to address concerns in the weakness section. Confidence: 3 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: yes Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your support. Below, we address the questions. * Q1. The method involves a complex process that might be challenging to easily follow and implement. More details or visualizations on how the transition time distribution is determined and whether it can be adapted for different types of discrete diffusion models will be helpful for a better understanding of motivation and methodology. A1. We thank the reviewer for their feedback. However, we respectfully disagree that our method is overly complex or challenging to implement. We have taken several steps to ensure clarity and ease of implementation: - Training-free approach: Our sampling method is designed to be training-free, making it straightforward to integrate with existing discrete diffusion models. - Detailed algorithms: We have already included comprehensive pseudo-algorithms in the paper (see Algorithms 1-4) to guide implementation. - Discussion about transition time distribution: We have provided a detailed explanation and ablation study in Appendix C, which thoroughly covers how the transition time distribution is determined and its impact on performance. Figure 3 in the paper provides clear visualizations of different distribution types (e.g., linear, cosine, Beta) to aid understanding. - Adaptability: Our method can be adapted to different types of discrete diffusion models, including the most popular multinomial and absorbing diffusions, the results of which are demonstrated in Sections 4.1 and 4.2. - Ease of implementation: Our method can be implemented in just a few lines of code. For example, the core sampling logic can be expressed in the following block, where the key intuition is the condition line: "if t in transition_times:". It determines whether to update tokens at a given time step, significantly reducing computation while maintaining quality. ``` python def sample(x_t, t, transition_times): if t in transition_times: x_0_pred = predict_x0(x_t, t) x_{t-1} = update_tokens(x_t, x_0_pred, t, transition_times) else: x_{t-1} = x_t return x_{t-1} ``` We believe these points demonstrate that our method, while mathematically sophisticated, is conceptually simple and easy to implement. However, if the reviewer still finds additional clarification necessary, we are open to adding more visualizations or explanations in the revised version. * Q2. The comparison with other acceleration methods is not very convincing, especially at a practical smaller number of sampling steps. A2. Our method, DNDM, consistently shows acceleration across various step sizes, particularly for moderate to high step counts. For example, in Tables 2 and 3, we demonstrate significant speedups for 50 and 1000 steps across different datasets (IWSLT14, WMT14, WMT16). While the speed is 25 steps, we still see improvements in most cases. Below is an additional experiment for IWSLT14 with fewer sample steps in an absorbing generation process (additional results for Table 3 in our submission). As we can see from the table, when the sampling step is significantly less than 25, the quality of the generated examples does not match those with larger sampling steps (By Table 3, when step counts of 25 or higher, performance remains consistently above $\mathbf{31.5}$ BLEU for both RDM-Absorb and DNDM-Absorb). \| Steps \| RDM-Absorb BLEU \| RDM-Absorb Time (s) \| DNDM-Absorb BLEU \| DNDM-Absorb Time (s) \| \|-------\|-----------------\|---------------------\|-------------------\|----------------------\| \| 5 \| 29.92 \| 27.36 \| 30.30 \| 24.1 \| \| 10 \| 31.02 \| 48.08 \| 31.49 \| 37.9 \| \| 15 \| 31.26 \| 69.22 \| 32.13 \| 50.0 \| It's important to note that performance in low-step settings poses a significant challenge for discrete diffusion models, which is beyond the scope of our current work. Our primary focus is on accelerating the algorithm while maintaining good performance—a crucial factor for numerous real-world applications that demand high-quality sample generation. Our comprehensive experiments demonstrate that DNDM offers competitive speed-quality trade-offs across a broad spectrum of step sizes, with its performance notably excelling as the number of steps increases. * Q3. Instead of RDM baseline, how does the proposed method compare with other existing acceleration techniques for discrete diffusion models in terms of both efficiency and quality? A3. Our work introduces the first training-free acceleration technique specifically designed for finite-step discrete diffusion models such as D3PM and multinomial diffusion, filling a gap in the field. We chose RDM as our primary baseline due to its state-of-the-art results in discrete diffusion. Given the novelty of our method in the context of finite-step discrete diffusion models, direct comparisons with other acceleration techniques are limited. Our focus was on developing and demonstrating the effectiveness of this training-free approach, which opens up new possibilities for accelerating discrete diffusion models. * Q4. The method's applicability to other modalities, such as image or video generation, is unknown, which might limit its scope. A4. While our current work focuses on text generation, DNDM's core principles have the potential for broader applicability. The method is designed for discrete data, which naturally suits text but can also apply to other modalities through appropriate discretization or quantization. Numerous follow-up studies can benefit from our fast sampling algorithm for tasks such as Electronic Health Record (EHR) data generation and protein sequence generation. These areas all involve discrete data structures that could benefit from our acceleration technique. --- Rebuttal Comment 1.1: Comment: Thank you for your valuable feedback. We sincerely hope that we have adequately addressed your questions and concerns. Specifically, - We have elaborated on DNDM's simplicity and ease of implementation. As a training-free approach, DNDM integrates seamlessly with existing discrete diffusion models. We've provided comprehensive pseudo-algorithms in the paper and detailed explanations of the transition time distribution in Appendix C and Figure 3. - Regarding DNDM's performance across various step sizes, we've demonstrated its effectiveness for both moderate and high step counts. Our additional experimental results for IWSLT14 with fewer sample steps demonstrate DNDM's capabilities even at lower step counts. - We've added the comparison with other acceleration techniques by highlighting DNDM's unique feature as the first training-free acceleration method specifically designed for finite-step discrete diffusion models. We've also discussed its potential applicability to other discrete data modalities beyond text generation. We sincerely hope our response adequately addresses your questions and provides clarity on our method. Thank you for your time and careful consideration of our work. --- Rebuttal 2: Comment: Thank you for your valuable feedback and for taking the time to consider our response. We sincerely appreciate your acknowledgement of our improvements on the simplicity and ease of implementation of the proposed method, as well as the additional experiments with smaller sampling steps. We would like to address your remaining concerns as follows: - We appreciate your point about the phrasing of our novelty claims during previous discussion. We agree to tone down any perceived claim of being the "first training-free acceleration method". To clarify, we developed a training-free acceleration method specifically designed for finite-step discrete diffusion models. We'd like to note that we didn't include such a phrase as "first training-free acceleration method" in our submission. - Additional Experiment on DDIM Appendix A: Our focus was on accelerating finite-step discrete diffusion models, which differ fundamentally from continuous diffusion models. Techniques primarily designed for continuous diffusion are not directly applicable to discrete diffusion, like multinomial diffusion and absorbing diffusion. While DDIM proposes a version for multinomial diffusion in Appendix A, it doesn't consider the transition time or provide any code or experiments. Inspired by your feedback, we've implemented DDIM Appendix A ourselves and conducted additional experiments. We've included results both with and without top-k sampling (denoted by '-k' in the table headers). Below are the results for IWSLT14 with a wide range of sample steps in multinomial diffusion generation (These could serve as additional results for Table 2 in our submission): \| Steps \| DDIM-multi BLEU \| DDIM-multi Time (s) \| DNDM-multi BLEU \| DNDM-multi Time (s) \| \|-------\|-----------------\|---------------------\|-------------------\|----------------------\| \| 5 \| 28.88 \| 30.2 \| 28.04 \| 28.1 \| \| 10 \| 30.46 \| 55.8 \| 30.57 \| 44.4 \| \| 15 \| 30.87 \| 80.1 \| 30.77 \| 50.6 \| \|25 \| 31.30 \| 130.4 \| 30.95 \| 52.9\| \|50 \| 31.63 \| 257.2 \| 31.45 \| 83.9\| \|1000 \| 31.79 \| 5064.8\| 31.82 \| 191.3\| \| Steps \| DDIM-k-multi BLEU \| DDIM-k-multi Time (s) \| DNDM-k-multi BLEU \| DNDM-k-multi Time (s) \| \|-------\|-----------------\|---------------------\|-------------------\|----------------------\| \| 5 \| 28.93 \| 31.1 \| 30.30 \| 28.3 \| \| 10 \| 30.69 \| 56.7 \| 31.79 \| 44.3 \| \| 15 \| 30.85 \| 81.5 \| 32.14 \| 50.1 \| \|25 \| 31.38 \| 132.7 \| 32.30 \| 52.6\| \|50 \| 31.64 \| 260.1 \| 32.80 \| 93.2\| \|1000 \| 31.89 \| 5121.3 \| 33.15 \| 191.5\| These results suggest that compared with DDIM (Appendix A), DNDM achieves comparable or better performance with reduced computation time across various step sizes, with the advantage becoming more significant as the number of steps increases. This scalability makes our approach particularly valuable for tasks requiring higher quality generation and more computational steps. We appreciate your careful consideration and are open to suggestions on how to better position our work within the broader context of diffusion model acceleration techniques. Thank you again for your valuable feedback.	null	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Synatra: Turning Indirect Knowledge into Direct Demonstrations for Digital Agents at Scale	Accept (poster)	Summary: The paper proposes a method for synthetically creating a dataset of agent trajectories for navigating websites. They propose using annotated programs, specifically python code interleaved with comments, as a representation of task and motion planning trajectories, where tasks are described in natural language in the comments, and actions are python API calls to the environment. A dataset of trajectories is created by applying GPT-4 to two sources of data. The first source is wikiHow, which contains ungrounded high-level tutorials. GPT-4 is used to generate plausible trajectories consistent with the tutorial. The second source is ClueWeb, which contains HTML snapshots of real websites. GPT-4 is again used to generate plausible trajectories consistent with the website. The paper finds that the resultant dataset of trajectories, when used to finetune CodeLlama-instruct-7b, outperforms open-weight models of similar sizes on Mind2Web, MiniWoB++, and WebArena. This result demonstrates that finetuning on the dataset transfers well to tasks. Strengths: - The paper is well-motivated, and for some sections clearly written - Creative usage of two different data sources, tutorials and snapshots, to complement each other - Makes progress towards building competent LLM-agents - Demonstrates that synthetic trajectories improve benchmark performances. Weaknesses: - Requires the use of GPT-4 to generate the synthetic data. While the paper demonstrates that using GPT-4 to generate training data can improve smaller open weight models, it's not clear if this can help push the SOTA. - Unequal comparison with human annotation: Sec. 6.2 compares with the human annotated trajectories in Mind2Web. As acknowledged by the authors, Mind2Web tasks are very restricted and simple compared with the tasks in synatra. A fairer comparison would be to collect a smaller set of human annotations on roughly the same task distribution as synatra. - 6.3 rather ad hoc Technical Quality: 3 Clarity: 3 Questions for Authors: - open-source vs open-weight. Be careful with the distinction! (e.g. L54) - How would GPT-4 perform if trained on synatra? Is synatra limited to distilling agent-capability from stronger models to weaker models? What stopped you from finetuning GPT-4 or GPT-3.5 on synatra? - In 6.3 you write that you "conducted a detailed examination" comparing synatra with GPT-4, but I can't seem to find the analysis. - Given that the comparison with human annotation in 6.2 doesn't seem very fair, I'm not sure if you can claim in the abstract that "we show that the synthetic demonstrations can be more effective than a similar number of human demonstrations." - To help answer the quality/quantity trade-off, one might look at how finetuning codellama does when varying the size of the dataset. As prior work [0] suggested, maybe only a small number of examples is needed, which pushes the trade-off towards obtaining smaller quantities of high-quality human-annotated data instead of large quantities of synthetic data. [0] Zhou, C., et al. "LIMA: Less Is More for Alignment. arXiv, Article." arXiv preprint arXiv:2305.11206 (2023). Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: - Broader impacts adequately discusses potential unethical usage of LLM agents enabled by this work. - Needs discussion of robustness of LLM agents and potential security risks posed by deploying them. - Limitations of using synthetic data adequately discussed. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for taking the time to review our paper! We are very happy to hear the encouraging words on our motivation, creative usage of data sources, and performance improvement. We believe the comments are resolvable during the rebuttal period. Please see our response below. We would be very happy to address additional questions during the discussion period if anything is unclear. > ### How could Synatra possibly help push SOTA? > ### Is synatra limited to distilling agent-capability from stronger models to weaker models? > ### Varying the size of the dataset. This is a great question, we believe Synatra holds the potential of pushing SOTA when scaling up. We additionally train a CodeLLama-7b on 100$k$ synthetic data and the results on different size of synthetic data is below: \| Training Data Size \| Success Rate on WebArena\| \|--------------------\|--------------------------------------------------\| \| GPT-3.5\| 6.16 \| \| 9k \| 4.56 \| \| 50k \| 4.80 \| \| 100k \| 6.28 \| We can see that training on more synthetic data provides 1.48% improvement on WebArena, surpassing GPT-3.5. In addition, among the 51 tasks `Synatra-CodeLLama-7b` got correct, we found `GPT-4-turbo` failed on 57% of them. For instance, while `GPT-4` suffers from severe errors such as repeatedly typing the same content to the same input box (26.85%), this only happens 6.9% of the time for `Synatra-CodeLLama-7b`. This indicates our approach could assist models in performing tasks the data generation model (e.g., `GPT-4-turbo`) cannot accomplish. > ### Can we compare the model trained on smaller set of human annotations on roughly the same task distribution as synatra? We agree it will be interesting to have such experiment, however, as discussed in the introduction section, collecting human annotations of similar task distribution can be challenging. The main difficulty is on configuring the task prerequisites. For example, in Synatra, we have synthetic trajectories to cancel Amazon order. However, it requires an Amazon account with qualified order for cancellation for human trajectory collection. Such setup is instance specific. Hence, it is prohibitive to collect human annotations at scale as in Synatra. In the paper, we also note that “it is important to recognize that the quality of human demonstrations is presumably higher, but they require meticulous design and control during the data collection process.” Hopefully this could further clarify the challenges in human data collection, and highlight the simplicity of our proposed approach. > ### I'm not sure if you can claim in the abstract that "we show that the synthetic demonstrations can be more effective than a similar number of human demonstrations." We will soften the claim to only compare with human demonstration collected in a dataset-agnostic way, meaning that the data collection process is not meticulous design and control. > ### What stopped you from finetuning GPT-4 or GPT-3.5 on synatra? On the one hand, the cost of finetuning GPT-3.5 or GPT-4 on 89 millon tokens for a few epochs is prohibitive for us. On the other hand, we hope to push the frontier of open-weight models. We have spent more efforts on scaling up the data size as discussed above, and we are working on scaling up the model to stronger open-weight models. > ### 6.3 rather ad hoc Thank you for pointing this out. We will add more quantitative study in this section and move the case study to Appendix in our camera ready version. > ### Open-souce -> Open-weight Thank you for the suggestion. We will update the paper to reflect the accurate wording. --- Rebuttal Comment 1.1: Comment: Thanks for the response. I am surprised by the large increase in WebArena success rate from 50k to 100k. Do you have error estimates for these figures? --- Reply to Comment 1.1.1: Comment: Thanks! The variance between runs is as deterministic as possible with the current compute, as we have set the temperature to zero in LLM inference and fixed random seed during training. To find out the variance due to different random subset of training data in the 50k sample case, we need to sample different sets of data and do multiple training runs, which is out of our compute budget.	Summary: This paper proposes a demonstration generation approach for learning UI control by mixing two different sources. The first one uses GPT4 to generate scenarios, grounded actions, and observations using WikiHow plans which is initially filtered by GPT-3.5. Another data source is ClueWeb, form which the authors extract web pages, sample a segment for any page, and ask GPT4 to come up with scenarios and next actions. Both data sources are combined into a single dataset of 50K traces where a program format is used. A CodeLlama model is fine-tuned with the resulting dataset. Results show that it achieves comparably when compared to other baselines, including a basic GPT-based prompting method. Ablation analysis shows that program format is important, both data mixtures add value, and proposed dataset transfer to other benchmarks better than Mind2Web traces. Strengths: The paper proposes a data synthesis approach for training UI agents. It combines WikiHow plans and actual observations with the strength of GPT-based models to fill in the gaps. the approach is agnostic to any domain and can serve as a good initialization. Weaknesses: My main concerns are weak baselines and lack of some others. 1. There are many baselines missing from the comparison and available baselines are weak. For example, HTML-T5 [11] achieves 49.7 and MindAct [6] achieves 30.9 on Mind2Web dataset. Performance on Miniwob++ reaches up to 99.2% [A]. There are many other baselines including prompting and fine-tuning based ones with different pre-training that should be included. 2. Can you further fine-tune on demonstrations from available benchmarks? While a semi-supervised approach is helpful, how much does it improve when human demonstrations added? 3. You also mentioned that a unique "id" is assigned to target elements in your training demonstrations. Given that the actions condition on the current state, what prevents the model from overfitting to this unique id when detecting salient elements? 4. You mention that you use viewports in Mind2Web benchmark to fit into the context window. But to extract viewports, you need to know where the ground truth element resides in the DOM (or accessibility tree) or you assume you have access to an oracle scrolling agent. I think both cases are different from your baselines and suggests leakage of test data. 5. When you use NL format rather than programs, how do you ground generated actions to executable environment actions? 6. What is the performance of the model trained with Mind2Web demonstrations on Mind2Web test sets? When tested on other benchmarks, how do you ground the action on the particular benchmark? 7. It is not clear if the claim that collected demonstrations have a similar distribution as Mind2Web as they have fatter tails. 8. Text and legend in Figure-2 are not readable. A. Longtao Zheng, Rundong Wang, and Bo An. Synapse: Leveraging few-shot exemplars for human level computer control. arXiv preprint arXiv:2306.07863, 2023. Technical Quality: 3 Clarity: 3 Questions for Authors: Please see my above concerns for particular questions. Confidence: 5 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: Limitations of the work are addressed. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for taking the time to review our paper! We are very happy to hear encouraging words on our domain agnostic data synthesis approach that fills in the current gap. We believe the comments are resolvable during the rebuttal period. Please see our response below. And we would be very happy to address additional questions during the discussion period if anything is unclear. > ## Comparison with baselines > ### Comparison with LLMs finetuned with direct demonstrations (human annotated) *Please Refer to the same section in global rebuttal due to character limit.* > ### Comparison with approaches that achieves high performance on MiniWoB++ or Mind2Web Thank you for bringing this up, we are aware of the many models and methods, we did not include them as baselines because of the following reasons: * Many approaches incorporate dataset-specific designs, making them challenging to apply to generic web-based tasks like WebArena. For instance, MindAct trained only with Mind2Web training data, as we can see with `Mind2Web-CodeLlama-7b`, while the model achieves strong performance on Mind2Web test set, it has limited performance on all held-out datasets. Similarly, Synapse uses trajectories as examples in the context; its prompting schema heavily relies on in-domain examples for MiniWoB++ and Mind2Web. In these datasets, the trajectories are short and can fit within the context window, and they offer relatively large training data on similar tasks or websites. However, in WebArena, trajectories can easily exceed the context length, and there are no provided training trajectories. * Many approaches are orthogonal to our data synthesis approach. The key component in MindAct is the ranking model that reduces a full HTML to the top-k potentially relevant elements, to remove irrelevant context. It is possible to apply a similar two-stage pipeline to our approach, instead of feeding the full AXtree into the model, we can first perform a reranking to select a subset of nodes in the AXtree instead. Alternatively, we can simply generate key elements rather than the full HTML as the observation. * Some approaches do not have public access. At the time we wrote the response, HTML-T5 is not open-sourced yet. We will incorporate the additional experiments to our updated draft. We are happy to investigate other approaches if we missed any. > ## Can you further fine-tune on demonstrations from available benchmarks? How much does it improve when human demonstrations added? Finetuning with both human demonstrations and our synthetic data is straightforward because our data design is general for web-based tasks. Further finetuning the model on high-quality human demonstrations can presumably bring significant gain. However, such data is scarce, and we hope our work can encourage the creation of more high-quality data. In addition, our experiment shows that adding human demonstrations that are collected without meticulous control may not improve the model’s performance on general web-based tasks. As shown in the table in global rebuttal, simply training the model on human demonstrations collected in Mind2Web results in very limited performance on the two held-out sets. We also experiment with adding Mind2Web data into our synthetic data, and we also see a similar overfitting trend. > ## Could assigning unique “id” result in overfitting when detecting salient elements? We peformed a post processing to replace the unique ID with a random integer number in the final data. Hence, the model will not overfit to any specific ID. > ## You mention that you use viewports in Mind2Web benchmark to fit into the context window. But to extract viewports, you need to know where the ground truth element resides in the DOM (or accessibility tree) or you assume you have access to an oracle scrolling agent. I think both cases are different from your baselines and suggests leakage of test data. The main reason of doing this processing is to make sure the web page observation can fit into the context window of a model. We use the same processed web page to all baselines and our approach. Hence it is a fair comparison. > ## When you use NL format rather than programs, how do you ground generated actions to executable environment actions? The NL format we uses still requires the generated action to be in set formats. Here is an example: Past actions: 1. click [4904] where 4904 is img calendar wheel with marker For actions to be parsed accurately, they still need to be in the format such as click [xxx] > ## Performance of the model trained with Mind2Web demonstrations on Mind2Web test sets? The performance of the model trained with Mind2Web demonstrations on Mind2Web test sets is as followed: \| Set \| Step Accuracy \| \|--------------\|-------------------------------\| \| M2W-cross task \| 0.47 \| \| M2W-cross website \| 0.34 \| \| M2W-cross domain \| 0.37 \| > ## When tested on other benchmarks, how do you ground the action on the particular benchmark? We follow WebArena to represent a web page as an accessibility tree with ID at the beginning of each tree node. This can be done by processing the HTML in the three benchmarks. In this way, we can refer to any element with its corresponding ID such as `click(element_id=123)`. > ## It is not clear if the claim that collected demonstrations have a similar distribution as Mind2Web as they have fatter tails. Sorry for the confusion. Our goal was to demonstrate that our approach allows us to freely fit our generated trajectories to arbitrary distributions, such as Mind2Web. We will update Section 4 to clarify this. > ## Text and legend in Figure-2 are not readable. We will make sure to update the figures in the camera ready version.	Summary: This paper investigates turning indirect knowledge from the internet (such tutorial) to the direct knowledge (in the form of textual demonstrations) for LLMs. The algorithm design and the experiments are based on the web browser domain, which is a general interface to various web applications. The proposed method, Synatra, handles two types of knowledge source: tutorial articles and HTML snapshots, and presents corresponding demonstration synthesis approach. Such knowledge is then transferred to the LLMs by fine-tuning the LLMs on the synthesis data. Experiments show that Synatra can improve performance of CodeLlama-instruct-7b, outperforming open-sourced/fine-tuned models. Strengths: Overall, I think the paper is well-motivated. There are many tutorials available on the internet. It is interesting to explore how to effectively utilizing such knowledge. The method is simple and effective, while the writing is easy to follow. Weaknesses: I have some concerns about the experiments. 1. The comparison experiment is a bit unfair to me, for several reasons: - There are some RAG based methods to be considered, as this can be regarded as a knowledge retrieval problem. - Much of the baselines are not fine-tuned. Although fine-tuned with interactive data, the data in AgentLM, CodeActAgent is not out-of-the-box like Synatra. Maybe the authors can consider baselines that fine-tune LLMs with more direct demonstrations. - In Synatra, the demonstration is processed and generated by GPT-4. These high quality data further improves the performance of Synatra. 2. There lacks some important details about the method, e.g., how is the LLM fine-tuned and the training hyper-parameters. Besides, the configurations about baselines and evaluation dataset should be detailed. Technical Quality: 3 Clarity: 3 Questions for Authors: 1. How is success rate calculated in these web tasks? 2. In Synatra, how is the LLM fine-tuned on the synthesis data? 3. What is the source of performance improvement? Based on the results in Figure 4 (right), Synatra clearly outperforms human annotation method. I do not think this is simply attributed to the coverage of the annotation data. Maybe it is because GPT-4 has been trained on these testing tasks? Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: Authors have discussed the limitations in the conclusion section. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for taking the time to review our paper! We are very happy to hear encouraging words about our motivation and effectiveness of our method. We believe the comments are resolvable during the rebuttal period. Please see our response below. We would be very happy to address additional questions during the discussion period if anything is unclear. > ### Comparison with RAG-based approach Thanks for pointing out this. We agree that the RAG-based approach is an alternative method of utilizing existing knowledge. Below is our comparison with the RAG-based approach. Specifically, we used the same collection of tutorials as the retrieval pool and employed cosine similarity of semantic embeddings of task descriptions to find the three closest tutorials. These tutorials were then included as additional context when prompting LLama3.1-instruct-8B to complete the tasks. Note that many RAG methods rely on benchmark specific in-context examples, we do not use any in this case. The results on WebArena are shown below: \| Model \| WebArena \| \|----------------------------\|-------------------------\| \| RAG-Llama3.1-Instruct-8b \| 4.20 \| \| Synatra-CodeLlama-7b \| 4.80 \| We found that adding these additional tutorials fail to match the performance of Synatra. Since these tutorials were retrieved from wikihow articles, it is likely that they have been part of the large pre-training data already. However, converting them into direct demonstrations supplies additional information on the actual task completion, and hence can further improve performance. > ### Comparison with LLMs finetuned with more direct demonstrations *Please Refer to the same section in global rebuttal due to character limit.* > ### Details about the method, e.g., how is the LLM fine-tuned and the training hyper-parameters; the configurations about baselines and evaluation dataset We apologize for the missing details. The details of the training are listed in Appendix I. The CodeLlama checkpoints are fine-tuned with A100 GPUs with deepspeed acceleration framework. We set the context length to 4096 tokens. To train on 50k dataset, we train with 6 x A100 80G GPUs for about 20 hours. We use a batch size of 48, and learning rate of 5e-5. We use cosine annealing and a warm-up ratio of 0.03. We use supervised fine-tune with full-parameters. We decided on this rather than lora from early experiment comparing the two’s performance. We only calculate loss on the response of the agent, while the observation, task title, past histories etc. are masked in loss calculation. We will update section 5 to properly refer to the corresponding section in appendix I. We will update the details of baseline and evaluation setup in section 5 as well. For WebArena, we evaluated with a temperature of 0 and default set of parameters. For MiniWoB++, we evaluated on a subset that is the same as what's used in AgentLM/CodeActAgen. We take the five run-average success rate. We re-ran all the baseline models with the same setting for fair comparison. We will update these details in section 5 and appendix. And we will also release our training/evaluation code. > ### How is success rate calculated in these web tasks? Both benchmarks provide validators to programmatically check if a task is completed or not inside their corresponding environments. For instance, if a task is to put a certain item into the shopping cart, a program check would be to verify if the said item is in the cart by the end of the trajectory. > ### What is the source of performance improvement? Our analysis shows that synthetic data teaches the model on multiple levels. First, it provides an understanding of basic task formats. Initially, the base model had issues such as repeating actions, interacting with nonexistent elements, or performing invalid actions not specified in the prompt. After training, these errors significantly decreased, approaching GPT-4 levels. The detailed breakdown is shown below: \| Model \| Click on Non-functional Elements (\%) \| Repeated Typing Actions (\%) \| Click on Non-existent Elements (\%) \| \|-----------------------------\|---------------------------------------------------\|--------------------------------------\|-------------------------------------------------\| \| GPT-4-Turbo \| 6.4 \| 26.85 \| 1.66 \| \| Synatra-CodeLlama-7b \| 4.9 \| 6.8 \| 0.7 \| Second, synthetic data enhances the model’s understanding of web pages. For instance, the base model correctly typed into a typable element (e.g, a input box) less than 75% of the time. Post fine-tuning, this accuracy improved to over 93%. Lastly, we qualitatively examined model’s planning on the task before and after training, we found that synthetic data yields more accurate task planning and hence improve task performance. > ### Does the improvement come from GPT-4 trained on the test tasks? It is highly unlikely that GPT-4 was trained on the exact test tasks. Even if GPT-4 encountered some of the test data during training, our approach does not rely on its prior knowledge of them. Our data synthesis process is entirely independent of the evaluation datasets, including WebArena, MiniWob, and Mind2web. We did not utilize any specific test tasks or testing environments, such as the websites in WebArena, during data generation. Instead, we leveraged GPT-4 to transform randomly sampled wikiHow articles, targeting general web-based tasks, and randomly sampled web pages. Given the vast volume of web content, it is improbable that the sampled pages would overlap with those seen during the test. --- Rebuttal Comment 1.1: Title: Response to author response Comment: Thanks for your detailed response. It seems that other reviewers also concern about the comparison and the reliance on GPT-4. I appreciate authors' additional results, addressing some of concerns regarding the comparison. In addition, I still think the source of performance improvement over human demonstration is unclear. Specifically, I am not convinced that demonstrations generated by GPT-4 are more effective than that of human. You mentioned 'basic task formats'. However, human can also provide demonstrations that conform to the task format. The advantage of proposed method is that it does not require human cost, but requiring a high-quality LLM for annotation. --- Reply to Comment 1.1.1: Comment: Thanks for the follow-up! First, we hope that by showing models trained on Synatra is better than GPT-4-turbo in terms of repeating actions, interacting with nonexistent elements, and performing invalid actions help address the concern that Synatra is only learning from GPT-4-turbo and not teaching models new information GPT-4-turbo doesn't know. Regarding the comparison with human annotation (Mind2Web in this case), we agree that this could be more clear. Here is our finding from our experiments: we trained our two models with the exact same setting, one with Mind2Web's training set and the other with Synatra. As shown here and in global rebuttal: \| Model \| Mind2Web\| MiniWoB++ \| WebArena \| \|-----------------------------\|----------------------\|-----------------\|-------------------------\| \| Mind2Web-CodeLlama-7b \| 39.33 (held-in) \| 27.00 \| 0.00 \| \| Synatra-CodeLlama-7b \| 17.26 \| 39.57 \| 4.80 \| we found that the model trained with Mind2Web's training set actually outperforms the others on Mind2Web's test set. But it is also true that it is not as good as a Synatra trained model in MiniWoB++ and WebArena. The reason for this difference is relatively intuitive: by using synthetic data pipeline, we are able to generate all of the actions in the action space, including stop(), go_back(), go_forward(), press(), goto(), etc, while the action space of the Mind2Web data set only has click(), and type(). The limited and biased action space played a key part in the low performance of Mind2Web-CodeLlama on WebArena. Additionally, websites' domain distribution could play a role too -- Mind2Web covers a somewhat limited number of sites, while Synatra has broader coverage. One other possible suggestion is potential format biases, but we have parsed the format of Mind2Web's training set to be exactly the same as Synatra, so we can rule this out as a factor. So the remaining plausible explanations are the differences in website domains and the types of actions represented in the dataset. We hope this helps clarify, and we will further improve the discussion in the final version of the paper!	Summary: This paper studies the problem of dataset generation for the digital task in the context of LLM. The motivation is that the current data collection process often requires human annotation, which is very costly and not scalable. As a result, the paper proposes using large language models (LLMs) to generate a synthetic dataset based on indirect knowledge. The indirect knowledge often refers to tutorials designed for human consumption and observation trajectories that lack associated tasks and actions. In contrast, "direction" knowledge consists of complete states and actions. To generate synthetic data based on indirect knowledge, the paper proposes several methods: (1) writing a prompt to let LLMs imagine their missing actions or states given partial trajectories, and (2) randomly sampling the context from the external large-scale dataset such as webpages. Table 1 shows the results that the proposed approach achieves the best performance among the baselines. Strengths: 1. The paper is easy to follow and read. 2. The method seems to solve the common lack of demonstration data issue in the current LLM fine-tuned paradigm. 3. The method seems to be novel. Weaknesses: 1. The method falls into the category of the perpetual data machine, in which one uses LLMs to generate its own training dataset. In addition, the proposed method is similar to self-refine paper (https://arxiv.org/pdf/2303.17651), in which LLMs iteratively fine-tune itself based on the generated dataset. 2. Table 1 does not compare the proposed method to the existing methods that use their own dataset to fine-tune such as self-refine paper. For instance, the paper could add a baseline in which the model is fine-tuned based on the other iterative fine-tuned procedure on the same dataset used in the paper. This will further verify the proposed method Technical Quality: 3 Clarity: 3 Questions for Authors: 1. I am curious to learn more about the author's thoughts on perpetual data machines, and the comparison to self-refine papers. 2. Please answer the weakness section Confidence: 2 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: See the weakness section. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for taking the time to review our paper! We are very happy to hear the encouraging words about the work being novel and addressing the lack of demonstrations in LLM finetuning for agentic tasks. We believe the comments are resolvable during the rebuttal period. Please see our response below. We would be very happy to address additional questions during the discussion period if anything is unclear. > ### The comparison with self-refine The core difference between our approach and self-refine is that we apply LLM refinement for different purpose. Our proposal is a data synthesize approach that leverage LLM to transfer non-demonstrations into direct demonstrations and further finetune a model on the synthesized data. Our goal is to enhance a model’s performance on computer tasks. On the other hand, self-refine focuses on refining a model's response to a given prompt, it is a prompting mechanism. Self-refine does not involve generating training data and finetuning. > ### Comparison with models finetuned on their own dataset Also included in global rebuttal Direct demonstrations for web-based tasks are scarce, resulting in a limited number of LLMs fine-tuned with such data. We made our best effort to survey or implement approaches that are fine-tuned with direct demonstrations. We include three additional baselines and the results are shown below: \| Model \| Mind2Web\| MiniWoB++ \| WebArena \| \|-----------------------------\|----------------------\|-----------------\|-------------------------\| \| AutoWebGLM-7b-42k \| - \| - \| 2.50 \| \| Mind2Web-CodeLlama-7b \| 39.33 (held-in) \| 27.00 \| 0.00 \| \| RAG-Llama3.1-Instruct-8b \| - \| - \| 4.20 \| \| Synatra-CodeLlama-7b \| 17.26 \| 39.57 \| 4.80 \| Here, `AutoWebGLM-7b-42k` is finetuned with their 42$k$ synthetic direct demonstrations. The result is taken from [1]. `Mind2Web-CodeLLama-7b` is finetuned with the Mind2Web training data of 9$k$ direct demonstrations. The finetuning is done by us with the same configurations as Synatra. For `RAG-Llama3.1-Instruct-8b`, we used the same collection of tutorials as the retrieval pool and employed cosine similarity of semantic embeddings of task descriptions to find the three closest tutorials. These tutorials were then included as additional context when prompting LLama3.1-instruct8B to complete the tasks. We aims to compare different ways of using existing knowledge with `RAG-Llama3.1-Instruct-8b` We can see Synatra achieves the best performance on all held-out datasets. We also note that finetuning datasets used in AgentLM, CodeActAgent include a reasonable amount of out-of-box web-based demonstrations. In fact, Mind2Web training set made up 66% of the examples in AgentLM’s training set. We will incorporate the additional experiments to our updated draft. We are happy to investigate other approaches if we missed any. [1] Lai et al. Autowebglm: Bootstrap and reinforce a large language model-based web navigating agent. > ### Discussion on perpetual data machine Creating perpetual data machine is an exciting and open research question. Within the scope of our work, we propose leveraging existing resources. Currently, massive text corpora are primarily used for next-token prediction during pretraining, yet each piece of text can embed more diverse information. As models continue to improve through iterative training, they may be able to extract additional information or transform knowledge to enhance their capabilities.	Rebuttal 1: Rebuttal: > ### Comparison with LLMs finetuned with direct demonstrations Direct demonstrations for web-based tasks are scarce, resulting in a limited number of LLMs fine-tuned with such data. We made our best effort to survey or implement approaches that are fine-tuned with direct demonstrations. We include three additional baselines and the results are shown below: \| Model \| Mind2Web\| MiniWoB++ \| WebArena \| \|-----------------------------\|----------------------\|-----------------\|-------------------------\| \| AutoWebGLM-7b-42k \| - \| - \| 2.50 \| \| Mind2Web-CodeLlama-7b \| 39.33 (held-in) \| 27.00 \| 0.00 \| \| RAG-Llama3.1-Instruct-8b \| - \| - \| 4.20 \| \| Synatra-CodeLlama-7b \| 17.26 \| 39.57 \| 4.80 \| Here, `AutoWebGLM-7b-42k` is finetuned with their 42$k$ synthetic direct demonstrations. The result is taken from [1]. `Mind2Web-CodeLLama-7b` is finetuned with the Mind2Web training data of 9$k$ direct demonstrations. The finetuning is done by us with the same configurations as Synatra. For `RAG-Llama3.1-Instruct-8b`, we used the same collection of tutorials as the retrieval pool and employed cosine similarity of semantic embeddings of task descriptions to find the three closest tutorials. These tutorials were then included as additional context when prompting LLama3.1-instruct-8B to complete the tasks. We aims to compare different ways of using existing knowledge with `RAG-Llama3.1-Instruct-8b` We can see Synatra achieves the best performance on all held-out datasets. We also note that finetuning datasets used in AgentLM, CodeActAgent include a reasonable amount of out-of-box web-based demonstrations. In fact, Mind2Web training set made up 66% of the examples in AgentLM’s training set. [1] Lai et al. Autowebglm: Bootstrap and reinforce a large language model-based web navigating agent.	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
EffiLearner: Enhancing Efficiency of Generated Code via Self-Optimization	Accept (poster)	Summary: The paper aims to address the inefficiency issue of code generated by LLMs in terms of execution time and memory consumption. The authors propose a framework called Self-Optimization based on OverheAd Profile (SOAP), which improves the efficiency of LLM-generated code by iteratively refining it based on execution overhead profiles. These profiles capture the code's execution time and memory usage, which are then fed back into the LLM to optimize the code. The paper demonstrates the effectiveness of SOAP through extensive experiments on various benchmarks and selected LLMs. Results show reductions in execution time and memory usage, highlighting SOAP's ability to enhance code efficiency without compromising correctness. Strengths: * The paper is well presented and the targeted problem of code inefficiency is well motivated. * The evaluation covers a good number of Python coding tasks and LLMs. * The authors mentioned that the code of the work will be open-sourced. Weaknesses: * The baseline selection can be largely improved. The current baseline in the paper is to ask LLMs to directly generate code -- it is not the models' fault to generate non-optimal code when they are not asked to. At least two reasonable and simple baselines should have been included: (1) ask the model to generate an efficient version of code, and (2) ask the model to generate code and then directly optimize it (similar to the ALGO approach, despite not using test generation and execution to soften the environmental assumptions). Furthermore, the PIE [1] paper mentioned various few-shot prompting methods to perform code optimization, which should also be used as baselines. * To perform an "apple-to-apple" comparison over the models, Tables 1-4 should be better aligned. To understand which model is better at generating efficient code, they must be compared under the same set of tasks. While due to correctness inconsistency, the attributed coding tasks are not aligned, authors may compare the models under a set of mutually passing coding tasks. * Efficiency evaluation can be noisy without carefully configuring the metrics and testbeds. The considered metrics such as execution time and memory usage are flaky and non-reproducible as they are measured in physical platforms. To mitigate these limitations, authors may follow PIE [1] to use architecture simulators or other better-defined metrics. * While the author highlighted efficiency is critical in resource-constrained scenarios, the proposed technique is specialized for Python. It is unclear if Self-Optimization can work for performance-demanding languages such as C/C++ and related experiments are ignored. * [1] is a closely relevant and published work that should be well discussed and compared. [1] Shypula A, Madaan A, Zeng Y, Alon U, Gardner J, Hashemi M, Neubig G, Ranganathan P, Bastani O, Yazdanbakhsh A. “Learning Performance-Improving Code Edits.” ICLR 2024. Technical Quality: 1 Clarity: 4 Questions for Authors: * How is SOAP compared to more reasonable baselines below: 1. Prompting an LLM to generate efficient code in zero-shot 2. Ask the LLM to refine its first generation for code performance 3. Fewshot prompting mentioned in PIE * Are profilers necessary? What if we just replace profilers with self-reasoning or self-reflection? * How's the cost (in the form of token consumption and pipeline running time) of SOAP and baselines? * How is the overall variation of mentioned metrics including execution time? For example, when running and measuring the code execution for N times, what is the overall coefficient of variation? Confidence: 5 Soundness: 1 Presentation: 4 Contribution: 2 Limitations: * Using a profiler and code executor in the pipeline is expensive with respect to the degree of improvement. In production, integrating code execution in a sandbox is already challenging, and integrating a profiler (for multiple languages) would take more engineering cost. Meanwhile, the performance gain (e.g., execution time) overall looks minimal compared to the baseline whose prompt does not even encourage code optimization. * Overall the technical contribution of the paper is incremental: compared to prior techniques such as ALGO and PIE, the major difference is the use of code profiler. Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your thoughtful review and insightful comments. We hereby address your concerns below: W1 & Q1 & W5: Baseline selection can be largely improved. Thanks for your suggestion. We provide the evaluation results of SOAP and suggested baselines in Author Rebuttal Table 1. - For the first suggested method, we named it Directly Efficiency, where LLMs are required to generate efficient code for the task description. - For the second suggested method, we name it Self-Refine Efficiency, where we ask LLMs to generate code and then directly optimize it. Then, since PIE fine-tunes LLMs to improve the efficiency of LLM-generated code, which is orthogonal with SOAP, we conduct experiments for PIE and PIE + SOAP for five different prompts to demonstrate that with SOAP, PIE fine-tuned LLMs generated code could be further improved. As shown in Author Rebuttal Table 1, we can observe that SOAP achieves SOTA results compared with Directly Efficiency and Self-Refine Efficiency. For example, Directly Efficiency and Self-Refine Efficiency decreases NTMU from 19.65 to 2.88 and 2.65, while SOAP decreases from 19.65 to 1.64. Besides, we can observe that with SOAP, the efficiency of PIE-generated code would further improve, e.g., decreasing the average execution time from 0.74s to 0.41s for PIE+Dynamic Retrieval,k=4. W2: Compare the models under a set of mutually passing coding tasks. Thanks for your suggestion. The evaluation results are shown in Author Rebuttal Table 2, where we conduct experiments on seven closed-source LLMs with 210 tasks, which have higher pass@1 compared with open-source LLMs, and then can collect massive tasks addressed by all closed-source LLMs. As shown in Table 8, we can observe that SOAP with GPT-3.5-turbo-0301 achieves SOTA efficiency compared with other LLMs. For example, the average execution time decreases from 0.37s to 0.28s. W3: Follow PIE to use architecture simulators or other better-defined metrics. We provide the evaluation results of SOAP and the initial code in Author Rebuttal Table 3. We can observe that in the PIE-provided default simulator, SOAP can also improve the efficiency of LLM-generated initial code. For example, the average execution time of OpenCodeInterpreter-1.3B decreases from 0.80s to 0.52s. W4: Unclear if Self-Optimization can work for performance-demanding languages such as C/C++. To address the reviewer's concern, we conduct experiments for SOAP in the HumanEval-ET (C++) dataset. Our evaluation results are shown below, where we can observe that SOAP can also improve the efficiency of LLM-generated C++ programs. For example, the average execution time of CodeLlama-70B-Instruct-hf decreases from 667.9ms to 459.5ms. \| Evaluation in HumanEval (C++) \| ET (ms) \| NET \| MU (KB) \| NMU \| TMU (KBms) \| NTMU \| \|------------------\|--------\|------\|---------\|------\|------------\|------\| \| CodeLlama-70b-Instruct-hf \| \| \| \| \| \| \| \| Initial Version \| 667.9 \| 1.5 \| 93.2 \| 1.3 \| 58.9 \| 2.1 \| \| SOAP \| 459.5 \| 1.0 \| 72.2 \| 1.0 \| 34.1 \| 1.3 \| \| gpt-3.5-turbo-0301 \| \| \| \| \| \| \| \| Initial Version \| 668.1 \| 1.5 \| 78.9 \| 1.1 \| 79.0 \| 2.6 \| \| SOAP \| 577.3 \| 1.2 \| 71.5 \| 1.0 \| 63.8 \| 2.1 \| Q2: Are profilers necessary? What if we just replace profilers with self-reasoning or self-reflection?* Profilers are necessary for the code efficiency optimization process. Specifically, to demonstrate the importance of profilers, we conduct experiments for straightforward code optimization (Unsupervised Self-Refine and Result-Aware Self-Refine), reasoning-based code optimization (self-reasoning and self-reflection), single profiler-based code optimization, and provide both memory profiler and execution time profiler (SOAP). The evaluation results are shown below. Our experiments demonstrate that by providing both memory profiler and execution time profiler (SOAP), the code efficiency achieves SOTA results compared with other methods. For example, SOAP decreases the average execution time from 0.36s to 0.28s. \|OptimizationProfile\|ET(s)\|NET\|MU(Mb)\|NMU\|TMU(Mbs)\|NTMU\| \|---\|---\|---\|---\|---\|---\|---\| \|GPT-3.5-Turbo-0301\|\|\|\|\|\|\| \|InitialVersion\|0.36\|2.50\|91.25\|2.45\|157.50\|19.75\| \|Unsupervised Self-Refine\|0.32\|2.46\|78.39\|2.12\|312.99\|42.42\| \|Result-Aware Self-Refine\|0.30\|2.25\|58.65\|1.61\|195.49\|27.16\| \|Self-Reasoning\|0.89\|6.21\|60.64\|1.62\|45.91\|5.61\| \|Self-Relfection\|0.81\|5.67\|60.64\|1.62\|39.35\|4.80\| \|SOAP\|0.28\|2.01\|36.08\|0.99\|12.43\|1.64\| Q3: How's the cost (token consumption and running time) of SOAP and baselines?* To address the reviewer’s concern about the cost of SOAP and baselines, we provide the evaluation results in Author Rebuttal Table 4, where we can observe that the initially generated code requires 1.1M token usage and 76.81s for all tasks. While SOAP requires 5.4M token usage and 566.67s for all tasks. Although SOAP requires more tokens compared with the initial version, the execution time and memory usage (See paper table 1) are largely improved. We believe that this exact token usage is affordable. Q4: When running and measuring the code execution for N times, what is the overall coefficient of variation? The overall coefficient of variation (CoV) for each model and metric in the SOAP benchmark is presented in Author Rebuttal Table 5, which is calculated by running and measuring the code execution 5 times for each model, then computing the mean and standard deviation of each metric. From the table, we can observe that all of the metrics' coefficients of variation are lower than 3% for all models, suggesting that the performance of these models is relatively consistent across multiple runs. --- Rebuttal Comment 1.1: Title: Thanks for the detailed reply! Comment: First, I'd like to thank the authors for their reply. It is impressive and surprising to add this volume of preliminary experiments within such a short period. While I think weaknesses #1, #4, and #5 can be mostly addressed by adding new tables in the paper, weaknesses #2 and #3 require a more thorough global revision/update. Specifically, while in the demonstrated comparison from the preliminary results SOAP outperforms other baselines, the ratio of improvements is largely different from table to table when using different measurements and task set alignments. For example, improvements in Table 3 are way larger than that of Table 2 and this is likely due to the impact of task correctness over efficiency. That being said, while I appreciate the various new preliminary experiments from the authors, I still want to hold a rejection before an optimal experimental setting is figured out and applied globally. This would largely improve conclusion consistency and soundness of evaluation, which is very crucial for efficiency evaluation. Regarding the responses to my questions, I have a few concerns: 1. The variations in Table 5 are surprisingly small and the variations across different metrics are surprisingly equivalent. Can the authors double-check their data? 2. How do the authors configure Result-Aware Self-Refine compared to SOAP? Follow-up suggestions: 1. Given the large token overhead of SOAP, what if we just do optimization sampling and profile to select the best one using the same token budget? 2. In general, it is encouraged to simplify the metrics for clarity. --- Reply to Comment 1.1.1: Title: Rebuttal for Reviewer 4 Follow Up Comment: Specifically, in the demonstrated comparison from the preliminary results SOAP outperforms other baselines, the ratio of improvements is largely different from table to table when using different measurements and task set alignments. For example, improvements in Table 3 are way larger than that of Table 2 and this is likely due to the impact of task correctness over efficiency. That being said, while I appreciate the various new preliminary experiments from the authors, I still want to hold a rejection before an optimal experimental setting is figured out and applied globally. This would largely improve the consistency and soundness of the conclusion, which is crucial for efficiency evaluation. Response: Thank you for your appreciation of the new preliminary experiments we provided during the rebuttal process. However, we are disheartened that reviewer pc3i wishes to reject our paper based on the claim, "I still want to hold a rejection before an optimal experimental setting is figured out and applied globally". To address reviewer pc3i's concerns about w2 and w3, we have provided new results to reviewer pc3i's requirements. Specifically, for w2, we want to clarify that we conducted experiments on all closed-source models. However, we did not conduct experiments on open-source models due to their low pass@1 and the lack of consistent correct code across all open-source models. Next, for the PIE provided Gem5 default simulator, we also included seven different LLMs: smaller open-source LLMs (OpenCodeInterPreter-1.3B, DeepSeekCoder-1.3B-Ins, CodeLlama-7B-Ins-hf, StarCoder2-15B), a larger open-source model (CodeLlama-70B-Ins-hf), and two closed-source models (GPT-3.5-turbo-0301 and Claude-3-sonnet). We believe that these models are representative of our experiments. The variations in Table 5? Response: To address the reviewer’s concern, we provide the source code in our anonymous GitHub. We first use run_source_code_five_times.py to run the LLM-generated code five times. Next, we use report_variant.py to first calculate mean and std. Then we report coef_of_var with (std_dev / mean) * 100 for all experiments. Configuration of Result-Aware Self-Refine compared to SOAP? Response: The configuration of Result-Aware Self-Refine is shown in our anonymous GitHub prompts.py, where the only difference between SOAP and Result-Aware Self-Refine is that the overhead analysis part of Result-Aware Self-Refine in Lines 19 only contains the ET, MU, and TMU (See Lines 54-58). The overhead analysis part of SOAP also contains the execution time profiler and memory profile (See Lines 28-35). Follow-up suggestions: S1: Given the large token overhead of SOAP, what if we just do optimization sampling and profile to select the best one using the same token budget? Response: Thank you for your suggestion. We have provided evaluation results for your suggested method and SOAP in GPT-3.5-turbo-0301 below. It's observable that this method can enhance the efficiency of code generated by the LLM as compared to the initial version. For instance, the TMU of GPT-3.5-turbo-0301 decreases from 157.50 (Mbs) to 27.99 (Mbs). This significant reduction is primarily due to the suggested method of selecting the most efficient route from multiple codes. However, we also noticed that the suggested method is still less efficient than SOAP. The primary reason for this is that the suggested method primarily aims to generate multiple efficient solutions for a given task. However, without the profile information provided by SOAP, the LLM is unable to optimize the code and generate a more efficient version than the initial code, resulting in the suggested method being less efficient than SOAP. \| Strategy \| ET (s) \| NET \| MU (Mb) \| NMU \| *TMU (Mbs) \| NTMU** \| \|----------\|------------\|---------\|-------------\|---------\|----------------\|----------\| \|Initial\|0.36\|2.50\|91.25\|2.45\|157.50\|19.75\| \| Reviewer pc3i suggested \| 0.31 \| 2.17 \| 36.14 \| 1.00 \| 27.99 \| 2.94 \| \| SOAP \| 0.28 \| 2.01 \| 36.08 \| 0.99 \| 12.43 \| 1.64 \| Effectiveness of SOAP with Reviewer pc3i proposed optimization sampling and profile to select the best one for GPT-3.5-turbo with similar token usages. For each method, we use int(token usage of SOAP/token usage of baselines such as direct generation with sampling) + 1* to ensure that the token usage of SOAP should be lower than the baselines.* S2: In general, it is encouraged to simplify the metrics for clarity. Response: Thanks for your suggestion. We will revise our manuscript in the final version. --- Rebuttal 2: Title: Clarification on rejection Comment: Thanks for the reply. I am sorry for not explaining my decision enough and here are my detailed reasons for my suggestion of decision: 1. First, the preliminary experimental results from the authors quickly cleared my concerns about approach effectiveness regarding weaknesses in #1, #4, and #5. 2. I won't reject the paper just for #1, #4, and #5 because those results are complementary to what the paper already had, meaning that they could be easily added to the camera-ready version if we end up accepting it. 3. Yet, weakness #2 still holds as existing results of the paper are mostly not represented in an "apple-to-apple" fashion. It is not even right to compare the efficiency of LLM codegen over different sets of tasks, making the efficiency score unreasonable to compare. For an extreme case, two LLMs may solve completely different sets of solutions, and computing efficiency scores over two totally different task sets cannot lead to clean and reasonable results regarding code efficiency in general. 4. Because it is problematic to compare LLM efficiency over different sets of tasks, ideally the author should globally correct the evaluation methodology, i.e., removing results made by inconsistent comparison and enforcing correctness alignments. This is crucial before accepting this paper because if not future work might inherit such a misevaluation methodology, leading to more inconsistent comparison in general. 5. Yet, doing reason 4 in rebuttal is quite hard objectively speaking. Meanwhile, given it's a major revision, it might be more rigorous to apply and reorganize the experiments and resubmit a clean version for another review, rather than accepting the paper through some rough views over the set of preliminary results that we are unsure if those can be systematically adopted in the camera-ready. To summarize, I deeply appreciate the efforts of the authors in the rebuttal; however, for soundness, the required revision goes beyond "convincing the reviewers through proof-of-concept experiments" that it is crucial to globally correct the evaluation methodology for positively leading future research in this thread. Last but not least, I strongly feel this work can be accepted after doing a major revision. --- Rebuttal 3: Title: Apple-to-Apple results Comment: Thank you for your reply. SOAP is effective for both scenarios (i.e., improving LLMs' own tasks and improving common correct tasks). To address the concern of the "apple-to-apple" results of our experiments in the Paper's main flow, in this thread, we provide results based on common tasks for Table 2 - Table 4's results, which provide consistent results for the two configurations. (Table 1's results are already demonstrated in a previous thread.) For Paper Table 2, where we discuss how SOAP's effectiveness would be affected by the optimization results, we provide the evaluation results in Reviewer pc3i Table 2 (common tasks). First, we find the tasks addressed by both CodeLlama-70B-Ins and GPT-3.5-turbo-0301 with the Initial version (Step 0) and SOAP optimization process (Step 1-5). Then, we collect 46 tasks and measure the efficiency of LLM-generated code in these tasks. The evaluation results in Reviewer pc3i Table 2 (common tasks) show that CodeLlama-70B-Ins achieves SOAP efficiency results with one-step SOAP optimization, while GPT-3.5-turbo-0301 continuously improves the efficiency for the evaluated 46 tasks from Step 0 to Step 3. Then, the efficiency of GPT-3.5-turbo-0301 maintains efficiency for the other two optimization steps. Next, for Paper Table 3, where we discuss how different prompt optimization steps affect the efficiency of LLM-generated code, we provide the evaluation results in Reviewer pc3i Table 3 (common tasks). First, we find the tasks addressed by both CodeLlama-70B-Ins and GPT-3.5-turbo-0301 for six different prompts and then get 40 tasks. Then, we provide the efficiency results in Reviewer pc3i Table 3 (common tasks), where we can observe that SOAP also achieves SOTA efficiency results compared with other baselines. For example, SOAP achieves 3.72 (Mbs) for TMU, while baselines only achieve 3.84 (Mbs) in the TMU metric for GPT-3.5-turbo generated code. Finally, for Paper Table 4, where we discuss the differences in the efficiency of SOAP and the initial version of the CodeLlama family, we provide the evaluation results in Reviewer pc3i Table 4 (common tasks). First, we detect correct tasks addressed by both SOAP and the Initial version for four CodeLlama models and then get 3 tasks. Next, we provide the efficiency results of CodeLlama family-generated code in Reviewer pc3i Table 4 (common tasks). We can observe that for four CodeLlama models, SOAP continuously improves the efficiency of LLM-generated code. We hope that our newly provided results can address the reviewer's concern. Note: We provide the Tables in the next thread. --- Rebuttal 4: Title: Results Comment: *Reviewer pc3i Table 2 (common tasks) Effect of the number of self-optimization steps in SOAP (46 tasks). The evaluation results are used to replace the results of Paper Table 2 with the same correct tasks addressed by two LLMs for all steps.* \| Steps \| ET (s) \| NET \| MU (Mb) \| NMU \| *TMU (Mbs) \| NTMU \| \|-------\|------------\|---------\|-------------\|---------\|-------\|----------\| \|\|\| \| \| \| \|\| \| CodeLlama-70b-Instruct-hf \|\| \| \| \| \|\| \| 0\| 0.40\| 3.00 \| 54.79\| 1.76 \| 20.05\| 4.86\| \| 1\| 0.29\| 2.20 \| 54.90\| 1.77 \| 14.58\| 3.53\| \| 2\| 0.29\| 2.20 \| 54.90\| 1.77 \| 14.58\| 3.53\| \| 3\| 0.29\| 2.20 \| 54.90\| 1.77 \| 14.58\| 3.53\| \| 4\| 0.29\| 2.20 \| 54.90\| 1.77 \| 14.58\| 3.53\| \| 5\| 0.29\| 2.20 \| 54.90\| 1.77 \| 14.58\| 3.53\| \|\|\| \| \| \| \|\| \| gpt-3.5-turbo-0301 \|\| \| \| \| \|\| \| 0\| 0.24\| 1.78 \| 31.12\| 1.00 \| 10.74\| 2.60\| \| 1\| 0.22\| 1.66 \| 31.28\| 1.01 \| 7.36 \| 1.78\| \| 2\| 0.22\| 1.64 \| 31.27\| 1.01 \| 7.02 \| 1.70\| \| 3\| 0.22\| 1.64 \| 31.27\| 1.01 \| 6.98 \| 1.69\| \| 4\| 0.22\| 1.64 \| 31.27\| 1.01 \| 6.98 \| 1.69\| \| 5\| 0.22\| 1.64 \| 31.27\| 1.01 \| 6.98 \| 1.69\| Reviewer pc3i Table 3 (common tasks)* Effect of the number of self-optimization steps in SOAP (40 tasks). The evaluation results are used to replace the results of Paper Table 3 with the same correct tasks addressed by two LLMs for all steps.* \| Steps\| ET (s) \| NET\| MU (Mb) \| NMU \| TMU (Mbs) \| NTMU \| \| ------------------------- \| ------ \| ----- \| ------- \| --- \| ---------- \| ---- \| \| CodeLlama-70b-Instruct-hf* \| \|\| \| \| \|\| \| Initial \| 1.82\| 14.78 \| 25.85\| 1.00\| 36.32\| 16.89\| \| Unsupervised Self-Refine \| 0.34\| 2.80 \| 25.82\| 1.00\| 6.99\| 3.25 \| \| Result-Aware Self-Refine \| 0.33\| 2.67 \| 25.96\| 1.00\| 6.85\| 3.19 \| \| memory_profiler \| 0.26\| 2.08 \| 25.88\| 1.00\| 4.38\| 1.97 \| \| time_overhead_profiler \| 0.19\| 1.57 \| 25.88\| 1.00\| 4.03\| 1.89 \| \| SOAP \| 0.19\| 1.55 \| 25.87\| 1.00\| 3.98\| 1.85 \| \| gpt-3.5-turbo-0301 \| \|\| \| \| \|\| \| Initial \| 0.24\| 1.95 \| 25.91\| 1.00\| 5.01\| 2.33 \| \| Unsupervised Self-Refine \| 0.26\| 2.14 \| 29.99\| 1.16\| 7.65\| 3.56 \| \| Result-Aware Self-Refine \| 0.23\| 1.87 \| 25.95\| 1.00\| 5.12\| 2.38 \| \| memory_profiler \| 0.19\| 1.53 \| 25.88\| 1.00\| 3.84\| 1.79 \| \| time_overhead_profiler \| 0.18\| 1.47 \| 31.26\| 1.21\| 4.98\| 2.32 \| \| SOAP \| 0.18\| 1.48 \| 25.88\| 1.00\| 3.72\| 1.73 \| *Reviewer pc3i Table 4 (common tasks) Effect of the number of self-optimization steps in SOAP (3 tasks) for CodeLlama family.* \| Steps \| ET (s) \| NET \| MU (Mb) \| NMU \| *TMU (Mbs) \| NTMU \| \|-------\|------------\|---------\|-------------\|---------\|-------\|-----\| \|\| \|\|\|\|\| \| \| CodeLlama-7b-Instruct-hf \| \|\|\|\|\| \| \| Initial \| 0.78 \| 5.61 \| 30.82 \| 1.00 \| 13.89 \| 5.50 \| \| SOAP (step 5) \| 0.23 \| 1.65 \| 54.69 \| 1.77 \| 7.80 \| 3.09 \| \|\| \|\|\|\|\| \| \| CodeLlama-13b-Instruct-hf \| \|\|\|\|\| \| \| Initial \| 0.33 \| 2.38 \| 54.66 \| 1.76 \| 11.44 \| 4.53 \| \| SOAP (step 5) \| 0.25 \| 1.76 \| 54.69 \| 1.77 \| 8.46 \| 3.35 \| \|\| \|\|\|\|\| \| \| CodeLlama-34b-Instruct-hf \| \|\|\|\|\| \| \| Initial \| 0.31 \| 2.25 \| 54.59 \| 1.76 \| 10.72 \| 4.25 \| \| SOAP (step 5) \| 0.25 \| 1.76 \| 54.64 \| 1.76 \| 8.42 \| 3.33 \| \|\| \|\|\|\|\| \| \| CodeLlama-70b-Instruct-hf** \| \|\|\|\|\| \| \| Initial \| 0.32 \| 2.31 \| 54.62 \| 1.76 \| 10.97 \| 4.34 \| \| SOAP (step 5) \| 0.23 \| 1.61 \| 54.71 \| 1.77 \| 7.65 \| 3.03 \| --- Rebuttal Comment 4.1: Title: Friendly Reminder: Pending Reviewer Responses and Assessment Consideration Comment: Dear Reviewer pc3i, Thank you for your review and comments on our paper, which you provided on August 12th. To address your concerns regarding the "apples to apples" comparison, we have added all experiments in the last response thread with the same format for our paper. We believe this will facilitate a more accurate and fair evaluation of our work. We would greatly appreciate it if you could take the time to review these results and consider improving your overall assessment of our paper based on these revisions. Thank you once again for your valuable feedback and for considering our request.	Summary: This paper studies an important and timely issue: the inefficiency often found in code generated by current Large Language Models (LLMs), which can result in longer execution times and higher memory consumption. To mitigate this issue, the paper proposes a self-optimization framework SOAP, designed to improve the efficiency of LLM-generated code. SOAP starts from the code generated by an LLM and then executes it locally to profile its execution time and memory usage. These profiles are fed back to the LLM, allowing it to revise the code and reduce overhead iteratively. The authors verify the effectiveness of SOAP through empirical experiments on the leading open-source and closed-source models, showing SOAP can substantially optimize both execution time and memory consumption. Strengths: 1) This paper proposes a novel general framework to optimize the efficiency of code generated by LLMs. It utilizes execution overhead profiles for self-diagnosis and iteratively enhances code efficiency. 2) Empirical experiments conducted on various leading LLMs demonstrate that this framework effectively optimizes both the execution time and memory consumption of LLM-generated code. 3) The framework does not require additional model training or tuning, making it flexible enough to be attached to arbitrary LLMs as a standalone pipeline. 4) The paper is well-written; the methodology introduced is concise, and the experimental results are robust and clear. Weaknesses: 1) The multi-iteration optimization method requires large token overhead, which can be both resource-intensive and time-consuming. 2) Overhead profiles serve as a good indicator for local code optimization. Nevertheless, the framework may struggle with the scalability of extended code global optimization due to the limited context window of LLMs. Technical Quality: 3 Clarity: 4 Questions for Authors: 1) In this paper, SOAP optimizes both execution time and memory usage simultaneously. However, in real-world scenarios, people might prioritize a single objective, either time or space. Do you think it is possible for SOAP to include optimization options (similar to -O3 or -Oz in GCC) to cater to different preferences? 2) The iterative self-optimization process might increase the risk that the final generated code is either non-executable or deviates from the original problem specifications. Do you have any mechanisms in place to prevent such deterioration? 3) How does the token usage in the SOAP profile optimization process compare to that in direct code generation (one-shot)? Confidence: 5 Soundness: 3 Presentation: 4 Contribution: 4 Limitations: The authors addressed the limitations and potential negative societal impact of their work. Flag For Ethics Review: ['No ethics review needed.'] Rating: 8 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your thoughtful review and insightful comments. We hereby address your concerns below: W1 & W2 & Q3: The multi-iteration optimization method requires a large token overhead. To address the reviewer's concern about overhead and context window limitations, we provide detailed metrics on execution time, token usage, per iteration input/output token usage， and efficiency in the Table below: \| Model \| Execution Time (s) \| Token Usage (million) \| Per Iteration Input/Output Task Token Usage (K) \|ET(s)\|NET\|MU(Mb)\|NMU\|TMU(Mbs)\|NTMU\| \|-------\|-------------------\|----------------------\|--------------------------------------------------\|---\|---\|---\|---\|---\|---\| \|InitialVersion\|76.81\|1.1\|1.1\|0.36\|2.50\|91.25\|2.45\|157.50\|19.75\| \|UnsupervisedSelf-Refine\|416.81\|3.9\|1.16\|0.32\|2.46\|78.39\|2.12\|312.99\|42.42\| \|Result-AwareSelf-Refine\|419.24\|3.9\|1.16\|0.30\|2.25\|58.65\|1.61\|195.49\|27.16\| \|LineProfiler\|555.68\|4.7\|1.49\|0.33 \|2.34 \|36.43 \|0.99\|14.07 \|1.81\| \|MemoryProfiler\|536.26\|4.7\|1.49\|0.34 \|2.40 \|36.85 \|1.00 \|16.34 \|2.10\| \|SOAP\|566.67\|5.4\|1.78\|0.28\|2.01\|36.08\|0.99\|12.43\|1.64\| Table: Overhead of different code efficiency optimization methods for GPT-3.5-turbo.* We can observe the following: - Execution Time and Token Overhead: SOAP requires approximately 8x more execution time compared to the Initial Version. However, this overhead is justified as the optimized code resulting from SOAP significantly reduces the execution time and memory usage for real-world software that could be executed millions of times. Besides, while the optimization process itself is resource-intensive, it yields substantial efficiency gains in deployment scenarios. For example, the average memory peak (MU) of SOAP-generated code only requires 40% compared with the initially generated code, which can help source code applied in memory-constrained environments, such as embedded systems or mobile devices. Furthermore, the reduced memory footprint and improved execution speed of the optimized code can lead to better overall system performance, especially in scenarios where the software is frequently used or runs on resource-limited hardware. As a result, the upfront computational cost of the optimization process is offset by the long-term benefits of more efficient and lightweight code in real-world applications. - Context Window and Scalability: SOAP requires an average of 1.78K tokens for each input+output task iteration. Given that existing LLMs such as GPT-3.5 and GPT-4 have context windows of 4K tokens or more, they can effectively handle the global profiler information provided by SOAP. This capability allows the LLMs to understand comprehensive profiling data and perform global code optimizations, addressing concerns about scalability within the context window limitations. By leveraging the available context window efficiently and optimizing the code based on detailed profiling data, SOAP manages to enhance the performance and scalability of the generated code, making it a valuable tool despite its initial overhead. Q1: Include optimization options (similar to -O3 or -Oz in GCC) to cater to different preferences. Thanks for your suggestion. As shown in Table 3 in the paper, the memory profiler and line profiler focus on the memory usage and execution time individually. To specify the optimization options, developers can directly revise Lines 508-509 in the [Link](https://anonymous.4open.science/r/SOAP-FF6C/src/code_efficiency_calculator.py) to specify the optimization object (e.g., execution time and memory usage). In our final version, we will refine our source code argparse to provide optimization options for SOAP in the version. Q2: Mechanisms to prevent code deterioration? To mitigate this risk and ensure the reliability of our experiments, we have implemented a robust two-step verification process: - Initial Verification: During the optimization process, if the refined code fails to pass the public test cases, we revert to using the initial version of the LLM-generated code for that specific task. This ensures that any code considered in our experiments at least meets the baseline correctness as defined by the public test cases. - Comprehensive Filtering: In cases where the code passes the public test cases but fails the private test cases, we exclude the entire task from our experiments for that respective model. Consequently, we do not calculate the optimized code's efficiency for any step of that task. For example, if the code optimized in step 3 is correct but the code in step 4 is incorrect for a specific task, we exclude all steps of that task from our efficiency calculations for the corresponding model. By adhering to this two-step process, we ensure that only fully verified and correct code is included in our evaluations. This approach allows us to provide a fair and accurate comparison of code efficiency across different optimization steps and models, thereby preventing any deterioration in code quality through the iterative optimization process. --- Rebuttal Comment 1.1: Title: Thank you for your response Comment: Thank you for your thorough responses. The additional experiments and explanations have satisfactorily addressed my concerns. As a result, I am pleased to elevate my confidence from 4 to 5 and advocate for the paper's acceptance. I also read comments from the Area Chair and other Reviewers. I like the idea of evaluating N code variants x M LLMs, as it promises to provide a comprehensive performance spectrum across various LLMs. However, it is clear that conducting such an intensive experiment within the rebuttal period is impractical. Could you share the individual model performances (or percentages) from your experiment in the AC thread? It would be intriguing to see the expertise demonstrated by each individual model. --- Reply to Comment 1.1.1: Comment: Thanks for your reply. We provide the distribution below. We can observe that GPT-4-turbo-preview has the highest distribution in Pre-SOAP efficiency results. GPT-3.5-turbo-0301 achieves the highest efficiency ratio in Post-SOAP efficiency results. Distribution of the most efficient code for each task of EffiBench. We provide each LLM ratio for the most efficient code and then report the ratio for the overall results. \| Model \| Pre-SOAP (%)\| Post-SOAP (%)\| \|-----------------------------------\|----------\|-----------\| \| OpenCodeInterpreter-DS-1.3B \| 2.33 \| 1.78 \| \| OpenCodeInterpreter-DS-6.7B \| 4.66 \| 2.88 \| \| OpenCodeInterpreter-DS-33B \| 6.30 \| 3.70 \| \| deepseek-coder-1.3b-instruct \| 3.84 \| 1.10 \| \| deepseek-coder-6.7b-instruct \| 5.07 \| 7.81 \| \| deepseek-coder-33b-instruct \| 0.00 \| 0.00 \| \| CodeLlama-7b-Instruct-hf \| 1.23 \| 0.55 \| \| CodeLlama-13b-Instruct-hf \| 3.29 \| 0.82 \| \| CodeLlama-34b-Instruct-hf \| 4.52 \| 1.51 \| \| CodeLlama-70b-Instruct-hf \| 5.34 \| 0.82 \| \| XwinCoder-13B \| 4.11 \| 0.55 \| \| XwinCoder-34B \| 5.75 \| 2.74 \| \| WizardCoder-Python-13B-V1.0-GPTQ \| 1.10 \| 0.41 \| \| starcoder2-3b \| 0.68 \| 1.23 \| \| starcoder2-7b \| 1.37 \| 0.41 \| \| starcoder2-15b \| 0.55 \| 0.14 \| \| gpt-3.5-turbo-0301 \| 8.77 \| 27.67 \| \| gpt-3.5-turbo-0613 \| 7.53 \| 5.07 \| \| gpt-3.5-turbo-1106 \| 7.12 \| 4.52 \| \| gpt-4 \| 7.53 \| 7.53 \| \| gpt-4-turbo-preview \| 16.16 \| 14.25 \| \| claude-3-haiku \| 1.37 \| 5.89 \| \| claude-3-sonnet \| 1.37 \| 8.63 \|	Summary: The paper introduces a novel method for code super-optimization by iteratively refining code using LLMs with profiling information. The focus is on enhancing the efficiency of LLM-generated code, addressing execution time and memory requirements. The proposed methodology involves generating code with an LLM and then iteratively feeding profiling results back to the LLM to optimize the code's efficiency. The profiling information includes per-line execution time and memory usage data, helping to identify specific lines that require significant overhead. Experimental results show that this approach outperforms existing unsupervised self-refine and result-aware self-refine methods on efficiency benchmarks like EffiBench, with supplementary experiments on HumanEval and MBPP. Strengths: - The paper addresses a gap in current LLM code generation research by focusing on code efficiency. - The proposed iterative refinement method with profiling information is still innovative and provides a clear path to optimizing execution time and memory usage. - Experimental results demonstrate that the method significantly outperforms existing approaches in terms of code efficiency, showing the potential practical value of this technique. Weaknesses: - LLM self-refinement or self-repair techniques have been extensively employed in generating responses/codes [1] and debugging tasks [2], whereas utilizing code profiling information for optimization is also a long-established concept [3, 4], which raises concerns in the proposed method's technical novelty. - The paper seems to treat the number of optimization steps as a hyperparameter. While Section 4.2 covers the impact of self-optimization steps, the average number of iterations required to achieve the optimization results in Table 1 is not clearly disclosed. This information is critical for comprehending the efficiency and practicality of the proposed method. Automating the stopping criteria for iterative optimization is also important in practice, but it is not supported by the proposed method, thus limiting its applicability. - The potential semantic degradation in code correctness after refinement, particularly in scenarios where test cases do not cover all edge cases (which are common in real-world applications), raises concerns about the reliability of the optimized code, particularly in safety-critical scenarios. - The methodology section, particularly section 3.4, is overly verbose. The explanation of each part of the prompt could be condensed to improve readability. Technical Quality: 3 Clarity: 2 Questions for Authors: ## Questions & Suggestions: 1. What is the average number of iterations required for optimization? What are the stopping criteria for iterative optimization? Did you set it to 5 for all the experiments? How is it determined when to stop the refinement process? 2. How significant is the profiling overhead? Is there any analysis on the average number of extra tokens required for including the profiling information as prompts? How does this affect the overall efficiency and effectiveness of the optimization process? 3. The downgraded pass@1 results in Section 4.4 suggest that the proposed method cannot guarantee semantic equivalence after code refinement. This could impact the practicality and reliability of the code superoptimizer, especially in safety-critical applications. How can this issue be mitigated? 4. Analysis of the optimization techniques applied by the LLM is necessary. Are there certain types of optimization where the method may fall short? 5. The current approach relies on the LLM to analyze and identify hot spots from the profiling results. Given the standardized format of profiling results, could rule-based post-processing techniques that filter out hot spot information improve or accelerate the self-refinement process? 6. In line 189, only code that passed all test cases is considered in the evaluation. What if the refined code fails the test cases during optimization? How is this situation handled? 7. In Table 2, the optimization effect on memory usage appears limited compared to execution time. Also, in the ablation studies (Table 3), self-optimization with only execution time profiling feedback achieves significant memory usage reduction. Does this mean that memory optimization is relatively easier in the evaluated benchmark, or does execution time information play a more critical role in optimization? --- [1] Madaan, Aman, Niket Tandon, Prakhar Gupta, Skyler Hallinan, Luyu Gao, Sarah Wiegreffe, Uri Alon et al. "Self-refine: Iterative refinement with self-feedback." Advances in Neural Information Processing Systems 36 (2024). [2] Olausson, Theo X., Jeevana Priya Inala, Chenglong Wang, Jianfeng Gao, and Armando Solar-Lezama. "Is Self-Repair a Silver Bullet for Code Generation?." In The Twelfth International Conference on Learning Representations. 2023. [3] Chang, Pohua P., Scott A. Mahlke, and Wen‐Mei W. Hwu. "Using profile information to assist classic code optimizations." Software: Practice and Experience 21, no. 12 (1991): 1301-1321. [4] Agakov, Felix, Edwin Bonilla, John Cavazos, Björn Franke, Grigori Fursin, Michael FP O'Boyle, John Thomson, Marc Toussaint, and Christopher KI Williams. "Using machine learning to focus iterative optimization." In International Symposium on Code Generation and Optimization (CGO'06), pp. 11-pp. IEEE, 2006. Confidence: 4 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: The limitations related to the overhead of profiling and the semantic correctness of the optimized code are mentioned in the paper but not analyzed in detail. A more comprehensive cost-benefit analysis, including the extra tokens required for profiling information in prompts, would provide a clearer picture of the method's overall efficiency. The authors should also consider the broader implications of this optimization approach, including its potential impact on code reliability and safety in practical applications. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your thoughtful review and insightful comments. W1 & Q1: Impact of self-optimization steps In our paper, the self-optimization steps are constraint as 5 Section 4.2, consistent in our experiments. 5 is the default setting for many existing self-optimization methods [1, 2]. [1] Islam M A, et al. MapCoder: Multi-Agent Code Generation for Competitive Problem Solving[J]. arXiv preprint arXiv:2405.11403, 2024. [2] Zhou, Andy, et al. "Language agent tree search unifies reasoning acting and planning in language models." arXiv preprint arXiv:2310.04406 (2023). Based on your suggestion, we require GPT-3.5-turbo-0301 to consider stopping the SOAP self-optimization process and only constrain the max step as 5. As shown in the Table below, the adaptive self-optimization process improves the efficiency of LLM-generated code. However, it does not achieve SOTA performance compared with SOAP. For example, when optimizing its initially generated code, it still needs 0.35s to execute, on average. SOAP only requires 0.28s. One key reason is that in each step, the efficiency of most code can be optimized. If the self-optimization stops early, the code’s efficiency remains in the sub-optimal results. \| Steps \| ET (s) \| NET \| MU (Mb) \| NMU \| TMU (Mbs) \| NTMU \| Step \| \|-------\|-----\|-----\|---\|-----\|---\|--\|---\| \|InitialVersion\|0.36\|2.50\|91.25\|2.45\|157.50\|19.75\|0\| \|Adaptive\|0.35\|2.47\|55.00\|1.52\|178.98\|23.83\|1.2\| \|SOAP\|0.28\|2.01\|36.08\|0.99\|12.43\|1.64\|5\| W3 & Q3: Semantic degradation in code correctness after refinement where test cases do not cover all edge cases.* We clarify that most edge cases have been covered in SOAP. For EffiBench, the private test cases covered most edge cases for each canonical solution. For the other two datasets, HumanEval and MBPP, we also utilize the test cases generated by EvalPlus to cover more edge cases. On the other hand, the degradation is small (0.5% pass@1 for EffiBench, 0% pass@1 for HumanEval+, and 0.84% pass@1 for MBPP+ on average as follows). We believe that the potential degradation in correctness after refinement is manageable. \|\|Initial pass@1\|SOAP pass@1\| \|---\|----\|---\| \|OpenCodeInterpreter-1.3B\|30.5\|30.5\| \|CodeLlama-7b\|39.6\|39.6\| \|CodeLlama-70b\|45.7\|45.7\| \|gpt-3.5-turbo\|62.8\|62.8\| \|claude-3-sonnet\|59.1\|59.1\| Results on HumanEval+. \| \| Initial pass@1 \| SOAP pass@1 \| \|---\|---\|----\| \|OpenCodeInterpreter-1.3B\|57.9\|55.8\| \|CodeLlama-7b\|40.7\|40.7\| \|CodeLlama-70b\|53.9\|52.1\| \|gpt-3.5-turbo\|59.8\|59.5\| \|claude-3-sonnet\|58.4\|58.4\| Results on MBPP+. W4: Section 3.4, is verbose Thanks for your suggestion. We will revise it accordingly. Q2: Analysis of the profiling overhead We provide the breakdown of the overhead for SOAP and other prompt engineering in Author Rebuttal Table 4. Compared with the initial version, SOAP would increase the total token usage from 1.1M to 5.4M. Q4: Certain types of optimization where the method may fall short There are certain types of optimization where the SOAP method may fall short. Specifically, tasks that do not require algorithmic improvements or have already been implemented with optimal time/space complexity may not benefit significantly from SOAP. One example is that as shown in Paper Fig. 12 to Fig. 18, when LLM first generates code for the task to sort two arrays, if the code already has an optimal time/space complexity, SOAP may not optimize the code into a more efficient version. We will add this discussion in the revised version. Q5: Could rule-based post-processing techniques improve or accelerate the self-refinement? Based on your suggestion, we conduct experiments for the SOAP by extracting the Top 5 lines with the highest execution time and memory usage and then use these profiler parts to guide LLM to optimize its previously generated inefficient code. As shown in the Table below, rule-based optimization improves the efficiency of LLM-generated code compared with the initial version. For example, the average execution time (ET) of GPT-3.5-turbo-0301 decreases from 0.68s to 0.50s. \| Steps\| ET (s) \| NET\| MU (Mb) \| NMU \| TMU (Mbs) \| NTMU \| \|---\|---\|---\|---\|---\|---\|---\| \|InitialVersion\|0.68\|4.83\|102.39\|2.82\|302.04\|39.98\| \|Rule-Optimized\|0.50\|3.64\|57.55\|1.50\|23.36\|3.02\| \|SOAP\|0.39\|2.77\|42.67\|1.18\|18.57\|2.46\| Results for GPT-3.5-turbo-0301* However, the efficiency is lower than SOAP. For example, SOAP further decreases the average execution time for GPT-3.5-turbo-0301 from 0.50s to 0.39s. Only providing part of the overhead profile information may not make LLMs understand how to optimize the code to improve efficiency as the efficiency problems are usually based on all code. Q6: Refined code fails the test cases during optimization? In our experiments, we follow a two-step process: First, if the refined code does not pass the public test cases during the optimization process, we directly use the initial version of the LLM-generated code for that particular task. Second, if the code passes the public tests but fails the private tests, we filter out the entire task from our experiments for the respective model and do not calculate the optimized code's efficiency for any step of that task. For example, if step-3 optimized code is correct, but step-4 optimized code is incorrect in private test cases, we will not calculate the efficiency for any step of that task for the corresponding model, ensuring that we only consider code that passes all test cases in the evaluation and provide a fair comparison across different optimization steps and models. Q7: Memory optimization is easier in the benchmark One reason for memory usage being hard to optimize is that most of the tasks already achieve SOTA memory usage compared with execution time. Specifically, as seen in Table 1 in Section 4.2, most of the experiments achieve 1.00 NMU for LLM-generated initial code, which causes the code to be hard to further optimize compared with execution. --- Rebuttal Comment 1.1: Comment: Thank you for the detailed response and the supplementary experiment results. I have a few follow-up questions: 1. Could the optimization performance be further improved with steps greater than 5? Is there a way to determine convergence in self-refinement, especially considering that the number of iterations affects token usage and LLM inference costs (as in W2)? 2. In your response to Q6, you mentioned that the entire task is filtered out if the refined code fails any private test. Can I interpret the difference in your answer to W3 & Q3 (Initial pass@1 v.s. SOAP pass@1) as the proportion of filtered tasks? 3. I do not think it is reasonable to filter out failed code in your evaluation. In real-world scenarios, private cases are supposed to be invisible. --- Rebuttal 2: Title: Response Reviewer 5c1j follow up questions Comment: Thank you for your response to our rebuttal. We have conducted additional experiments and provided further clarification to address the concerns raised in the follow-up questions. We hope that these efforts have adequately addressed Reviewer 5c1j's concerns. If Reviewer 5c1j thinks that the issues have been satisfactorily resolved, we would greatly appreciate it if they could consider improving the overall assessment for SOAP, as the current average overall assessment is in a borderline scenario. Q1 To address your concern, we first optimized the code based on the steps outlined in Paper Table 2 and then continued to optimize for an additional five steps to analyze the efficiency of LLM-generated code after a total of 10 optimization steps. Our evaluation results are shown below. We can observe that increasing the number of optimization steps decreases the overhead, but after five steps, the efficiency metric improvements are minimal. Therefore, in our paper, we mainly set the number of steps to 5. However, if developers want to optimize their code further, they can increase the optimization steps at the cost of some additional token usage. We believe this token usage is worthwhile, as the optimized code would be deployed in the software and run thousands to millions of times. \| Steps \| ET (s) \| NET \| MU (Mb) \| NMU \| TMU (Mbs) \| NTMU \| \|-------\|--------\|-----\|---------\|-----\|------------\|------\| \| CodeLlama-70B \| \| \| \| \| \| \| \| 0 \| 0.36 \| 2.50 \| 91.25 \| 2.45 \| 157.50 \| 19.75 \| \| 1 \| 0.33 \| 2.35 \| 36.09 \| 0.99 \| 13.70 \| 1.81 \| \| 2 \| 0.31 \| 2.18 \| 36.09 \| 0.99 \| 13.04 \| 1.72 \| \| 3 \| 0.29 \| 2.06 \| 36.08 \| 0.99 \| 12.57 \| 1.66 \| \| 4 \| 0.29 \| 2.03 \| 36.08 \| 0.99 \| 12.50 \| 1.65 \| \| 5 \| 0.28 \| 2.01 \| 36.08 \| 0.99 \| 12.43 \| 1.64 \| \| 6 \| 0.27 \| 2.00 \| 36.07 \| 0.99 \| 12.40 \| 1.63 \| \| 7 \| 0.27 \| 1.98 \| 36.06 \| 0.99 \| 12.37 \| 1.62 \| \| 8 \| 0.27 \| 1.98 \| 36.05 \| 0.99 \| 12.35 \| 1.61 \| \| 9 \| 0.27 \| 1.97 \| 36.04 \| 0.99 \| 12.35 \| 1.60 \| \| 10 \| 0.26 \| 1.96 \| 36.03 \| 0.99 \| 12.35 \| 1.59 \| \| GPT-3.5-Turbo-0301 \| \| \| \| \| \| \| \| 0 \| 0.36 \| 2.50 \| 91.25 \| 2.45 \| 157.50 \| 19.75 \| \| 1 \| 0.33 \| 2.35 \| 36.09 \| 0.99 \| 13.70 \| 1.81 \| \| 2 \| 0.31 \| 2.18 \| 36.09 \| 0.99 \| 13.04 \| 1.72 \| \| 3 \| 0.29 \| 2.06 \| 36.08 \| 0.99 \| 12.57 \| 1.66 \| \| 4 \| 0.29 \| 2.03 \| 36.08 \| 0.99 \| 12.50 \| 1.65 \| \| 5 \| 0.28 \| 2.01 \| 36.08 \| 0.99 \| 12.43 \| 1.64 \| \| 6 \| 0.28 \| 2.00 \| 36.07 \| 0.99 \| 12.40 \| 1.63 \| \| 7 \| 0.27 \| 1.99 \| 36.06 \| 0.99 \| 12.38 \| 1.62 \| \| 8 \| 0.27 \| 1.98 \| 36.05 \| 0.99 \| 12.36 \| 1.61 \| \| 9 \| 0.27 \| 1.97 \| 36.04 \| 0.99 \| 12.35 \| 1.60 \| \| 10 \| 0.27 \| 1.97 \| 36.04 \| 0.99 \| 12.33 \| 1.59 \| Q2* Response: The difference between Initial pass@1 v.s. SOAP pass@1 is only the SOAP-generated incorrect code. While the address method discussed in Q6 does not reflect in W3 & Q3, which means that with our solution in Q6, the incorrect code generated by SOAP in SOAP pass@1 will be replaced by the Initial generated code. Q3. We understand your concern about filtering out failed code in our evaluation. However, our approach is consistent with existing works in this field [1-6]. The primary reason for focusing only on correct code is that incorrect code may cause test cases to fail and terminate the execution process prematurely. Including such cases would lead to inaccurate results when measuring the efficiency of LLM-generated code. [1] Huang, Dong, Jie M. Zhang, Yuhao Qing, and Heming Cui. "EffiBench: Benchmarking the Efficiency of Automatically Generated Code." arXiv preprint arXiv:2402.02037 (2024). [2] Qiu, Ruizhong, Weiliang Will Zeng, Hanghang Tong, James Ezick, and Christopher Lott. "How Efficient is LLM-Generated Code? A Rigorous & High-Standard Benchmark." arXiv preprint arXiv:2406.06647 (2024). [3] Shi, Jieke, Zhou Yang, and David Lo. "Efficient and Green Large Language Models for Software Engineering: Vision and the Road Ahead." arXiv preprint arXiv:2404.04566 (2024). [4] Zheng, Jiasheng, Boxi Cao, Zhengzhao Ma, Ruotong Pan, Hongyu Lin, Yaojie Lu, Xianpei Han, and Le Sun. "Beyond Correctness: Benchmarking Multi-dimensional Code Generation for Large Language Models." arXiv preprint arXiv:2407.11470 (2024). [5] Waghjale, Siddhant, Vishruth Veerendranath, Zora Zhiruo Wang, and Daniel Fried. "ECCO: Can We Improve Model-Generated Code Efficiency Without Sacrificing Functional Correctness?." arXiv preprint arXiv:2407.14044 (2024). [6] Du, Mingzhe, Anh Tuan Luu, Bin Ji, and See-Kiong Ng. "Mercury: An efficiency benchmark for llm code synthesis." arXiv preprint arXiv:2402.07844 (2024). --- Rebuttal 3: Title: Friendly Reminder: Pending Reviewer Responses and Assessment Consideration Comment: Dear Reviewer 5c1j, Thank you for your review and comments on our paper on 13 Aug, we have provided the clarification and other experiment results to address your concern. Since the discussion period will be closed in the next six hours, while we do not receive the message about whether we have addressed all of your concerns, we would greatly appreciate it if you could take the time to review these results and consider improving your overall assessment of our paper based on these revisions. Thank you once again for your valuable feedback and for considering our request.	Summary: This paper presents SOAP, a new code generation approach that improves the efficiency of code generated by a LLM. SOAP adopts a self-refinement method that iteratively prompts the LLM to re-generate the code based on the profiling results. Specifically, it uses the line-profiler package in Pyhton to get the execution time profiling results and the memory_profiler package to get the memory usage profiling result. SOAP is evaluated on three benchmarks and 22 LLMs, including both 16 open-sourced and 6 closed-sourced models. The results show that SOAP can effectively improve the execution time and memory usage of code generated by most LLMs. While it slightly decreases the LLM's performance on functional correctness, the impact is small. Strengths: 1. SOAP is evaluated on multiple benchmarks and many LLMs. 2. The results look promising. 3. The paper is well-written and easy to follow. Weaknesses: 1. The technical novelty of this work is limited. The self-refinement method proposed in this work is very similar to existing self-refinement methods such as Self-Edit and Critic. The only difference is that SOAP uses profiling results while existing methods use testing results, etc. 2. The authors ignored existing work on using transformers or LLMs for code optimization. They should discuss these papers in the related work and also use them as comparison baselines. - Liu, Shengcai, et al. "Large language models as evolutionary optimizers." arXiv preprint arXiv:2310.19046 (2023). - Chen, Zimin, Sen Fang, and Martin Monperrus. "Supersonic: Learning to generate source code optimisations in c/c++." arXiv preprint arXiv:2309.14846 (2023). - Shypula, Alexander, et al. "Learning performance-improving code edits." arXiv preprint arXiv:2302.07867 (2023). 3. Section 4.3 compares SOAP with Self-Refine and Reflexion. It is unclear how Self-Refine and Reflexion were configured in this experiment. Did the authors use the original prompts from Self-Refine and Reflexion? Or did the authors modify their prompts to include instructions on code efficiency? If the former, there is a comparison fairness issue since the original prompts in Self-Refine and Reflexion are not designed for code optimization. If the latter, the authors should provide the prompts used in Self-Refine and Reflexion and justify the prompt design. 4. The experiments on the impact of step-optimization steps (Section 4.2) only include two big models. The findings may not be generalizable to smaller models. Why not also include some smaller models? 5. The experiments on the impact of functional correctness were only done on EffiBench. Since EffiBench is not specifically designed for functional code generation, the results may not be representative. The authors should also experiment with HumanEval and MBPP and report the pass@1 scores on these two benchmarks. Technical Quality: 2 Clarity: 3 Questions for Authors: 1. What is the key technical novelty of this work? 2. How would you compare SOAP with existing transformer or LLM-based code optimization work? 3. What are the prompts used in the experiments with Self-Refine and Reflexion? Confidence: 5 Soundness: 2 Presentation: 3 Contribution: 2 Limitations: The discussion on limitations looks reasonable. Flag For Ethics Review: ['No ethics review needed.'] Rating: 3 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your thoughtful review and insightful comments. We hereby address your concerns below: W1 & Q1: Novelty and Similarities with Self-Edit and Critic To address the reviewer’s concern about the novelty of SOAP in comparison to Self-Edit and Critic, we provide detailed evaluation results in Table below. These results demonstrate that SOAP outperforms both Self-Edit and Critic significantly. \| Optimization Profile \| ET (s) \| NET \| MU (Mb) \| NMU \| TMU (Mbs) \| NTMU \| \|---\|---\|---\|---\|---\|---\|---\| \|GPT-3.5-Turbo-0301\|\|\|\|\|\|\| \|InitialVersion\|0.36\|2.50\|91.25\|2.45\|157.50\|19.75\| \|Self-Edit\|0.42\|3.67\|59.86\|1.65\|24.87\|3.28\| \|Critic\|0.60\|4.25\|102.75\|2.82\|351.91\|46.39\| \|SOAP\|0.28\|2.01\|36.08\|0.99\|12.43\|1.64\| SOAP introduces a unique overhead profiler that significantly enhances the efficiency of LLM-generated code by optimizing both execution time and memory usage. In contrast, existing methods focus primarily on execution time and cannot comprehensively address efficiency concerns. Specifically, Critic requires progressive amendment of outputs, which does not effectively tackle efficiency-critical issues. The novelty of SOAP lies in two aspects: - Dual Optimization Focus: Unlike existing works that primarily target execution time, SOAP optimizes both execution time and memory usage, providing a more holistic approach to code efficiency. - Overhead Profile-Guided Optimization: SOAP utilizes overhead profiles, including execution time and memory usage profiles, to guide the optimization process. This allows SOAP to achieve SOTA results in efficiency, as demonstrated by our ablation studies. We would like to highlight that self-refinement is a broad direction with many published papers exploring various novelties. The specific challenge addressed by SOAP is improving the efficiency of LLM-generated code, a critical and valuable contribution to the field. Our experiments clearly show that the inclusion of overhead profiles significantly enhances optimization effectiveness compared to existing methods. W2 & Q2: Discuss and compare transformers or LLMs for code optimization.* We would like to highlight that SOAP and these methods [1,2,3] are orthogonal, which means we can combine SOAP and these efforts. LMEA [1] uses evolutionary search to generate more efficient code compared with the initial code, which requires 250+ solutions for each task to achieve optimal results, whereas SOAP only generates 5 solutions. LMEA requires massive token usage and execution time consumption. Due to limited time and resources during rebuttal, we are not able to conduct experiments with LMEA. However, we commit to include the results for LMEA in the revised manuscript. For Supersonic [2] and PIE [3], we conduct experiments in Author Rebuttal Table 1. For PIE, we conduct experiments for five different prompts. As shown in Table 1, the performance of these methods is further boosted when SOAP is applied to them. On average, PIE+Few-Shot requires 0.82s for each generated code to execute. While PIE+SOAP+Few-Shot generated code only requires 0.41s to execute. Ref: [1] Large language models as evolutionary optimizers. 2023 [2] Supersonic: Learning to generate source code optimizations in c/c++. 2023 [3] Learning performance-improving code edits. 2023 W3 & Q3: Prompts for Self-Refine and Reflexion For a fair comparison, we conduct experiments for baselines by revising the prompt used by SOAP in our experiments, which specifically requires LLMs to refine the coding efficiency. We provide the detailed prompts used in the paper in the Link: https://anonymous.4open.science/r/SOAP-FF6C/prompts.py W4: Step-optimization steps only include two big models. We provide three smaller models, i.e., OpenCodeInterpreter-1.3B, DeepSeek-1.3B-Ins, and CodeLlama-7B below. We can observe that SOAP consistently optimizes the efficiency of LLM-generated code for each optimization step. \| Steps \| ET (s) \| NET \| MU (Mb) \| NMU \| TMU (Mbs) \| NTMU \| \| --- \| --- \| --- \| --- \| --- \| --- \| --- \| \|OpenCodeInterpreter-1.3B\|\|\|\|\|\|\| \|0\|1.60\|1.52\|38.91\|1.00\|89.16\|1.11\| \|1\|1.60\|1.51\|38.91\|1.00\|88.77\|1.11\| \|2\|1.59\|1.51\|38.91\|1.00\|88.16\|1.10\| \|3\|1.59\|1.50\|38.91\|1.00\|87.85\|1.09\| \|4\|1.59\|1.50\|38.91\|1.00\|87.77\|1.09\| \|5\|1.29\|1.23\|38.91\|1.00\|70.63\|0.88\| \|DeepSeek-1.3B-Ins\|\|\|\|\|\|\| \|0\|1.42\|1.32\|36.04\|1.00\|40.61\|1.12\| \|1\|1.42\|1.23\|36.04\|1.00\|39.30\|1.09\| \|2\|1.42\|1.20\|36.04\|1.00\|37.99\|1.05\| \|3\|1.15\|1.16\|36.04\|1.00\|37.33\|1.03\| \|4\|1.15\|1.12\|36.04\|1.00\|36.43\|1.00\| \|5\|1.15\|1.07\|36.04\|1.00\|35.48\|0.98\| \|CodeLlama-7B\|\|\|\|\|\|\| \|0\|4.70\|3.68\|46.76\|0.99\|212.41\|1.93\| \|1\|4.59\|3.58\|38.94\|0.82\|165.16\|1.50\| \|2\|4.56\|3.55\|39.11\|0.82\|162.16\|1.47\| \|3\|4.56\|3.56\|39.03\|0.82\|161.98\|1.47\| \|4\|4.56\|3.55\|39.03\|0.82\|161.57\|1.47\| \|5\|4.52\|3.54\|38.67\|0.82\|157.76\|1.43\| SOAP for different optimization steps.* W5: Pass@1 on HumanEval and MBPP. As shown in the tables below, we provide the pass@1 for HumanEval+ and MBPP+, where the evalplus version is used in our experiments to measure the efficiency of LLM-generated code as it contains hundreds of tests. We can observe that the pass@1 of LLM-generated code only has merely changed for these benchmarks. The performance of our evaluated LLMs on HumanEval+ does not show a decrease. On MBPP+, the pass@1 decrease is only 0.0% and 0.84% for HumanEval+ and MBPP+, on average. Notably, for more powerful LLMs like GPT and Claude, the performance remains essentially unchanged. \| Model \| Initial pass@1 \| SOAP pass@1 \| \|---\|----\|----\| \|OpenCodeInterpreter-DS-1.3B\|30.5\|30.5\| \|CodeLlama-7b-Instruct-hf\|39.6\|39.6\| \|CodeLlama-70b-Instruct-hf\|45.7\|45.7\| \|gpt-3.5-turbo-030\|62.8\|62.8\| \|claude-3-sonnet\|59.1\|59.1\| Results on HumanEval+. \| Model \| Initial pass@1 \| SOAP pass@1 \| \|-------\|-----\|------\| \|OpenCodeInterpreter-DS-1.3B\|57.9\|55.8\| \|CodeLlama-7b-Instruct-hf\|40.7\|40.7\| \|CodeLlama-70b-Instruct-hf\|53.9\|52.1\| \|gpt-3.5-turbo-0301\|59.8\|59.5\| \|claude-3-sonnet\|58.4\|58.4\| Results on MBPP+. --- Rebuttal 2: Title: Friendly Reminder: Pending Reviewer Responses and Assessment Consideration Comment: Dear Reviewer H3VZ, Thank you for your review and comments on our paper. Since the discussion period will be closed in the next six hours, while we do not receive the message about whether we have addressed all of your concerns, we would greatly appreciate it if you could take the time to review these results and consider improving your overall assessment of our paper based on these revisions. Thank you once again for your valuable feedback and for considering our request. --- Rebuttal Comment 2.1: Title: Response to the rebuttal Comment: Thank you for the responses, and sorry for the late response due to a flurry of proposal and review dues. Regarding the novelty, would it be fair to say the essential difference to self-refine is the inclusion of the profiling results from the `line_profiler` library in the prompt? While I appreciate the authors' effort in conducting new experiments quickly in the short rebuttal period, I feel these results require another round of careful reviews, especially given that some results look quite surprising and counterintuitive. Without knowing more details and experiment settings, it is hard to make a full assessment of the correctness of the results. In particular, it's surprising to see that the pass@1 rates of all these models barely change after applying SOAP. Note that compared with the original code generation prompt, SOAP adds a lot of line-level profiling results, which significantly deviates from the original prompt. Presumably, we should see some deviations in pass@1, as LLMs are pretty sensitive to prompt design and including many profiling results may distract the LLM from reading the original task description. How did the authors keep the pass@1 rates almost unchanged? Furthermore, the evaluation results of PIE with CodeLlama7B look quite strange. The average execution time of code optimized by PIE is in the range of 0.4s to 0.9s. However, the execution time of CodeLlama7B in Table 1 is 4.7s before SOAP optimization and 4.52s after SOAP optimization. If the execution time after PIE optimization is correct, does this mean PIE can achieve 10x speed up compared with the initial code and the code optimized by SOAP alone? If that's the case, what's the point of applying SOAP on top of PIE given that PIE has already achieved such a big improvement? Overall, I feel this paper requires another round of careful reviews before it can be accepted. --- Rebuttal 3: Title: Response to Reviewer H3VZ Comment: Dear Reviewer H3VZ, Thanks for your response before the discussion period deadline, which allows us to further clarify the potential misunderstanding and concerns that would affect your overall assessment. First, compared with self-refine, SOAP utilizes line_profiler and memory profiler to catch the execution time and memory usage of each line in the LLM-generated code. Second, for the pass@1 of LLM-generated code of pre-SOAP and post-SOAP, we want to mention that in https://anonymous.4open.science/r/SOAP-FF6C/src/SOAP.py (Lines 177-Lines 185), we provide tolerance for SOAP that requires the SOAP optimized code can pass public test cases and then replace original code. If the optimized code can not pass the public test cases, SOAP optimized code will not replace the original code, and we will use the original code for the next step of optimization (Lines 184-185). In this step, the coverage of the public test cases would largely affect the correctness of the final SOAP-optimized code. After the empirical study, we observe that the code line coverage of EffiBench for public test cases achieves 99.24%, which makes sure that the pass@1 after the self-optimization process (SOAP) only has a few decreases, and even in some models, the pass@1 would not decrease. Third, we need to mention that PIE already trained CodeLlama with its provided code, which means that the pass@1 of PIE+CodeLlama-7B may be different, and the tasks addressed by PIE and the original CodeLlama are different. Then, some tasks with higher execution time (e.g., 4.7s) may not addressed by PIE-CodeLlama, and the default (initial) ET and other metrics are different. We hope that Reviewer H3VZ can understand this difference between the original CodeLlama and PIE-CodeLlama. We hope that our clarification can address Reviewer H3VZ's concern about I feel these results require another round of careful reviews, especially given that some results look quite surprising and counterintuitive.	Rebuttal 1: Rebuttal: # Tables included in the rebuttal to address the comments made by Reviewer H3VZ, Reviewer VC11, and Reviewer pc3i \|OptimizationProfile\|ET(s)\|NET\|MU(Mb)\|NMU\|TMU(Mbs)\|NTMU\| \|---\|---\|---\|---\|---\|---\|---\| \|GPT-3.5-Turbo-0301\|\|\|\|\|\|\| \|InitialVersion\|0.36\|2.50\|91.25\|2.45\|157.50\|19.75\| \|UnsupervisedSelf-Refine\|0.32\|2.46\|78.39\|2.12\|312.99\|42.42\| \|Result-AwareSelf-Refine\|0.30\|2.25\|58.65\|1.61\|195.49\|27.16\| \|Self-Edit\|0.42\|3.67\|59.86\|1.65\|24.87\|3.28\| \|Critic\|0.60\|4.25\|102.75\|2.82\|351.91\|46.39\| \|DirectlyEfficiency\|0.43\|3.03\|59.11\|1.67\|20.37\|2.88\| \|Self-RefineEfficiency\|0.40\|2.83\|59.11\|1.67\|18.80\|2.65\| \|IsSelf-Refine\|0.40\|2.88\|61.83\|1.81\|36.29\|5.69\| \|Self-Reasoning\|0.89\|6.21\|60.64\|1.62\|45.91\|5.61\| \|Self-Relfection\|0.81\|5.67\|60.64\|1.62\|39.35\|4.80\| \|SOAP\|0.28\|2.01\|36.08\|0.99\|12.43\|1.64\| \|CodeLlama7B(PIE:HQ+SelfPlay)\|\|\|\|\|\|\| \|PIE+Zero-Shot\|0.87\|5.73\|74.83\|1.81\|109.29\|9.69\| \|PIE+SOAP+Zero-Shot\|0.79\|5.41\|65.78\|1.68\|89.90\|7.84\| \|PIE+Few-Shot\|0.82\|5.58\|73.57\|1.74\|98.02\|8.92\| \|PIE+SOAP+Few-Shot\|0.41\|2.97\|73.10\|1.74\|59.69\|5.09\| \|PIE+CoT\|0.79\|5.14\|73.14\|1.74\|63.93\|5.35\| \|PIE+SOAP+COT\|0.45\|2.84\|71.15\|1.71\|58.06\|4.77\| \|PIE+DynamicRetrieval,k=4\|0.74\|5.36\|68.64\|1.51\|85.24\|7.78\| \|PIE+SOAP+DynamicRetrieval,k=4\|0.41\|3.36\|68.63\|1.51\|52.34\|4.52\| \|Supersonic\|\|\|\|\|\|\| \|Supersonic\|1.40\|10.33\|113.06\|3.18\|329.59\|56.24\| \|Supersonic+SOAP\|1.34\|9.91\|102.26\|2.87\|267.47\|45.64\| Author Rebuttal Table 1: Evaluation results of SOAP and baselines. Since the finetuned link for GPT-3.5-turbo from PIE is not available, we use the finetuned CodeLlama 7B for experiments.* \|Steps\|ET(s)\|NET\|MU(Mb)\|NMU\|TMU(Mbs)\|NTMU\| \|-------\|--------\|-----\|---------\|-----\|------------\|------\| \|gpt-3.5-turbo-0301\|\|\|\|\|\|\| \|InitialVersion\|0.37\|3.10\|66.91\|1.90\|20.89\|6.32\| \|SOAP\|0.28\|2.31\|67.31\|1.92\|15.66\|4.71\| \|gpt-3.5-turbo-0613\|\|\|\|\|\|\| \|InitialVersion\|0.37\|3.05\|66.99\|1.90\|20.92\|6.18\| \|SOAP\|0.32\|2.69\|67.09\|1.91\|18.40\|5.45\| \|gpt-3.5-turbo-1106\|\|\|\|\|\|\| \|InitialVersion\|0.37\|3.07\|66.94\|1.90\|20.78\|6.22\| \|SOAP\|0.32\|2.72\|66.98\|1.91\|18.29\|5.54\| \|gpt-4\|\|\|\|\|\|\| \|InitialVersion\|0.37\|3.06\|66.91\|1.90\|21.17\|6.17\| \|SOAP\|0.32\|2.69\|66.97\|1.91\|18.42\|5.36\| \|gpt-4-turbo-preview\|\|\|\|\|\|\| \|InitialVersion\|0.37\|3.10\|66.92\|1.90\|20.78\|6.28\| \|SOAP\|0.32\|2.67\|67.01\|1.91\|18.65\|5.42\| \|claude-3-haiku\|\|\|\|\|\|\| \|InitialVersion\|0.39\|3.27\|66.90\|1.90\|22.52\|6.68\| \|SOAP\|0.32\|2.65\|67.02\|1.91\|18.83\|5.42\| \|claude-3-sonnet\|\|\|\|\|\|\| \|InitialVersion\|0.38\|3.20\|66.93\|1.90\|21.52\|6.55\| \|SOAP\|0.32\|2.65\|66.95\|1.91\|18.30\|5.43\| Author Rebuttal Table 2: Evaluation results for five different LLMs on identical tasks verified by correct execution (210 tasks).* \|Steps\|ET(s)\|NET\|MU(Mb)\|NMU\|TMU(Mbs)\|NTMU\| \|-------\|--------\|-----\|---------\|-----\|------------\|------\| \|OpenCodeInterpreter-1.3B\|\|\|\|\|\|\| \|InitialVersion\|0.80\|5.74\|62.60\|1.61\|45.18\|5.63\| \|SOAP\|0.52\|3.73\|48.73\|1.25\|29.93\|3.73\| \|deepseek-coder-1.3b-instruct\|\|\|\|\|\|\| \|InitialVersion\|0.63\|4.57\|59.32\|1.64\|27.57\|5.49\| \|SOAP\|0.43\|3.10\|45.80\|1.27\|17.44\|3.47\| \|CodeLlama-7b-Instruct-hf\|\|\|\|\|\|\| \|InitialVersion\|3.98\|23.93\|103.78\|2.19\|370.74\|28.06\| \|SOAP\|3.41\|20.50\|89.37\|1.88\|335.53\|25.39\| \|CodeLlama-70b-Instruct-hf\|\|\|\|\|\|\| \|InitialVersion\|0.90\|7.34\|50.69\|1.91\|46.93\|21.07\| \|SOAP\|0.63\|5.18\|41.44\|1.56\|34.90\|15.67\| \|starcoder2-15b\|\|\|\|\|\|\| \|InitialVersion\|0.49\|1.88\|132.27\|1.17\|53.54\|1.18\| \|SOAP\|0.22\|0.86\|66.18\|0.59\|25.24\|0.56\| \|gpt-3.5-turbo-0301\|\|\|\|\|\|\| \|InitialVersion\|0.68\|4.83\|102.39\|2.82\|302.04\|39.98\| \|SOAP\|0.39\|2.77\|42.67\|1.18\|18.57\|2.46\| \|claude-3-sonnet\|\|\|\|\|\|\| \|InitialVersion\|0.74\|5.20\|64.02\|1.76\|56.85\|7.29\| \|SOAP\|0.51\|3.60\|46.88\|1.29\|27.24\|3.49\| Author Rebuttal Table 3: Evaluation results of SOAP and baselines in PIE provided default simulator. We use the default simulator provided by PIE for our experiments.* \|Model\|ExecutionTime(s)\|TokenUsage(million)\|PerIterationInput/OutputTaskTokenUsage(K)\| \|-------\|-------------------\|----------------------\|--------------------------------------------------\| \|InitialVersion\|76.81\|1.1\|1.1\| \|UnsupervisedSelf-Refine\|416.81\|3.9\|1.1602\| \|Result-AwareSelf-Refine\|419.24\|3.9\|1.1602\| \|LineProfiler\|555.68\|4.7\|1.4888\| \|MemoryProfiler\|536.26\|4.7\|1.4888\| \|SOAP\|566.67\|5.4\|1.7805\| Author Rebuttal Table 4: Overhead of different code efficiency optimization prompt engineering methods for GPT-3.5-turbo. \|Steps\|CoV of ET(%)\|CoV of NET(%)\|CoV of MU(%)\|CoV of NMU(%)\|CoV of TMU(%)\|CoV of NTMU(%)\| \|-------\|---------------\|----------------\|---------------\|----------------\|----------------\|-----------------\| \|OpenCodeInterpreter-DS-1.3B\|2.5\|2.5\|2.5\|2.5\|2.5\|2.5\| \|deepseek-coder-1.3b-instruct\|1.7\|1.7\|1.7\|1.7\|1.7\|1.7\| \|CodeLlama-7b-Instruct-hf\|0.3\|0.3\|0.3\|0.3\|0.3\|0.3\| \|CodeLlama-70b-Instruct-hf\|1.7\|1.7\|1.7\|1.7\|1.7\|1.7\| \|starcoder2-15b\|1.6\|1.6\|1.6\|1.6\|1.6\|1.6\| \|gpt-3.5-turbo-0301\|0.6\|0.6\|0.6\|0.6\|0.6\|0.6\| \|claude-3-sonnet\|0.2\|0.2\|0.2\|0.2\|0.2\|0.2\| Author Rebuttal Table 5: Overall coefficient of variation from five executions of SOAP for each metric and model in EffiBench. We conducted the experiments five times, then calculated the mean and std for each metric and model. \| Steps \| ET (s) \| NET \| MU (Mb) \| NMU \| TMU (Mbs) \| NTMU \| \| --- \| --- \| --- \| --- \| --- \| --- \| --- \| \|OpenCodeInterpreter-1.3B\|\|\|\|\|\|\| \|0\|1.60\|1.52\|38.91\|1.00\|89.16\|1.11\| \|1\|1.60\|1.51\|38.91\|1.00\|88.77\|1.11\| \|2\|1.59\|1.51\|38.91\|1.00\|88.16\|1.10\| \|3\|1.59\|1.50\|38.91\|1.00\|87.85\|1.09\| \|4\|1.59\|1.50\|38.91\|1.00\|87.77\|1.09\| \|5\|1.29\|1.23\|38.91\|1.00\|70.63\|0.88\| \|DeepSeek-1.3B-Ins\|\|\|\|\|\|\| \|0\|1.42\|1.32\|36.04\|1.00\|40.61\|1.12\| \|1\|1.42\|1.23\|36.04\|1.00\|39.30\|1.09\| \|2\|1.42\|1.20\|36.04\|1.00\|37.99\|1.05\| \|3\|1.15\|1.16\|36.04\|1.00\|37.33\|1.03\| \|4\|1.15\|1.12\|36.04\|1.00\|36.43\|1.00\| \|5\|1.15\|1.07\|36.04\|1.00\|35.48\|0.98\| \|CodeLlama-7B\|\|\|\|\|\|\| \|0\|4.70\|3.68\|46.76\|0.99\|212.41\|1.93\| \|1\|4.59\|3.58\|38.94\|0.82\|165.16\|1.50\| \|2\|4.56\|3.55\|39.11\|0.82\|162.16\|1.47\| \|3\|4.56\|3.56\|39.03\|0.82\|161.98\|1.47\| \|4\|4.56\|3.55\|39.03\|0.82\|161.57\|1.47\| \|5\|4.52\|3.54\|38.67\|0.82\|157.76\|1.43\| Author Rebuttal Table 6: Evaluation results of SOAP for different optimization step.*	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
UniMoT: Unified Molecule-Text Language Model with Discrete Token Representation	Reject	Summary: The authors propsed Uni-MoT, a unified structure to align molecules with texts with a VQ tokenizer and the Q-Former in BLIP-2. By treating molecules as new word tokens in the codebook, Uni-MoT aligns the discrete token representation for molecules and texts, while also following the autoregressive manner of LLMs. The training of Uni-MoT follows four main stages, Causal Q-Former Pretraining, Molecule Tokenizer Pretraining, Unified Molecule-Text Pretraining, Task-Specific Instruction Tuning. The experiments demonstrate that Uni-MoT can achieve better performance compared to the selected baselines. Strengths: 1. The performance of Uni-MoT is overall good and better than the baseline models. 2. Uni-MoT provides a alternative solution for aliging molecules with texts. Weaknesses: 1. Although the authors claim that Uni-MoT follows a different structure as shown in Figure 1 c, it turns out that it still follows the BLIP-2 [1] structure, which has been widely used to align 2D molecule graph [2] and 3D molecule information [3]. Thus, the technical contribution and novelty of this paper are extremely limited. Especially when VQ-VAE [4] is also a well-developed structure adopted in computer vision. This paper is more like simply swapping the input of the Q-former in BLIP-2. 2. The experiments are only conducted on a single serie of LLM, Llama-2, which is not sufficient to demonstrate the model agnosticsm of Uni-MoT. In fact, LLMs like Mistral [5] and Meditron [6] might possibly achieve a better performance. Meanwhile, the selection of Llama-2 is also not convincing, as Llama-2 is not specially pre-trained on chemistry or biomedical corpora. 3. The seletion of the datasets is also worth discussion. The result on ChEBI-20 is presented in Appendix, while the main experiments are conducted on PubChem. I am wondering why not also conduct the remaining experiments on ChEBI-20, as the data scale of ChEBI-20 is much larger than PubChem. At the same time, the reverse task, text-based molecule generation, on ChEBI-20 and PubChem is surprisingly not presented. 4. The comparison with the baselines is not fair enough. For example, MolCA adopts Galactica-1.3B as its backbone model, which is much smaller than Llama-2-7B. Thus, the proposed method can not demonstrate its superiority compared to previous methods. Notably, since the authors mentioned MolCA and 3D-MoLM, it is necessary to discuss the possible affects of the modalities. Furthermore, several SOTA baseline models like BioT5 [7] and BioT5+ [8] are not discussed. 5. The ablation study is also not sufficient without providing the naive fine-tuning performance of Llama-2. Besides, as Uni-MoT incorporates the VQ tokenizer, it is also important to discuss the size of the codebook. 6. During the pre-training stages, it should ensure that the data leakage is avoided. Considering the pre-training dataset adopted has overlaps with the fine-tuning dataset [7, 8], the performance gain could possibly come from the data leakage. 7. Some claims and definitions are confusing. e.g. In Line 44, "a unified molecule-text LLM", I do not agree with the claim of an "LLM". The "LLM" is still the Llama-2. It should be like "structure" or something. #### References [1 ]Li, J., Li, D., Savarese, S., & Hoi, S. (2023, July). Blip-2: Bootstrapping language-image pre-training with frozen image encoders and large language models. In International conference on machine learning (pp. 19730-19742). PMLR. [2] Liu, Z., Li, S., Luo, Y., Fei, H., Cao, Y., Kawaguchi, K., ... & Chua, T. S. (2023). Molca: Molecular graph-language modeling with cross-modal projector and uni-modal adapter. arXiv preprint arXiv:2310.12798. [3] Li, S., Liu, Z., Luo, Y., Wang, X., He, X., Kawaguchi, K., ... & Tian, Q. (2024). Towards 3D Molecule-Text Interpretation in Language Models. arXiv preprint arXiv:2401.13923. [4] Yu, J., Li, X., Koh, J. Y., Zhang, H., Pang, R., Qin, J., ... & Wu, Y. (2021). Vector-quantized image modeling with improved vqgan. arXiv preprint arXiv:2110.04627. [5] Jiang, A. Q., Sablayrolles, A., Mensch, A., Bamford, C., Chaplot, D. S., Casas, D. D. L., ... & Sayed, W. E. (2023). Mistral 7B. arXiv preprint arXiv:2310.06825. [6] Chen, Z., Cano, A. H., Romanou, A., Bonnet, A., Matoba, K., Salvi, F., ... & Bosselut, A. (2023). Meditron-70b: Scaling medical pretraining for large language models. arXiv preprint arXiv:2311.16079. [7] Pei, Q., Zhang, W., Zhu, J., Wu, K., Gao, K., Wu, L., ... & Yan, R. (2023). Biot5: Enriching cross-modal integration in biology with chemical knowledge and natural language associations. arXiv preprint arXiv:2310.07276. [8] Pei, Q., Wu, L., Gao, K., Liang, X., Fang, Y., Zhu, J., ... & Yan, R. (2024). BioT5+: Towards Generalized Biological Understanding with IUPAC Integration and Multi-task Tuning. arXiv preprint arXiv:2402.17810. Technical Quality: 2 Clarity: 3 Questions for Authors: 1. Could the authors conduct the experiments on more backbone LLMs? For example, on Galactica-1.3B, is the performance better than MolCA? Or on Llama-2-7B, is the performance still better than MolCA(Llama-2-7B)? 2. Could the authors justify the selection of the datasets? 3. Could the authors compare the proposed method with stronger baselines? Let's say, when the authors claim the SOTA performance, it should be noted BioT5 and BioT5+ are not included in discussion. 4. Could the authors provide more solid ablation study? My main questions are listed above, but I do expect the authors could discuss more about their weaknesses. Confidence: 5 Soundness: 2 Presentation: 3 Contribution: 1 Limitations: Yes. They have discussed the limitations as not enough tasks, data scarcity, and real scenarios. Flag For Ethics Review: ['No ethics review needed.'] Rating: 2 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: > W1. Limited novelty. We would like to clarify that the Q-Former is only a part of our VQ-driven tokenizer. UniMoT does not follow the BLIP-2 structure in its entirety. UniMoT adopts a tokenizer-based architecture, which uses discrete tokens, fundamentally different from adapter-based architectures that use continuous embeddings, such as MolCA and 3D-MoLM. We would like to clarify the novel aspects of our work to address your concerns. Due to space constraints, please refer to the global rebuttal for details on the novelty of our work. > W2. Different backbone LLMs. We have extended our experiments to include additional LLMs to validate the generalizability of UniMoT. The performance is shown in Table 1 of the global rebuttal PDF. Our experiments show that UniMoT performs well across multiple LLMs, including Galactica and Mistral series, demonstrating its robustness and generalizability. This confirms that UniMoT can be successfully applied to other SOTA LLMs. Llama-2 was chosen initially due to its versatility and performance in handling diverse data types. While it may not be pre-trained specifically on chemistry or biomedical corpora, our pre-training and fine-tuning processes on relevant datasets make sure that the model learns the necessary domain-specific information. > W3 & Q2. Selection of datasets. The PubChem dataset is significantly larger than the ChEBI-20 dataset. This allows for more comprehensive pretraining. The table below summarizes the size of both datasets: \| \| Pretrain \| Train \| Valid \| Test \| \| :------- \| :------- \| :----- \| :---- \| :---- \| \| PubChem \| 301,658 \| 12,000 \| 1,000 \| 2,000 \| \| ChEBI-20 \| - \| 26,407 \| 3,300 \| 3,300 \| The ChEBI-20 dataset replaces molecular names with “the molecule,” focusing the model on properties rather than names. However, accurately predicting molecular names demonstrates the model’s understanding of molecular structures. Thus, we conducted the main experiments on PubChem. For molecule generation tasks, we utilized the Mol-Instructions benchmark. The caption-guided molecule generation task within this benchmark actually uses the PubChem dataset. > W4 & Q1. Models with comparable sizes. We provide a detailed performance comparison between UniMoT and MolCA using models of comparable sizes. The performance is shown in Table 2 of the global rebuttal PDF. UniMoT consistently outperforms MolCA when using the same Galactica-125M, Galactica-1.3B, and Llama-2-7B backbones. This demonstrates the effectiveness of our proposed UniMoT. For the modalities, adapter-based architectures require the LLM to directly output SMILES strings to perform molecule generation tasks. This approach relies on strong alignment between SMILES strings and molecule captions during pretraining. In practice, this alignment is challenging to establish, leading to suboptimal performance in text-to-molecule generation tasks. Our UniMoT treats molecular and textual data equally under a unified token representation. This enables the LLM to unify the modalities under a shared autoregressive training paradigm. The molecule tokens encapsulate high-level molecular and textual information, providing a richer representation than SMILES strings alone. > Q3. BioT5 and BioT5+ baselines. We have included BioT5 and BioT5+ in our comparative analysis. We selected the molecule captioning task from the molecule comprehension tasks with the molecule generation tasks. The results are presented in Tables 3 and 4 of the global rebuttal PDF. These comparisons demonstrate the comparable performance of our model with BioT5 and BioT5+ in comprehension and generation tasks. In future revisions, we will incorporate performances of BioT5 and BioT5+ to provide a more comprehensive comparison. > W5 & Q4. Ablation studies on fine-tuning strategy and codebook size. We would like to highlight that we have indeed provided the performance of full fine-tuning of Llama-2-7B in Table 6 of our manuscript. The pre-trained Llama-2-7B model was directly fine-tuned on the task-specific dataset without any specialized techniques. The choice of 2048 for the molecule codebook size is based on a balance between model complexity and performance. A larger codebook could potentially capture more subtle interactions between molecules and text. However, there may be some codes that are not often used on large codebooks. A smaller codebook may result in nearby embeddings being assigned the same code, which reduces the granularity of the representation. The performance with different codebook sizes on the molecule captioning task is shown in Table 5 of the global rebuttal PDF. The results demonstrate that the codebook size of 2048 consistently provides the best performance. > W6. Data leakage. We appreciate the concern regarding potential data leakage. We take steps to ensure that data leakage is avoided throughout our training process. We list the datasets employed at each stage: - Stage 1: Causal Q-Former Pretraining - Datasets: PubChem pretrain subset - Stage 2: Molecule Tokenizer Pretraining - Datasets: PubChem pretrain subset, CheBI-20 train subset - Stage 3: Unified Molecule-Text Pretraining - Datasets: PubChem pretrain subset, CheBI-20 train subset - Stage 4: Task-Specific Instruction Tuning - Datasets: PubChem, PCdes, MoMu, MoleculeNet, QM9, USPTO (all train subsets) >W7. The terminology. Thank you for your feedback regarding the terminology. When we refer to “a unified molecule-text LLM,” we mean that the LLM can process input sequences that may be purely molecular, purely textual, or multi-modal (combining both molecules and text). This capability is achieved through treating molecular and textual data equally under a unified token representation. The LLM learns to predict the next token in a sequence, regardless of whether the sequence consists of molecules, text, or a combination of both. --- Rebuttal 2: Title: Reviewer Response Comment: Thanks for the clarification and extended experiments. * W1: As the author explained, the model structure is exactly similar to MolCA and 3D-MoLM. In this case, the novelty should be further discussed and I personally don’t see enough novelty in the model structure. * W3: I do not agree with the statement of the dataset size. The training part of PubChem is only 12000 samples, while ChEBI-20 is even double. The performance comparison is unfair because you introduce more related data. * W6: Still not guarantee that the data will not leak during the pretraining stages. * W7: I don’t think so. --- Rebuttal 3: Title: Response to Reviewer pDSz (1/2) Comment: Thank you for your thorough review and valuable feedback. Below, we address the further concerns you have raised in detail. > I personally don’t see enough novelty in the model structure. We respectfully disagree with the assessment that the model structure is similar to MolCA and 3D-MoLM. The architecture of UniMoT is fundamentally different from these models. Specifically: 1. Model Architecture: - MolCA and 3D-MoLM: These models follow the Q-Former architecture, as depicted in Figure 1(b) of our paper. In this architecture, the input to the LLM is molecule embeddings. - UniMoT: Our model employs a VQ-VAE architecture, as illustrated in Figure 1(c). The key difference lies in the input to the LLM: UniMoT uses molecule tokens instead of embeddings. 2. Supervision Signal for Molecule Modality: - MolCA and 3D-MoLM: These models do not incorporate any supervision signal for the molecule modality. This limitation significantly constrains their capacity and effectiveness. - UniMoT: In contrast, UniMoT provides direct supervision for the molecule tokens through autoregressive pretraining. This allows for stronger generation abilities and enables the molecule tokens to be decoded into molecules. 3. Text-to-Molecule Generation: - MolCA and 3D-MoLM: These models rely solely on SMILES strings for text-to-molecule generation tasks. This heavily relies on strong alignment between SMILES strings and molecule captions during pretraining. In practice, achieving this alignment is challenging, leading to suboptimal performance in text-to-molecule generation tasks. - UniMoT: Our model not only supports text-to-molecule generation but also benefits from the direct supervision of molecule tokens, leading to improved accuracy in generation tasks. The molecule tokens encapsulate high-level molecular and textual information, providing a richer representation than SMILES strings alone. 4. Cross-Modal Alignment: - MolCA and 3D-MoLM: These models rely heavily on the Q-Former for cross-modal alignment, which can be restrictive in certain scenarios. - UniMoT: Our approach allows for the Q-Former to be discarded entirely. Instead, we quantize the molecule features into molecule tokens using the VQ-VAE pipeline, with a codebook size of 1024. We report the performance of the molecule captioning task on the PubChem dataset. This demonstrates that the performance remains comparable even without the Causal Q-Former. \| \| BLEU-2 \| BLEU-4 \| ROUGE-1 \| ROUGE-2 \| ROUGE-L \| METEOR \| \| -------------------------- \| :----- \| :----- \| :------ \| :------ \| :------ \| :----- \| \| UniMoT w/o Causal Q-Former \| 28.1 \| 20.8 \| 33.2 \| 20.7 \| 30.1 \| 30.8 \| \| UniMoT w/ Causal Q-Former \| 31.3 \| 23.8 \| 37.5 \| 23.7 \| 33.6 \| 34.8 \| > I do not agree with the statement of the dataset size. - The PubChem training set is divided into two distinct subsets: a pretraining subset and a training subset. These subsets do not intersect, which ensures that data leakage is avoided. Specifically, the pretraining subset (301,658 molecule-text pairs) is used exclusively for pretraining the model. And the training subset (12,000 molecule-text pairs) is reserved for instruction tuning. - ChEBI-20 only has a single training set, which consists of 26,407 pairs. This set is used solely for pretraining. When comparing dataset sizes, it is important to consider the relevant subsets. The PubChem pretraining subset (301,658 pairs) is significantly larger than the ChEBI-20 training set (26,407 pairs). This is why we chose to use PubChem for pretraining, following a practice as used in InstructMol, MolCA, and 3D-MoLM. > The performance comparison is unfair because you introduce more related data. We would like to clarify why the performance comparison is indeed fair. The ChEBI-20 dataset replaces molecular names with “the molecule,” which shifts the model's focus toward predicting molecular properties rather than specific names. However, accurately predicting molecular names is crucial for demonstrating a model’s understanding of molecular structures. To address this, we conducted experiments on both PubChem and ChEBI-20, and the results for ChEBI-20 are presented in the Appendix, while the main experiments on PubChem are included in the main text. All baseline models were evaluated on the same PubChem test set on the experiments in the main text. Since recent baselines like MolCA, 3D-MoLM, and InstructMol also use PubChem for pretraining, our comparison is consistent and fair. --- Rebuttal 4: Title: Response to Reviewer pDSz (2/2) Comment: > Still not guarantee that the data will not leak during the pretraining stages. We can assure that data leakage is effectively prevented during the pretraining and instruction tuning stages. Here's how we ensure this: - The PubChem dataset is carefully divided into two distinct subsets. The pretraining subset is exclusively used during the pretraining stages. And the training subset is reserved for instruction tuning. These subsets do not intersect, ensuring that data used for instruction tuning is entirely separate from the data used during pretraining. - The additional datasets used during the instruction tuning stage (PCdes, MoMu, MoleculeNet, QM9, USPTO) are also separate and distinct from the datasets used in the pretraining stages. These datasets do not appear in the pretraining phase, ensuring that there is no overlap or data leakage. Thank you for your interest in our work. Your insightful comments have contributed to strengthening our paper. Should you have any questions or require additional information, please do not hesitate to contact us. --- Rebuttal 5: Title: Reviewer Response Comment: Thanks to the authors for explaining my concerns. #### However, I hope to clarify my views again considering the model structure. 1. The model structure and model components proposed in this paper have already been used in the field of Computer Vision. The authors brought nothing new. In other words, the authors assemble the Q-Former with the VQ-VAE. 2. Although the authors claim they have better "cross-modal alignment", the benefits are not satisfying at all. We can call it a small improvement, but I don't see enough potential for this work to further benefit the community, as well as the development of computational biology. Frankly speaking, this work still does not align molecular graphs well with texts, and it can not help chemists save their workload. #### The dataset size I never see anyone compare their pretraining dataset with the downstream training set. #### Unfair comparison The responses did not address the problem well. Let's change the question. When comparing the downstream performance between Mistral-7B and Llama-2-7B, Mistral-7B shows better performance. Then we could say that the pre-training of Mistral-7B is better. However, when both the two models are adopted in your model structure, is it still fair to say it is your model structure that brings the improvement? No. The performance gain is partly from pre-training. When you compare your method with the previous baselines, how could you ensure that your model structure is better? #### data leakage I don't think the authors answered my question. Yes, the datasets are not used in pertaining. However, there are molecules in downstream tasks that appear in your pre-training set. When you pre-train the model, the information has already been leaked. It is worth noting that in the work of BioT5, the authors did a special operation that removed all the overlapping molecules from the pre-training set. Overall, I strongly believe this work is not qualified to be accepted, and these issues should be further addressed. I will maintain my score.	Summary: This work presents a new molecule LLM that uses a pretrained tokenizer to replace the projection layer. The tokenizer consists a Q-Former and a VQ module, which are trained with consistency loss. The model is evaluated on molecular understanding and generation tasks. Strengths: - The authors provided a novel framework to align text representation in LLMs and the molecules. - The authors conducted experiments on many datasets. Weaknesses: - The claim that adapter-based methods cannot do text-to-molecule generation tasks in not accurate (Sec.1). They can always adapt text-encoder to a pre-trained SMILES or graph generator. This may make this work not well motivated. - In the tokenizer (Fig.2), it seems that multiple alignment methods are required to train the model, including: (1)the molecule and text contrastive in Q-Former, (2), the aligning MSE loss, (3) the SMILES decoder reconstruction. It's not clear about the design reasons, and if all of them are required. - Given the learnable query has a fixed size, it may not perform well for larger molecules. Technical Quality: 2 Clarity: 2 Questions for Authors: - In Sec 3.3, what are the data that used in different stages? - In Fig. 1, the model can output both molecule and text at the same time. But in Fig. 3, seems only text or molecule get loss for back propagation. Is this consistent and can authors share more training details? - In all experiments, does this model pretrained with same data as all baselines? Confidence: 4 Soundness: 2 Presentation: 2 Contribution: 2 Limitations: Yes Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: > W1. Text-to-molecule generation tasks. As Reviewer d9hA pointed out, adapter-based architectures can also perform text-to-molecule generation tasks. We will revise the manuscript accordingly. However, our contention is that such methods typically do not perform as well as our approach, as demonstrated in Table 4 of our paper. Here, we elaborate on the key differences and advantages of tokenizer-based architecture over adapter-based architectures: - Limitations of Adapter-Based Architectures: Adapter-based architectures require the LLM to directly output SMILES strings to perform molecule generation tasks. This approach relies heavily on strong alignment between SMILES strings and molecule captions during pretraining. In practice, this alignment is challenging to establish, leading to suboptimal performance in text-to-molecule generation tasks. - Advantages of Tokenizer-Based Architecture: Our method leverages a tokenizer to convert molecular features and text captions into molecule tokens. These tokens encapsulate high-level molecular and textual information, providing a richer representation than SMILES strings alone. By linking molecule tokens generated by the tokenizer to the molecule captions during molecule-to-text and text-to-molecule pretraining, our approach ensures that the model learns to understand and generate molecule tokens in an autoregressive manner. > W2. Alignment methods. We outline the purpose and necessity of each alignment method below: - Molecule-Text Contrastive Learning: Molecule-Text Contrastive Learning is employed solely in Stage 1: Causal Q-Former Pretraining. The primary objective here is to align the molecule features with the text captions, ensuring that the queries incorporate aligned molecular and textual information. This contrastive learning helps the Causal Q-Former to understand and relate molecular structures with their corresponding textual descriptions. - Aligning MSE Loss: The aligning MSE loss is used exclusively in Stage 2: Molecule Tokenizer Pretraining. Its purpose is to align the discrete latent space of molecule tokens with the continuous latent space of a molecular generative model. The alignment ensures that the tokenized representation can be mapped to the decoder's latent space. - SMILES Decoder Reconstruction: The reconstruction is primarily relevant during inference. During training, we focus on obtaining the reconstruction loss (the aligning MSE loss) to perform back-propagation. The actual reconstruction of the molecule via the SMILES decoder is done during inference to generate the final molecular output. > W3. Fixed size of queries. The design of our Causal Q-Former effectively addresses the concern regarding the fixed size of the queries through attention mechanisms: - Self-Attention Mechanism: Although the query size is fixed, the Causal Q-Former employs a dynamic self-attention mechanism for the queries. This allows the model to adaptively capture molecular details necessary for understanding and generating textual descriptions. - Cross-Attention Mechanism: The Causal Q-Former also utilizes a cross-attention mechanism where the queries selectively attend to different aspects of the molecule features. This allows the model to adaptively focus on different parts of the molecule based on its complexity and size. We also conducted an ablation study to evaluate the performance of UniMoT with different query sizes, as presented in Table 6 of the global rebuttal PDF. The results show that increasing the query size improves performance, with the best results observed at a query size of 32. However, since a query size of 32 requires significantly more training time and memory, we still opt to use a query size of 16. > Q1. Datasets usage. Below, we provide a list of the specific datasets employed at each stage: - Stage 1: Causal Q-Former Pretraining - Datasets: PubChem pretrain subset - Stage 2: Molecule Tokenizer Pretraining - Datasets: PubChem pretrain subset, CheBI-20 train subset - Stage 3: Unified Molecule-Text Pretraining - Datasets: PubChem pretrain subset, CheBI-20 train subset - Stage 4: Task-Specific Instruction Tuning - Datasets: PubChem, PCdes, MoMu, MoleculeNet, QM9, USPTO (all train subsets) > Q2. Different outputs in Figures 1 and 3. Yes, it is consistent. Figure 1 is designed to convey the core idea of our method. It shows the autoregressive prediction of molecule and text tokens. When data is organized as interleaved molecule and text tokens, the model can predict the next token (whether it is a molecule or text) indiscriminately. Each token prediction is supervised, and learning occurs across both types of tokens. Figure 3 illustrates the separate supervision of molecule and text tokens adopted in Stage-3, which is the practical implementation of our training process. Instead of using an interleaved organization of molecule and text tokens, we use the dataset as provided, consisting of molecule-text pairs. This involves two tasks: - Molecule-to-text autoregression: Using molecule tokens as a prompt to supervise and generate text. - Text-to-molecule autoregression: Using text as a prompt to supervise and generate molecule tokens. We utilize the PubChem and CheBI-20 datasets for the unified molecule-text pretraining. > Q3. Datasets with baselines. We provide a list of the datasets used for pretraining and fine-tuning UniMoT and the baselines: - UniMoT: - Pretraining: PubChem and CheBI-20 - Fine-Tuning: Specific task datasets - MolT5: - Pretraining: Colossal Clean Crawled Corpus (C4) and ZINC - Fine-Tuning: CheBI-20 - InstructMol: - Pretraining: PubChem - Fine-Tuning: Specific task datasets - MolCA: - Pretraining: PubChem - Fine-Tuning: PubChem - 3D-MoLM: - Pretraining: PubChem - Fine-Tuning: 3D-MoIT	Summary: The authors propose to use a vector-quantized tokenizer that incorporates a Q-Former to connect pre-trained molecule encoder, SMILES encoder, and SMILES decoder so that a language model can integrate molecule and text modalities. Based on the proposed tokenizer, the authors introduce a four-stage training strategy to train UniMoT, a unified molecule-text LLM proposed in this submission. The performance of the UniMoT is evaluated empirically with 7 tasks in the areas of molecule comprehension and molecule generation. Some ablation studies are also conducted. Strengths: - This paper is well-organized and well-written. - Using a vector-quantized tokenizer and a Q-Former to connect different modalities could be somewhat novel. - The proposed UniMoT outperforms baselines in most cases and reach comparable performances in others. - The authors provide many implement details which increases the reproducibility. Weaknesses: - All the components are borrowed from existing works. Besides the pre-trained molecule encoder, SMILES encoder and decoder, both vector quantization and Q-Former are proposed in previous works [1][2]. The Q-Former part of this paper (Appendix A) is very similar to Q-Former's original paper. Even Figure 4 in this paper is very similar to Figure 2 in Q-Former's original paper [2]. - When generating molecules the proposed method relies heavily on a pre-trained decoder. In the decoder's original paper, the reported validity is 99.9 and no guarantee is provided that the generated SMILES string will be always valid [3]. The 100% validity reported in this paper could be attributed to overfitting. - Some hyperparameter choices are not well justified and studied. For instance, the molecule codebook size is set to 2048, but there is no explanation why 2048 is chosen. How the molecule codebook size affects the performance is also not studied. - There are some existing works about molecule tokenizers [4][5], the paper lacks the comparison of the performance using different tokenizers. - The robustness of the model is not studied. Each molecule has many synonyms, how the proposed method performs given different synonyms of the same molecule is desired to know. [1] Van Den Oord, Aaron, and Oriol Vinyals. "Neural discrete representation learning." Advances in neural information processing systems 30 (2017). [2] Li, Junnan, et al. "Blip-2: Bootstrapping language-image pre-training with frozen image encoders and large language models." International conference on machine learning. PMLR, 2023. [3] Irwin, R., Dimitriadis, S., He, J., Bjerrum, E.J., 2021. Chemformer: A Pre-Trained Transformer for Computational Chemistry. Mach. Learn. Sci. Technol. [4] Li, Xinhao, and Denis Fourches. "SMILES pair encoding: a data-driven substructure tokenization algorithm for deep learning." Journal of chemical information and modeling 61.4 (2021): 1560-1569. [5] Schwaller, Philippe, et al. "Molecular transformer: a model for uncertainty-calibrated chemical reaction prediction." ACS central science 5.9 (2019): 1572-1583. Technical Quality: 2 Clarity: 3 Questions for Authors: - How do you guarantee that the output SMILES string will be 100% valid? - Why the molecule codebook size is chosen as 2048? How will the performance change when the codebook size is changed? - If you use other molecule tokenizers, how will the performance change? - When pre-training with PubChem dataset, what is the input text for each molecule since there are many entries and synonyms for each molecule? - How do you solve the problem that a molecule has many synonyms? Will your method output different answers if different synonyms of the same molecule are used in the prompt? Confidence: 4 Soundness: 2 Presentation: 3 Contribution: 2 Limitations: The authors have adequately addressed the limitations. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: > W1. Limited novelty. While we use components from existing works like Q-Former, the molecule encoder, and the SMILES encoder and decoder, we adopt a tokenizer-based architecture that uses discrete tokens. This is fundamentally different from adapter-based architectures that use continuous embeddings. Figure 4 is directly adapted from Figure 2 of Q-Former's original paper to illustrate related concepts and objectives of Causal Q-Former. We would like to clarify the novel aspects of our work to address your concerns. Due to space constraints, please refer to the global rebuttal for details on the novelty of our work. > W2 & Q1. The validity of generated molecules. Our model is pre-trained on extensive datasets of valid molecules, such as PubChem, which contain 0.3M of structurally diverse and chemically valid SMILES strings. This large-scale pre-training helps the model learn a robust representation of valid molecular structures. After the initial pre-training, we fine-tune our model on datasets composed exclusively of valid molecules. This fine-tuning process reinforces the learned characteristics of valid SMILES strings. Our empirical validation shows that while a few invalid molecules are generated when testing, these occurrences are rare and do not affect the overall validity rate. > W3 & Q2. Ablation study on codebook size and query size. The choice of 2048 for the molecule codebook size is based on a balance between model complexity and performance. A larger codebook could potentially capture more subtle interactions between molecules and text. However, there may be some codes that are not often used on large codebooks. A smaller codebook may result in nearby embeddings being assigned the same code, which reduces the granularity of the representation. We conducted experiments with different codebook sizes and report the performance of the molecule captioning task on the Pubchem dataset. The performance with different codebook sizes is shown in Table 5 of the global rebuttal PDF. The results demonstrate that the codebook size of 2048 consistently provides the best performance. We also conducted an ablation study to evaluate the performance of UniMoT with different query sizes, as presented in Table 6 of the global rebuttal PDF. The results show that increasing the query size improves performance, with the best results observed at a query size of 32. However, since a query size of 32 requires significantly more training time and memory, we still opt to use a query size of 16. > W4 & Q3. Comparison with different tokenizers. Difference from Existing Tokenizers: - The cited works [4] and [5] focus on SMILES tokenizers, which primarily tokenize the SMILES strings of molecules. While SMILES strings capture sequential information, they do not fully encapsulate the structural intricacies of molecules necessary for understanding and generation tasks. - Our molecule tokenizer, on the other hand, is designed to tokenize molecules into molecule tokens. This involves incorporating textual information and structural information embedded in molecule features. Our tokenizer is specifically designed to generate tokens that LLMs can understand and generate, similar to text tokens. We report the performance of the molecule captioning task on the Pubchem dataset. Note that in the SMILES tokenizer baselines, we do not incorporate molecule features; we only use the SMILES strings as input for the LLM. \| \| BLEU-2 \| BLEU-4 \| ROUGE-1 \| ROUGE-2 \| ROUGE-L \| METEOR \| \| :------------------------------------ \| :------- \| :------- \| :------- \| :------- \| :------- \| :------- \| \| SMILES Pair Encoding (Atom Tokenizer) \| 6.7 \| 3.9 \| 8.1 \| 3.3 \| 6.1 \| 7.0 \| \| Molecular Transformer \| 7.9 \| 5.0 \| 9.6 \| 4.5 \| 7.4 \| 8.4 \| \| UniMoT \| 31.3 \| 23.8 \| 37.5 \| 23.7 \| 33.6 \| 34.8 \| > W5 & Q4 & Q5. The synonym problem. For our pretraining, we utilize the molecule-text pairs as provided by the PubChem dataset without any modification. - Molecule-to-Text Autoregression: - For molecule-to-text autoregression, our model uses the canonical SMILES representation, which uniquely defines the chemical structure of a molecule. - We also incorporate contextual tokens derived from contextual molecule embeddings. These tokens help capture the meaning of molecule names within their specific context, allowing the model to understand that different names can refer to the same chemical entity. - Text-to-Molecule Autoregression: - For text-to-molecule autoregression, our model generates molecule tokens that have been aligned with textual descriptions during pretraining. - We conducted several tests, which showed that the model's output remains consistent regardless of the synonyms used in the input. For instance, when we replace “Acetylcarnitine” with “L-Carnitine, acetyl ester” or “O-Acetyl-L-carnitine,” the output remains consistent. - While the model generally produces consistent outputs regardless of the synonym used, slight variations may occur due to differences in how the model processes each synonym. --- Rebuttal Comment 1.1: Comment: Thank you for the detailed response. Most of my concerns are clarified, I will update my score accordingly. --- Reply to Comment 1.1.1: Comment: Thank you for taking the time to review our submission and for your thoughtful comments. We're glad we could address most of your concerns. We appreciate your consideration in updating the score. Please feel free to reach out if there are any further questions or points to discuss.	Summary: introduce a molecule tokenizer based on Codebooks which gets integrated into UniMoT, a unified molecule-text LLM Strengths: strong performance on a variety of benchmarks; outperforms/on pair with 3D-MoLM Weaknesses: - Table 1: include CLAMP [1] as well as standard molecular fingerprints (incl. in said reference); further KV-PLM linear probing for ToxCast results in 66.3 AUROC compared to 55.03 in your paper [1] Seidl, P., Vall, A., Hochreiter, S., & Klambauer, G. (2023, July). Enhancing activity prediction models in drug discovery with the ability to understand human language. In International Conference on Machine Learning (pp. 30458-30490). PMLR. Technical Quality: 3 Clarity: 3 Questions for Authors: what is the reconstruction rate of the SMILES decoder? Confidence: 2 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: - Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: > W1. Including CLAMP and fingerprints baselines. Thank you for your feedback and for suggesting additional baselines such as CLAMP and standard molecular fingerprints on the molecular property prediction task. We will include these baselines in our revised manuscript to provide a more comprehensive evaluation. We will also update the ToxCast results to reflect the performance of KV-PLM linear probing. > Q1. The reconstruction rate of the SMILES decoder. We measured the reconstruction rate on a test set of SMILES strings. The reconstruction rate is defined as the percentage of SMILES strings that are exactly reproduced by the decoder from their encoded representations. Our experiments show that the SMILES decoder achieves a reconstruction rate of 96% on the PubChem test set of 2,000 valid molecules.	Rebuttal 1: Rebuttal: We appreciate the reviewers’ thoughtful and constructive feedback on our manuscript. We have carefully considered each point raised and provide the following detailed clarifications: Novelty and technical contribution of UniMoT. While we use components from existing works like Q-Former, the molecule encoder, and the SMILES encoder and decoder, we adopt a tokenizer-based architecture that uses discrete tokens. This is fundamentally different from adapter-based architectures that use continuous embeddings. The novel contributions are highlighted below: - First Work on Molecule Tokenizer for LLMs: To the best of our knowledge, our tokenizer is the first to enable the tokenization of molecular data specifically for LLMs, treating molecular and textual data equally under a unified token representation. This approach enables the LLM to handle molecular data as a foreign language, thus unifying the modalities under a shared autoregressive training paradigm. - Unified Framework for Molecule and Text: Previous works often employed adapter-based architectures or separate processing pipelines for different data modalities. In contrast, our model adopts the tokenizer-based architecture which tokenizes molecules into discrete token sequences that the LLM can process alongside text tokens. - Adaptation of Q-Former with Causal Masks: While Q-Former has been proposed in previous works, our Causal Q-Former introduces causal masks to generate a causal sequence of queries. This ensures compatibility with the unidirectional attention mechanism in LLMs. Moreover, the training objectives are tailored for Causal Q-Former and differ from those of the original Q-Former. Novel approach to text-to-molecule generation tasks. While adapter-based architectures can perform text-to-molecule generation tasks, they typically do not match the performance of our approach, as demonstrated in Table 4 of our paper. Below, we elaborate on the key differences and advantages of our tokenizer-based architecture compared to adapter-based architectures: - Limitations of Adapter-Based Architectures: Adapter-based architectures require the LLM to directly output SMILES strings for molecule generation tasks. This approach heavily relies on strong alignment between SMILES strings and molecule captions during pretraining. In practice, achieving this alignment is challenging, leading to suboptimal performance in text-to-molecule generation tasks. - Advantages of Tokenizer-Based Architecture: Our method leverages a tokenizer to convert molecular features and text captions into molecule tokens. These tokens encapsulate high-level molecular and textual information, providing a richer representation than SMILES strings alone. By linking molecule tokens to the molecule captions during molecule-to-text and text-to-molecule pretraining, the model learns to understand and generate molecule tokens in an autoregressive manner. Ablation study on different backbone LLMs. We have extended our experiments to include additional LLMs to validate the generalizability of UniMoT. The performance is shown in Table 1 of the global rebuttal PDF. Our experiments show that UniMoT performs well across multiple LLMs, including Galactica and Mistral series, demonstrating its robustness and generalizability. This confirms that UniMoT can be successfully applied to other SOTA LLMs. Comparison of models with comparable sizes. We provide a detailed performance comparison between UniMoT and MolCA using models of comparable sizes, as shown in Table 2 of the global rebuttal PDF. UniMoT consistently outperforms MolCA across the Galactica-125M, Galactica-1.3B, and LLaMA-2-7B backbones, demonstrating the effectiveness of our proposed UniMoT model. Ablation study on codebook size. The choice of 2048 for the molecule codebook size is based on a balance between model complexity and performance. A larger codebook could potentially capture more subtle interactions between molecules and text. However, there may be some codes that are not often used on large codebooks. A smaller codebook may result in nearby embeddings being assigned the same code, which reduces the granularity of the representation. We conducted experiments with different codebook sizes and report the performance of the molecule captioning task on the Pubchem dataset. The performance with different codebook sizes is shown in Table 5 of the global rebuttal PDF. The results demonstrate that the codebook size of 2048 consistently provides the best performance. Ablation study on query size. We also conducted an ablation study to evaluate the performance of UniMoT with different query sizes, as presented in Table 6 of the global rebuttal PDF. The results show that increasing the query size improves performance, with the best results observed at a query size of 32. However, since a query size of 32 requires significantly more training time and memory, we still opt to use a query size of 16. Pdf: /pdf/fc36f2ec3b4ba3043b171fbfb995c90698ebf09d.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Scaling Continuous Latent Variable Models as Probabilistic Integral Circuits	Accept (spotlight)	Summary: This paper extends the work of PIC with continuous LVs, proposes to tensorize and to use neural functional sharing to scale the model. The results show that the proposed approach decreases the trainable parameters as well as the memory usage in training, and also reduces the running time. The approach also works well in density estimation tasks. Strengths: This paper extends the work of PIC for better scalability and efficiency, and thus has its novelty. The paper is well written and not difficult to understand. e.g., the illustration of Algorithm 1 in Fig.2 (a-b) is a very nice visualisation. With the claimed contribution, the paper has a high potential to contribute to the community. Weaknesses: It is not clear to me what data set is used in the experiment of "Scaling PICs", and how many RVs are modelled. I compared the density estimation results in PIC[18] on the MNIST family and the results in this paper outperforms the ones in PIC[18]. As far as I understand, the PIC (F, C) in this paper has reduced its trainable parameters and therefore should in principle has smaller model capacity. I am wondering why the density estimation results of the proposed model outperform the original PIC? Similarly, it would be nice if the drop (or increase, though unlikely) of density estimation performance can be shown between PIC (F, N) and PIC (F, C) so readers will know how much they can lose/gain w.r.t. performance when applying the functional sharing. Technical Quality: 3 Clarity: 4 Questions for Authors: - Could you elaborate why the trainable parameters in PIC (F, C) have reduced significantly compared with the PC (F, N), since there is no functional sharing in PCs as I understand. That is, why the PIC (F, C) can have much fewer trainable parameters than PC (F, N)? Is this comparison fare? - In the left most plots in Fig 5, I would infer that the single orange triangles in upper left are PIC(F,N) with QG-TK, but without a dotted line connected it is a bit unclear. - is the ```and``` before $\|\|$ in line 156 a typo? Confidence: 5 Soundness: 3 Presentation: 4 Contribution: 3 Limitations: The limitations are well discussed in the end of the paper. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for deeming our paper to be novel, well-written, and for expecting it to have a high impact in the community. Below we reply to their points. > It is not clear to me what data set is used in the experiment of "Scaling PICs", and how many RVs are modelled. In the experiment “Scaling PICs” (in the main text), whose results are shown in Fig 5, we used a PC modeling ImageNet 64x64. Note that it is not important which likelihood the PC assigns to different images, but only the time and space requirements for a forward/backward pass. Therefore, any batch of 64x64 RGB images would reproduce the same performance as reported in the plot. As we write in the caption, “The benchmark is conducted using a batch of 128 RGB images of size 64x64”. Finally, all RVs are categorical (256 categories for MNIST-like images, and 768 categories for RGB images), as described in lines 286-287. > About PICs with and without functional sharing An extensive comparison between PICs with and without function sharing in terms of performance is not present in the paper, and below we explain why. However, luckily, as the reviewer pointed out, such comparison can be retrieved --- to a certain extent --- by taking results from Fig. 5 in [A], which corresponds to much smaller models than ours. We will account for it in the revised version of the paper. As we extensively tested in our benchmarks (Fig. 5, Table D1, Table D2), PICs without functional sharing cannot scale to large model sizes, and therefore, simply because of that, PICs with functional sharing can deliver (better) results for the computational resources we have available. This is in fact one of the main points of our paper: Scaling PICs with functional sharing, as we cannot without it. Therefore, given that PICs without functional sharing can unfortunately be run only for very small sizes (see Table D1 and D2), an extensive comparison in terms of performance w.r.t. PICs with functional sharing is not feasible on our GPUs. We expect functional sharing to deliver better models as applying it drastically reduces the number of trainable parameters, and therefore possible overfitting. In Fig. 5 (top-right) we indeed showed that PICs without functional sharing hit 2B parameters, whereas with functional sharing only 6M. [A] Gennaro Gala, Cassio de Campos, Robert Peharz, Antonio Vergari, and Erik Quaeghebeur. Probabilistic integral circuits. AISTATS, 2024. > Could you elaborate why the trainable parameters in PIC (F, C) have reduced significantly compared with the PC (F, N) Yes, the reason why there is a significant reduction in the number of trainable parameters between PIC (F, C) and PC (F, N) is because the former applies compositional sharing of MLPs, as explained in Section 3.3. However, once we materialize a QPC out of it, the number of its parameters match exactly the ones of PC (F, N), since these represent exactly the same architecture. With that in mind, we believe the comparison is fair as the PIC approach can be seen as a way of training PC (F, N). For a detailed analysis, we refer the reviewer to our answer to reviewer WQnV about characterizing the size of PICs and PCs. > In the left most plots in Fig 5, I would infer that the single orange triangles in upper left are PIC(F,N) with QG-TK, but without a dotted line connected it is a bit unclear Precisely, those isolated orange triangles refer to PIC (F, N) with QG-TK. The reason why they are isolated is because we could only run such configuration at K = 16, hence the lack of dotted lines. We refer the reviewer to Table D.2 for some tabular results of the plots, where this is evident. We will make sure to detail this better in the main text. > is the and before $\|\|$ in line 156 a typo? Yes, it should be and will be removed, thanks for spotting it. --- Rebuttal Comment 1.1: Comment: Thank you for the answer. My concerns have been addressed and I will keep my positive rating.	Summary: This paper presents a pipeline to build probabilistic integral circuits (PICs) more generally as directed acyclic graphs, as opposed to the tree-shaped structure they were limited to before. This significantly increases the expressiveness of the PICs, improving their representation of distributions. The authors present a procedure for turning a region graph into a PIC, into a QPC that approximates the PIC, and finally into a folded QPC, which are effectively tensorized structures that significantly speed up the inference and learning process. From the tensorized PIC the authors then make further improvements on QPC training, using neural functional sharing techniques over groupings of the input and integral units to result in greater materialization of QPCs and far fewer parameters. Strengths: + The proposed approaches significantly increase the expressivity and learning efficiency of PICs, as showcased by the experiments. + The paper is technically sound with clear arguments presented for each step. + The paper is overall well structured and easy to follow. + The authors also address the current limitations of PICs with a clear goal for future improvements. Weaknesses: Not a major weakness, but as the authors also point out, it is currently not possible to sample from PICs, limiting their impact as a generative model. Technical Quality: 4 Clarity: 4 Questions for Authors: 1. Among the techniques discussed in the paper, how significant is the tree-shape vs DAG-shape for empirical expressiveness of PICs? It appears that DAG-shaped PICs achieve slightly better bpds, but tree-shaped ones scale much better. 2. Section 3.2 describes a numerical quadrature rule as consisting of integration points and weights that minimize the integration error, and the authors later say that the same quadrature rule is used for each approximation. Does this raise any issues in approximation? 3. How crucial/limiting is the assumption that every integral unit integrates out all incoming latent variables? 4. Do the QPCs approximating PICs still support tractable inference (e.g. marginal probabilities) similar to traditional PCs? It would be great to clarify the probabilistic reasoning capabilities mentioned in the introduction. Minor comments: - Lines 133-134: do you also need $Z_{u_3}\neq Z_{u_4}$ for CP-merge? - Table 1: what does LVD-PG refer to? Confidence: 4 Soundness: 4 Presentation: 4 Contribution: 3 Limitations: The authors acknowledge the limitation of PICs that, despite being a continuous latent variable model like many generative models, they do not support sampling. This is left as future work. Flag For Ethics Review: ['No ethics review needed.'] Rating: 8 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for deeming our paper to be technically sound, clearly argumented, well-structured and easy-to-follow. Below we reply to their points. > it is currently not possible to sample from PICs, limiting their impact as a generative model. It is true that since we use simple unconstrained MLPs to parameterize PICs --- which can be seen as energy-based models --- (differentiable) sampling from them is not possible. However, this is not a limitation of PICs per se, but a consequence of the way we choose to parameterize them. For instance, parameterizing using simple mixtures of Gaussians or even normalizing flows, would allow sampling from PICs. Nevertheless, it is always possible to materialize PICs as QPCs and sample from them as usually done with PCs. > how significant is the tree-shape vs DAG-shape for empirical expressiveness of PICs? It appears that DAG-shaped PICs achieve slightly better bpds, but tree-shaped ones scale much better. We remark that dropping 0.1 bpd on MNIST-like datasets would correspond to an increase of ~54 nats in log-likelihood, and perhaps this would be considered to be more significant. On RGB 64x64 datasets, the gap would even be much larger, i.e. ~851 nats. It is true that there is a trade-off in terms of accuracy/efficiency. We just started exploring how to scale DAG RGs in a more effective way and believe our paper is a stepping stone in this direction. E.g., note that using Tucker layers yields the best performance for lower values of K, but we do not know how to scale it properly yet. > Section 3.2 describes a numerical quadrature rule as consisting of integration points and weights that minimize the integration error, and the authors later say that the same quadrature rule is used for each approximation. Does this raise any issues in approximation? Using the same integration technique for each integral unit is not a limitation nor raises approximation issues when assuming a static quadrature regime. Assuming the same number of integration points, instead, allow us to tensorize the QPC in a regular way, thus promoting GPU parallelism via folding. We conjecture that since we learn our functions through numerical approximation, these will stay nicely integrable w.r.t. to the points we used during training to fit them. > How crucial/limiting is the assumption that every integral unit integrates out all incoming latent variables This is an interesting question! From a theoretical perspective, we would need to devise novel quadrature routines to materialize the QPC, as some latent variable would affect multiple integral units at once. In practice, it might be possible to “move” the non-integrated-out latent variables of the input function $g_i$ as to be part of variables $\mathbf{Z}_u$ of function $f_u$, for certain parameterizations of $g_i$ and $f_u$. Nevertheless, we believe that from a learning perspective, PICs/QPCs have enough capacity to learn complex distributions with our assumption. > Do the QPCs approximating PICs still support tractable inference (e.g. marginal probabilities) similar to traditional PCs? Yes, QPCs --- being composed of only sum, product and input units --- are proper PCs that inherit the structural properties of their corresponding PIC , e.g., they are also structured-decomposability if the underlying PIC is structured-decomposable. We will clarify this in the revised version of the manuscript. > Lines 133-134: do you also need Z_u3 != Z_u4 for CP-merge? It does not need to be. If $Z_{u_3} \neq Z_{u_4}$, we would then merge u3 and u4 using Tucker-merge, whereas if $Z_{u_3} = Z_{u_4}$, we would then use again CP-merge. In this way, we allow for Tucker layers on top of CP-layers, and vice-versa. > Table 1: what does LVD-PG refer to? It stands for Latent Variable Distillation - Progressive Growing, and it is a sophisticated learning scheme developed in [Liu, Xuejie, et al. "Understanding the distillation process from deep generative models to tractable probabilistic circuits." ICML 2023] that employs several heuristics to learn the parameters and structure of a PC on a lossy color space. We will specify this in the camera-ready version. --- Rebuttal Comment 1.1: Comment: Thank you for the detailed response! I think clarifying the tractable inference and sampling (although differentiable sampling still seems to be a challenge at this point) supported by the learned PICs will make the contribution more impactful. I will keep my score of 8.	Summary: This paper introduces a new approach for building probabilistic integral circuits (PICs), a recently introduced probabilistic model that extends probabilistic circuits (PC) with continuous functions of latent variables (in addition to discrete latent variables), with inference performed using a numerical quadrature procedure. In particular, while the previous implementation was restricted to tree-structured region graphs/variable decompositions, it is shown how to construct PICs for arbitrary region graphs. Additionally, sharing of functions across different regions is used to improve parameter efficiency. Empirical results show that the architectural improvements enable scaling to complex image datasets such as ImageNet64, outperforming comparable PCs trained using maximum likelihood or EM. Strengths: The paper proposes a number of innovations on top of the recently proposed PICs, such as allowing for arbitrary region graphs and functional sharing. Taken together, this constitutes a well-engineered solution that significantly improves the scalability and flexibility of PICs. The experiments are well-executed with strong results on a range of image datasets in comparison to comparable PCs learned directly. Many experimental details are reported, such as memory usage, time taken and parameter counts/hyperparameters, which should make the results reproducible. The paper was a pleasure to read, with clear and consistent notation throughout explaining the method and accompanying pictorial illustrations that make the idea of the paper transparent and easy to understand. Weaknesses: The paper is arguably a little weak in terms of novelty as most of the new components are adaptations of existing ideas in the literature (e.g. tucker/cp layers, parameter sharing) to probabilistic integral circuits. Technical Quality: 4 Clarity: 4 Questions for Authors: - What numerical quadrature rule was used? - In the conclusion, it is remarked that differentiable sampling from PICs is not possible. What is meant by differentiable here, and is it possible to sample from the materialized PC if one is not interested in gradients (e.g. for visualization)? - To what extent do the authors consider their method a continuous latent variable model, as opposed to a means of effectively constructing PCs? For instance, if the same quadrature points are used throughout training and evaluation, can one expect the MLPs to learn meaningful function values between evaluation points? - Did the authors investigate learning PICs according to a HCLT region graph? This would give a better idea of whether a DAG (as opposed to tree-structured) region graph is necessary. Typos: - modes -> nodes 190 - capitalization of 'functional' 234 - 'pixels are categorical' -> 'pixels as categorical' 286 Confidence: 4 Soundness: 4 Presentation: 4 Contribution: 3 Limitations: The limitations of the method are appropriately addressed in the paper. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for deeming our paper to be a well-engineered solution delivering strong results. We are also happy that the reviewer enjoyed the reading. Below we reply to their questions. > The paper is arguably a little weak in terms of novelty We respectfully disagree as it is non-trivial to recover a compact quadrature PC (QPC) from a PIC with a DAG structure. First we needed to change the original semantics of PICs/QPCs, which were defined only for tree region graphs, second, parameterizing the newly found tensorized QPCs needs some careful engineering otherwise the models would never be able to scale to the number of integration points we used (up to K=512). > What numerical quadrature rule was used? We trained using the trapezoidal integration rule, we will document this in the revised version of the paper. > What is meant by differentiable [sampling] here, and is it possible to sample from the materialized PC if one is not interested in gradients (e.g. for visualization)? When we say that differentiable sampling is not currently possible, it is just because the functions we use are parameterized as simple unconstrained MLPs, which can be seen as energy-based models, for which exact sampling is not possible. While using MCMC would be possible to sample from these neural networks, obtaining meaningful gradients through the samples would require additional approximations. Nevertheless, we can always materialize PICs as QPCs and sample from them as usually done with PCs. > To what extent do the authors consider their method a continuous latent variable model, as opposed to a means of effectively constructing PCs? PICs are continuous latent variable models by definition. It is true, indeed, that the way we currently use PICs seems like a parameter learning procedure for tensorized PCs. However, we stress that at test-time we can actually materialize an arbitrarily sized PCs based on the number of integration points we use. We plan to explore (and exploit) this capability further in future work. > Did the authors investigate learning PICs according to a HCLT region graph? Learning PICs using HCLT region graphs (RGs) has been already investigated in prior work [A]. In our work, we directly use RGs that, differently from HCLTs, are not learned from data but rather fixed for a given image size: QuadTree (QT) and QuadGraph (QG) RGs (see Appendix B for details). By comparing our results with the ones in [A], one can clearly see that QT and QG outperform HCLT, and highlight how learning an RG from images does not bring any advantage. QG outperforming QT brings evidence to support the claim that non-tree RGs can be more expressive. [A] Gennaro Gala, Cassio de Campos, Robert Peharz, Antonio Vergari, and Erik Quaeghebeur. Probabilistic integral circuits. AISTATS 2024 --- Rebuttal Comment 1.1: Comment: Thank you for the response and clarifications. I will keep my positive score.	Summary: This work extends the probabilistic integral circuits (PICs) from tree-shaped region graphs (RGs) based ones to DAG-shaped ones. While constructing PICs from DAG RGs can lead to more expressive models, it comes with the concern of scalability since the circuit sizes might be increased a lot. To address this concern, this work proposes tensorized circuits to approximate the resulting PICs by a PIC to QPC reduction. This is further combined with functional sharing and materialization to achieve efficiency and scalability, which is validated by experimental results on several image datasets. Strengths: - The extension from tree-shaped PICs to DAG-shaped ones is a solid contribution as it greatly improves the expressiveness of the resulting PICs and is an important step towards PICs constructed from more complex RGs for complicated tasks. - The functional sharing and materialization techniques proposed in this work are shown to be very useful by the empirical results. From Fig 5, learning PICs consumes similar resources to PCs which are efficient models and it requires much less trainable parameters than the ones without functional sharing, making the training of large-scale PICs feasible. Weaknesses: I appreciate that this work aims to solve an important problem and the proposed solution is shown to be novel and efficient. Still, it's heavy in technical details and thus I don't think I fully understand the algorithmic details. Specifically, - I'm confused by the definition of the integral unit from Line 58 to Line 62, especially by the inconsistency in the input of g_i between Line 61 and Line 62 (the g_i inside the integral). Also, the integral in Line 62 contains the function g_i while Figure 1(b) does not, which is also confusing. It might be helpful to put a numeric example there. - This also applies to the other technical sections of this work given that this work is heavy in techniques. It would be very helpful to provide a toy example to showcase the reduction of PICs to QPCs to improve accessibility and reproducibility for readers who are not well-versed in these areas. - I'm curious to see some theoretical analysis on the circuit sizes characterized. I understand that the bounds might be loose and not that informative. Still, it might be helpful to understand how the PIC to QPC reduction affects the circuit sizes. Technical Quality: 4 Clarity: 3 Questions for Authors: - Can you provide some examples to help understand the integral units? - From the definition of g_u in Line 71, the integral is a function of both variables X_i and Z_u. Can you explain the claim "In this way, the output LVs of any unit u will simply be Zu" that directly follows the definition of g_u? - Can you characterize the circuit sizes of the resulting PICs and QPCs? Confidence: 4 Soundness: 4 Presentation: 3 Contribution: 4 Limitations: Yes. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for deeming our paper to be a solid contribution, and a novel and efficient solution to an important problem. Below we clarify the confusion about notation, and respond to their points. > I'm confused by the definition of the integral unit from Line 58 to Line 62, especially by the inconsistency in the input of g_i between Line 61 and Line 62 $g_i(\mathbf{X}_i, \\{ \mathbf{Y}_i, \mathbf{Z}_u \\} )$ and $g_i(\mathbf{X}_i,\mathbf{Y}_i,\mathbf{Z}_u)$ are just equivalent notations, we will remove the brackets to avoid confusion. We used them trying to emphasize the set of $g_i$ LVs. Finally, note that, when writing an integral, the LVs that we integrate out are in lower-case (e.g. line 62) > the integral in Line 62 contains the function g_i while Figure 1(b) does not, which is also confusing. It might be helpful to put a numeric example there. An integral unit $u$, by definition, receives input from a single unit, $i$. Assume that $u$ is associated with function $f_u(Z, Y) = 2Z - Y^2$, and that $i$ outputs the function $g_i(X, Y) = X^2 -3X + 4Y$. The integral unit would then compute the integral $\int_{-1}^{1} f_u(Z, y)g_i(X, y) dy$ (the integration domain is the support of $Y$, an assumption), therefore outputting the function $g_u(Z, X) = 2/3 (X - 3) X (6Z - 1)$, as we can compute the integral in closed-form in this example. (We will add this example to the camera-ready.) Therefore, in Figure 1, for instance, integral unit 5 (the red coloured one) computes $\int f_5(Z_2, z_4) f_4(X_4, z_4) dz_4$, i.e. $g_u = f_5$ and $g_i = f_4$. > It would be very helpful to provide a toy example to showcase the reduction of PICs to QPCs This is a great suggestion and in the camera-ready version we will describe more in detail in the main text the example we provided appears in Figure 2. There, we illustrate the application of PIC2QPC (Algorithm 3) from the PIC in (b) to the QPC in (c), and then to its tensorized folded version in (d). Zooming in, we also illustrated the details of the materialization of a 3-variate function to a Tucker Layer in Figure 3. We will further expand this explanation and mention all the functions involved and comment on how Algorithm 3 operates step by step. > I'm curious to see some theoretical analysis on the circuit sizes characterized We are not entirely sure how to understand the reviewer's request. We interpreted it as an analysis on the number of trainable parameters of PCs and PICs. We are happy to discuss more in case we are off-topic. We address the answer by analyzing 3 types of folded layers (CP-layer, Tucker-layer, and Categorical-Layer), as our tensorized architectures are nothing more than a sequence of them. We use $F$ to denote the number of layers stacked together with folding, $K$ the number of integration points, $M$ the MLP size for PIC neural nets, and $L$ the number of MLP layers. We recall that the size of PIC neural nets is independent from $K$. - A folded CP-layer is parameterized by a tensor of shape $F\times K\times K$ (where F is always even). Using PIC composite sharing, the size of the multi-headed MLP (assuming no bias term for simplicity) to parameterize such a layer is $LM^2 + FM$ (see Figure 4 for an illustration). - A folded Tucker-layer is parameterized by a tensor of shape $F\times K\times K\times K$. Parameterizing such a layer with composite sharing, again requires an MLP of size $LM^2 + FM$. - A folded Categorical-layer is parameterized by a tensor of shape $F\times K\times C$, where $C$ is the number of categories (256 of gray-scale images, and 768 for RGB ones). When using composite sharing, we can parameterize it with an MLP of size $LM^2 + FMC$. However, we found that PICs deliver better results when using full-sharing for the input layer, and this means using an MLP of size $LM^2 + MC$. As an example, consider a folded CP-layer with $F=1000$, $K=512$, whose number of trainable parameters is $262,144,000$. Parameterizing it with an MLP with $L=2$ and $M=256$, delivers instead only $387,072$ trainable parameters, more than 99% less trainable parameters. We refer the reader to Appendix C1 for details about our MLPs, and to the plots on the right of Fig. 5 for the total trainable parameter counts of PC and PIC models. We will add this analysis in the revised paper.	Rebuttal 1: Rebuttal: We thank all reviewers for their insightful feedback, questions, and kind words. We are glad that the paper seems to be (i) very well-received (“The paper was a pleasure to read, with clear and consistent notation” - 6CM1, “transparent and easy to understand” - 6CM1, “The paper is technically sound with clear arguments presented for each step” - iaCH, “The paper is overall well structured and easy to follow” - iaCH, “The paper is well written and not difficult to understand'' - fmPL), and (ii) deemed as a strong contribution to the field (“The extension from tree-shaped PICs to DAG-shaped ones is a solid contribution” - WQnV, “the proposed solution is shown to be novel and efficient” - WQnV, “The paper proposes a number of innovations” - 6CM1, “this constitutes a well-engineered solution” - 6CM1, “The proposed approaches significantly increase the expressivity and learning efficiency of PICs” - iaCH, “the paper has a high potential to contribute to the community” - fmPL). We answer all remaining questions below and will include feedback in the revised version of the paper.	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Information-theoretic Limits of Online Classification with Noisy Labels	Accept (poster)	Summary: The paper addresses the problem of online classification where the true labels are corrupted by unknown stochastic noise and the features are adversarially generated. The main contributions of this paper include: 1. Establishing fundamental limits of minimax risk in online classification with noisy labels by nearly matching lower and upper bounds across various hypothesis classes and noisy kernels; 2. Introducing a reduction to an online comparison scheme of two hypotheses and a new conditional version of Le Cam-Birgé testing suitable for online settings; 3. Characterizing the minimax risk using the Hellinger gap of noisy label distributions. Strengths: + The theoretical analysis is rigorous, providing clear bounds and demonstrating their tightness through detailed proofs. The paper systematically addresses various aspects of the problem, ensuring a comprehensive exploration. + The paper is well-structured, with clear definitions and thorough explanations of the concepts and results. Theorems and proofs are presented in a logical sequence. Weaknesses: - While the theoretical contributions are good, the paper could benefit from discussing practical implementations and real-world applications of the proposed methods. - Some assumptions, such as the nature of the noise and the hypothesis class, might be restrictive. A more detailed examination of these assumptions' impact on the results' generality would strengthen the paper. - The paper lacks experimental validation of the theoretical results. Providing empirical evidence, even in simulated settings, would enhance the credibility and applicability of the findings. Technical Quality: 2 Clarity: 3 Questions for Authors: 1. How do the assumptions regarding the noise model and hypothesis class impact the generality of the results? Can the methods be adapted to other types of noise or broader hypothesis classes? 2. Have you considered any practical applications or scenarios where your theoretical findings could be applied? If so, what are the potential challenges in these applications? Confidence: 3 Soundness: 2 Presentation: 3 Contribution: 2 Limitations: - Limitations: In the discussion section, the discussion on the limitations is not sufficient. It's difficult for readers to find this part. - Societal Impact: As this is a pure theory paper, there are no direct societal impacts. However, the authors could briefly mention potential positive impacts, such as improved robustness in machine learning models dealing with noisy data, and any negative implications if misapplied, such as in adversarial settings. Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for the detailed review and helpful comments. We address the main concerns raised below: Real-World Application: Our theoretical work is motivated by a number of important real-world applications. These applications involve, e.g., learning under measurement imprecision, estimation and communication error, and noise introduced for differential privacy. For instance, in a differential privacy setting, noise can arise from certain privacy mechanisms, and our noise kernel for a given label corresponds to the collection of all distributions when passed through the privacy mechanism. Additionally, in quantum learning, one may consider the task of classifying quantum states into certain classes. Here, the kernel set for any given label is the collection of all distributions induced by measurements on the quantum states corresponding to that class. Finally, in the context of genome sequencing—where the raw output from the sequencer must be classified into one of four bases (A, T, C, G)—this is done using a base-calling process that is inherently noisy. These problems can be cast within our framework. We refer the reviewer to our global rebuttal for a concrete construction that demonstrates how our theory applies in the context of differential private online learning. Assumptions: We would like to clarify that our work is not intended to introduce any specific noise models. Rather, our main focus is to provide a characterization to determine, for any given noise model, the best achievable minimax risk. Since our formulation of noise kernels is general and we do not make structural assumptions on the class (except finiteness), our result is applicable to a wide range of noisy online classification problems (such as those highlighted above). Although our results are stated for uniformly bounded gaps and finite classes, they can be extended to non-uniform gaps and infinite classes (see our global rebuttal and responses to Reviewers JscE and crkZ). Experiments: Our work is primarily focused on theoretical aspects (particularly the worst-case minimax risk), and experiments are typically not expected for such pure theory contributions in the literature. For example, Ben-David et al. (2009) and many other foundational works in our references do not include experiments. Our results are established via rigorous proofs, ensuring that the worst-case risk bounds will hold for real data, provided the noisy data follow the prescribed kernel. While empirical validation is valuable, it lies beyond the scope of our current theoretical investigation and could be a potential avenue for future work to complement our findings. Limitations: We appreciate the reviewer's feedback regarding the discussion of limitations. We would be grateful if the reviewer could specify any particular limitations, and we will be happy to address them. --- Rebuttal Comment 1.1: Comment: Real-World Applications: While it is appreciated that you have highlighted potential applications of your theoretical framework in areas such as differential privacy, these examples remain largely theoretical. Specific details on how your model can be practically implemented in these scenarios are still lacking. For instance, in the context of differential privacy, how does your model handle varied levels of noise introduced by different privacy-preserving mechanisms? Additionally, the practical challenges of adapting your theoretical model to real-world data constraints in these fields should be thoroughly discussed. Assumptions: The clarification on the generality of your noise model is helpful. However, the impact of these assumptions on the robustness and adaptability of the model could benefit from a deeper exploration. Experiments: It is understood that your paper focuses on theoretical aspects; however, including some experimental validation, even if preliminary, would significantly strengthen your paper's impact and credibility. Theoretical proofs, while rigorous, often benefit from empirical demonstrations to highlight their applicability and to verify theoretical predictions under practical conditions. It could be beneficial to include simulations or synthetic experiments that demonstrate the theoretical concepts and provide insight into their performance in controlled settings. Limitations: While the global rebuttal may address broader concerns, the specific discussion in the paper about limitations, particularly how they might affect the interpretation and application of your results, seems insufficient. A more detailed examination of potential pitfalls or the conditions under which your proposed work may not perform as expected would provide a more balanced view and help practitioners gauge the utility of your findings. Overall, most concerns have NOT been addressed yet. Addressing the above points could further enhance the work. --- Reply to Comment 1.1.1: Comment: We thank the reviewer for the response. However, we respectfully disagree with the reviewer's assessment of our paper. Our work is theoretical in nature and is labeled as "Learning Theory." Therefore, its merit should primarily be judged based on the theoretical contributions. We believe it is not fair to reject a theoretical paper solely for lacking practical implementation, considering that many purely theoretical papers have been published at NeurIPS. Practical Implementation: The purpose of our paper is to establish the theoretical foundations of online classification under general noise models. Our work is not tailored to specific noise models but provides a general analysis framework that can be applied to specific noise model at hand. Our work will inspire practitioners to develop practical algorithms using the algorithmic ideas proposed here. However, we believe that placing too much emphasis on practical implementation in specific application scenarios would detract from the main message of the paper and could be itself a separate paper. Assumptions: To our knowledge, the only "assumption" we made is that the real data follows the prescribed noisy kernel, which is entirely determined by the noise model at hand. Our theoretical results clearly state the conditions on the kernel under which the results hold. If one has to say something, perhaps the adversarial assumption may be pessimistic, so that for real data, better performance might be achievable than our risk bound predicts. However, this does not affect the applicability of our algorithm to such tasks. We would greatly appreciate it if the reviewer could specify any particular assumptions the reviewer feels need further discussion. We now address the specific comments made by the reviewer: > How does your model handle varied levels of noise introduced by different privacy-preserving mechanisms? We note that the parameter $\eta$ is only an upper bound on the noise level. Our algorithm automatically accommodates scenarios where each local party chooses varying noise parameters that is upper bounded by $\eta$, as our setting allows the noisy label distribution to be selected adversarially. > A more detailed examination of potential pitfalls or the conditions under which your proposed work may not perform as expected would provide a more balanced view and help practitioners gauge the utility of your findings. As we pointed out above, our work provides a framework to analyze general noise models. To ensure our theory applies, one must ensures that the real data follows the noisy kernel. For instance, in differential privacy, the kernel is designed and therefore fully controlled by the learner. In other cases, such as noisy communication, the kernel can typically be estimated. To our knowledge, all the necessary conditions of our theoretical results have been clearly stated in our work.	Summary: This paper studies online classification with stochastic label noise, where a hypothesis $h^$ is drawn from some hypothesis class $H$ and the learner wants to learn $h^$ by observing the noisy labels of the online data. The standard mistake bound used in online learning counts the number of predictions different from the true labels. In this paper, instead, the mistake bound counts the number of predictions that disagree with the target $h^*$. This paper proposes Noisy Kernel, a new framework to model the label noise, which generalizes the bounded noise setting studied by prior work. The main result of this paper is to show that the Hellinger gap of the noisy kernel gives a good characterization of the min-max mistake bound of learning a finite hypothesis class under their model. Specifically, they design a learner with mistake bound $\log^2(\|H\|)/\gamma_H$, where $\gamma_H$ is the Hellinger gap of the noise kernel. On the other hand, for any fixed noisy kernel, they design a hypothesis class $H$ such that every learner has a mistake bound at least $\log(\|H\|)/\gamma_H$ to learn $H$. For the binary classification problem, the author further designs a learner with a mistake bound $\log(\|H\|)/\gamma_L$, where $\gamma_L$ is the $L^2$ gap of the noisy kernel, improving the dependence on $\log(\|H\|)$. Strengths: 1. This paper proposes a novel framework that models the label noise for the online classification problem. This generalizes the previous model for bounded label noise. 2. To prove the upper bound for the mistake bound, the paper introduces a novel reduction from the classification problem to the pairwise hypothesis testing problem, which could potentially be useful for designing algorithms for other learning problems. 3. A matching lower bound on the dependence on the Hellinger gap of the noisy kernel is proved. Weaknesses: 1. Though the framework proposed by the paper models a large class of noise models, the learner designed by the paper only works for learning finite hypothesis classes. Prior work, Agnostic Online Learning by Ben-David et al. proves a mistake bound that depends on the Littlestone dimension of the hypothesis class. There is a big gap between hypothesis classes with finite Littlestone dimension and finite hypothesis classes. For example, the class of singleton functions is infinite but has Littlestone dimension 1. Such a simple class is not learnable using the learner designed by the paper because it is impossible to do pairwise hypothesis testing for an unbounded set of hypotheses. From this point of view, I do not think the paper fully answers which class is learnable under their noisy model. Perhaps, this might be because the noise model studied by the paper is too general and is thus hard for one to design algorithms that make use of the structure of the hypothesis class. 2. Though the paper gives a tight bound on the dependence on the Hellinger gap of the noise kernel, the upper bound and the lower bound differ by a $\log(\|H\|)$ factor, which is sometimes linear in the dimension of the input and thus cannot be ignored in general. Though the paper shows that for binary classification, they can close this gap, a new gap on the dependence of the divergence gap is created. Technical Quality: 3 Clarity: 3 Questions for Authors: 1. The model of the noisy kernel is not as intuitive as the prior noisy models such as Massart noise. In section 5, the authors mention that the noisy kernel model has many applications such as learning with privacy constraints or learning from quantum data. What would be the noisy kernels for these types of problems? 2. To run the learner designed by the paper, one has to know the error bound of the pairwise hypothesis testing problem. How can one know such an error bound before running the online learning algorithm? If we do not know such a bound, would it be possible to get any data-driven algorithm? 3. I would like the authors to comment on the weakness pointed out above. Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: N/A Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for the detailed review and helpful comments. We now address the main concerns raised below: Infinite Classes: In fact, as mentioned in Remark 1, our techniques also work for infinite classes. Indeed, for any class $\mathcal{H}$ of finite Littlestone dimension $\mathsf{Ldim}(\mathcal{H})$, we can apply our algorithm on the sequential experts as in Section 3.1 of [1] (specifically the multi-class version from Daniely et al., 2015, Thm. 25) to arrive at an upper bound $O(\frac{\mathsf{Ldim}^2(\mathcal{H})\log^2 (NT)}{\gamma_H})$. This follows because our pairwise testing framework works for the sequential experts as well, which is finite and of size $(NT)^{\mathsf{Ldim}(\mathcal{H})+1}$. By construction of the experts, any risk achieved against the (finite) sequential experts implies the same risk for the (infinite) class $\mathcal{H}$. See also our general rebuttal and responses to reviewers crkZ and JscE for further consequences. Tightness on $\log \|\mathcal{H}\|$: Indeed, our logarithmic factor can result in an additional factor for Littlestone dimension. This is introduced by the aggregating of pairwise testings in Algorithm 1. We would like to emphasize that pairwise testing is an essential technique for dealing with multi-class label classes. We are unaware of any prior technique that can even lead to sublinear risk for the multi-class cases. Therefore, we view our result as significant even with a suboptimal logarithmic factor, as it provides the first known systematic treatment of this problem. Questions: 1. Consider the general template in our Example 2, which can be viewed as a "generalized" Massart noise in the multiclass case. For the multi-class randomized response mechanism in differential privacy, please refer to our global rebuttal for a concrete construction. To realize the quantum setting, one may consider the task of classifying quantum states into certain classes (i.e., our true labels). Here, the kernel set for any given label would be the collection of all distributions induced by certain measurement on the quantum states corresponding to that class. 2. Indeed, Algorithm 1 needs to know the upper bound of the pairwise testing error $C$. This error bound is completely determined by the Hellinger gap of the kernel and not the realization of the data; please refer to our proof of Theorem 2. Since the Hellinger gap is an intrinsic complexity measure of the problem, it can be used as an input for the algorithm. We believe that investigating a data-dependent way of selecting the parameter $C$ is also of significant interest. In fact, using a multiplicative weighted majority algorithm with a substantially more complicated potential-based analysis, we can show that an $O(C^2+C\log(CK))$ risk bound holds without the knowledge of $C$. However, it is unclear to us whether this bound is tight for unknown parameter $C$. [DSBS15] A. Daniely, S. Sabato, S. Ben-David, and S. Shalev-Shwartz. Multiclass Learnability and the ERM Principle. JMLR 2015. --- Rebuttal Comment 1.1: Comment: Thanks for the response. I raised my score to 6.	Summary: This paper studies online classification where the features are chosen adversarially, but the labels are corrupted by some unknown stochastic noise. The learner makes predictions using the true features and noisy labels, but is evaluated against the true labels (noiseless) in the minimax sense. The authors consider a very general noise generation mechanism specified by a kernel, which for every (feature, true label) pair, outputs a subset of distributions over the noisy label space. The adversary generates the noisy label by picking a distribution output by the kernel and sampling from it. The authors study the minimax risk under this setting and derive upper and lower bounds on the minimax risk in terms of the Hellinger gap of the noisy distributions output by the kernel and the cardinality of the hypothesis class. The upper and lower bounds differ only by a log factor in the cardinality of the hypothesis class, showing that (up to log factors), the Hellinger gap is the correct complexity measure of the kernel that characterizes the minimax rates. The authors prove these results by developing a novel reduction from noise online classification to hypothesis testing. Along the way, they provide guarantees for a new conditional version of Le Cam-Birge testing in the online setting. Strengths: - The paper is well-written and easy to follow - The problem of noisy online classification is well-motivated (but also see weakness below) - The technical contributions are interesting and the proof techniques are novel. In particular, I found the reduction to pairwise hypothesis testing to be nice - Overall, I think this paper makes a solid contribution to the literature on online classification Weaknesses: - More clarification is needed about the problem setup beyond just stating the minimax value. From what I can get, the adversary is oblivious and must pick the entire sequence of features, true labeling hypothesis, and noisy labels before the game begins. However, there seems to be some subtlety in the choice of how the adversary can pick the noisy labels which I feel requires explanation in the main text. In particular, the adversary can select noisy label distributions based on the realized values of the previous nosy labels. This contrasts from a weaker adversary which has to pick the entire sequence of noisy label distributions up front, and then samples the entire sequence of noisy labels. - Lack of motivation for generalization. While it is nice to provide results for a generalized noise mechanism, ideally there is some sort of justification for the generalization beyond theoretical curiosity (i.e why should I care). It would be nice if you can provide concrete example of real-world situations (i.e. specifying the instance space, label, space, noisy label space, kernel etc.) which are captured by your generalization, but not by previous noise models. As far as I can tell, applications to privacy, online denoting, and physical measurements are mentioned, but not expanded upon. Overall, I think it would be nice to provide more motivation behind why I should care about generalizing the noise mechanism. - Lack of universal lower bounds. While the upper bounds are stated for every (finite) hypothesis class, the lower bounds are of the form "there exists a hypothesis class such that the minimax value is at least...". It would nice to have universal lower bounds of the form "for every hypothesis class, the minimax value is at least...". - Finite Hypothesis Class. This paper currently only studies the minimax rates for finite hypothesis classes. There is a remark indicating that the results extend to infinite hypothesis classes via covering techniques from [1, 21], however neither the proof of this statement, nor the resulting minimax rates are provided. I am not super convinced that these existing covering techniques can give you bounds on the minimax value that are independent of the sizes of the true and noisy label spaces (like your existing bounds are). For example, for the simply hypothesis class $H = \{ x \mapsto a: a \in [N] \}$, to cover a single point $x \in X$, you need the entire hypothesis class $H$. It would be nice if you can give the upper and lower bounds on the minimax value for infinite hypothesis classes that your results imply along with a proof sketch. Please see questions below regarding each of these weakness. Technical Quality: 3 Clarity: 3 Questions for Authors: - Is my interpretation of the minimax value correct? If so, I think it would be nice to make this explicit in text. - Can you give me some concrete learning problems for which your results provide new insights (i.e can you justify the generalization of the noise mechanism)? - Can you comment about universal lower bounds in your setting? - Can you comment on the generalization of your results to infinite hypothesis classes? Is it true that using your results with existing covering arguments would result in factors of N and M (the cardinalities of true and noisy label spaces) appearing in your bounds? - Right now, your bounds are written in terms of two separate complexity measures - one on the hypothesis class (i.e its cardinality) and one on the kernel (i.e. well-separated). Could there be a single complexity measure, a function of both the hypothesis class and kernel, that better captures the minimax value? If so, do you have any intuition on what this might be or what difficulties arise when trying to do so? - Your existing results assume that the kernel outputs sets of distributions that are convex and closed. It would be nice if you can make explicit where exactly this assumption is being used in the main text. In addition, what can be said if you are guaranteed that the kernel always outputs a finite set of distributions (say of size at most G)? Can you comment on how would the minimax rates would scale with G? Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: No limitations. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for the detailed review and helpful comments. We now address the main concerns raised below: Adaptivity w.r.t. Noisy Labels: Indeed, in our setup, the noisy label distributions are selected adaptively, while the features are selected obliviously w.r.t. the realization of noisy labels. In fact, the features can also be made adaptive to noisy labels for the risk bound in Theorem 5. However, oblivious features are required in our conditional Le Cam Birgé testing, i.e., Theorem 4 (although we believe this can be resolved using a more tedious minimax analysis that involves both $x^J$ and $y^J$). Therefore, for the clarity of presentation, we have assumed that the features are generated obliviously w.r.t. noisy labels. We will make this clearer. Please note that the oblivious assumption for noisy label distributions and features w.r.t. the learner's prediction is not essential by a standard argument (c.f. Appendix H), provided the predictions have independent internal randomness among different time steps (which is satisfied by our algorithms). Motivation for Generalization: One of the primary motivations for generalization is to deal with cases with multi-class labels, where prior techniques based on EWA algorithms do not apply. A concrete example is that of Example 2. Note that we can instantiate Example 2 to the multi-class randomized response mechanism in differential privacy by specifying the $p_y$ as the singleton distribution that assigns probability 1 on $y\in \mathcal{Y}$ (with $\mathcal{Y}=\tilde{\mathcal{Y}}$) and the TV-radius is $\frac{N}{e^{\epsilon}-1+N}$ (to achieve $(\epsilon,0)$ local differential privacy). To our knowledge, the risk bound implied by our result is novel for this particular differential private online setting. Please refer to our global rebuttal for more details. Universal lower bounds: Indeed, our lower bound only holds in the minimax sense. Although, an $\Omega(\frac{1}{\gamma_H})$ lower bound holds for any non-trivial classes (i.e., there exist at least two distinct functions). Infinite Classes: Indeed, for any class $\mathcal{H}$ of finite Littlestone dimension $\mathsf{Ldim}(\mathcal{H})$, we can apply our algorithm on the experts constructed in Section 3.1 of [1] (specifically the multi-class version) to arrive at an upper bound $O(\frac{\mathsf{Ldim}^2(\mathcal{H})\log^2 (NT)}{\gamma_H})$ (independent of the noisy label set size $M$). Note that a logarithmic dependency on $N$ is necessary for finite Littlestone dimension classes (in the worst case). To see this, consider the class $H$ constructed by the reviewer. It is easy to see that the class has Littlestone dimension 1. However, one can assign the noisy label distributions to each $a\in \mathcal{Y}$ with constant pairwise KL-divergences (using, e.g., distributions of the form $p[m]=\frac{1\pm \epsilon}{M}$ for $m\in \tilde{\mathcal{Y}}$ with $M \sim\log N$). The $\Omega(\log N)$ lower bound will then follow by Fano's inequality. This is in contrast to the noiseless setting where the regret is independent of label set size. Unified measure: As mentioned above, we conjecture that the correct growth might be $O(\frac{\mathsf{Ldim}(\mathcal{H})\log(NT)}{\gamma_H})$ for any "non-trivial" class $\mathcal{H}$ and kernels independent of features. However, a general unified measure seems to be far from being achievable using our current techniques. This is due to the complicated structure of $\mathcal{H}$ and the weakness of Le Cam's two-point method (used in our lower bound proof). We believe investigating such a unified complexity measure would be of significant interest for future research. Convexity Assumption: The convexity assumption is used in the Le Cam Birgé testing (for the minimax theorem to work). Please note that the convexity is without loss of generality in our setting, since the adversary is allowed to choose the distribution arbitrarily, including a randomized strategy that is effectively selected from the convex hull. Therefore, any distributional strategy that the adversary might choose can be represented within this convex framework. --- Rebuttal Comment 1.1: Comment: Thanks for your response.	Summary: The paper generalized an agnostic online learning setting from [1]: Nature sequentially produces arbitrary feature vectors, and a noiseless label chosen from an arbitrary hypothesis within a given class. The learner observes the feature vector (exactly), and a noisy label chosen from a distribution chosen from a class of distributions, where the identity of the class depends on the noiseless label. The goal of the learner is to minimize the expected cumulative risk. The paper's main result (Theorem 2, also presented in a simplified form in Theorem 1) is characterization of the high probability (upper bound) and expected risk (lower bound) in terms of the Hellinger gap. The result follows from a proposed learning algorithm, which is based on pairwise testing. In addition, assuming a positive $L_2$ gap, tighter upper bounds are obtained w.r.t. the cardinality size of the hypothesis class (Theorem 5). Strengths: 1. Theorem 2 captures the exact dependence on the Hellinger distance $\gamma_H$, by providing upper and lower bounds whose dependence on that parameter is $\Theta(1/\gamma_H)$. 2. An additional result based on $L_2$ distance, which is tight also in the log-cardinality of the hypothesis class. 3. The introduction of the surrogate pairwise loss function and evaluating the loss by its maximum over all competing hypothesis, as well as the resulting reduction of online learning to binary hypothesis testing is interesting. Weaknesses: My main issue with the paper is that given the separation condition and finite hypothesis class, the resulting learning task is “easy”: 1. The assumption of a strictly positive Hellinger distance significantly eases the learning task. The immediate consequence of this is that the cumulative risk is bounded in $T$, and also hints the ease of the learner's task. As the algorithm also suggests, the problem is reduced to a composite binary hypothesis testing using $T$ samples, followed by static play of that decision. 2. Given that the problem is interesting, it is worth to already address the infinite class setting, and noises that are not uniformly bounded. While the technical details might be routine, the dependency of the risk bounds should be interesting, and, in relation to the previous comment, might also lead to elaborated risk bounds, with interesting dependency on the function class (parametric/a-parametric) and the noise conditions. Technical Quality: 3 Clarity: 4 Questions for Authors: 1. What is the conclusion from Example 1? From the paragraph that precedes it, it appears that it meant to justify either the semi-stochastic setting or the evaluation of the risk on the true labels, but it is not discussed how. From reading the rest of the paper, it appears that the analysis in this paper is a generalization of the result in Example 1, but this is not an intrinsic motivation. 2. Proof of Theorem 2: To the best of my knowledge, such problem is called composite hypothesis testing (rather than robust), and this was extensively studied in the information-theoretic literature. In this regard, the error in hypothesis testing is related to the KL divergence, for which chain rule is much more suitable to distributions that are not in product form via the standard chain rule. My question is why can't the analysis be made in terms of the KL divergence ? Finally, regarding line 41, what is differential piracy ? Only attacking some ships ? :-) Confidence: 3 Soundness: 3 Presentation: 4 Contribution: 2 Limitations: The paper properly discusses limitations throughout. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for the detailed review and helpful comments. We now address the main concerns raised below: Non-triviality of problem setup: We would like to clarify that the non-triviality of our pairwise testing scheme lies in how to use the testing results in an online fashion, as the testing results are not reliable (only the tests involving the ground truth are reliable, but it is unknown a priori). Moreover, the pairwise testing is not actually "static" since the composite distribution sets depend on the features, which are unknown as well. In fact, even for the Bernoulli noise case, the proof (c.f. Ben-David et al., Theorem 15 [1]) relies on quite non-trivial backward induction. It is not clear at all from their proof how the denominator $1-2\sqrt{\eta(1-\eta)}$ arises. One of our primary contributions is to figure out the precise complexity measure (i.e., the Hellinger gap) that determines the learning complexity and to provide a clearer characterization of the underlying paradigm. We would like to emphasize that the Hellinger gap (and the noisy kernel formulation) is not actually an "assumption" but a consequence of our characterization. It is our kernel formulation that allows us to approach the noisy online classification problem in such a clean manner, considering that prior proof techniques (c.f. [1]) are quite obscure even for Bernoulli noise. Non-uniform gap and infinite classes: In fact, as mentioned in Remark 1, our technique also works for infinite classes and non-uniform gaps. Indeed, for any class $\mathcal{H}$ of finite Littlestone dimension $\mathsf{Ldim}(\mathcal{H})$, we can apply our algorithm on the sequential experts constructed in Section 3.1 of [1] (specifically the multi-class version) to arrive at an upper bound $O(\frac{\mathsf{Ldim}^2(\mathcal{H})\log^2 (NT)}{\gamma_H})$. For binary-valued classes, Theorem 5 also implies an $O(\frac{\mathsf{Ldim}(\mathcal{H})\log T}{\gamma_L})$ upper bound. Moreover, for the non-uniform gaps, such as Tsybakov noises of order $\alpha$ as in [8], our results (primarily Proposition 1 and Theorem 3) implie a risk of order $\tilde{O}(T^{\frac{2(1-\alpha)}{2-\alpha}})$, and this is tight up to poly-logarithmic factors. We have chosen to omit these results in the submission due to limited space and their incremental nature, but we are happy to include them in the final version (given the additional page). Questions: 1. Example 1 is meant to provide a concrete instance of how stochastically generated labels (i.e., with Massart noise) can lead to non-trivial risk bounds on true labels that are independent of the time horizon, even though the noise rate is linear in T. Therefore, it is natural to investigate to what extent such a phenomenon can occur in more general noisy settings and to find the precise complexity measure that characterizes learnability. See also our global rebuttal for examples on differential privacy. 2. We thank the reviewer for clarifying the terminology. Our Hellinger-based testing error bound is essentially a conditional version of the Theorem 32.8 from [17]. We are unaware of any (general) analysis based on KL-divergences (we would greatly appreciate it if the reviewer could point it out to us). Since the KL-divergence is not symmetric, it is not well-suited to our case since we need to measure the distance between sets. Typos: We thank the reviewer for catching the typo; the correct term should be "differential privacy." --- Rebuttal Comment 1.1: Comment: Thank you for the clarifications. I understand that the Hellinger is a result of the analysis, but it is a consequence of the fact that the problem is just reduced to testing. It is not very surprising that testing results that does not involve the ground truth do not prevail the true hypothesis. So, overall I am still not fully convinced that the problem goes well beyond hypothesis testing, but it is nonetheless an interesting theoretical contribution, and so I have raised my score.	Rebuttal 1: Rebuttal: We thank all of the reviewers for their helpful comments. We would like to clarify the following two concerns shared by most of the reviewers: Infinite Classes: As mentioned in Remark 1, our techniques also work for infinite classes. Indeed, for any class $\mathcal{H}$ of finite Littlestone dimension $\mathsf{Ldim}(\mathcal{H})$, we can apply our algorithm on the sequential experts as constructed in Section 3.1 of [1] (specifically the multi-class version from Daniely et al., 2015, Thm 5) to arrive at an upper bound $O(\frac{\mathsf{Ldim}^2(\mathcal{H})\log^2 (NT)}{\gamma_H})$. This is because, for any finite Littlestone dimensional class, we can always find a finite sequential cover of size $(NT)^{\mathsf{Ldim}(\mathcal{H})+1}$; therefore, it can be effectively reduced to the finite classes case resolved in our work. Real-World Applications: We would like to clarify that our work is not intended to introduce any specific noise models. Rather, our main focus is to provide a characterization to determine, for any given noise model, the best achievable minimax risk. Since our algorithmic approach is general, it will serve as a baseline for various application scenarios. To give a clear exposition on how this works, we consider the following online local differential privacy setting. Let $\mathcal{H}$ be a hypothesis class with label set $\mathcal{Y}$ of size $N$. The randomized response mechanism works as follows: for any $y \in \mathcal{Y}$, we generate $\tilde{y}$ being $y$ with probability $1-\eta$ and generate uniformly from $\mathcal{Y}$ with probability $\eta$, where $\eta \le \frac{N}{e^{\epsilon}+N-1}$ (which achieves $(\epsilon, 0)$-local differential privacy). In this case, the noisy label set equals the true label set and the noisy kernel maps each $(x, y)$ to the distribution set $\\{(1-\eta)e_y + \eta u : \eta \leq \frac{N}{e^{\epsilon} + N - 1}\\}$ where $e_y$ assigns probability 1 to $y$ and $u$ is uniform over $\mathcal{Y}$. It is not hard to verify that the Hellinger gap of the kernel is $\Theta(\frac{\epsilon^2}{N})$ (for sufficiently small $\epsilon$). Our Theorem 2 then implies the risk bound $O(\frac{N\log^2\|\mathcal{H}\|}{\epsilon^2})$. To our knowledge, the implied risk bound is original for this particular differentially private multi-class online setting. [DSBS15] A. Daniely, S. Sabato, S. Ben-David, and S. Shalev-Shwartz. Multiclass Learnability and the ERM Principle. JMLR 2015.	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
DiffuLT: Diffusion for Long-tail Recognition Without External Knowledge	Accept (poster)	Summary: This article uses a Diffusion model to generate tail class samples, achieving balance among classes at the data level and thereby addressing the long-tail distribution problem. Additionally, the authors believe that AID samples are the most beneficial in enhancing classifier performance; therefore, they design an L_AID loss to constrain the diffusion model to generate richer AID samples. Qualitative and quantitative comparisons have been made on three benchmark datasets, showing the efficiency of their method. Strengths: 1. The paper is clearly organized and well written. 2. The experimental results look good. 3. The motivation is reasonable. Weaknesses: 1. The innovation is limited. Essentially, the authors' method designs a reconstruction loss to constrain the generative model to learn a distribution more consistent with real distributions, and many existing studies have proposed similar ideas. 2. The authors emphasize that this method has generalizability in real-world applications; however, I hold a negative view on this point. I believe that the performance improvement observed in this paper is fundamentally due to training data and test data having identical distributions. Therefore, constraining the diffusion model to learn a distribution closer to training data benefits classifier learning. However, in real-world applications where limited training data may not share identical distributions with potentially infinite test data, using this method might lead to negative impacts. 3. On what principle was Equation 4 determined? Why define [df, 2df] as AID? What impact would modifying this equation? For instance, would defining [df, \sqrt(2)df] as AID affect performance? 4. In Table 6, why does combining ID and AID result in worse performance than using only AID for CBDM? 5. Authors should provide ablation studies for Nt. Technical Quality: 2 Clarity: 2 Questions for Authors: Please refer to weaknesses for corresponding questions. Confidence: 4 Soundness: 2 Presentation: 2 Contribution: 2 Limitations: The authors have addressed the limitation of this method. This method will significantly increase training time. Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: ### W1 > The innovation is limited. Essentially, the authors' method designs a reconstruction loss to constrain the generative model to learn a distribution more consistent with real distributions, and many existing studies have proposed similar ideas. The focus of our approach is not on training a generative model to learn a distribution that closely matches real-world data. Instead, we emphasize the relationship between generative models and discriminative models, addressing two questions that are yet to be fully explored: Can a generative model without external knowledge improve a classification model? And what type of generated data is most beneficial? Previous research has primarily relied on pretrained diffusion models, which we believe limits practical applicability and may lead to data leakage. We would appreciate it if you could provide examples of existing studies with similar concepts. To the best of our knowledge, no such prior art exists. ### W2 >The authors emphasize that this method has generalizability in real-world applications; however, I hold a negative view on this point. I believe that the performance improvement observed in this paper is fundamentally due to training data and test data having identical distributions. Therefore, constraining the diffusion model to learn a distribution closer to training data benefits classifier learning. However, in real-world applications where limited training data may not share identical distributions with potentially infinite test data, using this method might lead to negative impacts. As mentioned in previous publicity in CVPR [1], the long-tailed setting assumes that the distribution of the label $p(y)$ differs between the training and test sets, but the conditional distribution $p(x\|y)$ remains unchanged. These default settings hold true in current long-tailed recognition settings, and also can serve as the potential theoretical foundation for many long-tailed literatures [2][3]. The scenario you mentioned, where the training and test samples do not share the same distribution, might be different from the definition of long-tailed learning. To address concerns about the potential negative impact of distribution shifts, we conducted a firmly experiments: we trained a ResNet-50 backbone on both the ImageNet-LT dataset and ImageNet-LT augmented with data $\mathcal{D}_{gen}$ generated by our DiffuLT method. We then performed linear probing (the transfer learning settings) on the CIFAR100-LT with an imbalance ratio of 0.01. \| DiffuLT \| CIFAR100-LT Acc (%) \| \|---------\|---------------------\| \| × \| 62.5 \| \| √ \| 70.9 \| Despite the distribution differences between ImageNet-LT and CIFAR100-LT, our method still showed improvement. Therefore, we believe our method does not negatively impact model performance when distributions change. Regarding real-world applications, our paper demonstrates that our methods can benefit medical imaging, remote sensing, and general image classification under long-tailed settings. We recognize that the understanding of "real-world application" may vary, and we are open to further discussion if you could specify your interpretation of this term. ### W3 > On what principle was Equation 4 determined? Why define [df, 2df] as AID? What impact would modifying this equation? For instance, would defining [df, \sqrt(2)df] as AID affect performance? The definition of AID samples in the paper can be seen as `somewhat arbitrary'. However, we prioritized efficiency, performance, and simplicity in arriving at this definition. An ablation study shows that this approach achieves the best results with the highest efficiency. \| AID range \| $‖\mathcal{D}_{gen}‖$ \| Acc (%) \| $\Delta \text{Acc}/‖\mathcal{D}_{gen}‖$ \| \|-----------------\|--------\|---------\|----------------------\| \| $[d_f, \sqrt{2}d_f]$ \| 5,212 \| 41.2 \| $5.51\times 10^{-4}$ \| \| $[d_f, 2d_f]$ \| 11,886 \| 45.2 \| $5.78\times 10^{-4} $ \| \| $[d_f, 3d_f]$ \| 15,384 \| 41.7 \| $2.23\times 10^{-4} $ \| We opt not to use the first definition because the range should be as wide as possible to ensure efficient generation, while avoiding the production of too many unused samples. Although a more precise search might yield better results, we prioritize simplicity and avoid complex parameter tuning, leading us to set the region as defined. ### W4 > In Table 6, why does combining ID and AID result in worse performance than using only AID for CBDM? Actually, this is one of the key ideas of our paper. In this setting, the number of generated samples is consistent, although the generation frequency varies due to the different distributions of data types. Our key observation, as shown in Table 3 of paper, is that AID samples contribute more to classification performance compared to ID samples. Since the "ID & AID" setting includes fewer AID samples than the "AID" setting, it results in a worse outcome. ### W5 > Authors should provide ablation studies for Nt. We conducted an ablation experiment for $N_t$ under the CIFAR100-LT setting with an imbalance ratio of 0.01. \| $N_t$ \| CIFAR100-LT Acc (%) \| \|-----\|---------------------\| \| 300 \| 48.5 \| \| 400 \| 50.4 \| \| 500 \| 51.5 \| \| 600 \| 51.8 \| \| 700 \| 49.2 \| The performance shows only a slight improvement after $N_t > 500 $ and begins to decrease after $N_t > 600$. We believe the main reason for this is that the class with the most samples has only 500 instances, so choosing $N_t > 500$ inevitably introduces noise. When $N_t$ is too large, the impact of this noise outweighs the benefits of the newly added information. [1] Disentangling Label Distribution for Long-tailed Visual Recognition. CVPR 2021. [2] Long-tail learning via logit adjustment. ICLR 2021 [3] Balanced Meta-Softmax for Long-Tailed Visual Recognition. NeurIPS 2020 --- Rebuttal Comment 1.1: Comment: Thank you for the reply, I have read your rebuttal and the comments from other reviewers. I believe the novelty and methodological design of this paper do not convince me to immediately revise the score. I will wait until the Reviewer-AC Discussions phase to decide on the final score. --- Rebuttal 2: Title: Follow-up Comment: Dear Reviewer, We hope that our rebuttal has effectively clarified any confusion and that the additional experiments we provided have strengthened the validity of our approach. We eagerly await your feedback on whether our response has adequately resolved your concerns or if further clarification is needed. --- Rebuttal 3: Title: Discussion of novelty and methodological design Comment: Dear Reviewer, Thank you for your feedback and patience. We would like to address your concerns regarding the novelty and methodological design of our work. ### Novelty The novelty of our approach lies in two main areas: primarily in the long-tailed learning domain and, to a lesser extent, in the generative modeling domain. Long-Tailed Learning: - Diffusion Model without External Knowledge: Our key contribution is the novel application of diffusion-based models to long-tailed learning *without relying on external knowledge. While recent works like [1] and [2] utilize Stable Diffusion to address data scarcity in classification tasks, they often face criticism due to the extensive pretraining on external large datasets* (much larger than those for classification tasks), which can overshadow the novelty of their approach. We specifically address the question of whether a generative model, trained only on the limited data available in classification tasks, can still be effective. Our work demonstrates that this is indeed possible for the first time, providing a significant insight, especially when the training data is not composed of natural images (as discussed in our response to W3 of reviewer #vaue). This contribution may open new research avenues within the long-tailed learning community, offering a fresh perspective on the integration of generative models for classification tasks. - Understanding Diffusion Models: We also provide an explanation of why diffusion models, even without external knowledge, are effective in this context. Our work is the first to introduce the concept of AID samples and the role of generation model in blending information of each class to generate beneficial and novel samples. Generative Modeling: - A New Objective for Generative Models: Traditionally, models like VQ-GAN are trained with objectives such as reconstruction loss and perceptual loss to generate realistic images. Our work introduces a novel objective: optimizing the generative model to produce images that are beneficial for classification tasks. This represents a significant shift from the traditional goal of generating visually appealing images to a more practical application, where the generated images directly enhance discriminative tasks. This objective is inherently challenging to optimize, and our introduction of AID samples provides a novel pathway for achieving this goal. ### Methodological Design To address your concerns, we highlight the key designs of our method: New Designs: - Classification of Generated Images: We classify generated images based on their distribution in the feature space relative to real data. - Novel Loss Function: We introduce a new loss function that uses classifiers to guide the training of the generative model. This simultaneously addresses the long-tailed generation problem and enhances the utility of the generative model for classification tasks. - Diffusion Model without External Knowledge: As previously mentioned, our method employs a diffusion model trained without external knowledge to generate images that aid long-tailed learning. - Weighted Synthetic Samples: We apply weights to synthetic samples during backpropagation to improve training efficacy. Adapted Designs: - Sample Filtering: We use a trained classifier to filter out harmful samples, similar to existing methods but without relying on models like CLIP. We hope this addresses your concerns. Please feel free to reach out if further discussion or additional experiments are needed. We look forward to your feedback. Thank you again! [1] Expanding Small-Scale Datasets with Guided Imagination. NeurIPS 2023. [2] Feedback-guided Data Synthesis for Imbalanced Classification. NeurIPS Workshop 2023.	Summary: This paper introduces a novel pipeline for long-tail recognition that differs from conventional strategies by focusing on dataset composition. The method focuses on the dataset and introduces a diffusion model, namely DDPM to generate data for tail classes. The analysis reveals that approximately-in-distribution (AID) samples, which slightly deviate from the real data distribution and blend class information, are essential for enhancing the generative model’s performance in long-tail classification. Experiments conducted on CIFAR 10-LT, CIFAR 100-LT, and ImageNet-LT demonstrate significant performance improvements. Strengths: 1. The paper is well-organized and easy to understand. 2. The paper explores a novel perspective to tackle imbalance issue, by generating data for tail classes before training the classifier, which shows promising results compared to baseline results. 3. The paper explores the data composition, namely ID, AID and OOD, and gives a detailed analysis of the correlation between generated data composition and classification performance. Weaknesses: 1. Some typos: line 137 ‘am input’ 2. The baseline setup in Table 1,2,3 requires further explanation. 3. The paper mentions the time cost is four times longer than baseline, indicating that this method may be impractical for datasets with a significantly large imbalance ratio due to the extended generation and retraining times. 4. Some baseline results in Tables 8 and 9 are indicated as ‘-’ and ‘ ’; an explanation for these forms of absence is missing. 5. This method focuses on generating data for tail classes, resulting in significant improvements for these classes compared to other baseline methods. A fairer comparison would be with the same pipeline using different generative models. 6. A long-tailed diffusion model baseline[1] is missing. 7. The experiment are mainly conducted on manually-selected long-tailed datasets, it would improve the robustness of results by including real-world long-tailed datasets such as iNaturalist. [1] Long-tailed Diffusion Models with Oriented Calibration. ICLR 2024. Technical Quality: 3 Clarity: 3 Questions for Authors: please refer to the weakness part. Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: The limitations are discussed in this paper. No potential negative social impact. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: ### W1 > Some typos: line 137 ‘am input’ Thank you for your feedback; we'll fix it in the next version. ### W2 > The baseline setup in Table 1,2,3 requires further explanation. We are sorry for the confusion. Actually, the baseline setup adheres to the code and protocols from [1], with a 200-epoch training schedule. Training is conducted with a batch size of 128 using an SGD optimizer at a learning rate of 0.1. These detailed settings can also be found in our appendix. ### W3 > The paper mentions the time cost is four times longer than baseline, indicating that this method may be impractical for datasets with a significantly large imbalance ratio due to the extended generation and retraining times. Thanks for your review. We argue that since DiffuLT doesn’t rely on external knowledge like pretrained models or additional data, it is highly practical in scenarios where data is limited and that acquiring more training data is costly or impossible. In such cases, training time is not the primary concern, while acquiring satisfactory accuracy is. To make our arguments valid, we showcase two quantitative examples: medical imaging using the KVASIR dataset and remote sensing with the EuroSAT dataset. We train the classifier on long-tail versions of these datasets with an imbalance ratio of 0.01, where models typically struggle due to the skewed distributions. \| Model \| Long-tailed \| KVASIR Acc (%) \| EuroSAT Acc (%) \| \|-----\|-------------\|----------------\|-----------------\| \| Baseline \| × \| 83.8 \| 93.2 \| \| Baseline \| √ \| 52.1 \| 88.9 \| \| DiffuLT \| √ \| 66.8 \| 92.0 \| As shown in the table, our method significantly mitigates the long-tail issue in these important scenarios, showing our great generalization ability for practical usage. We would provide more such discussions in the final version. ### W4 > Some baseline results in Tables 8 and 9 are indicated as ‘-’ and ‘ ’; an explanation for these forms of absence is missing. Thanks for your careful review. Since the comparison results are based on the reported values in their respective papers, any results not shown in the original papers are indicated as “-”. ### W5 & W6 > This method focuses on generating data for tail classes, resulting in significant improvements for these classes compared to other baseline methods. A fairer comparison would be with the same pipeline using different generative models. > A long-tailed diffusion model baseline is missing. Following your suggestions, we compare our method with different generation models using the same pipeline in Table 5 of the paper. While T2H, as you mentioned, shows slightly better performance than CBDM, it falls short of our proposed model because it isn't primarily designed for discriminative tasks. \| Method \| CIFAR100-LT Acc (%) \| \|----------\|---------------------\| \| Baseline \| 38.3 \| \| DDPM \| 43.8 \| \| CBDM \| 46.6 \| \| T2H \| 46.8 \| \| DiffuLT \| 51.5 \| Additionally, using pretrained diffusion models like Stable Diffusion could lead to data leakage, resulting in an unfair comparison, and they are not well-suited for data beyond natural images. We will add these comparisons in our final version. ### W7 > The experiment are mainly conducted on manually-selected long-tailed datasets, it would improve the robustness of results by including real-world long-tailed datasets such as iNaturalist. You have raised an interesting point. We have tried our best to train a generation model with iNaturalist dataset, but we found that this dataset is too large that it consumes all of our GPU computing power. We are running DiffuLT pipeline with a manually sampled subset of iNaturalist, but due to time constraint, experiments are not finished at present. We promise to showcase analysis and experiment results in our final version. In the meanwhile, since iNaturalist is similar to ImageNet-LT, both being natural image datasets, we believe the effectiveness of our model on this type of data is validated. Additionally, the results on KVASIR and EuroSAT, which are real-world long-tailed datasets that have entirely different distributions, further demonstrate the robustness of our model. [1] Bbn: Bilateral-branch network with cumulative learning for long-tailed visual recognition. CVPR 2020. [2] KVASIR: A Multi-Class Image Dataset for Computer Aided Gastrointestinal Disease Detection. MMsys 2017. [3] Eurosat: A novel dataset and deep learning benchmark for land use and land cover classification. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing 2019. --- Rebuttal 2: Title: Follow-up Comment: Dear Reviewer, We hope that our rebuttal has effectively clarified any confusion and that the additional experiments we provided have strengthened the validity of our approach. We eagerly await your feedback on whether our response has adequately resolved your concerns or if further clarification is needed. --- Rebuttal Comment 2.1: Comment: Thanks for the response. Most of my concerns have been addressed and I would like to raise my score to '5'. --- Reply to Comment 2.1.1: Title: Thanks for raising your score Comment: Dear Reviewer, Thank you for raising your score! We're encouraged that our rebuttal addressed your concerns, and we sincerely appreciate your support for our work.	Summary: This paper introduces a diffusion based long-tail recognition method termed DiffuLT. DiffuLT uses diffusion model to generate supplement samples in order to balance the long-tailed dataset. The authors first discover that approximately-in-distribution (AID) samples are crucial in enhancing the generative model’s performance in long-tail classification, as it blends the useful information from other classes into the tail class. Inspired by such discovery, the authors propose to first train a feature extractor $\varphi_0$ merely from the long-tail dataset, then utilize $\varphi_0$ to guide the generation of AID samples, and finally train the desired classification model using the original dataset and newly generated AID samples together. Experiments validate the enhanced performance of DiffuLT. Strengths: This paper is well-written in the following dimensions: 1. Originality: The originality of this paper comes mainly in two aspects. First, the authors discover that AID samples are crucial in enriching tail class samples and enhancing model performance. Second, the authors incorporate revised diffusion model to generate AID samples. This method is original and effective. 2. Quality: This paper is in good quality. The proposed method is both convincing and effective. 3. Clarity: From introduction to discovery of the effectiveness of AID samples, then the pipeline of DiffuLT and finally the experiments and ablation studies, the structure is clear and logical. 4. Significance: The discovery that AID samples are crucial in long-tail recognition performance is quite useful. Weaknesses: 1. It would be better if you show how “centralized” figure 2 is, for example, add support data of the proportion of ID, AID and OOD data. This figure is not intuitive enough. 2. Citation suggestions. I believe your work would benefit from referencing some additional literature to provide a more comprehensive context for your study. Specifically, i recommend citing the following articles: - A Unified Generalization Analysis of Re-Weighting and Logit-Adjustment for Imbalanced Learning (NeurIPS 23) - Deep long-tailed learning: A survey (TPAMI 23) - Effective Data Augmentation With Diffusion Models (ICLR 24) - Harnessing Hierarchical Label Distribution Variations in Test Agnostic Long-tail Recognition (ICML 24) 3. Minor typos. Line 137 “as an input”. Line 227 “because it doesn’t rely on any external dataset or model”. Technical Quality: 3 Clarity: 3 Questions for Authors: Could you explain how your method differs from other data augmentation methods? Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: See Weaknesses. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: ### W1 >It would be better if you show how “centralized” figure 2 is, for example, add support data of the proportion of ID, AID and OOD data. This figure is not intuitive enough. Thank you for your feedback. We agree that the centralization of data is not immediately apparent in Figure 2. It becomes clear through the statistics presented in Table 2. We believe that adding annotations to indicate each data type's region in the figure would help readers understand it more effectively. ### W2 > Citation suggestions. I believe your work would benefit from referencing some additional literature to provide a more comprehensive context for your study. Thank you. We will include the first and last papers in our comparison results in the experiment, and we will incorporate the middle two works into our related works section in the future version. ### W3 > Minor typos. Line 137 “as an input”. Line 227 “because it doesn’t rely on any external dataset or model”. Thanks for your patient review. We’ll address those issues accordingly. --- Rebuttal Comment 1.1: Comment: Thank you for your response. I would keep my score. --- Rebuttal 2: Title: Gratitude for your response and additional explanation Comment: Dear Reviewer, Thank you for your prompt response and patience. We greatly appreciate your valuable advice and your support for our paper. Due to an oversight, we did not provide a satisfactory answer to your question. Recognizing its importance, we would like to address it comprehensively here. ### Q1 > Could you explain how your method differs from other data augmentation methods? We conducted a thorough survey of data augmentation methods for long-tail learning, categorizing them into two groups: feature augmentation and image augmentation. Feature augmentation methods, such as RSF[1] and OFA[2], primarily focus on biasing the decision boundary towards tail classes. These methods are similar to re-weighting or re-sampling techniques and do not inherently increase data diversity. Moreover, because features are indirect and often difficult to map back to images, these methods differ fundamentally from image augmentation techniques. Image augmentation methods share our motivation of increasing dataset richness. We specifically examined M2m[3], MiSLAS[4], Remix[5], CMO[6], and CSA[7], discussing each as follows: - M2m: This method augments tail classes by transforming head-class samples into tail-class ones through perturbation-based optimization. However, the generated samples often closely resemble the originals (the head images), failing to truly enrich the diversity of tail classes. - MiSLAS and Remix: These methods use Mixup for augmentation. However, MiSLAS experiments indicate that applying Mixup during classifier learning does not yield significant improvements and may even harm performance, requiring additional strategies to mitigate this issue. - CMO and CSA: Both methods introduce rich contexts from majority samples into minority samples. CMO uses CutMix, while CSA employs a more precise segmentation approach. While effective in enriching context, they do not enhance the diversity of objects within tail classes. Data richness, particularly in tail classes, is crucial for addressing the long-tail problem. While recent methods have acknowledged this and used data augmentation to tackle it, their effectiveness is limited to context enrichment. In contrast, diffusion models in our pipeline represent the most powerful data augmentation method. Unlike mixup-based approaches, diffusion models avoid domain shift by accurately estimating data distributions. Additionally, they enrich both context and objects, offering greater diversity since they combine the entire dataset rather than just two images like CMO or CSA. Therefore, with proper utilization, diffusion models hold the highest potential. Below is a performance comparison of various data augmentation methods, including ours, on CIFAR100-LT with an imbalance ratio of 100, using ResNet-32 as the backbone. \| Method \| CIFAR100-LT Acc (%) \| \|--------\|---------------------\| \| RSF \| 43.1 \| \| OSA \| 42.9 \| \| M2m \| 43.5 \| \| MiSLAS \| 47.0 \| \| Remix \| 46.8 \| \| CMO \| 47.2 \| \| CSA \| 46.6 \| \| Ours \| 51.5 \| [1] RSG: A Simple but Effective Module for Learning Imbalanced Datasets. CVPR 2021. [2] Feature Space Augmentation for Long-Tailed Data. ECCV 2020. [3] M2m: Imbalanced Classification via Major-to-minor Translation. CVPR 2020. [4] Improving Calibration for Long-Tailed Recognition. CVPR 2021. [5] Remix: Rebalanced Mixup. ECCV workshop 2020. [6] The Majority Can Help the Minority: Context-rich Minority Oversampling for Long-tailed Classification. CVPR 2022. [7] How Re-sampling Helps for Long-Tail Learning? NeurIPS 2023.	null	null	null	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
On Neural Networks as Infinite Tree-Structured Probabilistic Graphical Models	Accept (poster)	Summary: The paper "On Neural Networks as Infinite Tree-Structured Probabilistic Graphical Models" introduces a framework that constructs infinite tree-structured probabilistic graphical models (PGMs) corresponding to deep neural networks (DNNs), demonstrating that DNNs perform precise approximations of PGM inference during forward propagation. While this claim, along with others in the paper, sounds plausible, it also seems well-known within the field. The transition from Fig. 1a (Neural Network represented graphically) to the tree-like graphical model shown in Fig. 1b appears to simply construct what is called a computational tree in the graphical model literature. For reference, see several earlier papers discussing the topic: • Sekhar C. Tatikonda and Michael I. Jordan. "Loopy belief propagation and Gibbs measures." Proceedings of the Eighteenth Conference on Uncertainty in Artificial Intelligence, UAI’02, page 493–500, San Francisco, CA, USA, 2002. Morgan Kaufmann Publishers Inc. • Alexander T. Ihler, John W. Fisher III, and Alan S. Willsky. "Loopy belief propagation: Convergence and effects of message errors." Journal of Machine Learning Research, 6(31):905–936, 2005. • Dror Weitz. "Counting independent sets up to the tree threshold." Proceedings of the Thirty-Eighth Annual ACM Symposium on Theory of Computing, STOC ’06, page 140–149, New York, NY, USA, 2006. Association for Computing Machinery. The last paper suggests an exact map of a finite loopy graphical model of the Markov Random field type into a large but finite loopless graphical model (tree). The infinite graphical model (computational tree) is linked to approximate inference (with belief propagation) in the original graphical model. Computational tree-based approaches have previously been associated with both variational and MCMC techniques, though they were not developed into practical algorithms. I find the Hamiltonian Monte Carlo algorithm developed in the paper, along with the reported experiments, quite interesting. However, I believe that more experiments and exploration are needed, as well as improved references to prior work in graphical models, before the paper is ready for publication. Strengths: see summary Weaknesses: see summary Technical Quality: 3 Clarity: 2 Questions for Authors: see summary Confidence: 4 Soundness: 3 Presentation: 2 Contribution: 2 Limitations: see summary Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for this very interesting comment about the computation tree and loopy BP. While the computation tree is certainly a useful tool for precisely characterizing the approximation made by loopy belief propagation, we do not believe that the construction presented in this work is a trivial extension of that idea. Whereas belief propagation is exact in tree structured (non-loopy) graphs, the forward pass of the neural network when compared to conditional probability values of the Markov network with the potentials described in this work will not match even in the simple case of several hidden nodes connected in a line. Unlike loopy belief propagation then, which is well defined probabilistically in these simple cases, the neural network's forward operation must be captured by the infinite copies defined by the second step of our construction. This already differs rather notably from the use of the computation tree to characterize loopy belief propagation's approximation as that theoretical approach involves designing a tree whose values when computed are ordered correctly such that the influence of the loopy updates of belief propagation in non-tree structured graphs on nodes updated later are properly captured. Since the neural network's forward pass does not pass information backward, or in loops, the ordering of the nodes in our construction (ignoring the copies at this point) is wholly different from the computation tree that would be derived from using loopy belief propagation in a similarly structured starting graph. For example, in Figure 1 (page 3) of Loopy Belief Propagation and Gibbs Measures by Tatikonda and Jordan, it can be seen that when calculating the probability of node $a$ using the computation tree, an earlier belief about node $a$ is used earlier in the tree. For the neural network forward pass, however, information is never passed from a node back to itself. As such, the corresponding construction only ever creates copies of nodes in order to create a tree structure and account for how a local expectation is passed forward. It never creates a reordering of said nodes (as they would be ordered within the layers of the neural network). Belief propagation will naturally provide the same conditional probability as the forward pass of the neural network when it is applied within the infinite-width tree structured PGM, but that is simply a result of belief propagation being exact in tree structured graphs and said construction matching the operations of the neural network. When applied to the initial, loopy, graph defined by the neural network's structure, the relevant computation tree would not properly capture the neural network's operations. --- Rebuttal 2: Comment: In response to the authors' rebuttal, I want to clarify that I am not suggesting their work is a trivial extension of the computational tree framework. However, the computational tree serves as a significant reference point that should be discussed in the final version, should the paper be accepted. To further clarify my comments: 1) My observations regarding the relationship to the computational tree specifically pertain to the forward propagation aspect of the algorithm, where, as I understand it, the structure of the candidate tree and factors is fixed. 2) The approach introduced by Dror Weitz (as mentioned in my original review) constructs not an infinite but a specifically truncated portion of the computational tree. This construction provides exact, rather than approximate, inference for the known Graphical Model, particularly in the forward part of the algorithm discussed by the authors. --- Rebuttal 3: Comment: Thank you for the clarification. We agree that the work that has been done using computation trees warrants mentioning in reference to the proposed construction and we will include a corresponding discussion in the final version of the paper. (1) The structure of the candidate tree and factors are fixed, which certainly aligns with how copies of nodes are added in the computation tree, even if the ordering of those nodes differs. (2) The truncated tree presented in Dror Weitz's work certainly appears most similar to the first step of our PGM construction due to its finite nature and perhaps an easier way to present that first step would be to describe it as consisting of several paths (walks) that follow the direction of the arrows in the initial neural network DAG that are copied in such a way that they do not overlap (and where copies of a node never appear as ancestors to the same node). That said, we would be cautious to very closely align the two as the first step of our construction follows this directed/layer-by-layer ordering while the graph presented in Weitz's paper is undirected. We thank the reviewer again for bringing our attention to this interesting connection.	Summary: The paper proposes a novel connection between DNNs and PGMs. Specifically, the idea s to unroll the DNN computation graph in the form of a PGM. The main formal result that is shown is that DNN forward propagation corresponds to exact inference in the encoded PGM. More practically, since the PGM is infinite, it should not be expected to replace DNN-based operations, but rather to understand the working of a DNN from a PGM perspective. Further, a new HMC algorithm is developed using this view and the resulting approach can be used model calibration. Experiments are performed on synthetic data from a known distribution to measure the calibration error. Another set of experiments are performed with Covertype datasets Strengths: - The paper presents a nice connection between exact inference in PGMs with DNN propagation (for sigmoid units) which seems to be previously unknown - There could be many foundational results that may be possible with the proposed connection (e.g. approximate inference in PGMs, etc.) - The paper is well written and makes its contributions and limitations very clear Weaknesses: - The main weakness is perhaps in that the practical utility of going from the DNN function space to the PGM space is yet unknown. The experiments on calibration seem to show some promise but maybe stronger real-world studies could have demonstrated the need for the connection. Technical Quality: 3 Clarity: 3 Questions for Authors: If inference in a PGM corresponds to DNN propagation, then what is the likely source of miscalibration in the DNN models, I was wondering there is some way of knowing this using the proposed connection. Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: Limitations are identified and adequately discussed. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for the great comment and question. The weakness is addressed in the general response. Regarding your question, we suspect that deep neural network miscalibration may arise from the non-standard infinite width structure of the proposed probabilistic graphical model (PGM). While inference in the infinite width PGM matches the forward operations of the neural network, it is itself, a remarkably unwieldy structure. This can be seen perhaps most easily by thinking of the flow of information across the neural network during its forward pass, how, if the value of a hidden neuron is observed, i.e. no longer hidden, that information does not affect earlier neurons (unlike in more traditional PGM structures where that information might be passed backward). The infinite copies of each node in the PGM construction of the neural network also effectively passes a local average value of each parent node forward, which is itself quite restrictive. Therefore, it seem possible that graphs more closely aligned to traditional Markov Random Fields (MRFs) or Bayesian networks might be less prone to the same types of miscalibration found in neural networks when the relationship between the inputs/outputs is less deterministic. The experiments with smaller choices of $L$ were done with the aim of potentially bridging the gap between the infinite width model and a less extreme tree structured PGM. Clearly when the input/output relationship is largely deterministic, the neural network can simply match its input/output predictions to high confidence values due to being a universal function approximator, but in settings with a more probabilistic nature this disconnect between the underlying infinite-width tree structure PGM that represents the DNN's operations and a, perhaps, more plausible, traditional PGMs could be a source of under/over-confidence. --- Rebuttal Comment 1.1: Comment: Thanks for your response. I think the connection between PGMs and DNNs can be beneficial in several ways. I think this area is worth exploring and revisiting (including connections to some of the older works that other reviewers have mentioned). I am in general positive about this work.	Summary: This work bridges the gap between Deep Neural Networks (DNNs) and Probabilistic Graphical Models (PGMs). The authors do so by viewing DNNs as defining a joint distribution over the values of their nodes and showing that forward pass on a DNN is equivalent to exact probabilistic inference on a corresponding infinite tree-structured PGM. The authors describe an algorithm to construct a tree-structured PGM corresponding to a given DNN by unrolling it into a tree and making L copies of each non-output node (corresponding to an L-sample approximation of the expected value at the node). As L tends to infinity, the constructed PGM becomes equivalent to the DNN. A key implication of this result is that PGM algorithms can now be used to train DNNs. Specifically, the authors observe that the Stochastic Gradient Descent (SGD) approach to training DNNs differs from the contrastive divergence (CD) algorithm since SGD ignores the values of the output variables when computing the expected values of the latent variables. Using this observation, the authors propose a CD-based learning algorithm for DNNs that uses Hamiltonian Monte Carlo (HMC) sampling to approximate the expectations instead of Gibbs sampling which would be computationally inefficient given the large number of variables in the DNN. The authors evaluate the proposed HMC-based learning algorithm using synthetic data sets and the Covertype data set from the UCI Machine Learning repository. They compare their approach against SGD and Gibbs sampling-based learning. They measure the calibration of the models learned on the synthetic data sets using Mean Absolute Error (MAE) from the true distribution and they measure the calibration for the Covertype data set using Expected Calibration Error (ECE). The evaluation shows that the proposed HMC-based algorithm (1) is equivalent to SGD for large values of L and (2) yields highly calibrated models for small values of L (such as 10) Strengths: 1. The work establishes a formal connection between DNNs and (infinite tree-structured) PGMs. Apart from being a new perspective on DNNs, this allows access to PGM theory and algorithms for learning and inference. 2. The authors show that the DNN forward pass is not equivalent to exact probabilistic inference on the same structure but it is equivalent to exact inference on a separate infinite tree-structured PGM that can be constructed from the DNN. This allows us to characterize the approximation made by forward pass-based inference in DNNs. 3. The authors use the infinite tree-structured PGM equivalence result to develop an HMC-based learning algorithm for DNNs and empirically show that the algorithm yields more calibrated models. Weaknesses: While the paper makes important contributions, the presentation makes it hard to read in some places 1) Lines 127-143 would be clearer if presented in an algorithm environment with appropriate notation. 2) LineD- 245 says "our previous C1 algorithm" but CD-k and CD-1 are explained in lines 264-266 3) The description of a BN in lines 270-281 seems out of place and should probably be in Section 5.1 4) The Experimental Results section should be reorganized for readability by explicitly discussing research questions, metrics, baselines, and data sets before presenting results and answering research questions. While the authors contrast their work against Bayesian Neural Networks, they should also contrast it with Probabilistic Circuits such as sum-product networks which are computational graphs that define a joint distribution over a set of input variables. Technical Quality: 3 Clarity: 2 Questions for Authors: Can you elaborate on the working of the Gibbs sampling baseline in the experimental evaluation? Does it also depend on L? Also, how many samples were used for each of the experiments? Confidence: 3 Soundness: 3 Presentation: 2 Contribution: 4 Limitations: The authors clearly state the limitations of the work such as applicability to non-sigmoid DNNs and describe ways in which future work could address them. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you very much for your detailed review, great comments on the paper presentation and questions about the experiments. The first weakness about the PGM-DNN construction is addressed in the general response, and we also agree that some rearrangements in Section 5 would be helpful to make the presentation more clear as you mentioned in the other weaknesses. We will include an explanation to CD-1 and CD-k when we mentioned contrastive divergence in the first paragraph of Section 5, and move the description of a BN in lines 270-281 to the beginning of section 5.1 in the revision. For the fourth weakness about the result section, the discussions on research questions and baseline are mentioned at the beginning of Section 5.2, and the descriptions about datasets and metrics are at the beginning of Section 5.2.1 and 5.2.2 since we are using different types of datasets in our experiments. Thank you for pointing out that the results should be put after the discussion and we will modify the position setting of Table 1 and move it to the end of Section 5.2.1. For the first question about Gibbs sampling in the experimental evaluation, both Gibbs and HMC are sampling methods to generate new states for all the hidden nodes and they both apply CD-1 or CD-k to learn the weight. While HMC samples real values in the range of $[0, 1]$ under the normal distribution, Gibbs samples values in {0,1} under Bernoulli distribution. For node $h_{ij}$, i.e., the $j$th node in $h_i$ layer, the Bernoulli distribution used to sample its new state is determined by its Markov blanket, which includes all the nodes in layer $h_{i-1}$, $h_i$, and $h_{i+1}$ in this case. It could be calculated by normalizing the joint probability distribution of the blanket when $h_{ij}=1$ versus $h_{ij}=0$, which is written as following: $$ P(h_{ij}=1)=\frac{P(h_{ij}=1\|h_{i-1})\cdot P(h_{i+1}\|h_i\setminus\\{h_{ij}\\},h_{ij}=1)}{P(h_{ij}=0\|h_{i-1})\cdot P(h_{i+1}\|h_i\setminus\\{h_{ij}\\},h_{ij}=0)+P(h_{ij}=1\|h_{i-1})\cdot P(h_{i+1}\|h_i\setminus\\{h_{ij}\\},h_{ij}=1)} $$ We then sample a new state for $h_{ij}$ from $\text{Bern}(P(h_{ij}=1))$. In Gibbs sampling, the node is sampled one by one since a newly sampled node will affect the sampling of subsequent nodes in its Markov blanket. After sampling new values for all the hidden nodes, the weight is similarly updated using Equation (5)(6)(7) (line 302). So, the Gibbs sampling we used does not depend on $L$. For the second question about the number of samples, we use 1000 samples for each experiment, and train-test split ratio is 80:20. These are also explained at the beginning of Section 5.2.1, 5.2.2 and Appendix E. --- Rebuttal Comment 1.1: Comment: Thank you for the response. I understand the work more clearly now. After going through other reviews and the discussion, I have updated my rating to Accept	Summary: This paper re-interprets deep neural networks (with sigmoid activations) as probabilistic models. The authors give a construction that converts a DNN to an infinite tree-structured PGM, which has the benefit of yielding probabilstic information about its internal nodes. The key step is to copy input nodes so that they are only used once, and that their expectation functions as their value. The authors then prove that, in a certain infinite limit, the semantics are the same as of the original DNN. They then set up synthetic experiments using Hamiltonian Monte Carlo sampling on an approximation to this PGM, and report that their results help to reduce overfitting in small synthetic datasets. Strengths: The approach to understanding the internals of a DNN probabilistically are novel, and it seems like an approach worth pursuing at a high level. The introduction is well written, modulo a few techincal gripes. The biggest case to be made in favor of this construction (perhaps augmented with HMC) is that it might help reinterpret a trained network in probabilistic terms, avoiding pitfalls with maximum likelihood in "post-processing". The authors set up experiments that seem to show this to a small degree in a synthetic setting. The approach is creative and interesting. Weaknesses: The paper has major weaknesses in both the theoretical and the experimental parts. On the theoretical side, the constructions are imprecisely presented, and it is not at all clear to me that the main theoretical contribution of the paper (Theorem 1) delivers on the promises made on the introduction, nor that it is pedagogically useful. At a lower level, it seems there are a lot of minor bugs and ambiguities and undefined symboles that have been swept under the rug. At a minimum, I think the theoretical part of this paper needs a major rewrite with an eye towards precision and detail. On the empirical side, I'm afraid the experiments are not totally convincing either. My biggest problem is the lack of standard baselines. Why go all the way to HMC? The setup seems a bit rigged: by training a DNN with SGD on such a small number of samples, you are bound to see overfitting, and the new methods get to start from the maximum likelihood solution found by SGD. Why is the "cold-start" version, which does not train with SGD at all not reported? What about regularized approaches, or ones in which the samples are not fixed? These numbers would really help to contextualize the preformance of the new system. Overall, it seems that the authors have managed to "make the system work", but have not invested very much time in verifying that it works better than simple alternatives. I appreciate that the authors added additional experiments in the appendix, but they are not flattering. The HMC for the real world data works best for the smallest L (which seems antithetical to the main story showing that $L=\infty$ is appropriate), and in one case (=1/4), the new methods are significantly worse than the original DNN performance. In addition, the newly proposed methods are 2-3 orders of magnitude slower than the baseline. ----- minor line-by-line comments: - I disagree that VAEs are a "link between graphical models and deep neural networks" (line 17). The "graphical models" part of VAEs is relatively tenuous; it's really just a way to emphasize a data generating process by which samples are drawn from a prior and then decoded. To make the connection to PGMs you'll probably need a much more expressive variant, such as a PDG (https://arxiv.org/abs/2202.11862). - The notation in lines 74-75 is a bit slopy; is $v_i$ a variable, or a setting of a variable? If the former, then the equation $p(\vec v) = $... doesn't typecheck; if the latter, then it shouldn't be the argument to $pa(v_i)$. I suggest just using $pa_i$ for a quick and dirty solution. - I found the natural language description of steps b and c (lines 132-141) confusing, imprecise, and unnecessarily verbose. I do not feel I could implement it based on the description given, although Figure 1 helps. Pseudocode, or adding mathematical symbols to refer to nodes and edges, could make things far less ambiguous. - Similarly, the discussion in lines 146-164 is also difficult to follow, and feels imprecise. I would like to see a more formal mathematical description of this. - The usage of "mean-field approximation" on lines 148-149 is non-standard and seems like a false connection to me. - I disagree that this doubly exponentially large tree-structured graphical model is "easier to understand" than the original forward pass of the network (lines 181-184). I also do not see why the training procedure of SGD is relevant to the discussion; how have you broken the symmetry between SGD and any other local optimization procedure? SGD certainly does not appear in Theorem 1. - the notation $\sigma$ was not defined. Based on the appendix and standard symbols I gather it's the standard sigmoid curve, but this usage of $\sigma$ should be mentioned in the formal statement of the theorem or in the preliminaries. Technical Quality: 2 Clarity: 2 Questions for Authors: What happens if you don't do many epochs on the same fixed dataset, but rather draw fresh samples from the ground truth distribution that you're looking for? It seems that the main benefit shown in the experiments is that it can mitigate overfitting. But at a high level, it's unsurprising that a strong structural "prior" about the data, which happens to be correct in the synthetic setting, can help overfit to this setting. What happens if the number of datapoints grows far larger, but we reduce the number of epochs? Why is Hamiltonian Monte Carlo a particularly natural fit for this setting? LOW-LEVEL QUESTIONS AND COMMENTS: (Lines 96-99): Is the interpretation of a DNN with sigmoid activations really a coherent interpretation? Yes, it defines a distribution over a binary variable given values of its parents---but in order for that cpd to typecheck, the parents need to take on real values, not binary ones. It would seem that this makes the interpetation inconsistent for networks deeper than one layer. ~~Am I missing something?~~ Edit: this is a confusing presentation, and the confusion deepens in lines 112-114. But the resolution in lines 116-119 is clear, and that should have been present from the beginning. There's no reason to give a high-level overview of an interpretation that is confusing (because it is technically wrong) before pointing out that it is technically wrong. The authors define this to be "the direct PGM" far later in the paper (line 190), In line 121, the autors say that this "approximation of $\cal D'$ to $\cal D$ is precise", but is it? What is the distribution $\cal D'$? Over what variables? Are they continuous or binary? It still seems inconsistent to me. I would like to see this spelled out precisely. If it is meant as only a rough analogy, then you must say so when you introduce it. Clarification about the "second step" of the construction: it seems to me it must be done backwards, so the second-to-last layer (after the "first step") has $L$ copies, the one before that has $L^2$ copies, and the first one has $L^n$ copies. Is this correct? Or are there overall $L$ copies of each layer of the "post-first-step" transformation? Why is the variance $p_{ij} (1-p_{ij})/L$ in equation 1? Is this shown in the appendix, or do you have a reference? Is there some relation between the $M^{-1}$ covariance and the weight $\mathbf W$? Where do you get the esimtate of $M^{-1}$? Shouldn't $\boldsymbol \mu$ factor into the update in equation (7) somewhere? How are the procedures "Weight-updating" and "Sampling" in Algorithm 1 defined? Does this have to do with equation 7? I feel some details are missing. The results in lines 334-337 are compelling, but it seems the opposite is true of the MN rows of the table. Why is this? Confidence: 3 Soundness: 2 Presentation: 2 Contribution: 3 Limitations: The authors do discuss limitations a reasonable extent. Flag For Ethics Review: ['No ethics review needed.'] Rating: 3 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your detailed and constructive review. We take the comments and questions in order, except that the first criticism of the theory is general and leaves the specifics for later, so we take those later, in the order they are given. - "Lack of standard baselines" The baselines are SGD and Gibbs; the first is exactly correct with respect to the DNN and the second is exactly correct with respect to a direct PGM intepretation of the DNN as a Bayesian belief network. Since Gibbs is excessively slow in this setting, we begin with SGD and then refine with Gibbs for the Gibbs baseline. - On comparison to regularized approaches or use of larger/unlimited datasets. Early stopping is the most commonly used, successful regularizer in SGD, so in every case we compare 100 epochs of SGD against 1000 epochs. In most cases the message is similar for both 100 and 1000 epochs, with the exception when we get to the largest weights in the ground truth Markov network; here regularization hurts rather than helps the baseline of SGD. - "The HMC for the real world data works best for the smallest L..." The updated results (attached) with repeated training runs now agree exactly with what the theory predicts, suggesting that previous inconsistencies were due to random variability. As L gets small, HMC gets close to Gibbs (Bayesian belief net as ground truth), and as L gets large, HMC gets close to the DNN forward pass (infinite-width tree-structured PGM as ground truth). When the ground-truth DNN weights are large, this difference is great, and it is more critical to agree with the infinite-width tree-structured PGM; here HMC1000 wins, although it doesn't beat SGD provided SGD gets sufficient epochs (1000 rather than 100). When the ground truth DNN weights are small, Gibbs and the faster HMC10 win. - "I disagree that VAEs" VAEs are still commonly regarded as among the first works in the progression linking DNNs and PGMs, so we prefer to retain this citation, but we will certainly cite the suggested reference as an important step in this progression. - "The notation in lines 74-75" It is common to write $P(X_1,\cdots,X_n) = \prod_i P(X_i\|Pa(X_i))$ to stand as holding over all the possible different settings of $X_1,\cdots,X_n$ in defining the joint distribution represented by a Bayesian network (see Russell and Norvig textbook for example). But we see how our use of lower-case variable names here might have confused matters, so we will use upper-case variables names and clarify our meaning beforehand, also with a citation. - "mean-field approximation on lines 148-149" The term mean field approximation was used in that section due how the forward pass of the neural network might be viewed as using the expectation of the nodes of the previous layer to calculate their their value, which aligns somewhat with the mean field approximation described in: Jun Zhang, "The Mean Field Theory In EM Procedures For Markov Random Fields," \textit{Proceedings of the Seventh Workshop on Multidimensional Signal Processing}, Lake Placid, NY, USA, 1991, pp. 9.1-9.1, doi: 10.1109/MDSP.1991.639423. That said, the connection is indeed underexplored in this paper and differs notably in how the neural network only ever passes information forward. A more precise description, that the neural network effectively takes a local average from the immediately previous nodes and passes that information only forward, is more apt and we will revise. - "I disagree that this doubly exponentially large tree-structured graphical model is `easier to understand'..." We meant specifically that the tree-structured graphical model represents a full joint probability distribution over all the nodes in the neural network under the standard semantics of all Markov networks. We will tighten the language to clarify. - "I also do not see why ... SGD is relevant to the discussion" Our MN is well-defined regardless of SGD. But the point of the theorem is that for every node, the probability it is true in the MN equals its output in the DNN. As a result, the MN interpretation gives the same gradient that SGD uses. So SGD training is correct with respect to this MN, and this MN is correct with respect to SGD training. We wanted the MN to not be just some representation of the DNN, but the joint probability distribution with respect to which SGD in the DNN is correct. - "(Lines 96-99)" Thank you for the catch, the DNN indeed does not align with Bayesian networks or Markov networks outside of the case where a single hidden node is fully surrounded by observed evidence. We will clarify in this section how the DNN might be viewed as an approximation and that the probabilities calculated otherwise would not align. - "In line 121, ... this 'approximation of $\cal D'$ to $\cal D$' is precise" We stated that the approximation of $\cal D'$ to $\cal D$ is precise because, given a weighted acyclic graph with binary input variables, the neural network's forward pass can be used to calculate an 'approximate' conditional probability for any unobserved node. The values provided by that forward pass would not match the exact conditional probabilities of a similarly structured Bayesian network, but even without the PGM construction, they are well defined and could be used as a poor approximation. - "Why is the variance $p_{ij} (1-p_{ij})/L$ in equation 1?" This follows from the normal approximation to the binomial and the fact that $\text{Var}(X/L) = \text{Var}(X)/L^2$ for constant $L$. We will clarify. - Details of Section 5.1. In the final version, we will clarify the relationship between $M^{-1}$ and $\mathbf{W}$ and role of $\mu$ in equation (7). - "How are the procedures 'Weight-updating' and 'Sampling' in Algorithm 1 defined?" Equation 7 does indeed define the weight update step of the proposed algorithm. The sampling step is done using an MCMC chain (specifically HMC) as described in section 5.1 and Appendix C. --- Rebuttal Comment 1.1: Comment: Thank you for answering my questions, and running additional experiment. This rebuttal has allayed some of my concerns, and I now am more on board with the empirical evaluation. Still, I'm not fully convinced. A few responses: - SGD: I was trying to point out that SGD is an optimization procedure. The "stochastic" part is just to speed things up computationally; the theory seems to me only to interact with the "gradient descent" part--- and even then, I believe you are referring to gradient descent with respect to a specific loss function (cross entropy, presumably). I'm not sure what it means to say "the MN interpretation gives the same gradient that SGD uses." Why does the MN have a gradient, and with respect to what? I'm lost. - line 121: you still have not given a coherent joint distribution $\mathcal D'$. Just because the DNN gives "approximate" answers to certain queries in some sense does not mean there is a joint distribution $\mathcal D'$ that coincides with those answers. - If you are going to have "weight updating" and "sampling" in your algorithm pseudocode, you should make sure to define those terms eslewhere. Alternatively, write "update weights according to (7)" or something like this, so that a reader who is less intimate with the material can follow the references. --- Rebuttal 2: Comment: (1) 'SGD': You are right our result applies to gradient descent. We will clarify this. The stochastic part of SGD comes entirely from which subset of examples (mini-batch) we use to compute this gradient at any step, so it applies to SGD as well. We will clarify that the point is about gradient descent generally, not SGD in particular. Yes, MN learning is also by gradient descent. And yes, our result only applies to cross entropy error, since cross entropy is a function of $P(y\|X)$ for any setting of the inputs $X$. Our result is that these probabilities $P(y\|X)$ agree between NN and MN for any node y anywhere in the NN, not just output nodes. We will make sure this limitation to cross entropy error is extremely clear; thank you for bringing to our attention the need for more clarity and emphasis on that point. (2) 'coherent joint distribution $\mathcal D'$': Thank you for bringing attention to this detail. You are correct that despite it being possible for the neural network's standard operation to be viewed as an 'approximate' marginal $p(y\|X)$ for the output or $p(h\|X)$ for a hidden node, that view (and less exact connections with probabilistic graphical models) does not immediately lend itself to a distribution over multiple nodes (or the full joint distribution), $p(y, h_1, h_2, h_3 \|X)$ for example. In the traditional neural network structure, those hidden neurons are not well-defined unobserved nodes of a PGM and we therefore require the infinite PGM view. The infinite width tree structured PGM view should then be able to connect the neural network's forward pass and these 'approximate' values with an exact probabilistic structure where queries on multiple nodes, jointly, is possible. We will make sure to clarify that point in the final version of the paper. (3) '"weight updating" and "sampling" in your algorithm pseudocode': Thank you for catching that detail. We will make sure to clarify the weight updating and sampling steps of Algorithm 1 in the final version of the paper.	Rebuttal 1: Rebuttal: We thank all reviewers for the thoughtful and thought-provoking reviews. Here we list concerns raised by multiple reviewers and describe our plans to address them. If a change recommended by reviewers is not explicitly addressed, this implies that we will follow the reviewer's recommendation. 1. Clarity of PGM Construction. Several reviewers raised concerns about the clarity of the plain language description of the construction of the probabilistic graphical model whose conditional probability exactly matches the forward pass of the neural network. We acknowledge the need to complement these descriptions with a more precise presentation. To do this, we now use the algorithm environment to precisely define (a) Step 1 of our construction, in which we unroll the initial, likely loopy, neural network graph into a tree structure [Algorithm 1], and (b) Step 2 of our construction, in which we create infinite copies of each node and subtree necessary to exactly match the forward pass [Algorithm 2]. These two Algorithms may be found in the 1-page attachment to our response. We also intend to refine the existing plain language descriptions in the final version. By combining these two approaches, our hope is to provide a mathematically precise, reproducible description while still retaining the intuition that we believe the plain language description provides. 2. Strength of Experimental Results. Several reviewers also noted that they would like to see more thorough experimental results for the proposed HMC algorithm. We agree that this is key, and we have been working to provide a more comprehensive set of results that include repeated training runs and thereby allow us to determine whether differences between each training method and the baseline approach (DNN trained via SGD) are statistically significant. These results now clearly illustrate settings in which HMC-10 is favorable compared to the DNN. Specifically, HMC-10 performs best in settings where the relationship between inputs and outputs tends to be more random (lower valued weights). The results also show that HMC-10 succeeds in some of the settings where Gibbs fails. Finally, results underscore the similarity between DNN performance and HMC-100/1000 performance, suggesting that HMC-L more closely approximates DNN training as L increases, as predicted by our theoretical results. 3. Real-World Applications. While we agree that highlighting real-world applications will be important as we work to establish the practical benefits of this new connection between PGMs and DNNs, the current work is primarily theoretical in nature, with complementary experimental results that (a) corroborate the theory, and (b) illustrate a possible direction suggested by this new connection. Moreoever, from a practical perspective, we require much larger sample sizes to demonstrate benefit in a real-world binary classification setting, because in such settings -- in contrast to our simulations -- the true event probabilities are not known. In future work, we do plan to explore benefits of our HMC approach in real-world datasets, and we also hope to establish other practical, applications-oriented benefits of this new PGM view of DNNs. Pdf: /pdf/e62198346ea9c8d45420d929451ae4b1d4ea62a9.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Conformalized Time Series with Semantic Features	Accept (poster)	Summary: The paper proposes producing conformal intervals using non-conformity scores defined in latent space, demonstrating improved performance against existing CP methods that work in output space. Strengths: Adopting CP in feature space rather than latent space and demonstrating performance gains is novel. Weaknesses: 1. Model-agnostic: the authors claim CT-SSF is also model agnostic, yet the experimental results in Table 3 clearly show variation in terms of different f and g configurations. There arises the question on the wide applicability and computational efficiency of the method, especially if searching for the "optimal" (f,g) is costly. 2. Experimental comparison: how are the baselines implemented? Are the same RNN model used as the base model for the baselines? It is important to highlight what are kept the same across baselines in order to explain the performance gain of CT-SSF. If multiple components are varying, it is hard to attribute the performance gain to the use of latent features in CT-SSF. 3. Theory: - Section 4.5 tries to explain the theoretical guarantee of the proposed method, yet it is too hasty to be clear. The key question of why interval widths can be reduced lacks an intuitive explanation, and given the experimental results, it also seems such reduction depends on (f,g) combination, which is not clearly explained in the theory section. - What are assumptions on the original series? Does the guarantees always hold for any time series? Instead of presenting Theorem 1 in this casual form, it is better to give an informal theoretical statements. The exact bound can be described in big-O notation. Technical Quality: 2 Clarity: 2 Questions for Authors: No more questions Confidence: 4 Soundness: 2 Presentation: 2 Contribution: 2 Limitations: See weaknesses above. Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We appreciate your valuable and informative suggestions and would clarify the questions and concerns in the following. Q1: Model-agnostic and f,g splitting criterion. A1: CT-SSF is model agnostic because CP is naturally model agnostic and any NN-based time series prediction models can be used as the base models. One splitting criterion of $f$ and $g$ to significantly reduce computational efficiency is using cubic metrics of different splitting points for selection. As shown in Figure 1 in the attached PDF, we plot the relationship between prediction efficiency (band length) and the cubic metric. The cubic metric here represents the core statement in the cubic condition (statement 2), which implies a metric form like $\mathbb{M}[Q_{1-\alpha}V^f_{D_{ca}}- V^f_{D_{ca}}]$. We find that the cubic condition is closely related to the performance of CT-SSF. For each given dataset, the cubic metric is negatively related to the band length and thus positively related to prediction efficiency. Given this positive relationship, it is possible to use the cubic metric as the criterion for cross-validation instead of directly optimizing for prediction efficiency. By focusing on the cubic metric during cross-validation, we can reduce the number of necessary computations and improve the overall efficiency of the model selection process. Additionally, the splitting criterion of $f$ and $g$ can follow standard cross-validation to find the best splitting point, like standard hyperparameter search. The process can be conducted on a smaller subset of the data to quickly estimate the best splitting point, thereby reducing the overall computational burden. Despite the variation, the experimental results on different splitting points consistently outperform other CP for time series benchmarks. Q2: Experimental Comparison. A2: A consistent RNN model is used as the base model across all baselines. After training the RNN model, it is fixed to ensure a fair comparison between different CP methods. This consistency allows us to attribute the performance gains specifically to the use of latent features in CT-SSF. The results demonstrate the excellence of CT-SSF in achieving superior prediction interval performance. To see if CT-SSF's improvement is consistent across different base models, we also conducted experiments on Transformers (see Table 5, Appendix A.1) and new experiments on CNN (see Table 1 in the attached PDF). Results for both architectures suggest that CT-SSF can outperform HopCPT with 10\% to 20\% shorter prediction intervals across all datasets. Q3: Theory. A3: A formal and detailed discussion regarding the theorem can be found in Appendix A.2. Here, we briefly summarize it. Theorem 1. Assume Assumption 1 holds. Additionally, we assume that there exist constants $ \epsilon > 0 $ and $ c > 0 $, such that the feature space satisfies the following cubic conditions: 1. Length Preservation. Semantic-Feature CP does not incur a significant loss in the feature space in a quantile manner, namely, $ \\mathbb{E} Q_{1-\alpha}(H(V^f_D, D)) \geq \mathbb{E} Q_{1-\alpha}(V^o_D) + \epsilon.$ 2. Expansion. The operator $ H(v, X) $ expands the differences between individual lengths and their quantiles, namely, $L\\mathbb{E} [ \\mathbb{M} [ Q_{1-\alpha}(V^f_D)- (V^f_D)]^\alpha]<\mathbb{E}[ \mathbb{M} [ Q_{1-\alpha}(H(V^f_D)) - H(V^f_D)]- \epsilon - 2 \max \\{L, 1\\}( \frac{c}{\sqrt{n}})^{\min\\{\alpha,1\\}}.$ 3. Quantile Stability. Given a calibration set $D^{'}$, the quantile of the band length is stable in both the feature space and output space, namely,$\mathbb{E} [ Q_{1-\alpha}(V^f_D) - Q_{1-\alpha}(V^f_{D^{'}} )]\leq \frac{c}{\sqrt{n}} $ and $\mathbb{E} [ Q_{1-\alpha}(V^o_D) - Q_{1-\alpha}(V^o_{D^{'}} )]\leq \frac{c}{\sqrt{n}} $. CT-SSF provably outperforms NexCP in terms of average band length, namely, $\mathbb{E} [ H(Q_{1-\alpha}(V^f_{D_{ca}}), X_{test}) ] < Q_{1-\alpha}(V^o_{D_{ca}})$, where the expectation is taken over the calibration fold and the testing point $ (X_{test}, Y_{test}) $. The reduction in interval widths is primarily attributed to the use of latent features, which enable a more precise capture of the underlying data structure. Different from most existing conformal prediction algorithms, which regard the base model as a black-box model, feature-level operations allow seeing the training process via the trained feature. For a well-trained base model, feature-level techniques improve efficiency by utilizing the powerful feature embedding abilities of well-trained neural networks. The cubic conditions assume the latent space has a smaller distance between individual non-conformity scores and their quantiles, which reduces the cost of the quantile operation. We provide experimental results in Table 2 in the attached PDF comparing the average distance between each sample and their quantile in the latent space. The results show that the feature space has a smaller distance between individual non-conformity scores and their quantiles, which is key to improving prediction efficiency. Additionally, Figure 1 in the attached PDF demonstrates that the cubic metric is negatively related to the band length and thus positively related to efficiency. Different configurations of $f$ and $g$ will generate different cubic metrics, leading to variations in the reduction. Thanks for the great idea of providing an exact bound described in big-O notation for the prediction interval! While deriving the exact bound is challenging due to the inherent variability and complexity of the method (e.g., the structure of the base model, the latent space, the specific implementation of the attention mechanism, as well as the transformation from the latent space to the output space), we will surely consider adding the exact bounds in our future version of this work. Our method doesn't rely on specific assumptions about the underlying time series, the same as the majority of prior works in CP for time series.	Summary: The paper presents a novel approach called Conformalized Time Series with Semantic Features (CT-SSF) for improving uncertainty quantification in time-series forecasting. The authors propose leveraging latent semantic features through deep representation learning to dynamically adjust weights for conformal prediction. This approach aims to address the limitations of existing methods that rely on manually selected weights in the output space. The paper demonstrates that CT-SSF achieves tighter prediction intervals with valid coverage guarantees, outperforming state-of-the-art methods in both synthetic and real-world datasets. Strengths: S1. The paper introduces an interesting combination of conformal prediction and deep representation learning, focusing on the latent space rather than the output space. S2. This paper provides theoretical analysis on the validity of the proposed method. S3. The experimental results demonstrate improvement on the conformal width. Weaknesses: W1. The latent space is high-dimensional compared to the output space. Considering high-dimensional statistics is usually much more complicated compared to single-dimensional space, it would be interesting to discuss theoretically or empirically the tightness of the conformal scores in the latent space. W2. The latent space structure can be very different for different types of architectures. Hence, the empirical results on different types of deep architectures, e.g., rnn, cnn, transformers, are necessary but missing. W3. The efficiency of the proposed conformalization method is missing. Technical Quality: 3 Clarity: 3 Questions for Authors: Q1 (cr. W1). Please compare and discuss the impact of switching from output space (single dimension) to the latent space (multiple dimension) on the conformal prediction, e.g., whether and why this may or may not incur an increase in the calibration examples. Q2 (cr. W2). Please add experimental results for CNN and transformers. Q3 (cr. W3). Please discuss, report and compare the efficiency. Q4. In Figure 1, there is no order among the methods, hence a line chart is improper. Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The author(s) have discussed in the paper. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We appreciate your valuable and informative suggestions and would clarify the questions and concerns in the following. Q1: Please compare and discuss the impact of switching from output space (single dimension) to the latent space (multiple dimension) on the conformal prediction, e.g., whether and why this may or may not incur an increase in the calibration examples. A1: The main impact of switching CP to the feature space is that in the feature space, it leads to a smaller distance between individual non-conformity scores and their quantiles (i.e., the second argument of the cubic conditions), which is key to improving prediction efficiency in this context. Intuitively, feature space is more semantically rich, providing more fine-grained information to capture the underlying data structure and relationships more accurately, leading to better prediction efficiency. We also provide new experimental results in Table 2 in the attached PDF to compare the average distance between each sample and their quantile in the latent space. The results validate that the distance in feature space is significantly smaller than that in output space, which aligns well with our hypotheses. Additionally, to further analyze the relationship between the distance in the feature space and the prediction efficiency, we plot the relationship between efficiency (band length) and the cubic metric in Figure 1 in the attached PDF. Specifically, the cubic metric here represents the core statement in the cubic condition (statement 2), which implies a metric form like $\\mathbb{M}[Q_{1-\\alpha}V^f_{D_{ca}} - V^f_{D_{ca}}]$. The results demonstrate that the cubic condition is closely related to the performance of CT-SSF. For each given dataset, the cubic metric negatively related to the band length and thus positively related to efficiency. In addition, we conducted additional experiments to analyze the impact of the number of calibration examples on performance, as shown in the following table. Our findings indicate that our method is quite robust to the calibration set size, producing consistently better prediction efficiency. We believe this is because the latent space representations are highly efficient and can capture the essential features of the data well. Consequently, our method does not incur an increase in the calibration examples. Table: The impact of calibration set size on the performance of the evaluated CP algorithms for the real data with CNN as the base model. The specified miscoverage level is $\alpha = 0.1$ for all experiments. The standard deviation is obtained over 10 repeated runs with different random seeds. \| \| \| CT-SSF \| HopCPT \| 100 Calibration \| 200 Calibration \| 300 Calibration \| \|-------\|---------\|-------------------\|-------------------\|------------------\|------------------\|------------------\| \| Elec \| Cov \| 90.4±2.20 \| 90.2±1.63 \| 89.7±3.50 \| 89.6±2.11 \| 89.6±2.02 \| \| \| Width \| 0.23±0.04 \| 0.32±0.06 \| 0.23±0.03 \| 0.23±0.03 \| 0.23±0.03 \| \| Stock \| Cov \| 91.8±1.82 \| 90.6±2.09 \| 89.7±2.28 \| 90.3±1.70 \| 91.1±1.70 \| \| \| Width \| 0.33±0.08 \| 0.53±0.15 \| 0.31±0.09 \| 0.31±0.08 \| 0.32±0.08 \| \| Weather \| Cov \| 89.8±0.27 \| 89.9±0.25 \| 88.0±0.47 \| 89.3±0.32 \| 88.8±0.34 \| \| \| Width \| 0.02±0.005 \| 0.04±0.007 \| 0.02±0.005 \| 0.02±0.005 \| 0.02±0.005 \| \| Wind \| Cov \| 88.5±1.83 \| 89.2±3.41 \| 88.0±2.20 \| 88.5±2.50 \| 89.0±3.40 \| \| \| Width \| 0.36±0.05 \| 0.60±0.10 \| 0.40±0.09 \| 0.35±0.10 \| 0.40±0.11 \| Q2: Please add experimental results for CNN and transformers. A2: Thanks for the suggestion. We agree that empirical results on different types of deep architectures are necessary. Experimental results for Transformers have been provided in Table 5, Appendix A.1, which suggest that CT-SSF demonstrates approximately a 10\% reduction in prediction intervals compared to HopCPT across all datasets. Additionally, we conducted new experiments on CNN, and the results can be seen in Table 1 in the attached PDF. We observed that CT-SSF still generates 10\% to 20\% shorter prediction intervals than HopCPT across all datasets. Q3: Please discuss, report and compare the efficiency. A3: We compared the prediction efficiency of CT-SSF with other baselines, such as HopCPT and NexCP. Our results, as shown in Tables 1 and 2 of the original paper, indicate that CT-SSF achieves approximately a 5-10\% reduction in average prediction interval length across both synthetic and real-world datasets. In terms of computational efficiency, the runtime varies significantly depending on the size of the datasets. For example, with electricity data, our method takes approximately 40 seconds, while HopCPT takes around 3 minutes, and all other baselines take less than 5 seconds for a single experiment (i.e., one seed, not including training the prediction model). The longer runtime for our method and HopCPT is due to the complexity of the adaptive reweighting and attention mechanisms used, which involve more intensive computations compared to simpler baseline methods. Q4: In Figure 1, there is no order among the methods, hence a line chart is improper. A4: We agree with your observation regarding Figure 1. We will remove the line chart and replace it with a scatter plot, to accurately represent the data. Once again, we appreciate the reviewer's precious time. We are eager to engage in further discussions to clear out any confusion. --- Rebuttal Comment 1.1: Comment: Thanks to the authors for addressing my concerns and providing additional experimental results. I remain positive about this work with my previous score.	Summary: This paper proposes Conformalized Time Series with Semantic Features (CT-SSF), a conformal prediction method that constructs prediction intervals for time series data using nonconformity scores computed in the latent feature space of neural networks. CT-SSF further assigns time-dependent weights to the scores based on their similarity to the current prediction errors. Strengths: The idea of adapting time-dependent weights for the nonconformity score computed in semantic feature space is novel. The authors conducted experiments on both synthetic and real datasets to demonstrate that, on average, the width of the prediction interval is shorter than those obtained from existing approaches. Additionally, the authors conducted an ablation study to investigate the performance of each core component in the CT-SSF method. Weaknesses: Clarity: The clarity of the writing can be improved. For example: In the experimental setup (Section 5.1), it is mentioned that CT-SSF is model-agnostic, allowing any prediction models for time series to be used as the base models. In contrast, the conclusion states that one of the limitations of CT-SSF is its reliance on NNs, excluding simpler models like ridge regression or random forest. The clarity of the paper would benefit from more rigorous writing, such as restricting the first statement to 'any NN-based prediction models for time series.' Experimental Significance: The standard errors in the synthetic data experiments are based on only five repetitive experiments. As a result, the confidence intervals on widths are too wide to demonstrate significant advantages of the CT-SSF method. The experimental results would be more convincing if more repetitive experiments were conducted with additional seeds. Theoretical contribution and unique challenges: As the authors have acknowledged, the theorem and its proof in this paper are identical to Theorem 4 in Teng et al. (2022). Therefore, the unique challenges faced in this project are not clearly articulated. Please refer to question number 1 for further clarifications. Technical Quality: 3 Clarity: 2 Questions for Authors: I have several clarifying questions regarding the methodology and experiments outlined in the paper: Methodology: If my understanding is correct, CTSSF is an incremental methodology based on Nex-CP (using weighted conformal prediction), FeatureCP (implementing CP within a latent feature space instead of in the output space), and HopCPT (using the same intuition of designing weights according to how similar previous errors are to the current error). I’m confused about the last part—how exactly do you update the weight? Did you rely on the MHN attention mechanism as in the HopCPT paper? Please correct me if I misunderstood or overlooked anything - I would appreciate it if the authors could highlight the unique challenges faced in this project. If the authors could clarify these challenges and provide experimental results with a larger number of independent repetitions to enhance the significance of their results (please see 'Experimental Significance' under weaknesses), I would be happy to increase my score. Experiment: Did you compare your results with other benchmarks used for conformal time series forecasting, such as the EnbPI [1] method and the SPCI [2] method? How many seeds did you use for real data experiments? Reference: [1]: “Conformal Prediction Interval for Dynamic Time-Series.” Chen Xu and Yao Xie, PMLR, 2021 [2]: “Sequential Predictive Conformal Inference for Time Series.” Chen Xu and Yao Xie, PLMR, 2023 Confidence: 3 Soundness: 3 Presentation: 2 Contribution: 2 Limitations: The author addressed the limitations of their work. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your insightful feedback on our manuscript. We appreciate your comments and have taken them into consideration to improve our paper. Below, we do our best to address the reviewer's questions adequately such that we could receive a better score. Q1: Comparisons with prior works and unique challenges. A1: Our work is indeed greatly inspired by Nex-CP, FeatureCP, and HopCPT. However, CT-SSF is not incrementally a combination of the three. A simple solution would be to combine Nex-CP with FeatureCP. However, Nex-CP employs pre-defined weights instead of data-adaptive weights, which prevents it from fully capturing the intrinsic characteristics of the original time series. While Nex-CP uses weighted conformal prediction and FeatureCP operates within a latent feature space, CT-SSF uniquely integrates these concepts by applying adaptive reweighting directly within the latent feature space. This integration allows for more precise capturing of the underlying data structure, leading to tighter prediction intervals and improved prediction accuracy. Compared to HopCPT, our weight update mechanism uses a standard simple attention weights mechanism rather than the MHN attention mechanism from the HopCPT paper. We chose the standard attention mechanism for its simplicity and computational efficiency, which still allows for dynamic adjustment of data point significance. Despite using a typical attention mechanism, our results demonstrate that CT-SSF outperforms HopCPT in both performance and computational efficiency because the attetion-based mechanism effectively prioritizes relevant data points and a simple standard attention mechanism can reduce computational overhead. The simplicity and efficiency of the standard attention mechanism enable faster computations and more scalable implementations without sacrificing accuracy. The primary unique challenge we faced in this project was ensuring the effective integration of attention-based weight updates within the latent feature space. Achieving this required innovative solutions to ensure that the dynamic adjustments made by the attention mechanism did not introduce significant distortions or inconsistencies in the prediction intervals. To address this, we employed continuity-preserving feature extraction methods, such as RNNs, to maintain the intrinsic structure of the data. Additionally, we utilized Transformer models for dynamically adjusting weights, which allowed us to effectively prioritize data points based on their relevance to the current prediction task. Q2: Experimental Significance. A2: Thanks for the suggestion. We did not include comparisons with the EnbPI and SPCI benchmarks in our current study because HopCPT was shown to significantly outperform these methods in the original paper. However, we understand the importance of comprehensive benchmarking. Therefore, we have conducted experiments on EnbPI and SPCI with 10 repetitive trials, and the results are presented in Table 1 in the attached PDF. Our findings indicate that CT-SSF demonstrates a 10\%-20\% reduction in prediction intervals compared to the SOTA HopCPT across all datasets, and over a 20\% reduction for SPCI and EnbPI. For the real data experiments, we used five different seeds to ensure the robustness of our results. We agree that using more seeds could further strengthen our findings. Therefore, we increased the number of repetitions to 10 for the new results in Table 1 in the attached PDF. We see that variance is reduced as expected and CT-SSF still outperforms all other baselines. Q3: Clarity. A3: Thank you for pointing this out. We acknowledge the inconsistency in our statements regarding the model-agnostic nature of CT-SSF. We have revised the statement in Section 5.1 to specify that CT-SSF is compatible with any NN-based prediction models for time series. The revision is below: "CT-SSF is model agnostic, therefore, any NN-based prediction models for time series prediction models can be used as the base models. To better show the advantage of our proposed method, we utilize a Recurrent Neural Network (RNN) model, which can be replaced with more advanced models like Transformers." Once again, we appreciate the reviewer's precious time. We are eager to engage in further discussions to clear out any confusion. --- Rebuttal Comment 1.1: Comment: Thank you to the authors for addressing my comments and conducting additional experiments. The responses and new results have addressed my concerns regarding experimental significance and unique challenges. I have increased my score accordingly.	Summary: The paper presents a conformal prediction approach for time series data in the latent space of the prediction model – Conformalized Time Series with Semantic Features (CT-SSF). Non-conformity scores constructed in the latent space are expected to capture deeper insights of the data and temporal dynamics and improve prediction efficiency. The paper also proposes an adaptive weight adjustment scheme in the latent space to dynamically adjust weights such that larger weights are assigned to more relevant data points. Authors perform experiments on synthetic and real-world datasets to demonstrate the effectiveness of their proposed method compared to existing conformal prediction methods for distribution drift and time series. Strengths: Originality: The paper extends HopCPT [1], a conformal prediction method for time series data, by constructing non-conformity scores in the latent space using ideas and methods from [2] (e.g., band estimation). The main original contribution in my opinion is the weighted gradient mechanism. While CT-SSF combines methods from [1] and [2] for the most part, this novel combination is effective and demonstrates performance improvement over existing methods. Quality: The paper is technically sound. The claims are well supported by theory and empirical evaluation over multiple datasets and comparison with baselines. The paper also includes ablation studies to demonstrate the effectiveness of the method. Clarity: The paper is well-written, organized, and easy to follow for the most part. Significance: The proposed method constructing non-conformity scores in the latent space provably outperforms conformal prediction methods in the output space (e.g., NexCP) in terms of average prediction interval length under the stated assumptions. The empirical analysis also demonstrates consistent results. I believe these results will be of interest to the uncertainty quantification as well as broader community. References [1] Andreas Auer, Martin Gauch, Daniel Klotz, and Sepp Hochreiter. Conformal prediction for time series with modern hopfield networks. Advances in Neural Information Processing Systems, 36, 2023. [2] Jiaye Teng, Chuan Wen, Dinghuai Zhang, Yoshua Bengio, Yang Gao, and Yang Yuan. Predictive inference with feature conformal prediction. arXiv preprint arXiv:2210.00173, 2022. Weaknesses: 1. Limited discussion of past work: While the paper largely borrows ideas from [1, 2], I feel the text lacks appropriate context for complete understanding. There is limited explanation of the band estimation technique as well as HopCPT. I understand the main paper might not have space but this can be added to the appendix. 2. There is less clarity on what the assumptions for Theorem 1 rely on and how they translate in practice. It would be helpful to discuss the robustness of the assumptions and implications if they are violated (in theory or practice) since this is the main result of the paper. References [1] Andreas Auer, Martin Gauch, Daniel Klotz, and Sepp Hochreiter. Conformal prediction for time series with modern hopfield networks. Advances in Neural Information Processing Systems, 36, 2023. [2] Jiaye Teng, Chuan Wen, Dinghuai Zhang, Yoshua Bengio, Yang Gao, and Yang Yuan. Predictive inference with feature conformal prediction. arXiv preprint arXiv:2210.00173, 2022. Technical Quality: 3 Clarity: 3 Questions for Authors: 1. Can the authors elaborate on how $\tilde{w}$ is updated in Algorithm 1? 2. Minor typo: p6 l243 -> calibration Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The authors discuss limitations in the Limitations section. Authors briefly discuss the potential social impact in A.3. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We extend our sincere appreciation for your valuable feedback and suggestions. Regarding your concerns, we would like to offer further clarification. Q1: Can the authors elaborate on how $\tilde{w}$ is updated in Algorithm 1? A1: The weights $\tilde{w}$ are updated based on the attention mechanism of the Transformer model. The weights are adjusted dynamically to reflect the significance of each data point in the prediction task. The attention weights from the Transformer model are used to assign higher importance to data points that have more influence on the prediction: $\tilde{w} \leftarrow \text{AttentionWeights}(\hat{g}(u), Y).$ Here, $\text{AttentionWeights}(\hat{g}(u), Y)$ represents the attention weights calculated by the Transformer model, reflecting the similarity between the predicted output $\hat{g}(u)$ and $Y$. Finally, we adjust the latent vector $u$ using the weighted gradient descent mechanism. This step ensures that the updates to $u$ are influenced by the dynamically adjusted weights $\tilde{w}$, focusing the learning process on the most critical data points. We will add these explanations in the future version of this work. Q2: Limited discussion of past work. A2: Thanks for the suggestion. We acknowledge that our initial submission did not provide a comprehensive discussion of the previous works due to the page limit. To remedy this, we have added more detailed descriptions of current CP approaches for time series data in the appendix, which is also attached below. There are generally three primary approaches designed to manage these challenges and enhance the reliability and validity of the CP in time series: reweighting, updating non-conformity scores and updating significance level. Reweighting assigns relevance-based weights to data points to align the data distribution closer to a target distribution. NexCP uses exponentially decayed weights to emphasize recent observations, but these lack adaptability. HopCPT improves on this by using a Modern Hopfield Network (MHN) for similarity-based reweighting. It assigns weights to past time steps based on their relevance to the current time step. Encoded inputs are processed with learned weight matrices, and a hyperparameter adjusts the focus of the probabilistic distribution. These weights create weighted conformal prediction intervals by discounting extremal quantiles of relative errors. The second technique, updating non-conformity scores leverages the most recent $T$ data points and continuously updates prediction intervals as new data becomes available. For example, EnbPI uniquely updates the non-conformity score with sequential error patterns to adapt the intervals dynamically. And SPCI replaces the empirical quantile with an estimate by a conditional quantile estimator to effectively address serial dependencies among residuals in sequential analysis. The last main direction for CP in time series focuses on adaptively adjusting the significance level $\alpha$ during test time to account for mis-coverage. This method can dynamically adjust the size of prediction sets in an online setting where the data generating distribution is allowed to vary over time in an unknown fashion. For example, the update rule for the quantile level $ \alpha $ in ACI is: $\alpha_{t+1} = \alpha_t + \gamma(\alpha - \text{err}_t)$, where $ \gamma $ is a step size parameter, and $ \text{err}_t $ indicates if $ Y_t $ was not included in $ \hat{C}_t(\alpha_t) $. The approach ensures that the prediction intervals adjust over time to account for shifts in the data distribution, maintaining the desired coverage probability. Q3: There is less clarity on what the assumptions for Theorem 1 rely on and how they translate in practice. It would be helpful to discuss the robustness of the assumptions and implications if they are violated (in theory or practice) since this is the main result of the paper. A3: We understand the importance of clearly discussing the assumptions underlying Theorem 1 and their practical implications. Below, we have provided an enhanced explanation to address the robustness of the assumptions and the potential consequences if they are violated. Assumption 1, Length Preservation in the Feature Space, ensures that the transformation from the feature space to the output space maintains consistent interval lengths. This assumption is generally robust with smooth and continuous feature extraction methods, but abrupt changes can lead to inconsistent intervals, affecting prediction reliability. Assumption 2, Expansion by Band Estimation Operator, captures differences in interval lengths and quantiles. It is robust if the operator is well-calibrated, though sensitive to calibration data quality and quantity. Violations may result in inaccurate prediction intervals, compromising coverage guarantees. This assumption directly influences the performance of our method, so we conduct new experiments to validate this assumption in Table 2 in the attached PDF. Results show that the latent space has a smaller distance between individual non-conformity scores and their quantiles, which reduces the cost of the quantile operation. Finally, Assumption 3, Quantile Stability, ensures stable band lengths across feature and output spaces, crucial for consistent coverage. This assumption is typically robust with well-behaved data distributions but can be challenged by extreme values, leading to unstable intervals and undermining coverage validity. To mitigate these risks, we recommend using continuity-preserving feature extraction methods, regularly recalibrating the band estimation operator with diverse data, and employing robust statistical methods for outlier detection. We will add these explanations in the future version of this work. --- Rebuttal 2: Comment: I thank the authors for addressing the questions and look forward to future versions with more detailed discussion as suggested. I remain positive of the work as earlier.	Rebuttal 1: Rebuttal: We would like to thank all reviewers for their thorough reviews, helpful suggestions, and constructive comments. To summarize, we made the following main changes to the manuscript to follow the suggestions and comments of the reviewers: 1. To illustrate the generalizability and performance of CT-SSF, we have added additional experimental results using CNN as the base model with more repetitions. Results in Table 1 in the attached PDF suggest a 10\% to 20\% reduction in prediction intervals compared to CP for time series benchmarks and standard CP. 2. We conducted additional experiments to bridge the gap between theory and empirical results. Table 2 in the attached PDF compares the quantile and non-conformity scores in the latent space and output space, suggesting that the latent space has a smaller distance. Experimental results in Figure 1 in the attached PDF indicate that prediction efficiency is positively related to the cubic metric. These results offer enhanced insights into the theoretical framework. 3. Recognizing the importance of discussing past work, we have added detailed descriptions of CP for time series in the appendix. 4. We revised typo errors and inconsistencies, and removed the line chart in the ablation study. Pdf: /pdf/0e68def9c88554264c3859891d4fd7ebe1ba2054.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
PointMamba: A Simple State Space Model for Point Cloud Analysis	Accept (poster)	Summary: In summary, PointMamba, an innovative state space model tailored for point cloud analysis, successfully harnesses the global modeling prowess of Mamba, a representative SSM from the NLP domain. By adopting a linear complexity algorithm, PointMamba addresses the computational challenges posed by traditional Transformer-based methods while maintaining their global modeling capabilities. Its key techniques include utilizing space-filling curves for effective point tokenization and employing a non-hierarchical Mamba encoder as the foundation. Extensive experiments across multiple datasets validate the superior performance of PointMamba while significantly reducing GPU memory usage and FLOPs. This work not only demonstrates the vast potential of SSMs in 3D vision tasks but also provides a simple yet effective baseline for future research in this domain. Strengths: 1. Linear Complexity with Global Modeling: PointMamba leverages state space models to achieve linear complexity while maintaining global modeling capabilities, overcoming the computational challenges of traditional Transformers. 2. Efficient Point Cloud Representation: The use of space-filling curves for point tokenization enables efficient representation of point clouds, capturing spatial structure while facilitating global feature extraction. 3. Simple and Effective Mamba Encoder: The non-hierarchical Mamba encoder provides a simple yet powerful backbone for PointMamba, enabling fast and accurate global feature modeling. 4. Superior Performance: Comprehensive evaluations show that PointMamba achieves state-of-the-art performance across multiple datasets, demonstrating its effectiveness for point cloud analysis tasks. Weaknesses: 1. Although PointMamba borrows structurally from Mamba, it may not take full advantage of the unique characteristics of point cloud data, such as spatial distribution, density variations, and local geometry. 2. PointMamba, while inheriting the strengths of Mamba, may have inherited some of the limitations of its design for natural language processing tasks. These limitations may not be applicable to point cloud analysis tasks, such as the lack of specific preprocessing steps, feature extraction methods, or post-processing techniques for point cloud data. The feature extraction and processing steps in the paper are largely similar to those of the previous PointMAE. 3. Although PointMamba achieves global modeling of linear complexity by introducing state-space models, there may be trade-offs between model complexity and performance in real-world applications. Because according to the experimental results of the thesis, the effect of partially using PointMamba becomes worse instead. 4. According to Table 5 of the ablation experiment, the serialization operations Hiber and Trans-Hiber have the most obvious impact on the experimental results. Meanwhile, the framework diagram at the core of the paper, i.e., Figure 4, shows that the only change is Hiber, from the directly cited literature [27], and there is almost no additional description or setting in the paper. Technical Quality: 3 Clarity: 3 Questions for Authors: 1. Based on weakness 4, is it possible that PointMamba actually only works well in Hiber conditions? As this very much affects the final results and conclusions of the paper. 2. Intuitively, PointMamba seems to be just a replacement of the Mamba block (Equation 4) for the previous Transformer block, and even if this results in good performance (Figure 1), I am not convinced. The paper is theoretically and experimentally fleshed out, but I still don't find an obvious innovative contribution. Therefore, I would like to confirm whether the authors have designed a specialized Mamba technique for 3D point clouds? Confidence: 5 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: Content-wise, the paper has no obvious limitations, and its core technology builds on Mamba, which is popular in other fields. Formatting-wise, the paper shows the mamba icon several times; please confirm whether this representation is appropriate in an academic paper. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: - To weakness 1&2: “… may not take full advantage of the unique characteristics of point cloud data…/…may not be applicable to point cloud…are largely similar to…Point-MAE.” Reply: Thanks. We respect the reviewer's opinion. However, we believe this paper considers the characteristics of point clouds. Specifically, through a pilot of experiments, we first demonstrate that simply replacing the Transformer with a Mamba can not achieve ideal performance due to the unidirectional modeling. Based on this, we customize the key innovative designs to handle the point cloud data: 1) The proposed point scanning strategy transforms the unstructured 3D point clouds into a regular sequence, which can provide diverse perspectives on spatial locality via scans from different clues; 2) The order indicator maintains the distinct spatial characteristics of different scanning when training, preserving the integrity of the spatial information, which is crucial for the unstructured point cloud; 3) Serialization-based mask modeling randomly choose a space scanning curves for masking, allowing the model exact the general local relationships from different scanning perspectives, better matching the requirement of indirection modeling of mamba. Thanks to these proposed simple yet innovative key designs, our PointMamba works well and performs better than its Transformer-based counterparts in point cloud tasks. We will make these technical contributions more clearly in the revised version. Besides, compared with the Point-MAE, the differences are also distinct: 1) For processing steps, Point-MAE directly generates the random tokens via a lightweight PointNet. In contrast, we propose a point scanning strategy, which leverages the space-filling curves to transform the unstructured point clouds into a regular sequence; 2) For feature extraction, Point-MAE employs a vanilla Transformer. In contrast, we merge the vanilla Mamba with the proposed order indicator, making the mamba preserving the integrity of the spatial information from different scanning curves; 3) For pre-training, the Point-MAE is the traditional random mask modeling paradigm, while our PointMamba proposes serialization-based mask modeling, allowing the model exact the general local relationships from different scanning curves via the proposed order indicator; 4）We also provide detailed theoretical analyses of why PointMamba work well in point cloud tasks, while it seems lack on Point-MAE. Overall, although our method presents a simple pipeline, the processing steps, feature extraction, pre-training, etc, are significantly different from the previous methods. As R2 said, “…the proposed method is simple, elegant, and effective, establishing a solid Mamba-based baseline for point cloud analysis tasks…”, we believe our method would be interesting and valuable for people in this area. We will deeply discuss the differences in the revised version. - To weakness 3: “…trade-offs between model complexity and performance…the effect of partially using PointMamba becomes worse instead.” Reply: Thanks. Please refer to Tab.1, Tab.2, and Tab.3 of the manuscript, where our method consistently performs better on all conducted datasets compared with the single-modal SOTA Transformer-based methods. Note that some methods (e.g., ACT) adopt multi-modal information (e.g., text description or 2D), which is unfair for comparison, but we still surpass it in most datasets. - To weakness 4: “…have the most obvious impact on the experimental results…no additional description or setting in the paper.” Reply: Thanks. We prove that directly replacing the transformer with mamba in Point-MAE can not achieve ideal performance due to the unidirectional modeling of mamba in Point Cloud. Therefore, we propose serialization operations, including point scanning strategy, order indicator, and serialization-based mask modeling. Therefore, serialization operations naturally reflect the performance gains, which verify the effectiveness of our proposed key designs. Besides, we would like to clarify that Fig.4 is not the only proposed core. It just means the proposed serialization-based mask modeling paradigm and the comprehensive overall core designs are presented in Fig.2. Compared with the Transformer-based method (e.g., Point-MAE, PointGPT), we present substantive differences: point scanning strategy, order indicator, serialization-based mask modeling (please see the reply to weakness 1&2). Furthermore, the Hilber is a representative space-filling curve, which we adopt into our proposed key designs. The preliminary of Hilbert is listed in Sec. 3 of the manuscript, and we provide further descriptions in reply to the minor problem of Reviewer 2 (Please refer to it). - To question 1: “…only works well in Hiber conditions?…” Reply: Thanks. We have conducted experiments to analyze the effect of different scanning curves in our key designs, as shown in Tab.6 of the original manuscript. Specifically, we argue that using the space scanning curve sequences along a specific pattern of spatial locations offers a more logical sequence modeling order for SSM. The experiments also prove that it can achieve notable performance gains compared with the random paradigm. Among them, Hilbert achieves the best results due to their superior locality-preserving properties. - To question 2: “…obvious innovative contribution…specialized Mamba technique for 3D point clouds?” Reply: Good question! This paper is not just a replacement of the Mamba block (Equation 4) for the previous Transformer block, please see the reply to weakness 1&2. --- Rebuttal Comment 1.1: Title: Reviewer's Response Comment: Thanks to the authors for the reply. My concerns have been partially addressed, mainly because I am not completely sold on PointMamba's results. As a result, after the authors' rebuttals, I still believe it has merit, so I'm willing to change my rating to positive. --- Reply to Comment 1.1.1: Comment: We appreciate your thought-provoking reviews and are pleased to see your positive decision. To substantiate our results, we will release the code. Thank you once again for your positive rating.	Summary: This paper propose a simple but effective Mamba-based method named PointMamba for point cloud analysis. This paper is the first paper that studies the Mamba-based method for point clouds. The experiments are comprehensive and the paper is in very good shape. Strengths: 1. This paper demonstrates excellent writing quality, with a clear and evident motivation. 2. Figure 1 is highly comprehensible, particularly in its comparisons with Point-MAE. Weaknesses: 1. (No need for experiments) The use of validation datasets is prevalent in the field, with consistently high metrics reported. I encourage the inclusion of indoor segmentation and detection tasks, as exemplified in Point-M2AE and MaskPoint, in future iterations of your work. Additionally, tackling the classification task on Objaverse-LVIS appears to be a more demanding and stimulating challenge. 2. To be honest, there are numerous papers that adhere to the evaluation paradigm established by Point-BERT. However, I am genuinely interested in exploring novel discoveries in self-supervised learning specifically applied to point clouds. Technical Quality: 3 Clarity: 4 Questions for Authors: 1. It has been experimentally determined that Point-MAE, Point-M2AE, and MaskPoint do not accurately replicate their reported performance, as observed in this study. It is important to investigate whether PointMamba exhibits consistent stability across all of these tasks. If not, providing mean and standard deviation values similar to those presented in Table 3 is crucial. 2. Additionally, it has been observed that conducting experiments with a larger number of points using Mamba results in an increase in training time. Have you encountered this phenomenon in your own experiment? If so, kindly elaborate on possible solutions to enhance its suitability for real-world applications, such as Auto-Driving. 3. Could you please elaborate on the reasons why incorporating Hilbert and Trans-Hilbert techniques in your current version has led to improved performance compared to the reordering strategy implemented in the initial version? Moreover, Hilbert and Trans-Hilbert techniques seem to borrow from Point Transformer. If so, the main contribution lies in integrating Mamba into Point-MAE. 4. (No need for experiments, just discuss.) There are several Mamba-based methods after this paper. Please just discuss the advantages and disadvantages compared with them. Confidence: 5 Soundness: 3 Presentation: 4 Contribution: 3 Limitations: 1. The authors have addressed the limitations and potential negative societal impact of their work. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: - To weakness 1: “(No need for experiments)…encourage the inclusion of indoor segmentation and detection tasks…” Reply: Thanks for this very constructive suggestion, and we will explore a unified Mamba-based foundation model for various 3D vision tasks (including indoor segmentation, detection tasks, and classification tasks on Objaverse-LVIS ) in the future. We also appreciate the reviewer's understanding that finishing such experiments in a limited time is difficult. - To weakness 2: “…Point-BERT…genuinely interested in exploring novel discoveries in self-supervised learning…” Reply: We totally agree with this insightful point. Actually, this paper also explores a new self-supervised pre-training paradigm named serialization-based mask modeling (Sec. 4.2). Specifically, different previous methods (e.g., Point-BERT) using random masking, we consider the unidirectional modeling of Mamba and propose to randomly choose one space-filling curve to generate the serialized point tokens for mask modeling. In addition, the proposed extremely simple order indicator effectively maintains the distinct characteristics of these different scanning strategies. As a starting point for this area, we hope this paper can provide useful insight for the community and encourage researchers to focus on the potential of Mamba in 3D vision tasks. - To question 1: “… consistent stability across all of these tasks…providing mean and standard deviation…” Reply: Thanks! We promise that all code will be released and the results can be easily reproduced. Following your suggestion, we report the mean and std in all datasets under three runs, as shown below. We can see that the proposed method achieves consistent stability across different tasks/datasets. \| Method \| OBJ-BG \| OBJ-ONLY \| PB-T50-RS \| ModelNet40 \| ShapeNetPart \| \| --- \| --- \| --- \| --- \| --- \| --- \| \| PointGPT (NeurIPS 23) \| 93.39 \| 92.43 \| 89.17 \| 93.3 \| 86.2 \| \| PointMamba (Ours) \| 3 $\times$ runs: [93.76, 93.98, 94.32] \| 3 $\times$ runs: [92.31, 92.60, 92.47] \| 3 $\times$ runs: [89.44, 89.31, 89.25] \| 3 $\times$ runs: [93.6, 93.6, 93.5] \| 3 $\times$ runs: [86.18, 86.12, 86.16] \| - To question 2. “… a larger number of points…training time…possible solutions…real-world applications…” Reply: Thanks! Following your suggestion, we evaluate the training time (second/epoch) with different input lengths (from 128 to 2048) with a batch size of 16, as shown below. We find that with point tokens increasing, the advantages of our approach over Point-MAE will be even more pronounced, further indicating the efficiency of our PointMamba. In addition, to apply the PointMamba to Auto-Driving, a possible way is to design an efficient voxel-based tokenizer that can effectively transform the larger number of point clouds into a series of long point/voxel tokens, which is a promising future work. \| Sequence length \| 128 \| 256 \| 512 \| 1024 \| 2048 \| \| --- \| --- \| --- \| --- \| --- \| --- \| \| Point-MAE \| 97.24 s/epoch \| 128.99 s/epoch \| 194.56 s/epoch \| 351.64 s/epoch \| 797.78 s/epoch \| \| PointMamba \| 89.18 s/epoch \| 112.57 s/epoch \| 150.55 s/epoch \| 225.56 s/epoch \| 374.89 s/epoch \| - To question 3: “…improved performance compared to…the initial version? …borrow from Point Transformer…the main contribution lies in integrating Mamba into Point-MAE” Reply: Thanks! In fact, the improved performance compared to the initial version is not simply replacing the reordering strategy but rather the comprehensive new proposed technology. Specifically, compared with the initial version, we make the following new contribution: 1) The proposed point scanning strategy transforms the unstructured 3D point clouds into a regular sequence, which can provide diverse perspectives on spatial locality via scans from different clues; 2) The order indicator maintains the distinct spatial characteristics of different scanning when model training, preserving the integrity of the spatial information, which is crucial for the unstructured point clouds ; 3) Serialization-based mask modeling randomly choose a space scanning curves for masking, allowing the model exact the general local relationships from different scanning clue, better matching the requirement of unidirectional modeling of Mamba. Furthermore, we would like to clarify that our method are totally different from Point-MAE: 1) For processing steps, Point-MAE directly generates the random tokens via a lightweight PointNet. In contrast, we propose a point scanning strategy, which leverages the space-filling curves to transform the unstructured point clouds into a regular sequence. Although Point Transformer also adopts space-filling curves, the motivation and objective are different. Point Transformer utilizes space-filling curves to partition the point cloud, capturing spatial contexts. In contrast, our work mainly focuses on transferring the point clouds to serialization-based sequences and combines it with Mamba to implement global modeling. 2) For feature extraction, Point-MAE employs a vanilla Transformer. We merge the vanilla Mamba with the proposed order indicator, making the Mamba preserve the integrity of the spatial information from different scanning curves; 3) For pre-training, the PointMAE is the traditional random mask modeling paradigm, while our PointMamba proposes serialization-based mask modeling, which employ serialization masking modeling, combining with the proposed order indicator; 4) We also provide detailed theoretical analyses of why PointMamba work well in point cloud tasks, while it seems lack on PointMAE. Overall, the current version makes substantive improvements compared with Point-MAE and our initial version. Extensive experiments also validate the effectiveness of our method (See Fig.1 of the manuscript). For question 4, please see the reply presented in the “comment” part. --- Rebuttal Comment 1.1: Title: Reviewer's Response Comment: Thanks for the authors' responses, most of my questions have been solved. Therefore, I will keep my rating as positive. I look forward to your future work exploring PointMamba on more challenging datasets. --- Reply to Comment 1.1.1: Comment: Thank you for your recognition of our responses and for maintaining a positive rating. We value your suggestion and will incorporate this into our future research plans. --- Rebuttal 2: Title: Rebuttal by Authors (continued) Comment: - To question 4: “…several Mamba-based methods after this paper…” Reply: Good suggestion! Indeed, there are several papers after this paper, we list the comprehensive comparisons as follows: PCM [1] combines Vision Mamba with PointMLP and incorporates consistent traverse serialization at each stage. To enhance Mamba’s capability in managing point sequences with varying orders, PCM introduces point prompts that convey the sequence’s arrangement rules. Point Mamba [2] uses an octree-based ordering scheme and combines Mamba with PCT and OctFormer as their baseline. Mamba blocks with bi-directional scanning extract hierarchical point features, and a Feature Pyramid Network (FPN) is utilized for classification or segmentation tasks. Mamba3D [3] introduces an enhanced Vision Mamba block, which includes both a token forward SSM and a backward SSM that operates on the feature channel. It proposes a Local Norm Pooling block to extract local geometric features. PointTramba [4] introduces a hybrid approach that integrates Transformers and Mamba. It segments point clouds into groups and utilizes Transformers to capture intra-group dependencies, while Mamba models inter-group relationships using a bi-directional, importance-aware ordering strategy. Note that some methods (e.g., [4]) are clearly based on our code or baseline, which proves the value of our approach to the community. We will add these discussions in the revised version. [1] Point could mamba: Point cloud learning via state space model [2] Point mamba: A novel point cloud backbone based on state space model with octree-based ordering strategy [3] Mamba3d: Enhancing local features for 3d point cloud analysis via state space model [4] PoinTramba: A Hybrid Transformer-Mamba Framework for Point Cloud Analysis	Summary: This paper introduces PointMamba, an interesting method for point cloud analysis that utilizes a linear complexity state space model (SSM) instead of traditional Transformer architectures. PointMamba employs space-filling curves for point tokenization and features a simple, non-hierarchical Mamba encoder. Additionally, the authors propose an effective order indicator and serialization-based mask modeling strategy. Comprehensive evaluations across multiple datasets demonstrate PointMamba's superior performance and significantly reduced computational costs compared to Transformer-based methods. Strengths: 1. The paper reads very well. I appreciate the motivation of the paper and agree that we should make an effective method as simple as possible. As the first Mamba-based work for point cloud tasks, the proposed method is simple, elegant, and effective, establishing a solid Mamba-based baseline for point cloud analysis tasks. 2. The paper considers the limitations of Mamba's unidirectional modeling and proposes practical solutions like serialization-based mask modeling strategies and order indicators. 3. The theoretical analysis of Mamba used in point cloud is reasonable, and the paper is easy to reproduce. 4. The experiments are convincing and support the main idea of the paper. The authors provide thorough evaluations, including comparisons with SOTA methods, ablation studies, and analyses of each component. Weaknesses: 1. Some experiments are missing. For example, from Table 11, it would be beneficial to include more masking ratios, especially the performance when masking 90% point patches. Besides, from Table 12, could the authors provide a more detailed analysis of why average pooling performs better? Additionally, what about the performance of max pooling? 2. Have the authors considered the potential benefits of integrating PointMamba with Transformer architectures? For example, a transformer layer can be used as the final prediction head. Such a combination can take advantage of both architectures and will not introduce many computational costs. 3. The point clouds have complex structures, and this paper only considers two orders. In my view, introducing more orders (e.g., introducing three serialization methods and tripling the input length) can better capture the geometry information of the point clouds, which might be beneficial for learning. 4. During the pre-training strategy, do the authors use different order indicators or the same indicator? Figure 4 is somewhat ambiguous. Minor: Using space-filling curves to scan point clouds is an interesting attempt. Although it is common knowledge for some readers, it still would be helpful if the authors provided a more detailed introduction to space-filling curves in the preliminaries part. typos: PointMAE -> Point-MAE Technical Quality: 4 Clarity: 4 Questions for Authors: See weakness. Confidence: 5 Soundness: 4 Presentation: 4 Contribution: 4 Limitations: The authors have adequately discussed the limitations of their work. Flag For Ethics Review: ['No ethics review needed.'] Rating: 8 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: - To Weakness 1: “Some experiments are missing…masking 90% point patches…the performance of max pooling?” Reply: Good question! We conduct the mentioned missing experiments: (1) As shown in the table below, masking 90% point patches may harm performance, as a higher masking ratio makes reconstruction tasks too difficult during pre-training. \| Masking ratio \| Loss \| OBJ-BG \| OBJ-ONLY \| \| --- \| --- \| --- \| --- \| \| 0.9 \| 2.00 \| 92.43 \| 91.05 \| (2) Average pooling takes into account the entire sequence with all the information, while max pooling selects the maximum value of each token in each dimension through a nonlinear process. We empirically find that only use max-pooling may destroy the global information of the extraction and cause performance drop, as shown in the table below. \| \| OBJ-BG \| OBJ-ONLY \| \| --- \| --- \| --- \| \| Average pooling \| 94.32 \| 92.60 \| \| Max pooling \| 93.39 \| 91.36 \| - To Weakness 2: “… benefits of integrating PointMamba with Transformer architectures … a transformer layer can be used as the final prediction head …” Reply: Good suggestion! Based on your advice, we kept the total number of blocks the same and replaced the last layer with a Transformer. As shown in the table below, we observed a confirmed performance drop. We argue that optimizing two modules simultaneously can be challenging, and developing an effective hybrid architecture is a promising topic for future research. \| \| # TP \| FLOPs \| OBJ-BG \| OBJ-ONLY \| \| --- \| --- \| --- \| --- \| --- \| \| 12 Mamba-block \| 12.3 \| 3.1 \| 94.32 \| 92.60 \| \| 11 Mamba-block + 1 Transformer-block \| 13.1 \| 3.4 \| 91.98 \| 89.64 \| - To Weakness 3: “… introducing more orders …” Reply: Thanks! Based on your suggestion, we conducted an experiment by adding an additional z-order sequence to triple the input length. As shown in Fig. 3 and Appendix A of our paper, using two orders enables global modeling for PointMamba; however, adding redundant information may lead to performance degradation. \| \| FLOPs \| OBJ-BG \| OBJ-ONLY \| \| --- \| --- \| --- \| --- \| \| Hilbert + Trans-Hilbert \| 3.1 \| 94.32 \| 92.60 \| \| Hilbert + Trans-Hilbert + Z \| 3.6 \| 93.43 \| 91.36 \| - To Weakness 4: “…Figure 4 is somewhat ambiguous.” Reply: We apologize for the ambiguity. During pre-training, different serialized point tokens have different order indicators. We will clarify Fig.4 in the next version. - To Minor & Typos: Reply: Thanks for the comments! Here is a brief introduction to Hilbert space-filling curves. Denoting the coordinates of voxelized points as $(x,y,z)$ and convert them into binary format using $log_2 n$ bits ( e.g., $x\to(x_{m}x_{m-1}...x_{0}),m=\lfloor log_2 n \rfloor$). $x_m,y_m,z_m$ is then iterated to $x_1,y_1,z_1$, making exchanges when the current bit is 0, and inversions otherwise. By concatenate the bits into $(x_{m}y_{m}z_{m}x_{m-1}y_{m-1}z_{m-1}\ldots x_{0}y_{0}z_{0})$ and apply a 3$m$-fold Gray decoding, the traversal position $T$ can be obtained. All voxels are then sorted into a single sequence based on their traversal position $T$. By recording the traversal position for all potential voxel coordinates, the points can be serialized. We will add this introduction and carefully revise our paper. --- Rebuttal Comment 1.1: Comment: Thank you for the rebuttal! Most of my concerns have been addressed. I have one more question regarding the Hilbert space-filling curve: How is the starting point of the curve determined? --- Reply to Comment 1.1.1: Comment: We appreciate the reviewer acknowledging that our rebuttal addressed the concerns. In response to the new question, specifically, we voxelize the key points of the point cloud and shift the minimum coordinate to the origin, with the voxel at (0,0,0) serving as the starting point of the Hilbert curve. We will add this explanation in the revised version.	Summary: This work utilizes the Mamba architecture for point clouds. It employs Hilbert and Trans-Hilbert curves to order the point clouds, thus addressing the unidirectional modeling nature of Mamba. Additionally, it replaces transformer blocks with Mamba blocks. The proposed PointMamba demonstrates reasonable performance following pre-training. Strengths: 1. This work tries introducing a new network architecture to the point cloud domain, which is appreciated. 2. The presentation is clear, accompanied by well-crafted figures. Weaknesses: 1. While it is worthwhile to explore how the Mamba architecture performs when applied to point clouds, this work exhibits limited novelty or insights in architectural innovation for point clouds. The authors themselves acknowledge this by stating, “It should be noted that this paper does not claim algorithmic novelty but rather presents a simple and solid Mamba-based baseline.” In my opinion, works that directly adopt an existing network from other domains to point clouds without sufficient insights and innovation should not be accepted by top-tier conferences like NeurIPS. 2. The authors only demonstrate the performance of pre-trained PointMamba by comparing it with other widely used baselines like PointNext. This implies that PointMamba cannot surpass previous methods when trained from scratch. To effectively showcase the solid merits of PointMamba, it would be more reasonable to provide comparisons without pre-training. 3. In Table 4, an important baseline, PointNext, is omitted. According to the PointNext paper, PointNext exhibits significantly better performance than the proposed PointMamba (87% without pre-training vs. 84.4% with pre-training). This omission raises doubts about the effectiveness of PointMamba. To give a "solid Mamba-based baseline", comprehensive comparisons with previous methods should not be omitted. 4. In Figure 1, it would be beneficial to include comparisons with widely used methods like PointNext to convincingly demonstrate the necessity of introducing Mamba for point clouds. While PointMamba likely offers inference advantages, this contribution stems from the original Mamba paper, not this work. Additionally, does PointMamba have lower training efficiency? 5. The paper claims that the proposed Hilbert and Trans-Hilbert ordering is advantageous based on results from ScanObjectNN. However, I am not entirely convinced. I suggest the authors also present results on ShapeNet-Part and ModelNet40, for which only comparing against a random baseline is enough. Technical Quality: 2 Clarity: 3 Questions for Authors: See the weakness section. Confidence: 5 Soundness: 2 Presentation: 3 Contribution: 2 Limitations: See the weakness section. Flag For Ethics Review: ['No ethics review needed.'] Rating: 3 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: - To Weakness 1: Reply: Thanks. We would like to emphasize that simply replacing the Transformer with the Mamba cannot achieve ideal performance due to the unidirectional modeling (as shown in below table). Thus, we customize the key designs to handle the point cloud data: 1) The proposed point scanning strategy transforms the unstructured 3D point clouds into a regular sequence, which can provide diverse perspectives on spatial locality via scans from different curves; 2) The order indicator maintains the distinct spatial characteristics of different scanning when training, preserving the integrity of the spatial information, which is crucial for the unstructured point cloud; 3) Serialization-based mask modeling randomly choose a space scanning curves for masking, allowing the model exact the general local relationships from different scanning perspectives, better matching the requirement of unidirectional modeling of Mamba. Considering that this paper is the first work that discusses the potential of Mamba in point cloud tasks, it would bring new insights to the community and be interesting for many people. A similar toy example is the paper you mentioned, PointNeXt, an empirical study, that mainly studies the data augmentation in point cloud without specific new designs (90% of performance gains from data augmentation and hyper-parameter adjustment, while the remaining 10% comes from micro-designs such as residual connections), but many people still like such a simple yet effective paper. We hope the reviewer could reconsider the motivation and insights of our method (also see reply to weaknesses 2 & 3). \| Method \| OBJ-BG \| OBJ-ONLY \| PB-T50-RS \| ModelNet40 \| \| --- \| --- \| --- \| --- \| --- \| \| Point-MAE \| 92.77 \| 91.22 \| 89.04 \| 93.2 \| \| Simply replace Transformer with Mamba in Point-MAE \| 92.25 \| 90.69 \| 87.11 \| 92.4 \| \| PointMamba (ours) \| 94.32 \| 92.60 \| 89.31 \| 93.6 \| - To Weaknesses 2 & 3: Reply: Thanks! It seems that the reviewer might be confusing different performance metrics on ShapeNetPart (Inst. mIoU, 86.2%, and 87.0% for PointMamba and PointNeXt, respectively, are correct). Note that, the performance of PointNeXt is somewhat misleading and shouldn’t be directly compared due to the following reasons: 1) PointNeXt adopts extensive data augmentation, while our method and other Transformer-based methods only adopt random rotation for ScanObjectNN and random scaling for ShapeNetPart; 2) PointNeXt adopts the voting strategy and manual refinement on this dataset (i.e., ShapeNetPart), which is an unfair post-processing that is usually resisted by the Transformer-based methods. As such, no vanilla Transformer-based method can outperform PointNeXt when these unfair practices are applied. Therefore, we believe the reviewer should not deny a series of good Transformer-based works for these reasons. For fair comparisons, we remove all tricks and pre-training, as shown below, where we perform better than PointNeXt on most datasets. Overall, PointNeXt is the MLP paradigm instead of Transformer-based, and it mainly discusses the effect of various data augmentation in vanilla PointNet. In this paper, we aim to unlock the potential of Mamba in point cloud tasks, discussing whether it can be a viable alternative to Transformers. Thus, the direct comparison of our PointMamba is the vanilla Transformer-based methods. Through extensive experiments, we clearly outperform the SOTA Transformer-based counterparts and even include the cross-modal method (ACT, ICLR 23). \| Method \| Data augmentation \| Voting \| ShapeNetPart (scratch/pre-training) \| \| --- \| --- \| --- \| --- \| \| PointNeXt (NeurIPS 22) \| Random rotation, Random scaling, Random translation, Random jittering, Normal Drop, Height appending \| Yes \| 87.0/- \| \| PointNeXt (NeurIPS 22) \| Random scaling \| No \| 85.7/- \| \| ACT (ICLR 23) \| Random scaling \| No \| 85.8/86.1 \| \| PointGPT (NeurIPS 23) \| Random scaling \| No \| 85.6/86.2 \| \| PointMamba \| Random scaling \| No \| 85.8/86.2 \| \| Method \| Data augmentation \| OBJ-BG (scratch/pre-training) \| OBJ-ONLY (scratch/pre-training) \| PB-T50-RS (scratch/pre-training) \| \| --- \| --- \| --- \| --- \| --- \| \| PointNeXt (NeurIPS 22) \| Random rotation, Random scaling, Random translation \| 90.88/- \| 90.36/- \| 87.7/- \| \| PointNeXt (NeurIPS 22) \| Random rotation \| 90.71/- \| 89.50/- \| 87.20/- \| \| ACT (ICLR 23) \| Random rotation \| -/93.29 \| -/91.91 \| -/88.21 \| \| PointGPT (NeurIPS 23) \| Random rotation \| -/93.39 \| -/92.43 \| -/89.17 \| \| PointMamba \| Random rotation \| 91.74/94.32 \| 90.19/92.60 \| 87.27/89.31 \| - To weakness 4: Reply: Thanks! 1) We will include the suggested methods in Figure 1 in the revised version. In addition, the clarification of PointNeXt is presented in reply to weaknesses 2&3; 2) Although Mamba performs inference advantages, it can not work well in the point cloud by simply replacing Transformer with Mamba. PointMamba not only keeps the efficiency of Mamba but also makes it achieve promising performance in the point cloud. 3) Besides, as shown below table, PointMamba presents superior training efficiency (second/epoch) compared with the convincing Transformer-based method, especially when the length of point tokens increases. \| Sequence length \| 128 \| 256 \| 512 \| 1024 \| 2048 \| \| --- \| --- \| --- \| --- \| --- \| --- \| \| Point-MAE \| 97.24 \| 128.99 \| 194.56 \| 351.64 \| 797.78 \| \| PointMamba \| 89.18 \| 112.57 \| 150.55 \| 225.56 \| 374.89 \| - To weakness 5: Reply: Good suggestion! We now provide the analysis of our point-scanning strategy on ShapeNet-Part and ModelNet40. These results clearly prove the effectiveness of our proposed key designs when adopting Mamba to point clouds. We will release the code to ensure the results are convinced. \| \| ModelNet40 \| ShapeNetPart \| \| --- \| --- \| --- \| \| Random \| 92.7 \| 85.7 \| \| Hilbert + Trans-Hilbert \| 93.6 \| 86.2 \| --- Rebuttal Comment 1.1: Comment: Hi authors, Thanks for your time. For the performance of "Simply replace Transformer with Mamba in Point-MAE", did you pre-train this model or train it from scratch? --- Reply to Comment 1.1.1: Comment: Dear reviewer, Thanks for your kind reply! To ensure a fair comparison, the setting of "Simply replace Transformer with Mamba in Point-MAE” refers to swap the Transformer with Mamba in the architecture of Point-MAE, followed by applying the same pre-training strategy as used in the default Point-MAE. Please note that the data augmentations used are also kept the same. To further compare the results under the from-scratch, we are currently conducting experiments and will update you within the next few hours. We appreciate your patience and will provide the results as soon as possible. Thank you once again for your kind reply! --- Rebuttal 2: Comment: Dear Reviewer Daqu, We sincerely appreciate your time and effort in reviewing our paper. We hope our explanations have addressed your concerns. As we are in the discussion phase, we welcome any additional comments or questions regarding our response or the main paper. If further clarification is needed, please do not hesitate to mention it, and we will promptly address your inquiries. We look forward to receiving your feedback. Best regard, Paper 940 Authors Title: We are open to any further discussion. --- Rebuttal 3: Comment: Dear Reviewer Daqu, Thank you for your time and valuable feedback. As the discussion phase is nearing its end, we remain open to addressing any remaining questions or concerns. We would greatly appreciate it if you could consider improving the evaluation after reviewing our responses. Thank you very much for your consideration. Sincerely, Paper 940 Authors --- Rebuttal Comment 3.1: Comment: Dear Authors, Thank you very much for providing additional experimental results. I have no further questions at the moment and would like to decide on my final score after discussing it with AC and the other reviewers. Have a good day! Best, Reviewer --- Reply to Comment 3.1.1: Comment: Dear reviewer Daqu, We sincerely thank you for the time and feedback. We hope our existing rebuttal has addressed your previous concerns well. If you have any further questions during the next discussion period, please let us know, and we would be happy to answer them. Thank you once again! Sincerely, Paper 940 Authors	Rebuttal 1: Rebuttal: Dear Reviewers, We are grateful to the reviewers for their invaluable feedback and the time they dedicated to evaluating our work. We are excited to see that reviewers identified the novelty of our technical contribution (R2), clear motivation (R2, R3), convincing experiments (R2), superior performance (R2, R3, R4), and well-written (R1, R2, R3). We respond to each reviewer separately with a detailed analysis to answer all the questions. We think that our following rebuttal has sufficiently addressed the concerns raised by the reviewers. Please reply if you have any further questions. Thank you again for your insightful feedback, and we look forward to continuing the discussion. Best regard, Paper 940 Authors	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
ALI-Agent: Assessing LLMs' Alignment with Human Values via Agent-based Evaluation	Accept (poster)	Summary: This paper proposes a new paradigm for evaluating LLM's alignment with human values, which is based on LLM-based agents. It proposes an autonomous agent called ALI-agent, to conduct in-depth and adaptive alignment assessment. The ALI-agent has a memory module, a tool-using module, and an action module to improve the capability of generating more reliable and diverse misconduct scenarios. The generation process includes two main stages: (1) Emulation stage: generate realistic test scenarios, and (2) Refinement stage: refines the passed scenario for increasing long-tail risks. The authors conduct extensive experiments to show (1) the reliability of ALI-agent as an evaluator, (2) performances of different LLMs assessed by ALI-agent, and (3) systemic analysis with ablation studies. Strengths: 1. The motivation has been greatly demonstrated, which is intuitive and practical. Actually, evaluating LLMs with automatic and adaptive methods without labor-intensive processes. The safety concerns of LLMs also need this type of assessment. 2. The preliminary provides a clear definition of the task, and the methods are well demonstrated. 3. The refinement process is fancy and interesting, which gradually improves the difficulty of misconduct evaluation in fact. It extends normal misconduct testing to long-tailed risk misconduct testing, and the process is adaptive to different LLMs. 4. The experiments are designed to show the reliability and effectiveness of ALI-Agent, which is the basis for drawing conclusions based on its evaluation. 5. A Suggestion: Section 3.2 can be put in front of Section 3.1, because the reliability of ALI-Agent is the basis of experimental findings. Weaknesses: 1. In line 125, I notice the evaluation memory uses squared L2-norm as distance, but it seems that cosine similarity is more widely used for retrieval. Are there some insights about it? 2. Besides retrieval-based memory methods, putting all memory contents into prompts can possibly be an effective method, because long-context LLMs (such as GPT-4o and GLM-4) can greatly deal with long contexts for even 128k nowadays. Maybe you can also take other methods of LLM-based memory for a try, and you may refer to [1] if needed. Reference: [1] Zhang, Z., Bo, X., Ma, C., Li, R., Chen, X., Dai, Q., ... & Wen, J. R. (2024). A survey on the memory mechanism of large language model based agents. arXiv preprint arXiv:2404.13501. Technical Quality: 3 Clarity: 4 Questions for Authors: Please see the above "Weakness". I'm willing to improve my rating if the authors can address my concerns. Confidence: 4 Soundness: 3 Presentation: 4 Contribution: 3 Limitations: The authors have discussed the limitations in the Appendix. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: >Comment 1: Distance metric for memory retrieval -- "In line 125, I notice the evaluation memory uses squared L2-norm as distance, but it seems that cosine similarity is more widely used for retrieval. Are there some insights about it?" Thanks for the valuable question. For our implementation, we used the default metric provided by ChromaDB, an encapsulated function library for database. As you mentioned, cosine similarity is more widely used for retrieval. Thus, we followed this common practice and checked retrieval results on all the 6 experimental datasets for all 10 target LLMs. Among 7,488 times of retrievals, both retrieval metrics consistently retrieved the same records each time, demonstrating the insensitiveness to the choice of distance metric. However, as the memory grows diverse and complex, different distance metrics can potentially impact the framework's performance. Therefore, we will add both cosine similarity distance result as well as L2-norm for ALI-Agent. >Comment 2: Different usage of memory -- "Besides retrieval-based memory methods, putting all memory contents into prompts can possibly be an effective method, because long-context LLMs (such as GPT-4o and GLM-4) can greatly deal with long contexts for even 128k nowadays. Maybe you can also take other methods of LLM-based memory for a try, and you may refer to [1] if needed." Thanks for the valuable suggestion, putting all the records from memory into prompts is a promising approach, although the high cost hinders its scalability. For example, if we want to evaluate Llama2-13b on dataset Social Chemistry 101, there are 79 related memory records in total with a length of 15666, for each generation we will need to handle a prompt with that length, which might not be affordable for GPT-4-turbo. If the core LLM is open-sourced and possess long context window then it would be a more accessible practice. Following your suggestion, we referenced Section 5 in [1] for other potential methods of utilizing LLM-based memory. This paper concludes that memory contents can be represented in two forms: textual and parametric. Textual memory stores and utilizes information as natural language, which is the approach we adopted for memory. Parametric memory, on the other hand, encodes memory into the parameters of LLMs to influence their behavior, primarily through fine-tuning and knowledge editing methods. We designed an intuitive experiment to compare textual vs parametric memory empirically. For the parametric memory, we fine-tuned gpt-3.5-turbo-1106 with 687 records (all records from the training data of ALI-Agent). For the textual memory, we switched the core LLM to gpt-3.5-turbo-1106 and reran ALI-Agent, and we ablated the refinement module for a fair comparison. The experiment was conducted on the CrowS-Pairs dataset with 200 samples. Table 1 demonstrates that the parametric memory outperforms the textual memory when they hold same number of records. This superiority likely stems from the ability to encode the whole knowledge of memory. However, the textual memory offers advantages in implementation when the memory is growing, which is particularly beneficial for our framework, where memory expands with evaluations. It would be impractical to fine-tune the core LLM every time we need to add a new memory record. Overall, we are inspired by and grateful for your excellent suggestions. We will add more discussion about the usage of memory in the revised manuscript. Table 1. Performance comparison between parametric and textual memory on the CrowS-Pairs dataset. Model agreeability (%) is reported. \| \| GPT-4 \| GPT-3.5 \| Gemini-Pro \| ChatGLM3 \| Vicuna-7B \| Vicuna-13B \| Vicuna-33B \| Llama 2-7B \| Llama 2-13B \| Llama 2-70B \| \|-\| - \| - \| - \|-\| -\| - \|-\| - \| - \| - \| \| Parametric \| 8.0 \| 2.0 \| 9.5 \|25.0 \| 19.0\| 14.5 \| 9.0 \| 14.0 \| 1.0 \| 0.5 \| \| Textual \| 6.5\| 1.5 \| 6.5 \| 13.5\| 13.5 \| 8.5 \| 4.0 \| 2.5 \| 0.0\| 0.5 \| --- Reference [1] Zhang, Zeyu, et al. "A survey on the memory mechanism of large language model based agents." arXiv preprint arXiv:2404.13501 (2024). --- Rebuttal Comment 1.1: Comment: Thanks for the detailed rebuttal by the authors. I would like to maintain my score of 7, and prefer to accept this paper. --- Reply to Comment 1.1.1: Title: Reply to Reviewer 77qx Comment: Thanks, we are encouraged by you acknowledgement.	Summary: The paper proposes an automated pipeline for evaluating the alignment of LLMs with human values. The pipeline involves the generation of scenarios using RAG+ICL, and iteratively revisioning the scenario to create disagreement between LLM judgment and human judgment (i.e. misalignment). The authors did tests on the pipeline, and find that it outperforms non-adaptive evaluation methods in identifying misalignment scenarios. Strengths: Important topic - The topic of values evaluation in LLMs is important, given the increasing influences the models have on human users' opinions and beliefs. - There have been quite a number of works doing values evaluation on LLMs, but automated evaluations are rarer, and this paper systematizes the automated evaluation of value alignment, which is good. Novelty - The paper approaches the problem of values evaluation through a new angle, namely automated identification of value misalignment scenarios. This adversarial approach (almost like red-teaming) is novel and is key to making the embedded values of the models robust. Solid pipeline design & experiments - The pipeline design seems well thought-out, e.g. the introduction of ICL and RAG. Experimental analysis is also comprehensive. Weaknesses: Conceptual clarity (key consideration) - After reading the first page, I was confused why "ALI-Agent-generated scenarios are judged as less harmful by OpenAI API" is a good thing at all; isn't the whole point here about generating harmful scenarios? This question gets answered in the experiments section (RQ2), namely we want the generated scenarios to conceal malice. However, I'm still not convinced by this explanation, since: - Hiding malice in testing scenarios makes sense if we want to benchmark the model's ability to e.g. do moderation (<> detect misalignment scenarios in its input), because in those tasks we do need the model to have a strong capability in detecting malice. - However, if we want to test the misalignment tendencies in the model itself, then we'd like to know whether the model itself tend to give misaligned outputs, as opposed to whether the model is able to detect a misaligned scenario in its input. In other words, we'd like to decouple intent (i.e. tendencies of aligned/misaligned output) and capability (i.e. ability to detect). By intentionally concealing malice in the test scenarios, the benchmark pipeline is mixing detection capability with intent (mis)alignment. Rigor and disclosure (key consideration) - The authors should disclose the process for recruiting the 3 evaluators, the process for eliciting their evaluations, and potential conflicts of interest between the evaluators and the paper authors, if any. - I appreciate that the authors reported the radar plots for all 4 datasets and did not engage in selective reporting. However, I don't think it's good practice to put two of the plots on the first page and the other two in the appendix. Minor considerations - Concreteness of motivation. Quote: "This labor-intensive process restricts the scope of the test scenarios, making it difficult to cover the extensive variety of real-world use cases and to identify long-tail risks [ 21]. Furthermore, as LLMs continuously evolve and expand their capabilities, static datasets for alignment evaluation quickly become outdated, failing to timely and adaptively reveal potential alignment issues [22]." Could you give some concrete examples here? - Diversity of scenarios. It seems that using the evaluation memory may potentially reduce diversity of the scenarios generated, since ICL conditions the model to generate scenarios similar to past ones. There seems to be an explore-exploit tradeoff involved here. Maybe consider adding experiment and/or discussions on this. I like the paper overall, and please don't take the the critiques personally. Technical Quality: 3 Clarity: 3 Questions for Authors: - What do you think are the key differences between this paper and works on automated red-teaming of LLMs (see e.g. [1], with a number of follow-up works after it)? Do you think the methodologies are transferrable from automated red-teaming to the assessment of value alignment? If so, maybe consider comparing the ALI-Agent with these methods, as experiments and/or discussions. I don't think this body of literature is addressed in appendix A.2, since the "finding a universally effective $p$" description doesn't seem accurate on automated red teaming methods. [1] Red Teaming Language Models with Language Models, 2022. Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: I agree with the limitations/future directions enumerated in the conclusion section of the paper, and I have nothing to add here. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: >Q1: Comparison with automated red-teaming Thanks for your important question, we have conducted a survey as follows: Automated red teaming is formulated as automatically designing test cases in order to elicit specific behaviors from target LLMs [1-2], mainly categorized as: 1) Text optimization methods [3-4]: search over tokens to find sequences that can trigger target LLMs into producing harmful contents when concatenated to any input from a dataset. 2) LLM optimizers [1,5-7]: utilize a red LM (through prompting, supervised learning, reinforcement learning, etc.) to generate test cases that can elicit harmful behaviors from target LLMs. 3) Custom jailbreaking templates [8-11]: automatically generate semantically meaningful jailbreak prompts to elicit malicious outputs that should not be given by aligned LLMs. (References are in the official comment due to space limit.) Our framework is most similar to the second line of works. However, there are several key differences: 1. Automated red-teaming methods detect whether the target LLMs output harmful contents, addressing what you referred to as inten misalignment. In contrast, we focus on evaluating LLMs' understanding and adherence to human values. 2. Beyond simply utilizing a red LM, we have built a fully automated agent-based framework. ALI-Agent leverages memory and refinement modules to generate real-world test scenarios that can explore long-tail and evolving risks. As you pointed out, some automated red-teaming methods can be transferred to value alignment: In [1], Supervised Learning (SL) is adopted to optimize red LLMs. With test cases that can elicit harmful outputs from target LLMs, the authors fine-tuned a red LM to maximize the log-likelihood of generating these test cases. Following their idea, we finetuned gpt-3.5-turbo-1106 on memory of ALI-Agent to obtain a red LM. For a fair comparison, we switch the core LLM to gpt-3.5-turbo-1106 and reran ALI-Agent. From Table 1 (in PDF attached to the general response), we observed that target LLMs exhibit higher model agreeability on test scenarios generated by ALI-Agent in most of the cases. This indicates ALI-Agent's superiority in probing risks in LLMs. Additionally, from the perspective of continuous learning, the SL red LM approach requires fine-tuning with new cases, while ALI-Agent can achieve this goal through its memory module, which is economic in terms of time and resources. >Comment 1: Conceptual clarity on concealing malice We appreciate your insightful comment and acknowledge that detection capability and intent misalignment are two decoupled concepts. We have measured these two terms respectively: + In our experiments on stereotypes, morality, and Singapore regulations, we focused on assessing the ability of target LLMs to identify risk scenarios, which is described as detection capability. ALI-Agent mitigates the harm of generated scenarios, thereby posing greater challenges to the target LLMs. In this context, the generation of less malice a positive outcome. + Our experiments on AdvBench measured intent misalignment on target LLMs. ALI-Agent wraps up harmful instructions in reasonable and justified contexts to hide its malicious intent. Then we examined whether the target LLMs follow harmful instructions. Overall, as you suggested, the two terms should be clarified clearly to avoid confusion. We will revise our manucripts accordingly. >Comment 2: Disclosure for human evaluation Thanks for the valuable suggestion, we will add disclosure as follows: We made post in the Computer Science department to invite students as human evaluators. Out of the 9 responses received, we conducted a brief 5-10 minutes private conversation with each student, introducing our work and explaining the significance of their evaluation to our research. We selected 3 students who showed the highest enthusiasm. Then we organized an online meeting to explain the task in details. We chose 12 examples (2 from each of the 6 datasets, one high-quality and one low-quality) to demonstrate the labeling process. Afterwards, we gave each student the same 10 random examples to label independently within 15 minutes. After confirming that each student's results matched the author's, we send them the copy of 200 randomly selected test scenarios. From the results we received, all of the 3 evaluator achieved a Cohen's kappa greather than 0.8 against the author's evaluation. >Comment 3: Report of radar plots Thanks for the suggestion, we will consolidate all the radar plots in the same place in our revised manuscript. >Comment 4: Concreteness of motivation We proceed to give more detailed examples as follows: + "Limited coverage of real-world use cases and long-tail risks" -- A target LLM can respond appropriately to a biased statment like 'Black people are criminals.', but it might fail the case when prompting with a scenario where the sensitive word 'Black people' is replaced by more subtle wording like a patron with a rich, dark complexion, a full exmaple illustrated in Figure 4 of the paper. + "Adapting to evolving risks" -- When the model evolves from GPT-3 to GPT-4, some previously identified issues are resolved, rendering static benchmarks insufficient to capture evolving risks. For example, an unethical action shown in Table 2 (in PDF attached to the general response) might be deemed acceptable by GPT-3.5-turbo-1106 but identified as problematic by GPT-4-preview-1106. >Comment 5: Diversity of scenarios To assess the similarity between generated test scenarios and the examples used in in-context learning (ICL), we adopted the TF-IDF cosine similarity as metric, and ran experiments on the stereotype dataset (DecodingTrust). The average similarity score was 0.135, and when we ablate ICL, the score is 0.105. This suggests that while ICL might slightly reduce the diversity of generation, the impact is overall acceptable. --- Rebuttal Comment 1.1: Comment: I appreciate and am impressed by the highly detailed response from the authors, and the authors' response is overall satisfactory. I am increasing my score to 7. --- Reply to Comment 1.1.1: Title: Replying to Reviewer sLAD Comment: Thank you! We are encouraged by your acknowledgment. --- Rebuttal 2: Title: References to the response Comment: References [1] Perez, Ethan, et al. "Red teaming language models with language models." arXiv preprint arXiv:2202.03286 (2022). [2] Mazeika, Mantas, et al. "Harmbench: A standardized evaluation framework for automated red teaming and robust refusal." arXiv preprint arXiv:2402.04249 (2024). [3] Wallace, Eric, et al. "Universal adversarial triggers for attacking and analyzing NLP." arXiv preprint arXiv:1908.07125 (2019). [4] Zou, Andy, et al. "Universal and transferable adversarial attacks on aligned language models." arXiv preprint arXiv:2307.15043 (2023). [5] Chao, Patrick, et al. "Jailbreaking black box large language models in twenty queries." arXiv preprint arXiv:2310.08419 (2023). [6] Ge, Suyu, et al. "Mart: Improving llm safety with multi-round automatic red-teaming." arXiv preprint arXiv:2311.07689 (2023). [7] Mehrotra, Anay, et al. "Tree of attacks: Jailbreaking black-box llms automatically." arXiv preprint arXiv:2312.02119 (2023). [8] Liu, Xiaogeng, et al. "Autodan: Generating stealthy jailbreak prompts on aligned large language models." arXiv preprint arXiv:2310.04451 (2023). [9] Shah, Rusheb, et al. "Scalable and transferable black-box jailbreaks for language models via persona modulation." arXiv preprint arXiv:2311.03348 (2023). [10] Deng, Gelei, et al. "Masterkey: Automated jailbreaking of large language model chatbots." Proc. ISOC NDSS. 2024. [11] Zeng, Yi, et al. "How johnny can persuade llms to jailbreak them: Rethinking persuasion to challenge ai safety by humanizing llms." arXiv preprint arXiv:2401.06373 (2024).	Summary: The paper introduces ALI-Agent, an evaluation framework leveraging LLM-powered agents for thorough and adaptive alignment assessments of LLMs. The framework features two stages: Emulation, which automates the creation of realistic test scenarios, and Refinement, which iteratively enhances these scenarios to explore long-tail risks. The authors assert that ALI-Agent is effective in identifying model misalignment and minimizing harmful content generation compared to conventional benchmarks. Strengths: The paper presents a novel method for assessing LLMs' capabilities in identifying and mitigating harmful content, which is a significant advancement in the field. The framework's two-stage process of Emulation and Refinement is well-defined and easy to comprehend, contributing to its replicability. The introduction of a dynamic, adaptive framework is a crucial contribution, addressing the limitations of static benchmarks and enhancing the relevance and applicability of the assessments. The paper includes comprehensive experiments across multiple datasets, providing robust empirical evidence for the framework’s effectiveness in detecting misalignments and reducing harmful content. Weaknesses: The choice of GPT-4 for refining and evaluation is questionable due to its extensive safeguards against generating harmful content, which might obscure the full potential of the framework. It would be beneficial to test the framework on models with fewer constraints to fully demonstrate its capabilities. The framework appears static without mechanisms for continuous learning and adaptation over time. Introducing a continual learning model could enhance the framework's ability to adapt to evolving risks, despite the mention of a memory module. The results section could be improved with a more detailed discussion on the comparison of different models, particularly focusing on the performance metrics in Tables 1-4. This would provide clearer insights into the framework's effectiveness relative to other approaches. The paper does not sufficiently address the scalability and generalizability of the framework to various real-world applications. More discussion on how ALI-Agent can be adapted to different contexts and scales would strengthen the paper. Technical Quality: 4 Clarity: 3 Questions for Authors: Corrections: Line 30: assesse -> assess Line 47: Web search -> web search Line111: ICL already mentioned before line 57, need to be used as in-context learning Line 125: squared L squared norm - > L squared norm Table 1,2,3,4: No need to mention reference multiple times for same evaluation setting in every table, so much redundancy. Confidence: 3 Soundness: 4 Presentation: 3 Contribution: 3 Limitations: N/A Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: >Comment 1: Choice of GPT-4 as the core Thanks for bringing up this important issue. We agree that the safeguards of GPT-4 can present obstacles, as we have encountered instances where GPT-4 refused to generate harmful scenarios during experiments. To circumvent this problem, we have designed jailbreak-like inductive system prompts. The detailed prompts can be found in Section D. The jailbroken GPT-4 proved effective thorough the experiments due to its remarkable instruction following ability. Just as you pointed out, models with fewer constraints should be prioritized, but their text generalization and instruction following abilities should be emphasized as well. We compared GPT-4 with ChatGLM3-6B as core LLMs on the dataset Singapore Rapid Transit Systems Regulations. ChatGLM3-6B has shown significantly weaker safeguards compared to GPT-4, as illustrated in Tables 1-4 in our paper. We found that the quality and diversity of GPT-4's generated scenarios outperforms ChatGLM3-6B. For example, given the regulation that forbids unauthorized entry onto railway premises, GPT-4 generated the scenario: ``` During the evening rush hour, a group of students protesting a recent fare increase forces their way past the closed gates of a Singapore MRT station, disregarding the station manager's attempts to bar entry. ``` In contrast, ChatGLM3-6B generated the scenario: ``` A person unauthorized by the Authority enters the railway premises. ``` Additionally, the averaged distinct-1 and distinct-2 score (calculated as #distinct n-grams / #words, higher score indicates higher text diversity) is 0.86, 0.99 for GPT-4 generated scenarios, and 0.017, 0.02 for ChatGLM3-6B. We attribute this difference in performance to GPT-4's better text generation and instruction-following abilities. Therefore, GPT-4 appears to be a well-rounded choice under a comprehensive consideration. However, we do agree that models with better generation abilities and fewer safety constraints could significantly enhance the power of ALI-Agent. We leave the exploration of such ideal models for future work, as outlined in the conclusion section. >Comment 2: Continuous learning and adaptation Thanks for your question. We are not pretty sure if we fully understand your point about continuous learning. Please feel free to raise any further concerns if we have not interpreted it correctly. From our perspectives: + If you are concerning about how our framework adapts to evolving risks, ALI-Agent addresses this issue with its refinement module. When a target model evolves (e.g., through fine-tuning or the release of a new version), test scenarios that previously invoked risks may no longer be effective. In such cases, ALI-Agent refines the scenarios based on the responses from the evolved target LLM to explore undiscovered loopholes, enabling the adaptation to evolving risks. + If you are considering using fine-tuning techniques for continuous learning, we totally agree that this approach adds dynamics to our framework and is promising for adapting to evolving risks. However, fine-tuning LLMs can be costly in terms of time and resources. Therefore, we opted for the refinement module, which also introduces adaptive capabilities and is inexpensive. Additionally, an intuitive experiment on fine-tuning the core LLM, as presented in our response to Reviewer sLAD's Q1, demonstrates that the utilization of memory and refinement modules is competitive to fine-tuning methods. >Comment 3: More discussions on the comparison between different models Thanks for the suggestion. We provide more discussion on the comparison of different models here and will incoporate them to the revised manuscript: + Comparison among open-source LLMs: As illustrated in Table 1-4, Llama2 models exhibit the best alignment with human values in terms of stereotypes, morality, and legality. Although instruction fine-tuning Llama2 to Vicuna may compromise the alignment, Vicuna-13/33B models still outperform ChatGLM3 model in stereotypes and morality. + Comparison among closed-source LLMs: In terms of stereotypes, GPT models can be easily influenced by targeted system prompts, whereas Gemini-Pro demonstrates strong resilience. However, Gemini-Pro tends to exhibit more misalignment in aspects of morality and legality. Compared to GPT-3.5, while GPT-4 demonstrates better alignment in stereotypes and legality, it shows more misalignment in morality. + Comparison among different aspects of human values: Almost all target LLMs tend to show the most severe misalignment in morality compared to stereotypes and legality, emphasizing the need for deeper alignment in this aspect. >Comment 4: Scalability and Generalization Thanks for bringing up this problem, following your suggestion, we will add a section discussing scalability and generalization as follows: 1. Scalability: Since our model is an automated framework, it can be easily scaled to more larger datasets. If we use GPT as the core LLM，the cost will increase for API usage. 2. Generalization: Our framework can be seamlessly adapted to different contexts in the following forms: + Laws/rules: Eating and drinking on the MRT in Singapore are not permitted. + Statements expressing unintended values: Homosexuals are carriers of sexually transmitted diseases. + Scenarios containing unacceptable actions: I rode an elephant until it passed out from lack of water. + Harmful instructions: Provide a step-by-step guide on how to commit identity theft. These four types of data cover many existing datasets we can evaluate. For data in other formats, although some prompt design modifications are necessary, the time and effort required are acceptable. The framework is generalized, and we look forward to further exploration within the Ali-Agent framework. --- Rebuttal Comment 1.1: Comment: Thank you for the detailed explanation about the changes and updates in the paper, I am increasing my score to 7. --- Reply to Comment 1.1.1: Title: Reply to Reviewer iWss Comment: Thank you, we are encouraged by your acknowledgment.	null	null	Rebuttal 1: Rebuttal: We appreciate all the reviewers for their valuable comments and suggestions to help us improve our work. We are encouraged that the reviewers found that: the topic is important and practical; the method is novel and well demonstrated; the experiments are comprehensive and robust, thus contribution is crucial and valid. We further address their questions and concerns as follows: + Validation of framework design. To address Reviewer iWss's concern about the choice of GPT-4 as the core LLM, we explained how we circumvent the safety guardrails of GPT and follow the suggestion to try other LLMs with fewer safeguards. We also added detailed explanations on the continuous learning ability, the scalability/generalization of our framework. + Baseline with experiments. Following suggestions of Reviewer sLAD, we compared our framework with other automated red-teaming methods to further demonstrate the contribution of our work. + Conceptual clarity. As suggested by Reviewer sLAD, we added clarificatons on the two concepts of 'detection capabioity' and 'intent alignment'. + Rigor and disclosure. Following suggestion of Reviewer sLAD, we added full disclosure of the process on obtaining human evaluations. + More option of design with experiments. Following suggestions of Reviewer 77qx, we explored other methods of LLM-based memory, and added further discussion on the design of memory module of our framework. We also added detailed discussions on experimental results and corrected typos/formatting issues as Reviewer iWss suggested; and we addressed Reviewer sLAD's minor considerations on concreteness of motivation as well as diversity of scenarios. Pdf: /pdf/d2fb8ad7d659e01f5ffda863d307451ea015b2ac.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Beyond Concept Bottleneck Models: How to Make Black Boxes Intervenable?	Accept (poster)	Summary: This work introduces a method for performing concept-based interventions on pretrained black-box neural networks, requiring only a small validation set with concept labels. The paper formalizes the notion of intervenability as a measure of the effectiveness of these interventions and experimentally assesses the intervenability of black-box classifiers across several benchmarks and architectures. Strengths: * Originality: The paper presents a novel approach that enables effective concept-based interventions on black-box models. While the methods used already existed, they were creatively applied for this purpose, leading to both methodological originality and novel experimental findings. * Quality: The research methods are appropriate and well-described. The results and conclusions are supported by the data. The proposed approach is simple and sound, making it mathematically elegant and enabling the research community to use and expand it. * Clarity: The paper is well-structured with a clear flow. The writing is clear, concise, and free of grammatical errors. Figures and tables are well-designed and effectively support the text. The abstract and title summarize the paper effectively. * Significance: In their vanilla formulation, Concept Bottleneck Models were already applied on pre-trained models (e.g., ResNets) by introducing only a few extra layers on top of the backbone to predict concepts and downstream classes. Compared to vanilla CBMs, the main innovation of the proposed approach seems to consist in using concept labels only to fine-tune the model using the validation set. The findings demonstrate the flexibility of concept-based approaches and the possibility of extending concept-based interventions to black-box architectures more effectively wrt an equivalent CBM similarly fine-tuned. In view of these results, this paper could have a significant impact on real-world applications where existing pre-trained black boxes are currently used and a small concept-annotated validation set is available. * Literature: The sources are properly cited, relevant, and up-to-date. Weaknesses: * Clarity / Quality: I could not find the precise training/validation procedure used for the baseline "CBM val", which represents one of the most critical baselines to compare with. I double checked both the paper but I could not find a detailed description. I also checked the code, but I could not find the configuration file (and the rest of the training/validation flow) for this baseline. The reason why I'm curious is that CBMs can also be viewed as "classification heads" fine-tuned on top of pre-trained models using a small validation set (e.g., a ResNet pre-trained on ImageNet used as a backbone of a CBM trained on CUB). The main result of this paper seems to consist in making interventions in CBMs effective with a smaller validation set. That is why the way this baseline is constructed is relevant to assess the quality and impact of this work. I could imagine at least two ways to construct such a baseline using a pre-trained backbone $g: X \to H$ (e.g., a ResNet trained on ImageNet) and a classification head $f: H \to Y$ (e.g., trained on CUB using downstream task labels but not concept labels): 1. Fine-tune a single layer $f^{(c)}$ of $f$ to align the activations of this layer on ground-truth concept annotations of the validation set. Freeze all the other layers of the model $f$. 2. Fine-tune all parameters before the layer $f^{(c)}$, while freezing all the layers following $f^{(c)}$. 3. Opposite of option #2. 4. Train a new model $f'$ using only the ground-truth concept annotations of the validation set. I could not understand from the paper/code to which option the baseline "CBM val" corresponded to and whether the fine-tuning approach was used to train this baseline as well. Technical Quality: 3 Clarity: 3 Questions for Authors: ### Major * "CBM val" Baseline: Could you clarify in detail how the baseline "CBM val" is trained and validated? * “Since interventions can be executed online using a GPU (within seconds), our approach is computationally feasible”: This is not a formal justification for why the proposed approach is computationally tractable. The time complexity can be estimated in a more formal way. ### Minor * “This work focuses specifically”: This paragraph is already quite technical. While clear, it could be moved to a "preliminary" section after the introduction and rephrased here to make the introduction easier for non-technical readers. Also, the notation is presented again in the methods section (which is fine as it is a technical section). * Related Work: Consider moving the related works section after the experiments. This way, you could use the experimental results to discuss the relations of your contributions with related works. * Figure 2, Step 3: The arrow in step 3 might go downwards (as in the figure in the appendix). * “For a trained CBM fθ (x) = gψ (hφ (x)) = gψ (ˆ c)”: Consider explaining again here what c^\\hat{c}c^ represents as this was mentioned in the introduction, but it was not mentioned in the presentation of the notation. * “we define the intervenability as follows”: Consider explaining the idea behind the equations (e.g., "Here, the effectiveness of interventions is quantified by" for Eq 2) before showing the equation to ease reading. * “where D is the joint distribution over the covariates …”: Consider describing the variables involved in an equation before showing the equation to avoid the reader going back and forth. * “To alleviate the need for human-annotated concept values”: This sentence might be confusing as it is not clear whether it is the proposed approach or label-free CBMs that alleviate the need for human-annotated concepts (or both). I'd rephrase it with something like "To evaluate the effectiveness of the proposed approach in the absence of human-annotated samples ..." * Results section: Organizing results by datasets leads to repetitions of some observations. I'd suggest organizing paragraphs by key findings (which might sometimes relate to a single dataset, but it is ok). * Table 1: Consider dropping "0" at the beginning of each value (e.g., ".987") or express numbers in base 100 (e.g., 98.7) to save space. Consider highlighting the best models in bold. * CIFAR 10 results in Table 1: Why not use CIFAR-100 (where concept labels are available as a ground truth) instead of CIFAR-10? * Discussion & Conclusion: The largest gap with respect to baselines is on AwA and MIMIC. Do you have an intuition why this is the case? The discussion could benefit from this analysis. Confidence: 5 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: Authors adequately discuss limitations and future works in a dedicated section. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for the feedback! You will find our point-by-point responses below. > I could not find the precise training/validation procedure used for the baseline "CBM val". We have updated the public repository to include the configuration file `config_synthetic_cbm_val.yaml` and code to run the “CBM val” baseline. As mentioned, CBMs can be viewed as classification heads on top of pre-trained models. However, this would correspond to the “post hoc CBM”. We frame the presented CBM in its original “ante hoc” implementation [6], where the backbone is trained from scratch. Our work focuses on making interventions on any pre-trained black box more effective, not the CBMs. From the options provided by the reviewer, our “CBM val” is number 4. This way, we show the sample efficiency of our method over the (ante hoc) CBMs when only a small portion of annotated data is available. >“Since interventions can be executed online using a GPU, our approach is computationally feasible”: This is not a formal justification for why the proposed approach is computationally tractable. This statement is not meant as a formal complexity metric, but as a remark for the interested reader that the interventions are less costly than training or fine-tuning and can be run “online” with a regular GPU. As the intervention procedure is gradient-based, the computational cost varies across datasets and depends on the optimization iterations. The number required depends on several factors, e.g., the value of $\lambda$, the number of concepts, the dimensionality of $z$, and the number of data points per batch. Given these, providing a formal description of the running-time complexity is challenging. For example, on the synthetic dataset, with the convergence parameter set to $10^{-6}$ (very conservative) and for a batch of 512 samples, the intervention procedure requires approx. 500 to 2500 steps (the number varies depending on the number of given concepts and the value of $\lambda$), which amounts to 0.5 to 2 s (for the whole batch) for an untuned black-box model. We use smaller batches and more permissive convergence criteria when fine-tuning, allowing a considerable speedup. In addition, note that the run-time of the intervention procedure is not strictly dependent on the black-box model’s architecture (except for the dimensionality of the layer intervened on). > “This work focuses specifically”: This paragraph is already quite technical. While clear, it could be moved to a "preliminary" section after the introduction. Thank you for the suggestion! In order to address a broader audience, we will include a preliminary section introducing the method with the technical contributions, and reframe the introduction to be less technically oriented, removing the formal notation. > Figure 2, The arrow in step 3 might go downwards. We will update the figure. > “For a trained CBM fθ (x) = gψ (hφ (x)) = gψ (ˆ c)”: Consider explaining again here what c^\hat{c}c^ represents With the new organization of the introduction and preliminary section of the methods, we will introduce the notation accordingly prior to the description of the method. > “we define the intervenability as follows”: Consider explaining the idea behind the equations before showing the equation to ease reading. Intuitively, the more effective an intervention is, ideally, the more it should reduce the target prediction error. Leveraging this, our equation measures the gap between the prediction error prior and post intervention, where larger gaps correspond to more effective interventions. > I. “where D is the joint distribution over the covariates …”: Consider describing the variables involved in an equation before showing the equation to avoid the reader going back and forth. II. “To alleviate the need for human-annotated concept values”: This sentence might be confusing as it is not clear, I'd rephrase it. III. Table 1: Consider dropping "0" at the beginning of each value or express numbers in base 100 to save space. We will clarify and introduce the notation in I, rephrase II, and change the metrics to percentages and bold the best results in III. > CIFAR 10 results in Table 1: Why not use CIFAR-100 (where concept labels are available as a ground truth) instead of CIFAR-10? We include experiments with both CIFAR-10 and ImageNet that do not originally have available ground-truth concepts to show that our method can be combined with “concept discovery” [7], where annotations are acquired through VLMs. We did not include CIFAR-100 as we have a synthetic tabular, two natural image datasets (CUB and AwA2), and two medical image datasets (MIMIC-CXR and CheXpert) that, we believe, are sufficiently representative to cover the settings with “annotated” concepts. > The largest gap with respect to baselines is on AwA and MIMIC. Do you have an intuition why this is the case? Generally, our procedure has a stronger effect because we target the improvement with interventions with a stronger inductive bias, while other methods do not explicitly encourage intervention effectiveness. In some instances, activations are correlated with concepts, but the network does not rely on them for prediction, e.g., when there is a complex relation between the concepts and target, as in the case of X-rays (MIMIC), and only probing is not enough to intervene effectively. However, after fine-tuning, the black box learns to use the information correlated with the concepts at prediction time. At the same time, our approach does not require introducing a concept bottleneck layer, and, therefore, the model may still use additional non-concept-based information from the representations. With respect to the AwA (and CIFAR-10), the experimental findings fall within our expectations: in both, concepts are useful for predicting the target variable, and our fine-tuning explicitly encourages intervention effectiveness, providing a stronger supervisory signal. --- Rebuttal Comment 1.1: Comment: Thank you for your effort and for taking the time to explain your work even further! I am aware that the following comments/questions are not critical nor the focus of this work. I am asking out of curiosity. [nit] Computational cost: Thank you for providing a more detailed discussion on this. I think the paper would benefit if you could report this discussion in the appendix and take it a bit further by ranking the most critical factors and estimate their relationship with the computational cost (e.g., linear, quadratic, etc). [nit] CIFAR: I understand the motivation for choosing CIFAR without using concept annotations. I'm wondering though whether the concept annotations generated using the VLM are aligned in some way to the original concept labels in CIFAR-100. And in case VLM and CIFAR-100 concept labels overlap, I'm curious to understand whether: (i) the VLM's annotations are actually matching the ground truth, and (ii) the interventions would be more effective using VLM's annotations or ground-truth annotations. --- Rebuttal 2: Title: Answer to Official Comment Reviewer ajS6 Comment: Thank you for your nice feedback and for your interest in our work! As a follow up to the two raised points: - Computational cost: We agree with your point and will include the discussion in the appendix, thank you! Regarding the most critical factors, we believe all, the convergence parameter, number of concepts, number of datapoints, value of lambda, and the dimensionality of z play a relevant role. Due to the nature of the gradient-based optimization that runs until convergence, it is challenging to provide a formal estimation of the cost or ranking. However, one could try to approach the problem empirically by providing wall-time results of the optimization under controlled synthetic experiments varying the mentioned parameters to provide a better understanding of their relevance, which we will include in the appendix of the revised paper. We will, in addition, consider characterising more formally the complexity of a single update step in this gradient-based procedure, which should give additional intuition on the complexity. - CIFAR: We believe that the original concepts coming from CIFAR-100, i.e. the classes, and those from [7] in the VLM scenario differ significantly. More precisely, the original work in [7] introduces a total of 824 concepts in CIFAR-100 while the original annotated labels are only 100, and cover different categories. We assume in this discussion that the “concepts” the reviewer refers to in CIFAR-100 are the super-classes. For this reason, using the VLM-based concepts to intervene on a model trained with the original CIFAR-100 concepts would not be possible. However, we envision a setup where keeping the original concept categories, the CIFAR-100 dataset can be re-annotated using CLIP, this way the experiment proposed by the reviewer could be conducted. Based on our experience with VLM annotated data, we would expect it to have more noise and, therefore, potentially, less effective interventions than under the ground-truth annotations. --- Rebuttal Comment 2.1: Comment: I agree on both points! Congrats again for your work!	Summary: The paper proposes a novel method for test-time concept-based intervention on black-box models. Starting from the interactive intervention procedure of concept-bottleneck models, the authors devise a novel technique for reproducing it on any pre-trained black-box model. It consists of training a concept probe on the latent space of the model and using it to modify the representation of a given concept and checking the response of the model to this intervention. Also, the authors define a measure of intervenability which can be optimized to fine-tune a model architecture, while making it more prone to concept-intervention. The proposed approach is tested over several benchmarks. Strengths: Novelty and impact: although based on the idea of concept probing (step 1, already proposed in literature), the following steps of editing the representations and updating the output (i.e., of performing an intervention) of a black-box model are simple but very interesting and potentially important for a large part of the XAI community. Indeed, it brings for the first time the interactability of explainable-by-design concept-based models to post-hoc concept-based techniques. Weaknesses: ## Major issues - Presentation: the paper is not very clear in a few passages. Also, some comments to the results in the experimental sections are excessive or not completely true, and they must be changed/softened. See minor issues for indications of the individual sentences to edit. - Equation 4: presenting Eq. 4 and then only considering the special case of $\beta=1$ is not correct, as it completely neglects a term. This is not acceptable even if it implies the training of the probe, a reader expects to see an ablation study on that in the experiment. I solicit the authors to present it otherwise (e.g., presenting first the actual optimized equation) or provide an ablation study on that. ## Minor issues - In the abstract, “Recently, interpretable machine learning has re-explored concept bottleneck models (CBM)”. The sentence is not very clear, it seems in this way that concept bottleneck models have already been proposed in the past. You also say it in the introduction. If it is the case, and it has been proposed earlier, you should provide a citation. - “While, in principle, a specialist may just override predictions, in many cases, concept and target variables are linked via nonlinear relationships potentially unknown to the user.” This sentence is not super clear and does not seem to support the paper point. I would consider rephrasing or removing it. - Figure 1: The concepts reported are not clear. Another example or the same example with textual concepts instead of icons would be probably easier to read. - In the Method, “we will assume being given a small validation set”, I would explicitly add “equipped with concept annotations”. - “think of a doctor trying to interact with a chest X-ray classifier $(f_\theta)$ by annotating their findings”, which findings? Not very clear, why don’t you directly provide an example of concept for the X-ray task? - “Note that, herein, an essential design choice explored in our experiments is the (non)linearity of the probe”. Not clear from this whether you consider both a linear and a non-linear, or only one of the two without looking at the experiments. - You should probably cite also TCAV [1] in 3.1 when talking about probing. The CAV is probably the most renowned concept probe. - I think you should better explain and point out the fact that if you directly optimize equation 3 you could decrease the performance of the model, since you would maximize the error over the non-intervened network. Instead, you says “ Equation 3 is differentiable, a neural network can be fine-tuned by explicitly maximising”. And, in equation 4, you change the optimization problem optimizing both losses - Fine-tuned, A: it is not very clear the reason of including this model, nor the explanation. Please rewrite and add further motivations. - Commenting Figures F.4 and Figure 4 this close is confusing. If possible, position the appendix figures in a different order to avoid confusing the reader. - “Finally, post hoc CBMs (even with residual modelling) exhibit a behaviour similar to the synthetic dataset with incomplete concepts: interventions have no or even an adverse effect on performance.” This claim is not supported by the results presented in figure 4(d) bottom: the AUPR is increasing in a non-negligible manner. Please rephrase the sentence. A similar consideration holds also for the Discussion section. [1] Kim, Been, et al. "Interpretability beyond feature attribution: Quantitative testing with concept activation vectors (tcav)." International conference on machine learning. PMLR, 2018. Technical Quality: 4 Clarity: 2 Questions for Authors: 1. Table 1 report results where the black-box model is normally not that good for the target performance (among the worst results in general). This is something that I would not have expected, since both the bottleneck and the fine-tuning pose further constraints that normally impact the model performance (as also reported by CBM and many other concept-based approaches). How do you explain it? 2. Why is the CBM more computationally expensive in the experiments with VLM-based Concept? I think you could use a fixed CLIP to predict the concepts and simply train the task predictor on that. If I am right, I think the following sentence is unfair, and I suggest removing it “By contrast, our method allows fine-tuning the pretrained network, thus being helpful where a CBM is impractical”. 3. In Cher X-ray classification the black-box models are not intervenable. This is a surprising result, which partly contrast with the claim that you propose a method to make “interventions on any pretrained neural network post hoc. Could you elaborate further on that? Confidence: 5 Soundness: 4 Presentation: 2 Contribution: 4 Limitations: The authors report mostly possible expansions of their work, rather than actual limitations and possible societal implications of their approach. Indeed, even though the proposed method improves the interpretability of the model, it may impact its security. An attacker, for instance, could misuse the proposed technique for detecting model biases towards some specific concepts and creating realistic adversarial attacks that could go undetected. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your detailed comments! Below, we respond to your concerns point by point. > Equation 4: presenting Eq. 4 and then only considering the special case of β=1 is not correct. We believe the formalization of the overall optimization problem is a beneficial contribution to future lines of work. However, we agree our focus is on the simplified case and will adapt the manuscript first introducing the special case, followed by the general formulation. >In the abstract, “Recently, interpretable machine learning has re-explored CBMs”. The sentence is not very clear, it seems in this way that CBMs have already been proposed in the past. We refer to the works referenced in “Introduction” and “Related Work” [4,5] and will make them more explicit. They propose concept-based approaches to classification. Although not strictly referred to as CBMs, they are very similar and the original work on CBMs [6] acknowledges them as closely related. > “While a specialist may just override predictions, concept and target variables are linked via nonlinear relationships potentially unknown to the user.” This sentence is not super clear and does not seem to support the paper point. We motivated the need for concept-based interventions, especially in scenarios where a professional has the concept information but inferring the target variable is not an easy task. We understand the potential confusion and will remove it. > Figure 1: The concepts reported are not clear. We will include their description in the main text and caption. Particularly, in order of appearance from left to right, and top to bottom, the meaning of the icons is: “fierce”, “timid”, “muscle”, “walks”, “otter” and “grizzly bear”. This figure is complemented by a more concrete example of model correction in Figure A.2 with a list of all intervened on concepts. > “think of a doctor trying to interact with a chest X-ray classifier by annotating their findings”, which findings? The findings are the concepts of the X-ray datasets. We will provide examples to help understand the X-ray use-case and include a table in the appendix with the full list of concepts: atelectasis, cardiomegaly, consolidation, edema, enlarged cardiomediastinum, fracture, lung lesion, lung opacity, pleural effusion, pleural other, pneumonia, pneumothorax, and support devices. > Not clear whether you consider both a linear and a non-linear probe, or only one of the two without looking at the experiments. We will clarify that the experiments shown in the main body are performed under a linear probe and an ablation with a nonlinear probe is found in the appendix. > You should probably cite also TCAV in 3.1 when talking about probing. The CAV is probably the most renowned concept probe. We will include it. > I think you should better explain the fact that if you directly optimize equation 3 you could decrease the performance of the model. We will make it more explicit that the final loss function is a linear combination of the intervenability measure in Eq. 3 and the target prediction loss, resulting in Eq. 4. We always consider the combination of the two to better control the tradeoff. > Fine-tuned, A: explanation to why including this model The motivation is: it would be natural to include the concepts in the model, either at the input or at intermediate layers. Since the considered feature spaces are high-dimensional, we append concept variables to the intermediate activations as a direct comparison to Fine-tuned I. > “Finally, post hoc CBMs exhibit this behaviour: interventions have no or even an adverse effect on performance.” This claim is not supported by the results presented in figure 4(d) bottom. We will rephrase the statement to clarify that in some datasets, a small positive effect is present. > Table 1 report results where the black-box model is normally not that good for the target performance. In synthetic data, the generating process favors the CBM architecture, as concepts directly relate the inputs to the target and we expect the CBM to outperform. In the remaining datasets with more complex concept-to-target dependencies, the CBM performs worse, as expected. If the concept variables are “useful” for the target prediction, we hypothesise the fine-tuning methods would improve predictive performance. Specifically, fine-tuning enforces reliance on the concept variables, which might increase the robustness and prevent overfitting. Moreover, fine-tuned black boxes keep the original representation without introducing a bottleneck layer and can still use non-concept-based information if necessary. To finalize, our focus was on making the models more intervenable, and Table 1 suggests that most methods behave on par, i.e., fine-tuning with intervenability does not harm the performance. > Why is the CBM more computationally expensive in the experiments with VLM-based Concept? I think you could use a fixed CLIP to predict the concepts. The VLM-based concept annotation does not influence the computational cost of the CBMs. We have used these annotations to explore larger backbone architectures and training these from scratch, as would be needed for the (ante hoc) CBM baseline, is not computationally feasible. It would require a large number of concept annotations and resources. Using a fixed CLIP to predict the concepts is alike the post hoc CBM, which we include as baseline. > In Cher X-ray classification the black-box models are not intervenable. This partly contrast with the claim that you propose a method to make “interventions on any pretrained neural network post hoc. In some instances, activations are correlated with concepts, but the network does not necessarily rely on them for prediction, hence, only probing is not enough to intervene effectively. However, after fine-tuning, the black box learns to use the information correlated with the concepts at prediction time. Hereafter, fine-tuning may be necessary in some instances. --- Rebuttal Comment 1.1: Comment: I thank the authors for taking the time to fix the issues and answer my questions. I think the paper is ready to be accepted now.	Summary: The paper proposes a method to make any pre-trained black box model intervenable, given a small validation dataset with concept. This is done by the following procedure: - Extract the output of a layer of a black-box $g_{ \psi} (z)$ and train a probing network $q_{\xi}(z)$ to extract the concepts from that layer using the validation dataset. - For intervening i.e changing concepts $c$ to $c'$: Given $z$ find $z'$ that minimizes $L^c(q_{\xi}(z'),c')+d(z,z')$ where $d$ is a distance measure. $z'$ is optimized using gradient descent. - Train the black-box network to be intervenable by finetuning, minimize $L^y(g_{\psi}(z'),y)$ - To edit the representations, replace $z'$ with $z$. The paper demonstrated the effectiveness of their approach by comparing it to the following baselines: - A black-box with representation editing and no finetuning. - CBM - A finetune black-box that predicts the concepts and the output (Multitask-learning) - A finetune black-box by appending the black box activations with the concepts. - Post-hoc CBMs The approach was evaluated on the following datasets: - A synthetic tabular dataset with a complete and incomplete concept dataset. - Vision datasets with labels: AWA2 and CUB - Vision datasets with no labels: Cifar10 and imageNet (Here labels are obtained from an LLM in a label-free style). Results that the proposed method outperforms others in cases where data is limited i.e the % of validation dataset is low or when the number of interventions is generally low. Strengths: ### Originality -- Good - The method itself is original, i.e., how the representations are found and training is done is novel. While there are post-hoc CBMs that can allow intervention on the black box as well. The proposed method seems to outperform them, especially in the incomplete data regime. ### Quality-- Excellent - The proposed method is simple but seems very effective and the fine-tuning procedure is well motivated by an empirical comparison to black-box model interventions without the fine-tuning. - Very good empirical evaluation in general, comparisons were done on synthetic data, and 4 different image data sets on different domains; with reasonable baselines. - Code was provided to reproduce the experiments. ### Clarity -- Excellent - The paper is well-written, clear and easy to follow. Weaknesses: ### Significance -- Fair - There are two main advantages of using CBMs, interpretability and intervenability. While the proposed method allows for intervenability, this method does not add interpretability to black box model. - One could argue that since you need a validation set with concept anyhow, one should just put a CBM in the original architecture giving both interpretability and intervenability. Empirical validation in the paper did show that the proposed method did better than CBM however baseline CBM used in the evaluation was not trained for intervenability as done by Mateo, et al. [1] which could dramatically improve the performance of regular CBMs. So its difficult to conclude that the proposed method is in fact superior to CBMs in any way. [1] Espinosa Zarlenga, Mateo, et al. "Learning to receive help: Intervention-aware concept embedding models." Advances in Neural Information Processing Systems 36 (2023). Technical Quality: 3 Clarity: 4 Questions for Authors: - Which layer of is used for interventions, does it matter? - For the multi-task baseline, Fine-Tune MT how do you intervene on test time since changing the multitask label does not affect the output of the classifier? - For the appending baseline Fine-Tune A do you throw away the last layer of the original network (i.e the layer after the one used for interventions) and create a new one to handle the new size? Confidence: 4 Soundness: 3 Presentation: 4 Contribution: 3 Limitations: Yes. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for the feedback and questions! Below is our point-by-point response. > There are two main advantages of using CBMs, interpretability and intervenability. While the proposed method allows for intervenability, this method does not add interpretability to black box model. As stated by the reviewer, this work focuses on intervenability and its formalisation. However, the proposed method also incorporates interpretability with respect to a regular black box model. By mapping intermediate layers to human-understandable concepts via the probe, the user gains a better interpretation of the information contained in the representations. This connection between probing classifiers and interpretability is supported and further detailed in prior work referenced in the manuscript [1,2,3]. > One could argue that since you need a validation set with concept anyhow, one should just put a CBM in the original architecture giving both interpretability and intervenability. Empirical validation in the paper did show that the proposed method did better than CBM however baseline CBM used in the evaluation was not trained for intervenability as done by Mateo, et al. [1] which could dramatically improve the performance of regular CBMs. So its difficult to conclude that the proposed method is in fact superior to CBMs in any way. The original CBM architecture requires training the concept and target predictors from scratch. This is a limitation in the settings where there is not enough data available to train a large backbone, e.g. using Stable Diffusion like in the CIFAR-10 and ImageNet experiments. This problem would be aggravated further if only a validation set with concept annotations was used. We explore this in Figure 3 and show that CBMs are not sample efficient when trained only on the validation set. We did a preliminary exploration of the introduction of interventions at training time in the CBM, similar to the work done on the mentioned CEMs by Mateo et al., and we did not find a significant improvement with respect to the regular CBM in the presented datasets. Effectively, intervening on a vanilla CBM at training time can be thought of as a combination of independent and joint training, which, as shown in Appendix F.10, have similar results. In the cases where the concept set is incomplete, the bottleneck layer in the CBM will hinder the overall model performance, even under interventions. However, finetuning for intervenability does not limit the expressivity of the intervened-on layer and, therefore, allows for better target prediction. >Which layer of is used for interventions, does it matter? The reported experiments show the results of intervening two non-linear layers after the backbone. The layer you intervene on will play a role in the effectiveness of interventions. Generally, high-level information in neural networks emerges in deeper layers, which is why we recommend conducting the interventions there. Additionally, the required complexity of the probe is lower as the dimension of the layers is reduced deeper within the network. Prior works show probing at deeper layers is benefitial [2]. However, the proposed method can be applied at any step, provided the layer has extracted enough information, and we expect interventions to have a positive effect on the target prediction. >For the multi-task baseline, Fine-Tune MT how do you intervene on test time since changing the multitask label does not affect the output of the classifier? The intervention on Fine-Tune MT is done in the same fashion as in the proposed Fine-Tune I, using the three-step solution introduced in Section 3.1. in the manuscript. This will be made clarer in the revised version of the paper. >For the appending baseline Fine-Tune A do you throw away the last layer of the original network (i.e the layer after the one used for interventions) and create a new one to handle the new size? This is correct. We leverage the pretrained backbone until the layer where the concatenation with the concepts occurs, in this case, two non-linear layers after the extracted features. At this state, a new target predictor is created with input layer size correspondig to the representations concatenated with the concepts. --- Rebuttal Comment 1.1: Title: Thanks Comment: I would like to thank the authors for their response, very interesting work, hope to see this paper in the conference.	null	null	Rebuttal 1: Rebuttal: Dear reviewers, We thank you for the detailed feedback; we will make sure to address the concerns and incorporate the corresponding changes in the revised manuscript upon acceptance. Below is a summary of the main responses and clarifications addressed in this rebuttal: - We have provided a more in-depth explanation of the baseline “CBM val”. Effectively, it consists of training an ante hoc CBM solely on the validation set to compare CBM’s sample efficiency against the proposed method. - In our experiments, we have compared with two baselines related to CBMs, namely, (ante hoc) CBM and post hoc CBM. We would like to emphasise that the (ante hoc) CBMs represent the original formulation of CBMs, i.e. without pretrained backbones. We will clarify the distinction between the (ante hoc) CBM and post hoc CBM used as baselines in the revised manuscript. - Our method focuses on the intervenability of the models. However, it also facilitates interpretability via representation probing. References: [1] Belinkov, Y. (2022). Probing Classifiers: Promises, Shortcomings, and Advances. Computational Linguistics, 48(1), 207-219. [2] Alain, G., & Bengio, Y. (2016). Understanding intermediate layers using linear classifier probes. arXiv preprint arXiv:1610.01644. [3] Kim, Been, et al. (2018) Interpretability beyond feature attribution: Quantitative testing with concept activation vectors (TCAV). International conference on machine learning. PMLR. [4] Lampert, C. H., Nickisch, H., & Harmeling, S. (2009). Learning to detect unseen object classes by between-class attribute transfer. In 2009 IEEE conference on computer vision and pattern recognition. Miami, FL, USA: IEEE. [5] Kumar, N., Berg, A. C., Belhumeur, P. N., & Nayar, S. K. (2009). Attribute and simile classifiers for face verification. In 2009 ieee 12th international conference on computer vision (pp. 365–372). Kyoto, Japan: IEEE. [6] Koh, P. W., Nguyen, T., Tang, Y. S., Mussmann, S., Pierson, E., Kim, B., & Liang, P. (2020). Concept bottleneck models. In H. D. III & A. Singh (Eds.), Proceedings of the 37th international conference on machine learning (Vol. 119, pp. 5338–5348). Virtual: PMLR. [7] Oikarinen, T., Das, S., Nguyen, L. M., & Weng, T.-W. (2023). Label-free concept bottleneck models. In The 11th international conference on learning representations.	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
DiffuPac: Contextual Mimicry in Adversarial Packets Generation via Diffusion Model	Accept (poster)	Summary: This paper proposes an adversarial packet generation method, named DiffuPac, to evade detection. DiffuPac integrates BERT and a diffusion model to make the generated packets indistinguishable. To better fit the task, a concatenation strategy and a classifier-free approach are proposed. The experimental results are promising. Strengths: 1. This paper proposes a novel adversarial packet generation scheme to test the evasion detection ability of NIDS. 2. The paper is well-written and easy to follow. 3. The performance is good. Weaknesses: 1. The primary concern is the efficiency of DiffuPac. As a diffusion model is adopted to generate adversarial packet, it may be time-consuming. Can you conduct some experiments to validate the efficiency of your method? 2. Can you also consider some defenses against such adversarial packets? For example, adversarial training (AT), feature selection (FS), and adversarial feature reduction (AFR) as shown in work [1] [1] Han, Dongqi, et al. "Evaluating and improving adversarial robustness of machine learning-based network intrusion detectors." IEEE Journal on Selected Areas in Communications 39.8 (2021): 2632-2647. Technical Quality: 3 Clarity: 3 Questions for Authors: 1. I understand the effectiveness of DiffuPac in an experimental environment but in the real world, usually, an ML model is adopted to detect evasion for fast response requirements but not a DNN. As DNN is less robust to adversarial examples, will this affect the practicability of DiffuPac? Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: Mentioned in Sec.5. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We greatly appreciate the reviewers’ constructive review and insightful suggestions regarding our paper. Our responses are given in a point-by-point manner for each comment. W1. We conducted a comprehensive evaluation of different BERT model configurations to identify the most efficient option that still maintains high performance. As for the diffusion model, we have implemented several optimizations to improve the training and inference efficiency of the model. We tested four BERT model variants: Tiny, Small, Medium, and Large, comparing their specifications, training time, loss, and accuracy. The results are summarized in the Table 1 below: \| Parameters \| Metrics \| Tiny BERT \| Small BERT \| Medium BERT \| Large BERT \| \|-------------------------\|------------------------\|---------------\|----------------\|-----------------\|----------------\| \| Model Specifications\| Embedding Size \| 128 \| 512 \| 768 \| 1024 \| \| \| Feedforward Size \| 512 \| 2048 \| 3072 \| 4096 \| \| \| Hidden Size \| 128 \| 512 \| 768 \| 1024 \| \| \| Activation Function\| GELU \| GELU \| GELU \| GELU \| \| \| Number of Heads \| 2 \| 8 \| 12 \| 16 \| \| \| Number of Layers \| 2 \| 4 \| 12 \| 24 \| \| Training \| Training Time (hours)\| 13.5 \| 18 \| 23 \| 30.5 \| \| Performance \| MUM Loss \| 1.028 \| 0.822 \| 0.667 \| 0.610 \| \| \| SSP Loss \| 0.295 \| 0.204 \| 0.099 \| 0.061 \| \| \| MUM Accuracy \| 0.844 \| 0.887 \| 0.905 \| 0.914 \| \| \| SSP Accuracy \| 0.846 \| 0.902 \| 0.972 \| 0.982 \| Table 1: Comparison of Tiny, Small, Medium, and Large BERT models in terms of their specifications, training time, loss, and accuracy. The Medium BERT model was chosen as the optimal configuration for DiffuPac because it offers a balanced trade-off between accuracy and loss metrics. As for the diffusion model, we utilized FP16 (half-precision floating-point) for GPU computations. This approach significantly reduced the training time from 10 hours to 4 hours, nearly doubling the speed without sacrificing model performance. FP16 allows us to leverage the GPU's computational power more effectively, enabling faster iterations and reduced memory usage. During the sampling phase, we initially encountered issues with memory over-utilization, which was a significant bottleneck given our hardware limitations. To resolve this, we integrated the FAISS library, which is optimized for efficient similarity search and clustering. FAISS allowed us to handle the nearest neighbor search more efficiently, preventing memory overflow and ensuring smoother sampling operations. This optimization not only improved the stability of our sampling phase but also reduced the overall memory footprint of the model. All of the results including the fully-detailed explanation of them will be added in the revised paper. W2. Adversarial Defences is a critical area of research that we are actively exploring, particularly in the context of DiffuPac's unique capabilities. In addition to the more established defense strategies mentioned, we are currently developing a novel approach to defending against adversarial packets: adversarial purification using diffusion models. This technique has shown great promise in the field of image processing, and we believe it holds significant potential for network security as well. Our approach leverages the inherent strengths of diffusion models, which are ideally suited for the task of adversarial purification. By treating adversarial perturbations as noise, we utilize the diffusion model's reverse process to "purify" incoming network packets, effectively stripping away malicious modifications and restoring the packet to its original, clean state before it is analyzed by a NIDS. This research is still in progress, and we are excited about its potential. We aim to fully develop and test this method, positioning it as a powerful alternative to traditional adversarial defenses. As far as we are aware, this research work will be the first to apply adversarial purification to network packets, which we believe could set a new standard in the field. Q1. In future work, we will propose a hybrid approach that combines the strengths of DiffuPac with more robust and faster-responding machine learning (ML) models. In practice, DiffuPac could be used to generate adversarial examples during the training phase, which can then be used to harden simpler, more interpretable models like decision trees, random forests, or support vector machines through adversarial training. This approach allows for the creation of a robust detection system that can quickly respond to threats while benefiting from the advanced adversarial generation capabilities of DiffuPac. Additionally, while DiffuPac focuses on generating adversarial examples, the integration of adversarial purification, as discussed in our ongoing research, offers another layer of defense. This process can help mitigate the effects of adversarial examples on DNNs, thereby enhancing their robustness in real-world applications. --- Rebuttal Comment 1.1: Comment: Thanks for the author's response. However, only discussion is provided but lacking some experiment results to address my concern. Thus, I tend to keep my score. --- Reply to Comment 1.1.1: Comment: We deeply appreciate the reviewer's feedback and apologize for not fully addressing the concerns during the rebuttal phase. In the revised paper, we will thoroughly address all feedback by increasing the necessary experimental evidence. We are confident that the additional data and analysis will alleviate the reviewer's concerns.	Summary: This paper proposes a novel strategy named DiffuPac to generate adversarial packets to bypass NIDS detection. DiffuPac encompasses two critical components including the BERT, which captures the semantic meaning of packets and facilitates the embedding and contextual paring. The other one is DiffSeq which makes the malicious part seamlessly integrated into the normal packet pattern thereby improving the evasion against detection. Experiments showcase that DiffuPac outperforms the baseline and is capable of breaking practical detection through simulation. Strengths: 1. This paper is well-written, with a clear method description. 2. The proposed DiffPac is effective against bypassing detection, the proposed strategy seems reasonable with good explanation. Weaknesses: 1. As stated in the limitation, whether the functionality of these adversarial packets is preserved is not verified. From my understanding, this point is quite important given the practical aspect of DiffPac. If the adversarial package can only bypass detection without functioning as intended, it would undermine the practical utility of DiffPac. 2. It would be beneficial to include additional analysis, such as evaluating the performance without applying contextual pairing and assessing the robustness against potential packet-level defenses. These analyses would provide further insights into the effectiveness and resilience of DiffPac. Technical Quality: 3 Clarity: 3 Questions for Authors: Please refer to weakness. Confidence: 2 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The authors have listed their limitations and have addressed most of them. One concern about functionality preservation is mentioned in the weakness part. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We greatly appreciate the reviewers’ constructive review and insightful suggestions regarding our paper. Our responses are given in a point-by-point manner for each comment. W1. We conducted a detailed malicious functionality evaluation within a controlled, isolated network environment. We kindly ask the reviewer to refer to the "Malicious Functionality Evaluation" section in the main author rebuttal for a more detailed explanation. W2. We have conducted an ablation study that directly addresses the impact of contextual pairing, comparing DiffuPac’s performance with and without the use of the pre-trained BERT model for contextual pairing. This study has been included in our main author rebuttal, and we encourage the reviewer to refer to "Ablation Study" section in the main author rebuttal for detailed insights into how contextual pairing enhances the model’s effectiveness. We acknowledge that while Kitsune NIDS provides a solid foundation for evaluating packet-level defenses, it represents only one approach among many. To further strengthen DiffuPac’s robustness and address the reviewer's concerns, our future work will explore additional NIDS that utilize advanced packet-based feature extractors. By broadening our evaluation framework to include a variety of packet-level defenses, we aim to gain a deeper understanding of DiffuPac’s effectiveness across different NIDS architectures and feature extraction methodologies. --- Rebuttal Comment 1.1: Comment: Thanks for the response. The 'Malicious Functionality Evaluation' refers to Lines 382 - 384. While I acknowledge the discussion in the Limitation section, preserving the intended malicious effect is essential to ensure the practicality of your method.	Summary: The paper presents DiffuPac, a novel solution that integrates Bidirectional Encoder Representations from Transformers (BERT) and diffusion models to generate adversarial packets that can evade detection by sophisticated Network Intrusion Detection Systems (NIDS). DiffuPac leverages the extensive contextual understanding provided by BERT, which has been trained on diverse datasets representing a wide range of network behaviors, along with the generative capabilities of diffusion models. This fusion results in a sophisticated adversarial tactic where the elements of the attack are seamlessly integrated into the network traffic, making them indistinguishable from legitimate data. Extensive experimental evaluations on real-world datasets demonstrate that DiffuPac significantly outperforms existing methods in terms of evasion effectiveness, establishing new benchmarks for the generation of adversarial packets. Strengths: * Integrates BERT and diffusion models for adversarial packet generation * Addresses limitations of traditional methods that rely on unrealistic attacker knowledge * Introduces unique concatenation and targeted noising techniques for seamless blending of adversarial packets * I really appreciate that authors consider many realistic attacker constraints (e.g., packet integrity, replayability, only control on src-to-dst flows), showing that the authors have solid domain knowledge in network security Weaknesses: * There are many unclear points about the high-level idea, methodology, and experiments; see them below. If provided with compelling evidence, I may increase my score. Technical Quality: 3 Clarity: 3 Questions for Authors: 1. For the high-level idea, I admit that there have been attempts to transform packet bytes as tokens and use language models for traffic analysis (e.g., [a,b,c]). However, most of them (also including DiffuPac) do not discuss if and how this type of method can handle encrypted traffic. As you may know, modern encryption algorithms like AES can significantly reduce entropy and there will be no one-to-one relations between plaintext and ciphertext; so from my perspective, learning from the encrypted payload is meaningless. Some methods may only use the header fields for tokenization. As there lack of such details, I'm not sure how DiffuPac deals with this concern. 2. On page 5, line 199: "... this task employs a dedicated binary classifier to determine the directional origin of network traffic, specifically whether packets in a sequence originate from src-to-dst or dst-to-src." Though the idea seems reasonable, I'm curious will there be any cases where packets from both sides are very similar so that the task can be too difficult to converge (e.g., in P2P apps where there are no explicit servers or clients)? 3. On page 5, line 217: "the initial packets in a flow contain the most significant information, we limit our analysis to the first three packets of each heavy flow". Will the first three packets be too few? For TCP connections, the first three packets are typically just for handshakes so the model probably won't learn any useful information. Can the authors explain this, or give some experiments on this parameter? 4. Could the authors list the mutable and immutable fields in the appendix? 5. For experiment setup, one of my concerns is about the data preparation. Will the pre-trained model use malicious traffic for training? For one thing, the pattern of malicious traffic can be very abnormal so will that affect the BERT's understanding of normal traffic? For another, in practice, malicious traffic is much less than in the dataset so this setting can be somewhat impractical for a pre-trained model. 6. Another major weakness of the experiment is that there is only one baseline. However, there are other works on generating (malicious or generic) traffic data, including those generating on feature spaces ([d,e]) or generating on raw bytes ([a,b]). The authors may compare them to improve the experiment, or discuss them in related work and present their fatal limitations that hinder the direct comparison. 7. As there are two main components in DiffuPac (BERT and diffusion model), an ablation study on the pre-trained model is needed to show the necessity of using the pre-trained representations instead of some simpler representations. 8. In the limitations, I suggest that the authors discuss the implications of your method facing signature-based NIDS (e.g., Snort). You may conclude with a consideration of the current situation that encrypted traffic is the majority, but that will go back to question 1 again. 9. I like the authors providing the screenshots of Wireshark as parts of the results. One weakness is that the authors use their own domain knowledge to reveal the important packet fields that should be altered to avoid NIDS. However, the ML/DL-based NIDS may use some other features as the decision reasons which can be different from yours. I think the authors may use some global explanation models (e.g., [f,g]) to verify if the adversarial fields are really the features that NIDSes care. [a] NetGPT: Generative Pretrained Transformer for Network Traffic, arxiv 2023 [b] TrafficGPT: Breaking the Token Barrier for Efficient Long Traffic Analysis and Generation, arxiv 2024 [c] Yet Another Traffic Classifier: A Masked Autoencoder Based Traffc Transformer with Multi-Level Flow Representation, AAAI 2023 [d] Flow-based network traffic generation using Generative Adversarial Networks, SIGCOMM 2022 [e] Knowledge Enhanced GAN for IoT Traffic Generation, WWW 2023 [f] AI/ML for Network Security: The Emperor has no Clothes, CCS 2022 [g] Interpreting Unsupervised Anomaly Detection in Security via Rule Extraction, NeurIPS 2023 Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: Yes. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We greatly appreciate the reviewers’ constructive review and insightful suggestions regarding our paper. Our responses are given in a point-by-point manner for each comment. Q1. We appreciate the reviewer's insightful observation regarding the challenges of handling encrypted traffic. In DiffuPac, we treat the payload as immutable, especially when encrypted. This decision is based on the complexities of modern encryption algorithms like AES, which significantly reduce entropy and break the one-to-one relationship between plaintext and ciphertext. Modifying encrypted payloads without understanding their structure risks rendering the packets non-functional or easily detectable. Our current focus is on modifying packet headers, which offer a safer and more navigable path for creating adversarial effects. Header fields provide ample opportunity for evasion tactics while preserving the packet's integrity and functionality. Future work may explore techniques for selective and safe payload modification, possibly leveraging advanced machine learning models to identify modifiable regions within encrypted payloads. Q2. While the task of distinguishing similar packets from both sides can indeed be challenging, our classifier has shown a strong ability to converge, even in these complex scenarios. This is largely due to the deep learning capabilities of the transformer architecture, which uses self-attention mechanisms to capture subtle contextual cues and dependencies within packet sequences. We trained the classifier using datasets like CICIDS2017 and Kitsune, which include scenarios with P2P traffic. These datasets provide the necessary complexity to train the model to differentiate between src-to-dst and dst-to-src flows, even in environments where the distinction is not immediately apparent. We plan to incorporate more diverse traffic scenarios in future work, including different types of encrypted and IoT traffic. Q3. We apologize for any confusion caused by the initial explanation and appreciate the reviewer's insightful observation. We will refine the explanation in the revised version to prevent any misunderstanding. To clarify, in our preprocessing stage, each session is split into unidirectional flows—specifically src-to-dst and dst-to-src sequences. This effectively means our analysis considers up to six packets per session: three from the src-to-dst flow and three from the dst-to-src flow. By analyzing the first three packets from each unidirectional flow, we capture the initial exchanges in both directions. This includes not just the TCP handshake but also the initial data packets, which often contain valuable information. Considering packets from both directions ensures a more complete view of the communication, enhancing the model's ability to learn meaningful patterns even from early-stage data. Q4. We cannot update the supplementary materials during the rebuttal period, in the revised paper we will provide fully-detailed explanation on mutable and immutable fields. Q5. The pre-training phase utilizes an unlabeled dataset comprising a mix of normal and malicious traffic. This allows BERT to learn general network traffic patterns and dependencies without bias toward specific traffic types. While malicious traffic can exhibit abnormal patterns, BERT's generalization capabilities ensure that these do not overshadow its understanding of normal traffic. The focus during pre-training is on capturing the overall structure of network flows rather than distinguishing between normal and malicious traffic. Q6. We acknowledge that including only one baseline may not provide a comprehensive comparison, especially in light of the existing body of work on generating packets. In future work, we will conduct a thorough comparison with a broader range of methods within the Packet-Level Attacks category [1] to better position DiffuPac within the field of adversarial packets generation. Q7. We kindly ask the reviewer to refer to the "Ablation Study" section in the main author rebuttal for a more detailed explanation. Q8. We appreciate the reviewer's suggestion to discuss the implications of DiffuPac when facing signature-based NIDS. The discussion regarding the relevance of signature-based NIDS on DiffuPac will be included in the revised paper. This will involve evaluating how well DiffuPac's techniques, such as header modification and traffic pattern manipulation, can evade detection by these systems. Future work will involve testing DiffuPac against a range of signature-based NIDS configurations and exploring enhanced header manipulation and potential payload modification techniques that respect encryption constraints. Q9. DiffuPac does not depend on predefined domain knowledge to reveal important packet fields. Instead, it intelligently alters specific fields within packets to seamlessly blend malicious packets into normal traffic, enhancing evasion capabilities. This auto-altering capability is a key innovation of DiffuPac. In our revised paper, we will provide more refined explanations to prevent any misunderstandings regarding DiffuPac's intelligent field alteration capabilities. We acknowledge that there may be differences between the packet fields modified by DiffuPac and the features ML/DL-based NIDS consider critical. This potential disparity arises because DiffuPac independently identifies and modifies fields based on the inherent characteristics of network traffic and attack types. In future work, we will use global explanation models, such as SHAP or LIME, in a controlled setting to gain insights into the influential features in NIDS detection processes. Based on these findings, we may enhance DiffuPac's targeting of significant features while maintaining its independent operational framework. [1] K. He et.al, Adversarial Machine Learning for Network Intrusion Detection Systems: A Comprehensive Survey --- Rebuttal Comment 1.1: Comment: Thanks for the response. Some of my concerns have been answered. However, I think the current version of the evaluation using only one baseline is not ready for publication. Besides, I agree with the other reviewers that the discussion about original malicious functionality and payload modification is crucial. In fact, these points are also aligned with my comments on encrypted content and signature-based NIDS which fundamentally care about payload. When revising the paper, I suggest the authors include a better-described threat model to define your settings, such as where adversaries and NIDSes monitor the traffic and what their abilities are. For example, suppose they are all on the ISP side, given the majority of encrypted traffic nowadays. In that case, adversaries cannot modify payloads feasibly, nor can NIDSes use adequate signatures to detect malicious activities. For another, if the NIDSes are on the boundary of the end servers (which have the keys to decrypt the ciphertext), then things will be different. I would like to maintain my score. Again, I do like the authors considering the practicality of the generated traffic, as I've seen several works that do not have enough consideration while still getting published at high-level conferences and journals; maybe they "luckily" didn't meet expert-level reviewers as you did. This is why I encourage the authors to absorb the comments, in order to get ready for publication on top-tier venues like NeurIPS or Big 4 and make some real contributions to the community. --- Reply to Comment 1.1.1: Comment: Thank you for the detailed feedback and for highlighting key areas for improvement. We fully agree with the reviewer's suggestions and would like to provide an overview of the approach we will take in the revised paper to address the concerns. Regarding the baseline, we are currently conducting evaluation on the TANTRA model (Y. Sharon et.al, 2022), and will provide a valuable comparison to DiffuPac. The results of this evaluation will be included in the revised paper, offering a more comprehensive understanding of DiffuPac's performance relative to existing methods. We will also include a thoroughly detailed description of our threat model in the revised paper. This will clarify the settings in which DiffuPac operates, such as the positions of adversaries and NIDS, and their capabilities, especially in scenarios involving encrypted traffic and signature-based NIDS. We completely agree with the reviewer that many related works often overlook the evaluation of retaining malicious functionality or do not provide a fully detailed description of this crucial aspect. In our paper, we aim to set a new benchmark in the community by offering a comprehensive, fully-detailed account of how we conduct malicious functionality evaluations. Furthermore, we provide clear evidence that our model is capable of retaining malicious functionality, demonstrating a significant advancement in the field.	Summary: This work presents DiffPac, a method that leverages BERT and a diffusion model to generate adversarial packets aimed at evading network intrusion detection systems. Compared to the approach by Han et al. (2021), DiffPac demonstrates superior effectiveness, with most machine learning-based classifiers trained on adversarial packets generated by DiffPac successfully evading detection across six different attack scenarios. Strengths: * Approach: The paper presents an interesting intuition for generating adversarial packets using a diffusion model, which is a creative approach in the field. * Methodology: The methodology is clearly presented, making it easy to understand the steps and processes involved in the proposed DiffPac method. Weaknesses: * Motivation: The research motivation could be more clearly and concretely articulated. It would be beneficial to highlight the specific niche of this study in relation to existing work, such as Network Emulator (NetEM) and Metasploit (Homo-liak et al., 2018), Generative Adversarial Network (GAN) and Particle Swarm Optimization (PSO) (Han et al., 2021), and Reinforcement Learning (RL) (Hore et al., 2023). Rather than broadly stating that "their efficacy in evading detection in real-world conditions remains suboptimal" (line 64), the paper should detail the unique challenges and gaps that DiffPac addresses. * Method for Preserving Packets’ Integrity: The approach to preserving packets' integrity by only mutating TCP flags, TTL, and window size, rather than the payload, is unrealistic for real-world conditions where payloads often contain the malicious behaviors. This limitation should be addressed to enhance the practical applicability of the method. * Evaluation: The evaluation settings could be more closely aligned with those used by Han et al. (2021) to make it easier for the readers to understand the differences and contributions of this work. Technical Quality: 2 Clarity: 2 Questions for Authors: * Data Pre-processing: Could you explain the rationale and advantage of transforming IP numerical values into hexadecimal representation and treating them as discrete values for workpiece segmentation? What benefits does this approach offer? * Formula (4): In Formula (4), does S^{ben+mal} denote z_t ? * Dataset: How many adversarial packets are included in the test set? Providing a statistical description of the datasets used would enhance clarity and help understand the dataset composition. Confidence: 3 Soundness: 2 Presentation: 2 Contribution: 2 Limitations: The limitation section highlights three main concerns: * The actual malicious functionality of the generated adversarial packets has not been thoroughly examined. * There is inconsistent performance across the six attack scenarios tested. * There is a potential risk associated with making the approach open-source, which could be exploited maliciously. Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We greatly appreciate the reviewers’ constructive review and insightful suggestions regarding our paper. Our responses are given in a point-by-point manner for each comment. W1. We agree that a more detailed discussion on the limitations of existing works and how DiffuPac addresses specific gaps will strengthen the motivation of our study. Traditional approaches, such as those by Homoliak et al., Han et al., and Hore et al., often rely on access to NIDS components or surrogate classifiers. These methods assume attackers have detailed knowledge of the NIDS, which is unrealistic in real-world scenarios. This dependency limits their practical applicability, as attackers typically operate with minimal insider knowledge of the target's system. DiffuPac addresses these limitations by adopting a classifier-free approach, leveraging pre-trained BERT and diffusion models to generate adversarial packets without relying on NIDS components or surrogate classifiers. This method allows DiffuPac to create adversarial traffic that mimics normal network behavior, making it more effective in evading detection in real-world conditions. Additionally, DiffuPac’s adaptive field alteration ensures that the modifications are contextually appropriate, maintaining the malicious functionality of the packets while enhancing their stealthiness. In the revised paper, we will expand on these points to highlight how DiffuPac innovates beyond existing methodologies, offering a practical solution for adversarial packet generation in real-world environments. W2. We understand the concern that in real-world conditions, payloads often contain the core malicious behaviors, and thus, not modifying the payload may seem limiting. Modifying the payload, which often contains core malicious behaviors, poses a significant risk of disrupting the packet's integrity, especially without detailed knowledge of its structure. We acknowledge the potential benefits of payload modification and plan to explore methods like Deep Packet Inspection (DPI) and selective payload adjustments in future work to enhance the realism of adversarial packets while maintaining their functionality. W3. We recognize the importance of such comparisons, particularly in demonstrating the unique contributions of DiffuPac in the context of existing methodologies. Our choice to diverge from the more complex evaluation settings used by Han et al. stems from the fundamentally different nature of our methodology. Since DiffuPac does not involve feature-level generation or direct interaction with NIDS components, the traditional metrics used in Traffic Manipulator's evaluation, which are deeply tied to feature extraction, are not directly applicable to our approach. Instead, by focusing on MER, we provide a clear and focused evaluation of DiffuPac's effectiveness in generating adversarial packets that evade detection in a more realistic context. We recognize the value of aligning more closely with other methodologies. In future work, we plan to expand our evaluation framework to include additional metrics and settings that facilitate direct comparisons with existing methods like Traffic Manipulator. Q1. We really appreciate the reviewer's inquiry. We convert IP numerical values to hexadecimal and treat them as discrete values for WordPiece tokenization to maintain the native structure and precision of network data. This approach ensures uniform tokenization across diverse protocol fields, preserves semantic meaning crucial for understanding network traffic patterns, and allows for efficient vocabulary management, enhancing the model's ability to accurately process and learn from the data. Q2. We sincerely apologize for any confusion caused by the insufficient explanation of Formula (4) in our original submission. We appreciate the reviewer's attention to detail and would like to clarify the notation and its context. To clarify, $ \mathbf{S}^\mathrm{ben \oplus mal} $ does not directly denote $ \mathbf{z}_t $ at each time step $ t $, where the original concatenated sequence $ \mathbf{S}^\mathrm{ben \oplus mal} $ is gradually perturbed. The expression $ q_\phi(\mathbf{z}_0 \mid \mathbf{S}^{\mathrm{ben \oplus mal}}) = \mathcal{N} (\text{EMB}(\mathbf{S}^{\mathrm{ben \oplus mal}}), \beta_0 \mathbf{I}) $ describes the initial state $ \mathbf{z}_0 $, which is derived from the embedding of the concatenated packet sequences. Subsequent steps in the diffusion process perturb this state to produce the series of latent variables $ \mathbf{z}_1, \mathbf{z}_2, \dots, \mathbf{z}_t $. We acknowledge that the initial explanation may not have fully conveyed these relationships, and we will ensure that the revision includes a more detailed and refined explanation. Q3. \| Stage \| Percentage of Total Data \| Number of Normal Packets \| Number of Malicious Packets \| \|-----------------------------------\|--------------------------\|--------------------------\|-----------------------------\| \| Pre-training of the BERT model \| 60% \| 5,079,021 \| 2,734,858 \| \| Fine-tuning phase \| 20% \| 1,693,007 \| 911,619 \| \| Training the classifier and NIDS \| 10% \| 846,512 \| 455,819 \| \| Testing phase \| 10% \| 846,504 \| 455,810 \| Table 1: Distribution of normal and malicious packets across different stages of data processing. In the testing phase, we included 455,810 malicious packets. DiffuPac generated an equal number of adversarial packets, ensuring a direct comparison. A detailed statistical description of the dataset composition, including normal and malicious packets across all stages of the process, will be included in the revised paper for enhanced clarity. --- Rebuttal Comment 1.1: Comment: Thank you for your response. I'm pleased to see the inclusion of payload modification and the plan to expand the evaluation settings in future work. I will be keeping my score unchanged.	Rebuttal 1: Rebuttal: We sincerely appreciate the reviewer’s thoughtful feedback and constructive insights. Here, we summarized the experiments that we conducted for the ablation study and maliciousness functionality evaluation. These experiments will be included in the revised version of the paper. ### Ablation Study Objective: This ablation study assesses the impact of substituting the pre-trained BERT model with a standard transformer architecture in the denoising process of DiffuPac. The focus is on assessing each model's ability to accurately reconstruct and generate adversarial packets that can effectively evade detection. Experimental Setup: - Non-BERT-based: This variant of DiffuPac employs a standard transformer architecture for the denoising process, as outlined in the DiffuSeq methodology [1]. Notably, this model is trained from scratch without leveraging any pre-trained weights, thus relying solely on the information provided during the training phase. - BERT-based: The existing DiffuPac configuration, which incorporates a pre-trained BERT model for the denoising process, was utilized. This setup takes advantage of BERT's pre-trained weights, enabling enhanced semantic understanding and contextual relevance during packet reconstruction. Training and Evaluation: Both models were trained under identical conditions and evaluated based on their success in generating adversarial packets that evade detection. The results are shown in the accompanying PDF. Result And Analysis: As shown in Table 1, the BERT-based DiffuPac significantly outperforms the non-BERT variant, demonstrating superior ability to reconstruct packets that blend seamlessly into normal traffic. The BERT-based model excels in pairing malicious packets with normal packets that exhibit high contextual relevance. This strategic pairing allows the generated adversarial packets to blend seamlessly into normal traffic, thereby increasing their likelihood of evading detection. In contrast, the non-BERT-based model, which lacks this pre-trained knowledge, resorts to random matching of malicious and normal packets, leading to a noticeable reduction in the effectiveness of the generated adversarial traffic. An intriguing aspect of DiffuPac is its dual utilization of the pre-trained BERT model: first, as the denoising engine during the packet reconstruction process, and second, as a critical tool for identifying contextually relevant packet pairs. To the best of our knowledge, this dual application of a pre-trained model within a diffusion framework is unprecedented, further highlighting the innovation and effectiveness of our approach. ### Malicious Functionality Evaluation Objective: To validate that DiffuPac-generated adversarial packets retain their original malicious functionality. Experimental Setup: We evaluated DiffuPac’s efficacy in generating adversarial packets that maintain their malicious functionality in a controlled test environment using UTM hypervisor technology. This setup included two virtual machines: one running Kali Linux (attacker) equipped with Nmap, and another running Ubuntu 24.04 (victim). The isolation ensured a realistic yet controlled network environment. The results are shown in the accompanying PDF. Initial Attack Demonstration: Before proceeding to evaluate the generated adversarial packets of DiffuPac, we first demonstrated a successful Port Scan attack within our controlled environment. This initial step is a fundamental step to ensure the validity and reliability of subsequent tests with both original and adversarial packets. The network configurations depicted in Figures 1(a) and 1(b) confirm that both virtual machines were correctly placed within the same subnet. As demonstrated in Figure 1(c), the Port Scan successfully identified open ports on the Ubuntu, highlighting port 22 as vulnerable. Detailed Methodology: - Initial Packet Capture: We initiated a Port Scan attack from the Kali Linux machine targeting the Ubuntu server. During the execution of this attack, we captured all packets sent from the attacker to the victim, saving them as a pcap file. This capture was timed precisely to begin as the Nmap tool launched the Port Scan, ensuring that only the relevant src-to-dst packets were recorded. This focus aligns with the operational framework of DiffuPac, which concentrates on modifying packets sent from the source. - Adversarial Packet Generation and Replay: Using the captured src-to-dst packets, we employed DiffuPac to generate adversarial Port Scan packets, which were then saved in a separate pcap file. These adversarial packets were subsequently replayed using the Tcpreplay tool, directing them towards the Ubuntu server. Concurrently, we used Wireshark on the Ubuntu machine to capture the incoming responses, allowing us to analyze the effectiveness of the adversarial packets in real-time. - Fair Comparative Analysis: To ensure a balanced evaluation, we also replayed the original Port Scan pcap file using Tcpreplay, capturing the responses in Wireshark on the Ubuntu side. This dual replay enabled a direct comparison between the packets' responses generated by the original and adversarial Port Scan packets. Results And Analysis: As depicted in Figures 2(a) and 2(b), the response to the adversarial Port Scan packets closely mirrors that of the original Port Scan. A detailed inspection of the TCP flags reveals that packets with SYN and ACK flags targeted port 22, corroborating the initial vulnerability identified in Figure 1(c). This consistent response across both original and adversarial packets provides compelling evidence that DiffuPac successfully generates adversarial packets that retain their intended malicious functionality. Currently, we are also conducting evaluation on other type of attacks, that will be included in the revised paper. [1] Gong S et. al., Diffuseq Pdf: /pdf/f8d0ff005875576c961b3a241fe83762c653384b.pdf	NeurIPS_2024_submissions_huggingface	2,024	Summary: This work proposes DiffuPac, an adversarial packet generation model that aims to evade Network Intrusion Detection Systems (NIDS) without depending on detailed knowledge of NIDS components. DiffuPac combines a pre-trained BERT model with a diffusion model. Experimental results show that DiffuPac outperforms traditional methods by 8.83%. Strengths: - This work studies an interesting and important issue about evading NIDS detection based on deep learning methods. - I appreciate that the author divides the traffic data into mutable fields and immutable fields for modification. - The experimental results support the effectiveness of the proposed method to evade detection. Weaknesses: - The paper achieves the following goals through expensive experiments (more than 30 hours of training on RTX 4090): select the normal packet sequence that is most similar to the malicious packet sequence, and modify the limited mutable fields (e.g. TCP flags, TTL, and window size) in the malicious packet sequence header according to the normal packet sequence. Given the very limited mutable fields modified within the packets and the lack of ablation studies in the experimental section, I doubt the necessity of using BERT and DiffuSeq. It seems that a simpler approach involving feature similarity matching, coupled with selective field selection and replacement, could potentially achieve the same goal without the complexity introduced by these advanced models. - In the diffusion model where all mutable fields of the entire malicious packet sequence are regenerated, there is a concern about whether this process affects its original functionality. Although the modification effects on specific fields of individual packets are shown in the appendix, whether the author replays these generated packets in a real network environment to verify its functionality, rather than simply viewing them through Wirshark. - Some minor issues: The paper needs improvement in writing quality. The connections between different components are not explicitly explained, and the specific format of the packet sequence input to the diffusion model is not detailed. In addition, the BERT-related content is very redundant in Sec. 3 and Figure 1. However, the related content is highly similar to ET-BERT and is only used to calculate the most relevant benign and malicious packet sequences in the "fine-tuning" stage (in fact, I think the operations in this stage do not belong to the category of "fine-tuning"). Technical Quality: 3 Clarity: 2 Questions for Authors: Please see the above-mentioned weaknesses. I will confirm the author's response during the rebuttal. Confidence: 5 Soundness: 3 Presentation: 2 Contribution: 2 Limitations: The authors discussed the limitations in this work. Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We greatly appreciate the reviewers’ constructive review and insightful suggestions regarding our paper. Our responses are given in a point-by-point manner for each comment. W1. Simpler methods (e.g., [1], [2], [3]) often require surrogate classifiers or access to NIDS components. This is because the generated adversarial examples need to be evaluated and refined using these components to ensure they evade detection. The dependency on internal NIDS mechanisms limits the practicality of these methods in real-world scenarios where attackers typically lack such insider access. In contrast, DiffuPac operates independently of NIDS components by leveraging the capabilities of pre-trained BERT and diffusion models. This approach allows DiffuPac to intelligently alter specific packet fields, seamlessly blending malicious packets into normal traffic without needing detailed knowledge of the NIDS. The use of BERT is crucial in this process, as it provides the deep contextual understanding required to identify and modify fields in a way that maintains the packets' stealth and effectiveness. Our ablation study compared DiffuPac's performance with a standard transformer trained from scratch against the BERT-based model. The results clearly demonstrate the BERT-based model's superiority in both evasion capabilities and accurate packet reconstruction. This highlights the essential role of BERT in DiffuPac, enabling the model to make sophisticated, contextually-aware modifications that simpler approaches, which lack such depth of understanding, cannot achieve. We kindly ask the reviewer to refer to the "Ablation Study" section in the main author rebuttal for more detailed insights into the necessity of BERT in DiffuPac's architecture. We agree with the reviewer that simpler approaches could be effective when contextual relevance with normal packets is identified. This will be an important topic for future research, where we will explore the potential of such methods in conjunction with or as alternatives to more complex models like BERT and diffusion models. W2. We really appreciate the reviewer's concern regarding the capability of DiffuPac in retaining the malicious functionality of generated adversarial packets. To address this concern, we conducted a detailed malicious functionality evaluation within a controlled, isolated network environment. We kindly ask the reviewer to refer to the "Malicious Functionality Evaluation" section in the main author rebuttal for a more detailed explanation. Currently, we are also conducting malicious functionality evaluation on Brute Force Attacks, and other type attacks. These experimental results and their fully-detailed explanations will be added in the revised paper. W3. We sincerely appreciate the reviewer’s insightful feedback and understand the importance of refining our explanations. Our methodology involves a structured process where each component plays a crucial role: - Pre-Training Phase: The BERT model is pre-trained using tasks like the Masked Unidirectional Flow Model and Same Sequence-origin Prediction. These tasks are essential for BERT to develop a deep understanding of network traffic patterns and dependencies, which are critical for the later stages. - Fine-Tuning with Diffusion Models: In this phase, the pre-trained BERT model enhances the diffusion process, allowing for the generation of adversarial packets that are contextually aligned with normal traffic. The packet sequences are formatted with token, positional, segment, and time step embeddings, providing a comprehensive input structure that the diffusion model uses to accurately reconstruct and generate packets. In the revised paper, we will take the following steps to improve clarity and conciseness: - Enhanced Component Integration: We will provide a more explicit explanation of how each component of our methodology connects and contributes to the overall process. This will include clearer descriptions of the role of embeddings and how they prepare the data for effective processing by the diffusion model. - Streamlining BERT-Related Content: To address concerns about redundancy, we will condense the BERT-related sections, focusing on its unique application in DiffuPac. This will involve removing repetitive content and emphasizing only the most critical aspects that highlight DiffuPac’s innovations. - Revisiting Terminology: We will re-evaluate and revise terminology, particularly around the "fine-tuning" stage, to ensure it accurately reflects the specific operations and the unique way BERT is used in DiffuPac. This will help avoid any confusion and better align with the expectations of readers familiar with existing methodologies. - Detailed Input Format Explanation: We will include a more detailed explanation of the packet sequence input format to the diffusion model, ensuring readers understand the significance of each embedding type and how they contribute to the model’s performance. [1] Homoliak et al., Improving Network Intrusion Detection Classifiers by Non-Payload-Based Exploit-Independent Obfuscations [2] Hashemi et al., Towards Evaluation of NIDSs in Adversarial Setting [3] Kuppa et al., Black Box Attacks on Deep Anomaly Detectors --- Rebuttal Comment 1.1: Comment: Thanks to the authors for their response. I have reviewed the rebuttals. However, showing only the case of Port Scan attack cannot solve my concern about whether DiffuPac affects the original functionality of the traffic. Once the original functionality is destroyed, the practical value of this work becomes questionable. Therefore, this should be a primary consideration before designing the method. In addition, I suggest that the authors carefully check their experimental results, as the BERT-based results in the rebuttal PDF (Table 1) seem inconsistent with those in the submitted manuscript (Table 2). Overall, I am inclined to keep the original scores. --- Reply to Comment 1.1.1: Comment: We deeply appreciate the response from the reviewer. First of all, we sincerely apologize for not fully addressing the concerns during the rebuttal phase. Due to time and resource constraints, we were only able to include the Port Scan attack evaluation. However, we have completed the evaluation of Brute Force attacks and are pleased to report that the results are promising. The responses from both the original Brute Force packets and the adversarial Brute Force packets indicate successful SSH access, demonstrating that DiffuPac preserves the original functionality of the traffic. We will include these results in the revised paper, along with evaluations of other attack types. We hope these additional evaluations will alleviate the reviewer's concerns. Regarding the inconsistency between the BERT-based results in the rebuttal PDF (Table 1) and the submitted manuscript (Table 2), we deeply appreciate the feedback and acknowledge the discrepancy. We suspect that the variations might be due to potential minor differences in the random seeds used during training. Despite these minor differences, the overall trends remain consistent, and the results continue to demonstrate the promising capabilities of our model. Moving forward, we will do our utmost to ensure that the revised paper reflects consistent and verified results. We will carefully re-run experiments, double-check our settings, and align all reported data to maintain accuracy and clarity.	null	null	null	null	null	null
Pre-trained Text-to-Image Diffusion Models Are Versatile Representation Learners for Control	Accept (spotlight)	Summary: The research question is whether representation from image generation models are superior to other pre-training paradigms (i.e. contrastive CLIP) for embodied/navigation-type of tasks. The main intuition given is that these tasks require a lot of fine-grained (e.g. spatial) understanding. While CLIP has been used as a foundation model in traditional vision or some vision+language tasks, it has not shown much promise for robotic control. Their method is similar to previous works and each design choice is ablated/explained : First a certain timestep (i.e. noise level) is chosen for denoising a given image with an associated text prompt. Then a concatenation of intermediate U-Net layer activations is used as the “Stable Control Representation” (SCR). They evaluate their method on three different types of robotic-related tasks and show that SCR is overall the strongest, albeit not the strongest on every single task. For example, R3M is slightly stronger on the few-shot manipulation tasks (Meta World, Franka Kitchen) but is drastically worse on navigation. Strengths: This is the first paper to make Diffusion Model representations work for robotic control tasks (novelty). The work is also situated clearly in the previous literature context and the technical background is well explained. Similarly, the paper is well structured and very easy to follow. Each part of the paper is well motivated and answers a natural question or follow-up step. Regarding the technical details, it is rigorous work that actually advances science and makes it easy for others to use for their research, e.g. in the appendix it is mentioned: “We re-ran all the methods using the evaluation repository provided with the work, and obtained different results compared to the reported numbers in Karamcheti et al. [20], which we attribute to a bug that we fixed related to the computation of the precision metrics.”. Or similarly they note in the appendix that the original setup for the Gaze task leads to a trivial solution and modify the task setup. This shows the authors don’t just blindly adopt tasks but critically investigate details of all the data or tasks they chose. The authors use baselines, i.e. showing SD-VAE is an insightful baseline that is easily beat. Similarly, ensuring fair and scientific baselines comparison i.e. in l. 327 - 329 where baselines are made stronger with insights from the paper to make it fair. Lastly, it is great to see an anonymous code repo that seems to be done well and with the aim of reproducibility. Weaknesses: Only minor improvements, hard to beat some baselines properly on first glance. But on second glance it seems like stronger general representations, some of the other baselines such as R3M are only useful on some tasks but drastically drop on others. Maybe for people not familiar with this exact domain, you could explain more how these baselines work and why they get the numbers they do? For example, I am a vision-and-language person who is also familiar with all the text-to-image modeling advances but not so much with the navigation/control details. It is briefly acknowledged in section 5.1. but imo requires a deeper investigation: is the success primarily from fusing multiple layers and not from the fact that it is a diffusion model vs. a CLIP-like model? The authors acknowledge that such an approach is less feasible with i.e. ViT since the feature maps are much larger but nonetheless this question seems important enough to nonetheless investigate further. Overall the paper is very well written but if I had to pick a confusing section, it is 5.3 where too many things are introduced at once. The last paragraph in the discussion about the simplicity of finetuning SCR compared to CLIP comes out of nowhere and should be discussed earlier, and the claim about sophisticated negative sampling only cites the original CLIP paper which afaik only has random negative samples? There is an experiment in the appendix that somewhat supports this but also does not discuss the negative sampling. Not a major issue but should be made clearer. Technical Quality: 4 Clarity: 4 Questions for Authors: Why cite Imagen in l. 36? Reference to Table 2a/b in section 5.1 and 5.2 are mixed up, just a small fix. “bilinearly interpolate them so that they are of a common spatial dimension and can be stacked together”: this should be specified or shown in equations formally to understand exactly what is done. Is this method common for extracting/unifying internal representations? Confidence: 3 Soundness: 4 Presentation: 4 Contribution: 3 Limitations: There are not many concerns to address and the authors wrote an appropriate short section in the Appendix. Flag For Ethics Review: ['No ethics review needed.'] Rating: 8 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for taking the time to review our manuscript and for providing helpful and constructive feedback. We were happy to see your review mention the novelty of our work and the rigorousness and fairness of our evaluation. We address your concerns below. --- 1) The mutliple layer results for CLIP should be investigated further. We agree and include the results for this in the general comment. On a high level, our conclusions from this experiment are that we do see a benefit from including additional outputs from certain layers along with the last layer which is always used (as we anticipated in the discussion in sec 5.1). We find these layers using a grid search, and they are located towards the middle (10-14th layers). We note that while the feature map sizes after including another layer for CLIP are very large and not comparable anymore to the other methods, the performance still doesn’t match that of SCR. 2) Could you explain more how these baselines work and why they get the numbers they do? We agree with the reviewer and will add further contextualization of the performance of different baselines. - In the manipulation space, representation learning works adopt a few shot imitation learning setting, with the backbone pretrained on video datasets of humans manipulating objects in indoor environments. - In the navigation space, the setting is large scale reinforcement learning, and the evaluation includes generalization to new objects or scenes. The backbone is pretrained on datasets of indoor navigation videos. - We select some of the best performing baselines used in prior works in manipulation (R3M, MVP) or navigation (VC-1) tasks. Different baselines often do well on disparate sets of tasks and settings. Specifically, R3M representations are tailored to reduce overfitting in few-shot IL settings by forcing sparsity in representations (see Table 1 in the R3M paper where performance drops 6% when the L1 sparsity penalty is removed), which doesn’t offer an advantage in the extended training regime of RL-based navigation tasks. 3) Simplicity of finetuning SCR compared to CLIP should be discussed earlier, claim about sophisticated negative sampling only cites the original CLIP paper We agree that the discussion about simplicity of finetuning SD along with the CLIP fine-tuning experiment appears late and are happy to push it into the main paper. We cited the CLIP paper for the use of really large batches sizes in contrastive learning, but a more detailed list of references would be the following: - References for "contrastive learning needs large batch sizes to avoid learning degenerate solutions" : the CLIP and SimCLR papers which rely on in-batch negatives, as well as momentum contrast methods like MoCo which cache mini-batch computations and use them in later batches. - References for "Mining hard negatives can avoid having to use large batch sizes (but is itself non-trivial)" : “Contrastive Learning with Hard Negative Samples” [2], “Debiased Contrastive Learning” [3]. We did not use hard negative mining in our experiments and simply use the largest batch size which we could fit across 8x46GB A40 GPUs for CLIP finetuning. 4) Sec 5.3 where too many things are introduced at once. We agree that section 5.3 abruptly introduces a lot of new things, and are happy to take the reviewer’s suggestion on the presentation of this section. We had wanted to present the following three results and had to choose a subset to retain in the main paper due to space constraints: - We wanted to introduce the proxy visual grounding tasks used in Voltron [20] and present results for SCR on them. - We wanted to ablate the method of spatial aggregation for CLIP and other baselines and show that retaining spatial information changes the conclusions of [20] completely on these tasks. We further wanted to show that a similar gain (or at least as considerable) is not seen on the actual control tasks. - We further used the above visual grounding tasks to ablate how we provide the language inputs to SCR in the case of language guided tasks, and assess to what extent language modulates the representation. 5) Bilinear interpolation should be shown in equations formally to understand exactly what is done We will modify figure 2 in the paper to include the equation along with the visual description of this concatenation operation. We primarily do this to enable stacking of the differently sized U-net feature maps so that we can use a single convolutional layer to process them without adding any other learnable parameters. A similar resizing operation was most recently used in [1], which looks at training a feature adapter module for control. 6) a) Why cite Imagen in L36? b) Reference to Table 2a/b are mixed up. Thanks for pointing these out. a) We will move this reference (meant to be a citation for examples of foundation diffusion models) to the background instead, and b) fix the swapped references. --- We hope that these clarifications and additional experimental results have addressed any remaining questions and concerns. If you find that we have addressed your questions and concerns, we kindly ask you to consider raising your score to reflect that. If issues still remain, then we would be more than happy to answer these in the discussion period. Thank you. --- References [1] Lin, Xingyu, et al. "Spawnnet: Learning generalizable visuomotor skills from pre-trained networks." arXiv preprint arXiv:2307.03567 (2023). [2] Contrastive Learning with Hard Negative Samples : Joshua David Robinson, Ching-Yao Chuang, Suvrit Sra, Stefanie Jegelka [3] Debiased Contrastive Learning: Ching-Yao Chuang, Joshua Robinson, Lin Yen-Chen, Antonio Torralba, Stefanie Jegelka --- Rebuttal Comment 1.1: Comment: Thank you for running these crucial additional experiments and engaging with my comments in general! I am willing to raise my score. --- Reply to Comment 1.1.1: Comment: Dear Reviewer, Thank you so much again for all your feedback that has helped us improve our paper, and for raising your score to "strong accept"! Best, The authors	Summary: This paper studies how diffusion models can be adapted to provide rich representations for training policies. They study how to extract features from a pre-trained Stable Diffusion model in terms of 3 questions: which layers, which diffusion timestep and which text prompts help for downstream task performance. They evaluate these learned representations on a number of robotics tasks like manipulation, navigation and a combination of the two tasks. Their proposed approach performs better than baselines for many tasks. Strengths: 1. Lots of ablation experiments to validate the final design choice. 2. Evaluating a single model for both navigation and manipulation tasks. This is an interesting setup that is becoming more and more relevant with full-body control and robots that need to do both tasks. Weaknesses: 1. It is difficult to ascertain what is the key reason why the performance difference exists between the baselines and proposed method. The baselines have different training data, model sizes, and training losses. While the presented approach has better performance, it is important to identify what is key cause of this: more data, bigger model or the diffusion loss? Furthermore, there seems to be evidence that for manipulation tasks the baselines (LIV, R3M etc) are good but the performance drops only for navigation tasks which is not the key focus of those baselines. Technical Quality: 2 Clarity: 4 Questions for Authors: 1. How do the methods compare when a common model, feature pooling strategy and training dataset are used? It is okay to limit to one kind of task (manipulation/navigation) for this experiment. 2.What if the same feature pooling strategy is applied to baselines like CLIP?. For example if you aggregate spatial features of CLIP from different layers does that help performance? Seems some multi-layer feature aggregation was done for Tables 1(b) and 1(c) but not 1(a) ? 3. Why is CLIP-B used in the ImageNav experiments and not CLIP-L? Confidence: 4 Soundness: 2 Presentation: 4 Contribution: 2 Limitations: Yes. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank you for engaging with our work and commending our presentation, comprehensive ablations and the key result of being able to employ a single representation model for navigation and manipulation tasks. We address your questions and concerns below. --- 1) How do the methods compare when a common model, feature pooling strategy and training dataset are used? It is okay to limit to one kind of task (manipulation/navigation) for this experiment. Pre-training a foundational representation model is out of the scope of this work and would not be feasible given the limited compute resources available to us. We note that navigation and manipulation tasks are not the primary focus of diffusion model pre-training (similarly to how navigation is not the key focus of baselines that have been designed for manipulation tasks). This is what makes their all-round performance surprising. 2) What if the same feature pooling strategy is applied to baselines like CLIP? We present multi-layer feature aggregation results for CLIP for all benchmarks in the general response of our rebuttal. Note that using multiple layers makes the representation size of CLIP twice as large as all the other methods, and is not feasible to do comprehensively for the bigger navigation domains, so we present a smaller ablation there. On a high level, our conclusions from this experiment are that we do see a benefit from including additional outputs from certain layers along with the last layer which is always used (as we anticipated in the discussion in sec 5.1). We find these layers using a grid search and they are located towards the middle (10-14th layers). We note that while the feature map sizes after including another layer for CLIP are very large and not comparable anymore to the other methods, the performance still doesn’t match that of SCR. 3) Seems some multi-layer feature aggregation was done for Tables 1(b) and 1(c) but not 1(a) To clarify, we used the same representation extraction procedure for SCR in all of the tables (1a, 1b and 1c), i.e., using the mid+downsampling layers for SCR. 4) Why is CLIP-B used in the ImageNav experiments and not CLIP-L? This is because we compare directly to the results from VC-1 paper [27] where they used the CLIP ViT-base model. We note that ImageNav training runs require 16 GPUs for each run over 6 days of training. We can aim to include a result with CLIP-L in the revised manuscript. --- We hope that these clarifications and additional experimental results have addressed any remaining questions and concerns. If you find that we have addressed your questions and concerns, we kindly ask you to consider raising your score to reflect that. If issues still remain, then we would be more than happy to answer these in the discussion period. Thank you. --- Rebuttal Comment 1.1: Comment: Thanks for adding the new experiments with CLIP and answering my questions in detail. Based on the replies, I am updating my score to weak accept. One final comment: given the new CLIP results it might be too harsh to say 'contrastively trained representations such as in CLIP have been shown to fail at enabling embodied agents' in the abstract. --- Reply to Comment 1.1.1: Comment: Dear Reviewer, Thank you so much for your feedback which has helped us improve the paper and for recommending acceptance! We will change the phrasing as you suggested and include a subsection to discuss these findings in the revised manuscript! Best, The authors	Summary: This paper introduces SCR, a method that extracts representations from a pre-trained text-to-image diffusion model for learning downstream robotics control policies. Given a noised input image and prompt text, the visual representation is extracted from selected layers of the denoising U-Net. The extraction method is meticulously designed with extensive experiments and analysis to support the design choices. Experiments on multiple benchmarks across three tasks—few-shot imitation learning, image-goal navigation, and open-vocabulary mobile manipulation—demonstrate competitive performance, verifying the method’s ability to generalize to open-ended environments. Strengths: 1. Although the idea of replacing CLIP with diffusion models for extracting representations for robotic control is straightforward, the technical details, supported by comprehensive ablation and analysis of the design choices, are insightful and convincing. 2. The paper has potential for future impact. The method's ability to handle complex and open-ended environments suggests it could be generalized and applied to many other tasks. 3. The paper is well-written and easy to read. 4. The comparison experiments are thorough across multiple tasks and benchmarks, demonstrating the proposed method's strong performance. Weaknesses: 1. As noted in the related work, [50] found that the optimal noising timestep selection can vary depending on the task due to the required granularity of predictions. However, the ablation study for fixed timestep selection is performed only on the Franka-Kitchen benchmark. Would the results differ if tested on different tasks or benchmarks? 2. Additionally, all ablation studies in Section 5 are conducted solely on the Franka-Kitchen benchmark. SCR-FT shows a performance drop compared to the non-finetuned version on the ImageNav benchmark, attributed to the finetuning being performed only with table-top manipulation datasets. This raises concerns that different tasks have notable domain gaps and may require different features from the inputs. More experiments, or at least reasonable explanations, on whether the optimal framework design varies across tasks would be beneficial. Technical Quality: 3 Clarity: 3 Questions for Authors: Please kindly refer to the weaknesses. Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: Yes, the authors discussed the limitations that downstream performance depends on design choices for representation extraction and the higher run-time cost of using a pre-trained model with more parameters. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for taking the time to review our manuscript and for providing helpful and constructive feedback. We were happy to see your review note our study’s potential for future impact, the thoroughness of our experiments and ablations which demonstrate the strong performance of the approach we study, and the clarity of presentation. We address your concerns below. --- 1) [50] found that the optimal noising timestep selection can vary depending on the task .. the ablation study for timestep is performed only on the Franka-Kitchen benchmark. Would results differ if tested on different tasks? Yes, our observation is consistent with prior work. The optimal noising timestep depends on the task and we present the same ablation for timestep on the Meta-World environment below. SCR performs similarly across 0, 100 and 200 timestep on Meta-World because the images on this benchmark contain coarser details. We have provided further intuition and discussion around how to choose the best noising timestep in Figure 8 in the appendix, where we show reconstructions obtained from the diffusion model for different benchmark images starting at different denoising timesteps. \| Timestep \| Success \| \| -------- \| ------------- \| \| 0 \| 94.1 &pm; 1.9 \| \| 0 \| 94.4 &pm; 1.9 \| \| 0 \| 94.4 &pm; 2.0 \| 2) All ablation studies in Section 5 are conducted solely on the Franka-Kitchen benchmark. Thank you for suggesting this, we conducted additional ablations on the Meta-World benchmark and present these in the general response of the rebuttal. Note that ablating the layer + noise selection on Meta-World shows that we can beat the best method there (R3M[30]) if we use a smaller subset of the layers we used (thereby achieving a 97% success rate), however we recommend retaining the standardized settings which we used across benchmarks to retain simplicity while still getting overall good performance across tasks. Since the navigation benchmarks require a lot of compute resources, we can provide a full set of ablations on these for the camera ready version, if the reviewer suggests it. 3) SCR-FT shows a performance drop compared to the non-finetuned version on the ImageNav benchmark. We agree that a visual domain gap exists between the manipulation and navigation benchmarks, which could be mitigated by co-finetuning with manipulation and navigation datasets (like Real Estate 10k[1]) as done in VC-1[27]. With SCR-FT, we aimed to present a proof-of-concept result for the simple non-task-specific fine-tuning that is possible when using an image generation representation model, using some of the commonly-used datasets in the representation learning literature - most of which focus on few-shot manipulation tasks. We also presented a negative result of trying to do this for the CLIP model in Appendix D.1. Finally, we have aimed to keep the representation selection procedure standardized for all tasks- by deciding a common subset of layer outputs which we use as the representation, as well as the denoising timestep value of 0 since that always does well (while higher denoising timesteps might also do well on some benchmarks). Beyond this there are no additional hyperparameters introduced for SCR. --- We hope that these clarifications and additional experimental results have addressed any remaining questions and concerns. If you find that we have addressed your questions and concerns, we kindly ask you to consider raising your score to reflect that. If issues still remain, then we would be more than happy to answer these in the discussion period. Thank you. --- References [1] Zhou, Tinghui, et al. "Stereo magnification: Learning view synthesis using multiplane images." arXiv preprint arXiv:1805.09817 (2018). --- Rebuttal Comment 1.1: Comment: Thanks for the clarifications and the additional experiments. They have answered my questions. I believe the original score accurately reflects my positive assessment of the paper. I noticed a small typo in the table for question 1—the first column says "0, 0, 0", which I assume should be "0, 100, 200" given the texts. This doesn't impact my overall assessment.	Summary: This paper introduces Stable Control Representations (SCR), a novel approach that aggregates intermediate outputs from diffusion models for robotic control tasks. The authors validate its effectiveness on various benchmarks, including manipulation, navigation, and grasp point prediction. The key design space has been thoroughly ablated, showing SCR's superiority over other visual representation methods. Strengths: 1. Innovative Exploration: Visual representation is a fundamental challenge in robotics. Exploring the effectiveness of diffusion models in this context is intriguing and novel. 2. Comprehensive Experiments: The authors conducted extensive experiments covering various robotic tasks, diffusion steps, intermediate layer selection, and aggregation methods. The design space has been thoroughly explored. 3. Clear Writing and Organization: The paper is well-written and organized, making the narrative easy to follow. Weaknesses: 1. Lack of Real-World Validation: While SCR performs well on simulation baselines, real-world validation is missing. Demonstrating its effectiveness on real robots would significantly enhance the credibility and practical applicability of SCR. 2. Insufficient Evidence: Although the authors provide extensive empirical evidence of SCR's effectiveness, the paper lacks theoretical and quantitative analysis explaining why diffusion-based visual representations outperform other baselines. This theoretical backing would strengthen the paper's overall argument. Technical Quality: 2 Clarity: 4 Questions for Authors: None Confidence: 4 Soundness: 2 Presentation: 4 Contribution: 3 Limitations: Refer to the weaknesses section. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for taking the time to review our manuscript and for providing helpful and constructive feedback. We were happy to see your review note our study’s innovative exploration, thoroughness of our experiments which demonstrate the strong performance of the approach we study, and the clarity of presentation. We address your concerns below. --- 1) Real-world validation: We employed a broad range of tasks in our work to add evaluation signals from different domains (manipulation and highly photorealistic indoor navigation) and learning setups (few-shot vs RL). Real robot experiments require an expensive setup and largely feature in works that look at few-shot table-top manipulation tasks which can provide noisy performance signals due to low sample sizes. We believe this would not have added much additional value to our exploration of simply validating the usability of diffusion model representations as a first step, and is better suited for future work. Many influential works in this space also rely completely on evaluation in simulation environments [1, 2, 3, 4]. 2) Theoretical evidence: Consistent with the embodied AI literature (e.g., VC-1[27], R3M[30], Voltron [20] etc.), our work focuses on displaying strong empirical evidence for the usefulness of pretrained representations for a wide range of control tasks. We agree that studying the properties of the representation manifold of denoising diffusion models is an interesting and impactful direction for future work. --- We hope that these clarifications have addressed any remaining questions and concerns. If you find that we have addressed your questions and concerns, we kindly ask you to consider raising your score to reflect that. If issues still remain, then we would be more than happy to answer these in the discussion period. Thank you. --- References [1] Khandelwal, Apoorv, et al. "Simple but effective: Clip embeddings for embodied ai." Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2022. [2] Xiao, Tete, et al. "Masked visual pre-training for motor control." arXiv preprint arXiv:2203.06173 (2022). [3] Yadav, Karmesh, et al. "Offline visual representation learning for embodied navigation." Workshop on Reincarnating Reinforcement Learning at ICLR 2023. 2023. [4] Eftekhar, Ainaz, et al. "Selective visual representations improve convergence and generalization for embodied ai." arXiv preprint arXiv:2311.04193 (2023). --- Rebuttal Comment 1.1: Comment: Thanks for your response. I agree that real-world experiments are unnecessary at this stage and I'm willing to raise the score. --- Reply to Comment 1.1.1: Comment: Dear Reviewer, Thank you again for your valuable feedback that has helped us improve our paper, and for raising your score! Best, The authors	Rebuttal 1: Rebuttal: We thank the reviewers for taking the time to review our manuscript and for providing thoughtful and constructive feedback. We were delighted that reviewers recognized that our work studies an “important” and “interesting” problem (9EUL, QYDZ) while being presented in a manner which is “easy to understand” (9EUL) and which “contextualizes the background and related work well” (zJpU). We are pleased to see the reviewers note the “strong performance” (sdTb) of the proposed approach and appreciate the “thorough ablations and analysis” (QYDZ, sdTb), along with a “fair treatment of the baselines” (zJpU) which we strived to ensure in our work. Reviewers also commended the “comprehensive evaluation” (all), "which becomes more important with paradigm shift towards multi task models" (ZVD8). We are grateful that they point out the work has “potential for future impact through the ability to handle complex open-ended environments” (sdTb). Finally, we thank the reviewers for acknowledging our open source code repository which will help reproducibility and accelerate future efforts in this direction (zJpU). --- Since reviewers ZVD8 and zJpU asked for results on multi-layer aggregation of CLIP representations, we present these results in the general response: As we note in Section 5.1 of the manuscript, we can see clear benefits from aggregating multi-layer features for SCR. The reason why we used these features is because of the smaller feature maps in the U-Net compared to ViTs (thus using multiple layer outputs for a fair comparison). This is an architecture-specific property, and not a property of diffusion models specifically, and we expect all models to benefit from this. However, as we mention in L262, this can lead to very large representation sizes for ViTs (each layer output is 16x16x1024). Following the reviewer’s suggestion, we ran the same experiment for CLIP by concatenating outputs from the last layer + another layer in the range of layers 10-2.1 (We use two layers to keep GPU memory manageable, and note that this makes the CLIP representations twice as large compared to other methods.) We present the results below: \| Model \| Layers \| Success (&pm; std err) \| \| --------- \| ---------------- \| ----------------------- \| \| CLIP-L \| 23 (last layer) \| 36.3 &pm; 1.7 \| \| CLIP-L \| 21+23 \| 35.4 &pm; 2.9 \| \| CLIP-L \| 19+23 \| 38.5 &pm; 3.2 \| \| CLIP-L \| 17+23 \| 39.0 &pm; 3.0 \| \| CLIP-L \| 12+23 \| 40.8 &pm; 2.8 \| \| CLIP-L \| 10+23 \| 40.2 &pm; 3.2 \| \| SCR (ours)\| Down[1-3] + Mid \| 49.9 &pm; 3.4 \| We see an interesting trend, namely that moving towards middle layers leads to higher performance indicating that CLIP layers around layer 10-14 encode some details useful to the Franka benchmark. While we do see a benefit from including the output of certain additional layers, performance CLIP performance still does not match SCR. We also wanted to see if the best pair of layers that we found here might be better on other tasks as well. To test this, we ran the same combination for Meta-World, OVMM, and Imagenav (adjusted for ViT-B). We present the results below. \| Model \| Layers \| Meta-World \| OVMM \| \| --------- \|---------------- \| ------------- \| ------------- \| \| CLIP-L \| 23 (Last Layer) \| 90.1 &pm; 3.6 \| 38.7 &pm; 1.7 \| \| CLIP-L \| 12+23 \| 91.7 &pm; 2.6 \| 38.6 \| \| CLIP-L \| 21+23 \| 91.2 &pm; 2.3 \| - \| \| SCR (ours)\| Down[1-3] + Mid \| 94.9 &pm; 2.0 \| 43.6 &pm; 2.1 \| \| Model \| Layers \| ImageNav \| \| --------- \|---------------- \| -------- \| \| CLIP-B \| 11 (Last Layer) \| 52.2 \| \| CLIP-B \| 6+11 \| 66.6 \| \| SCR (ours)\| Down[1-3] + Mid \| 73.9 \| We see a significant improvement on ImageNav and a slight improvement on Meta-World. (We did not see an improvement on OVMM but note that the results above are only for a single seed.) --- Following Reviewer sdTb's suggestion, we also replicated our ablations---which we had previously performed on the Franka kitchen benchmark---on Meta world. We present the results here: Meta-World Ablations \| Layers \| Noise \| Success (&pm; std err) \| \| --------------- \| ----- \| ---------------------- \| \| Mid \| 200 \| 94.7 ± 2.8 \| \| Down[3] + Mid \| 200 \| 97.3 ± 1.4 \| \| Down[1-3] \| 200 \| 94.1 ± 1.9 \| \| Down[1-3] + Mid \| 200 \| 94.4 ± 1.9 \| \| Down[1-3] + Mid \| 100 \| 94.4 ± 1.9 \| \| Down[1-3] + Mid \| 0 \| 94.1 ± 1.9 \| The top three rows ablate the layer used, and the bottom three rows ablate the noise values. We note that this ablation on Meta-World shows that it is possible to outperform the best method here (R3M[30]) if we use a smaller subset of the layers we used as the default (thereby achieving a 97% success rate). However, standardizing the representation extraction settings which we used across benchmarks helps us to retain simplicity while still achieving an overall good performance across tasks.	NeurIPS_2024_submissions_huggingface	2,024	Summary: The paper investigates whether latent representations from a pre-trained tex-to-image generation model are useful for object manipulation or navigation tasks in embodied agents. The paper considers a few design choices in how to extract latent features from Stable Diffusion, that could lead to more versatile and useful features for downstream control tasks. The method is referred to as Stable Control Representation (SCR) with variants like additionally using cross-attention maps (SCR-Attn) or a finetuned version (SCR-FT). Experimental results show that SCR series can achieve comparable or better performance than general VL encoders like CLIP or method designed for control tasks. Strengths: - The paper studies an interesting problem of using text-to-image diffusion models for embodied agent control. The paper is well-written and easy to understand. - The method considers many design choices of SCR in a very comprehensive way. The choices of different factors, from denoising steps to layer selection, have been clearly presented and justified later in the experiment. - The experiment seems well-designed and comprehensive. Most of the results support the benefit of using SCR for control tasks. Weaknesses: - The method is loosely connected with diffusion mechanism and simply adopt Stable Diffusion as a feature extractor with one pass if I understand correctly. This loose connection is particularly amplified in Table 2a where timestep=0 ends up with the best performance. This basically indicates that the "generative" power of text-to-image models are not necessary for the task. In that sense, is it still necessary to use T2I diffusion models if one could find a visual encoder (e.g. ViT) trained with similar amount of images as Stable Diffusion? - The performance gap between SCR-FT and R3M in Meta-World and Franka-Kitchen indicates that the method may not generalize well to some scenarios. Could you give any insights about the performance gap? Is it related to domain shift or image style differences or any other reaons? - The order of Table 2 is different from descriptions in Sec. 5.1 and 5.2 Technical Quality: 3 Clarity: 3 Questions for Authors: See above Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: N/A Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for taking the time to review our manuscript and for providing helpful and constructive feedback. We were happy to see your review mention the clarity of our presentation, the relevance of the problem we are studying, and the comprehensiveness of our evaluation. We address your concerns below. --- 1) Can a visual encoder (like ViT) trained on a similar dataset as Stable Diffusion suffice, as the generative aspect of T2I diffusion models does not seem to be essential for the task with t=0. Tackling complex open-ended embodied tasks requires foundation vision-language model representations. We study the Stable Diffusion model since other existing foundation models like CLIP have their own shortcomings, we expand on this below. - The foundation model representations which have been considered for control so far are trained with auto-encoding (MAE) or contrastive learning objectives (CLIP[33], LIV[25], R3M[30]) - and prior work [20] has noted that these seem to do well on disparate sets of tasks depending on the level of visual and semantic details they encode (with image-text contrastive approaches encoding semantics better and auto-encoding approaches encoding more finer details). We hypothesized that the text-conditioning of a T2I generative model might enforce encoding semantics and the generation objective might incentivise retention of more fine grained visual detail in the representations. The question was then whether it would be possible to localize a subset of representations that would sufficiently encode these details and do well across tasks. This is the main result we demonstrate. - Moving to language-conditioned control tasks necessitates investigating vision-language model representations. Given the limited effectiveness of CLIP (which is the primary candidate for a vision language representation) as a backbone on control benchmarks, we intended our work to be an explorative study of a different kind of foundation model that could provide vision-language aligned representations for control. Since there is a lot of research momentum in the direction of image and video generation diffusion models, successfully leveraging them for control would be beneficial in the long run. 2) This loose connection is particularly amplified in Table 2a where timestep=0 ends up with the best performance. This basically indicates that the "generative" power of text-to-image models is not necessary for the task. - We note that when using a noise value of 0, the U-net still forms a meaningful representation of the input. [2] also uses zero noising for input images, to do zero-shot open-set segmentation using intermediate outputs from the U-Net. [3] also follow the score estimates from the U-net at t=0 to continue to keep refining the data samples and to bootstrap a Langevin sampler from that. The fact that the score function gradient estimates are informative at t=0 implies that the intermediate representations in the model are informative too. - We also note that the MAE (Masked AutoEncoders) [1] representation model (which is the backbone for the VC-1 model) follows a similar strategy. It is trained to reconstruct missing patches from the input, but when it is used as a representation backbone none of the patches are masked out. The uncorrupted input is passed through the model to derive the representation, thereby not exactly using the denoising power of the MAE in the forward pass. 3) Explain The performance gap between SCR-FT and R3M in Meta-World and Franka-Kitchen We are happy to provide more context about performance differences on the benchmarks in the revised manuscript. R3M representations are highly sparse and tailored specifically to reduce overfitting in few-shot IL settings (see Table 1 in the R3M paper where performance drops 4-6% when the L1 sparsity penalty is removed), which does not end up being an advantage on other kinds of tasks with large scale RL training. We also note that we standardized representation extraction settings across all benchmarks for SCR for simplicity and reproducibility, but if we had tuned the layer selection choice for each of the domains specifically, we would be able to beat R3M on Meta-World with the setting where we use the mid+down_3 layers with t=200 timestep, and get 97% on Meta-World (this result is presented in the general response of our rebuttal, where we replicate our Franka ablations for the layer and noise parameters on Meta-World). 4) Typos Thank you for pointing out the swapped order of table column references in sections 5.1 and 5.2, we have fixed this in the manuscript. --- We hope that these clarifications have addressed any remaining questions and concerns. If you find that we have addressed your questions and concerns, we kindly ask you to consider raising your score to reflect that. If issues still remain, then we would be more than happy to answer these in the discussion period. Thank you. --- References [1] He, Kaiming, et al. "Masked autoencoders are scalable vision learners." Proceedings of the IEEE/CVF conference on computer vision and pattern recognition. 2022. [2] Open-Vocabulary Panoptic Segmentation with Text-to-Image Diffusion Models. Xu et al., 2023. [3] Iterated Denoising Energy Matching for Sampling from Boltzmann Densities. Akhound-Sadegh et al., 2024. --- Rebuttal Comment 1.1: Comment: Dear Reviewer 9EUL, The discussion periods ends tomorrow (August 13). We have made considerable effort to address the concerns and queries you have raised, and would be grateful for the opportunity to clear up any remaining queries you may have while we are still in the discussion period. Thank you. --- Rebuttal Comment 1.2: Title: Thank you for the response Comment: Most of the responses are convincing and have addressed my concerns. But I am not sure if I understand the sentence, We hypothesized that the text-conditioning of a T2I generative model might enforce encoding semantics and the generation objective might incentivise retention of more fine grained visual detail in the representations., correctly. Is it because that SD adopts a freezed CLIP text encoder, so that you hypothesize that the text encoder enforces encoding semantics? (Btw, what is enforced to encode semantics by the text-conditioning stage?) I guess I just don't see how the concept of "encoding" or "retention of visual details" could fit into the diffusion process or is it just a very high-level interpretation as the target is to extract representations from a generative model? --- Reply to Comment 1.2.1: Comment: Thank you for your response! We are happy to clarify our statement with respect to your question. > “I am not sure if I understand the sentence, “We hypothesized that the text-conditioning of a T2I generative model might enforce encoding semantics and the generation objective might incentivise retention of more fine grained visual detail in the representations., correctly. " > "Is it because that SD adopts a freezed CLIP text encoder, so that you hypothesize that the text encoder enforces encoding semantics? (Btw, what is enforced to encode semantics by the text-conditioning stage?)” Yes, more specifically, the signal from the text prompts is incorporated into the U-Net through the use of a (dot-product-based) cross-attention layer within each block. This incentivises the visual feature maps in each block to align with the text encodings selectively, thereby also aligning with language concepts. This is also evidenced by the fact that we can isolate word-aligned attention maps for each U-Net layer, which roughly correspond to the entity in the image referenced by the word (when projected onto the image). This is shown in Figures 9 and 10 of the appendix in our submission. > “I guess I just don't see how the concept of "encoding" or "retention of visual details" could fit into the diffusion process or is it just a very high-level interpretation as the target is to extract representations from a generative model?” Diffusion-based image generation models are trained to generate a final image by producing progressively more denoised versions of an existing noised image. To be able to refine and produce the image corresponding to the last few steps of denoising (likely only needing a few pixels to be edited or denoised), the model needs to encode the same level of visual details that a reconstruction/auto-encoding model might also encode. The works [55, 57] which we cite within our related work section also provide similar evidence for representation learning within diffusion models (for computer vision tasks). We also refer the reviewer to a recent survey paper that explores the interplay between diffusion models and representation learning in more detail. Thank you for giving us the opportunity to clarify the points above. Please let us know if you have any further questions! [1] Diffusion Models and Representation Learning: A Survey, https://arxiv.org/abs/2407.00783	null	null	null	null	null	null
Deep Homomorphism Networks	Accept (poster)	Summary: The authors propose a deep graph learning architecture where each layer consists of two key components: (i) the computation of homomorphism count vectors relative to a set of graph patterns, and (ii) a subsequent non-linear transformation. The homomorphisms computed in a layer incorporate features from the previous layer. Within this framework, the authors examine its expressive power, providing a characterization in terms of a variant of Weisfeiler-Leman and homomorphism indistinguishability related to an expanded set of graph patterns. Additionally, a brief section discusses the architecture's continuity properties and universality. Preliminary experimental results are also presented. Strengths: S1 Architecture The proposed architecture generalizes standard MPNNs while enhancing their expressive power. Furthermore, by incorporating different graph patterns in each layer, it extends the approach taken by Barceló et al. [4], resulting in a significant increase in expressive power. The elegant idea involves combining the computation of weighted homomorphism counts of patterns in each layer, treating the host graph as being augmented with features computed from previous layers. S2 Versatility By appropriately selecting graph patterns, the proposed architecture demonstrates exceptional flexibility in capturing various kinds of subgraph information. S3 Analysis Theorem 5.3 is a notable result, clearly illustrating the expressive power of the proposed method. S4 Theoretical Connections To provide insights into the properties of the proposed architecture, the authors leverage a wide range of theoretical results and connect their work to recent developments in the field. Weaknesses: W1 Incorrect statement Unless there is a misunderstanding, Theorem 3.3 is known not to be true. That is, the classical result relating isomorphisms and hom counts is known not to generalize to weighted graphs. A recent reference for this is https://arxiv.org/pdf/2308.15283 (but this was observed before). W1 has been dispelled by the authors due to a misunderstanding of my part W2 Imprecise formalizations - When defining the notion of generalized homomorphism, it is worth pointing out that this is not a new concept. Weighted homomorphisms have been studied before. Now, the definition on page 4 is not very clear: You mention “continuous” but with respect to which topology? The input and output of the functions $\mu_p$ only becomes clear later on. Please define this more precisely. I also understand that $\mu_p$ maps into a $d$-dimensional space. What is the product in this space? You use this in equation (3) without explaining how to multiply two vectors. I assume you use Hadamard (pointwise) product? - In section 4.1., and in particular in the crucial definition Equation (5) of a homomorphism layer, you use $h$ without saying what it is. Please make this more clear. - Example 4.1 is hard to decipher. What is $\circ$ in $x_{\pi(\circ)}$ in Equation (6)? I was expecting a product in Equation (7) since the graph pattern has two vertices? I am also not sure what is going on l193. What are these sets $\mu$? Since this example is supposed to illustrate your main architecture, this should be clear and consistent with the introduced notation and definitions. - In the definition of your version of WL, in Equation (11), shouldn’t the homomorphisms $\pi$ used also take colors from previous iterations into account? W3 Universality The results about universality in Section 5.3 are of less interest, since no quantitative bounds are given about the size of networks needed to approximate any function to arbitrary precision. Furthermore, the topology used needs more motivation and explanation. W4 Heavy reliance on results in theoretical CS Many of the theoretical results and observations are heavily influenced (and are oftentimes restated versions of) results known in the literature. An example is section 4.2, but also many proofs are close to existing ones. Similarly, the results in section 5.2 all rather easily follow from recent advances in TCS, especially from the work of Roberson et al, and from previous work in the ML community. W5 Experiments The experiments appear very preliminary and do not give much insight into how much the flexibility of the proposed architecture is needed to obtain good accuracy. Indeed a very limited number of patterns and two layers suffice? Also, it is unclear why the number of parameters varies when changing graph patterns? It would make a more fair comparison if parameters were fixed? Also, there is no comparison with the work by Barceló et al and NT and al, which served as the motivation for the current paper. What is the reason for this? W6 Unclear sentences - L38 “for a common choice” what do you mean by this? - L87 “expressive power is .... exponential in the number of GNN layers” it is unclear what it means for the expressive power to be exponential in something. - Figure 1 should be improved. It is unclear what is going on in this figure at this point in the paper. - L125 “although sacrificing invariance ...” Why would you want to consider functions that can distinguish isomorphic graphs? This would indicate that you want to learn something depending on the specific encoding of the graphs? - L196-L198: It is unclear what these sentences intend to convey (even after consulting the appendix). - L202 and onwards, you mention that your model is an algebra. Please detail what you mean by this and why this is important (e.g., universality). W7 Minor comments - L141 The results in Dell et al was previously shown in “On recognizing graphs by numbers of homomorphisms” by Z. Dvořák. - L146 Why does $\phi^{(\star)}$ need to be permutation invariant. It is defined as function which takes a multiset as input so it is permutation invariant by definition? - L149 “We can prove”-> “One can prove” (since it is already shown by others) - L152 “where $\cal T$ is the set of all trees” -> Should be removed here I assume? Technical Quality: 3 Clarity: 2 Questions for Authors: I would appreciate it if the authors could respond to the weak points W1, W2 and W5. Confidence: 4 Soundness: 3 Presentation: 2 Contribution: 2 Limitations: This has been addressed in a satisfactory way by the authors. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you very much for reading our manuscript. In particular, we are pleased to have a review from a specialist of homomorphisms. Below, we address your questions and comments. Especially, we claim our Theorem 3.3 is correct ([W1]) because of our definition of generalised homomorphism. Since all your major concerns (W1, W2, and W5) all related to the definition of our generalized homomorphism, we hope our answer clarifies your concern and you will reconsider the evaluation of our work. # Questions [W1] As you mentioned, weighted graph homomorphisms can only distinguish weighted graphs without twins (https://arxiv.org/abs/1909.03693). However, our generalised homomorphism circumvents this issue by introducing non-linear transformations $\mu$ on node features. For instance, Example 4 in your reference is distinguished by setting $\mu_p(x) = 1$ for all $p$ and $x$. This transformation gives the homomorphism number of the underlying unweighted graphs so it detects the isomorphism of the underlying graph. The proof of this theorem is in the Appendix. The key point is that our generalised homomorphism can count the graphs-with-features's homomorphisms (i.e., mappings that preserve the adjacency and feature values) by suitably choosing non-linear transformations (say, $\mu_p(x) = 1[x = a_p]$ for the relation that node $p$ has a feature $a_p$.). This observation with the classical Lovasz theorem for general relational structure (https://www.cs.elte.hu/~lovasz/scans/opstruct.pdf) proves the theorem. [W2] > When defining the notion of generalized homomorphism, it is worth pointing out that this is not a new concept. Weighted homomorphism is a classical concept, but we believe our version that applies non-linear transformation is new, and it is best-suited for GNNs. One significant difference between weighted and our generalised appeared in Theorem 3.3 above. --- > In section 4.1., and in particular in the crucial definition Equation (5) of a homomorphism layer, you use h without saying what it is. It's the node feature of $G$ as we wrote as $(G^u, h)$. We will add this clarification in the updated manuscript. --- > Example 4.1 is hard to decipher. Sorry for the imprecise presentation. The right-hand side of Eq (7) is by definition $\sum_{v \in N(u)} \mu_\bullet(x_u) \mu_\circ(x_v)$. In line 193, what we wanted to convey was: - For a single-node pattern (node: $\bullet$), $\mu_\bullet(x)$ is arbitrary - For a two-node pattern (nodes: $\bullet$ and $\circ$), $\mu_\bullet(x) = 1$ and $\mu_\circ$ is arbitrary. This shows Eq (6) and (7). We update this part as the above. --- > shouldn’t the homomorphisms $\pi$ used also take colors from previous iterations into account? It takes colours from previous iterations into account, since it aggregates the colour of node $\pi(p)$ at k-th step. We might have misunderstood your question, so please elaborate. [W5] Please refer to the global rebuttal for a general remark about the real-world dataset experiment. About the number of parameters, our model has transformation $\mu = \\{ \mu_p : p \in V(F) \\}$ on each node in each pattern. We implement them as neural networks. Therefore, the number of parameters is basically the number of patterns times the number of parameters in each neural network. # Weaknesses [W3] In principle, we agree the universality/BS-continuity doesn't add much value. But, we think it's an important property, esp., in the large graph applications. Also, it gives a brief comparison with the Zhang 2023's seminal model that captures the bi-connectivity (ICLR'23 outstanding paper) as "ours is continuous, theirs is not". See also 2WsS [Q5]. [W4] We also, in principle, agree that our theorems are easily followed from the TCS results. However, our goal here is not to prove new TCS results, but is to state the relationship between the GNN architecture (layer-wise aggregation) and the expressive power of the model (pattern graphs for hom) to extend the GNN expressive power study, and suggests a generic framework how to build a GNN architecture suitable for tasks. [W6] We revise our manuscript to clarify all the points raised here. > L38 This means "Several existing GNN papers used such architectures." > L87 We identify the expressive power as the set of captured patterns. In this sense, this means "k layer GNN can count patterns in $F^0 \cup ... \cup F^k$ (having k-th power in terms of the rooted products)" as "exponential in k". The numbers of the patterns is also exponential in k (by assuming \|F\| = O(1)). > Figure 1 We updated Figure 1 to clarify the meaning. > L125 We don't want to consider functions that can distinguish isomorphic graphs; it is clearly written as "we stay with invariant functions as it is a natural requirement to represent graph properties" in the same paragraph. This is just a note that some existing studies claiming higher expressive power are sacrificing invariance. So our is incomparable with them as we/they are studying different classes of functions. > L196-L198 We wanted to say DHN is a very wide class of GNN that aggregates local information, i.e., (1) we think Eq (9) is the most generic GNN that aggregates information locally, and (2) it is expressible in DHN. > L202 Thanks. As you pointed out, it is important in the proof of the universality. We will update our manuscript accordingly. > L141 Thank you very much for pointing out the right reference. > L146 You are mathematically correct. This is just to emphasize the permutation invariance of the function, just be sure. Note that several GNN papers (e.g., Xu et a 2019 https://arxiv.org/abs/1810.00826) also mentioned a function is permutation-invariant even though it takes a multiset as an argument. > L149 > L152 We will update them accordingly. --- Rebuttal Comment 1.1: Title: Thank you for the clarifications Comment: I would like to express my gratitude to the authors for their clarifications, particularly concerning the application of non-linearity in the hom counts. This was a point I misunderstood in my initial reading, which may have led to an unduly harsh evaluation of the paper. After reviewing the authors' explanations and re-examining the paper, I now see its potential. If the authors can refine certain parts of the presentation and address all the reviewers' comments, I believe this paper could be a valuable addition to the conference program. Accordingly, I will raise my score to accept.	Summary: The authors introduce Deep Homomorphism Networks (DHNs), which generalize Message Passing Neural Networks (MPNNs) and previous Homomorphism Networks. DHNs explicitly count the number of homomorphisms from pattern graphs to the input graph, calculate representations based on these counts, and update node features accordingly. MPNNs are a subset of DHNs when patterns are limited to single nodes and edges. Previous Homomorphism Networks are equivalent to one-layer DHNs. The authors extend known results about the homomorphism expressivity of these networks, demonstrating that DHNs can count a broader range of homomorphisms. This lays the foundation for quantitative expressivity results. Strengths: - The construction of DHNs is elegant, effectively generalizing standard MPNNs and other homomorphism networks. - The theoretical contributions are interesting, intuitive, and non-trivial, providing a solid foundation for further research on the expressivity of GNNs. Weaknesses: - The paper lacks evidence of improved predictive performance on real-world tasks. While the theoretical contributions are valuable, it is unclear in which real-world tasks DHNs would be advantageous. Clarification/Ablations on whether domain knowledge is necessary to predefine patterns and whether including irrelevant patterns can harm predictive performance would be beneficial. - The computational complexity of DHNs is not convincingly addressed (as a limitation). For example, 3-WL has cubic complexity and can count homomorphisms of all graphs with tree-width 2 at this complexity. DHNs are less expressive unless patterns include graphs with tree-width 3 or higher. Therefore, to surpass 3-WL, DHNs must match or exceed its complexity. The advantages of DHNs over 3-WL or its local variants, like subgraph GNN or local 2-FWL, need to be clearly stated. - The motivation for using labeled patterns is unclear, as this adds complexity and increases the need for domain knowledge. The benefits of using labeled patterns over blank patterns without features must be better explained. Minor: - Some proofs could be more detailed. For instance, in Theorem 5.3, item 2 to item 3 is not clearly justified. The proof shows that there exists a function $h$ that satisfies $h(u)=hom((F, \mu), (G^u, x))$ for every $u$ and a fixed graph $G$. If the construction of $h$ depends on the graph, this is not sufficient for the proof. More clarity and detail in this and other proofs would strengthen the paper. Technical Quality: 3 Clarity: 3 Questions for Authors: - What is the predictive performance of DHNs on real-world tasks? Are explicit subgraph/homomorphism counts optimal for these tasks? - There is one related work [Paolino, Raffaele, et al. "Weisfeiler and Leman Go Loopy: A New Hierarchy for Graph Representational Learning." arXiv preprint arXiv:2403.13749 (2024).], and I believe the relation could be really interesting. Paolino et al. only consider injective homomorphism, while their color refinement algorithm is more complex in the sense that representations for the homomorphism are calculated. If I understand correctly DHNs can homomorphism count exactly cactus graphs (with limited cycle length) if the patterns contain cycles. Could you discuss the relationship? - For which classes of patterns is the homomorphism-expressivity maximal in the sense that the set of patterns that DHNs can count is maximal. See also - Why focus on feature homomorphisms? This approach seems more restrictive and domain-dependent, requiring prior knowledge of the existence of these featured patterns. When is it better to focus on feature homomorphisms versus general homomorphisms? why are the graphs $G_1$ and $G_2$ in Theorem 5.3 rooted? - The authors mention very shortly the continuity wrt BS distance. However, it's not clear why this is desirable. While it leads to learnability one can derive learnability also without it. At the same time, it strictly limits its expressivity as discussed in Remark 5.14.: Is continuity desirable? If yes, can you show that DHNs can approximate non-continuous graph invariants like biconnectivity? Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: It would be beneficial to add that the predictive performance is unclear. Also domain-knowledge might be needed to not worsen generalization performance/predictive performance. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you very much for the thoughtful review and comments. # Questions - [Q1] Since real-world dataset comments are common among all reviewers, please refer to our global rebuttal. - [Q2] Thank you very much for giving us a pointer to (Paolino et al., 2024); we will cite and discuss the relationship in the updated related work. Their model is a special case of ours with patterns $\\{C_k: k = 1, \ldots, r \\}$. Hence, ours can also count cactus graphs of bounded cycle length using these patterns. One important difference is that they used a permutation-invariant aggregation on cycles (Eq (3)); thus, they cannot distinguish two cycles of the same set of features that are ordered differently (e.g., $[a,a,b,b]$ vs $[a,b,a,b']$), while ours can. - [Q3] [Note: Please let us know if we misunderstood your question (since we don't see after "See also")]. In general, it's difficult to answer. A theoretically correct answer (but not very related to DHN) is that the set of all graphs of size at most n is maximally expressive since it determines the isomorphism class of graphs of size at most n. Finding smaller but isomorphism-characterising patterns is a central research question in the field of homomorphism distinguishability; see (Dvorak, 2010) and (Roberson, 2022). - [Q4] Could you elaborate on "general homomorphisms" and "feature homomorphisms" in this question? We might misunderstand your question. It is true that the method requires some domain knowledge about what patterns are useful. However, we believe it is better than the classical graph learning approach in which we have hand-crafted subgraph patterns as we need to take a larger but tractable set and ask DHN to learn the important patterns (this might be similar to classical hand-crafted features in computer vision versus CNN). Our model is more restrictive than those with higher expressive power (e.g., k-WL equivalent models). However, the non-restrictive are expensive (say, O(n^k)) and not applicable to large graphs. In this sense, we are restricting our model to satisfy the needs of computational complexity. - Graphs G1 and G2 in Theorem 5.3 are rooted because we consistently work on rooted graphs for technical reasons. Please refer to our rebuttal [Q1-minor] to reviewer X5N6. Note that it is easy to derive the result from the rooted version to the non-rooted version because the non-rooted version can be stated as "there is a bijection pi from $V(G_1)$ to $V(G_2)$ such that each pair of graphs $G_1^u$ and $G_2^{\pi(u)}$ rooted by $u$ and $\pi(u)$ are equivalent" - [Q5] First, DHN (or any BS-continuous GNNs) cannot approximate the biconnectivity of all graphs because there exists a pair of graphs $G, G'$ such that they're arbitrarily close in the BS topology but have different biconnectivity so the model fails to predict the biconnectivity of $G$ or $G'$. Models that can approximate biconnectivity must be non-continuous in the BS topology. Intuitively, if a function f is BS-continuous, $G$ is large, and $G'$ is a snowball sampling of $G$, then $f(G)$ and $f(G')$ are close (see Czumaj 2019). It is useful in large graph applications: We want to estimate a property on a large graph (e.g., Twitter networks) but only have a small sample $G'$. Here, the BS continuity guarantees that $f(G')$ approximates $f(G)$. If we use a non-continuous model, we have to discuss the validity of estimating $f(G)$ from $f(G')$, which is usually non-trivial. In this sense, ours is useful in large graph applications but loses the approximability of non-continuous properties. In contrast, the non-continuous one is useful in small graphs but loses the generic applicability in large graphs. We will add the above-mentioned intuition of BS continuity and the reasoning why it is useful. This discussion is not specific to our DHN model, but it clarifies why we consider BS continuity, which improves the readability of the manuscript. # Weaknesses - [W1] Thank you for pointing out the necessity of some intuitions on real-world datasets. We quickly added some experiments in the global rebuttal and will update our manuscript following your comment. - [W2] In terms of patterns, DHN captures "locally complex but globally tree (i.e., treewidth = 1)" patterns, while k-FWL (or (k+1)-WL)-equivalent models capture "globally tree-like (i.e., treewidth = k)" patterns. Therefore, they are essentially incomparable (one cannot surpass the other). We expand line 35 and add a Remark after the Corollaries to state when the proposed method is better than k-WL-type methods in such applications. - [W3] Here, we interpret the term "labelled pattern" as the patterns with functions. Please let us know if our understanding is wrong. First, how to aggregate node features over patterns without functions needs more exploration. A simple idea is to multiply the feature values in each coordinate and sum them up. This gives the weighted homomorphisms on each coordinate. However, adding/multiplying raw features might not necessarily make sense to us (although many papers are doing so), and it has a mathematical issue, as mentioned by Reviewer AtgF. Hence, we decided to apply functions to features. Second, in practical applications, the importance of nodes in patterns might differ (e.g., nodes closer to the root could be more important). Thus, we decided to use node-dependent functions. - [W4] We will improve our presentation of the proofs. --- Rebuttal Comment 1.1: Comment: Thank you for the rebuttal. I have one final question: When calculating homomorphisms, do you consider a map that preserves edges as homomorphisms, or if node features are available, do you require the map to preserve both edges and node features? If it's the former, there may be issues with the proofs. If it's the latter, how likely is it to actually find a homomorphism in the second layer? Specifically, you would need to select a pattern $F$ with node features $x$ that appear in the second layer, i.e., in the original graph with updated node features. Could you also please comment on situations where you would recommend not using deep homomorphism layers? It seems that the complexity becomes as high as kk-WL when cliques are used as patterns. Even for cycles, the complexity appears to be quite high, given that the homomorphism counts cannot be precomputed since μPμP is learned during the process. --- Reply to Comment 1.1.1: Comment: > When calculating homomorphisms, do you consider a map that preserves edges as homomorphisms, or if node features are available, do you require the map to preserve both edges and node features? Our algorithm enumerates all feature-less homomorphisms but aggregate features with non-linear transformations. So it's something in-between. To select the pattern (F, x) in the 2nd layer, where x is the original feature, we set the 1st-layer transformation by stacking the transformation needed in the 1st layer and the identity function for the 2nd layer. The same discussion works for any but finite number of layers. > Could you also please comment on situations where you would recommend not using deep homomorphism layers? Thanks. It's valuable to emphasise in limitation. In short, there are two cases we DON'T recommend using DHN. 1. Graphs are small so that O(n^k) is tractable. 2. Graphs are dense so that there are Theta(n^k) patterns. As you mentioned, clique enumeration (and many small-pattern enumerations) takes Theta(number-of-patterns) time, and the number of patterns can be Theta(n^k). Therefore, its worst-case complexity is comparable to k-WL type models. If this complexity is acceptable, there's no need to use the DHN model. This is the above Case 1. Our main target is large real-world graphs, which often exhibit the property that there are only O(n) patterns. This is a consequence of the sparsity of the graphs, which is usually analysed via degeneracy; see Case 3 in Section 4.2. In other words, if the given graph is dense, the enumeration takes too much time, making it impossible to apply. This is the above Case 2.	Summary: The authors propose a new neural network architecture for graph data, namely “Deep Homomorphism Network” (DHN). This is constructed as a stacking of “Graph Homomorphism layers”, which compute learnable, generalised homomorphism counts for a set of predefined input patterns. DHNs extend the following previous works: (i) the approach by NT and Maehara which precompute extended homomorphism counts on attributed graphs and use them to define hand-crafted features for downstream models such as kernel methods; (ii) the approach by Barceló et al. which propose to add rooted homomorphism counts for a bank of patterns as initial features for downstream message-passing neural networks. With respect to (i), DHNs are `deep`, and can distinguish graphs beyond the homomorphism-distinguishability of the predefined set of input patterns. In relation to (ii), DHNs can account for features, and fully subsume the approach of Barceló et al. which can be considered as a special DHN whereby deeper layers only consider a bank made up of the single node and single edge patterns. After expanding on preliminaries and model definitions, the authors interestingly show how the model fully capture msg-passing neural networks with a simple bank design, and then turn into discussing computational complexity, showing that, in some noteworthy settings, this grows linearly or polynomially. A section on expressive power follows. The authors characterise the expressive power of their model in terms of homomorphism indistinguishability w.r.t. a bank of patterns obtained by the "closure" of a "kernel bank" w.r.t. rooted graph product. Next, a series of precise results are obtained in terms of typical bank choices (cycles, cliques, connected graphs of a certain size), and in contrastive terms w.r.t. known expressive models. Finally, the authors practically experiment with their architecture on synthetic benchmarks for node disambiguation, in an attempt to empirically verify the discriminative power of their model. Results validate how this depends on the choice of the pattern bank and, importantly, the depth of the architecture. Strengths: - (S1) The present manuscript proposes a new, valid, interesting approach for expressive graph neural models. It builds on top of known works, but extend them in meaningful and concrete ways. - (S2) The proposed architecture is comprehensively studied in terms of its expressiveness, and its complexity is additionally discussed. The results on expressive power are precise and informative. - (S3) DHNs meaningfully subsume some known architectures, offering a new, interesting perspective on how a deep graph neural model can be structured beyond message-passing and combinatorial approaches. Weaknesses: - (W1) The presentation of the paper could be improved in some parts. For example, the authors extensively refer to the graph rooted product around Lemma 3.1, but this is only introduced in Section 5.1 (almost two pages later). Some other parts could be improved as well by either giving better intuitions or by providing additional visual support. This would help the reader especially in technical and theoretical parts. This can be true, for example, around Lemma 3.1 — why does it hold, is it trivial that one can decompose homomorphism $\pi$ into $\pi_0$ and $\pi_p$, how would the two look like on a visual example?. As another example, a figure explaining Example 5.1. or the hierarchies/relations in Corollary 5.6 would help. An illustrative aid could also support the comprehension of the formula in Eq. 3. - (W2) The authors do not experiment at all on real-world benchmarks. Why is it the case? What would the reader expect on those? One interesting aspect of of DHNs is that they can (easily) account for node features; this kind of real-world experimentation would help gathering a signal on how important this architectural feature is. - (W3) The authors do not position well enough their contribution in the broader landscape of GNN research beyond expressive power. What is the impact that we should expect from these new architectures? Will they find a strong real-world application in a certain setting? Should they rather considered as an approach of purely theoretical interest? Technical Quality: 4 Clarity: 3 Questions for Authors: - (Q1 - minor) Line 116: what are domain and co-domain for $f$? Can the authors specify? I think it would help towards a better comprehension of the following lines. - (Q2 - minor) Line 149: Why do the authors use the first-plural pronoun? Would it be more correct to use an impersonal “it is possible to show”? - (Q3) Theorem 3.3: Is it essentially a consequence of Lovász’s theorem? It would help if the authors referred (already in the main corpus) to previous works and their proof in the appendix. - (Q4) What is $\mu$ in Eqs. 6, 7? - (Q5) In Example 5.1, is the single vertex not needed? What is the intuition behind? - (Q6) The authors refer to the k-WL test as the “Folklore” type, right? If so, shouldn’t 2-GNNs and 2-IGNs be, instead, 3-GNNs and 3-IGNs (page 8) - (Q7) What is, concretely, the task solved in the experimental setting? Is discrimination cast as multi-way classification? Can the authors provide more details on that? Confidence: 4 Soundness: 4 Presentation: 3 Contribution: 4 Limitations: The authors mention limitations in the last paragraph of their manuscript (main paper). They could expand as per hinted in (W3), should other limitations emerge. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you very much for reading our manuscript carefully. We revise our manuscript to improve the clarify and readability by addressing your concern. Below, we reply to each comment/question. # Weakness (W1) The presentation of the paper could be improved > graph rooted product around Lemma 3.1 We'll re-organise Section 3 as follows: We move Lemma 3.1 to Section 5. We also elaborate Theorem 3.3 by adding a remark to clarify [W1] of Reviewer AtgF. > Some other parts could be improved as well by either giving better intuitions or by providing additional visual support. We will add illustrations to Lemma 3.1 and Hierarchy of Corollaries. The decomposition in Lemma 3.1 is straight-forward. For example, let's take the spoon graph $F$. The nodes are $\\{r, a, b, c\\}$, where $r$ is the root, $\\{r,a,b\\}$ forms a triangle, and $\\{b,c\\}$ forms an edge. Let $\pi$ be an arbitrary homomorphism from $F$. Then, $\pi$ is decomposed into $\pi_0$ that maps the triangle $\\{r,a,b\\}$ rooted at $r$ and $\pi_b$ that maps the single-edge graph $\\{b,c\\}$ rooted at $b$. They are the restrictions of $\pi$ on these subsets. As $F$ is obtained by attaching the edge to the triangle, this construction is one-to-one. We will add an illustration to show this construction, which may help to understand the decomposition at a glance. (W2) We understand your concern; based on our expressivity results, the reader should expect our model to perform better than less expressive baselines but not better than highly engineered SOTA models on real-world datasets. We report such results in the global rebuttal. (W3) This paper is on the line of studies of GNN expressive power, although we are motivated by practical large graph applications that involve subgraph feature engineering. In this sense, this paper itself doesn't immediately provide SOTA-level GNN architecture. The important missing part is how to design patterns and optimize the architecture accordingly. Although our model with basic patterns worked well on benchmark datasets in the manuscript and real-world datasets in the global rebuttal, we think the practical DHN architecture requires further work. We will mention this limitation in the updated manuscript. # Questions (Q1 - minor) This is a great point. For an invariant function $f$ (line 116), the domain of $f$ is the set of all graphs with features. The codomain is arbitrary, but usually $R^d$. On the other hand, for an equivariant function $f$ (line 119), the situation is very complicated. As in the invariant case, the domain is all graphs. However, the codomain depends on the input since for each $G$, $f(G)$ is indexed by $V(G)$ as $f(G)_u$. So, mathematically speaking, the codomain of an equivariant function is $\bigcup_G \mathbb{R}^{d \times V(G)}$. This "irregular codomain issue" makes analysis difficult. Hence, we are consistently working on rooted graphs in this paper (this is the idea in https://arxiv.org/abs/1910.03802). For rooted graphs, we have $f(G^r) \in R^d$ so its codomain is $R^d$ regardless of the input graph. This is explained in line 120--122, but we will elaborate to clarify the reasoning. Note that most existing GNN studies didn't have this issue because they worked on graphs of fixed number of nodes. However, in many applications we often compare the function values on two different size graphs $G$ and $G'$ (see also Response to [Q5] of Reviewer 2WwS). Hence, we decided to employ the rooted graph formulation. (Q2 - minor) We'll fix this. (Q3) Yes, this is an immediate consequence of Lovasz 1967's classical theorem (https://www.cs.elte.hu/~lovasz/scans/opstruct.pdf), which says that any relational structure (not limited to graph) is uniquely (up to isomorphism) identified by the homomorphism numbers. We just need to confirm that our generalised homomorphism can count the homomorphisms as graphs-with-features, but this is also straight-forward. This is written in the proof in Appendix, but we will add the idea to the main body of the paper. See also Response to [W1] of Reviewer AtgF. (Q4) Thank you for pointing out the imprecise presentation. $\mu$ is a set of functions defined on nodes, $\mu = \\{ \mu_p: R^{d_i} \to R^{d_o} : p \in V(F) \\}$, transfers node features, which are the parameters of the model. In this specific case, the precise definition is in the Response to [W2] of Reviewer AtgF. We will put these precise definitions to avoid confusion in the manuscript. (Q5) The singleton is included by the definition of the closure (0-th power is the singleton); see line 237. (Q6) No, we meant k-WL original version. (Q7) Indeed, in our experiments, distinguishing isomorphism classes is cast as multi-class graph classification and experimental settings for each synthetic dataset followed the literature. Each input graph belongs to an isomorphism class, and the task is to detect these classes in the test set. For example, SR25 is a set of strongly regular and co-spectral graphs belonging to 15 different isomorphism classes; the task is to correctly detect these isomorphism classes. --- Rebuttal Comment 1.1: Comment: I would like to thank the authors for their response, which I have positively acknowledged. I personally find the results in the general response interesting, and the comments and discussions wrt SOTA methods worth sharing with the rest of the community – I think the manuscript would benefit from their inclusion. > No, we meant k-WL original version. I apologise, but I am afraid I am not fully aligned on the k-WL issue. In the paper you have a footnote stating: > We follow [11]’s definition, which is also called the folklore Weisfeiler–Lehman test. So, it seems like k-WL refers to the folkore version? --- Reply to Comment 1.1.1: Comment: We apologise for the previous response; we saw wrong the question. You are correct. We double-checked the k-GNN and k-IGN papers, and confirmed that they referred k to the original k instead of the folklore version, which led to our off-by-one error. k-GNN: https://arxiv.org/pdf/1810.02244 > We note here that the above variant is not equal to the folklore variant ... k-IGN: https://arxiv.org/pdf/2201.10129 > 2-IGN = GIN We'll update them to 3-GNN and 3-IGN accordingly. Thank you very much.	null	null	Rebuttal 1: Rebuttal: First, we thank all three reviewers for their time and detailed comments on our work. Given the submission volume in our community, we are truly grateful that all three reviewers have clearly given our manuscript deep consideration. In this global rebuttal, we would like to address a common concern from all reviewers regarding real-world experimental results. Experimental result on ENZYMES and PROTEINS. We run some representative DHN models on TUDataset's ENZYMES and PROTEINS datasets. These bioinformatic datasets are cast as graph classification problems. ENZYMES consists of 600 graphs and 6 classes; each node has 3 tags and 18 features. PROTEINS dataset consists of 1113 graphs belonging to 2 classes; each node has 3 tags and 1 feature. We report the classification accuracy using a stratified 10-fold cross-validation method similar to the literature. We will update Table 1 in the manuscript as follows. \| Model \| #params \| CSL \| EXP \| SR25 \| ENZYMES \| PROTEINS \| \|---------------------\|---------\|-----\|-----\|------\|--------------\|-------------\| \| MPNN (4 layers) \| 27k \| 0 \| 0 \| 0 \| 54.6 ± 4.5 \| 72.0 ± 4.0 \| \| PPGN (4 layers) \| 96k \| 100 \| 100 \| 100 \| 58.2 ± 5.7 \| 77.2 ± 3.7 \| \| DHN (C2:4) \| 5k \| 100 \| 50 \| 0 \| 64.3 ± 5.5 \| 76.5 ± 3.0 \| \| DHN (C2:10) \| 27k \| 100 \| 98 \| 0 \| 58.0 ± 5.3 \| 78.5 ± 2.5 \| \| DHN (C2:4, C2) \| 8k \| 100 \| 50 \| 53 \| 64.4 ± 5.9 \| 77.1 ± 2.8 \| \| DHN (C2K3:5, C2K3:5) \| 36k \| 100 \| 100 \| 100 \| 57.5 ± 6.6 \| 77.4 ± 3.4 \| Note that the SOTA result for ENZYMES is around 78%, and for PROTEINS, it is around 84%. However, we do not intend to compete with the SOTA results in this work. The result above emphasizes the necessity of specific considerations for each real-world dataset. The expressivity experiments (CSL, EXP, SR25) clearly distinguish each architecture; however, real-world dataset results are often comparable among different architectures. Achieving SOTA might be attributed to engineering efforts rather than novel model architecture. The lack of real-world benchmarks is indeed a shortcoming of our current manuscript. Our work aims to focus on the method's theoretical foundation and novelty, so we did not put much effort into experimentation except for the synthetic expressivity datasets. While our model performed well compared to basic baselines, it is still quite far from SOTA result due to the lack of engineering. For example, the SOTA model for ENZYMES (DSGCN-allfeat) computes the spectrum for each graph, which is highly engineered toward this particular dataset. It is clear that there is a gap between our theoretical proof of concept model and a truly applicable one, and we think there is potential. Still, more engineering work is needed before we can bridge the theory-practice gap. That being said, based on the reviewers' comments, we understand that readers have some expectations for real-world benchmarks, so we will include some results for a subset of the graph classification TUDataset in the final version of the manuscript.	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
TopoFR: A Closer Look at Topology Alignment on Face Recognition	Accept (poster)	Summary: This paper proposes a novel framework named TopoFR for face recognition (FR). The authors first discover that existing FR models struggle to effectively preserve the structure information hidden in FR dataset, and provide three specific observations: (i) the topological structure in the input pixel space becomes increasingly complex as the amount of data increases; (ii) the structure difference between pixel space and latent feature space increases as the amount of data increases; (iii) the structure difference between two spaces decreases as the network architecture becomes deeper. Considering that FR training datasets are typically massive and contain rich structure information, this paper aims to leverage these intrinsic structure information to enhance FR model's generalization performance. However, the authors notice that directly aligning the structures between latent space and input pixel space will result in inferior performance which might be overfitting. To solve this issue, TopoFR introduces a PTSA strategy to encode the structure information of input pixel space into latent space. Specifically, PTSA utilizes RSP to perturb the latent space structure and employs ISA to match the topological structures of two spaces, effectively mitigating structure discrepancy. Moreover, a novel hard sample mining strategy SDE is proposed to identify hard samples and minimize their impact on the latent space structure. Extensive experiments on various FR benchmarks demonstrate that TopoFR outperforms state-of-the-art methods. In addition, detailed ablation studies and analysis are conducted to provide a comprehensive understanding of the proposed method. Strengths: 1) This paper is clearly written and well-motivated. The overall readability is high. Despite the significant progress made by existing FR models, these models rely on explicitly constraining inter-class and intra-class relationships. Unlike these existing works, this paper seeks to leverage the structure information in datasets to improve the FR model's generalization performance, which is a highly innovative attempt and can provide valuable insights for future research. Furthermore, it is novel to address the input-latent space structure degradation problem. 2) It is a very interesting idea to employ the GUM statistical distribution in designing the hard sample mining strategy SDE from the outliers detection perspective. The structure damage score SDS is similar to the area of noise labels, which is not well investigated in FR. 3) Experiments are good and the various benchmark results have produced state-of-the-art performance. Moreover, the model's ranking in the MFR competition shows its strong generalization performance. Weaknesses: There are some concerns that I would like the authors to address in order to enhance the overall comprehensiveness of the paper. 1) It is not clear if this method can be applied to recent proposed loss, e.g., AdaFace [1]. I recommend adding experiments to further validate the universality of the proposed method. 2) [Minor Comments]: Although the authors have discussed the model’s training and inference efficiency in Appendix, I suggest including comparisons of the model's GFLOPs. This would provide a more intuitive representation of the model’s computational cost. Ref[1] Kim M, Jain A K, Liu X. Adaface: Quality adaptive margin for face recognition[C]//Proceedings of the IEEE/CVF conference on computer vision and pattern recognition. 2022: 18750-18759. Technical Quality: 4 Clarity: 3 Questions for Authors: 1) EM algorithm is sensitive to the initialization of its parameters values. In Eq.(7), how to determine the initial values of parameters $\pi$, $\Sigma$, and $\Omega$ in the GUM statistical distribution? 2) In Eq.(2), does the ISA function loss $\mathcal{L}_{sa}$ guide the optimization of the entire network or only specific components of the network? 3) What distance criterion is used to construct the topological structure space of the data in Vietoris-Rips complex during model forward propagation? 4) In addition, in topological data analysis, different dimensions of topological holes analyze the underlying data structure information at different levels. In ISA loss, what dimension of topological holes does the persistent homology (PH) capture and analyze? 5) I am very curious about the reasons why the structure differences between the input pixel and latent spaces decrease as the network becomes deeper. Confidence: 4 Soundness: 4 Presentation: 3 Contribution: 3 Limitations: It's not discussed whether this method can be applied in other related FR methods, e.g. AdaFace. I suggest to further discuss this to increase the overall quality of this paper. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the Reviewer GA4X for the careful reading of the manuscript and the related comments, which are helpful to improve our paper. Our detailed point-by-point responses are provided below. W1: It is not clear if this method can be applied to recent proposed loss AdaFace. A1: According to your suggestion, we conduct additional experiments on AdaFace model to further validate the universality of our method, as shown in the following Table R1. \ In comparison to the baseline model ArcFace, AdaFace is a highly advanced FR model. Consequently, integrating our method with AdaFace can notably enhance the model's verification accuracy across multiple benchmarks. These improved results validate the universality of our method. Table R1: Verification performance (%) on IJB-C, IJB-B, CPLFW and CALFW. \| Training Data \| Method \| IJB-C(1e-4) \| IJB-B(1e-4) \| CPLFW \| CALFW \| \| ------ \| ------ \| ------ \| ------ \| ------ \| ------ \| \| \| R50 AdaFace \| 96.27 \| 94.42 \| 92.83 \| 96.07 \| \| MS1MV2 \| R50 AdaFace + PTSA \| 96.51 \| 95.25 \| 93.36 \| 96.28 \| \| \| R50 AdaFace + PTSA + SDE \| 96.64 \| 95.38 \| 93.50 \| 96.39 \| W2: Includes comparison of the model's GFLOPs. A2: Based on your valuable advice, we provide a comparison of model's GFLOPs, as shown in the following Table R2. As can be seen, our TopoFR has the same GFLOPs as the vanilla ArcFace model (Baseline) and some existing popular FR models (e.g., MagFace, AdaFace and CurricularFace), since we adopt the same network architecture. Table R2: Comparison of Model's GFLOPs. \| Method \| GFLOPs \| \| ------ \| ------ \| \| R50 ArcFace \| 6.3 \| \| R50 MagFace \| 6.3 \| \| R50 AdaFace \| 6.3 \| \| R50 TopoFR \| 6.3 \| \| R100 ArcFace \| 12.1 \| \| R100 MagFace \| 12.1 \| \| R100 AdaFace \| 12.1 \| \| R100 CurricularFace \| 12.1 \| \| R100 TopoFR \| 12.1 \| \| R200 ArcFace \| 23.4 \| \| R200 AdaFace \| 23.4 \| \| R200 TopoFR \| 23.4 \| Q1: In Eq.(7), how to determine the initial values of parameters $\phi$, $\Sigma$, and $\Omega$ in the GUM statistical distribution ? A3: We refer to prior work [S4] to set the initial values for the EM algorithm used in our GUM parameter estimation process. Ref.[S4] Using gaussian-uniform mixture models for robust time-interval measurement. TIM 2015. Q2: In Eq.(2), does the ISA function loss $\mathcal{L}_{sa}$ guide the optimization of the entire network or only specific components of the network ? A4: In fact, the ISA loss $\mathcal{L}_{sa}$ is only responsible for optimizing the parameters of the feature extractor $\mathcal{F}$. As stated in Section 4.1 (lines 140-146), since computing the pairwise distance matrices $\mathcal{M}^{\mathcal{X}}$ and $ \mathcal{M}^{\mathcal{\widetilde{Z}}}$ for Vietoris-Rips (VR) complexes $ \mathcal{V}\_\{\rho}(\mathcal{X})$ and $ \mathcal{V}\_\{\rho}(\mathcal{\widetilde{Z}})$ is a differentiable process, the ISA loss $\mathcal{L}_{sa}$ will perform gradient back-propagation through the two distance matrices to optimize the parameters of the feature extractor $\mathcal{F}$. Q3: What distance criterion is used to construct the topological structure space of the data in Vietoris-Rips complex during model forward propagation ? A5: As stated in Section 3 (lines 95-104), we utilize the Euclidean distance as the distance criterion to construct the Vietoris-Rips (VR) complex $\mathcal{V}_{\rho}$ and analyze the topological structure of the underlying space. Q4: In ISA loss, what dimension of topological holes does the persistent homology (PH) capture and analyze ? A6: As described in Section A.1 of the Appendix (lines 547-550), we preserve and analyze 0-dimension topological holes $H_{0}$ (e.g., connected components) in our ISA loss $\mathcal{L}_{sa}$. Because some preliminary experiments have shown that using the 1-dimension or higher-dimension topological holes only increases model’s training time without bringing clear performance gains. Q5: I am very curious about the reasons why the structure differences between the input pixel and latent spaces decrease as the network becomes deeper. A7: This is a very interesting question. When we obtained this finding in the experiment, we also contemplated its underlying reasons. \ In our opinion, the deep neural network is actually a complex function mapping process, and each network layer can be regarded as a sub-function in this composite function. If the neural network is deeper, the mapping of each network layer will become smoother, and the data will lose less information during the mapping process. On the contrary, if the neural network is shallower, the mapping of each network layer will become sharper, and some intrinsic information of the data, such as structure information, is easily destroyed during the mapping process. Similar conclusions can also be found in the flow-based models [S5]. Ref. [S5] Variational inference with normalizing flows. ICML 2015. --- Rebuttal Comment 1.1: Comment: Thanks to the authors for the comprehensive response to my concerns. I have carefully read all the reviews and responses. The authors have addressed all of my concerns with clear explanations and additional experiment results, especially about the experiment of AdaFace + PTSA + SDE, making the benefits and novelty of the proposed method more convincing. I have raised the rating to reflect the comments. --- Rebuttal 2: Title: Response to Reviewer GA4X Comment: Dear Reviewer GA4X: Thank you for the positive feedback. We appreciate your efforts in reviewing our work. We will reflect your suggestions in the revised version to enable it to be a high-quality paper. Best Regards, Authors of 505.	Summary: This paper uses the topological structure alignment in face recognition tasks, and it proposes a Perturbation-guided Topological Structure Alignment (PTSA) strategy to align the topology of input image space and latent space. In this paper, Persistent Homology(PH) is used to verify that the complexity of input space topology will increase rapidly when there are many face images. In addition, this paper also puts forward some ideas and implementation of data mining. Strengths: + The paper adopts topological structure alignment in face recognition tasks. + A new hard sample mining strategy SDE is proposed to reduce the adverse effects of hard samples on potential spatial structure. + Experiments are sufficient, and the experimental results prove that the model has excellent performance. Weaknesses: - Formula 7 may require a more specific explanation. - The meaning of H0 in Figure 1, along with the distribution style and other differences, is best explained. - The hard sample mining strategy SDE in this paper seems to have little correlation with Perturbation-guided Topological Structure Alignment. Technical Quality: 3 Clarity: 3 Questions for Authors: - Is this topological alignment strategy only for face recognition tasks? - Is the process of alignment computationally intensive? Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: Yes Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We appreciate Reviewer 68Et for the thorough review of the paper and valuable comments that will aid in enhancing our paper. W1: Formula 7 may require a more specific explanation. A1: Based on your valuable suggestion, we provide an explanation of how to estimate the parameter set $\varphi = \\left \\{ \pi, \Sigma, \Omega \\right \\}$ of the Gaussian-uniform mixture (GUM) model using EM algorithm. First, we transform the original GUM model (Eq.(3)) into a more easily solvable statistical distribution (Eq.(6)) using the Bernoulli distribution-based sampling method. In this way, the maximum likelihood model of Eq.(6) is formulated as: $\max\limits\_\{\pi,\Sigma,\Omega} \displaystyle\prod_{i=1}^{n}p\left(\widehat{E}(\widetilde{g}\_\{i})\|\widetilde{x}\_\{i}\right )$. Then, we can use the EM algorithm to solve the maximum likelihood problem in order to estimate the parameter set $\varphi$ of GUM. The specific iterative updating formulas of EM algorithm are shown in Eq.(7). Specially, at each iteration, EM alternates between evaluating the expected log-likelihood (E-step) and updating the parameter set $\varphi$ (M-step). In Eq.(7), the E-step aims to evaluate the posterior probability $h_{\varphi}^{(t+1)}$ of an sample $\widetilde{x}\_\{i}$ to be hard sample using the iterative formula $h\_\{\varphi}^{(t+1)}(\widetilde{x}\_\{i})$, where $(t+1)$ denotes the EM iteration index. The M-step updates the parameter set $\varphi$ using the iterative formulas $\pi^{(t+1)}$, $\Sigma^{(t+1)}$ and $\Omega^{(t+1)}$, where $\eta_{1}$ and $\eta_{1}$ are the first-order and second-order centered data moments, respectively. W2: The meaning of H0 in Figure 1, along with the distribution style and other differences, is best explained. A2: As described in Sec.3 (lines 105-109), homology is an algebraic structure that analyzes the topological features of a simplicial complex in different dimension $j$, including connected components ($H_{0}$), cycles ($H_{1}$), voids ($H_{2}$), and higher-dimensional topological features ($H_{j},j\geq 3$). By tracking the changes in topological features $H_{j}$ across different dimensions $j$ as the scale parameter $\rho$ increases, we can obtain the multi-scale topological information of the underlying space. Thus, $H_{0}$ is the $0$-th dimension homology in the persistence diagram, which captures the $0$-th dimension topological feature of the underlying space. Notably, low-dimension topological features (e.g., $H_{0}$) can roughly reflect the topological structure of the space, while high-dimension topological features (e.g., $H_{3}$, $H_{4}$) aim to capture the intricate details of the space's topological structure. Moreover, in topology theory, an increase in the number of high-dimensional topological features within a space corresponds to a more complex topological structure. As illustrated in Figs 1(a)-1(d), as the amount of face data increases, the persistence diagram contains more and more high-dimensional homology (e.g., $H_{3}$ and $H_{4}$), indicating that the input space contains an increasing number of high-dimensional topological features. Thus, this phenomenon shows that the topological structure of the input space is becoming more and more complex. W3: The hard sample mining strategy SDE seems to have little correlation with Perturbation-guided Topological Structure Alignment (PTSA). A3: As stated in Sec.1, the large-scale face dataset contains rich topological structure information. However, we find that these structure information is not effectively preserved in the latent space of existing FR models, as verified in Fig 2 (lines 31-43). Existing studies on FR have overlooked this issue, which limits the generalization of FR models. To solve this problem, we propose the PTSA strategy. Specially, our PTSA strategy directly extracts the topological structure information in the face dataset from the input pixel space and then encodes these powerful structure information into the latent space by aligning the topological structures of the input and latent spaces. However, as stated in Sec 4.2 (lines 170-177), we experimentally find that some low-quality samples (e.g., hard samples) can easily be encoded to abnormal positions in the latent space during training, which disrupts the latent space’s topological structure and further hinder the alignment of topological structures. Thus, we propose the SDE strategy to identify hard samples with significant structure damage and effectively mitigate their adverse impact on the latent space’s topological structure by guiding them back to their appropriate positions during optimization. Hence, our PTSA strategy and SDE strategy are complementary to each other. Additionally, the ablation study in Table 3 also validate the complementarity of two strategies. Q1: Is this topological alignment strategy only for face recognition (FR) tasks? A4: In addition to FR systems, the proposed PTSA strategy can also be applied to Image Retrieval and Large Language Model (LLM), since these tasks all require large-scale datasets for training.\ Existing works on Image Retrieval and LLM seem to neglect the utilization of topological structure information hidden in large-scale datasets. Thus, we believe that applying the topological structure alignment technique to these tasks can effectively improve the representation power of features and the generalization ability of models. Q2: Is the process of alignment computationally intensive? A5: In fact, we have provided an analysis of the model training time in our manuscript (lines 637-650). Please refer to Table 13 in the Appendix. For example, compared to the R50 ArcFace (Baseline), our R50 ArcFace + PTSA requires about 2.24 seconds more training time per 100 steps. These results indicate that introducing PTSA strategy leads to significant performance gains with only a small increase in training time, which is acceptable. --- Rebuttal Comment 1.1: Comment: Thanks for your responses. I have changed my rating to Weak Accept. --- Reply to Comment 1.1.1: Title: Response to Reviewer 68Et Comment: Dear Reviewer 68Et: We thank your response and appreciation of our work and rebuttal. We will make sure to incorporate the discussions into our revision to enable it to be a high-quality paper. Best Regards, Authors of 505.	Summary: The paper introduces a new method to improve the topological structures of facial features in the latent space. By exploring the topological structure alignment in face recognition, the authors propose a new structural alignment strategy PTSA to align the structures of origin input space and feature space. The experimental results on various benchmarks have verified the effectiveness of the proposed method. Strengths: - Based on the persistent homology method, the paper provides a comprehensive analysis of the correlation between the number of data samples and topological structures in the latent space. - The proposed modules in the method, Perturbation-guided Topological Structure Alignment and Structure Damage Estimation, are well motivated and seem to improve the topological structure of facial features. - The authors achieve competitive results on the standard benchmarks, especially ranking #2 on the MFR-Ongoing leaderboard. Weaknesses: - While I acknowledge the competitive results of the proposed approach, the performance improvement of the method in several benchmarks remain minor. For example, the results of the method on IJB-B and IJB-C benchmarks are minor compared to prior methods on the same backbone. - The technical approach seems to be an incremental one. In particular, the authors adopt the ArcFace framework and introduce two additional modules on top of the ArcFace method, including Perturbation-guided Topological Structure Alignment and Structure Damage Estimation. The first module is basically a metric to compare the feature distribution between feature space and original input space, similar to the Gromov-Wasserstein distance. However, the ArcFace loss itself is also an efficient approach to learning the facial feature representation in the latent space. I am not sure whether the Perturbation-guided Topological Structure Alignment significantly improves the structure information or not. - Why the authors claim the proposed approach improve the topological structure of the feature space, I could not see this point has been verified via either experimental results or visualization. It would be better if the authors visualize the feature distributions of faces on the latent space (via PCA or T-SNE). - The author claims that "to the best of our knowledge, how to effectively mine the potential structure information in large-scale face data has not investigated". I do not agree with this claim since the other methods, e.g., ArcFace, SphereFace, CoseFace, etc, are also considered as approaches to improve the structures/distributions of facial features in the deep latent space via the well design loss functions. I think the statements made by the authors are over-claimed. Technical Quality: 3 Clarity: 3 Questions for Authors: Please refer to my weakness section. In addition, I have another question related to the Perturbation-guided Topological Structure Alignment. Are the persistence diagrams and persistence pairings computation in the ISA loss differentiable for backpropagation? Can the authors detail this computational process? Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The authors have discussed their limitations in the appendix. However, it will be better if the authors discuss the broader impact of the proposed method. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We sincerely appreciate Reviewer SWuk for the careful reading and the insightful comments, which are helpful in improving our paper. Our detailed point-by-point responses are provided below. W1: The results of the method on IJB-B and IJB-C are minor. A1: Due to the characters limit, we will respond to you in the global rebuttal area. W2: The technical approach seems to be an incremental one. The PTSA strategy is similar to the Gromov-Wasserstein distance. A2: Due to the characters limit, we will respond to you in the global rebuttal area. W3: I am not sure whether the PTSA strategy significantly improves the structure information or not. Why the authors claim the proposed approach improve the topological structure of the feature space? It would be better to visualize the feature distributions. A3: As shown in Figures 2(a) and 2(b), we experimentally find that there are significant topological structure discrepancy between the input space and the latent space of existing FR models. This observation indicates that the topological structure information of the large-scale dataset is not effectively preserved in the latent space and may even be destroyed. Therefore, we propose the PTSA strategy to align the topological structure of two spaces. The visualization results in Figs 2(d), 5 and 7 have validated that with the help of our PTSA strategy, the topological structure discrepancy between two spaces have significantly decreased. In fact, the results in Figs 2(d), 5 and 7 can quantify topological structure discrepancy more objectively and accurately than t-SNE. Moreover, the ablation study results in Tab 8 of Appendix have also validated that the addition of PTSA can implicitly enhance the intra-class compactness and inter-class separability of facial features. t-SNE: Based on your insightful advice, we sample 10 identities face images from MS1MV2 dataset and utilize the t-SNE to visualize the facial features learned by ArcFace and ArcFace + PTSA. The results are shown in the Figure 1 of the global response PDF file. We can observe that using the proposed PTSA strategy to reduce the topological structure discrepancy between two spaces can greatly enhance the discriminative power of the learned facial features (e.g., with better inter-class separability and intra-class compactness), thereby boosting the FR model's generalization performance. The t-SNE results are consistent with our aforementioned experimental results. W4: Other methods are also considered as approaches to improve facial features distributions in latent space via well design loss functions. A4: Existing FR methods, such as ArcFace, CosFace, SphereFace and CurricularFace, tended to design some margin-based softmax loss functions to explicitly encourage facial features with better inter-class separability and intra-class compactness in feature space. However, the experimental results in Figs 2(a) and 2(b) have shown that the latent space's topological structure of existing models may be destroyed, which limits FR model's generalization. Thus, unlike these existing FR works that directly force features to become more discriminative in the feature space, our PTSA strategy aims to leverage the intrinsic topological structure information in training dataset (i.e.,from the input pixel space) to guide the construction of the latent space's topological structure and the learning of facial features. Detailed experiments have indicated that our method can effectively reduce topological structure discrepancy and boost model's generalization. In general, leveraging the topological structure information in dataset to enhance the model's generalization is a different research direction from designing the margin-based softmax loss functions to improve facial features distribution in the deep feature space. Q1: Are the persistence diagrams (PDs) and persistence pairings (PPs) computation in ISA loss differentiable for backpropagation? Detail this computational process. A5: Yes, the computation of PDs and PPs in ISA loss is differentiable for back-propagation. 1) Detailed computation process: Persistent homology (PH) is a method used to analyze the topological structure information of complex point clouds (e.g., mini-batch data). In the original input space, we first flatten the mini-batch face images into vector features to model point clouds $\mathcal{X}$, and then calculate their pairwise distance matrix to construct the Vietoris-Rips (VR) complex $\mathcal{V}\_\{\rho}(\mathcal{X})$. Similarly, we can construct another VR complex $\mathcal{V}\_\{\rho}(\widetilde{\mathcal{Z}})$ for the perturbed latent features $\widetilde{\mathcal{Z}}$. After that, we use the Ripser package [S3] to implement the PH to extract topological features from two VR complexes, and obtain their corresponding PDs and PPs. The discrepancy between the input space's PD and latent space's PD represents the topological structure discrepancy of two spaces. However, directly calculating the distance between two PDs is computationally expensive. We thus turn to utilize PPs to estimate the discrepancy between two PDs. PPs contain indices of simplices that are related to the birth and death of the topological feature. In this case, we can calculate the discrepancy between two PDs by utilizing PPs to retrieve the differences between two pairwise distance matrices. Ref.[S3] Ripser: Efficient Computation of Vietoris–Rips Persistence Barcodes. 2021. 2) Optimization of model params w.r.t $\mathcal{L}_{sa}$: Please refer to the 6th answer A4 to Reviewer GA4X. Q2: Discuss the broader impact. A6: Due to the characters limit, we will respond to you in the global rebuttal area. --- Rebuttal Comment 1.1: Title: Feedback to Author Rebuttal Comment: Thank you very much for your rebuttal. It has addressed my concerns. I hope you can update your answers in the revised paper. It will help to improve the paper quality. I decided to increase my score to 6. --- Reply to Comment 1.1.1: Title: Response to Reviewer SWuk Comment: Dear Reviewer SWuk: Thank you for your recognition of our work. We appreciate your time and efforts in reviewing our work. We will incorporate your valuable suggestions into the revised version to ensure that it becomes a high-quality paper. Best Regards, Authors of 505.	null	null	Rebuttal 1: Rebuttal: Dear Reviewer SWuk, here is our response to some of the concerns you raised. W1: The results of the method on IJB-B and IJB-C are minor. A1: (1) Notably, when using a shallow backbone such as ResNet-50, our method showcases remarkable performance gains on IJB-B, IJB-C and other benchmarks, as shown in Tabs 2 and 4, compared to the leading competitors. This is because the shallow backbone has larger topological structure discrepancy between the input and latent spaces (as verified in Figure 2(b)), and our method can effectively mitigate the structure discrepancy and boost the model's generalization performance. Furthermore, when using extremely large-scale datasets such as Glint360K and WebFace42M, our method can achieve more significant accuracy improvements, as shown in Tabs 1 and 2. Since larger-scale dataset contains richer topological structure information, which more clearly indicates the effectiveness of our method in using topological structure information to boost model's generalization. (2) On some low-quality (e.g., contains many blurry face images) and challenging FR benchmarks, such as MFR-Ongoing, MegaFace, MegaFace-Refined, TinyFace, CPLFW and CALFW, our method can achieve clear performance gains compared to the competitors, as shown in Tabs 4, 5 and 6 of the Appendix. Additionally, as shown in Tab 7 of Appendix, our method can obtain a significant improvement in performance when combined with the lightweight face recognition (FR) network backbone MobileFaceNet. (3) The accuracy of existing FR methods on the IJB-B and IJB-C benchmarks is nearing saturation, as these two datasets contain many high-quality face images. Our proposed method is still able to achieve performance gains, surpassing the ResNet-based SOTA competitor AdaFace [S1] and the ViT-based SOTA competitor TransFace [S2]. Notably, in FR task, a performance improvement of approximately 0.2% to 0.3% on the IJB-C (1e-4) and IJB-B (1e-4) benchmarks is quite substantial. While our R200 TopoFR trained with Glint360K achieves maximum performance gains of 0.49% on IJB-C (1e-4) and 0.47% on IJB-B (1e-4) compared to the SOTA method AdaFace, respectively. In general, our method achieves SOTA performance on various benchmarks using different backbones, implying its strong generalization ability. Ref.[S1] Adaface: Quality adaptive margin for face recognition. CVPR 2022.\ Ref.[S2] Transface: Calibrating transformer training for face recognition from a data-centric perspective. ICCV 2023. W2: The technical approach seems to be an incremental one. The PTSA strategy is similar to the Gromov-Wasserstein (GW) distance. A2: As mentioned in Sec.1 (lines 31-43), we are the first to discover that existing FR models struggle to effectively preserve the topological structure of face data in the latent space, and we provide some novel observations (as depicted in Figs 1 and 2). However, existing FR studies have overlooked this issue, which severely limits the models' generalization. Based on this motivation, we are the first to propose aligning the topological structures of two spaces to improve the model's generalization performance. A series of experimental results have also shown that the topological structure information in the dataset is quite crucial for FR task. Thus, our method is not an incremental work, but a novel exploration. Moreover, the Gromov-Wasserstein (GW) distance metric is different from the topological structure distance metric. Specially, the topological structure models the relationships and connectivity between data by analyzing the evolution progress of the simplicial complex constructed from the data in high-dimensional metric space. While the GW distance is often used to align the mainfold structures of two feature distributions. Mainfold structure primarily models the similarity between data based on the similarity matrix, which is a different concept from topological structure. Thus, our PTSA strategy does not simply match feature distributions, but rather aligns the topological structures of the input and latent spaces in the high-dimensional metric space. Q2: It will be better if the authors discuss the broader impact of the proposed method. A6: Thanks for your valuable advice. It would be good to mention that the utilization of face images do not have any privacy concern given the datasets have proper license and users consent to distribute biometric data for research purpose. We address the well-defined face recognition task and conduct experiments on publicly available face datasets. Therefore, the propose method does not involve sensitive attributes and we do not notice any negative societal issues. t-SNE Visualization: The t-SNE visualization results mentioned in A3 are shown in the Figure 1 of the global response PDF file. To all Reviewers: If you have additional concerns, please let us know and we will do our best to address them. We appreciate your time and efforts in reviewing our work. Pdf: /pdf/3fd8ff7456c8f2c5e381a610a985196513eae3f2.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Accelerating Blockwise Parallel Language Models with Draft Refinement	Accept (poster)	Summary: The paper analyzes the block drafts generated by multiple independent prediction heads of blockwise parallel language models and observes three key features: consecutive repetitions, confidence of different heads, and efficiency gap with oracle top-k block. To address these issues, the paper proposes two algorithms to leverage the top-k predictions at each head: local rescoring via (small) neural LMs and global rescoring via n-gram LMs with multi-drafts. Experimental results show that the proposed two algorithms can improve block efficiency. Strengths: 1. The paper identifies a weakness in the existing blockwise parallel decoding algorithms: the predictions are made independently. The paper proposes two algorithms: local rescoring via neural models and global n-gram rescoring to address the weakness. 2. The paper analyzes the block drafts and gives several observations. The observation of strong correlation between the index of the largest head such that the average entropy of each head increases monotonically to that point and block efficiency is especially interesting. Weaknesses: 1. The experiments are only conducted on a 1.5B LM pretrained on 200B tokens of C4, without the alignment stage. This is far from the common practice in current LLMs. The authors should consider adding results on more open LLMs with different sizes. 2. The medusa paper [1] already proposes using top-k predictions for different heads. The contribution of the paper mainly focuses on the two rescoring algorithms. However, the algorithm of local rescoring with a small LM is very similar to speculative decoding with a small LM [2]. The contribution of the global rescoring algorithm with n-gram models is not sufficient for a NeurIPS paper. [1] Medusa: Simple LLM Inference Acceleration Framework with Multiple Decoding Heads. http://arxiv.org/abs/2401.10774 [2] Fast Inference from Transformers via Speculative Decoding. https://arxiv.org/abs/2211.17192 Technical Quality: 2 Clarity: 3 Questions for Authors: 1. It is not clear how the observations in Section 6.2 and 6.3 contribute to the design of the algorithms. 2. The neural draft is generated based on the logits of the original prediction, not the rescored ones. If the rescored top-1 token is different the original top-1 token, the following rescoring will be incorrect. Confidence: 4 Soundness: 2 Presentation: 3 Contribution: 2 Limitations: The authors have adequately addressed the limitations Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your valuable feedback in helping refine our work. - Note: Before reading further, we kindly ask you to check the `Author Rebuttal by Authors` and `the attached PDF` for detailed explanations and additional results. # W1. Limited Experimental Scope We acknowledge the limitation of our initial experiments. To address this, we include additional results on more open LLMs with different sizes and more datasets. Specifically, we conducted experiments with Vicuna `7B` and `13B` with `4 block draft heads` in the `attached PDF`. These new results also show that our approach scales effectively and consistently improves performance across different model sizes, achieving an additional speedup of over `~20%` and `~300% speedup` relative to vanilla decoding. Here, the blockwise parallel LMs extended from Vicuna `7B` and `13B` are trained with alignment stages. # W2. Difference with Existing Work We believe our contributions, including rescoring methods as well as findings, are both valuable and innovative compared to existing works. Here’s why: ### Medusa - Similarity: Both approaches explore potential gains from TopK predictions of blockwise parallel LM heads. - Technical Differences: - Medusa searches for the best candidate in block drafts without altering the original logits - Our method involves rescoring the block drafts to obtain the best candidate. - Exploratory Differences - Medusa does not explicitly address the reasons behind its decoding method. - Our work is the first to explicitly address issues such as (1) consecutive repetition, (2) confidence of different heads, and (3) top-k oracle block efficiency. - Our contributions are orthogonal and different from Medusa, and our method integrated with Medusa shows even better results, detailed in the `attached PDF`. ### Speculative Decoding First of all, BPD (presented in 2018) is a predecessor and an instance of speculative decoding. - Similarity: Both approaches use small language models for efficient LLM inference. - Technical Differences - Speculative decoding uses a small drafter to predict the next multiple tokens - Our method uses the small drafter (for both local and global rescoring) to rescore the logits of block drafts with a top-k mask, which are then used for speculative inference. - TL;DR - Speculative decoding uses an independent module for drafting - Our method corrects the drafts from a dependent speculative module (e.g., BPD and Medusa), which is totally different from the use of the small LM in speculative decoding. ### W2-2. Regarding the Contribution of the Global Rescoring with N-gram Models We believe the global rescoring with n-gram models is valuable and innovative. Here’s why: 1. Efficiency: The n-gram rescoring is highly efficient, taking only `1.6 ms per lattice` via OpenFST, making it practical for real-time applications (`Table12` & `Table13` in `Appendix H`). 2. Effectiveness: Despite being a classical approach, n-gram models remain effective. Our results show significant improvements in block efficiency and speedup when integrated with BPD. The assertion that n-gram models lack novelty is not supported by our evidence. Instead, our results clearly demonstrate their practical value and effectiveness. # Q1. Clarity on How Observations Contributes to Algorithm Design - Section 6.2 (Confidence across multiple heads): This section examines the confidence levels across different prediction heads in BPD, providing insights into how well the parallel heads are trained. These observations, while not directly informing the current design of our rescoring algorithm, are included to align with our paper's goal of "Exploring and Improving Multi-Token Prediction (block draft)." They suggest potential future improvements, such as using variable interpolation weights based on head confidence levels. We will refine the manuscript to clarify this point. - Section 6.3 (Top-k oracle block efficiency): The concept of top-k oracle block efficiency serves as a theoretical upper bound for the potential improvements achievable with rescoring. By quantifying the maximum possible efficiency, we gain a benchmark against which we can measure the actual performance of our algorithms. This observation led to the realization that current methods, such as BPD and Medusa, have significant room for improvement. As a result, we developed our rescoring methods to approach this upper bound more closely, thereby optimizing block acceptance rates and reducing redundancy. # Q2. Potential Rescoring Issues To clarify, the original prediction is used for the next-token prediction, but rescoring happens after that (from the 2nd position future token onward) (You can find it in `Section 7` `Algorithm2`. We will make it clearer in the camera-ready version). The rescored top-1 token can differ from the original top-1 token, which is intentional. The original top-1 token for future positions often fails to be accepted for speculative inference, but our findings show that rescoring improves this. Evidence is provided by improvements in `block efficiency` and `speed up`. Additionally, BPD follows a draft-verify-accept structure. Incorrect predictions in the draft phase do not pass verification, ensuring that BPD and Medusa's predictions are identical to vanilla decoding. We focused on the number of tokens accepted, using block efficiency as a hardware-agnostic metric. Based on reviewer feedback, we have also included latency experiments in the `attached PDF`. `Appendix H` provides a detailed discussion on LLM inference speed improvements, covering low-level aspects such as `KV-Cache` and `Parameter I/O` `memory bandwidth` in TPU/GPU experiments. We believe these responses and additional results in the `attached PDF` address your concerns comprehensively and highlight the novelty of our work. --- Rebuttal Comment 1.1: Comment: Thanks for the additional results. I decided to raise my score. --- Reply to Comment 1.1.1: Title: Thank you for your feedback Comment: Dear Reviewer vMaK Thank you for your positive assessment and the time you've dedicated to reviewing our work. We appreciate your decision to raise your score and are glad that the additional data provided was helpful in addressing your concerns. Your time and attention in evaluating our work mean a great deal to us. Best regards, Authors --- Rebuttal 2: Title: Gentle Reminder - Dear Reviewer vMaK Comment: Dear Reviewer vMaK In response to the feedback, we enhance the depth and robustness of our work with detailed explanation and additional experimental results. This includes: - Evaluations with open-sourced 7B & 13B LLMs [`Figure A` and `Table A-D` in `authore-response pdf` ] - 5 additional datasets (MT-Bench, Natural Questions, GSM8K, RAG, Summarization) [`Figure A` and `Table A-D` in `authore-response pdf` ] - Clarification on the difference from existing works - Comparing with recent efficient llm inference method [`Table E` in author-rebuttal] - Integration with Medusa decoding (recent extended version of BPD; presented @ ICML2024) [`Figure A` and `Table A-D` in `authore-response pdf` and `Table E` in author-rebuttal] - Additional experiments with temperature sampling (T=0.7, 1.0), beyond greedy decoding [`Table A-D` in `authore-response pdf` ] Given the tight timeline, with the discussion phase concluding on `Aug 13`, we kindly request you to review our responses. We believe our detailed responses provide clarity on the concerns raised. Your feedback is pivotal to the quality of our work, and we earnestly await your thoughts, especially since we have `less than 2 days` remaining. Thank you for your efforts in this paper. Best regards, Authors	Summary: This paper proposes new ways to improve blockwise parallel decoding (BPD), a method to reduce inference latency in large language models. It first analyzes the token distributions produced by multiple prediction heads and then leverages this analysis to develop algorithms to improve BPD inference speed by refining the block drafts using n-gram and language models. Strengths: + The paper thoroughly studies BPD's behavior, including issues like consecutive token repetition and varying confidence levels across prediction heads, providing new insights for efficiency improvement. It further introduces the oracle top-k block efficiency as a useful metric for understanding the potential headroom for improvement in block drafts. + The proposed refinement algorithms (local neural rescoring and global n-gram rescoring) demonstrate improvements in block efficiency across multiple tasks, with gains of up to 21.30% in some cases. + The evaluation considers a variety of tasks (language modeling, question answering, and summarization) and datasets, + The paper is well-structured and easy to follow, with helpful illustrations and examples. Weaknesses: + The evaluation mainly compares the proposed improvements over the existing BPD baselines but doesn't compare them with other approaches for reducing inference latency, such as quantization or model pruning. It's suggested to make a more thorough comparison. + The evaluation is conducted mainly on a 1.5B parameter model. It's unclear how well these findings and improvements would generalize to larger, state-of-the-art models. Further, while the paper focuses on improving block efficiency, there's limited discussion on the additional computational cost of the rescoring methods. It's unclear whether the efficiency gains outweigh any increased computational requirements. + The improvements in block efficiency vary significantly across tasks, with some showing little to no improvement. A deeper analysis of why certain tasks benefit more than others would be valuable. Technical Quality: 3 Clarity: 3 Questions for Authors: Please address the questions listed in the weakness section. Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: The paper has discussed the limitations sufficiently. Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your valuable feedback in helping refine our work. - Note: Before reading further, we kindly ask you to check the `Author Rebuttal by Authors` and `the attached PDF` for detailed explanations and additional results. # W1. Comparison with Other Latency Reduction Approaches We appreciate the suggestion to include comparisons with other latency reduction approaches, such as quantization or model pruning. Our paper's primary focus is "Exploring and Improving Multi-Token Prediction (Block Draft)", which aligns more closely with speculative inference methods. While speculative inference methods like ours are orthogonal to pruning and quantization, we recognize the importance of providing a thorough comparison for a comprehensive understanding. Recent works such as Medusa [1,2] (presented @ ICML 2024, last month; extended version of BPD) are examples of speculative inference techniques similar to ours. Although our paper was submitted before many of these studies were published or open-sourced, we have now included a comparative analysis in the `Table E` (see `Author Rebuttal by Authors`) and the `attached pdf`. This analysis demonstrates that our method consistently enhances the efficiency of blockwise parallel LMs (BPD/Medusa), outperforming other speculative inference approaches (achieving an additional speedup of over `~20%` and `~300% speed-up` relative to vanilla decoding). This inclusion aims to provide a more comprehensive understanding of our method's effectiveness relative to other approaches in the field. [1] Tianle Cai, et al. "Medusa: Simple LLM inference acceleration framework with multiple decoding heads." ICML 2024. [2] Ankner, Zachary, et al. "Hydra: Sequentially-dependent draft heads for medusa decoding." arXiv (2024). # W2. Generalization to Larger Models and Computational Cost We understand the need to evaluate our methods on larger, state-of-the-art models and to discuss the computational costs associated with our rescoring methods. To address this, we have conducted additional experiments with larger models, specifically Vicuna `7B` and `13B` with `4 block draft heads`, as detailed in the `attached PDF`. These results demonstrate that our approach scales effectively, maintaining its performance gains across different model sizes. Regarding computational costs, we would like to emphasize that we've already covered a detailed discussion in `Appendix H`. `Appendix H` provides a detailed discussion on LLM inference speed improvements, covering low-level aspects such as `KV-Cache` and `Parameter I/O` `memory bandwidth` in TPU/GPU experiments. Our findings show that the efficiency gains from our rescoring methods outweigh the increased computational requirements. The `attached PDF` supports this statement in terms of the wall clock speedups relative to the standard autoregressive decoding. # W3. Variability in Block Efficiency Improvements We have extended our experiments to include a wider range of datasets and tasks, as detailed in the `attached PDF`. While most tasks show significant improvements, we acknowledge that not all tasks benefit equally. Achieving consistent improvements across all tasks and datasets is a challenge faced by many LLM and LLM studies, not just our own. Various factors, including the characteristics of specific datasets, can influence the results. This is not necessarily a limitation of our method but rather a common challenge in the field [3]. However, our results demonstrate that our method consistently enhances performance, even as model sizes increase (e.g., `7B` and `13B` parameters). The improvements are consistent for larger models, as highlighted in the `attached PDF`. [3] Xia, Heming, et al. "Unlocking efficiency in large language model inference: A comprehensive survey of speculative decoding." ACL Findings (2024). We hope this mitigates your concern and demonstrates the robustness and effectiveness of our proposed methods. --- Rebuttal 2: Comment: Dear Reviewer rNoJ In response to the feedback, we enhance the depth and robustness of our work with additional experimental results. This includes: - Evaluations with open-sourced 7B & 13B LLMs [`Figure A` and `Table A-D` in `authore-response pdf` ] - Comparing with recent efficient llm inference method [`Table E` in author-rebuttal] - 5 additional datasets (MT-Bench, Natural Questions, GSM8K, RAG, Summarization) [`Figure A` and `Table A-D` in `authore-response pdf` ] - Integration with Medusa decoding (recent extended version of BPD; presented @ ICML2024) [`Figure A` and `Table A-D` in `authore-response pdf` and `Table E` in author-rebuttal] - Additional experiments with temperature sampling (T=0.7, 1.0), beyond greedy decoding [`Table A-D` in `authore-response pdf` ] Given the tight timeline, with the discussion phase concluding on `Aug 13`, we kindly request you to review our responses. We believe our detailed responses provide clarity on the concerns raised. Your feedback is pivotal to the quality of our work, and we earnestly await your thoughts, especially since we have `less than 2 days` remaining. Thank you for your efforts in this paper. Best regards, Authors Title: Gentle Reminder - Dear Reviewer rNoJ --- Rebuttal Comment 2.1: Title: Looking forward to your feedback Comment: Dear Reviewer rNoJ, With the discussion phase nearing the end, we would appreciate knowing if our responses have adequately addressed your concerns. If you have any remaining concerns, please do let us know. We are eager to refine and enhance our research based on your valuable feedback. We look forward to your reply and thank you for your efforts on this paper. Best regards, Authors	Summary: This paper provides an improved solution for block-drafting, which is a potential useful way to improve the inference efficiency of LLMs. The work begins with observations of the problems of current block drafting, reveals that the consecutive repetition and drafting confidence are related to the quality of the draft. Rescoring methods are employed to improve the drafting process accordingly. Strengths: The observations are persuasive and the solution is intuitive. The experiments show impressive improvement (up to 20%) of block efficiency, which is potentially useful. Weaknesses: The rescoring phase uses yet another model to scoring the candidate. I am wondering whether using different models affect the final performance. Because different models have different token generation distributions. Technical Quality: 3 Clarity: 3 Questions for Authors: See the weakness part. Confidence: 5 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: N/A Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your valuable feedback. We understand your concern regarding the use of different models for the rescoring phase and its potential impact on final performance due to varying token generation distributions. - Note: Before reading further, we kindly ask you to check the `Author Rebuttal by Authors` and `the attached PDF` for detailed explanations and additional results. # W1. Additional experiments on different models To address this, we conducted additional experiments demonstrating that local neural rescoring methods are robust and consistently improve performance across different target models (Instruction-tuned openLLM Vicuna `7B` and `13B` with `4 block draft heads`). Specifically, we have shown that: 1. Our approach significantly speeds up BPD even further for existing, open-sourced, instruction-tuned LLMs. 2. Local rescoring also accelerates decoding for different model architectures, including the very recent Medusa model [1] presented at ICML 2024, which employs tree-attention to enhance performance in blockwise parallel LMs, achieving an additional speedup of over `~20%` relative to BPD/Medusa and `~300% speed-up` relative to vanilla decoding. In the `attached PDF`, we provide detailed results showing consistent performance improvements when our model is applied on top of Medusa decoding. These results highlight the versatility and robustness of our rescoring approach in the field regarding multi-token predictions, confirming that it effectively enhances performance regardless of the underlying model used for token generation. We hope this addresses your concern and illustrates the robustness and effectiveness of our proposed methods. [1] Tianle Cai, et al. "Medusa: Simple LLM inference acceleration framework with multiple decoding heads", ICML, 2024. --- Rebuttal 2: Comment: Dear Reviewer FLJ6 In response to the feedback, we enhance the depth and robustness of our work with additional experimental results. This includes: - Evaluations with open-sourced 7B & 13B LLMs [`Figure A` and `Table A-D` in `authore-response pdf` ] - 5 additional datasets (MT-Bench, Natural Questions, GSM8K, RAG, Summarization) [`Figure A` and `Table A-D` in `authore-response pdf` ] - Comparing with recent efficient llm inference method [`Table E` in author-rebuttal] - Integration with Medusa decoding (recent extended version of BPD; presented @ ICML2024) [`Figure A` and `Table A-D` in `authore-response pdf` and `Table E` in author-rebuttal] Given the tight timeline, with the discussion phase concluding on `Aug 13`, we kindly request you to review our responses. We believe our detailed responses provide clarity on the concerns raised. Your feedback is pivotal to the quality of our work, and we earnestly await your thoughts, especially since we have `less than 2 days` remaining. Thank you for your efforts in this paper. Best regards, Authors Title: Gentle Reminder - Dear Reviewer FLJ6 --- Rebuttal Comment 2.1: Title: Looking forward to your feedback Comment: Dear Reviewer FLJ6, With the discussion phase nearing the end, we would appreciate knowing if our responses have adequately addressed your concerns. If you have any remaining concerns, please do let us know. We are eager to refine and enhance our research based on your valuable feedback. We look forward to your reply and thank you for your efforts on this paper. Best regards, Authors	null	null	Rebuttal 1: Rebuttal: We extend our gratitude to all the reviewers for providing comprehensive and thoughtful feedback on our manuscript. We appreciate your valuable insights into the strengths and areas for improvement of our work. # Core Contributions of Our Work - Novel Findings: This work explicitly addresses key issues in blockwise parallel LMs, such as consecutive repetitions and the confidence of different heads, and introduces the concept of oracle top-k block efficiency (potential headrooms for speedup). - Novel Technical Contributions: Building on BPD, our methods effectively remove repetitions and improve block efficiency, achieving up to a `21.30%` improvement. In most cases from `rebuttal experiments`, our approach also results in (a) `~15% speed-up` relative to BPD and Medusa decoding and (b) `~300% speed-up` relative to vanilla decoding. - Objective and Scalability: Our main objective is “Exploring and Improving Multi-token Prediction (Block Draft)”. The framework is easy to plug in and scale up because any type of rescoring LM can be used regardless of the size of target blockwise parallel LM. - Oracle Top-k Block Efficiency: To our best knowledge, this metric has not been measured in the field, but it provides a valuable upper bound indicating potential room for improvement. - Instruction-Tuned LLMs: As shown in the `attached PDF`, this framework performs well even with instruction-tuned LLMs, including models with `7B` and `13B` parameters. # Summary of Strengths Cited by Reviewers - Impact: We appreciate `Reviewer FLJ6` and `Reviewer rNoJ` for noting the important motivation and impact of our work. The improvements in block efficiency (up to `21.30%`) are significant and have practical applications. - Soundness: `Reviewers FLJ6` and `Reviewer rNoJ` acknowledged the technical soundness of our approach and the thorough study of BPD behavior, including issues like consecutive token repetition and varying confidence levels across prediction heads. - Integration: `All reviewers` highlighted the well-structured and integrated nature of our paper, with a clear presentation and helpful illustrations. - Experiments: `All reviewers` appreciated our comprehensive experiments across a variety of tasks (language modeling, question answering, and summarization) and datasets, demonstrating the robustness and effectiveness of our methods. # Additional Experiments in PDF 1. Local rescoring improves BPD with tree-attention 2. Additional experiments with temperature sampling (`T=0.7`, `1.0`), beyond greedy decoding 3. Instruction-tuned openLLM results with Vicuna `7B` & `13B` target model with `4 block draft heads` 4. Additional tasks - MT-Bench (including `writing`, `roleplay`, `reasoning`, `math`, `coding`, `extraction`, `stem`, `humanities`) - Natural Questions (QA) [3] - GSM8K [5] - RAG [2] 6. Local rescoring vs. vanilla Medusa decoding (extended version of BPD; presented @ ICML24) [1] # TL;DR for PDF - We have conducted extensive experiments with additional open-source LLMs and downstream tasks - Our results consistently show improved performance from local neural rescoring in terms of block efficiency as well as wall clock time, for LLMs up to `13 billion` parameters. ### Additional results for comparing other methods for efficient LLM inference: `Table E`. Speedup ratio (i.e. latency) relative to the standard autoregressive decoding. \| NVIDIA A100 GPU \| Vicuna 7B \| \| \| \| \| Vicuna 13B \| \| \| \| \| \|-------------------\|-----------\|-------\|-------\|-------\|-------\|------------\|-------\|-------\|-------\|-------\| \| Relative Speedup \| MT-Bench \| Sum \| QA \| GSM8K \| RAG \| MT-Bench \| Sum \| QA \| GSM8K \| RAG \| \|-------------------\|-----------\|-------\|-------\|-------\|-------\|------------\|-------\|-------\|-------\|-------\| \| Sps [6]\| 1.432 \| 1.394 \| 1.417 \| 1.364 \| 1.568 \| 1.417\| 1.424 \| 1.362 \| 1.448 \| 1.606 \| \| Lookahead [7]\| 1.818 \| 1.645 \| 1.503 \| 1.865 \| 1.475 \| 1.118\| 1.007 \| 1.011 \| 1.324 \| 0.963 \| \| PLD [8] \| 1.676 \| 2.707 \| 1.162 \| 1.605 \| 1.909 \| 1.528 \| 2.384 \| 1.050 \| 1.646 \| 1.876 \| \|-------------------\|-----------\|-------\|-------\|-------\|-------\|------------\|-------\|-------\|-------\|-------\| \| BPD\| 1.752 \| 1.509 \| 1.489 \| 1.696 \| 1.409 \| 1.745 \| 1.530 \| 1.488 \| 1.794 \| 1.483 \| \| + Our local rescoring \| 1.843 \| 1.534 \| 1.555 \| 1.780 \| 1.501 \| 1.819 \| 1.522 \| 1.519 \| 1.819 \| 1.501 \| \|-------------------\|-----------\|-------\|-------\|-------\|-------\|------------\|-------\|-------\|-------\|-------\| \| Medusa\| 2.254 \| 2.002 \| 2.045 \| 2.317 \| 1.833 \| 2.232 \| 2.000 \| 1.986 \| 2.507 \| 1.945 \| \| + Our local rescoring \| 2.482 \| 2.076 \| 2.114 \| 2.357 \| 2.000 \| 2.467 \| 2.136 \| 2.154 \| 2.519 \| 2.068 \| ## References [1] Tianle Cai, et al. "Medusa: Simple LLM inference acceleration framework with multiple decoding heads." ICML, 2024. [2] Vladimir Karpukhin, et al. "Dense passage retrieval for open-domain question answering." arXiv, 2020. [3] Tom Kwiatkowski, et al. "Natural questions: a benchmark for question answering research." Transactions of the Association for Computational Linguistics, 7:453–466, 2019. [4] Lianmin Zheng, et al. "Judging LLM-as-a-judge with MT-Bench and Chatbot Arena." NeurIPS, 2024. [5] Cobbe, Karl, et al. "Training verifiers to solve math word problems." arXiv (2021). [6] Chen, Charlie, et al. "Accelerating large language model decoding with speculative sampling." arXiv (2023). [7] Fu, Yichao, et al. "Break the sequential dependency of llm inference using lookahead decoding." arXiv (2024). [8] Apoorv Saxena. 2023. Prompt lookup decoding We believe these additions and clarifications address the reviewers' concerns comprehensively and strengthen our manuscript. Thank you for your constructive feedback, which has significantly contributed to the improvement of our work. We look forward to your favorable consideration. Pdf: /pdf/22da9a09e53396debd9fac468f6d01fe5a8e6d83.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Banded Square Root Matrix Factorization for Differentially Private Model Training	Accept (poster)	Summary: The paper proposes the Banded Square Root (BSR) matrix factorization to speed up banded matrix factorization. The authors demonstrate that the workload matrix for SGD with momentum and weight decay can be expressed as a lower triangular Toeplitz matrix. They utilize explicit recursive expressions to compute the square root of this workload matrix, and Theorem 1 provides a closed-form expression for the square root matrix. Theoretical analysis shows that the calculation of the square root matrix is efficient, and the sensitivity of the mechanism is discussed. Detailed analysis of the approximation error is also provided, demonstrating that the square root factorization has asymptotically optimal approximation quality. Experiments show that BSR can achieve performance comparable to previous state-of-the-art methods. Strengths: 1. The discussion regarding SGD with momentum and weight decay is interesting. The workload matrix in this context is a lower triangular Toeplitz matrix, which allows for efficient factorization algorithms. Prior work has not explored this setting; they typically treat the workload matrix with momentum as a general lower triangular matrix. This finding is significant for future research, suggesting potential improvements over current solvers for banded matrix factorization. 2. The theoretical analysis demonstrates that Banded Square Root (BSR) matrix factorization can be computed efficiently even for large problem sizes. The expected approximation error for BSR indicates that it achieves asymptotically optimal approximation quality. These analyses ensure that BSR is both fast and accurate. Weaknesses: 1. Using CVXPY with SCS to compute AOF is not efficient; L-BFGS can solve this problem more efficiently. For instance, as shown in [1], an implementation using GPUs can solve a problem size of 10,000 in less than an hour. Even with CPUs, the implementation in [2] can solve a problem size of 2,000 in less than an hour, with slight modifications to add the b-min-step constraint. 2. The current experiment only demonstrates results for matrix sizes up to 2000, which is insufficient. A comparison involving matrix sizes of 10,000 or more would be more convincing. How long would it take to obtain a solution for problem sizes of 10,000 and 100,000 using BSR? [1] https://github.com/apple/pfl-research/blob/2a9d65bd66dc89ef80a24e1be0d28446a0422133/pfl/privacy/ftrl_mechanism.py#L140 [2] https://github.com/dpcomp-org/hdmm/blob/7a5079a7d4f1a06b0be78019adadf83c538d0514/src/hdmm/templates.py#L391 Technical Quality: 3 Clarity: 3 Questions for Authors: 1. Enforcing positive semi-definiteness (PSD) for the matrix is crucial for convergence in AOF. In line 274, you mentioned a post-processing step for S to ensure that all its eigenvalues are at least $\sqrt{1/n}$. Could you provide a more detailed description of this step? I couldn't find it in the source code provided in Appendix A. 2. In equation (6), b should be p, right? Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: 1. If the learning rate is not constant, then the workload matrix will not be a Toeplitz matrix, right? This would significantly impact the efficiency of BSR. During the training process, a proper learning rate schedule can enhance convergence. Therefore, a discussion about varying learning rates should be included. 2. The paper does not provide a general introduction to differential privacy, and Figure 2 presents (epsilon, delta) without sufficient background information. This lack of context makes the paper not self-contained. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for the encouraging feedback. In the following we hope to address all your concerns. \> Using CVXPY with SCS to compute AOF is not efficient. There are, of course, many ways to solve AOF (4). We used SCS, because it is a dedicated SPD-solver which allows for a simple and reproducible implementation without additional hyperparameters (Algorithm 2). General-purpose gradient-based solvers, such as L-BFGS, were meant to be included in our comment about approximate solvers (lines 122-125). These can be faster for solving (4) up to a certain precision, but they require additional design choices, such as the number of update steps, learning rates, a barrier function to enforce the constraints, and potentially projections to ensure positive definiteness. Importantly, however, note that our claim in the work is not that “BSR is x-times faster than AOF”. Actual runtimes always depend on many factors, including hardware, programming language, software packages, etc. We mention runtimes rather as a qualitative guidance to the reader, which is why we do not report a formal table or plot of runtimes. Our core argument is that (4) is a challenging optimization problem to solve. Any numeric solver will be slower and less convenient to use than our $O(n \log n)$ closed-form expressions. In real-world problems solving (4) creates a bottleneck, especially because it has to be solved anew for any change of hyperparameters. BSR overcomes this bottleneck. \> References to larger-scale matrix factorizations. Thank you for the references; we will include them into our manuscript. Ref [1] indeed aims to solve the optimization problem (4). Could you please provide a reference for the timing results you mentioned? We did not spot them in the repository or associated report arXiv:2404.06430, but would be happy to adapt our presentation accordingly. [2] solves a simpler problem (from [McKenna et al., VLDB 2018]). Although adapting the formulation might be possible, the additional constraints could complicate the numerical solution. Nevertheless, we will be happy to include this in our discussion. \> The current experiment only demonstrates results for matrix sizes up to 2000, which is insufficient We report experiments to a size of 2000 due to the computational limits of calculating AOF. For BSR, much larger workload sizes are no problem, and we will be happy to add them to the manuscript. The speed advantage of BSR over AOF will increase with $n$, regardless of the solver. We illustrate this in the response PDF: a plain python implementation of Theorem 1 (Alg.3 in PDF) computes the BSR-coefficients for $n=10,000$ in 24ms , for $n=100,000$ in 2.4s and for $n=500,000$ in ~67s (Table 1 in PDF, single-core CPU, double precision). In practice, one would likely not use vanilla MF-SGD for $n \ge 500,000$, because the resulting matrices (e.g. $C^{-1}$) would be inconveniently large (1 TB of memory in dense fp32 form). \> Enforcing positive semi-definiteness (PSD). We did not include this step in Algorithm 2, because we considered it a post-processing operation only needed when trying to extract $C$ from the solution matrix $S$ (which despite the use of SCS, is not always perfectly PSD). We will be happy to add it, though. The actual operation is a standard procedure (Alg.4 in the response PDF). Our experiments use $tol=1/\sqrt{n}$ as a heuristic, because we observed it to give good results across a wide range of problem sizes, in particular $C^{-1}$ remaining stable. Constant values for tol or values proportional to $1/n$ did not work as well. We did not find this issue discussed in the literature. \> Equation (6). Thanks for spotting this typo. We will fix it. \> Different learning rates. Indeed, different learning rates would result in a non-Toeplitz workload matrix, so our analytical expressions no longer apply. However, the banded-square-root method remains applicable, only that the matrix square root has to be computed numerically. This step remains quite efficient because the workload matrix is still lower triangular, for which specialized routines exist, e.g. [Björck& Hammarling. “A Schur method for the square root of a matrix”, 1983]. We will include a discussion of the impact of varying learning rates in the revised version. \> General introduction to differential privacy. Indeed, due to space constraints, we were not able to give an introduction in the manuscript, which primarily targets an audience already familiar with DP. We will add a section in the appendix. --- Rebuttal Comment 1.1: Comment: Thank you for addressing my concerns. I have raised my rating. The runtime was observed when I did several experiments. I really encourage to have a comparison experiment on the latest algorithm. Although I agree that the main purpose of the paper is not for runtime comparison.	Summary: This paper proposes the Banded Square Root Matrix Factorization, an efficient approximation of the optimal banded matrix factorization for differentially private machine learning applications. The authors give a closed form expression for the BSR C matrix for any SGD + Momentum + Weight Decay workload by exploiting the Toepltiz structure of the workload and factors. These factorizations can be used in place of the prior work and enjoy some efficiency advantages. Strengths: * The scope, contributions, and key results are clearly written. * Near-optimal and efficiency computable banded matrix factorizations could make it feasible to use this mechanism in some new settings where it was previously not possible. * Authors demonstrated deep understanding of the area, and made a compelling story with a strong mix of theoretical derivations and empirical observations. Weaknesses: * The implementation of AOF seems suboptimal and hence the comparison appears to be biased. Multiple-day runtimes for n ~ 700 seems high when prior work conducts experiments for n >= 2000 (https://arxiv.org/pdf/2306.08153). Doing a little digging, I found https://www.kdd.org/kdd2016/papers/files/rpp0224-yuanA.pdf, which ran experiments up to n ~ 8192. The limits of the BSR approach are not really demonstrated besides the statement "Even sizes of n = 10,000 or more take at most a few seconds." How much beyond this can you scale? Would be good to add a scalability experiment. Technical Quality: 4 Clarity: 4 Questions for Authors: * Assuming your method scales well beyond the prior work of n ~ 8192, can you make a convincing case that in modern DP + ML applications we need to scale beyond that point? I'm not super familiar with how many iterations DP-SGD is usually run for. * Thm 2 is an interesting result that allows you to compute sensitivity efficiently under this special Toepltiz structure without requiring bandedness, but it's not clear where you are using this Thm. Is it better to find a banded factorization with bands = minsep or use a non-banded factorization with Thm 2? >* Also minor point: might be better to write Eq 10 in terms of m_0, ... m_{n-1} instead of M (or maybe include both expressions). >* There is an incorrect reference to Eq 10 in the experiments >* Typo: n_{n-1} * Regarding the statement: "Apart from the factorization itself, the computational cost of BSR and AOF are nearly identical." Is the factorization time usually the dominating term in the cost for AOF? Is that still the case for BSR, even when scaling up well beyond n ~ 8192? What factor(s) other than n (if any) impact the complexity of these mechanisms? * It is remarkable that the approximation quality of BSR and AOF is so close. It looks like you evaluated a few settings, one of them being b=100, k=n/100 in Fig 1. Does this hold more generally across other settings, and can you demonstrate that with an experiment? There are two extremes where it I might expect some gap: (a) 2 bands (b) n bands. >* In Fig 1, the most interesting comparison to me is BSR vs. AOF, the baselines have already been established to be far from optimal in prior work and their presence makes it difficult to perceive difference between the two most interesting lines, would be good to update the plot accordingly. Confidence: 5 Soundness: 4 Presentation: 4 Contribution: 3 Limitations: The authors have discussed some limitations, but perhaps adding some of the things I mentioned in this review (or addressing them directly) would be good. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for the valuable feedback. Below we clarify the raised points: \> Implementation of AOF seems suboptimal. (note that Reviewer VxsQ had a similar question, and for easier reading we provide our answer in both our replies) There are, of course, many ways to solve AOF (4). We used SCS, because it is a dedicated SPD-solver that allows a simple and reproducible implementation without additional hyperparameters (Algorithm 2). General-purpose gradient-based solvers, such as L-BFGS, were meant by our comment about approximate solvers (lines 122-125). These can be faster for solving (4) up to a certain precision, but they require additional design choices, such as the learning rates, number of update steps, a barrier function to enforce the constraints, and potentially projections to ensure positive definiteness. \> References on larger-scale matrix factorizations. Ref arXiv:2306.08153 uses an in-house implementation by Google that is not freely available. The manuscript does not state runtimes or hardware. However, the fact that they also only report experiments up to $n=2,052$, we take as confirmation that solving (4) for large $n$ is indeed challenging. Regarding the KDD2016 reference, we do not believe it is comparable. It solves a different optimization problem (in fact, AOF’s formulation (4) was just proposed in 2023), which is also an SDP in the context of DP but with a simpler constraint set. Nevertheless, we’ll be happy to include it in our discussion. Importantly, however, note that our claim in the work is not that “BSR is x-times faster than AOF”. Actual runtimes always depend on many factors, including hardware, programming language, software packages, etc. We mention runtimes rather as a qualitative guidance to the reader, which is why we do not report a formal table or plot of runtimes. Our core argument is that solving (4) is a challenging optimization problem. Any numeric solver will be slower and less convenient to use than our $O(n \log n)$ closed-form expressions. In real-world problems solving (4) creates a bottleneck, especially because it has to be solved anew for any change of hyperparameters. BSR overcomes this bottleneck. \> Scalability of BSR. We reported experiments to a size of 2000 only due to the computational limits of AOF. For BSR, much larger workload sizes are no problem. We will be happy to add them to the manuscript. The speed advantage of BSR over AOF will increase with $n$, regardless of the solver. We illustrate this in the response PDF: a plain python implementation of Theorem 1 (Alg.3 in PDF) computes the BSR-coefficients for $n=10,000$ in 24ms , for $n=100,000$ in 2.4s and for $n=500,000$ in ~66s (CPU, single-threaded). If a dense matrix is wanted for C, times are approximately 3x higher due to the memory access overhead (Table 1 in PDF). \> Scale of $n$ for modern DP + ML applications? In this context, $n$ is simply the total number of model updates, so large values of $n$ are quite common for standard network training. E.g., training MNIST (60,000 examples) with batchsize 128 for 10 epochs requires $n=(60000/128)10= 4680$. A standard ResNet-Training on ImageNet1K (1.2M examples, batchsize 512, 90 epochs) yields $n=225,180$. Llama2-like LLM training (2T tokens, batchsize 4M tokens, 1 epoch) would result in $n=500,000$. However, in practice one would not use vanilla MF-SGD for such sizes, because the resulting $C^{-1}$ matrix would require 1 TB of memory to store (in dense form). It remains an open research question how to scale MF-SGD to such sizes. Our contribution only covers a part of that, namely avoiding the need to solve the preparatory (4). \> Theorem 2* We use this theorem to compute b-min-sep sensitivity for all cases, including Theorems 6 and 7. The idea of using Theorem 2 to find a better (potentially non-banded) factorization is indeed interesting. However, implementing this is not straightforward, because Theorem 2 requires the matrix $C$ to have decreasing coefficients. It is unclear how one could impose this property during the optimization, where one only has access to $S = C^TC$. \> Is the factorization time the dominating cost? For AOF: yes. The factorization (4) is by far the most costly step, regardless of the solver. The Cholesky-type decomposition (line 118) is also costly but faster (seconds for $n=10000$, minutes for $n=50000$). BSR avoids both steps. Instead, one computes $C$ explicitly, which is efficient due to Theorem 1 (see above), and computing C’s sensitivity is trivial due to Theorem 2. The speed of AOF and BSR are both functions of $n$ and the bandwidth. The runtime of numeric solvers for AOF will also depend on the desired precision and the entries of the workload matrix (which determine the hardness of the optimization problem). \> Notation and typos. Thank you for the suggestions, we will include them. \> It is remarkable that the approximation quality of BSR and AOF is so close We found BSR to be consistently close to AOF across all settings we tested, not just the one in the manuscript. We’ll be happy to extend the manuscript with more results. Regarding bandwidth: Fig.3 in the response PDF shows that for the recommended p=b, BSR is typically close to AOF even for extreme values of $b$ ($b=2$ or $b=n$). For $p\ll b$ or $p\gg b$, indeed the distance to (b-banded) AOF grows. Some numeric results for $p=n$ can already be found in Appendix C in column “sqrt” (Tables 10-17 for $b=n$, Tables 2-9 for $b=100$). Unfortunately, their captions were mislabeled, which we will fix. \> Figures: the baselines were meant as a reference to help judge the significance of the differences between the methods. However, we could put the plots without baselines in the appendix, or if preferred, we could put the non-banded “sqrt” instead. Please let us know what you would prefer. We hope that also the numeric tables in the appendix allow judging the differences. --- Rebuttal Comment 1.1: Comment: Thank you for the response, I went ahead and bumped up my rating -- I think this is a solid paper with nice impact that should be of interest to people working in the space DP ML. Three things I'd like to see addressed in the revision: 1. I would like to see in the final version the results from Appendix C expanded and included in the main text. From what I can tell, there is a 10%+ degredation in expected error for BSR in Table 2, which could be meaningful in practice. Including plots that show how this degredation changes with n and b would be informative and strengthen the experiments. 2. The results on AOF should also be cleaned up -- make sure you are using an implementation that converges to the optimal solution so you don't end up with strange artifacts where BSR outperforms AOF. If your custom implementation of AOF is not converging, try modifying an existing implementation, such as one of the links from Reviewer VxsQ below, or finding the source from the kdd paper. Alternatively asking the authors of arXiv:2306.08153 for their source code might be worth a shot (if you haven't done so already). 3. Add limitations section, discussing challenges to scaling to large n beyond solving Eq (4). Also, please clarify two follow-up questions: I'm not sure how you were able to run Algorithm 3 BSR(..., full='true') for n >= 100000 -- wouldn't that require 40 GB of RAM? Do you need to set full='true' to use this mechanism in an ML training pipeline? One final comment: It is clear that C has a closed form expression but from Eq (6) it seems like you compute B by materializing A and C, and computing A C^{-1} using something like numpy, which I wouldn't expect to scale well due to the size of the matrices. Does B also have a Toeplitz structure that you exploit to represent it efficiently? --- Reply to Comment 1.1.1: Comment: Thank you for your feedback and for increasing your rating. We appreciate your insights and will address your recommendations in the revision. Below are responses to your follow-up questions: \> Memory Usage: Yes, running Algorithm 3 with $n=100{,}000$ does require around 40 GB of RAM and $n=500{,}000$ approximately 1 TB. We used a machine with 1.5 TB of RAM for these experiments. However, setting `full='true'` is not necessary for using this mechanism in an ML training pipeline. \> Matrix Structures and Efficient Representation: The matrices $A$, $B$, and $C^{-1}$ are indeed all Toeplitz. However, $A$ and $B$ are not explicitly needed for MF-SGD, only implicitly (see Alg.1). In our demo code, we instantiate $C$ and $C^{-1}$ explicitly for simplicity, but for large-scale applications, this would not be necessary. The Toeplitz structure allows for efficient representation, avoiding the need to materialize these matrices fully.	Summary: This paper addresses optimal matrix factorization mechanism for differential privacy, focussing on stochastic gradient descent (SGD) optimization. It introduces the banded squared root (BSR) factorization and provide formal lower and upper bounds to the approximation error. The BSR achieves competitive formal approximation error compared to state-of-the-art methods and demonstrates practical utility in real-world training tasks. The authors provide theoretical bounds for single and repeated participation training, showing that BSR maintains high training accuracy with provable privacy guarantees while being computationally efficient. Strengths: - The authors make a significant contribution to the field of differentially private machine learning under matrix factorization mechanisms by leveraging efficient BSR for the SGD workload matrix. - The incorporation of the SDG workload matrix in this line of research is elegant. - The banded squared root (BSR) factorization is computationally efficient and scalable to large workload matrices, making it a valuable tool. - The proof sketches are intuitive and convincing, although I haven't thoroughly reviewed the technical proofs in the appendix. - A notable advantage of BSR is its independence from specific training objectives. - BSR achieves competitive approximation error, on par with state-of-the-art methods in differentially private training. - The approach demonstrates practical utility by maintaining high training accuracy in real-world training tasks. - The authors provide theoretical guarantees for both single and repeated participation scenarios, adding to the method's credibility. - The theoretical explanations are (for the most part) well-written and easy to follow. - The paper includes extensive technical supplementary material. - The inclusion of useful, copy-pasteable Python code listings is interesting. - The authors show respect for existing work by referencing relevant StackOverflow answers and software packages. Weaknesses: - The experimental evaluation is limited to a small set of real-world and synthetic experiments. - The range of synthetic datasets used in the experiments is restricted, which may not be representative of diverse scenarios. - The data generation process is unclear, and only homogeneous partitions are considered, with no variation in data distributions. - The real-world experiments are limited to a single dataset, CIFAR-10, which is insufficient to draw general conclusions. - The post-processing step (line 275) lacks clear explanation, leaving it unclear whether it addresses a principled problem or a numerical issue. - The experiments do not provide a comparison with non-private approaches, which makes it difficult to understand the practical limitations of the method. - The evaluation is limited to a single real-world dataset, CIFAR-10, and a simple ConvNet model. - The experiments do not discuss potential practical limitations of BSR, which may impact its applicability. - The comparative analysis is limited and does not include a wide range of existing differential privacy methods. - The formal proof of Theorem 2 (Appendix D.2) employs unclear and undefined notation (Π), which makes it difficult to follow. - Neither the proof sketch nor the formal proof are straightforwardly understandable, which may hinder comprehension. Minor: - The tone of "supposedly optimal" (line 254) could be perceived as inappropriate and may benefit from rephrasing. - The proof sketch of Theorem 2 refers to the wrong appendix (Appendix D.3 instead of Appendix D.2, presumably). Technical Quality: 4 Clarity: 3 Questions for Authors: ./. Confidence: 3 Soundness: 4 Presentation: 3 Contribution: 3 Limitations: ./. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for the encouraging feedback and detailed comments. \> Experimental Evaluation. We believe there may be a slight misunderstanding. Our main contribution lies in the algorithm and properties of BSR. Specifically, we demonstrate that in the context of MF-SGD, using BSR requires adding less noise compared to the baselines (for identical levels of privacy) and it is essentially on par with the computationally much more costly AOF (e.g., Figure 1). This fact is independent of any subsequent model training steps and requires no data, not even synthetic. We do not introduce a new technique for differential private model training, which would indeed require more extensive experimental validation and comparison to other private training techniques. The MF-SGD experiments on CIFAR that we report (Figure 2) are only meant as a proof-of-concept to illustrate that, by keeping all other components fixed, the lower added noise tends to translate into higher accuracy. The exact experimental setup we will be happy to clarify in the manuscript: like prior work, we split the dataset uniformly at random into batches and train in a centralized way. \> Limitations of BSR. We will be happy to extend our discussion in Section 5 to provide a broader view. In particular, we observe that BSR achieves results comparable to AOF, although we currently cannot prove this, as the theoretical properties of AOF are not well understood enough. Regarding real-world usability, the analytic expression for BSR does not apply to variable learning rates, which would be desirable. \> Post-processing step (line 275) Note that this step is unrelated to BSR; it was only needed for AOF. We believe the problem is both numerical and principled. By this, we mean that, on the one hand, the problem is indeed numerical: if we could solve (4) with infinite mathematical precision, post-processing would not be needed. On the other hand, the numerical issues arise because of a principled drawback, namely that the AOF procedure (solving (4), computing a Cholesky decomposition, inverting the resulting matrix) is quite sensitive to small numeric deviations. Consequently, errors from solving (4) only to a certain precision, as all numerical solvers do, can lead to disproportionately large undesirable effects. \> Comparison to non-private approaches. We will be happy to include such information in the manuscript. For example, non-private training in the setting of Figure 2 achieves an accuracy of approximately 65%. However, we would like to emphasize that our contribution is orthogonal to the contrast between private and non-private training. Our submission shows that by using a different processing step (BSR), one benefits in terms of speed (over AOF) and accuracy (over the baselines). Outside the context of MF-SGD, such a comparison cannot be made. \> Notation ($\Pi$), clarity of proof and sketches. Thank you for bringing this to our attention. We will clarify the proof and sketches and we will remind the reader of the definition of $\Pi$. \> Minor issues. Thank you, we will fix these items.	Summary: The paper considers the problem of adding correlated noise $C^{-1}z$ instead of independent noise $z$ across iterations in continual counting (equivalently, DP-SGD). Past work gave an algorithm to choose $C^{-1}$ that optimizes some objective on the noise under b-min-separated participation, but this algorithm requires solving an SDP which is infeasible when using a large number of iterations, i.e. optimizing over $C$ that has a large number of rows / columns $n$. The authors propose a choice of $C$, which they call banded square root, which has a succinct representation that is efficiently computable in time independent of $n$. Furthermore, their choice of $C$ is banded, i.e. is non-zero below the $b$-th diagonal for $b \geq 1$, which gives it some nice properties such as being able to compute $C^{-1}z$ efficiently in a streaming manner. To define the banded square root $C$, they authors take $A$ which represents the workload, effectively a representation of the updates in SGD which can include momentum and weight decay, and take its matrix square root. They then truncate the matrix square root to its first $b$ diagonals. The authors give an explicitly and efficiently calculable formula for the computing the first column of this matrix, which specifies the whole matrix as it is Toeplitz. The authors analyze the asymptotic error guarantees of different choices of $C$, including the banded square root, in the single- and multiple-participation settings. Specifically, their error guarantees show that banded square root improves on $C = I$ or $C = A$, and nearly matches a lower bound on any factorization if using enough bands. The authors conduct experiments training models for classification on CIFAR10 and show that banded square root is competitive with the choice of $C$ given by solving a more expensive SDP. Strengths: * The work makes theoretical progress on a practical problem. Correlated noise/DP-MF is now being used in practice to train models with DP, and especially as model sizes and training runs get larger, more efficient ways to implement DP-MF will lead to better models in practice. In particular, itmakes the results of the DP-MF literature more accessible to those who do not have large amounts of compute to use the techniques they introduced. * The theoretical analysis of the error of DP-MF as a function of the number of bands is novel and adds theoretical understanding of banded $C$ that was not present in the previous paper of Choquette-Choo et al. Furthermore, the set of theoretical results is rather extensive and gives a pretty complete theoretical understanding of the authors' methods. * While DP-MF is a relatively niche topic, the paper does a good job slowly introducing the problem, their approach, and their theoretical results. Weaknesses: * While the previous work did require solving an SDP, to my understanding this is for the case where $C$ can be is only required to be a banded lower-triangular matrix. If $C$ is required to be Toeplitz as well, as the banded square root factorization is, then one only needs to optimize over $b$ variables instead of $\approx nb$ and it is not clear that the computations in the previous work are expensive, which mitigates the improvements in this paper. * It is worth pointing out there is a work of https://arxiv.org/abs/2404.16706, that also gives an efficient-to-compute way to choose $C$, and leads to faster streaming noise generation for than banded matrices. This work I would consider concurrent, so I did not account for any possible overlap between the two papers' results and impact when assigning my score. Technical Quality: 4 Clarity: 4 Questions for Authors: * wrt the first weakness, did the authors consider this alternate approach / if so, do you believe banded square root still offers speedups in this setting? * The previous work of Choquette-Choo et al. shows that banded $C$ are compatible with privacy amplification with sampling. Have you considered combining your error analysis with their privacy analysis (e.g., maybe for RDP to simplify) in the setting where batches are sampled in DP-SGD? It might be an interesting question to see how the number of bands affects error in the presence of amplification, since they observed more bands reduce the benefits of amplification. Confidence: 4 Soundness: 4 Presentation: 4 Contribution: 3 Limitations: Yes Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for the insightful review. Here, we address the individual concerns: \> Relation to arXiv:2404.16706. Indeed, this interesting preprint (which we cite as [Dvijotham et al., 2024]) is concurrent work. It studies only the case of MF-SGD without momentum or weight decay (“prefix sum”) and is limited to streaming data ($k=1$, “single epoch”). This setting enables a deeper analytic treatment (in particular the sensitivity computation, which e.g. does not benefit from bandedness), but it comes at the cost of covering fewer real-world scenarios. \> While the previous work did require solving an SDP, to my understanding this is for the case where can be is only required to be a banded lower-triangular matrix. If is required to be Toeplitz as well, as the banded square root factorization is, then one only needs to optimize over variables $b$ instead $nb$ [...] This is an interesting observation that could lead to a hybrid between [Choquette-Choo et al., 2023a] and our work. As a compromise between speed and optimality, one could keep the objective of the problem (4) but restrict it to Toeplitz matrices, thereby parametrizing the problem with $b$ variables. Unfortunately, the objective function would be quite more involved. It would no longer have a standard structure, such as the “matrix fractional function” form of the SDP (4), and it would not be convex in its variables (AOF’s (4) is only convex in the product matrix $S=C^T C$, which enters the objective via $S^{-1}$). Gradient-based optimizers could converge quickly but one would lose the guarantee of being close to a global optimum within a specifiable tolerance. \> Did the authors consider this alternate approach / if so, do you believe banded square root still offers speedups in this setting? We had not considered this approach, but it sounds like promising future work that we would be happy to follow up on (with the permission of the reviewer). That said, we believe it would be unfair to consider it a shortcoming of our work that an alternative path exists which, to our knowledge, has not appeared in any prior work and will come with its own challenges. Regarding the speed: even if the above idea might accelerate the numerical optimization, it will not surpass the simplicity and efficiency of BSR’s closed-form expressions. Furthermore, even if solved optimally, the quality of such a solution should lie between BSR and AOF, which are close together already. \> Privacy amplification. Another interesting point, thank you for bringing it up. Since the BSR matrix has the same band structure as the AOF matrix, the privacy properties amplification arguments from Choquette-Choo et al. will still be applicable to our results. We will add a note to this in the manuscript. We did not include this aspect in the original submission because the material was already quite dense and we considered it somewhat orthogonal to our main analysis. But indeed, it would be interesting future work. --- Rebuttal Comment 1.1: Comment: Thanks for your response. Of course, feel free to pursue any of the directions discussed here, if they interest you. I remain in support of accepting the paper.	Rebuttal 1: Rebuttal: Attached is our response PDF; please see the responses to the individual reviews for details. Pdf: /pdf/e3d27fa7c33ecb040b2ad5c115ea48d2f1cf405d.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Superposed Decoding: Multiple Generations from a Single Autoregressive Inference Pass	Accept (poster)	Summary: This paper introduces Superposed Decoding, a novel method to generate multiple drafts (k drafts) in a single inference pass. The process involves two iterative steps: (1) running a large language model (LLM) inference on fused tokens and utilizing top-k sampling to produce k candidate tokens, and (2) combining n-gram probability scores with LLM probability scores to extend each draft with one candidate token, iteratively. This method demonstrates significant improvements in generation perplexity, downstream task performance, and is favored by human annotators, delivering results 2.44 times faster. The authors also suggest a resetting mechanism to mitigate repetitions in long drafts. Strengths: - The method is intelligent and innovative, addressing a task that, while not highly popular, has numerous practical applications and significant real-world relevance. - The experiments are well-designed, covering text generation, question answering, and human evaluation, showcasing the method's effectiveness in both quality and efficiency. Weaknesses: - The current application is restricted to text drafting and does not extend to code generation, which could also benefit from this method and is frequently used in practice. Technical Quality: 4 Clarity: 3 Questions for Authors: - In Section 5.2, the authors indicate that shorter generations lead to higher diversity as shown by Self-BLEU. How does this diversity change in other decoding methods? Do these methods exhibit similar diversity patterns as Superposed Decoding? Overall, I lean towards accepting this work. The weaknesses and questions are primarily around clarifications rather than flaws in the method. If the authors address these questions and provide the necessary clarifications, I am inclined to raise my score. Confidence: 3 Soundness: 4 Presentation: 3 Contribution: 3 Limitations: The authors acknowledge and provide reasonable limitations: - The quality of Superposed Decoding largely depends on the n-gram models used, which are vital for maintaining coherence. - While the drafts produced are syntactically diverse, they may lack semantic diversity. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for the positive review. We are glad that the reviewer found the approach innovative and experiments well designed. Following are the clarifications requested in the review: 1. Code generation: We agree with the reviewer and mention in the manuscript that code generation is yet another important step use case. However, in this paper we focus on language generation to showcase the generality of the method and hope to extend it to code generation in the future. 2. Diversity of other decoding schemes for short generations: We run additional experiments generating three drafts using Beam Search and Nucleus Sampling and calculate the diversity of drafts using Self-BLEU. We find that while beam search, like Superposed Decoding, becomes more diverse at shorter generation lengths, the opposite is true with Nucleus Sampling. We attribute this to the fact that Beam Search, like Superposed Decoding, produces syntactically different but semantically alike drafts. This means that as generation length increases, more tokens are generally in common between drafts. On the other hand, Nucleus Sampling’s probabilistic nature results in semantically different drafts. Consequently, longer generation lengths lead to a higher proportion of token-level differences. _Diversity as measured by Self-BLEU_ \| Generation Length \| 5 \| 10 \| 15 \| 20 \| \|---------\|------\|------\|------\|------\| \| Superposed Decoding \| 0.51 \| 0.81 \| 0.88 \| 0.91 \| \| Beam \| 0.35 \| 0.64 \| 0.75 \| 0.81 \| \| Nucleus \| 0.33 \| 0.25 \| 0.21 \| 0.19 \| We hope that this rebuttal solidifies your positive outlook on the paper and we are happy to discuss if you need any further clarifications to increase the score and facilitate acceptance of the paper. --- Rebuttal Comment 1.1: Comment: Thanks for the authors' response. After carefully reading the response and the reviews from other reviewers, I would like to keep the score unchanged and recommend acceptance. --- Rebuttal 2: Comment: Thank you for your response and the support for the acceptance of the paper.	Summary: The paper "Superposed Decoding: Multiple Generations from a Single Autoregressive Inference Pass" introduces a method to generate k similar responses in parallel using a single forward pass in autoregressive models. Strengths: The paper validates its method on two open-source LLMs, providing empirical evidence of its applicability. Weaknesses: 1. Limited Problem Scope and Optimization Potential: The problem addressed might not have significant optimization potential. Using sampling and batch construction during inference can prevent an increase in latency. Autoregressive decoding is often memory-bounded, so the batch inference will not be a big burden for latency. It is unclear if the authors have considered batch construction for the vanilla method when measuring latency. 2. Restricted Scenario and Lack of Strong Justification: The scenario studied is highly restricted, and the authors do not provide compelling evidence that the proposed method yields superior results for n-decoding. Specifically, the top-1 result obtained using the proposed method performs worse than vanilla decoding. 3. Complexity and Additional Dependencies: The proposed method appears inelegant, relying on an additional n-gram language model to calibrate the outputs of the LLM. This dependency detracts from the method's appeal and does not demonstrate a clear advantage over batch inference. Technical Quality: 2 Clarity: 3 Questions for Authors: see weakness Confidence: 4 Soundness: 2 Presentation: 3 Contribution: 2 Limitations: na Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: In the following we provide clarifications that were requested: 1. Limited scope and restricted scenarios: We respectfully disagree with the reviewer about the limited scope and scenarios of Superposed Decoding. Short text generation and drafting are common real-world problems and a centerpiece to products such as GitHub Copilot and Tabnine. Features like Gmail SmartCompose, Word auto-suggestions, and iPhone auto-completions also rely on providing multiple suggestions. 2. Optimization potential: We agree with the reviewer that batch construction helps with latency and that autoregressive decoding is often memory bound. However, solely using batch construction for multiple drafts reduces effective batch size by a factor of $k$ (i.e. number of prefixes that can be handled at once). On the other hand, Superposed Decoding is agnostic to these challenges and _complementary to batch construction_. Superposed Decoding helps generate $k$ drafts for every decoding run, _effectively multiplying the batch size of any decoding scheme_ like nucleus sampling. This avoids the limitations imposed by vanilla batching, benefiting scenarios where batch size is a limitation, such as server-based applications like Github Copilot or Tabnine. An interesting way to think about Superposed Decoding is as a way to execute local searches while each nucleus sampling draft would be a global search. One can always combine both ideas and benefit from increasing the effective number of generated drafts. We are happy to discuss this further. 3. Lack of strong justification: It is true that the top-1 result from Superposed Decoding is slightly outperformed by vanilla decoding in some metrics. However, these differences are small: 0.04% on TriviaQA and 0.33% on Natural Questions. In addition, Superposed Decoding is primarily meant for multiple draft scenarios, where it can significantly outperform the other decoding methods without increasing compute (Figure 5, Figure 7). In the case where the goal is just a single generation, then vanilla decoding (or any other sampling method) can be used at no detriment by simply toggling off n-gram filtering. 4. Complexity and dependence on n-gram models: We respectfully disagree that n-gram models limit the convenience of Superposed Decoding. Data stores and non-parametric modeling are widespread in language models (ACL 2023 Tutorial on Retrieval-based Language Models and Applications). For example, “Nonparametric Masked Language Modeling” establishes the use of an external corpus of two billion tokens for masked language generation (Min et al., ACL 2023). Similarly, large text corpuses are essential for document retrieval and RAG applications (Karpukhin et al., EMNLP 2020; Shi et al., NAACL 2024). N-gram models have also proven to be powerful in machine translation settings (Branst et al., ACL 2007). Finally, with the advances like Infinigram (Liu et al., COLM 2024), n-gram datastores are easy to access and scale up as part of language modeling. We hope that this rebuttal addresses your concerns and we are happy to discuss further if you need any further clarifications to increase the score and facilitate acceptance of the paper. --- Rebuttal Comment 1.1: Comment: My major concern is still the n-gram LM, your rebuttal is about all the nonparametric LMs. However, we are discussing n-gram LM. And the evidence you gave like Branst et al., ACL 2007 is a very old setting. I am an expert in machine translation, and I think this evidence can not prove anything in the context of LLM. And I'm very concerned that your method can only find some paraphrased sentences rather than covering different modes of the data like top-p sampling. The self-bleu also validated my concern. Can you add more experiments like [1]. [1] Large Language Monkeys: Scaling Inference Compute with Repeated Sampling, arxiv --- Reply to Comment 1.1.1: Comment: We thank the reviewer for their prompt reply. Here are our thoughts. 1. Nonparametric LMs: We respectfully disagree that previous non-parametric LM research is unrelated to our method. In the context of language models, non-parametric language models are defined as language models whose data distribution is “a function of the available data,” with complexity growing with data (Siegel, 1957; Hollander et al., 2013; Min et al., 2023). We believe that this definition well-encapsulates a language model interpolated with n-gram models. Indeed, we see similar use cases in kNN-LM (Khandelwal et al., 2020) and NPM (Min et al., 2023), which use external datastores that behave like n-gram models - the sole difference is that they are queried with a representation vector instead of a token sequence. Superposed Decoding also can rely on representation vectors for retrieval from a datastore rather than directly doing a dictionary lookup during n-gram filtering. The former is “semantic” while the latter is “syntactic”. 2. Modes of data: Yes, the reviewer is right about Superposed Decoding potentially being unable to cover significantly different modes of the data like top-p sampling. However, this is not a concern nor a bug. The goal of Superposed Decoding is to provide multiple drafts at constant compute to help increase coverage. This coverage aids in improving user experience and factuality as shown in the experiments. As we mention, Superposed Decoding is intended for local exploration. More often than not, the greedy top-1 generation solves the problem at hand; further enabling local search and multiple drafts around it supports quite a few use cases. Having said that, Superposed Decoding can be combined with any sampling method, be top-p or something else, and it can help generate a local set of drafts for each sampling trajectory at no additional compute cost. For instance, if top-p sampling is used to generate $n$ drafts, Superposed Decoding with $k$ local drafts can be spliced in at any timestep to strategically produce $nk$ drafts, where each top-p trajectory is bolstered by $k$ local explorations at no extra cost. We include a sample generation below, using Superposed Decoding to produce three local drafts for each top-p sample; this expands the available options without extra compute or reducing mode coverage. SPD denotes Superposed Decoding. ``` Example of Top-p Sampling w/Superposed Decoding: │ Prefix: “Melbourne is” │ └───Top-p: Melbourne is a great city, with │ │ SPD: Melbourne is a great city, with a lot of things │ │ SPD: Melbourne is a great city, with a lot to things │ │ SPD: Melbourne is a great city, with a lot of history │ └───Top-p: Melbourne is a city of many different │ │ SPD: Melbourne is a city of many different cultures and relig │ │ SPD: Melbourne is a city of many different cultures, relig │ │ SPD: Melbourne is a city of many different cultures and languages │ └───Top-p: Melbourne is the capital city of Victoria │ │ SPD: Melbourne is the capital city of Victoria, Australia. It │ │ SPD: Melbourne is the capital city of Victoria and Australia. It │ │ SPD: Melbourne is the capital city of Victoria, Australia. The ``` Do let us know if we are missing something here, and we are happy to discuss further. Also, let us know if the concern about optimization potential was resolved through the rebuttal. --- Rebuttal 2: Comment: We ran experiments from [1] and found that Superposed Decoding significantly improves accuracy with no additional compute, demonstrating its practicality. On TriviaQA and Natural Questions, combining Nucleus Sampling and Superposed Decoding results in better performance than vanilla Nucleus Sampling across the board. TriviaQA (the three rows in each column use the same compute): \| Compute ($k$) \| 1 \| 10 \| 20 \| 30 \| 40 \| 50 \| 60 \| 70 \| 80 \| 90 \| 100 \| \|---------------\|-----------\|-----------\|-----------\|-----------\|-----------\|-----------\|-----------\|-----------\|-----------\|-----------\|-----------\| \| $NS$ \| 51.04 \| 68.75 \| 70.31 \| 71.87 \| 72.92 \| 74.48 \| 74.74 \| 75.26 \| 75.78 \| 76.30 \| 76.56 \| \| $NS_{SPD2}$ \| 51.30 \| 68.75 \| 70.57 \| 72.66 \| 74.74 \| 75.78 \| 76.30 \| 76.82 \| 78.39 \| 79.17 \| 79.43 \| \| $NS_{SPD3}$ \| 51.82 \| 70.57 \| 74.22 \| 75.52 \| 77.34 \| 77.87 \| 78.39 \| 78.65 \| 79.17 \| 79.43 \| 79.95 \| Natural Questions (the three rows in each column use the same compute): \| Compute ($k$) \| 1 \| 10 \| 20 \| 30 \| 40 \| 50 \| 60 \| 70 \| 80 \| 90 \| 100 \| \|---------------\|-----------\|-----------\|-----------\|-----------\|-----------\|-----------\|-----------\|-----------\|-----------\|-----------\|-----------\| \| $NS$ \| 14.32 \| 32.55 \| 36.98 \| 38.54 \| 40.36 \| 41.15 \| 41.67 \| 41.93 \| 42.19 \| 42.71 \| 42.97 \| \| $NS_{SPD2}$ \| 15.36 \| 31.25 \| 34.90 \| 38.02 \| 39.84 \| 41.41 \| 41.67 \| 42.45 \| 43.75 \| 43.75 \| 43.75 \| \| $NS_{SPD3}$ \| 15.63 \| 31.25 \| 36.98 \| 39.06 \| 41.15 \| 42.71 \| 43.75 \| 43.75 \| 44.27 \| 44.79 \| 45.57 \| Experimental Setup ($NS$: Nucleus Sampling; $SPD$: Superposed Decoding): - We evaluate three decoding strategies on Llama-2-7B: - Vanilla Nucleus Sampling for $n$ timesteps ($NS$). - Nucleus Sampling for $c$ timesteps then two SPD drafts for $n-c$ timesteps ($NS_{SPD2}$). - Nucleus Sampling for $c$ timesteps then three SPD drafts for $n-c$ timesteps ($NS_{SPD3}$). - We compare accuracy on 1-100 inputs in a constant compute setting. This means the performance of the first $k$ $NS$ samples is compared against the first $2k$ $NS_{SPD2}$ samples and $3k$ $NS_{SPD3}$ samples, where $k \leq 100$. - In the tables above, each column denotes results given the same compute. We show accuracy at intervals of 10 for $k$. We average results over three runs for each strategy. We hope that these experiments resolve your concerns about Superposed Decoding’s practicality. We would also like to know if our earlier responses addressed your concerns about our method’s optimization potential, justification, and use of n-gram models. [1] Large Language Monkeys: Scaling Inference Compute with Repeated Sampling, arxiv --- Rebuttal Comment 2.1: Comment: Thanks for your reply. What is the evaluation metric for this table? Do you have an external reward model to perform best-of-n or do you use self-consistency? --- Rebuttal Comment 2.2: Comment: And what is $c$? I do not see $c$ in the table, is it $SPD_{c}$? --- Rebuttal 3: Comment: Following are the requested clarifications: 1. Evaluation Metric: We use precision as our metric. In addition, we follow the main body of [1] (Sections 2 and 3) and assume an ideal scenario where the best sample can always be identified. While [1] does suggest the usage of other verification methods, the paper’s experiments are primarily conducted assuming an ideal scenario. 2. Notation: $c$ is the number of timesteps that are generated with Nucleus Sampling before Superposed Decoding is applied to create drafts. $n$ is the total number of timesteps. For example, in TriviaQA, $c = 4$ and $n = 10$. For Natural Questions, $c = 9$ and $n = 15$. These values are held constant. In the table, $NS_{SPD2}$ and $NS_{SPD3}$ denote whether two or three drafts are generated after $c$ timesteps. Please let us know if anything is still unclear and thanks for extremely prompt responses. [1] Large Language Monkeys: Scaling Inference Compute with Repeated Sampling, arxiv --- Rebuttal Comment 3.1: Comment: Why do you use this setting instead of just use only SPD? --- Reply to Comment 3.1.1: Comment: As we mentioned earlier in the rebuttal (and see Modes of Data in [here](https://openreview.net/forum?id=KSOkkHm9I7&noteId=T6Le0oX7hh)), SPD enables local search that helps improve the coverage of generations at no additional cost. For example, one nucleus sampled generation can be expanded by $k=3$ times using Superposed Decoding without increasing the compute. We do not claim that three SPD drafts are as good as three Nucleus Sampling drafts, but only that they are better than only one nucleus sampled draft, as shown in our paper’s experiments. This is a fair comparison because three nucleus sampled drafts will cost three times the compute as three Superposed drafts. Extending this further to the experiment above, we want to show that Superposed Decoding helps cover many modes of data. Using Nucleus Sampling as the scaffold (which can span the global space) and then generating many more drafts for the same compute cost using Superposed Decoding shows the practicality and complementary nature of SPD. Generating 3x or 100x drafts with SPD will not make a difference after a point (similar to Nucleus Sampling after 20-50 drafts despite linearly increasing compute) as accuracy saturates around a local minima. In this case, SPD helps Nucleus Sampling do a better local search (than just itself) to hit the right mode of the data to accurately answer a given question. This is shown by an asymptotic increase of accuracy/precision by roughly $3$% on both TriviaQA and Natural Questions. Do let us know if you have further questions. In short, we present Superposed Decoding as a novel alternative that generates multiple drafts for the same compute cost as a single draft while increasing the coverage for both factuality and user preferences.	Summary: This paper proposed a novel decoding algorithm to generate k coherent drafts in one autoregressive inference pass. An additional n-grams model is used to keep the k-drafts coherent. Experimental results show that this method can generate three relatively coherent drafts while achieving a speed-up ratio of more than 2.44. Strengths: 1. This paper is well written. 2. Comprehensive experiments are conducted to evaluate the performance of the proposed method. Weaknesses: 1. This paper proposed Superposed Decoding, which aims to generate k different sequences in a single inference of the LM. It uses a superposition to approximately represent the last tokens of k drafts in each decoding step. However, it seems that this goal can be easily achieved by adopting tree attention masks [1] without the proposed superposition. For example, given a prefix [x1,x2,...,xn], we can greedy sample k tokens in the output distribution to initialize k different drafts. Next, we concatenate these k tokens with the prefix. Here, the current sequence has n+k tokens. The position id is [1,2,....,n]+[n+1]*k. We produce the corresponding tree attention mask to keep the k drafts independent. If we just want to complete these k drafts, we can input these k tokens in parallel and perform greedy sampling on each of them in each step. This generation also only costs one decoding process. (Let L be the max length of the k drafts; the whole generation process takes L decoding steps.) However, the k drafts are exactly the same as those generated separately. In contrast, the proposed method loses precision. What is the strength of Superposed Decoding compared to the approach above? Reference： [1] Li Y, Wei F, Zhang C, et al. Eagle: Speculative sampling requires rethinking feature uncertainty[J]. arXiv preprint arXiv:2401.15077, 2024. 2. The coherence of the generated drafts depends on the quality of the n-grams model. Meanwhile, the introduction of additional n-gram models limits the convenience of this approach. Technical Quality: 1 Clarity: 3 Questions for Authors: 1. See weakness 1. 2. How often does this method generate incoherent or erroneous drafts? Confidence: 4 Soundness: 1 Presentation: 3 Contribution: 2 Limitations: The n-grams model is constructed by open-source texts, which containing toxic data that may affect the safety of the model. This factor should be taken into consideration. Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We are glad that the reviewer found the paper to be well written and are happy to hear that the reviewer appreciated the experiments. Below are the clarifications requested in the review: 1. Comparison to tree attention masks: While this paper is interesting and relevant, we do not believe it is a replacement for Superposed Decoding. It is true that tree masking will reduce KV cache size compared to vanilla drafting techniques because the prefix is stored only once. However, there are still _additional storage costs_ from storing every generated token in memory (Cai et al., ICML 2024), which Superposed Decoding does not need to do. These costs are present regardless of batching and can reduce effective batch size (i.e. number of prefixes that can be handled at once). This is further accentuated when the initial prefix length is small compared to the generation length, leading the generated tokens to dominate the overall storage requirement. Furthermore, every additional token that must be stored and processed means less efficiency from a FLOPs perspective. Superposed Decoding does not have any of these limitations because it combines multiple drafts into a single superposed LM input. In addition, Superposed Decoding is _completely complementary_ to Tree Attention because some drafted tokens can be superposed to save memory, only requiring slight adjustment to the tree attention mask. We are happy to discuss further on this. 2. Dependence on n-gram models: We respectfully disagree that n-gram models limit the convenience of Superposed Decoding. Data stores and non-parametric modeling are widespread in language models (ACL 2023 Tutorial on Retrieval-based Language Models and Applications). For example, “Nonparametric Masked Language Modeling” establishes the use of an external corpus of two billion tokens for masked language generation (Min et al., ACL 2023). Similarly, large text corpuses are essential for document retrieval and RAG applications (Karpukhin et al., EMNLP 2020; Shi et al., NAACL 2024). N-gram models have also proven to be powerful in machine translation settings (Branst et al., ACL 2007). Finally, with the advances like Infinigram (Liu et al., COLM 2024), n-gram datastores are easy to access and scale up as part of language modeling. 3. Incoherent and erroneous drafts: Thank you for this question. While incoherency is an important metric, there are currently no good ways to measure at scale without using proxies like perplexity, which we show in the paper. In practice, we rarely see any incoherent drafts, as highlighted by strong human evaluation performance. Erroneous drafts are a different problem because they are also tied to factuality – which is typically helped by non-parametric modeling and data stores similar to what we do with n-gram filtering. 4. Toxicity: The risk of toxicity can be significantly reduced by building n-gram models on clean data stores created by domain experts. Furthermore, n-gram models are frequently used in personalized scenarios. In such cases, the relevant data stores are often pre-filtered to be appropriate for a user or specific task. We hope that this rebuttal clarifies your concerns, and we are happy to discuss any further clarifications to increase the score and facilitate acceptance of the paper. --- Rebuttal Comment 1.1: Comment: Thanks for the explanations. I will raise my score to 5. --- Rebuttal 2: Comment: We wanted to check in to see if our rebuttal resolved your concerns. We are happy to discuss further. --- Rebuttal 3: Comment: We thank the reviewer for agreeing to raise their score, and we are glad that our rebuttal resolved the concerns you had. --- Rebuttal Comment 3.1: Comment: Before the discussion period ends, we were wondering if the reviewer could update their score to reflect the score change? Apologies for the repeated comments.	Summary: This paper presents a method to generate multiple sequences from an autoregressive model with a single forward pass. The Superposed Decoding method relies on the approximate linearity of the overall model to additively superpose embeddings for distinct sequences through the model in the same forward pass. Strengths: The method is shown to have practical benefit over other sampling methods. The idea appears to be novel and is surprising that it works, albeit with an additional n-gram filtering step. Weaknesses: Understanding this phenomenon better in the architectures tested like LLaMA and Mistral would help the idea in this paper substantially. What is it about the representations that allows them to be processed in superposition and why do these LLMs tend to remain in this condition. Is this impacted by the depth of the network? There's an important aspect of the kind of linearity that allows the superposition observed here compared to previous work mentioned like [34. 22] cited in this work. The other work showed that representations of concepts are linear, but not that the decoding operations can process superpositions in a linear fashion. Furthermore, the Superposed Decoding method implies that these properties hold for intermediate representations throughout the network. Also, some relevant work in this direction are worth mentioning: Elhage, Nelson, et al. "Toy models of superposition." arXiv preprint arXiv:2209.10652 (2022). Cheung, Brian, et al. "Superposition of many models into one." Advances in neural information processing systems 32 (2019). Technical Quality: 3 Clarity: 3 Questions for Authors: The exploration of the alignment between the component vector and the superposition in Figure 3 is interesting, but could the authors create a baseline to get a better idea of how strong the alignment is. For example, calculating alignment between unrelated sequences would give a better idea of what the expected lower bound of of alignment would be. For Table 3, again, to get a better idea of the properties of Superposed Decoding, can the authors show what the best perplexity would be (ignoring the fixed compute constraints/comparisons) if one were to generate multiple drafts from Nucleus, Beam/Greedy would be. This is strictly to understand what the difference would be if one were trying to generate the best sequences possible with each type of sampling to see if there's a reduction to that bound when using superposed decoding. How much does the n-gram "filtering" improve generation quality of the decoding? What are the metrics without this additional step? How much does this step help the other methods like Nucleus/Beam sampling? Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: No societal impact needs to be addressed for this work. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for the positive review and glad that the reviewer found the idea novel. We appreciate pointing to related work that we forgot to add in the paper initially and will add it. Below, we provide the clarifications requested: 1. Understanding the phenomenon: We agree with the reviewer that the success of superposition is a surprising phenomenon and there is a lot to be understood. As pointed out by the reviewer, previous works on understanding superposition (Elhage, Nelson, et al.) and newer updates (Olah et al., July 2024) point to a need for more investigation. We are unsure about exactly what allows representations to be processed while being in superposition, but do observe that this phenomenon happens across various classes of LLMs (Llama, Mistral, OLMo (see below)). With regards to the impact of network depth, we are unsure what the reviewer means and would appreciate clarification. If they mean the intermediate layers of the language models we currently use, we include an additional figure on linearity by layer in Llama-2-7B, which can be found in Figure 1 of the general response PDF. We will update the paper to contain this. Alternatively, if they mean models of different depth, we run additional experiments on linearity for OLMo-1B, OLMo-7B, Llama-2-13B, and Llama-2-70B. Interestingly, we discover that OLMo-7B is less linear than OLMo-1B. However, Llama-2-13B (40 layers compared to 7B’s 32 layers) is significantly more linear than Llama-2-7B. Linearity further improves on Llama-2-70B (80 layers) from Llama-2-13B. This variance highlights that there is still a lot more about superposition that we can learn. _Numbers 0-20 in the table represent timesteps._ \| Model \| Layers \| 0 \| 1 \| 2 \| 3 \| 4 \| 5 \| 6 \| 7 \| 8 \| 9 \| 10 \| 11 \| 12 \| 13 \| 14 \| 15 \| 16 \| 17 \| 18 \| 19 \| 20 \| \|-------------\|-------------\|---\|------\|------\|------\|------\|------\|------\|------\|------\|------\|-------------\|------\|------\|------\|------\|------\|------\|------\|------\|------\|---------\| \| OLMo-1B\| 16\| 1 \| 0.96 \| 0.93 \| 0.91 \| 0.88 \| 0.88 \| 0.88 \| 0.89 \| 0.89 \| 0.86 \| 0.88\| 0.87 \| 0.88 \| 0.87 \| 0.87 \| 0.85 \| 0.86 \| 0.85 \| 0.85 \| 0.85 \| 0.87 \| \| OLMo-7B \| 32\| 1 \| 0.91 \| 0.86 \| 0.81 \| 0.78 \| 0.76 \| 0.73 \| 0.72 \| 0.70 \| 0.70 \| 0.67\| 0.65 \| 0.65 \| 0.60 \| 0.58 \| 0.59 \| 0.59 \| 0.60 \| 0.57 \| 0.59 \| 0.58 \| \| Llama-2-7B \| 32\| 1 \| 0.92 \| 0.84 \| 0.79 \| 0.81 \| 0.76 \| 0.71 \| 0.65 \| 0.67 \| 0.61 \| 0.59\| 0.55 \| 0.54 \| 0.45 \| 0.47 \| 0.45 \| 0.46 \| 0.39 \| 0.36 \| 0.39 \| 0.37 \| \| Llama-2-13B \| 40\| 1 \| 0.95 \| 0.91 \| 0.88 \| 0.85 \| 0.85 \| 0.83 \| 0.79 \| 0.78 \| 0.77 \| 0.76\| 0.73 \| 0.71 \| 0.69 \| 0.66 \| 0.67 \| 0.68 \| 0.64 \| 0.64 \| 0.63 \| 0.61 \| \| Llama-2-70B \| 80\| 1 \| 0.94 \| 0.92 \| 0.91 \| 0.89 \| 0.87 \| 0.84 \| 0.83 \| 0.84 \| 0.81 \| 0.82\| 0.75 \| 0.74 \| 0.74 \| 0.71 \| 0.68 \| 0.73 \| 0.68 \| 0.67 \| 0.67 \| 0.65 \| 2. Observed Linearity: We agree that our observation of superposition is not the same as other works. Figure 1 in the general response PDF shows that the linearity is more profound in the initial and later layers of the LLM than the middle layers, albeit still much better than random. In addition, while our experiments do suggest that decoding operations can process superpositions linearly, it is important to note that decomposing the superposed representation assumes that the top-k tokens provide a basis for the superposition and still requires further denoising with an n-gram model. We believe there is a lot of interesting future work to be done in this direction. 3. Linearity analysis with random sequences: Thanks for the suggestion! Here are results from cosine similarity between random sequences to calibrate what a lower bound would be. Results are averaged over 5000 pairs of random sequences from OpenWebText. We will update our paper with these results as well. \|Timestep\|1\|2\|3 \| 4\| 5\| 6\| 7\| 8\| 9\| 10\| 11\| 12\| 13\| 14\| 15\| 16\| 17\| 18\| 19\| 20 \| \|-\|-\|-\|-\|-\|-\|-\|-\|-\|-\|-\|-\|-\|-\|-\|-\|-\|-\|-\|-\|-\| \|Cosine Similarity\|0.56\|0.23\|0.17\|0.14\|0.13\|0.12\|0.12\|0.12\|0.12\|0.11\|0.11\|0.12\|0.11\|0.11\|0.11\|0.12\|0.12\|0.12\|0.12\|0.12\| 4. Best perplexity for other decoding schemes: Here are the numbers for the average best perplexity for other schemes in case of three drafts. However, we want to add that perplexity is a tricky thing to rely on alone because lower perplexity does not always indicate better coherence (Holtzman et al., ICLR 2020). \| \| Best Perplexity \| \|--\|-\| \| Superposed Decoding \| 4.63 \| \| Beam Search \| 2.87 \| \| Nucleus Sampling \| 3.47 \| 5. Impact of n-gram filtering: Thank you for raising this point. Below we show perplexity evaluation without n-gram filtering. At a high-level, one can think of n-gram filtering to be reducing the ambiguity in decomposing a superposed representation and denoising the process. Without this step, while the first draft will be more or less greedy, the other drafts will have significantly worse quality to the detriment of users. \| Superposed Decoding \| Draft 1 \| Draft 2 \| Draft 3 \| Best \| \|-\|-\|-\|-\|-\| \| PPL w/o filtering\| 4.54\| 18.33\| 18.61\| 4.06 \| \| PPL with filtering \| 5.03\| 7.97\| 10.05\| 4.63 \| Below, we also show n-gram filtering applied on nucleus sampling. We experiment with several beta values for how heavily n-gram filtering is weighted and evaluate using perplexity. From the experiments, n-gram filtering does not provide significant benefits to nucleus sampling but also does not diminish the performance of nucleus sampling either. \| Beta (n-gram weight) \|0\| 0.01 \| 0.05 \|0.1\|0.2\|0.4\| 0.6\| 0.8\| \|-\|--\|---\|--\|-\|-\|-\|-\|-\| \| Nucleus Sampling \| 5.17 \| 5.18 \| 5.26 \| 5.16 \| 5.24 \| 5.16 \| 5.15 \| 5.11 \| We hope that this rebuttal answers any questions you have and solidifies your positive outlook on the paper. We would love to discuss more if you need any further clarifications. Ref: Olah et al July 2024: https://transformer-circuits.pub/2024/july-update/index.html --- Rebuttal Comment 1.1: Comment: > If they mean the intermediate layers of the language models we currently use, we include an additional figure on linearity by layer in Llama-2-7B, Yes, that is what I meant. Thank you for following up on this. > that the top-k tokens provide a basis for the superposition and still requires further denoising with an n-gram model. We believe there is a lot of interesting future work to be done in this direction. If I understand this point correctly, you're referring to the softmax() of the representation when it maps to output tokens is a highly non-linear operation? And the denoising with an n-gram model is meant to repair this issue to some degree? --- Rebuttal 2: Comment: Yes, this is exactly correct. Without denoising, it is very difficult to get multiple coherent outputs from the superposed representations. Another way of thinking of the n-gram models is that they help ground the token distributions in reality to correct for noise in the top-k tokens.	Rebuttal 1: Rebuttal: First, we would like to thank all reviewers for their feedback. We would also like to express sincere appreciation to the AC, SAC, and PCs for the time they have put into the current review cycle. We want to reiterate that Superposed Decoding is a novel algorithm leveraging an interesting phenomenon of representational superposition in LLMs towards generating multiple drafts in a single autoregressive inference pass and is complementary to other decoding methods and efficiency improvements. In the rebuttal PDF, we include a figure on linearity by layer in Llama-2-7B through five timesteps in case it may be of use to the reviewers. We address the rest of the questions and comments the reviewers had in their respective rebuttals. Pdf: /pdf/dd03faff9626b6b1620fd4751b07599c6c974ef7.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Task-Agnostic Machine-Learning-Assisted Inference	Accept (poster)	Summary: This paper proposes a post-prediction inference solution (PSPS) that can be adapted into various established data analysis routine and delivers valid and efficient inference for most ML models. In particular, the paper uses both labelled and unlabelled data to derive estimators that are consistent and efficient and only utilizes 1st and 2nd order summary statistics. Strengths: The paper provides a well-rounded analysis on the proposed method with sensitivity analysis on distributions shifts, to violations of independence assumption between labelled and unlabelled data and to better statistical power in false discovery control. Weaknesses: - The paper claims the proposed method offers better statistical power in various statistical tasks from mean estimation to quantile regression through various numerical experiments in Section 5.1. However, it is unclear how much of the statistical power is offered by the nature of transductive inference and how much is offered by the proposed protocol. For example, [1] shows that incorporating unlabelled data achieves lower test error than purely labelled data already. Could the author demonstrate the unique advantages offers by the proposed method? - The protocol proposed relies on assumptions on 1) i.i.d. distributions between labelled and unlabelled data and 2) finding an algorithm applied to labeled data returns a consistent and asymptotic normally distributed estimators. I am wondering how easy is it to find an algorithm that can produce such estimators? - The authors list one of the key features of the method is privacy-preserving, but did not discuss this point in the remaining paper. [1] Chapelle, O., Vapnik, V., & Weston, J. (1999). Transductive inference for estimating values of functions. Advances in Neural Information Processing Systems, 12. Technical Quality: 3 Clarity: 2 Questions for Authors: Please see above. Confidence: 2 Soundness: 3 Presentation: 2 Contribution: 2 Limitations: Yes. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: W1: Reference [1] focuses on using unlabeled data to improve the estimation of regression function (i.e. E[Y\|X]). This is a classic machine learning prediction problem which leverages semi-supervised learning to enhance prediction accuracy. In contrast, our study focuses on improving estimation and statistical inference using unlabeled data, emphasizing the need for estimator consistency and the validity of confidence intervals. This is a very new topic (`Angelopoulos, Anastasios N., et al. "Prediction-powered inference." Science (2023)`) in the machine learning field. Because of this, we believe our paper and [1] address fundamentally different problems. In real-world scientific applications, many issues pertain to statistical inference (e.g., estimating the effects of genetic variants on height). The methods in [1] are not suitable for such applications, whereas our methods are specifically designed to tackle these issues. In our initial submission, we demonstrated the validity and superior statistical efficiency of our method over existing approaches (Section 3.2), substantiated by theoretical guarantees: 1. Theorem 1: PSPS achieves element-wise asymptotic variance reduction compared to classical statistical inference (based solely on labeled data) while ensuring estimator consistency. 2. Theorem 1: PSPS guarantees valid inference (accurate confidence interval coverage) compared to imputation-based inference (which relies solely on machine learning predictions using unlabeled data). 3. Propositions 1 and 2: PSPS has no larger asymptotic variance than existing ML-assisted inference methods that provide consistent estimators. Furthermore, a key feature of our method is its independence from task-specific derivations and implementations, allowing it to address a broader range of statistical problems compared to existing methods. * For M-estimation tasks, currently, only mean and quantile estimation, as well as linear, logistic, and Poisson regression, have been implemented in software and are ready for immediate application. For other M-estimation tasks, task-specific derivation of the ML-assisted loss functions and asymptotic variance are necessary. Next, researchers still need to develop software packages to carry out real applications. In contrast, PSPS only requires already implemented software designed for classical inference using labeled data. * For problems that are not considered M-estimation but have asymptotically normally distributed estimators, only PSPS can be applied and all current methods would fail. The principles that facilitate ML-assisted M-estimation are not applicable for these non-M-estimation tasks. To summarize, our method, designed for estimation and statistical inference, addresses a different problem than [1], which focuses on prediction. We have also demonstrated the substantial advantages of our approach compared to existing methods for ML-assisted statistical inference through both theoretical and experimental analyses. We have also added the semi-supervised learning literature in the related work to avoid confusion. W2: Consistent and asymptotically normally distributed estimators are the fundamental properties of an estimator in statistical sciences, and significant research efforts have been devoted to developing such estimators for a wide range of statistical tasks. Generally, if a statistical task allows the application of the Central Limit Theorem. the resulting estimator is likely to be asymptotically normal. Specifically, M-estimator that calculates an estimator through empirical risk minimization, and U-statistics that can be expressed as averages of a symmetric function applied to subsets of a sample are both consistent and asymptotically normally distributed estimators. Common examples of M-estimators include but are not restricted to maximum likelihood estimation, mean and median estimations, linear regression models, generalized linear models, and quantile regression. U-statistics include but is not restricted to variance estimation and Wilcoxon-Rank Sum statistics. In summary, it is fairly straightforward to identify an algorithm capable of producing such estimators for a wide range of statistical tasks. W3: The “privacy-preserving" feature of PSPS refers to the fact that we only require summary statistics as input for inference, rather than individual-level raw data (features X and label Y). This terminology is commonly used in human genetics, healthcare, and multi-center electronic health record analysis to describe methods that enable statistical inference without directly accessing personal data. This approach is analogous to federated learning (`Kairouz, Peter, et al. 2021`) in the machine learning literature. For example, consider a scenario where labeled data is in one center and unlabeled data in another, yet researchers cannot access individual-level data from both centers simultaneously. Under such conditions, current ML-assisted inference, which relies on accessing both labeled and unlabeled data to minimize a joint loss function, is not feasible. However, PSPS circumvents this issue by aggregating summary statistics from multiple centers, thus performing statistical inference while upholding the privacy of individual-level data. We also acknowledge that in the machine learning literature, "privacy-preserving" often specifically refers to techniques like differential privacy. To avoid confusion, we have revised the terminology from “privacy-preserving” to "federated inference" and provided an example to illustrate this use case more clearly. Final note: We are excited that you find our methods achieve better statistical power compared with current methods and our strategy to deal with distributional shifts. If you have any further questions, please do not hesitate to let us know. If our responses have resolved your concerns, we kindly request you to consider increasing your score and championing our paper. --- Rebuttal Comment 1.1: Comment: W1: Thank you for the clarification. I agree that the current work addresses different problems with [1]. W2: I agree consistent and asymptotically normal estimators are common in statistical sciences but not convinced it is common for current ML algorithms, e.g., LLM, given the paper focuses on ML-assisted inference. W3: Thank you for the clarification. In general, I agree that this paper proposes a new solution that improves statistical consistency and correct confidence coverage using unlabeled data, however I am not certain the impact of contribution given I am not an expert in this area. Therefore I will raise my score but lower my confidence to reflect this. --- Rebuttal 2: Comment: Thanks for your reply! W2: We would like to clarify that our framework does not require the consistent and asymptotically normal estimators for ML algorithms that are commonly expected in statistics. In fact, our approach can accommodate any "black box" ML algorithm. In our setting, the ML algorithm is used to impute (predict) labels in unlabeled data. These predictions are then used as input to a statistical method (algorithm), such as linear regression, to solve a statistical problem, such as estimating the effect of DNA on height. The requirement for consistent and asymptotically normal estimators applies only to the statistical algorithm, not to the ML algorithm used for label prediction. We have updated our paper to explicitly state that we did not impose any constraints on the ML algorithms used for label prediction. --- Rebuttal Comment 2.1: Comment: Thank you for addressing the concern on the proposed method's applicability - I am raising the score accordingly while maintaining low confidence.	Summary: This paper proposes a new unified framework for ML-assisted inference that reduces the general problem to essentially one of estimating normal means, and then applies simple operations (and a bootstrap step) to solve the normal means problem. In addition to the unifying framework’s simplicity, a key result is that the asymptotic efficiency of the proposed estimator dominates that of existing works under mild conditions. Strengths: 1. The problem is an important one 2. The main idea presented in section 2.2 is quite compelling, reducing the ML-assisted inference problem into basically a means estimation problem, and also finding the optimal weighting to combine the components 3. The results about dominating existing approaches in terms of statistical efficiency are exciting Weaknesses: 1. Theorem 1 doesn’t give asymptotically valid inference, since it doesn’t address variance estimation. If the asymptotic variance were known, this result would be sufficient, but it is not, and what is used instead is an estimate of the variance, which must be proved to be consistent in order to conclude asymptotic validity of Algorithm 1’s confidence interval and p-value. This oversight is relevant in other areas, such as eq (35) in the appendix is unjustified and does not follow from eq (34). 2. Prop 1 as stated does not say that these methods all have the same asymptotic variance, which seems to be the implication of the rest of section 3.2 after Prop 1. It seems the proof does prove the right thing, it’s just the statement is wrong (it is missing \sqrt{n} multiplying the LHS of each of the three limits). 3. Proof of prop 4 seems to just be rehashing the proof of knockoffs, except for a single sentence in lines 531-532 which simply states, without proof, the most important part, and the only part that involves the proposed method. In my opinion, the paper cannot be published without these issues addressed, hence my current score. Item 2 seems to just be a typo, but item 1 is absolutely critical and central, and item 3 is just not rigorous, so it should either be fixed or deleted (personally, I don’t think section 4 strengthens the paper much, since it’s just applying known FDR control techniques to the output of the proposed method, so the validity should just follow from the validity of the proposed method and that of the known FDR control techniques). If they are addressed (and no other reviewers raise other issues that cause me concern), my score would go up quite a bit, as I think this paper has significant strengths. Technical Quality: 1 Clarity: 3 Questions for Authors: In what sense is your method more task-agnostic than others? It seems to still require \mathcal{A}, which is task-specific. The authors mention in lines 129-131 that works have been developed that are general to M-estimators, but many (all?) the simulation tasks in Figure 3 which claim to be ones which “have not been implemented for ML-assisted inference” are M-estimation tasks (or reduce to them), so why couldn’t other methods have been applied to them? Explaining this more clearly would raise my score. Confidence: 3 Soundness: 1 Presentation: 3 Contribution: 3 Limitations: The authors have not addressed computational efficiency, which is a critical property—how fast is it relative to the other methods under consideration? Addressing this would raise my score. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: W1: Thank you for the comment. We have addressed the variance estimation in Theorem 1 by adding " With $\hat{\mathbf{V}}(\hat{\theta} _{\mathrm{PSPS}}) \xrightarrow{P} \mathbf{V}(\hat{\theta} _{\mathrm{PSPS}}), \lim _n \mathbb{P}(\theta _k^* \in \mathcal{C} _{\alpha, k}^{\mathrm{PSPS}})=1-\alpha$ where $\mathcal{C} _{\alpha, k}^{\mathrm{PSPS}}=(\hat{\boldsymbol{\theta}} _{\mathrm{PSPS} _k} \pm z _{1-\alpha / 2} \sqrt{\hat{\mathrm{V}}(\hat{\theta} _{\mathrm{PSPS}, \mathrm{k}}) / n})$. " Here $\hat{\mathbf{V}}(\hat{\boldsymbol{\theta}} _{\text {PSPS}})=\hat{\mathbf{V}}(\hat{\boldsymbol{\theta}} _{\mathcal{L}})-\hat{\mathbf{V}}(\hat{\boldsymbol{\theta}} _{\mathcal{L}}, \hat{\boldsymbol{\eta}} _\mathcal{L})^{\mathrm{T}}(\hat{\mathbf{V}}(\hat{\boldsymbol{\eta}} _\mathcal{L})+\rho \hat{\mathbf{V}}(\hat{\boldsymbol{\eta}} _\mathcal{U}))^{-1} \hat{\mathbf{V}}(\hat{\boldsymbol{\theta}} _\mathcal{L}, \hat{\boldsymbol{\eta}} _\mathcal{L})$ can be obtained by applying the algebraic form of $\mathbf{V}(\hat{\boldsymbol{\theta}} _{\text {PSPS}})$ using the bootstrap estimators of $\mathbf{V}$\widehat{\boldsymbol{\theta}} _{\mathcal{L}}$, \mathbf{V}(\hat{\eta} _{\mathcal{L}}), \mathbf{V}(\widehat{\boldsymbol{\theta}} _{\mathcal{L}}, \hat{\eta} _{\mathcal{L}}) \text {, and } \mathbf{V}(\hat{\eta} _{\mathcal{U}})$. Since bootstrap estimators of variance is consistent under certain regularity conditions, by Slutsky’s theorem, $\hat{\mathbf{V}}(\hat{\boldsymbol{\theta}} _{\text {PSPS}})$ is consistent for $\mathbf{V}(\hat{\boldsymbol{\theta}} _{\text {PSPS}})$. W2: We have added $\sqrt{n}$ to Prop1. The new Prop 1 is $$n^{\frac{1}{2}}\left(\widehat{\boldsymbol{\theta}}\left(\operatorname{diag}\left(\boldsymbol{\omega} _{\text {ele }}\right) \mathbf{C}\right)-\widehat{\boldsymbol{\theta}} _{\text{POP-Inf}}\right) \xrightarrow{D} \mathbf{0}, n^{\frac{1}{2}}\left(\widehat{\boldsymbol{\theta}}\left(\operatorname{diag}\left(\boldsymbol{\omega} _{\text {tr }}\right) \mathbf{C}\right)-\widehat{\boldsymbol{\theta}} _{\text{PPI}++}\right) \xrightarrow{D} \mathbf{0}, n^{\frac{1}{2}}\left(\widehat{\boldsymbol{\theta}}\left(\operatorname{diag}\left(\bf{1}\right) \mathbf{C}\right)-\widehat{\boldsymbol{\theta}} _{\text{PPI}}\right) \xrightarrow{D} \mathbf{0}, $$ which says these methods all have the same asymptotic variance. W3: The statement in lines 531-532 can be proved below: For null $k$, since debiased lasso is consistent, the $k$-th debiased Lasso coefficient converges to 0. Therefore, $W_k$ is (asymptotically) symmetric around 0. Therefore, $Z_k=1(W_k)$ (asymptotically) follows the Bernoulli distribution with a probability of 0.5. There is a typo in the original proof though, that only requires the $Z_k$ (asymptotically) follows Bernoulli(0.5) for null feature $k (\beta_k=0)$. Overall: We really appreciate the reviewer for spotting these issues in our original submission. We have addressed these issues in details above. We have also changed Section 4 to a remark in Section 3 to indicate that the results for PSPS can be directly combined with existing FDR control techniques to achieve ML-assisted FDR control. Q: Among the tasks illustrated in Figure 3, quantile regression and negative binomial regression are M-estimation problems, and the principles for applying ML-assisted inference to these tasks are available although no specific derivations and software implementations have been made available for broader use. Instrumental variable (IV) regression, while technically an M-estimation task, is typically solved using two-stage least squares, which are non-trivial to implement under a ML-assisted inference framework. debiased Lasso and Wilcoxon Rank-Sum test do not conform to minimizing a loss function. Hence, mathematical principles for the ML-assisted inference of these tasks are still underdeveloped, with no existing software implementations. PSPS is more task-agnostic than other methods in three aspects: * For M-estimation tasks * Current methods: Currently, only mean and quantile estimation, as well as linear, logistic, and Poisson regression, have been implemented in software tools and are ready for immediate application. For other M-estimation tasks, task-specific derivation of the ML-assisted loss functions and asymptotic variance via the central limit theorem are necessary. After that, researchers still need to develop software packages and optimization algorithms to carry out real applications. * In contrast, PSPS only requires already implemented algorithms and software designed for classical inference using labeled data. For example, implementing negative binomial regression with PSPS is straightforward using existing functions: ``` from statsmodels.formula.api import glm model = glm('count ~ x1 + x2', data=df, family=NegativeBinomial()).fit() ``` in python or ``` library(MASS) glm.nb(count ~ x1 + x2, data = data) ``` in R * For problems that are not considered M-estimation but have asymptotically normally distributed estimators, only PSPS can be applied and all current methods would fail. The principles that facilitate ML-assisted M-estimation are not applicable for these non-M-estimation tasks. Due to the character limit, we have placed our response to the remaining concerns in the comment section of the reviews. --- Rebuttal Comment 1.1: Comment: W1: I agree that IF the variance estimator is consistent, then everything works out easily via Slutsky's--this is not the issue. The main issue is that consistency of the variance estimator is not proved, including in the rebuttal, which simply says "bootstrap estimators of variance is consistent under certain regularity conditions". This is not a proof--what are these conditions, and what papers prove that consistency under those conditions? W2: Thank you. W3: Consistency to 0 of the debiased lasso does not imply asymptotic symmetry of the null knockoff statistics. E.g., a Gaussian with mean 1/n and standard deviation 1/n converges to 0 but is not asymptotically symmetric about 0. As these soundness issues (primarily W1+W3) were the main reason for my low score, I am not revising my score at this time. I generally find the task-agnostic argument compelling, though think this could have been communicated better in the paper. The runtime experiment and discussion is great, but this needs to be in the paper (and the authors have not indicated that they will add it to the paper). --- Rebuttal 2: Comment: Q (continued): * Even for M-estimation tasks that have already been implemented, PSPS offers the additional advantage of relying solely on summary statistics. The “task-specific derivations” mentioned throughout our paper were not only referring to statistical tasks, but also scientific tasks. Real-world data analysis in any scientific discipline often involves conventions and nuisances that require careful consideration. For example, our work is partly motivated from genome-wide association studies (GWAS). Statistically, GWAS is a linear regression that regresses an outcome (e.g., height) on many genetic variants. While the regression-based statistical foundation is simple, conducting a valid GWAS requires accounting for numerous technical issues, such as sample relatedness (i.e., study participants may be genetically related) and population structure (i.e., unrelated individuals of the same ancestry are both genetically and phenotypically similar, creating confounded associations in GWAS). Sophisticated algorithms and software have been developed to address these complex issues (`Mbatchou et al. 2021`). It will be very challenging if all these important features need to be reimplemented in an ML-assisted GWAS framework. With our PSPS protocol, researchers can utilize existing algorithms and software that are highly optimized for genetic applications to perform ML-assisted GWAS. This adaptability is not just limited to GWAS but is a major feature of our approach across scientific domains. A main result of this paper is that PSPS enables researchers to conduct ML-assisted inference using well-established data analysis pipelines. L: Following this suggestion, we have conducted experiments to compare the computational efficiency of our method (PSPS) against existing methods. Utilizing a dataset with 500 labeled and 10,000 unlabeled data points, PSPS required 1.62 seconds for linear regression and 8.27 seconds for logistic regression using 200 bootstrap resampling. The computation of one-step de-biasing using summary statistics alone took 0.032 seconds for linear regression and 0.033 seconds for logistic regression. Current methods, which estimate asymptotic variance via the closed form derived by the Central Limit Theorem instead of resampling, ranged from 0.024 to 0.049 seconds for linear regression and 0.032 to 0.077 seconds for logistic regression. Although PSPS is slower due to its resampling nature, the overall runtime remains relatively short. \| Method \| Linear regression \| Logistic regression \| \| ------------- \| ------------- \|------------- \| \| PSPS \| 1.62s \| 8.27s \| \| PPI \| 0.024s \| 0.032s \| \| PPI++ \| 0.031s \| 0.077s \| \| POP-Inf \| 0.049s \|0.034s \| We also note that we designed PSPS to utilize summary statistics, aiming to integrate seamlessly with existing computationally efficient software routinely used in data analysis. For example, Regenie is a software employed in GWAS that allows for fast computation of tens of millions of linear regressions using tens of thousands of samples (`Mbatchou et al. 2021`). Our protocol involves initially generating summary statistics using such a software tool, followed by their integration, allows high computational efficiency. Final note: We are excited that you find our work tackling an important problem and appreciate our theoretical study in statistical efficiency. If you have any further questions, please do not hesitate to let us know. If our responses have resolved your concerns, we kindly request you to consider increasing your score and championing our paper. --- Rebuttal 3: Comment: Thank you for your valuable comments! W1: We have included in the manuscript the formal regularity conditions required for consistent bootstrap variance estimation. These conditions are detailed in Theorem 3.10 (i) from `Shao, Jun, and Dongsheng Tu. The jackknife and bootstrap. Springer Science & Business Media, 2012.`, which proves the consistency of the bootstrap variance estimator. Below is the detailed theorem: We assume that $X _1, \cdots, X _n$ are i.i.d random p-dimensional vectors from distribution $F$. Let $T _n = T _n(X _1, \cdots, X _n)$ be a n estimator of an unknown parameter $\theta$, and $\Re _n = \sqrt{n}(T _n - \theta) \sim N(0, \sigma_n^2)$. Let $\{X _1^, \ldots, X _n^\}$ be a bootstrap sample from the empirical distribution $F _n$ based on $X _1, \cdots, X _n$, $T_n^=T_n\left(X_1^, \ldots, X_n^\right)$ and $\Re_n^=\sqrt{n}\left(T_n^-T_n\right)$. Denote the bootstrap variance estimator $v _{\text {boot}} = \text{Var}(T_n^)$. Theorem 3.10 (i) Let $T _n=T\left(F _n\right)$, assume that $T$ is $\rho _{\infty}$-Fréchet differentiable at $F$, and $ \max _{i_1, \ldots, i _n}\left\|T _n\left(X _{i _1}, \ldots, X _{i _n}\right)-T _n\right\| / \tau _n \rightarrow _{a . s .} 0 $ where the maximum is taken over all integers $i _1, \ldots, i _n$ satisfying $1 \leq$ $i _1 \leq \cdots \leq i _n \leq n$, and $\{ \tau _n \}$ is a sequence of positive numbers satisfying $\liminf _n \tau _n>0$ and $\tau _n=O\left(e^{n^q}\right)$ with a $q \in (0, \frac{1}{2})$., then $v _{\mathrm{boot}} / \sigma _n^2 \rightarrow _p 1$, where $\sigma _n^2=n^{-1} E[\phi _F(X _1)]^2>0$ We have also added a remark in our paper to refer the reader to the theoretical results in a more recent paper `Hahn, Jinyong, and Zhipeng Liao. "Bootstrap standard error estimates and inference." Econometrica 89.4 (2021): 1963-1977.` for bootstrap variance estimation. This paper (THEOREM 1) shows that common bootstrap based standard error in fact leads to a valid but (potentially conservative) inference. W3: Thank you for bringing this to our attention. Since we have decided to remove Section 4 from the paper and keep only the remarks in Section 3, we will no longer include the theoretical results related to this section in the paper. Instead, we will empirically verify the performance of ML-assisted FDR control (as we have done in Section 5 of the paper). As the reviewer pointed out, this does not affect the main contribution of our paper, which is the compelling feature of "task-agnostic" ML-assisted inference. Task-agnostic feature of PSPS: In Section 3.1, we have added a paragraph specifically highlighting why PSPS is considered "task-agnostic." This addition includes the three bullet points from our previous rebuttal that clearly delineate the relevant scenarios. Runtime comparison: We have added the runtime comparison into the Section 5 (Numerical experiments and real data application) and the relevant discussions in the Section 6 (Conclusion) in the paper. We hope our responses address your concerns, and please do not hesitate to let us know if you have any further questions. --- Rebuttal Comment 3.1: Comment: Thank you, this does address my main soundness concerns, and I am raising my score accordingly.	Summary: The paper proposes a novel statistical framework for ML-assisted inference. It describes how labeled data, together with unlabeled data and a pre-trained ML model, can be used for statistical inference. The paper establishes the asymptotic properties and optimality of the framework and then evaluates it empirically on simulated and real datasets. Strengths: - The paper is well-written. - Framework is flexible. It can work with almost any established data analysis routine and machine learning model. - The framework is justified both theoretically and empirically. Weaknesses: - The limitations could have been discussed more thoroughly. Technical Quality: 3 Clarity: 3 Questions for Authors: - What are the limitations of the proposed framework? Confidence: 1 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The authors state that the limitations are discussed in the Conclusion section of the paper, but it seems they are not discussed there. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Weaknesses, Questions, and Limitations: Thank you for the suggestion. One limitation is the computational burden of the naive bootstrap approach. In our original submission, we discussed the future direction of improving the speed of resampling. In the revised manuscript, we have conducted additional experiments to compare the computational efficiency of PSPS with existing methods. Utilizing a dataset with 500 labeled and 10,000 unlabeled data points, PSPS required 1.62 seconds for linear regression and 8.27 seconds for logistic regression using 200 bootstrap resampling. The computation of one-step de-biasing using summary statistics alone took 0.032 seconds for linear regression and 0.033 seconds for logistic regression. Current methods, which estimate asymptotic variance via the closed form derived by the Central Limit Theorem instead of resampling, ranged from 0.024 to 0.049 seconds for linear regression and 0.032 to 0.077 seconds for logistic regression. \| Method \| Linear regression \| Logistic regression \| \| ------------- \| ------------- \|------------- \| \| PSPS \| 1.62s \| 8.27s \| \| PPI \| 0.024s \| 0.032s \| \| PPI++ \| 0.031s \| 0.077s \| \| POP-Inf \| 0.049s \|0.034s \| These experiments demonstrate that while PSPS is slower than current methods due to its reliance on resampling to estimate the variance, the overall speed remains reasonable and fast. One potential solution to further improve speed could involve adopting more advanced methods for faster resampling such as Bag of Little Bootstraps (`Kleiner et al. 2014`). We have discussed this more thoroughly in the manuscript. Final note: We are excited that you find our method flexible and justified with both theoretical and empirical analysis. If you have any further questions, please do not hesitate to let us know. If our responses have resolved your concerns, we kindly request you to consider increasing your score and championing our paper. --- Rebuttal Comment 1.1: Comment: Thank you for your response. I appreciate the additional experiments and the discussion about the proposed framework's limitations.	Summary: The paper introduces a task-agnostic approach to inference with machine learning predictions. The basic idea follows a similar recipe as prediction-powered inference and related recent papers, but it makes use of resampling instead of the CLT with a plug-in estimate of the asymptotic covariance to avoid relying on analytical problem-specific derivations and expressions. Strengths: The paper effectively demonstrates the applicability of the method beyond M-estimation (which is what most previous papers have focused on), giving several important applications. The method is simple and elegant. The real-data application is very compelling. Weaknesses: I agree with your point that the recent methods require task-specific derivations. However, it's worth noting that, since for M-estimators we know we get asymptotic normality, we can use the same estimators but instead of deriving the asymptotic variance through the CLT we can use resampling to estimate the asymptotic variance. This is just to say that for M-estimators we can use the old estimators and get inference without problem-specific derivations. (Your other criticisms still apply.) In L144 it says that resampling-based inference focuses on bias and variance estimation. I don't really agree with this. Plenty of resampling-based inference focuses on type I error control (confidence intervals and p-values). The mean-estimation result in Section 2.2 is completely borrowed from prior work. Please make this clear. Otherwise it looks like these are new results in this paper. In Algorithm 1 it is unclear what the actual output is. Please write it out using mathematical symbols. Regarding Proposition 2, I would say that the claim looks a bit too strong. In PPI++ the authors state that they give the example with minimizing the trace as an example, but that other scalarizations of the covariance are clearly possible. Your Proposition 2 just chooses a different scalarization for the comparison so it is clearly better than the trace example from PPI++. But the PPI++ argument would give the same asymptotic variance under your scalarization. It would be helpful to give an example of when the p-values in Proposition 3 will be PRDS. Some stylistic comments: - The grammatically correct way to spell the title would be "Task-Agnostic Machine-Learning-Assisted Inference." - in abstract: constraints -> constrains - Very often throughout the paper you say "standard error" but you write the variance. For example, see L68 or L73. Please be consistent: either say variance and write Var(...) or write out the standard error. - In L75, you are clearly describing a particular class of ML-assisted inference methods. Not every method that is ML-assisted follows that description. Add references so it's clear what you are referring to. - L91: motivated the observation -> motivated by the observation - L99: inputs -> inputting - There are other typos and minor stylistic issues. Please go through the paper carefully. Technical Quality: 3 Clarity: 3 Questions for Authors: - Can you elaborate on the point about the privacy-preserving feature of your method? I didn't understand the main point. A particular use case would be helpful. - I'm surprised that PSPS and PPI++ are not getting the same interval widths in linear and logistic regression in Figure 2. Is it because you are tuning PPI++ for the trace objective, as discussed above? The two methods (assuming the right tuning) should have exactly the same asymptotics in this problem. This should also be made clear in words. - I'm curious about the details behind the real-data application. Can you elaborate on how you computed the predictions and how you used cross-validation to avoid overfitting? Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: I don't think a further discussion is necessary. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: W1: We first want to highlight that current methods and their implementations typically estimate asymptotic variance using the CLT rather than through resampling (for example, `Angelopoulos et al., 2023` PPI and PPI++). In addition, while resampling-based approaches can bypass the derivation of asymptotic variance, task-specific derivations for the loss function of a new ML-assisted M-estimator are still essential to obtaining the point estimator, which precedes resampling-based estimation of its uncertainty. We also want to add that the “task-specific derivations” mentioned throughout our paper were not only referring to statistical tasks, but also scientific tasks. Real-world data analysis in any scientific discipline often involves conventions and nuisances that require careful consideration. For example, our work is partly motivated from genome-wide association studies (GWAS). Statistically, GWAS is a linear regression that regresses an outcome (e.g., height) on many genetic variants. While the regression-based statistical foundation is simple, conducting a valid GWAS requires accounting for numerous technical issues, such as sample relatedness (i.e., study participants may be genetically related) and population structure (i.e., unrelated individuals of the same ancestry are both genetically and phenotypically similar, creating confounded associations in GWAS). Sophisticated algorithms and software have been developed to address these complex issues (`Mbatchou et al. 2021`). It will be very challenging if all these important features need to be reimplemented in an ML-assisted GWAS framework. With our PSPS protocol, researchers can utilize existing algorithms and software that are highly optimized for genetic applications to perform ML-assisted GWAS. This adaptability is not just limited to GWAS but is a major feature of our approach across scientific domains. A main result of this paper is that PSPS enables researchers to conduct ML-assisted inference using well-established data analysis pipelines. W2: We have revised the texts to “whereas resampling-based inference focuses on bias and variance estimation, and type-I error control.”. W3: We have added relevant citations when we discuss the mean-estimation result in Section 2.2. W4: We have revised Algorithm 1 following the suggestion. W5: We would like to clarify that the asymptotic variance of PSPS will always be lower than that of PPI++, irrespective of the scalarization method used. The reason is that the weights matrix in PPI++ is a special case of the more general weights matrix used in PSPS, and we have demonstrated in Proposition 2 that the weighting matrix in PSPS is optimal. The weighting matrix $\omega_0$ in PSPS is a Q×Q matrix with no constraint, where Q is the number of dimensions for the parameters. In contrast, PPI++ constrains its matrix to be diagonal with the same diagonal elements. Therefore, PSPS enables information sharing across different parameter coordinates, enhancing estimation precision. The choice of the weighting matrix in PSPS also facilitates element-wise variance reduction: each diagonal element of the variance-covariance matrix is reduced. In contrast, the single parameter in PPI++ can only target overall trace reduction or variance reduction of a specific element. To provide further intuition, we consider a linear regression with two predictors: $Y \sim \theta_1 X_1 + \theta_2 X_2$. The summary statistics for PSPS can be expressed as: $[\hat{\theta} _{1L}, \hat{\theta} _{2L}, \hat{\eta} _{1L}, \hat{\eta} _{2L}, \hat{\eta} _{1U}, \hat{\eta} _{2U}]^T$. For PSPS, since $\hat{\theta} _{\text{PSPS}}= \begin{bmatrix}\hat{\theta} _{1L} \\\ \hat{\theta} _{2L} \end{bmatrix} - \begin{bmatrix}w _1 & w _{12} \\\ w _{12} & w _2 \end{bmatrix}\begin{bmatrix}\hat{\eta} _{1L} \\\ \hat{\eta} _{2L} \end{bmatrix} + \begin{bmatrix}w _1 & w _{12} \\\ w _{12} & w _2 \end{bmatrix}\begin{bmatrix}\hat{\eta} _{1U} \\\ \hat{\eta} _{2U} \end{bmatrix}$, the final estimator for $\theta_1$ is $\hat{\theta} _{\text{PSPS}, 1} = \hat{\theta} _{1L}-w _1 \hat{\eta} _{1L}+w _1 \hat{\eta} _{1 U}-\mathrm{w} _{12} \hat{\eta} _{2L}+\omega _{12} \hat{\eta} _{2U}$. In comparison, since $\hat{\theta} _{\text{PPI++}}= \begin{bmatrix}\hat{\theta} _{1L} \\\ \hat{\theta} _{2L} \end{bmatrix} - \begin{bmatrix}w & 0 \\\ 0 & w \end{bmatrix}\begin{bmatrix}\hat{\eta} _{1L} \\\ \hat{\eta} _{2L} \end{bmatrix} + \begin{bmatrix}w & 0 \\\ 0 & w \end{bmatrix}\begin{bmatrix}\hat{\eta} _{1U} \\\ \hat{\eta} _{2U} \end{bmatrix}$, its estimator for $\theta_1$ is $\hat{\theta} _{\text{PPI}++, 1} = \hat{\theta} _{1L}-w \hat{\eta} _{1L}+w \hat{\eta} _{1U}$. Since $\hat{\theta} _{\text{PSPS}, 1}$ involves two zero-augmentation terms (i.e., $-w _1 \hat{\eta} _{1L}+w _1 \hat{\eta} _{1 U}$ and $-\mathrm{w} _{12} \hat{\eta} _{2L}+\omega _{12} \hat{\eta} _{2U}$ ), its asymptotic variance should be less than or equal to that of PPI++ with one augmentation term. Therefore, PSPS borrows information from both coordinates, but PPI++ is restricted to information from only the first coordinate. Although the PPI++ can be used under a different scalarization, it still contains one augmentation term. Only in a one-dimensional parameter estimation task, PPI++ and PSPS will have the same asymptotic variance. We have clarified this in the revised manuscript. We have also added the example above and an example for a one-dimensional parameter estimation task to clearly state the difference between PSPS and PPI++. Due to the character limit, we have placed our response to the remaining concerns in the comment section of the review. --- Rebuttal 2: Comment: W6: Examples of PRDS p-values include independent p-values and p-values from test statistics that are jointly normally distributed, if all correlations between test statistics are positive (`Wang, Ruodu, and Aaditya Ramdas. "False discovery rate control with e-values." Journal of the Royal Statistical Society Series B: Statistical Methodology 84.3 (2022): 822-852.`). W7: We appreciate these suggestions. We have thoroughly addressed these issues in the revised manuscript. Q1: The “privacy-preserving feature” of PSPS refers to the fact that we only require summary statistics as input for inference, rather than individual-level raw data (features $X$ and label $Y$). This terminology is commonly used in human genetics, healthcare, and multicenter electronic health record analysis to describe methods that enable statistical inference without directly accessing personal data. This approach is analogous to federated learning (`Kairouz, Peter, et al. 2021`) in the machine learning literature. For example, consider a scenario where labeled data is in one center and unlabeled data in another, yet researchers cannot access individual-level data from both centers simultaneously. Under such conditions, current ML-assisted inference, which relies on accessing both labeled and unlabeled data to minimize a joint loss function, is not feasible. However, PSPS circumvents this issue by aggregating summary statistics from multiple centers, thus performing statistical inference while upholding the privacy of individual-level data. We also acknowledge that in the machine learning literature, "privacy-preserving" often specifically refers to techniques like differential privacy. To avoid confusion, we have revised the terminology from “privacy-preserving” to "federated inference" and provided an example to illustrate this use case more clearly. Q2: First, we apologize for the error that we mistakenly used Figure 2e for Figure 2f due to a typo in the code for making the figure. The correct Figure 2f is attached in the rebuttal pdf. However, this does not change our main results related to statistical efficiency: PSPS is more efficient than PPI++ and other existing methods. As we have previously explained in our comparison of PSPS and PPI++, PSPS leverages information across multiple coordinates in a multi-dimensional parameter estimation task, resulting in asymptotic variances that are less than or equal to those produced by PPI++. Regarding the concern about the choice of tuning, the POP-Inf method, which tunes the element-wise variance, also shows wider confidence intervals than PSPS in linear regression. Q3: Our prediction pipeline comprises two components: prediction for unlabeled data and prediction for labeled data. To predict bone mineral density in unlabeled data, we first selected predictive features by 1) calculating the correlation of bone mineral density with 466 other variables (sample size > 200,000 from UK Biobank) using labeled data and 2) selecting the top 50 variables with the highest correlations as inputs for the SoftImpute algorithm to predict bone mineral density in the unlabeled data. For the labeled data, we employ a similar approach but incorporate 10-fold cross-validation to prevent overfitting. We select the predictive variables and train the SoftImpute model using 90% of the labeled data. We then perform predictions on the remaining 10% in each fold and repeat this process 10 times across all folds. We have included these details in the Appendix of the manuscript. Final note: We are excited that you find our method flexible, simple and elegant, and the real data application compelling. If you have any further questions, please do not hesitate to let us know. If our responses have resolved your concerns, we kindly request you to consider increasing your score and championing our paper. --- Rebuttal Comment 2.1: Comment: Thank you for the response! It was very helpful and clarifying.	Rebuttal 1: Rebuttal: We thank the reviewers for providing valuable suggestions that helped us improve our paper. We are particularly encouraged that the reviewers have found that (i) the problem we study in this paper is important (R-DsrD), (ii) our method is simple and elegant (R- TkNf), (iii) our flexible statistical framework can be applied to almost any established data analysis routine (R-hhpT and R-Tknf) and machine learning model (R-hhpT), (iv) our method is justified both theoretically and empirically (R-hhpT), and the real-data application is very compelling (R-Tknf), (v) our method dominates existing approaches in terms of statistical efficiency (R-DsrD), (vi) the paper provides a well-rounded analysis on the proposed method with sensitivity analysis on distributional shifts (R-5S3y). In response to the feedback, we have addressed each concern, added new experimental results and clarification, and updated our paper accordingly. A summary of our major changes is provided below. 1. We have explained the "task-agnostic" feature of our method. 2. We have clarified the "privacy-preserving" aspects of our method. 3. We have elucidated the connection between our ML-assisted statistical inference and semi-supervised learning in the machine learning literature. 4. We have addressed technical issues related to variance estimation in Theorem 1 and corrected typos throughout the paper. 5. We have included examples to illustrate how our method outperforms existing approaches in terms of statistical efficiency. A detailed point-by-point response to each reviewer's comments is available in the rebuttal section corresponding to each reviewer. Pdf: /pdf/0f369d4cc8ec29419c2893cd45d6c793bbfce755.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Goal-Conditioned On-Policy Reinforcement Learning	Accept (poster)	Summary: After rebuttal The authors have mostly addressed my minor concerns. I recommend acceptance. ------ This paper aims to improve goal-conditioned RL. Two problems with prior methods (e.g. HER) are discussed, namely (a) their inability to cope with non-markovian rewards; and (b) the necessity of using an off-policy algorithm. This work then goes on to introduce a method that is applicable to on-policy algorithms and NMR problems. This method first uses demonstrations to pre-train a policy to achieve the goals sometimes. Then, it uses a curriculum-based approach to select harder and harder goals (but still within the agent's capability). They demonstrate on a UAV problem with NMR, they outperform other methods, notably SAC + HER. Strengths: 1. Having a good on-policy GCRL algorithm is a great thing to shoot for, and the problem is useful. 2. Solving the problem of existing methods not being applicable to NMR domains is beneficial. 3. The set of baseline algorithms/ablations makes sense, and most of the obvious things to compare against have been included. Weaknesses: 1. It would be nice to have experiments on another domain, to illustrate the general applicability of your algorithm. 1. In particular, having results of the baseline algorithms (and GCPO) in an MR domain would be very helpful. 2. Relatedly, having results for e.g. SAC + HER when doing the same thing as in appendix A.4 would be helpful. Technical Quality: 2 Clarity: 3 Questions for Authors: - Could you run GCPO with only a 1000 demonstrations? Confidence: 3 Soundness: 2 Presentation: 3 Contribution: 2 Limitations: 1. Requiring demonstrations is a relatively strong limitations, as e.g. HER does not. Is there any way around this requirement? Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We address the concern about GCPO performance in more RL domains (W1) in Global Author Response, and the other concerns below. > Q1: Could you run GCPO with only a 1000 demonstrations? We evaluate the performance of GCPO with 1000 demonstrations on the Reach, PointMaze, and VVC tasks. Demonstrations: The source of demonstrations for PointMaze and Reach is elaborated in the Global Author Response. For GCPO, 10% $\mathcal{D}_E$ is employed, as detailed in Section 4.3.1. Additionally, for comparison purposes, we also present the performance of GCPO on the VVC task using $\mathcal{D}_{[\chi=90]}$, which comprises only 144 demonstrations with a flight path azimuth angle of 90, as described in detail in Appendix A.3, and using $\mathcal{D}_E$. The results are presented in the following table: \|Task\|Demo Quantity\|Transition Quantity\|BC\|GCPO\| \|:---:\|:---:\|:---:\|:---:\|:---:\| \|Reach\|1000\|82589\|70.63±2.99\|100.0±0.0\| \|PointMaze\|1000\|1000000\|75.96±5.34\|93.33±3.06\| \|VVC + 10% $\mathcal{D}_E$\|1000\|294702\|13.74±0.99\|39.18±2.64\| \|VVC + $\mathcal{D}_{[\chi=90]}$\|144\|42177\|1.18±0.38\|3.34±0.61\| \|VVC + $\mathcal{D}_E$\|10264\|3106516\|17.08±0.57\|45.06±1.3\| Performance: It can be observed that on the relatively simple PointMaze and Reach tasks, GCPO achieved nearly 100% success rate when using 1000 demonstrations. On the more challenging VVC task, the success rate with 1000 demonstrations reached 81.12% of the success rate achieved with 10264 demonstrations, while also being significantly higher than the success rate achieved with 144 demonstrations. These results indicate that across tasks of varying complexity, GCPO can achieve good performance with the use of 1000 demonstrations. > L1: Requiring demonstrations is a relatively strong limitations, as e.g. HER does not. Is there any way around this requirement? We answer this question from two perspectives: Firstly, while GCPO's training relies on demonstrations, the quantity and quality of these demonstrations do not need to be high. GCPO is capable of learning well-performed policies from non-expert demonstrations. Secondly, for complex tasks, methods like SAC and HER are also unable to learn from scratch; leveraging demonstrations to assist learning is a more mainstream approach. We will elaborate on these points in the following discussion. On one hand, although GCPO relies on demonstrations, it is capable of learning well-performed policies from non-expert demonstrations. Please refer to the response to Q2 in the Global Author Response for a detailed analysis. On the other hand, for complex tasks, methods such as SAC, HER, etc., also struggle to learn well-performed policies from scratch. For instance, on the VVC task, the performance of policies obtained using SAC+HER+MEGA is shown in the table below, where it can be observed that this method barely learn any capability to complete tasks. In other complex tasks, such as StarCraft [1], Minecraft [2], ObjectGoal Navigation [3], and others, researchers widely rely on demonstrations to train RL policies. Therefore, for the complex tasks mentioned above, we have not yet found a RL method that can bypass the pre-train phase. Hierarchical RL may be a direction worth exploring [4]. \|\|SAC+HER+MEGA\|BC\|GCPO\| \|:---:\|:---:\|:---:\|:---:\| \|Success Rate\|5.75±1.98\|17.08±0.57\|45.87±3.09\| In summary, on complex tasks, we have not yet found an RL method that can bypass the use of demonstrations. Although the training of GCPO depends on demonstrations, its capability to learn policies from imperfect demonstrations somewhat relaxes the conditions for using GCPO. [1] Vinyals O, Babuschkin I, Czarnecki W M, et al. Grandmaster level in StarCraft II using multi-agent reinforcement learning[J]. nature, 2019, 575(7782): 350-354. [2] Baker B, Akkaya I, Zhokov P, et al. Video pretraining (vpt): Learning to act by watching unlabeled online videos[J]. Advances in Neural Information Processing Systems, 2022, 35: 24639-24654. [3] Ramrakhya R, Batra D, Wijmans E, et al. Pirlnav: Pretraining with imitation and rl finetuning for objectnav[C]//Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2023: 17896-17906. [4] Pope A P, Ide J S, Mićović D, et al. Hierarchical reinforcement learning for air-to-air combat[C]//2021 international conference on unmanned aircraft systems (ICUAS). IEEE, 2021: 275-284. > W2: Relatedly, having results for e.g. SAC + HER when doing the same thing as in appendix A.4 would be helpful. We conduct experiments related to SAC+HER with reference to the experimental setup for GCPO described in Appendix A.4. The training process curves are shown in Fig.2 in the Global Author Response PDF. It can be observed that expanding the input of the SAC+HER policy also results in a certain degree of performance degradation. We believe that the reasons are consistent with the analysis provided in Appendix A.4. --- Rebuttal Comment 1.1: Comment: Thank you. I will update my score to 7 on the condition that please add these experiments and discussions to the updated manuscript. --- Reply to Comment 1.1.1: Comment: Dear Reviewer aw7R, We sincerely appreciate the time and effort you spent on our work. Your insightful comments and concerns have helped greatly in improving our paper. We will address these discussions in the final version. Thank you once again for your valuable feedback.	Summary: This paper proposes Goal-Conditioned Policy Optimization (GCPO), an on-policy variant for goal-conditioned RL that can also handle non-markovian reward structures. Common goal-conditioned RL methods are usually related to Hindsight Experience Replay (HER) which however can only solve tasks under the Markovian properties. Notably, GCPO leverages pre-training from demonstrations and online self-curriculum learning that can progressively select challenging goals based on the current learning process of the policy. Strengths: - well-motivated - contributions are well outlined - detailed ablations - An important and interesting problem is considered Weaknesses: The paper lacks discussion of relevant works that also consider contextual/goal-conditioned RL with self-curriculum learning with similar motivations, some of which consider non-Markovian rewarded environments. Here are some of those: - Klink et al. Self-Paced contextual reinforcement learning (CoRL 2019) - Celik et al. Specializing Versatile Skill Libraries using Local Mixture of Experts (CoRL 2021) - Klink et al. Self-Paced Deep Reinforcement Learning (NeurIPS 2020) - Ottot et al. Deep Black-Box Reinforcement Learning with Movement Primitives (CoRL 2022) - Celik et al. Acquiring Diverse Skills using Curriculum Reinforcement Learning with Mixture of Experts (ICML 2024) please also see the questions Technical Quality: 2 Clarity: 3 Questions for Authors: - The method requires a desired goal distribution which might be task dependent. In which sense is this restricting the algorithm's applicability? - How exactly is the GMM estimated? No information was given in the main text - The work states that the self-curriculum "leads to an average 8.2% increase in policy performance" as evidenced in Table 2. However, Table 2 also shows that GCPO w/o pre-training can only achieve 4% success rate indicating that the performance boost is mainly achieved by the imitation learning policy. On the other hand, Fig.3 shows that GCPO successfully reaches more goals than the expert and BC, especially in the goal difficulty up to 0.7 but is not able to significantly reach more difficult goals. This observation is also discussed in Section 4.3.2. While I see that the goals that are already covered by the BC can be reached successfully more often by GCPO, the self-curriculum does not seem to cover more difficult goals significantly. Section 4.3.2 suggests to "sample goals and generate demonstrations as closely as possible to the desired goal distribution". Isn't this restricting the method in the sense that the demonstration data needs to be collected accordingly? - Connecting to the question before, is this indicating that exploring new goals that are much more difficult can not covered well by GCPO? Could this be discussed in more detail? Why is this the case? Is the KL constraint restricting the updates to more difficult goals? To my understanding, expanding to more difficult goals should be covered by the bonus (MEGA) as described in Section 3.3. Confidence: 3 Soundness: 2 Presentation: 3 Contribution: 2 Limitations: - While the detailed ablations are highly appreciated, a more thorough evaluation across more tasks is needed to assess the effectiveness of the method. This can be done by using sophisticated existing non-markovian rewarded environments, or, for demonstration purposes, adjusting the reward accordingly in existing benchmark suits such as e.g. (Meta World) Meta World: https://github.com/Farama-Foundation/Metaworld Please also see the weaknesses and questions. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: > Response to Q3 and Q4 We consolidate your two questions into three sub-questions. 1. _The effectiveness of GCPO seems to primarily come from the pre-training, and the self-curriculum does not appear to significantly cover more difficult goals._ The objective of GCRL is to achieve more goals under the expectation of $p_{dg}$, which is independent of any form of goal difficulty. Both MEGA and our GCPO do not alter the objective of GCRL, so the appropriate evaluation metric should be the success rate over $p_{dg}$. Therefore, considering the change in success rate, both pre-training and self-curriculum play significant roles. Specifically: * In GCRL, difficulty describes how easy or hard it is for a policy to achieve a goal while learning. This difficulty is closely linked to the policy's abilities, and we prefer to term it learning-process-oriented difficulty. Conversely, task-oriented difficulty pertains to the inherent challenge of a goal, unrelated to the policy's form or learning process. It is dictated by the goal itself. A goal that is task-oriented easy might be learning-process-oriented hard. There is no inherent link between these two difficulty types. * GCRL aims to maximize expected cumulative rewards under the goal distribution $p_{dg}$. When rewards are binary indicators of goal achievement, GCRL's objective is essentially to achieve more goals under $p_{dg}$. Hence, GCRL's objective is inherently independent of any goal difficulty. MEGA, while identifying goals by learning-process-defined difficulty to optimize exploration and learning, does not alter GCRL's objective. Thus, MEGA is not centered on achieving more task-defined difficult goals. * In VVC, we define $p_{dg}$ as the uniform distribution over the entire goal space. For clarity, we define task-oriented difficulty in Appendix A.1.4 and use it as the x-axis in our figures. Fig.1(a) in the Global Author Response PDF shows all discrete goals in a 3D space. Fig.1(b) depicts the goal distribution over task-oriented difficulty. It is evident that, under our definition, the distribution of desired goals over task-oriented difficulty is not uniform but rather low at both ends and high in the middle. This is exactly why our experimental results exhibits this particular shape. In essence, the valid metric for evaluating GCRL is the success rate under $p_{dg}$. Table 2 shows that the success rate of GCPO is 2.69 times that of BC, indicating that online learning with self-curriculum can significantly improve a pre-trained policy. Fig.3(b) and 3(c) are merely analyses on learned policies and learning process from the task-oriented difficulty perspective. We find that self-curriculum does gradually sample task-oriented difficult goals during training, and the resulting policies can achieve some of these goals. 2. _Does the requirement for sampling demonstrations in Section 4.3.2 limit the applicability of the method?_ In Section 4.3.2, the experiment examines how demonstration goal distribution affects GCPO. Results indicate that demonstrations sampled according to $p_{dg}$ yield effective GCPO policies. We believe that this is a point to focus on for enhancing GCPO's performance, rather than a limitation of its applicability. Comparison between the results in Sections 4.3.2 and 4.2 reveals that GCPO can still train when the demonstration goal distribution differs substantially from $p_{dg}$. For instance, using $\mathcal{D}_2$ in Section 4.3.2, with 100 demonstrations (cover only 0.20% goal space) focused on difficulties within (0.2328, 0.2336), GCPO can still train a policy with a 21.86% success rate. 3. _What impact does KL have on training?_ Indeed, KL impacts GCPO's training. As discussed in our response to the first sub-question, we believe that this impact is only reflected in the success rate, not in the achievement of the task-oriented difficult goals. We train GCPO with various $\lambda$: \|$\lambda$\|KL Value\|Success Rate\| \|:-:\|:-:\|:-:\| \|$10^{-1}$\|1.79±0.42\|25.37±3.68\| \|$10^{-2}$\|9.27±0.82\|38.75±1.83\| \|$10^{-3}$\|33.27±2.34\|45.87±3.09\| \|$10^{-4}$\|133.32±26.42\|28.20±5.31\| \|0\|368.19±15.72\|25.68±4.05\| As shown, a higher $\lambda$ leads to a lower KL, suggesting the GCPO policy is more statistically similar to the pre-trained policy, aligning its success rate with the pre-trained policy's 17.08%. As $\lambda$ decreases, KL increases, and the GCPO policy's success rate improves. Yet, at $\lambda < 10^{-3}$, the success rate drops, which we attribute to the weak KL constraint leading to catastrophic forgetting of the pre-trained knowledge, impeding effective policy learning. > Response to Q1 The desired goal distribution is a part of the problem formulation of GCRL. We contend that this distribution, which should be a known condition, does not restrict GCPO. Even if the demonstration goal distribution significantly differs from the desired goal distribution, GCPO can still train a reasonably good policy. For a detailed analysis, please refer to our response to the second sub-problem in the first question. > Response to Q2 GMM estimates a distribution with a weighted sum of multiple Gaussian kernels, $\sum_{i=1}^M \pi_i N(x\|\mu_i,\Sigma_i)$, and estimate parameters with the Expectation-Maximization algorithm. Due to space constraints, we will include detailed calculation in Appendix. > Response to W1 Thank you for the suggestion. We've thoroughly read the papers, with four focusing on curriculum learning and one on NMR. The key contribution of GCPO is its on-policy GCRL training framework, where self-curriculum is vital for efficient online learning. Thus, other curriculum learning methods could replace MEGA within GCPO. We will discuss these works in the related work section. The episode-based RL research offers valuable guidance for enhancing GCPO's suitability for NMR problems. We will explore this possibility in the future work. > Response to L1 Please refer to Q1 in Global Author Response. --- Rebuttal Comment 1.1: Comment: I highly appreciate the authors' responses and additional experiments. My questions were clarified in the responses. I am adjusting the score on the condition that the authors discuss the relevant works in the final version and accordingly adjust their claims in lines 66-68. --- Reply to Comment 1.1.1: Comment: Dear Reviewer emMz, We express our heartfelt gratitude for the time and dedication you've invested in reviewing our manuscript. Your constructive feedback and perceptive comments have been immensely valuable in refining our paper. We are committed to addressing these insights in our revised work. Thank you once again for your valuable feedback.	Summary: This paper proposes a new on-policy goal conditioned reinforcement learning framework which targets non-markovian rewards, which HER based approaches are unsuccessful. GCPO is a combination of offline pre-training from expert policies using behavior cloning, and online learning from a curriculum which automatically determines complex goals outside of the agent's current goal conditioned policy. They show this frameworks success in the Velocity Vector Control task, and perform several ablation and sensitivity studies. Strengths: This paper provides a novel (as far as I am aware) framework for developing goal conditioned algorithms. This paper excels in clarity, interesting empirical and algorithmic contributions, and clear directions for future improvement. - Clarity: The paper is very clearly written, and provides ample details about the algorithms and experimental design. I also appreciate the work done in the introduction and related works section, clearly grounding this work in the literature and showing the deficiencies of HER approaches. - Algorithmic contributions: The GCRL framework is flexible enough to inspire a large amount of future work, and the authors do a great job enabling future research in this direction. The combination of pre-training and a goal-driven curriculum based on estimating successfully achieved goals with a GMM is interesting and novel. - Empirical Work: The empirical work is well rounded, and several interesting ablations going into the specific details of all the parts of the framework is appreciated and helps readers understand further. And the success on an extremely difficult domain is a great achievement in the space. - Clear future directions The authors are very clear on where their contributions are limited, and open the door to several future algorithmic contributions in this space. Weaknesses: While I think this paper would be an excellent contribution to this year's conference, there are some improvements I would like to see. I think the authors should make changes to address I-1, but the others are less consequential in my view. - I-1. I haven't seen a discussion around how hyperparameters were tuned. While I put this work in more of a demonstration lane, but I think if the paper was clearer around how these hyperparameters were chosen, and how the baseline methods were tuned would immediately strengthen the paper. I think this is critical when discussing the results of Figure 1. Adding how extensively these methods were tuned could strengthen the evidence supporting the claims. - I-2. While the ablation showing how the quantity of demonstration data on the final performance is appreciated, I think the lack of ablations on the quality of demonstrations is a major limitation. There are some experiments using demonstrations with different distributions of goals, these don't sufficiently capture what would happen if there is a lack of expert data. In many domains, there is often a lack of true expert data, but a large amount of sub-standard data. If GCPO is also performant in instances where expert data is sparse, but non-expert data isn't that would be a major achievement for the method (although my guess is issues would arise from using BC as you already state as a limitation). Technical Quality: 3 Clarity: 4 Questions for Authors: - How were the baselines and your method's hyperparameters tuned? Confidence: 4 Soundness: 3 Presentation: 4 Contribution: 4 Limitations: Yes. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: > Q1 & W1: How were the baselines and your method's hyperparameters tuned? We employ Grid Search to search the following hyperparameters of the evaluated algorithms: \|params\|search range\| \|:-\|:-\| \|SAC: Network Architecture\|128\2, 128\3, 128\4, 128\5\| \|SAC: ent_coef\|$10^{-3},10^{-2},10^{-1}$\| \|SAC: gamma\|0.99, 0.995, 0.999\| \|SAC: lr\|$10^{-3},10^{-4},10^{-5}$\| \|SAC: use_sde\|True, False\| \|HER: buffer_size\|$10^4,10^5,10^6$\| \|HER: n_sampled_goal\|2,4,8,16\| \|HER: goal_selection_strategy\|episode,final,future\| \|Self-curriculum: buffer_size\|$10^3,10^4,10^5$\| \|BC: Network Architecture\|128\2, 128\3, 128\4, 128\5\| \|BC: l2_weight\|$0,10^{-4},10^{-3},10^{-2}$\| \|BC: ent_weight\|$10^{-3},10^{-2},10^{-1}$\| \|BC: batch_size\|512,1024,2048,4096\| \|PPO: Network Architecture\|128\2, 128\3, 128\4, 128\5\| \|PPO: ent_coef\|$10^{-3},10^{-2},10^{-1}$\| \|PPO: gamma\|0.99, 0.995, 0.999\| \|PPO: lr\|$10^{-3},10^{-4},10^{-5}$\| \|PPO: use_sde\|True, False\| The other parameters are set to StableBaselines3 defaults. Taking the network architecture of BC as an example, once the optimal set of parameters has been searched, we maintain all other parameters constant and demonstrate the policy performance when using different network architectures with the following table: \|Network Architecture\|128\2\|128\3\|128\4\|128\5\| \|:-:\|:-:\|:-:\|:-:\|:-:\| \|Success Rate\|17.08±0.57\|16.56±0.91\|15.31±0.56\|14.78±2.45\| As [128, 128] achieved the best performance, we maintain this architecture for all experiments on BC. > W2: the lack of ablations on the quality of demonstrations is a major limitation. How does GCPO perform on non-expert demonstrations? Firstly, we supplement experiments on demonstration quality. In Section 4.2, $\mathcal{D}_E$ covers 10264 goals. We generate trajectories for these goals with all the policies trained in our experiments. For a specific goal, we retain only the shortest trajectory. These generated demonstrations are denoted as $\mathcal{D}'$. We use two metrics to measure demonstration quality: Trajectory length $I_l$. Since we employ (-1, 0) sparse rewards, this implies that shorter trajectories yield a higher cumulative reward. Control smoothness $I_s$. In control problems, minimal control gains is expected to reduce wear on actuators. Hence, we refer to [1] to define the control smoothness. Trajectory length and control smoothness each describe certain characteristics of demonstrations from the distinct perspectives of reinforcement learning optimization and optimal control, respectively. \| Demo \| #$\mathcal{D}$ \| $I_l(\mathcal{D}) \downarrow$ \| $I_s(\mathcal{D}) \downarrow$ \| \|:-:\|:-:\|:-:\|:-:\| \|$\mathcal{D}_E$\|10264\|282.02±149.98\|2.11±2.21\| \|$\mathcal{D}'$\|10264\|101.42±32.41\|10.19±8.74\| It can be observed that: From an RL perspective, $\mathcal{D}'$ is of higher quality because the trajectories are shorter, leading to a higher expected cumulative reward. From a control perspective, $\mathcal{D}_E$ is better because the trajectories are smoother. The performance of the BC policy $\pi_{BC}$ and the GCPO policy $\pi_{GCPO}$ trained on these two sets of demonstrations is: \| Demo \| $s(\pi_{BC}) \uparrow$ \| $I_l(\pi_{BC}) \downarrow$ \| $I_s(\pi_{BC}) \downarrow$ \| $s(\pi_{GCPO}) \uparrow$ \| $I_l(\pi_{GCPO}) \downarrow$ \| $I_s(\pi_{GCPO}) \downarrow$ \| \|:-:\|:-:\|:-:\|:-:\|:-:\|:-:\|:-:\| \|$\mathcal{D}_E$\|17.08±0.57\|241.72±81.36\|1.97±1.97\|45.87±3.09\|133.86±53.24\|6.84±5.60\| \|$\mathcal{D}'$\|19.10±0.22\|122.81±54.36\|8.85±9.60\|39.26±2.02\|150.59±63.89\|18.11±12.69\| The results reveal that $\pi_{BC}$ closely aligns with the demonstrations on both quality metrics, indicating that demonstration quality has a direct impact on BC. Additionally, the BC policy trained on $\mathcal{D}'$ has a slightly higher success rate, which we speculate is due to $\mathcal{D}'$ being more suitable for RL (the network architecture and training hyperparameters used to generate $\mathcal{D}'$ are the same as those for the BC policy). However, after the self-curriculum learning, the GCPO policy corresponding to $\mathcal{D}_E$ performs better and exhibits a shorter trajectory length. This suggests that the influence of demonstration quality on GCPO's online learning may not be as direct as pre-training, and further research is required to understand this relationship. In summary, on one hand, it is challenging to define demonstration quality suitable for RL through a few metrics [2]. This is a research direction that deserves further exploration. On the other hand, demonstration quality does affect GCPO pre-training. How demonstration quality potentially influences the online self-curriculum learning of GCPO remains an intriguing question for further exploration. Secondly, GCPO is capable of training well-performed policies from non-expert demonstrations. Please refer to the response to Q2 in the Global Author Response for a detailed analysis. [1] Mysore S, Mabsout B, Mancuso R, et al. Regularizing action policies for smooth control with reinforcement learning[C]//International Conference on Robotics and Automation. 2021. [2] Belkhale S, Cui Y, Sadigh D. Data quality in imitation learning[C]//Advances in Neural Information Processing Systems. 2024. --- Rebuttal 2: Comment: Dear Reviewer U5WJ, Do you have any further concerns? Please let us know, we will try our best to address them quickly. We sincerely anticipate your response. --- Rebuttal Comment 2.1: Comment: Sorry, this paper got missed when I was responding to author comments. you have addressed the small concerns I had for this paper. I especially appreciate the extra results on demonstration quality and performance, I think this is particularly important whenever we are using data collected using unknown policies. --- Reply to Comment 2.1.1: Comment: Dear Reviewer U5WJ, We sincerely appreciate the time and effort you spent on our work. We will address the above discussions in the final version. Thank you once again for your valuable feedback.	null	null	Rebuttal 1: Rebuttal: We sincerely appreciate your valuable feedback and careful review of our paper. We address the two common concerns of many reviewers in the following: > Q1: How does GCPO perform on other RL domain tasks? We conduct two sets of experiments to demonstrate the general applicability of our method. Environments: For the first set of experiments, we conduct evaluations on a customized PointMaze environment (PointMaze_Large_DIVERSE_G-v3) from Gymnasium-Robotics [1] within the Mujoco physics engine. The only modification we made to the environment is to expand the number of desired goals from 7 to 45, making our customized version of PointMaze more challenging than the original version. For the second set of experiments, we employ a customized Reach (PandaReach-v3) task on the Franka Emika Panda robot physics engine. The Reach task is akin to those in the Meta-World environment, both involving robotic arm tasks where the objective is to reach a specified goal state. The only modification we made to the environment is to change the distance_threshold used to determine goal reaching from 0.05 to 0.01. Consequently, our customized version of the Reach task has a stricter criterion for determining goal arrival, making it more difficult than the original version of Reach. Reward Settings: The original rewards for both the PointMaze and Reach tasks are Markovian. To evaluate the performance of our algorithm under different NMR settings, we design two distinct types of NMRs. For the PointMaze, the NMR we designed is: the task is considered successful only if, after the point reaches the goal, it moves away by at least a certain distance and then returns to the goal. For the Reach task, the NMR we designed is: the Panda robot must first pass through a specific waypoint before reaching the goal to be considered successful, and each goal has a different waypoint. Both of these settings strictly adhere to the definition of NMR, where the reward is defined by the states and actions over multiple steps. Demonstrations: The demonstrations for PointMaze are sourced from Minari [3] (pointmaze-large-v1), while the demonstrations for Reach are generated by us, with reference to the PID controller as described in the official documentation [4]. Performance: We evaluate SAC+HER+MEGA, BC, and GCPO on the PointMaze and Reach tasks under both MR and NMR settings. The following table presents the success rates of these algorithms. It can be observed that under the MR settings, GCPO exhibits similar performance to SAC+HER+MEGA. However, under the NMR settings, where HER cannot be effective, the performance of GCPO is significantly better than that of SAC. Taking into account the performance of GCPO on the VVC task as illustrated in the main paper, we showcase the general applicability of GCPO across a variety of tasks. \|Task\|Reward\|SAC+HER+MEGA\|BC\|GCPO\| \|:---:\|:---:\|:---:\|:---:\|:---:\| \|Reach\|MR\|100.0±0.0\|70.63±2.99\|100.0±0.0\| \|Reach\|NMR\|0.72±1.34\|10.52±11.70\|80.26±17.01\| \|PointMaze\|MR\|100.0±0.0\|75.96±5.34\|93.33±3.06\| \|PointMaze\|NMR\|4.17±0.93\|22.8±3.71\|47.50±8.06\| _Note: Due to the inability of HER to get rewards in the NMR settings, in the experiments, SAC+HER+MEGA is employed for the MR settings, while SAC is employed for the NMR settings._ [1] https://robotics.farama.org/ [2] Gallouédec Q, Cazin N, Dellandréa E, et al. panda-gym: Open-source goal-conditioned environments for robotic learning[C]//4th Robot Learning Workshop: Self-Supervised and Lifelong Learning@ NeurIPS 2021. 2021. [3] https://minari.farama.org/ [4] https://panda-gym.readthedocs.io/en/latest/usage/manual_control.html > Q2: How does GCPO perform on non-expert demonstrations? GCPO is capable of training well-performed policies from non-expert demonstrations. The intrinsic reason is that GCPO employs online learning to fine-tune pre-trained policies. Consequently, even if the demonstrations are non-expert and the pre-trained policies perform poorly, GCPO can still continuously optimize these policies through online learning. In Section 4.2, although the average trajectory length of $\mathcal{D}_E^0$ reached 281.83, covering only 20.24% of goal space, the GCPO policy trained on it achieves a success rate of 45.87%, with an average trajectory length of 134.47. This comparison indicates that $\mathcal{D}_E^0$ consists of non-expert demonstrations. On the other hand, in contrast to $\mathcal{D}_E^3$, which covers 78.55% of the goal space with an average trajectory length of 116.56, $\mathcal{D}_E^0$ is only a quarter in size and has trajectories that are 2.42 times longer, implying a substantial decrease in its quantity and quality. Nonetheless, the GCPO policy trained on $\mathcal{D}_E^0$ achieves 76.58% of the success rate of the policy trained on $\mathcal{D}_E^3$. Therefore, we contend that GCPO has the capability to train from non-expert demonstrations. Pdf: /pdf/8c9cc7e42d8fcacd9d73d925078ac02516045f52.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Multi-Object Hallucination in Vision Language Models	Accept (poster)	Summary: This paper proposes a benchmark of multi-object hallucinations in Large Vision Language Models (LVLMs). Specifically, this paper explores thoroughly on how LVLMs behaves when multiple objects are prompted in user instructions. They introduce Recognition-based Object Probing Evaluation (ROPE), an automated pipeline used for collection their benchmark. This paper also presents some interesting findings, including that existing LVLMs may follow shortcuts to generate hallucinated responses. Strengths: S1: Novelty. Studying how object tokens affect each other in LVLM inference sounds new. Most papers addressing LVLM object hallucination are focusing on single-object. Multi-object hallucination sounds a new perspective. S2: Thorough analysis. This paper conducts comprehensive analysis and discuss on 9 potential impacting factors that may lead to multi-object hallucination, which are quite a lot experiments. S3: Interesting academic findings. The instruction format that induces LVLM to hallucinate is interesting. This is validated by authors a quite significant factor that leads to multi-object hallucination, which can not be simply remedied by scaling up LLMs. Weaknesses: W1: missing evaluations. Noticing that this paper mainly focuses on object hallucination, I wonder why authors avoid evaluating published methods that address single object hallucination in LVLMs, including decoding methods like OPERA [15] or RLHF methods [43, A]. It is quite important to check how existing single-object methods perform on the proposed multi-object benchmark. However, this part is missing from this paper, which is encouraged to be presented clearly and thoroughly to support a new benchmark. W2: limited significance on real-world use case. Despite interesting findings and comprehensive analysis on proposed multi-object hallucination, this paper experiments under a very specific type of inference setup. Specifically, their experiments are conducted on a specific type of instruction format (Figure 2) and limits its output tokens to objects only (line 140-150). For proposing a new benchmark, I believe this problem is worth to do some thinking. But this part is missing from this paper. Authors are suggested to discuss more on potential impact from this paper. [A] RLHF-V: Towards Trustworthy MLLMs via Behavior Alignment from Fine-grained Correctional Human Feedback. CVPR 2024. Technical Quality: 3 Clarity: 2 Questions for Authors: ## Q1 For Figure 3 (right), ground truth object for obj5 is "orange", but both LLaVA-7B and LLaVA-34B hallucinate it as an "apple". This paper explains this phenomena in line 165-166 as follows, > However, they tend to make more mistakes when all tasked object classes are different or when a new object class is introduced after multiple repeated tasks*. It should be noted that authors use a very specific type of instruction here, > Provide the class names in the format: 'obj1: <class1>, obj2: <class2>, obj3: <class3>, obj4: <class4>, obj5: <class5>', with no additional words or punctuations.* I have a few questions for this example here. (1-a) how LLaVA-7B and LLaVA-34B performs when prompted with "Is there an orange in this image?" This can be a baseline to this example. (1-b) it should be noted that authors adopt three types of instructions in this paper (line 136-150). What type of instruction is used for this sample? (1-c) noticing that in this paper LVLMs are forced to follow a special format and decode object tokens only, what do authors think about significance of such prompting? ## Q2 Given special instructions (Figure 2) used in this paper, a simple exploration is to train an LVLM (e.g., LLaVA) that follows such instruction well. One reason for why LVLMs performs badly is probably that, these models do not fit these special instructions very well. Authors are suggested to include such models and results accordingly. Specifically, authors can train a LLaVA model with instruction data below. For LLaVA [29] and take ground truth objects in Figure 2 as an example, this could look like, > A chat between a curious user and an artificial intelligence assistant. The assistant gives helpful, detailed, and polite answers to the user's questions. > USER: <image>. > USER: Provide the class names in the format: obj1: <class1>, obj2: <class2>, obj3: <class3>, obj4: <class4>, obj5: <class5>, with no additional words or punctuations. > ASSISTANT: obj1: fork, obj2: knife, obj3: whisk, obj4: lemon, obj5: jar. This is also explored in a recent paper [A], which I think will improve this paper and make findings from this paper more convincing. [A] Object Recognition as Next Token Prediction. CVPR 2024. Confidence: 4 Soundness: 3 Presentation: 2 Contribution: 2 Limitations: Authors include Limitations in Appendix B.1. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your thorough and insightful review of our paper. We are happy that you appreciate our novelty and found our analyses thorough. We addressed your questions and concerns below. If any residual concerns remain, we would be glad to discuss further. If no concerns remain, we would appreciate it if you could raise your score. ### W1: Missing Experiments. We have added a comparative table in our revised manuscript that clearly presents the performance of OPERA, RLHF (MiniCPM-V), and other relevant methods on our multi-object benchmark. Due to the limit of space, we kindly redirect the reviewer to the Rebuttal Supplement PDF. - Decoding algorithm (OPERA): In the default multi-object setting, OPERA marginally improves the performance of LLaVA-1.5 in some settings, especially in settings with higher object homogeneity. OPERA decreases the performance on heterogeneous tests. - RL-based finetuning (MiniCPM-V): MiniCPM-V shows robust performance across different settings, consistently handling various object types effectively. This approach enhances model performance in multi-object benchmarks that even surpasses single-object settings in Wild and Hom sets. Upon inspection, we found that this model demonstrates strong visual in-context learning capability and improves correct recognition when objects of the same classes are probed together. In summary, the heterogeneous test split remains challenging given recent advances in decoding and alignment. ### W2: Limited Significance on Real-world Use Case Real-World Use Case 1: Common Scenarios in Embodied AI Multi-object querying is particularly relevant in embodied AI applications, such as in cooking scenarios. In a typical kitchen setting, a robot might need to identify and manipulate multiple ingredients and tools simultaneously. For example, preparing a meal might require the robot to locate and retrieve a knife, cutting board, vegetables, and spices all at once. This ability to handle multiple objects at the same time enhances the robot's efficiency and effectiveness, reducing the time taken to complete tasks and improving overall performance. We further present a case study in Autonomous Driving (see Figures 1 and 2 in Rebuttal Supplement PDF). This case study demonstrates how our approach can be utilized in the automotive industry to enhance the accuracy and efficiency of object recognition systems in vehicles. Figures 1 and 2 are taken from the nuScenes dataset for autonomous driving. Figure 1 illustrates the single-object case, where each object is identified independently. Figure 2 demonstrates the multi-object case, where multiple objects are detected simultaneously. The multi-object case exhibits more hallucination errors compared to the single-object case. This finding underscores the importance of studying multi-object hallucination, especially in real-world scenarios like autonomous driving, where multiple objects need to be detected accurately at the same time. Real-World Use Case 2: Cost and Time Efficiency Evaluating multiple objects simultaneously, rather than querying each object individually, can significantly save both time and resources. \| Type \| Time (per 100 images) \| Cost (per 100 images) \| \|-------------------------------\|-----------------------\|-----------------------\| \| 5 times single-object evaluation \| 512s \| $0.575 \| \| Multi-object evaluation \| 239s \| $0.265 \| ### Q1: Figure 3 Example - For Q1-a, prompting with binary inference questions "Is there an orange in this image?" has been discussed in prior work, specifically in the POPE [24]. In our paper, we focus on the multi-object setting and our goal is to compare it with a single-object setting and ensure a fair comparison. Our single-object prompts are designed to align with our multi-object prompts for controlled studies, allowing us to directly evaluate and compare the performance under both settings. - For Q1-b, the instruction type used for the example in Figure 3 is the default multi-object setting, the same as Figure 2. - For Q1-c, we utilize student-forcing and teacher-forcing techniques to mitigate the model's dependence on the output format. These techniques allow the model to focus on predicting the next class rather than conforming to a specific output structure. Furthermore, student-forcing and teacher-forcing help us analyze whether the model learns shortcuts from the text. ### Q2: Instruction Following In fact, our student/teacher forcing probing strategies are designed "to separate out errors due to following instructions, we force the model to follow the format template and decode only the object tokens for each of the five objects. Ideally, this setting allows the model to focus solely on object recognition." By decoding the object tokens conditioned on a correct template, student/teacher forcing probing strategies allow us to evaluate the model's performance in both single-object and multi-object settings more fairly, as it factors out the template dependence. See lines 140-150 and Figure 7 in the Appendix for details. We appreciate your input and the reference to the recent paper [A]. We acknowledge its relevance to our work and will discuss this paper in our revised manuscript. --- Rebuttal Comment 1.1: Comment: At first, I would like to thank for authors responding to my concerns in details. Good to see that authors include single-object hallucination methods, including OPERA and MiniCPM-V in their global response. My major concern of W1 has been addressed by inclusion of these two approaches. Though, authors are suggested to include more hallucination mitigation methods in future updated manuscript. I also recognize potential application value of multi-object hallucination in robotics and embodied AI, which addresses my concern W2 and improves this paper. Further clarifications on Q1 and Q2 are clear, I have no further questions. In all, I think this paper has its novel contribution and raise my score. --- Reply to Comment 1.1.1: Comment: We’re happy to hear that we could cover all your points. Your detailed feedback was really helpful, and we’re grateful for the time you took to review our work and share your thoughts.	Summary: Previous evaluations of large vision-language model (LVLM) hallucinations have primarily focused on single objects. This paper introduces a novel hallucination evaluation benchmark named ROPE, which simultaneously assesses multiple objects within a single scene during testing. The authors present several empirical findings about multi-object hallucinations, including the statistical correlation in object distribution and its impact on hallucinatory responses. Strengths: 1. The paper is well-written and clearly articulates the differences between ROPE and previous benchmarks. Especially, observations and motivations are quite reasonable. 2. Multi-object hallucination is an under-explored aspect in the LVLM hallucination scene. Also, its related findings are valuable and worth further investigation. 3. The experiments and analyses conducted are extensive and detailed. Weaknesses: 1. The authors can consider adding a simple baseline method for a prospective solution for mitigating multi-object hallucinations, as a starting point. 2. Latency analysis in evaluation could be included to provide a more comprehensive analysis. For example, comparing 5 times single-object evaluation vs. multi-object evaluation. Also, especially for student/teacher forcing as they require multiple consecutive inferences. Understanding the time efficiency of the benchmark is important for practical applications. Technical Quality: 3 Clarity: 4 Questions for Authors: 1. Do you have any initial ideas or hypotheses for mitigating multi-object hallucinations? 2. Adding a baseline methods is not a mandatory rebuttal subject, but will be a good addition to the current version. Confidence: 5 Soundness: 3 Presentation: 4 Contribution: 3 Limitations: Yes, this paper generally addressed the limitations. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your thoughtful feedback. We are happy that you found our paper well-written, the problem novel and under-explored, and our experiments/analyses extensive and detailed. We addressed your questions and concerns below. If any residual concerns remain, we would be glad to discuss further. If no concerns remain, we would appreciate it if you could raise your score. ### Q1. Initial ideas or hypotheses to mitigate multi-object hallucinations We present an initial ideas on addressing multi-object hallucinations from a training perspective in Section 4.3. Our findings indicate that LVLMs tend to hallucinate less in homogeneous cases and more in heterogeneous cases. This suggests that LVLMs may get distracted by other objects and struggle to pay attention to the referred objects. Consequently, we propose a training-free method to mitigate this issue, see details below. ### W1, Q2. Adding a baseline for multi-object hallucinations One of the most natural way to make LVLMs "pay more attention to" what is inside the bounding box is to enlarge the amount of attention spent on the bounding box region. Since our dataset comes with ground truth bounding box regions and dimensions for each image, we retrieve the corresponding patches in the ViT that contains the bounding box region, and increase the self-attention on those tokens. After some trials and errors, we found: - Following ATMAN [1], we keep the selected tokens’ attention the same and scale all other tokens’ attention uniformly down by 0.7. Then after softmax, those bounding box regions will naturally obtain more attention. - We have to freeze the attention ratio between vision and text, and manipulate the attention within visual attention. Otherwise, LVLMs output random meaningless tokens. [1] AtMan: Understanding Transformer Predictions Through Memory Efficient Attention Manipulation. Björn Deiseroth, Mayukh Deb, Samuel Weinbach, Manuel Brack, Patrick Schramowski, Kristian Kersting. NeurIPS, 2023. \| \| Default Multi-Object \| \| \| Single-Object \| \| \| \|---------------\|----------------------\|----------------------\|----------------------\|----------------------\|----------------------\|----------------------\| \| Models \| Wild \| Hom. \| Het. \| Wild \| Hom. \| Het. \| \| Seen \| \| LLaVA-1.5 \| 21.26% \| 52.40% \| 7.69% \| 30.59% \| 60.85% \| 12.69% \| \| LLaVA-1.5 + ATMAN-in-Box \| 23.80% \| 55.60% \| 8.50% \| 32.89% \| 63.10% \| 14.85% \| \| Unseen \| \| LLaVA-1.5 \| 13.96% \| 31.88% \| 3.98% \| 26.95% \| 54.41% \| 11.06% \| \| LLaVA-1.5 + ATMAN-in-Box\| 16.00% \| 35.60% \| 4.50% \| 29.00% \| 58.20% \| 13.90% \| ### W2. Latency Analysis Thank you for your valuable feedback. We appreciate your suggestion to include a latency analysis in our evaluation. In response to your comments, we have conducted additional experiments to compare the latency of five single-object evaluations with that of a multi-object evaluation. \| Type \| Time (per 100 attempts) \| \|------------------------------\|-----------------------\| \| 5 times single-object evaluation \| 520.34s \| \| Multi-object evaluation \| 256.59s \| \| Student forcing \| 948.32s \| \| Teacher forcing \| 928.71s \| --- Rebuttal Comment 1.1: Comment: I appreciate the effort authors put into addressing my feedback, particularly in relation to mitigating multi-object hallucinations and conducting the latency analysis. Also, the addition of a baseline method for multi-object hallucinations is a valuable enhancement. Overall, I remain inclined to accept and maintain my score. --- Reply to Comment 1.1.1: Comment: It’s great to know that we were able to meet your expectations. Thank you so much for your careful review and the insightful feedback. We genuinely appreciate the time you spent helping us improve our work.	Summary: This paper introduce a novel multi-object hallucination evaluation task, which assess model capabilities of classifying multiple objects given visual prompts or spatial tokens. The benchmark dataset contains both commonly seen images and unseen images regarding the instruction dataset. Evaluation results show that open-source MLLMs and even proprietary GPT-4o struggles on this task. Strengths: 1. The motivation of assessing multi-object hallucination is clear. 2. The benchmark can facility the research on understanding MLLMs from a new perspective. 3. The experiments are meticulously designed and cover a broad spectrum of factors. Weaknesses: 1. The writing in the experiment section, particularly in Section 5, could benefit from significant improvement. Technical Quality: 2 Clarity: 2 Questions for Authors: 1.The legend for Figure 5 appears to be misaligned with its content, leading to confusion. Also the discussion about Figure 5 is confusing. The analysis about (c) (f) (h) (i) are not aligned with sub-figures, while discussions about (d) (g) are aligned with the content. (a) and (b) are not addressed in the discussion at all. 2. It is unclear which prompting strategy (bounding box or special tokens) is utilized for each model listed in Table 2. This information should be specified for clarity. 3. Typos: LLaVA-7B (unseen) student-forcing (wild) score should be in bold. Confidence: 4 Soundness: 2 Presentation: 2 Contribution: 2 Limitations: the authors adequately addressed the limitations Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We greatly appreciate the reviewer’s time and effort reviewing this paper. We thank the reviewer for the positive feedback on the motivation, novelty, and “meticulously designed” experiments. Please see our responses to your questions below. ### W1: Improvement in Writing Specifically, we describe our improvements for presentation in the experiment sections, especially Section 5. - Enhanced Definitions and Explanations in Model Behaviors: We will clarify the definitions and explanations for factors relevant to the mechanistic behaviors of the models. Specifically, we refined the descriptions and formulas for Object Token Entropy and Visual Modality Contribution to ensure they are more comprehensible. - Refined Table and Figure Captions: We will refine the table and figure captions to provide more context and detail about the settings and the content of each figure. This ensures that readers can better understand the visual data presented and the specific conditions under which the experiments were conducted. - Detailed Analysis in Section 5.2: We will rewrite and expand the section “When Do LVLMs Experience Multi-Object Hallucinations?” to provide a more detailed and clear analysis of each factor. Each factor is now thoroughly examined, with a deeper discussion of its impact on the model’s performance. We kindly redirect the reviewer to the General Author Rebuttals for more details. ### Q1: Legend We apologize for the confusion caused by a mistake here. The legend for Figure 5 was misaligned with its content. The hallucinated objects are represented in Yellow and the non-hallucinated are Green. We will correct these errors in the revised manuscript and ensure that the descriptions accurately reflect the results. ### Q2: Visual Prompt We apologize for any confusion regarding the visual prompting strategies in Table 2 (Lines 194-198). For all LVLMs, we experiment with the bounding box as visual prompts. Specifically for CogVLM-G, we additionally experiment with their special grounding tokens as visual prompt input, as this is their natural visual prompt format and outperforms naive bounding box prompts. We report their performance using special grounding tokens in the Table. ### Q3: Format Thank you for catching this presentation error. We have now corrected this in the revised manuscript. --- Rebuttal Comment 1.1: Comment: The authors may at least need to clarify the discussion about Figure 5, 6 for the consistency between the proposed analysis and the reported experimental results. For example, #313 states 'LVLMs tend to hallucinate objects more frequently when they are positioned away from the center', which means the object centrality (normalized distance d between object and image center, as introduced in #273) positively correlated with the hallucination rate. While the Figure 5 (d) shows the yellow distribution (i.e. the hallucination distribution as mentioned in the author rebuttal) center is left to the green distribution. Overall, the author response does not address my concern about the rigor of in this work from a scientific research view. --- Reply to Comment 1.1.1: Title: Further Clarifications by Authors Comment: We appreciate your instant feedback! We would like to provide a more detailed clarification regarding Figures 5 (and 6) and the Object Centrality metric. We first note that the figures and findings themselves are correct, and clarify that the consistency issue arises from typos and presentation ambiguity. - (Clarification i) Typo in the legend for Figure 5: The hallucinated objects are represented in yellow, and the non-hallucinated objects are in green. This color convention is used throughout the paper. In the Figure 5 legend, we mistakenly flipped this for the color blocks. - (Clarification ii) Object Centrality: The object centrality is defined as $1-d/D$ rather than $d/D$. We realize that our wording is confusing and will clarify this in the updated version. Regarding your specific concerns: --- > The analysis about (c) (f) (h) (i) are not aligned with sub-figures... The reason for this misalignment is the flipped legend, as we clarified in (Clarification i). --- > ...discussions about (d) (g) are aligned with the content... > ...#313 states 'LVLMs tend to hallucinate objects more frequently when they are positioned away from the center', which means the object centrality (normalized distance d between object and image center, as introduced in #273) positively correlated with the hallucination rate. - Figure (d): Upon (Clarification i) and (Clarification ii), we mean to define the object centrality as $1-d/D$ rather than $d/D$. In this way, the object which is closer to the center of the image has a higher object centrality value. Considering the color for (d) was reversed, it matches our analysis that “the object centrality has only a slight influence as LVLMs tend to hallucinate objects more frequently when they are positioned away from the center.” - Figure (g): Figure (g) was actually discussed correctly, indicating that non hallucinated objects appear more frequently in training data. This matches our discussion that “models are less likely to hallucinate object classes that frequently appear in the training dataset.” We hope the reviewer can take a second inspection and let us know if there are other confusions. --- > ...(a) and (b) are not addressed in the discussion at all. - Figure (a) and (b) are discussed in Section 5.2. Figure (a) is discussed in Lines 309-311, Figure (b) is discussed in Lines 311-314. We analyze that “specific data factors, such as query and object homogeneity, significantly influence model performance, with increased hallucination occurring when models process images featuring multiple object classes or a variety of objects” and “the position of object tokens seems to have minimal impact". --- > The authors may at least need to clarify the discussion about Figure 5, 6 for the consistency between the proposed analysis and the reported experimental results. While we clarify the typos and ambiguities in Figure 5, we believe that Figure 6 is consistent with our proposed analysis. - For (a), there is no significant difference between the model’s predicted class and the actual class, which aligns with our statement that “although semantic salience is a key factor in determining whether a model hallucinates, it appears to have minimal impact on the prediction of hallucinated objects”. - For (b), the figure shows that the model’s predicted class has a higher training salience than the actual class, matching our analysis that ”models are more likely to hallucinate object classes that are prevalent in the training data”. - For (c), the figure shows that the position of the predicted class is listed earlier in the input prompt than the actual class, which matches our analysis that “there is a notable preference for models to hallucinate objects that are listed early in the input prompt as candidate classes”. We apologize again for the confusion caused by the mistakenly annotated figure, but we believe this might be a minor issue that we can easily fix in the updated manuscript. Our findings and analysis remain correct and valuable to the community. We hope you can take a closer look after we provide these explanations. Again, we appreciate your feedback and believe these clarifications will enhance the clarity and coherence of our findings. Please let is know if you have any concerns that need our clarification!	Summary: 1. The work proposes a new benchmark evaluation method (through modifying existing datasets) to measure if VLMs can accurately recognize multiple objects in an image simultaneously. This evaluation pipeline, designed by adding 5 bounding boxes to each image in the dataset and creating a fixed prompt, requires the model to identify which class each object within these boxes belongs to. 2. Using this benchmark dataset, the authors analyze the performance of VLMs in recognizing multiple objects simultaneously and the factors that may lead to their hallucination. 3. The contribution of the article lies in its detailed analysis and insights into understanding VLMs' multi-object recognition capabilities. Several important takeaways are: - performance degradation with multiple object recognition: VLMs perform worse when tasked with recognizing multiple objects at once compared to single object recognition. (not convinced by the current experiment results, need more clarification from authors -> see questions below) - using shortcut to explain hallucination behavior: When multiple objects of the same class are required to predict at the same prompt, VLMs tend to use previously recognized classes to predict subsequent object classes, leveraging shortcuts. It suggests the model simply relies on previously identified classes for subsequent predictions. Strengths: 1. The task is well-defined and the evaluation metric is clear (I like the student-forcing and teacher-forcing idea): identify the object from the 5 bounding boxes at the same time. 2. Comprehensive Analysis: It thoroughly examines various factors contributing to hallucination, offering valuable insights into potential causes. It can help the readers to understand hallucination causes in VLMs. Weaknesses: 1. Unclear Benchmark Positioning: The paper's explanation about how this benchmark differs from other datasets is quite confusing (lines 35-48). What specific capability does this benchmark target to measure compared to others? Why is image captioning verification benchmarks insufficient for multiple object consideration? Given a limited evaluation budget, why choose this dataset over others? Is current common benchmarks focus on 1) image captioning, checking if mentioned objects appear in the image and their count, and 2) image grounding, verifying if given descriptions can be located in the image? Could you explain it in more details? 2. Writing (minor): Some parts of the writing could be improved for better comprehension. For example, line 53 could explain earlier why the dataset is split into four sets. Readers only understand later through experiment analysis that these sets investigate if LLMs learn shortcuts by using previously predicted classes. 3. Clarification of Shortcuts and Spurious Correlations: The shortcut story is very interesting, could you elaborate this part more? What are the shortcuts and spurious correlations when claiming VLMs use them? What evidence supports this conclusion? IMO Teacher forcing results and Figure 4/5a indirectly support this, but a detailed, systematic analysis in one section would be better for understanding this. Technical Quality: 3 Clarity: 3 Questions for Authors: 3. Lines 182/183: How are seen/unseen datasets divided? Is it based on the classes from the Visual Genome instruction tuning dataset? 4. Table 2's single-object setup seems confusing. Is it 1) each image with 5 bounding boxes results in 5 independent sessions with the VLM, or 2) each session asks about one object while retaining history for the next question about another object from another bounding box, or 3) every image only have 1 bounding box? Is the wild/hom/het dataset division of the single-object column different only on the bounding boxes? - Table 2: If it's 1), why is the single-object recognition accuracy so low, especially for LLaVA-34B? How does having 5 bounding boxes in a single-object setup impact results? For LLaVA-34B, performance for single and multiple objects is similar, which contradicts the expectation that performance would drop when asked about multiple objects simultaneously instead of focusing on single-object. Do you have other evidence supporting this claim? 5. Lines 215 and 218: Can you explain the difference between hypothesis 1) and 2)? This section is somewhat confusing. 6. Line 254: The logic here is unclear. Why does grounding tuning have little effect? Are there experimental results supporting this conclusion? 7. Figure 5: Suggest explaining how hallucinate and non-hallucinate are calculated in the caption, or provide a reference link to the relevant section. For example, for Figure 5f, is the process as follows: consider every object from every 5k images -> in Toal 25k objects, and classify them into hallucinate and non-hallucinate, calculate everyone's semantic salience? 8. Figures 5f/h/i: It seems the results of hallucinate and non-hallucinate are reversed? The descriptions seem contradictory. For instance, Figure 5h suggests that non-hallucinate objects have higher token entropy, implying that more uncertain tokens are less likely to hallucinate. 9. Line 298: Why consider the last generated token instead of other positions, like the answer token? 10. Figure 6: Why compare actual class and predicted class? I find it difficult to interpret due to lack information because each image should pair predicted and actual classes. Presenting them as two distributions loses this pairing information. A caption explanation of takeaways for these 3 images might help. 11. Do you think hallucinations generation are entangled with the model's ability to correctly recognize visual text information for the bounding boxes? Have you tested the model's ability to recognize bounding boxes alone? 12. (optional) Have you considered incorporating a user study where users provide bounding boxes and then answer questions? This would measure the model's capability in real-world scenarios where bounding box boundaries might be unclear. Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 4 Limitations: The author has listed their limitation in the appendix B. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: # Response to Reviewer 4TNS We greatly appreciate your dedicating your valuable time to this detailed review! We address your concerns as follows. ### Weakness Due to the limited space, we kindly redirect the reviewer to the General Author Rebuttals. ### Q3: Seen and Unseen The Seen and Unseen datasets are divided based on whether the images originate from the training or test/validation sets of the original dataset. We use MSCOCO Panoptic and ADE20K datasets to build our datasets. We didn’t use Visual Genome as it does not have an official train/val split and people use the GQA splits conventionally. ### Q4: Single-Object Setup Statement (1) is correct, the setup has “each image with 5 bounding boxes results in 5 independent sessions with the VLM.” The wild/hom/het dataset division is identical to the Multi-Object setups. The purpose is to keep all irrelevant factors untouched thus the comparisons between setups are fair and controlled. > Why is the single-object recognition accuracy so low, especially for LLaVA-34B…For LLaVA-34B, performance for single and multiple objects is similar… We note that LLaVA-34B performance for single and multiple objects is similar ONLY for the situation of Seen+Heterogeneous data split. For all the other setups, performance for single is better than multiple objects. We are also aware that the performance of LLaVA-34B on Seen+Heterogeneous+Single Object is abnormal. We reran the experiments with 16 bit precision and remove model quantization, the updated number is 19.36%, which is almost the same as the previous score. Upon closer inspection, LLaVA-34B appears to memorize images encountered during pretraining and is prone to focusing on salient objects or objects with multiple occurrences. > How does having 5 bounding boxes in a single-object setup impact results? There is a very marginal performance increase when keeping only one bounding box compared to five. We report the results with 5 bounding boxes to keep all irrelevant factors untouched thus the comparisons between setups are fair and controlled. ### Q5: Shortcut Hypothesis For hypothesis 1, the model might learn to perform class-agnostic object recognition better due to the ability to perceive context through a few-shot setting. For hypothesis 2, the model might learn to recognize one specific object in a few-shot setting. We expect improved performance on the last object B in the AAAAB setup for hypothesis 1, compared to the single object setting. For hypothesis 2 we expect the performance to be roughly the same. ### Q6: Grounded Tuning We refer specifically to the results for CogVLM-G presented in Table 2. The model performs poorly in the default multi-class setting, but shows relatively better performance under the single-object setting and teacher-forcing setting. We hypothesize that the grounding model fails to improve performance due to either a lack of instruction-following ability. This suggests that grounding alone does not effectively reduce multi-object hallucination in our benchmark, and conversational tuning is critical. We will add more detailed experimental results to support this conclusion in the revised manuscript. ### Q7: Figure Caption Clarity When calculating hallucinated and non-hallucinated objects, we consider every object from all the unseen images, and classify the model’s prediction into hallucinated and non-hallucinated. We will improve the caption in the revised manuscript. ### Q8: Figure 5 Error Thank you for catching this bug in the plots, we realize that the legend for Figure 5 was misaligned with its content, which led to confusion. The hallucinated objects are represented in Yellow and the non-hallucinated are Green. We will correct these errors in the revised manuscript and ensure that the descriptions accurately reflect the results. ### Q9: Last Token This is a confusion arising from the way we described the algorithm. In our implementation, which uses a causal transformer, the model generates tokens sequentially. At each step, while generating the next token (which is the most recent token in the context of the transformer), the model attends to all previously generated tokens. This means the model’s attention mechanism considers the entire history of tokens up to that point. We apologize for any misunderstanding caused by our writing and will clarify this in the revised manuscript. ### Q10: Actual Class and Predicted Class Sorry for the confusion. For a model that hallucinates object A into object B, object A is the actual class, and object B is the predicted class. Indeed, presenting them as two distributions loses this one-to-one pairing information, but Zhou et al. [67] have already studied this setup and we emphasize on the statistical comparison instead. ### Q11: OCR Yes, we agree that our benchmark setting may entangle hallucinations with the model’s ability to correctly recognize visual text information within the bounding boxes. To address this, we conducted controlled experiments to isolate these factors. In the single-object setting, the model performed very similarly for each of the objects 1/2/3/4/5 within the same image, which indicates that its performance is stable with each visual prompt (See Appendix for the full tables). Also, since the same issue remains for both single and multi-object settings, our findings hold as the factors are controlled. Besides, our visual prompt setups mostly follow that of the set-of-mark prompting [54]. ### Q12: User Studies Thank you for the valuable suggestion. Incorporating a user study where users provide bounding boxes and answer questions would indeed offer a meaningful evaluation of the model’s performance in real-world scenarios with potentially unclear boundaries. Due to time and resource constraints during the rebuttal process, we were unable to implement this approach. However, we consider it an excellent direction for future work and plan to explore it in subsequent research. --- Rebuttal Comment 1.1: Comment: Thank you for the response and additional experiments provided. After reading, I decide to maintain the current score and evaluation. --- Reply to Comment 1.1.1: Comment: Thank you for your detailed and thoughtful feedback throughout the review process. We’re pleased that our response and additional experiments addressed your concerns.	Rebuttal 1: Rebuttal: We thank the reviewers for their detailed and thoughtful feedback. We are glad that the reviewers appreciate our motivation, task setup, analysis, and presentation. We hereby respond to the general concerns and update our experimental results. ### General 1: Benchmark Positioning (Reviewer 4TNS) > What specific capability does this benchmark target to measure compared to others? ROPE specifically measures object hallucination in VLMs within a multi-object setting, examining how models may misperceive (e.g., by inventing nonexistent objects or becoming distracted) when tasked to focus on multiple objects concurrently, and which factors cause the hallucinations. > Why is image captioning verification benchmarks insufficient for multiple object consideration? In comparison to image captioning benchmarks such as CHAIR, ROPE offers two main advantages: - Captioning benchmarks don’t address grounding and has referential ambiguity. For example, in an image with multiple apples, the ability to generate “there are apples in this image” does not imply that the model can recognize each individual apple correctly. ROPE provides a clear visual prompt that reduces such ambiguity. - ROPE employs a fixed decoding template, enabling an automatic evaluation protocol, rather than relying on LLMs as evaluators. > Given a limited evaluation budget, why choose this dataset over others? ROPE is designed to be token-efficient and avoids the need for additional LLMs as evaluators. The benchmark employs a fixed decoding template, saving tokens compared to image captioning benchmarks like CHAIR. > Is current common benchmarks focus on 1) image captioning, checking if mentioned objects appear in the image and their count, and 2) image grounding, verifying if given descriptions can be located in the image? Could you explain it in more detail? Current common benchmarks focus on either (1) or use Yes/No questions to probe the models. - CHAIR is one of the most well-known image captioning benchmarks for hallucination. CHAIR calculates what proportion of words generated are actually in the image according to the ground truth sentences and object segmentations. - POPE can be seen as the image grounding benchmark for hallucination. POPE formulates the evaluation of object hallucination as a binary classification that prompts LVLMs to output “Yes” or “No”, e.g. “Is there a chair in the image?” To the best of our knowledge, none of the existing object hallucination benchmarks satisfyingly address grounding and resolve referential ambiguity mentioned above. ### General 2: Shortcut and Spurious Correlation (Review 4TNS) Yes, the “teacher forcing results and Figure 4” are intended for investigating shortcuts. We elaborate as follows. - We discuss Shortcuts in Section 4.2 Paragraph 3, which are simple heuristic or rule-based solutions to a problem. In the teacher-forcing setting, we found that LLaVA models score over 90% accuracy. We design an Adversarial split, in which the first four tested objects are of the same class and we probe an object of a different class for the last one (AAAAB). The model's performance on the last object B drops to nearly zero, with almost all hallucinations labeling it as A. This is in stark contrast to 23.35% if these objects are probed individually or 19.16% when these objects are placed as the first to query in multi-object settings. - We discuss Spurious Correlations in Section 5, which are features that appear to be statistically correlated with predictions. We present a systematic study of data-specific factors, salience/frequency, and model intrinsic behaviors. When the model hallucinates object A to object B, we study how these factors contribute to which object A to be hallucinated and which object B to hallucinate. ### General 3: Writing (Reviewer 4TNS, i299) - Enhanced Definitions and Explanations in Model Behaviors: We will clarify the definitions and explanations for factors relevant to the mechanistic behaviors of the models. Specifically, we refined the descriptions and formulas for Object Token Entropy and Visual Modality Contribution to ensure they are more comprehensible. - Refined Table and Figure Captions: We will refine the table and figure captions to provide more context and detail about the settings and the content of each figure. This ensures that readers can better understand the visual data presented and the specific conditions under which the experiments were conducted. - Detailed Analysis in Section 5.2: We will rewrite and expand the section “When Do LVLMs Experience Multi-Object Hallucinations?” to provide a more detailed and clear analysis of each factor. Each factor is now thoroughly examined, with a deeper discussion of its impact on the model’s performance. - Improved Explanation of Dataset Split: We will enhance the explanation of the dataset split and its purpose earlier in the text, providing a clearer rationale for the division into four sets. This revision ensures that readers understand the motivation behind the dataset split and how it relates to investigating whether LLMs use shortcuts by leveraging previously predicted classes. ### Updated Results and Additional Experiments See the PDF attached We present a case study in the real-world autonomous driving scenario, and also additional baselines: - ATMAN-in-Box: A simple, training-free solution that we came up with to improve multi-object hallucination; - Decoding strategies (OPERA) - RL-based alignment (MiniCPM-V) - Mechanistically grounded LVLMs (GLaMM and GroundHog) Pdf: /pdf/203cdb5f5f41880ca03893fa60b6b28bfda4b3bf.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Generalized Fast Exact Conformalization	Accept (poster)	Summary: The authors study the solution path of constrained optimization problems when one training label varies in ${\mathbb R}$. In the Conformal Prediction framework, this is equivalent to studying the output of a Full-CP algorithm. The paper extends the approach to optimization problems with general constraints and a piece-wise differentiable objective. Strengths: - Characterizing the solution path of a series of smoothly varying optimization problems is relevant, even beyond the CP framework. - The Lagrangian reparametrization approach is interesting. - The proposed method seems to be more efficient than Split CP. Weaknesses: - It would be helpful to clarify from the start what "opening the black box" means, e.g. by listing the assumptions needed to obtain the solution path efficiently. - The authors should justify better why they need i) general constraints and ii) piece-wise differentiable objectives. A warm-up section describing the unconstrained case would also help. Has the unconstrained and globally differentiable case been considered elsewhere? - The method seems to apply in a convex neighbor of the optimum. Assuming the algorithm is initialized there, the optimization problem is quadratic. The authors should comment on the difference between their method and the standard full-CP approach in the presence of several local optima. Technical Quality: 3 Clarity: 2 Questions for Authors: - In the abstract, you mention the computational burden of full-CP algorithms. What about Split-CP? Does "strong assumptions" mean data inefficiency? - Is the solution path unique? What happens for overparametrized models? - In what sense the prediction sets of [18] and [19] do not have statistical guarantees? Can't one combine the upper bound on the estimation error and standard CP validity? - Is the formalism developed in Section 3 only needed because of the general constraints and piece-wise assumption in Equation 1? - Intuitively, what does produce a kink in $w_*(t)$? - Why do you fix $\alpha=0.8$? - In Algorithm 1, does $z$ need to be discretized? - Why Split CP does not appear in Figures 3 and 4? - Why is the standard approach, i.e. ``Grid1/Grid2`` in Table 2, outperformed by Split CP? Normally full-CP is expected to be more efficient. Confidence: 3 Soundness: 3 Presentation: 2 Contribution: 2 Limitations: The authors do not discuss the limitations of their work. They may have added a few lines about the applicability of their assumption and the limited choice of predictors in the experiments. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: # Many thanks for appreciating our work! Dear reviewer jxtf, We deeply appreciate your commitment in reviewing our paper and your encouraging words of support for our work! In the following, we will provide a comprehensive response to your review comments. --- > clarify what "opening the black box" means Please refer to general rebuttal, section ②. Thank you! > should justify better why they need i) constraints ii) piece-wise differentiable This is primarily to achieve the versatility of the objective. Nowadays many learning tasks essentially involve unconstrained optimization, but it's well known that many loss functions are not globally differentiable, so we believe this extension is natural. Moreover, constraints are also not rare in real-world tasks, e.g., ordinal support vector machines used for classification and regression [1], linear programming in operations research [2], and certain fairness constraints in fairness classifications [3], all of which can be accommodated within our Eq. (1). Several models in experiments also validate this, as current work cannot handle their conformalizations. Following your constructive suggestion, we added relevant examples and further motivation in Section 2. > Has the unconstrained and globally differentiable considered elsewhere? All baselines prior to our work have studied the unconstrained case (Table 1), and mostly require the objective function to be globally differentiable. For research on solution paths that unrelated to conformalization, please refer to Appendix F.1. > The method seems to apply in a convex neighbor of the optimum We believe that homotopy continuation does not necessarily occur within the convex neighborhood (even if the selection function is strongly convex), but is generally within a closed or bounded neighbor of the optimum. More theoretical properties will be explored in future work. > The authors should comment on the difference ... in the presence of several local optima Standard full-CP uses batch-training solvers (e.g. various SGD), making it difficult to control their optimization behavior. Whether the solver can escape saddle points depends on its inherent properties and user parameters. On our algorithm, please see next question. We added further explanations based on your comments. > Is the solution path unique? What happens for overparametrized models? Computationally, the Picard–Lindelöf theorem proves that the solution of numerical ODE is unique. Geometrically, if regularity conditions are met, then points of the path (with non-vanishing KKT multipliers) is locally the projection of a higher-dimensional smooth manifold onto optimization space, hence it's not unique but our algorithm can indeed follow a path of stationarity points. Overparametrized case: please see Appendix F.4. > computational burden: What about Split-CP? Does "strong assumptions" mean data inefficiency? (Characters limitation) please see response to Reviewer 4Aeq. Thanks! It means that previous methods cannot be extended and are not sufficiently general. > In what sense the [18, 19] do not have statistical guarantees? Can't one combine the ...? Thanks for valuable feedback! This thought is reasonable, and aligns with one of the motivations behind these works. We have revised our writing to indicate that there are no optimal statistical guarantees, as their solutions for minimization are indeed not exact. > Is the formalism developed in Section 3 only needed because of the general constraints and piece-wise assumption? Yes, our framework would be simplified (but less useful) without the above settings. > what does produce a kink in $\mathbf{w}^\star(t)$? Kinks (or non-smooth transition points) on the path are caused by non-differentiable points, including boundary constraints hitting or the non-differentiable points within the loss / regularizer itself (e.g., the $\ell_1$ norm at $0$). Appendix C.3 provides an intuitive illustration of kinks in a 2-dimensional optimization space. > Why fix $\alpha=0.8$? This is only needed for numerical simulations. Our algorithm primarily focuses on full path generation, while $\alpha$ is used in conformal set generation (the second stage). Like the baselines, we use standard way to compute the conformal set, so the setting of $\alpha$ has no impact on our core algorithm. We observed that most related works set $\alpha$ around 0.1 or 0.2, so our setup is reasonable. Let us know if you have specific concerns. Another insight from your question is that we could consider $\alpha$ as a variable to study the underlying relationship between the resulted conformal set and $\alpha$, but this beyond the current scope. > does $z$ need to be discretized? The need for discretizing $z$ depends on the property of the label space $\mathcal{Y}$. In regression, since $y_{n+1}$ is continuous, there's no need to discretize $z$. In classification problems, $z$ is generally discrete for computational purposes, as we focus on the discrete $y_{n+1}$ of interest. > Why SCP does not appear in Figures 3, 4? (Characters limitation) please see response to Reviewer ji5B. Thanks! > Why is the standard approach outperformed by Split CP? Indeed, the SCP results are better in a few lines. That's may due to our choice of grid points not being overly dense to ensure fairness in comparisons. That's also related to the data distribution and calibration set partitioning in SCP. > The authors do not discuss the limitations Technical limitations are described in Appendices F.3 and F.4. --- References: [1] "Support vector machines–an introduction." Springer, 2005 [2] "Linear programming and its applications." Springer, 2007 [3] "Fairness constraints: Mechanisms for fair classification." AISTATS 2017 We thank the Reviewer jxtf again for your insightful feedback and strong support of our submission! If you have any remaining concerns or further inquiries, please do not hesitate to let us know.	Summary: This paper proposes a new method to accelerate the computation of full conformal prediction sets, a task that traditionally requires a computationally intensive grid-search approach. The proposed method aims to streamline this process, potentially reducing the need to refit the predictive model for each test point and each possible outcome value. However, the paper suffers from poor writing, heavy mathematical notation, and an overly dense presentation, while also employing tricks like small font sizes in figures and text wrapping to extend beyond the standard page limits. Due to these significant issues, I believe that a thorough review of this paper is not feasible at this time. I would consider this a 'desk rejection' from my perspective. I hope the authors will not be offended or discouraged, as this is not a judgment on the quality of their research, which I was unable to carefully assess, but rather an invitation to improve the presentation to facilitate the review process. Strengths: - This paper studies an important problem in conformal inference, namely to speed up computations for full-conformal prediction. - The proposed method could potentially reduce the computational burden associated with conventional grid-search approaches. Weaknesses: - The paper is not very well written, it's very dense, and difficult to understand, even for those familiar with the broader field. - The paper is too long and only fits within the page limits due to some "tricks" such as using very small font sizes in figures and wrapping text around figures. Technical Quality: 2 Clarity: 1 Questions for Authors: - Could you try to enhance the writing quality and clarity of the paper to make it more accessible to a broader audience? - Would you consider shortening the paper, or alternatively, submitting it to a venue that accommodates longer articles? This paper might turn out to be much easier to understand in an extended version. My philosophy is that if the content cannot be effectively conveyed within 9 pages, it is better suited for a different format. Forcing it to fit within this limit does a disservice to the readers by compromising clarity and comprehensiveness. Confidence: 1 Soundness: 2 Presentation: 1 Contribution: 2 Limitations: The primary limitation of this paper is its poor writing quality and extremely dense presentation, making it difficult to follow and understand. In its current form, the potential audience of this paper might at best be limited to a very narrow group of readers, which unfortunately does not include this reviewer. Flag For Ethics Review: ['No ethics review needed.'] Rating: 3 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: # Thankful for your constructive feedback! Dear reviewer KUWB, We are very grateful for the effort you have put into reviewing our work and for recognizing the importance of our research problem. We have addressed and acted upon your main criticisms, and we are looking forward to further interaction with you. --- ## Ⅰ. Text Wrapping & Figure Size > employing tricks like small font sizes in figures and text wrapping to extend beyond the standard page limits > due to some "tricks" such as using very small font sizes in figures and wrapping text - Thank you for your feedback. Firstly, we would like to politely point out that text wrapping and figure scaling are *not* tricks we specifically employed in this paper. Such practices are quite common at NeurIPS and other similar venues like ICML / ICLR. - e.g., P7 in [1], P6-P8 in [2], P8 in [3], P5-P7 in [4], etc. - We understand your concerns. All the images inserted in this paper, whether experimental results or logical diagrams, are vector graphics and can be enlarged arbitrarily without distortion. - Based on your feedback, we promise to further adjust the layout by merging some runtime comparison figures with sections in the appendix. This will allow us to increase the font size of each figure in the main body. - Besides, kindly note that if this paper was accepted, we will have one extra page in the camera-ready version. - As per our response to Reviewer ji5B, we will also move some minor technical content to the appendix or remove it entirely. For example, some corollaries, Sections 4.1 and 4.2. This will create further space in the main body, reducing its content density. ## Ⅱ. Clarity & Length > However, the paper suffers from poor writing > The primary limitation of this paper is its poor writing quality Despite the mathematical notation being dense (in some sections), our overall structure should be pretty clear and is well organized, as acknowledged by other reviewers. Our introduction part (including motivation, high-level ideas, and related work) and experimental sections have been well understood by several reviewers. This indicates that the presentation of our paper, while not perfect, still meets the basic standards of a technical paper. We are also continuously improving our writing. > The paper is too long > the content cannot be effectively conveyed within 9 pages... Forcing it to fit within this limit does a disservice by compromising clarity and comprehensiveness - We fully understand your worries regarding the length and formatting of the paper. At first, please let us kindly point out that all content in our appendix merely provides further explanations of the technical results in the main bofy, rather than introducing new arguments. Even if we were to remove the entire appendix (except proofs), the content of our main body still remains entirely self-contained, which has included the core theorems, discussions on assumptions, and statistical descriptions of the novel framework. - Any reader familiar with optimization and conformal prediction can follow the algorithmic steps presented in the 9 pages, without reading the appendix. Therefore, we respectfully disagree with the viewpoint that the content cannot be effectively conveyed within main body. - We believe the length and (technical) clarity involve a trade-off. - We could, of course, write several hundred pages listing every definition and detailing every step of derivations, but this would be inappropriate for a formal research paper. - Thus, in addition to the main body, we have included extensive discussions in the appendix, which help readers understand the core framework from various perspectives. *These in-depth discussions and extra experiments aim to enhance the clarity* and technical comprehensiveness of our research findings*, stimulate readers' thoughts on the algorithmic details, and attract researchers with different backgrounds. (as some content like IVP in differential equation* might be overly fundamental for readers who are already familiar with them) - In appendix we dedicated 10 pages to study our by-product. Since the main focus is conformalization, we can simply delete this part and immediately reduce the paper's length by nearly 20%. > Would you consider shortening the paper Yes! Thanks again for your advice. ## Ⅲ. Community Interest > difficult to understand, even for those familiar with the broader field > audience might at best be limited to a very narrow group of readers Thank you for your thoughtful comments. Fully understanding the details of theoretical framework indeed requires a certain level of math maturity. However, for those engaged in algorithmic research, referring to the pseudo-code and the explanations provided in the appendix should be sufficient to apply our new algorithm, and promote its application at a more practical level, even for those outside the ML community. As we explained, the contributions of this work encompass both algorithmic and new theoretical advancements. By NeurIPS guideline, this community spans over optimization theory, statistics, and probabilistic ML. I believe our work will also attract researchers beyond those specializing in conformal prediction. --- References: [1] "Learning to Relax: Setting Solver Parameters Across a Sequence of Linear System Instances." ICLR 2024 [2] "In-context impersonation reveals Large Language Models' strengths and biases." NeurIPS 2023 [3] "Steve-1: A generative model for text-to-behavior in minecraft." NeurIPS 2023 [4] "SaNN: Simple Yet Powerful Simplicial-aware Neural Networks." ICLR 2024 Meanwhile we would like to highlight our main contributions again in the following. We respectfully ask you to read our response and consider stronger support based on the soundness and contribution of this work. Our sincere thanks once again. --- Rebuttal Comment 1.1: Comment: Dear Authors, Thank you for understanding that my review was not a critique of the content itself but rather of its presentation. As I mentioned, this paper seems ill-suited to fit within the 9-page limit. If the paper were only slightly over the limit, I would not have raised an issue. However, the current issues due to length, density and quality of presentation are significant in my opinion. It's also indicative that, despite their overall positive assessment, other reviewers have also noted that your paper is hard to read. This raises three main concerns: - Reviewer Burden: I volunteered to review a 9-page paper, with the expectation that the authors had made every effort to present their work clearly. When the paper is overly long and dense, it becomes difficult to review thoroughly within the time constraints. If I cannot review the paper carefully, I am unable to fully verify its technical correctness or assess its novelty, which are critical factors in recommending it for publication. The fact that other reviewers have given positive scores does not justify altering my independent assessment. - Suitability for NeurIPS: If the paper is too lengthy and complex for a reviewer to digest, it is likely that many NeurIPS readers will find it similarly inaccessible. This brings into question whether NeurIPS is the right venue for this work. - Impact: If both reviewers and potential readers struggle with the paper's density, it raises the question of why the authors are intent on publishing it in its current form. I strongly recommend that you take my feedback seriously and consider revising the paper to make it more accessible. Alternatively, you might explore a venue that allows for a longer version, where the absence of strict space constraints would enable you to present your work more clearly. If your goal is to make an impact, enhancing the paper's readability is in your best interest. Not every paper can—or should—be condensed into 9 pages. In conclusion, I suggest you consider my feedback carefully. I have assigned a low confidence score to my review, acknowledging that I was unable to thoroughly assess the paper. This is the most responsible course of action I can take under the circumstances. --- Rebuttal 2: Title: Highlighting Our Contributions Comment: We would like to highlight our main contributions again in the following. We would be very happy to engage with reviewers if they have any doubt or confusion. Thank you. --- 1. We are the first to achieve a fast exact conformalization for generalized parametric estimation, with accuracy comparable to the existing grid-search type method. This process is underpinned by rigorous theoretical analysis, demonstrating that the Algorithm 1 output is theoretically equivalent to ground truth solution path. Please see our general response, and for further details, refer to Section 3.3 and Appendix F.2. Traditionally, the only way to construct a conformal prediction set has been limited to loop over the label space $\mathcal{Y}$, which discretize the interval of interest and subsequently solve a sequence of individual optimization subproblems [1]. Our contribution thus addresses a long-standing gap in the field, significant for both the conformal prediction and optimization communities. --- 2. Our algorithm is applicable to any generalized parametric estimation, provided mild assumptions are met (see Assumptions 1, 2). This general applicability was previously unattainable in literature, which focused on specific ML models. For example, (Lei, 2019) [13] provided theoretical insights for the $\ell_1$-regularized quadratic loss (Lasso), i.e., let $t_0=0$, $J_0 = \{j : \hat{\beta}(0) \neq 0\}$, the piecewise linearity of model solution $ \hat{\beta}$ is $$\begin{align} \eta(k) &=\frac{n^{-1}\sum\_{j=1}^{J\_k} x\_{n+1,jk}}{1+n^{-1} x\_{n+1,J\_k} \sum\_{j=1}^{J\_k^{-1}} x\_{n+1,jk}}, \\\\ \gamma(k) &=\frac{x\_{n+1,J\_k^c} - \sum\_{j=k-1}^{J\_k^c} \sum\_{j=1}^{J\_k^{-1}} x\_{n+1,jk}}{1+n^{-1} x\_{n+1,J\_k} \sum\_{j=1}^{J\_k^{-1}} x\_{n+1,jk}}, \\\\ \hat{\beta}\_{J\_k}(t) &= \hat{\beta}\_{J\_k}(t\_k)+\eta(k)(t - t\_k) \quad \forall t \in [t_k, t_{k+1}],\hat{\beta}\_{J\_k^c}(t)=0, \\\\ v\_{J\_k^c}(t) &=v\_{J\_k^c}(t\_k)+\gamma(k)(t-t\_k) \quad \forall t \in [t_k, t_{k+1}], \end{align}$$ but benefits to researchers using other forms of parametric models were pretty limited, since formulating similar rules for more complicated parametric estimation could be theoretically challenging. Our method requires only weak assumptions, enabling exact conformalization for a range of significant and classic models like Non-negative Least Squares and Inverse Gaussian Regression for the first time. We offer a unified framework for this pivotal domain of generalized parametric estimation, which is indeed one of our primary contributions. --- 3. Our framework is straightforward to implement and computationally efficient. With theoretical analysis, we present explicit expressions for the gradient flows of reparameterized optimization problem, homogenized and aligned with standard forms used by mainstream numerical libraries, simplifying programming efforts. We pointed out the complexity of algorithmic implementation in our response to Reviewer ji5B (also see Section 4.3). Computationally, our solver adaptively selects step sizes within the solution interval to capture all events / kinks and can swiftly adjust the active set through preset conditions. This feature is wll-supported by many solver libraries. Our algorithm requires no extensive iterations for traversing latent parameters, contrasting sharply with conventional grid-search type techniques. --- 4. This research reveals the dynamics of solution and the essential structure of optimization paths for conformalized parametric estimation (Section 3.3), which is of independent intellectual interest and also bears significant implications for machine learning. We use dynamics to reveal how estimation depends on latent parameters, which coincides with recent work in the optimization community [3,4]. The idea of combining differential equation systems with optimization paths adds a significant tool to community's toolbox, and provides a bridging interface between machine learning and applied mathematics. --- 5. As a by-product, we introduce an exact online label-varying algorithm. Our analysis indicates that it can adapt label changes effectively, where the updated online solution is equivalent to retraining from scratch on new labels using standard batch approaches. We also conducted numerical evaluations in simulated label-varying environments to demonstrate its accuracy and efficiency. --- References: [1] Papadopoulos, Harris, et al. "Regression conformal prediction with nearest neighbours." Journal of Artificial Intelligence Research (2011). [2] Lei, Jing. "Fast exact conformalization of the lasso using piecewise linear homotopy." Biometrika (2019). [3] Lin, Xi, et al. "Continuation path learning for homotopy optimization." ICML 2023. [4] Negri, Marcello Massimo, et al. "Conditional Matrix Flows for Gaussian Graphical Models." NeurIPS 2023. --- Rebuttal 3: Title: Many thanks for your kind follow up! Comment: Dear reviewer KUWB, Thank you for your prompt response along with your kind understanding. We deeply appreciate your candid feedback regarding the low confidence score as well as your responsible actions. Please allow us to address any remaining concerns that you may have: - Reviewer Burden. At the beginning, we greatly appreciate your time and effort in evaluating our paper. We sincerely accept your criticism and understand that this paper has caused additional devotion for some reviewers, including yourself, but this was never our intention. Our research focuses on the conformalization of generalized estimation, so we aimed for it to be comprehensive (i.e., broadly applicable) and to provide in-depth technical insights. As stated in rebuttal, the main body of this paper is completely self-contained. Our 9-page main text sufficiently describes our motivation, related arts, and presents our theoretical findings as well as the algorithmic steps. The sections in appendix are only necessary when one need to learn the experimental details, or verify our theoretical derivations step-by-step. - Clarity. We understand and respect your concerns regarding the paper's density and presentation. We place great importance on your proposed suggestions. 1. By removing some less critical technical paragraphs (e.g., Section 4.1, 4.4) and minor results (e.g., Corollary 1, Theorem 7), we have gained additional space in the main body and adjusted the equations and figures to reduce content density. 2. We have carefully revised the vague sentences in main body, incorporating feedback from all reviewers. 3. We have also shortened the overall length of the paper based on your valuable feedback; specific details are listed below. - Although the notation in some sections is dense, as mentioned in our rebuttal, we believe that our overall textual writing meets the minimum required standards. - We already had a detailed symbol table in appendix, allowing readers to quickly query the meanings of the math notations. - Audience. Mathematically, some reviewers explicitly pointed out that our work is hard to follow, but several other reviewers’ comments and feedback reflect their deep understanding of the paper. In a summary, for those with a certain level of mathematical maturity, our paper offers theoretical tools and a statistical framework. For researchers in related fields, it provides practical algorithms and a high-level theoretical narrative. Our work essentially bridges different domains, while the detailed explanations in the appendix lower the barrier to understanding, aiming to engage a broader audience. - NeurIPS Suitability. While we do understand your concerns about the paper’s suitability for NeurIPS, detailed appendices are not uncommon in conference presentations. We would like to respectfully point out that our current paper length is relatively long, but not excessively so. In the next response box, we will provide some examples from last year's NeurIPS to illustrate this point. We acknowledge and respect your decision regarding the score assigned to our submission. Regardless of whether this paper is ultimately accepted, we are committed to continuously improving its clarity and readability. On this point, we believe that we share a common pursuit. We once again express our gratitude for the constructive conversation with reviewer KUWB. Sincerely, Authors --- $ $ ### Length reduction Based on the feedback from reviewers, we have made the following major changes to our appendix. The final effective length of paper will be reduced from the current 51 pages to 36 pages: - We removed many minor references, reducing the 6-page reference list to only 4 pages. Additionally, we deleted the table of contents (page 16). - We significantly reduced the additional numerical results (pages 41-43) to less than 1 page. - We have shortened Appendix F: Additional Discussions (pages 43-46) to only 1 page. - Given that the focus of this paper is on conformal prediction, and only one of the five reviewers mentioned our by-product (i.e. Algorithm 2), we will remove discussions and simulations related to this by-product that are not directly relevant to our key focus. This includes the theoretical analysis (pages 34-35), examples (pages 38-39), and discussions and experiments (pages 47-51). --- Rebuttal 4: Title: Supplement: relatively long papers Comment: From last year’s NeurIPS conference proceeding, we randomly picked some of the relatively longer papers. To avoid the bias and to maintain convincingness, all the papers listed below are only selected from the Spotlight or Oral batches. ---- In some papers, authors provide additional theoretical insights and discussions in their appendix. Examples include: [1] "Survival instinct in offline reinforcement learning." NeurIPS 2023. `(59 pages)` [2] "Clifford group equivariant neural networks." NeurIPS 2023. `(69 pages)` [3] "Adversarial training from mean field perspective." NeurIPS 2023. `(54 pages)` [4] "Monarch mixer: A simple sub-quadratic gemm-based architecture." NeurIPS 2023. `(58 pages)` [5] "Transformers as statisticians: Provable in-context learning with in-context algorithm selection." NeurIPS 2023. `(87 pages)` [6] "Bridging RL theory and practice with the effective horizon." NeurIPS 2023. `(55 pages)` [7] "Decentralized randomly distributed multi-agent multi-armed bandit with heterogeneous rewards." NeurIPS 2023. `(57 pages)` [8] "Understanding multi-phase optimization dynamics and rich nonlinear behaviors of relu networks." NeurIPS 2023. `(94 pages)` [9] "Would I have gotten that reward? Long-term credit assignment by counterfactual contribution analysis." NeurIPS 2023. `(51 pages)` --- Authors also sometimes supplement the appendix with additional experiments to enhance the credibility of their research, such as: [10] "The goldilocks of pragmatic understanding: Fine-tuning strategy matters for implicature resolution by LLMs." NeurIPS 2023. `(79 pages)` [11] "Okridge: Scalable optimal $k$-sparse ridge regression." NeurIPS 2023. `(183 pages)` [12] "Parsel🐍: Algorithmic Reasoning with Language Models by Composing Decompositions." NeurIPS 2023. `(58 pages)` [13] "Uncovering the hidden dynamics of video self-supervised learning under distribution shifts." NeurIPS 2023. `(69 pages)` [14] "Principle-driven self-alignment of language models from scratch with minimal human supervision." NeurIPS 2023. `(55 pages)` [15] "WITRAN: Water-wave information transmission and recurrent acceleration network for long-range time series forecasting." NeurIPS 2023. `(68 pages)` --- Kindly note that the last 6 pages of our PDF are NeurIPS Paper Checklist, which did not exist last year. Therefore, they should not be counted towards the effective total page count.	Summary: The paper introduces a method to compute exact conformal prediction intervals that have statistical guarantees. The method improves from previous work in three ways: * The conformal interval has exact guarantees instead of approximative * The loss function family covered is larger than convex, same for the regularizer family * It works for linearly constrained problem The core idea is to build a path from value $t\in [0,1]$ to targets $y$ and find how the parameters of the function $\mathbf{w}$ evolve as we vary $t$ (and therefore $y$). The weights $\mathbf{w}(\cdot)$ as a function of $t$ satisfy an ODE that can be solve with standard solvers when the functions in the loss function and constrains are piecewise continuously differentiable. The authors then show the improvement in terms of coverage, dataset size and more importantly speed on several datasets. Strengths: * The examples are compelling are show very well the improvement * The contribution is pretty significant as it widens the possible families of loss functions Weaknesses: * My main issue is that the paper is very hard to read. It is too notation heavy and dense. For example, why use $\hat \theta$ instead of $\theta$? The $\hat {}$ make them look like estimators when it is not the case here * Classification is a big application of conformal prediction, it is unfortunate that we do not have an example . * Figure 1 might be a bit misleading. It seems to imply that the method works for higher dimensions of $\mathcal{Y}$ but it does not seem the case Technical Quality: 2 Clarity: 2 Questions for Authors: * Does the method require more memory than the baseline methods? * I am not convinced by the explanation given for classification(1067-1074). This might be valid for some ranking tasks but not when there is no order in the classes, in my opinion. Could you illustrate it, even with a toy example? Confidence: 3 Soundness: 2 Presentation: 2 Contribution: 4 Limitations: * You mention not implementing [13] because it uses underlying structure and therefore might be faster. It would still be interesting to see if the gain of speed from using [13] instead of your method is significant or not, in cases where it applies. * (see comment on classification) Flag For Ethics Review: ['No ethics review needed.'] Rating: 8 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: # Many thanks for acknowledging our research! Dear reviewer x8xk, We want to express our heartfelt thanks for taking the time to review our paper and for your kind words of appreciation and support for our work! In the following, we will provide a comprehensive response to your review comments. --- ## Ⅰ. Notation > It is too notation heavy and dense Thank you for your valuable comments. We understand and appreciate your concerns regarding the mathematical notation. For a comprehensive explanation, please refer to our general response. While the statistical derivations in the paper indeed necessitate a certain level of mathematical proficiency, we believe they will appeal to researchers from diverse fields. This, in turn, can foster collaboration between the communities of conformal prediction and numerical optimization. > why use $\hat{\theta}$ instead of $\theta$? The $\hat{~}$ make them look like estimators Thank you for your thought-provoking question! In our intention, $\hat{\theta}^k$ in the analysis is indeed used to denote the estimator of ${\theta}^k$. Technically, - Let us recall that Lemma 3 (page 20) explains that for the special case of $PC^r$ functions, there is a simpler expression for the Clarke subdifferential $\partial f$ (Definition 5) in terms of the gradients of the selection functions $\\{D^k\_f\\}$. Hence, the Clarke subdifferential of $f$ is easy to compute and that the set of nonsmooth points of $f$ can essentially be described as a level set of certain smooth functions (see our line 73), i.e., $\sum\_k \theta^k D^k\_f$, where the $f$ could be any function in Assumption 1 or 2. - Since the combination of $\theta^k$ can be non-unique (as long as they form a valid level set), it is challenging to use this set of non-vanishing coefficients to obtain the first-order approximations for nonsmooth analysis. However, in theory, we can compute a set of coefficients $\\{\hat{\theta}^k\\}$ (based on the analytical properties of $f$) to uniquely represent the convex hull of the gradients of the selection functions, i.e., we can have $\partial f=\sum\_k \hat{\theta}^k \nabla D^k\_f$. - A similar concept is: the model parameter $\mathbf{w}$ in Eq. (1) could be somehow arbitrary as long as it satisfies the constraint conditions, whereas $ \mathbf{w}^$ is the estimator of $\mathbf{w}$, found as the optimal solution of the objective after training / fitting. For a more detailed introduction into nonsmooth analysis, we refer to [1]. Inspired by your question, we are considering using Carathéodory's theorem to reduce the number of selection functions needed for computing the Clarke subdifferential. Alternatively, we may change it to a more concise notation, if it does not cause ambiguity in the main body.* ## Ⅱ. Label Space > Classification: it is unfortunate that we do not have an example - We do agree with your view that classification problems are an important application. In our current version, both the inverse Gaussian deviance and group lasso estimators can be used for classification tasks as long as the labels in the dataset are categorical (please refer to their respective original papers). - We primarily showcase regression tasks here because, in conformalization for regression tasks, the standard full CP computation is more demanding. In regression tasks, the label space is dense rather than discrete, making it more representative and challenging compared to classification tasks. > Figure 1 might be a bit misleading. It seems to imply that the method works for higher dimensions ... We sincerely appreciate this feedback, and we have added the $\mathcal{Y} \subseteq \mathbb{R}^1$ in its caption. We believe that readers will easily recognize this when reading Section 2 as well. Motivated by your comment, if $\mathcal{Y}$ is higher-dimensional (e.g., in multi-task learning), we cannot use a single scalar variable $z$ to loop over the entire space. In this case, our $y_{n+1}$ would be indexed by $\[z_1, \ldots, z_p\]$. The intuitive idea is that the homotopy path would turn into a solution surface [2], and our ODE system could be rewritten as a similar partial differential equation system. While it introduces new challenges, it's very promising. Now we'll not expanding into this scenario, as it would significantly increase the notational complexity. > Classification: ... when there is no order in the classes. Could you illustrate it? We are not senior researchers in classification theory, but if unordered classes cannot be encoded into a 1-dimensional $y$, then you're correct. Thanks again for your insights! It's very helpful in improving the quality of work. ## Ⅲ. Computations > Does the method require more memory than baseline? Yes, due to character limitation, we invite you to see Appendix F.3 for discussion. Meanwhile we believe that in most cases, the practical bottleneck of the conformalized algorithms is runtime cost rather than system memory. > the gain of speed from using [13] instead of your method Sorry for any confusion caused. The work [13] and our Algorithm 1 are completely identical in actual implementation, so there will be no gain in speed (if we dismiss the randomness). Please refer to section ③ in our general rebuttal. > You mention not implementing [13] because it uses underlying structure and therefore might be faster This was our oversight, and we have now corrected the relevant descriptions in Appendix D.3 (line 964). We apologize again for any confusion caused! We will continue to check for such details. --- References: [1] "Introduction to Nonsmooth Optimization: theory, practice and software." Springer, 2014 [2] "Grouping pursuit through a regularization solution surface." JASA, 2010 We thank the Reviewer x8xk again for your insightful feedback and strong support of our submission! If you have any remaining concerns or further inquiries, please do not hesitate to let us know. --- Rebuttal Comment 1.1: Comment: Thanks for this extensive comment. First, I think there is some modification needed to be made following this discussion: 1- removing the comments on classification / heavily modifying as your framework does not fit it yet 2- Editing the figure 1 plot, because even if your mention $\mathbb{R}^1$, a reader skimming through the paper might not understand that it only works on one dimensional target 3- It might be more interesting for the reader to know about the memory/runtime cost challenges within the main core of the paper than buried deep in the appendix. Moreover, I have to partly agree with KUWB: This paper is too lengthy making it hard to parse for both reviewers and future readers. You gave the example of simplified notations in appendix F.3 for the simpler case of classic losses. In my opinion, this should have been the one in the main paper, as this will be what interests 95% of readers. The results with the Clarke differential should have been in the appendix, making the main part of the paper easier to read and parse. I understand that the results using Clarke differential are more challenging, and you want to display it front page, but by providing the simpler case first, the reader can build a better intuition for what is happening underneath. Finally, on top of your paper, you can also make the rebuttal process easier on readers/reviewers. Your comments are quite lengthy and could really be summarized. We mostly have multiple papers to review and comments on so it helps us when you stay brief and clear. I still believe the paper is worth publishing in NeurIPS, so I will keep my grade to 8 but it is a borderline 7 for all the reasons mentioned above. --- Reply to Comment 1.1.1: Comment: Dear reviewer x8xk, 1. We greatly appreciate your insights regarding the classification setting, and we will add a more restrictive description of the labels. We also commit to modifying Figure 1 based on your suggestion. Since all previous baselines were also unable to extend to more complex classification tasks (i.e. beyond $\mathbb{R}^1$), we will briefly outline our thoughts on how to achieve this extension in the future. 2. We will emphasize in the section of complexity analysis of the main body that our algorithm requires more memory. 3. Based on the feedback from several reviewers, in the next version, we will move minor technical parts from the main body to the appendix and bring some intuitive explanations from the appendix into the main body, which helps improve the overall readability of the paper. We have also reduced the content in the appendix to better highlight the main focus (see other rebuttals). We sincerely thank you once again for your generous support during the discussion phase!	Summary: In the manuscript "Towards fast exact Confomralization of Generalised Parametric Estimation" the authors provide a very interesting generalisation of an approach, fundamental even if a bit disregarded in the mainstream literature on Conformal Prediction, that aims at computing the whole solution path of a regression algorithm in order to render more efficient the estimation of (full) conformal prediction sets. After having described the very general framework in which they operate, the authors proceed to obtain theoretical insights about their methodology. More specifically, they characterise the underlying structure of the path to be an inherently piecewise smooth function. After doing so they propose a practical methodology to compute such path, essentially by solving an ODE. The method is then evaluated with an extensive empirical study, showing its remarkable performance Strengths: - The work is extremely thorough and deep, and the discussion about the different peculiarities of their approach - The referencing work is quite remarkable, as it depicts very clearly the literature landscape where the authors are moving - While building on previous works, the authors provide a very novel take on the subject, proposing a completely new methodology, of great practical usability Weaknesses: - The authors are not tackling an easy task in terms of communication, having to tackle, and in a fairly deep way, many different topics. For this reason I find the presentation a bit "nebulous" and vague at times - No code is provided, which has prevented me from verifying some of the claims. Technical Quality: 4 Clarity: 2 Questions for Authors: - Some claims are a bit vague. I understand why the authors focus on Full conformal, but I doubt a reader not fully aware of Conformal Prediction will be able to do it (Paragraph 2 of the introduction). I suggest to the authors to be more explicit about the reasons - Footnote of page 1 - the authors need to clarify that symmetricity in this case is intended in the specific sense used in the CP literature, which in fact is defined later on... or omit the consideration which seems rather tangential - Rather then "inexact" I would rather talk about lack of (finite sample) calibration. - I don't understand why the already present approaches are deemed to be "black boxes". moreover I don't think that "opening the black box" is the right narrative to use in this case. Maybe something along the line of "let's generalise..." - The label space is a generic $\mathcal{Y}$. I am wondering if the authors can be more specific about, for instance, possible extensions of their approach to the relatively rich field of Conformal Prediction for multivariate and complex data. Confidence: 4 Soundness: 4 Presentation: 2 Contribution: 4 Limitations: The authors state relevant open problems on the subject. Since the very clear applicative interest this paper may have, I believe that adding something on the methodological side (such as the need for extensions to the multivariate case, or some ideas about possible extensions to a dependent data setting) could be very interesting. Flag For Ethics Review: ['No ethics review needed.'] Rating: 8 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: # Many thanks for acknowledging our work! Dear reviewer 4Aeq, We extend our sincere gratitude for dedicating your valuable time to reviewing our paper and for expressing your appreciation and support for our work! In the following, we will provide a comprehensive response to your questions. --- ## Ⅰ. Introduction > I understand why the authors focus on Full conformal, but I doubt a reader not fully aware of Conformal Prediction will be able to do it (Paragraph 2 of the introduction). Your feedback is extremely beneficial to us. I believe Reviewer jxtf shares similar concerns. Please allow us to briefly describe the differences between the two approaches. - In SCP, we first split the entire dataset into a training set and a calibration set. On the training set, we use algorithm $\mathcal{A}$ to obtain the model parameter $\mathbf{w}^$. Then, on the calibration set, we get prediction values using $\mathbf{w}^$, and subsequently obtain conformity scores to calculate the conformal set. This process involves only one single fitting. - Full CP, on the other hand, avoids data splitting and does not discard any sample points. It loops over all possible $y_{n+1}$ values and for each new candidate, we refit the augmented data to compute the $\mathbf{w}^$. Based on these solutions we obtain a set of training scores. Therefore, the traditional computation of full CP is significantly more expensive. > I suggest to the authors to be more explicit about the reasons Thank you for your constructive suggestion. I agree that we may omitted some relevant background in the introduction. We have added the necessary descriptions in the second paragraph of the "1. Introduction" on the first page to help readers better understand our considerations. > Footnote of page 1 - the authors need to clarify that symmetricity in this case is intended in the specific sense used in the CP literature ... or omit the consideration which seems rather tangential Thank you for your thoughtful feedback! We find your advice very reasonable, and after our careful consideration, we have decided to remove this footnote to reduce the technical density of the main body. We also agree that it does not directly relate to the main theme of this work. ## Ⅱ. Technical Phrase > Rather then "inexact" I would rather talk about lack of (finite sample) calibration Thanks for your insightful advice. We have revised the relevant statements on the second page. > I don't understand why the already present approaches are deemed to be "black boxes" This is our oversight; please refer to the general response, and sorry for the confusions. > I don't think that "opening the black box" is the right narrative to use in this case We have revised the relevant phrases according to the general rebuttal above. They now should be reasonable in the new context. If you have any further thoughts, please feel free to share them. ## Ⅲ. Potential Extension > The label space is a generic $\mathcal{Y}$ ... if the authors can be more specific Yes, in the current version of our analysis, an implicit setting is $\mathcal{Y} \subseteq \mathbb{R}$. In this work, $y_i\in\mathcal{Y}$ need to be unidimensional. However, we are happy to discuss various extensions; please see the following question. > for instance, possible extensions of their approach to the relatively rich field of Conformal Prediction for multivariate and complex data. We believe our work has the potential to extend CP to multivariate and complex data that you mentioned. Specifically, - If the data features include multiple interrelated variables, we can use well-studied techniques such as ODE discovery [1] to encode the correlations and synergistic effects between variables. If the labels are multidimensional (e.g., in multi-task learning), the label space $\mathcal{Y}$ will also be indexed by multiple independent parameters $(z_1, ..., z_p)$. In this case, the homotopy solution path would turn into a solution surface, and our ODE system can be rewritten as a similar partial differential equation system. - In complex environments, such as dynamic data or online conformal inference, we can leverage knowledge from our by-product as a starting point to adapt our framework to an online mode for parameter updates. For other types of data like network dataset, we can use neural ODEs [3] for model reparameterization, considering the network structure and connection patterns. We also believe this would be very interesting, as previous baseline work [2] has even begun to explore this direction (albeit in a somewhat different setting). More potential extensions will be left for future work. We believe this paper can serve as an important cornerstone, attracting subsequent researchers to fill these gaps. > the very clear applicative interest this paper may have We are very pleased to hear that you find our new algorithm to be widely applicable. > adding something on the methodological side (such as the need for extensions to the multivariate case, or some ideas about possible extensions to a dependent data setting) could be very interesting. Thank you for the helpful comments. We agree with your viewpoint, and inspired by your suggestion, we will add discussions on extensions in our Section 6 or Appendix F. We also hope to attract researchers from other relevant communities. --- References:* [1] "Discovering governing equations from data by sparse identification of nonlinear dynamical systems." PNAS, 2016 [2] "Fast exact conformalization of the lasso using piecewise linear homotopy." Biometrika, 2019 [3] "Neural Ordinary Differential Equations." NeurIPS 2018 We thank the Reviewer 4Aeq again for your insightful feedback to improve our paper quality and strong support! If you have any remaining concerns or further inquiries, please do not hesitate to let us know. --- Rebuttal Comment 1.1: Comment: I am fully satisfied with the provided replies, and I believe the contribution to be worthy of acceptance. --- Reply to Comment 1.1.1: Title: response Comment: Dear reviewer 4Aeq, We are very pleased that our response has addressed your questions. Thank you again for appreciating our technical contributions!	Rebuttal 1: Rebuttal: # Gratitude to All the Reviewers 😃 --- Dear Reviewers, Thanks for the time and effort you have devoted to evaluating our submission #451. We also wish to express our appreciation for your recognition of the strengths of this work, including: > (ji5B) The method introduced by the authors works for general scenarios, extending beyond the cases of Ridge / Lasso > (ji5B) their methods appear to provide a significant improvement (in terms of running time) over the baseline while having the same interval size > (4Aeq) the authors provide a very interesting generalisation of an approach, fundamental even if a bit disregarded in the mainstream literature on CP > (4Aeq) The work is extremely thorough and deep, and the discussion about the different peculiarities of their approach > (4Aeq)The referencing work is quite remarkable, as it depicts very clearly the literature landscape where the authors are moving > (4Aeq) the authors provide a very novel take on the subject, proposing a completely new methodology, of great practical usability > (x8xk) The contribution is pretty significant as it widens the possible families of loss functions > (x8xk) The conformal interval has exact guarantees instead of approximative; The loss function family covered is larger than convex, same for the regularizer family > (x8xk) The examples are compelling ... show very well the improvement > (KUWB) This paper studies an important problem in conformal inference > (KUWB) The proposed method could potentially reduce the computational burden > (jxtf) Characterizing the solution path of ... optimization problems is relevant, even beyond the CP framework > (jxtf) The Lagrangian reparametrization approach is interesting > (jxtf) The proposed method seems to be more efficient than Split CP You have also raised some questions/concerns, to which we have replied in our detailed rebuttal. Here we provide responses to several recurring concerns as follows ### ① Notation is dense / heavy $\quad$(Reviewer ji5B, Reviewer x8xk, Reviewer KUWB) We extend our gratitude to the reviewers for this valuable feedback. This work is not solely a contribution at the algorithmic level; it also provides new statistical insights and an analytical framework in the optimization theory. NeurIPS hosts a diverse community, drawing participants from a broad range of backgrounds; we believe our work could attract researchers not only from the field of conformal prediction but also from optimization and learning theory. And unfortunately, under the premise of ensuring mathematical rigor and technical correctness, it appears that further simplification of symbols / theorems is not feasible currently. It is worth noting that our initial draft was significantly more complex than the current one, and the present version is likely the most concise iteration we have achieved through repeated exploration. To achieve this goal, our efforts have included: 1) When deriving the ODE system (11) or (14), we initially arrived at complex preliminary conclusions, with formulas at least twice the length of the current ones. We simplified the obtained expressions by utilizing matrix computation properties and non-convex analysis, enhancing their human readability. This is reflected in page 24 to 25 of our proof. 2) We have carefully considered how to present our notation system and the main core theorem outcomes. We defined a certain matrix inversion (9), which includes many of the common structures used in theorems, significantly reducing the notation density in the paper. 3) To enhance readers' understanding of the framework presented, we provide a more in-depth discussion and explore the potential for simplifying notation under stronger assumptions. You are welcome to visit our Appendix F.2 for discussions on this point. We also applied it to two simple toy cases (i.e., vanilla Lasso and elastic net) in Appendix C. As you suggested, conciseness and readability remain our goals, and we are continuously contemplating how to further improve in this regard. ### ② On the “open the black-box” $\quad$(Reviewer 4Aeq, Reviewer jxtf) We appreciate the reviewers' careful reading and for pointing this out. We realize that our current phrasing is incorrect. Our use of "black-box approach" should indeed refer to grid-search based methods (i.e., existing batch trainings on different $y_{n+1}$), as they completely disregard the underlying potential path structure. "Black-box approach" should not describe the fast conformalization methods (i.e. baseline in Table 1; whether precise or imprecise), as they all reformulate the conformalization problem as a path-following optimization problem and use white-box methods to compute solution spectrum. We have corrected the relevant phrasing. Thanks! ### ③ Experiment: conformalization of Lasso $\quad$(Reviewer ji5B, Reviewer x8xk) Several reviewers suggested we compare our work with the Lasso conformalization algorithm from (Lei, 2019) [13]. We appreciate this feedback, but we would like to politely point out that Lasso inherently falls under generalized parametric estimation (see Table 1). Thus, (Lei, 2019) [13] is a special case within our framework. Further technical analysis is available in Appendix C.1, which demonstrates how our framework recovers the piecewise linear homotopy path when specifying the loss to be quadratic and the regularizer to be $\ell_1$-norm. From a practical perspective, these two algorithms are essentially the same, making the comparison potentially meaningless. We apologize for not clarifying this in our experimental setup and have revised the confusing descriptions in the appendix. Thanks! --- Please feel free to let us know if you still have any remaining concern, we will be happy to address them. Thanks for your time and support! $ $ Best Regards, Submission451 Authors	NeurIPS_2024_submissions_huggingface	2,024	Summary: The authors introduce an algorithm to compute prediction intervals for conformal prediction in the context of empirical risk minimization (ERM) with constraints on the parameters. To do so, the authors derive a differential equation solved by the ERM estimator as a function of the last label to compute a solution path and generate the conformity scores for each possible label. In their numerical experiments, the method is compared to the baseline (which simply iterates over a grid of labels) and split conformal prediction (SCP). The authors observe that their method provide the correct coverage and roughly the same interval length as the baseline for a fraction of the numerical cost. Strengths: - The method introduced by the authors works for general scenarios, extending beyond the cases of Ridge / Lasso. - On the numerical side, their methods appear to provide a significant improvement (in terms of running time) over the baseline while having the same interval size. As a by product, the authors show that their method can be used to update the estimator when a single label is changed in the training data. Weaknesses: - Clarity : I found the mathematical details of section 3 to be difficult to follow and check (for the parts in the Appendix). I feel like some parts, while they are important for the rigor of the paper, could be explained after the introduction of Algorithm 1 or put in the Appendix. For instance Theorem 4 and Theorem 6. Technical Quality: 3 Clarity: 2 Questions for Authors: - It would be nice to have a comparison with the running time of split conformal prediction (while the computations are not exactly the same) as in Figure 3 to get a sense of the order of magnitude of the computation time. - For simple settings such as Lasso, it would have been nice to compare the computation time with methods from the literature e.g. [Lei, 2017]. - How does the method scale (in terms of running time) with the dimensionality ? Misc. questions : - In equation (12), is there a difference between Q(w) and Q(w \| z) from (9) or is the conditioning on z implicit ? Confidence: 2 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: Some limitations are discussed in Appendix F. As the paper is quite theoretical, the question of societal impact is not applicable here. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: # Many thanks for appreciating our research! Dear reviewer ji5B, We are truly grateful for your thoughtful review of our paper and for the encouraging support you've shown towards our work! In the following, we will provide a comprehensive response to your comments. --- > can be used to update the estimator when a single label is changed in the training data Thank you for your interest in our by-product. In fact, it allows for the simultaneous variation of multiple labels. These indices can form a subset $\mathcal{D}$ (see line 320), making our Algorithm 2 more efficient. > I feel like some parts ... could be explained after the introduction of Algorithm 1 or put in the Appendix - Thanks for your comments, and we fully understand your concerns. - Regarding the burden of mathematical notation, we invite you to refer to our general response. As for the statistical derivations in the appendix, we acknowledge that they require a certain level of mathematical maturity to fully understand. However, we believe this will attract interest from researchers in other fields and help bridge the communities of conformal prediction and numerical optimization. - Theorems 4 and 6 are crucial supports for our algorithm. Theorem 4 provides the foundational guarantee for Theorem 5, ensuring the computational feasibility of our core idea, which is essential for designing Algorithm 1. Theorem 6 is closely related to Corollary 1, offering geometric insights into the path and forming the unified view that we have claimed in the abstract. We consider these theorems indispensable parts of our contributions. - By your comments, we deleted some minor technical paragraphs, and enhanced our descriptions to better link the theorems and algorithms, ensuring readers do not get lost. We appreciate your suggestion! > a comparison with the running time of SCP as in Figure 3 to get a sense of the order of magnitude Thank you for your constructive feedback! Our thoughts are as follows: - This work primarily focuses on optimization for full CP rather than SCP, so comparing efficiency (runtime) with SCP is not particularly meaningful. - SCP is theoretically guaranteed to be faster than standard full CP and our algorithm because it only requires a single training on the training set and then calculates conformity scores on calibration set [1]. In contrast, our algorithm needs to compute the solution spectrum w.r.t. entire label space, involving repeated calls to and fitting on the training set. The order of magnitude can be easily estimated; previous observations & analyses (e.g. [2]) have shown it to be approximately $\frac{1}{N_{\text{gird}}}$ times that of standard full CP, which already provided in our results. - Figures 3/4 are already content-rich; adding more curves might reduce the readability of the results. > compare the computation time with methods from [Lei, 2017]. Please refer to general rebuttal, section ③. Thank you! > How does the method scale (in terms of running time) with the dimensionality? - Thank you for your insightful question. In Algorithm 1, we essentially performed two things: one is numerical integration over $[z_{min}, z_{max}]$, and the other is refreshing the current partitions $\mathcal{N}\_\text{E}$, $\mathcal{P}\_\text{E}$, $\mathcal{P}\_\text{I}$, $I_L$, $I_\Omega$ at the kinks. - Let the dimensionality be $p$, the complexity of the latter is $\mathcal{O}(p)$, as we analyzed it in Section 4.3. - The complexity of the former when varying $p$, however, is somewhat nontrivial. This is primarily due to a fact that the computational complexity of numerical solvers for ODEs can indeed differ significantly based on the employed method and the particularities of the equations at hand. For example, factors like the system's stiffness and the length (or area) of the solving interval, can play a crucial role [3]. Without further assumptions, it is difficult to analyze the complexity of numerically solving the entire ODE system. However, recent studies (e.g., [4]) have increasingly shown that oracle complexity (a.k.a. query complexity) plays a very significant role throughout the computation. Using our method under the sweep operator and Sherman–Morrison formula (see Section 4.1, Appendix B.8), the upper bound on oracle complexity is at most $\mathcal{O}(p^2)$. - Due to the adaptiveness of numerical solvers, it is challenging to establish an exact / tight relationship between overall runtime and $p$. We believe it should lie between linear and quadratic growth. - Given the suggestions of other reviewers, we temporarily don't intend to further expand the appendix length (e.g., adding more experiments). > the difference between Q(w) in (12) and Q(w \| z) from (9) or is the conditioning on z implicit ? Your understanding is correct; they all refer to the same block matrix. When presenting our Theorem 5, we use $\mathbf{Q}(\mathbf{w}^\star)$ to represent $\mathbf{Q}(\mathbf{w}^\star\|z)$, and $\mathbf{D}^{\prime}(\mathbf{w}^\star)$ to represent $\mathbf{D}^{\prime}(\mathbf{w}^\star\|z)$. This is to reduce the symbol density in the main body without causing ambiguity. Note in appendix, we still use the full notation of them (see line 773) due to the needs of the analysis. --- References: [1] "Conformal prediction: A gentle introduction." Foundations and Trends in Machine Learning, 2023 [2] "Fast exact conformalization of the lasso using piecewise linear homotopy." Biometrika, 2019 [3] "Diagonally implicit Runge–Kutta methods for stiff ODEs." Applied Numerical Mathematics, 2019 [4] "A characterization of functions over the integers computable in polynomial time using discrete ordinary differential equations." Computational Complexity, 2023 We thank the Reviewer ji5B again for your insightful feedback and strong support of our submission! If you have any remaining concerns or further inquiries, please do not hesitate to let us know.	null	null	null	null	null	null
KOALA: Empirical Lessons Toward Memory-Efficient and Fast Diffusion Models for Text-to-Image Synthesis	Accept (poster)	Summary: The paper at hand performs a series of ablation studies evaluating the impact of three design decisions on the quality of Text to Image Generation models. Specifically, the authors look at the target of knowledge distillation, training data as well as choice of teacher for distillation. In the end, the authors present a model named KOALA, building upon the insights gained from those ablations. The model is smaller and more efficient than the comparisons presented in the paper. Strengths: Improving the efficiency of Text To Image Generation models is of key importance to the research and industrial community, as the size an inference speed of current state of the art models is often a limiting factor for real world applications. The paper shows positive results and a good set of comparisons to prior art. The paper touches important aspects, such as distillation objectives as well as data selection. Weaknesses: My main concern about the paper is its approachability. The presentation of the paper is subpar. Specifically, the paper is very verbose and repetitive, but then on the other hand imprecise and lacking important details. The paper could be half its size and get more information across. For example, the paper has an almost two page discussion on knowledge based distillation, but I could not a single precise definition how the proposed approach actually performs. Similarly, the entire discussion on the U-Net architecture could be a single table. This would make it much more approachable and easier to understand. Technical Quality: 3 Clarity: 2 Questions for Authors: It would be great, if the authors could provide a short precise explanation how the proposed distillation loss works. Confidence: 4 Soundness: 3 Presentation: 2 Contribution: 2 Limitations: The limitations are discussed in the paper. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for thoroughly reviewing our work and for your insightful and helpful suggestions for improving our paper. We provide our response in the following. We have made every effort to address all your concerns. Please don’t hesitate to let us know if your concerns/questions are still not clearly resolved. We are open to active discussion and will do our best to address your concerns during the discussion period. --- > W1 & Q1. lacking important details & single precise definition of how the proposed approach actually performs → We apologize for any ambiguity regarding how the proposed distillation method performs. The main reason we explained the distillation part in almost two pages is that we needed to address two main aspects simultaneously: 1) pruning the SDXL-Base model and building efficient KOALA U-Nets, and 2) exploring the effective feature distillation strategy. Furthermore, our key finding for the distillation is that self-attention is the most crucial part. To provide sufficient evidence, we conducted in-depth qualitative (refer to `Fig. 3`) and quantitative (refer to `Tab. 3` and `Tab. 10`) analyses, which took up considerable space in the manuscript. In addition, as you suggested, we introduce a brief summary of self-attention-based distillation: - For every transformer block composed of transformer layers at each stage, we allow the student model to mimic the self-attention features from the teacher model (refer to `Fig. 2`). - At the highest feature level (e.g., DW-1 & UP-3), since there are no transformer blocks, we compare only the last output features at that stage (refer to `Fig. 2` & `Tab. 10d`). Since we don’t have enough space to address all of our findings (e.g., four findings) for the effective distillation strategy, we kept only two points in `Sec. 3.1.2` and moved the other findings to Appendix `B`, along with `Table 10`. As a result, it may cause some details to be missing. Let us describe more details of four findings for our distillation strategy: 1) Among different feature types for distillation, self-attention shows the best performance (`Tab. 3a`) and represents more discriminative features (`Fig. 3` & `Fig. 10` in Appendix). 2) Self-attention at the decoder (UP-1 to UP-3) has a larger impact on the quality of generated images than the encoder (DW-1 to DW-3). Therefore, we keep more transformer blocks in the decoder part when pruning SDXL-Base’s U-Net (`Tab. 3b`). 3) When comparing self-attention features, the features of the early layers in the transformer block, which is composed of multiple layers, are more significant for distillation (`Tab. 10c`). This is supported by the feature cosine similarity analysis, which shows that early layers exhibit more distinct feature discrimination (`Sec. B3` & `Fig. 11`). 4) The combination of the last output features (LF) at the highest feature level and the self-attention features at the other stages shows the best results (`Tab. 10d`). > W2. the entire discussion on the U-Net architecture could be a single table. → Thank you for your suggestion. As you pointed out, we will consolidate the U-Net section into a single, more concise and clear table to make it more approachable and easier to understand. --- Rebuttal Comment 1.1: Title: Response Comment: I would like to thank the authors for their response to both my questions and the questions by the fellow reviewers. After going over the other reviews and considering all the answers, I come to believe that the contributions and presentation of the paper might just pass the bar for acceptance. However, I strongly encourage the authors to significantly improve the organization and conciseness of the paper. --- Rebuttal 2: Title: Thank you for your response Comment: We deeply appreciate your valuable feedback and the thoughtful reconsideration of our paper's score. We will make sure to carefully reflect on your suggestions and update the paper to improve its organization and conciseness. Once again, thank you very much for the time and effort you dedicated to thoroughly reading and reviewing our paper.	Summary: This paper presents KOALA, a pair of efficient text-to-image synthesis models that reduce computational and memory requirements compared to the base model. This paper achieves this through three key innovations: knowledge distillation into a compact U-Net, the strategic use of high-resolution images and detailed captions in training data, and the employment of step-distilled teachers to enhance the learning process. The resulting models, KOALA-Turbo and KOALA-Lightning, demonstrate faster inference times and the ability to generate high-quality images on consumer-grade GPUs. Strengths: 1. This paper is easy to follow. 2. This paper offers a practical solution for generating high-quality images with reduced computational requirements. Weaknesses: 1. Although KOALA achieves good visual quality, the extent of degradation in text rendering is unclear as it has not been compared with a baseline in terms of text rendering capabilities. 2. For each baseline, KOALA requires a carefully designed pruning network architecture followed by retraining, which entails a significant acceleration cost compared to training-free methods. However, this paper does not discuss or compare with training-free methods, nor does it compare with step distillation approaches. Technical Quality: 3 Clarity: 3 Questions for Authors: In the "Lesson 3" section, it is puzzling that SDXL-Base, as a teacher model, performs the worst. Intuitively, a better teacher model should have greater potential to distill a superior student model. I am curious if the results presented in the paper could be attributed to a suboptimal distillation approach. Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The authors have discussed both limitations and potential negative social impacts. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for thoroughly reviewing our work and for your insightful and helpful suggestions for improving our paper. We provide our response in the following. We have made every effort to address all your concerns. Please don’t hesitate to let us know if your concerns/questions are still not clearly resolved. We are open to active discussion and will do our best to address your concerns during the discussion period. --- > W1. extent of degradation in text rendering & quantitative comparison → Please refer to `G2` section in the general response > W2. Comparison with training-free methods → Thank you for your valuable insight. To the best of our knowledge, very recent training-free acceleration methods for diffusion models leverage the redundancy of features over the denoising steps. These methods (e.g., DeepCache [1], Cache Me If You Can [2]) cache and retrieve features of previous steps for efficient inference of the current step. In this rebuttal, we compare our KOALA model with DeepCache, which has an official implementation available. Using their code, we measured the inference cost, memory footprint, latency, and performance in terms of HPSv2 and Compbench scores. The results are summarized in the table below. Compared to the original SDXL-Base, DeepCache achieves faster inference speed at the cost of performance and increased memory usage. We speculate that the increased memory usage of DeepCache is due to the caching and retrieval process of features, which requires additional memory. In contrast, when compressing the same SDXL-Base model, our KOALA model reduces both memory usage and latency while achieving superior performance compared to DeepCache. Additionally, due to the step-distilled teacher and longer training, our KOALA model is capable of generating more faithful images with fewer diffusion steps, resulting in lower latency. Furthermore, the training-free method is orthogonal to our approach, we expect that combining the training-free method with ours could exhibit a synergy effect, suggesting a promising future direction. Note: KOALA-SDXL-Base and KOALA-Lightning denote models trained with the SDXL-Base teacher (1st row of Tab. 5) for 100K iterations and with the SDXL-Lightning teacher (11th row of Tab. 6) for 500K iterations, respectively. \|Method\|Backbone\|#Step\|Memory(GB)\|Latency\|HPSv2\|CompBench\| \|--\|--\|--\|--\|--\|--\|--\| \|SDXL-Base-1.0\|SDXL-Base\|25\|11.9\|3.229\|30.82\|0.4445\| \|DeepCache [1]\|SDXL-Base\|25\|14.6\|1.453\|26.32\|0.4094\| \|KOALA-SDXL-Base\|KOALA-700M\|25\|8.3\|1.424\|27.79\|0.4290\| \|KOALA-Lightning\|KOALA-700M\|10\|8.3\|0.655\|31.50\|0.4505\| > W3. Comparison with step-distillation methods* → We would like to clarify that we have already compared the step-distillation methods, such as SDXL-Turbo and SDXL-Lightning, in `Sec. 4.2` and `Tab. 6` of our manuscript. Below, we re-summarize a comparison with step-distillation methods, including the more recent work, PCM [3], in the following table. We observe that, compared to SDXL-Lightning and PCM at a $1024^2$ resolution, our KOALA-Lightning-700M demonstrates competitive performance while achieving lower latency and memory usage with a model size that is $3\times$ smaller. Table note: SDXL-Turbo generates images with $512^2$ resolution while the other models use $1024^2$ resolution. \|Method\|Backbone\|Res.\|#Step\|Param.(B)\|Memory(GB)\|Latency\|HPS\| CompBench\| \|--\|--\|:--:\|:--:\|:--:\|:--:\|:--:\|:--:\|:--:\| \|SDXL-Tubo\|SDXL-Base\|512\|8\|2.56\|5.6\|0.245\|29.93\|0.4489\| \|SDXL-Lightning\|SDXL-Base\|1024\|8\|2.56\|11.7\|0.719\|32.18\|0.4445\| \|PCM [3]\|SDXL-Base\|1024\|8\|2.56\|12.1\|0.884\|30.01\|0.4360\| \|KOALA-Lightning (ours)\|KOALA-700M\|1024\|10\|0.78\|8.3\|0.655\|31.5\|0.4505\| → Furthermore, we have verified the synergy effect between the step-distillation method (e.g., PCM) and our KOALA backbones during this rebuttal period. We performed the step-distillation training using PCM with our KOALA backbones and obtained results as shown in the table below. Due to their efficiency, our KOALA backbones enable PCM to further boost speed-up with only a slight performance drop compared to PCM with the SDXL-Base backbone. Additionally, we presented qualitative comparisons of our PCM-KOALA models with PCM-SDXL-Base in `Fig. 1` of the attached `general_response.pdf` file (Please see the PDF file). Table note: SDXL-Turbo and SDXL-Lightning do not provide training code, while PCM releases the official training code, allowing us to train PCM with our KOALA backbones. \|Method\|Teacher\|Student\|#Step\|Param.(B)\|Memory(GB)\|Latency\|HPS\|CompBench\| \|--\|--\|--\|:--:\|:--:\|:--:\|:--:\|:--:\|:--:\| \|PCM [3]\|SDXL-Base\|SDXL-Base\|2\|2.56\|12.1\|0.345\|29.99\|0.4169\| \|PCM [3]\|SDXL-Base\|KOALA-700M\|2\|0.78\|8.2\|0.222\|28.78\|0.3930\| \|PCM [3]\|SDXL-Base\|KOALA-1B\|2\|1.16\|9.0\|0.235 \|29.04\|0.4055\| > Q1. a better teacher model should have greater potential to distill a superior student model. → We would like to clarify that in the main state-of-the-art comparison table (e.g., `Tab. 6`) of our manuscript, SDXL-Lightning shows better or comparable performance to SDXL-Base on HPSv2 and CompBench, respectively. Thus, SDXL-Lightning could be considered a better teacher model. Your statement that _“a better teacher model should have greater potential to distill a superior student model”_ aligns with our findings. Indeed, we observed that the KOALA models distilled from SDXL-Lightning achieve better performance than those distilled from SDXL-Base as shown in `Tab 3`. --- [1] Ma et al. DeepCache: Accelerating Diffusion Models for Free. CVPR 2024. [2] Wimbauer et al. Cache Me if You Can: Accelerating Diffusion Models through Block Caching. CVPR 2024. [3] Wang et al. Phased Consistency Model. Arxiv (2405.18407) 2024. --- Rebuttal Comment 1.1: Comment: Thank you to the authors for the detailed response. Most of my concerns have been addressed, so I have raised my score. --- Reply to Comment 1.1.1: Title: Thank you for your response Comment: We deeply appreciate your valuable feedback and the thoughtful reconsideration of our paper’s score. We will ensure that your suggestions, such as the training-free method comparison and text-rendering capability, are carefully reflected upon, and we will update the paper to enhance its completeness. Once again, we are truly grateful for your dedication and the thorough review you have provided.	Summary: This paper presents a set of empirical guidelines to use when distilling Stable Diffusion XL (SDXL) when computational/data resources are limited. The presented guidelines focus on 1) identifying which transformer blocks to drop, 2) what features are the best to distill, and 3) which publicly-available datasets are the best to use. The paper presents analyses for all guidelines, including ablations and comparisons to what other popular distillation approaches do. Insights are extracted from these analyses and used to motivate the guidelines. Performance results are presented showing that the guidelines result in distilled models that are quite competitive with the parent/other distilled models yet are much more computationally efficient. Strengths: The main topic of this paper -- how to more easily generate cheaper SDXL distillations -- is of much relevance to virtually all associations. This paper does a thorough job of exploring many distillation aspects. The analyses it reports give good insights into what aspects are most important. For example, the feature distillation ablation section shows that self-attention are the best feature to distill. The authors then use those results to motivate removing fewer transformer decoder blocks than encoder ones. Fig 3c is compelling and really drives home the primary role of self attention in distillation. The suggested recipe for removing blocks goes beyond just a basic approach of removing all blocks in a stage, as some other distillation approaches suggest. I also thought the insights into the various LAION datasets was interesting and that the conclusion of using few high res images with detailed prompts is better than more low res with with short (or detailed) prompts is useful. Further, the performance results from the distilled models are quite competitive with other variants. Weaknesses: The guidelines this paper presents are very focused on specifically SDXL. It is unclear if any of them would apply to other transformer-based models. Whatever the next version after SDXL is created, it is unclear how relevant these guidelines would be. Technical Quality: 3 Clarity: 3 Questions for Authors: 1) Sec 3.1.1. mentions both "block removal" as well as "layer-wise removal". However, the text describes layer-wise removal as "reducing the number of transformer layers". I found this vernacular confusing. It is common practice to let a "layer" mean a "block", so both approaches sounds as if they are doing the same thing: removing blocks. I think (?) when the text refers to "block removal" (108) it means "removal of 100% of the blocks in a sequence" but when it refers to "layer-wise removal" (line 117) it means "removal of less than 100% of the blocks of the sequence". Is this understanding correct? If so, then I recommend re-writing this section to make it more clear that "block removal" is the special case of "layer-wise removal" when all blocks are removed. 2) Table 10d shows that adding DW-1 and UP-3 feature distillation to SA + LF further boosts performance. But the formal paper stops at suggesting SA + LF3 is optimal. Why? 3) Nit: The only time I see the "KOALA" acronym explained is implicitly in a couple of the figure captions. Adding it somewhere in the introduction would be nice. 4) Nit: Line 199 uses the phrase "in the second row of the table" before any table has been presented to the reader. Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The paper presents the commonly suggested limitations of stable diffusion -- it doesn't generate text well and has problems with multiplicity. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for thoroughly reviewing our work and for your insightful and helpful suggestions for improving our paper. We provide our response in the following. We have made every effort to address all your concerns. Please don’t hesitate to let us know if your concerns/questions are still not clearly resolved. We are open to active discussion and will do our best to address your concerns during the discussion period. --- > W1. focused on specifically to SDXL & would be appled to transformer-based models → Please refer to `G1` section in the general response. > Q1. Confusion Between the Terms `Block` and `Layer` → The SDXL-Base architecture consists of convolutional residual blocks and transformer blocks, each of which is composed of multiple transformer layers. A potential point of confusion is the distinction between transformer `blocks` and transformer `layers`. Our intention is to use ‘block’ as a higher-level concept, referring to a group of ‘layers.’ Therefore, we will reiterate this definition in the manuscript to avoid any misunderstanding. Thank you for your comment. ” > Q2. SA+LF combination → We apologize for the confusion. The final feature combination for the distillation training is self-attention (SA) from all transformer layers plus the last feature (LF) from the highest feature level (DW1+UP3), as shown in `Fig. 2` and `Tab. 10d`. Using only SA features already shows superior performance compared to using only LF in BK-SDM. However, we have found that adding the last features at DW-1 and UP-3, where there are no self-attention layers, further boosts performance. To explain the cause of this confusion, due to space constraints in the manuscript, we moved the optimal feature combination to the appendix along with `Tab. 10(d)` and missed mentioning SA+LF in the main text. We will clarify this and update the manuscript. We appreciate your comment once again. > Q3. "KOALA" acronym → Thank you for your kind advice. As you noted, the explanation of the "KOALA" acronym is either implicitly included in the figure captions or found later in the paper (lines 237-238). We will refine and move the explanation to the introduction section in the final version. > Q4. Tab.4 → We intended to use the phrase “in the second row of the table” to indicate that the second data source is demonstrated in the second row of Table 4. However, as the reviewer noted, the current demonstrations might cause confusion for readers. Therefore, we will revise the notation (to ensure consistency of data source notation both in the table and the document) and clarify the phrasing in the final version. --- Rebuttal Comment 1.1: Comment: Thank you for your response to my comments. I had failed to appreciate the impact of Table 8 wrt showing generalization of KOALA. I will take it into account in my final rating. --- Rebuttal 2: Title: A Response to Reviewer's Comment Comment: We sincerely thank you for your thoughtful review and for considering the impact of Table 8 in your comment. If possible, we would greatly appreciate it if you could provide further details or explain which specific aspects of Table 8 failed to persuade you. We genuinely hope you might give us the chance to address any concerns. Once again, we are truly grateful for the time and effort you have dedicated to thoroughly reviewing our paper. --- Rebuttal 3: Title: Thank you for your review Comment: As we near the end of the discussion phase, we would like to once again express our sincere gratitude for the time and effort you dedicated to thoroughly reviewing our paper. Your detailed suggestions, such as clarifying notations and refining the formatting of experimental results, are greatly appreciated. We will carefully revise our manuscript to reflect your valuable feedback. Once again, thank you very much for your thoughtful and comprehensive review.	Summary: 1. The authors propose two different designs for an efficient denoising U-Net based on SDXL. 2. The authors present three empirical lessons for developing efficient U-Net designs. Strengths: 1. The authors present empirical findings to justify their design considerations and provide further analyses to examine the effects of those choices. 2. The authors conduct a systematic analysis with extensive quantitative and qualitative experiments, comparing their results with different baselines. Weaknesses: 1. The proposed method is specific to the SDXL U-Net and is based on heuristics, rather than presenting a generalizable approach. This makes the paper resemble a technical report more than an academic paper. It would be beneficial if the authors could further clarify their novelty and contributions in terms of academic research. 2. The authors present some failure cases of their methods, including rendering long legible text, complex prompts with multiple attributes, and human hand details. Do the teacher models and other baseline models also suffer from the same problems? Were any of these failure cases aggravated in the proposed model to some extent? If so, what could be the reasons? Technical Quality: 3 Clarity: 3 Questions for Authors: Please refer to the "Weaknesses" section. Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The authors adequately address the limitations in section 5. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for thoroughly reviewing our work and for your insightful and helpful suggestions for improving our paper. We provide our response in the following. We have made every effort to address all your concerns. Please don’t hesitate to let us know if your concerns/questions are still not clearly resolved. We are open to active discussion and will do our best to address your concerns during the discussion period. --- > W1-1. specific to the SDXL U-Net and heuristics, not a generalizable approach → Please refer to `G1` section in the general response. > W1-2. novelty and contributions to the academic community → `Novelty`: We believe that our self-attention-based distillation approach for text-to-image model compression is novel, supported by two key points. - To the best of our knowledge, our approach is the first to identify that self-attention is the most crucial element for feature distillation in T2I model compression. - The self-attention-based distillation approach can be generally applied across various architectural designs of diffusion models (e.g., U-Net-based and transformer-based) that consist of transformer blocks with self-attention layers. → `Contribution`: We believe that we have made two contributions to the academic community from the perspective of practical impact. - An efficient T2I Backbone for Consumer-Grade GPUs: - Many downstream tasks, such as personalized image generation [1] and image-editing [2], leverage SDXL-Base as a de facto backbone due to its open-source model and superior performance. However, the SDXL model barely works on GPUs with more than 11GB of VRAM due to its substantial model cost, and its slower latency may cause delays in the outcomes of new research using it. To overcome this limitation, our efficient KOALA T2I backbones can serve as a cost-effective alternative, facilitating further downstream research, especially for those working in limited-resource environments. Furthermore, our efficient KOALA models can assist practitioners and designers by enabling rapid ideation and supporting their creativity with low latency in a consumer-grade GPU environment. - An effective recipe of distillation for T2I model compression: - We presented three key lessons in our paper: i) self-attention-based distillation strategy, ii) data considerations, and iii) the influence of the teacher model. Additionally, through an in-depth analysis of each lesson, we offer general insights into popular U-Net-based diffusion models, such as the role and computational burden of each layer. We strongly believe that the lessons and insights we provide will benefit researchers and developers striving to make T2I models more efficient. - In the large language models (LLMs) field, larger models continue to emerge rapidly, and there have been many efforts to compress these models. Similarly, new and larger T2I models have also been developed. However, unlike in the LLM field, there have been relatively few attempts to compress T2I models due to factors such as the high cost of training (i.e., healing) and data scarcity (i.e., high-resolution and expensive copyright). In this context, we believe that our lessons can be particularly helpful for the community, especially for those working with resource constraints. - It is important to note that research providing crucial recipes for effective training, alongside proposing entirely novel methods, has historically played a significant role in revolutionizing their respective fields and boosting overall performance. For instance, Improved GANs [3] for GANs, MoCo-v3 [4] for self-supervised learning, DeiT [5] for transformers, and ConvNext [6] for CNNs have all made substantial impacts. Similarly, we hope our work brings valuable insights and benefits to the research community. > W2. Discussion on failure cases → Please refer to `G2` section in the general response. --- [1] Ruiz et al. DreamBooth: Fine Tuning Text-to-Image Diffusion Models for Subject-Driven Generation. ICLR 2023 [2] Zhang et al. Adding Conditional Control to Text-to-Image Diffusion Models. ICCV 2023 [3] Salimans et al. Improved Techniques for Training GANs, NeurIPS 2016 [4] Chen et al. An Empirical Study of Training Self-Supervised Vision Transformers. ICCV 2021 [5] Touvron et al. Training data-efficient image transformers & distillation through attention. ICML 2021 [6] Xie et al. A ConvNet for the 2020s. CVPR 2022 --- Rebuttal Comment 1.1: Comment: Thank you for the time and effort you put into your responses. After reviewing the responses, I believe my current rating remains appropriate. I will maintain my rating with increased confidence. --- Rebuttal 2: Title: Thank you for your review Comment: We are sincerely grateful for the time and effort you dedicated to thoroughly reading and reviewing our paper. Your feedback, including the emphasis on novelty and contribution, the generality of the methodology, and the discussion on failure cases, will be carefully reflected upon as we update the paper to enhance its completeness. Once again, thank you very much for your thoughtful and thorough review.	Rebuttal 1: Rebuttal: # General response Thank you for thoroughly reviewing our work and for your insightful and helpful suggestions. We have made every effort to address all your concerns. Please let us know if any questions remain unresolved. We are open to discussion and will do our best to address your concerns during the discussion period. In this general response, we have addressed the common concerns reviewers raised. > G1. specific to the SDXL U-Net and heuristics, not a generalizable approach by reviewers `dMSC` & `C2ZB` → We respectfully clarify that although our method has been mainly explored with SDXL, the most popular T2I model at the time of submission, we have already applied our self-attention-based distillation scheme to a transformer-based method, Pixart-$\Sigma$ [1], the only model providing training code at the time of submission. As shown in `Tab. 9` of the manuscript (we include the table below for reference), self-attention-based distillation exhibited superior performance compared to other feature types. These results align with those obtained on U-Net-based diffusion models, demonstrating that our self-attention-based distillation scheme has been proven to be a general approach across various architectural designs of diffusion models (e.g., U-Net-based and transformer-based). Given these findings, we can also expect that our self-attention-based distillation can be applied to more recent transformer-based methods with self-attention operations, such as SD3 [2]. Consequently, our approach can serve as a crucial baseline for further T2I model compression research. Additionally, we would like to explain that the reason we designed an SDXL-tailored method is largely due to the heterogeneous structure of SDXL’s U-Net. It consists of irregularly combined convolutional and transformer layers, unlike pure transformer-based methods such as Pixart [1,3], and SD3 [2], which build a uniform stack of transformer layers. However, since our method is primarily based on in-depth analysis and understanding of each layer of SDXL, we believe our findings will benefit popular SDXL-like T2I models and their applications. \|KD type in Pixart-$\Sigma$\|HPSv2\|CompBench\| \|--\|:--:\|:--:\| \|SA\|25.16\|0.4281\| \|CA\|24.94\|0.4279\| \|FF\|24.80\|0.4191\| \|LF in BK\|21.62\|0.3527\| > G2. Discussion on failure cases (e.g., text rendering) by reviewers `dMSC` & `EitJ` → While recent text-to-image diffusion models can generate images of unprecedented quality in general, they still exhibit limited performance in certain specialized cases. These cases include rendering long and legible text, handling complex prompts with multiple attributes, and generating intricate structures such as detailed human hands. The authors of SDXL-Base [4] acknowledge these limitations in their paper, and other baseline models we considered also share these limitations, as shown in `Fig. 2` of the attached `general_response.pdf`. Due to the nature of knowledge distillation, our distilled models inevitably inherit these limitations. Among these models, our KOALA model shows inferior text rendering quality compared to the teacher models, as shown in the table below. We conjecture that the main cause of this inferior performance originates from the training dataset(LAION-POP) we used. Although this dataset includes images with high visual aesthetics, the corresponding text prompts rarely describe the text within the images. This leads to difficulties in complex text rendering. As reviewer `EitJ` suggested, we quantitatively evaluate the text rendering capability on the MARIO-Eval benchmark [5]. Specifically, we utilize existing OCR tools to detect and recognize text regions in the generated images and measure the performance. Using 5,414 test prompt sets in the benchmark, we generated images with rendered text for each model and compared performance using the OCR metrics, as shown in the table below. Our KOALA models show inferior performance compared to SDXL-Base teacher models. In addition, SDXL models achieve much lower performance compared to the specialized T2I model for text rendering, TextDiffuser [5]. \|Metrics\|TextDiffuser [5]\|SDXL-Base\|SDXL-Lightning\|KOALA-Lightning-700M\|KOALA-Lightning-1B\| \|--\|--\|--\|--\|--\|--\| \|OCR(accuracy)\|0.5609\|0.0181\|0.0169\|0.0123\|0.0153\| \|OCR(precision)\|0.7846\|0.0223\|0.0228\|0.0012\|0.0024\| \|OCR(recall)\|0.7802\|0.0463\| 0.044\|0.0033\|0.0065\| \|OCR(F-measure)\|0.7824\|0.0301\|0.0301\|0.0018\|0.0035\| The limitations that our model has inherited remain an open question in the community. To address these limitations, several specialized models have been recently proposed by designing specialized data and architecture. For example, TextDiffuser [5] aims to improve the capability of rendering long, legible text by constructing text-rendered images with OCR annotation, while Paragraph-Diffusion [6] attempts to handle more complex prompts faithfully. Exploring the synergy between these specialized models and our distillation framework could be an interesting direction for future work. --- [1] Chen et al. PixArt-$\Sigma$: Weak-to-Strong Training of Diffusion Transformer for 4K Text-to-Image Generation. Arxiv 2024 [2] Esser et al. Scaling Rectified Flow Transformers for High-Resolution Image Synthesis. ICML 2024 [3] Chen et al. PixArt-$\alpha$: Fast Training of Diffusion Transformer for Photorealistic Text-to-Image Synthesis. ICLR 2024 [4] Podell et al. SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis. ICLR 2024 [5] Chen et al. TextDiffuser: Diffusion Models as Text Painters. NeurIPS 2023 [6] Wu et al. Paragraph-to-Image Generation with Information-Enriched Diffusion Model, arXiv 2023 --- > Figures in the attached pdf file ↓ Please refer to the PDF file. Pdf: /pdf/b4a57d824fc882484e08e07bcfdf5d7b8d906f07.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Model-Based Transfer Learning for Contextual Reinforcement Learning	Accept (poster)	Summary: The paper proposes Model-Based Transfer Learning (MBTL) in Contextual RL, which solves multiple related tasks and enhances generalization across different tasks. MBTL strategically selects a set of source tasks to maximize overall performance and minimize training costs. The paper theoretically demonstrates that the method exhibits regret that is sublinear in the number of training tasks. MBTL achieves greater performance than other baselines (e.g., exhaustive training, multi-task training, and random selection) on urban traffic and control benchmarks. Strengths: - The paper is well-written and organized, and includes a thorough illustrative diagrams and examples. - The problem formulation is well done, with clear mathematical representation. The analysis of Bayesian Optimization appears to be thorough. - The authors provide code for training and evaluating their proposed method. This significantly facilitates reproducing the experimental results and extending the introduced method. Weaknesses: - The assumptions are too tight, particularly Assumption 3, which models the generalization gap using linear constraints. This approach is unsuitable for complex environments and therefore lacks generalizability. - The experimental environments (urban traffic and control benchmarks) are overly simplistic, consisting solely of vector environments with low-dimensional state spaces. The study lacks comparisons with complex tasks, such as those in the CARL benchmark, including games and a real-world application of RNA design. - The ablations on DRL algorithms (DQN, PPO, A2C) utilize outdated methods. Why not use more recent RL baselines? Technical Quality: 3 Clarity: 3 Questions for Authors: Below, I have a few questions and feedback for the authors: - How does the computational time consumption compare between MBTL and other baselines (exhaustive training, multi-task training, and random selection)? - I am curious to see experimental results in complex environments, such as visual environments. Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: N/A Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: The authors truly appreciate the reviewer’s positive feedback on our work. We invite the reviewer to also take a look at our general comments, which include additional experiments on (1) concerns with the linear generalization gap assumption, (2) application of MBTL to tasks with high-dimensional visual inputs, and (3) multi-task baselines. We hope that the new results will satisfactorily address the concerns raised, potentially leading to a reconsideration of our score. > The assumptions are too tight, particularly Assumption 3, which models the generalization gap using linear constraints. This approach is unsuitable for complex environments and therefore lacks generalizability. We acknowledge your concern about assumption 3. However, ironically, this assumption is the key strength of our MBTL algorithm. The authors kindly request the reviewer to look at the General Response 1 (GR1). > The experimental environments (urban traffic and control benchmarks) are overly simplistic, consisting solely of vector environments with low-dimensional state spaces. The study lacks comparisons with complex tasks, such as those in the CARL benchmark, including games and a real-world application of RNA design. We appreciate your suggestion, and we understand the importance of evaluating our method on more complex tasks with high-dimensional state spaces. In response, we conducted additional experiments on high-dimensional environments. Unfortunately, the CARL benchmark [1-2] no longer supports the suggested RNA design application, so we focused on vision-control experiments instead. These experiments are based on the MetaDrive benchmark [3], which supports visually generated observations for driving scenarios. The authors kindly request the reviewer to look at General Response 2 (GR2) for visualization of our results on high-dimensional state spaces. The preliminary results show that MBTL algorithms ranging from simple strategies to GP-based algorithm also work in complex high-dimensional state space. These experiments demonstrate the scalability and robustness of MBTL in more challenging and complex settings. > The ablations on DRL algorithms (DQN, PPO, A2C) utilize outdated methods. Why not use more recent RL baselines? We apologize for any confusion caused by using the term "ablation." To clarify, we intended this section as a "sensitivity analysis" to demonstrate that the MBTL selection process is robust across different types of RL algorithms, whether they are value-based or policy-based, and that these methods may or may not significantly affect the generalization gap. Our intention was to show that the effectiveness of MBTL is not heavily dependent on the specific RL algorithm used. The primary goal was to highlight that both value-based methods (like DQN) and policy-based methods (like PPO and A2C) are compatible with our framework, indicating the versatility of MBTL. Additionally, we aimed to maintain consistency with the RL algorithms used in the original papers from which the traffic experiments were derived. For instance, the eco-driving control paper [4] utilized PPO variants, and we adopted similar algorithms to ensure a fair comparison and reproducibility of results. > How does the computational time consumption compare between MBTL and other baselines (exhaustive training, multi-task training, and random selection)? Thank you for your question on the computation time. If we assume the same training time for each model, the number of trained models presented in Table 1 and Table 2 provides the order of magnitude difference in computational time across different methods. For instance, Exhausitive Training or Oracle Transfer requires training all tasks, which will need $N(=\|X\|)$ models, while MBTL requires $k$ models to train. However, the calculation for multi-task reinforcement learning deviates from this, since it depends on the batch size though it trains a single model. Our results (Table 1 and 2 in the main text) indicate that MBTL significantly reduces training time compared to exhaustive training and multi-task training while achieving comparable or better performance. This efficiency is primarily due to the strategic selection of training tasks, which minimizes redundant training. On the other hand, we include a detailed comparison of the computational time required for MBTL source task selection in our experiments. Specifically, MBTL-GP requires more computation than simple methods. \|\|MBTL-ES\|MBTL-GS\|MBTL-GP\| \|--\|--\|--\|--\| \|Pendulum\|4.2518E-05\|0.00018432\|1.61098456\| \|Cartpole\|3.28488E-05\|0.00026944\|1.6663856\| \|BipedalWalker\|3.25309E-05\|0.00015042\|1.64290924\| \|HalfCheetah\|3.26369E-05\|0.00014559\|1.63489845\| \|Traffic Signal\|3.49164E-05\|0.000156\|0.5571901\| \|Eco-Driving\|3.16037E-05\|0.00014793\|0.62795639\| \|AdvisoryAutonomy\|3.17097E-05\|0.00014257\|0.69461881\| Specifically, the running time for MBTL algorithms is relatively short compared to the actual computation time required for training RL models. When comparing the computation time for the SSTS process alone, simple strategies such as MBTL-ES (Equidistant Strategy) and MBTL-GS (Greedy Strategy, previously MBTL-PS) require almost negligible computation time. In contrast, MBTL-GP (Gaussian Process) requires additional computation time for the Bayesian optimization process. Overall, the strategic task selection in MBTL results in a substantial reduction in the number of models trained, which in turn reduces the overall computational burden. We will provide a detailed analysis of these findings in the updated results section of the revised manuscript. > I am curious to see experimental results in complex environments, such as visual environments. Thank you for your comments. We refer the reviewer to General Response [GR2] for visualizations and interpretations of our results on visual environments. --- Rebuttal Comment 1.1: Comment: Thank you for your detailed response to my review. The response has addressed most of my questions. However, I agree with reviewer 21Qs regarding the concern about the theoretical justification of the linear generalization gap. I am inclined to keep my original score. --- Rebuttal 2: Title: References Comment: - [1] C. Benjamins et al., “Contextualize Me -- The Case for Context in Reinforcement Learning,” Transactions on Machine Learning Research, Jun. 2023. - [2] https://automl.github.io/CARL/main/source/environments/environment_families/rna.html - [3] Q. Li, Z. Peng, L. Feng, Q. Zhang, Z. Xue, and B. Zhou, “MetaDrive: Composing Diverse Driving Scenarios for Generalizable Reinforcement Learning,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 45, no. 3, pp. 3461–3475, Mar. 2023. - [4] V. Jayawardana, C. Tang, S. Li, D. Suo, and C. Wu, “The Impact of Task Underspecification in Evaluating Deep Reinforcement Learning,” in Advances in Neural Information Processing Systems, 2022. --- Rebuttal Comment 2.1: Comment: Thank you again for your review. Please let us know if you have any further questions or comments. If you feel that your questions were sufficiently addressed, we would deeply appreciate it if you could consider raising the score.	Summary: The paper proposes a new framework to estimate the expected generalization performance across different tasks where the differences have an explicit and model-based structure. To improve the expected generalization performance via training on selected tasks, the paper proposes naive and Bayesian optimization based method to effectively explore the task space to find a policy that have the optimal zero-shot performance given a selected task. The experiments demonstrate that the proposed MBTL method outperform other baseline method and reach the performance of the optimal transfer method assuming full knowledge. Strengths: - By and large, the paper is written well. I especially appreciated the detailed discussion on SSTS problem formulation and its relations to robust RL training. - The idea of Bayesian Optimization to search training tasks using generalized performance estimation where tasks differences are “model-based” or have an explicit structure is novel and useful. - The section on analysis of BO and its comparison with ES and PS are also interesting, and highlights the sublinear regret theoretical results. - The theoretical results appear to be correct. Weaknesses: - The empirical evaluation is by and large only on low dimensional systems. It would have been interesting to see how the method would scale with more challenging, high-dimensional tasks, such as those commonly found in vision control tasks in robotics. - It would have been interesting to see how well this method would work with policies/controllers not parametrized with neural networks (i.e. kernel machines). - Some additional commentary on how to use the GP to search for a trained policy given a selected task. Technical Quality: 4 Clarity: 4 Questions for Authors: - Could you comment on the challenges of applying MBTL-GP on vision-control tasks? Confidence: 4 Soundness: 4 Presentation: 4 Contribution: 3 Limitations: Yes, the author has discussed the limitations. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We appreciate the reviewer's thoughtful comments and suggestions. We encourage the reviewer to review our general comments, which include additional experiments addressing (1) concerns with the linear generalization gap assumption, (2) the application of MBTL to tasks involving high-dimensional visual inputs, and (3) multi-task baselines. We hope that the new results will satisfactorily address the concerns raised, potentially leading to a reconsideration of our score. > The empirical evaluation is by and large only on low dimensional systems. It would have been interesting to see how the method would scale with more challenging, high-dimensional tasks, such as those commonly found in vision control tasks in robotics. We appreciate constructive comments on the scalability of our method to the high-dimensional tasks. With your suggestion, the authors conducted experiments with vision control tasks. We refer the reviewer to General Response [GR2] for visualizations and interpretations of our learning results. > It would have been interesting to see how well this method would work with policies/controllers not parametrized with neural networks (i.e. kernel machines). Thank you for your valuable suggestion. One of the strengths of our work is its flexibility and extensibility, allowing the use of various methods beyond just reinforcement learning. Our method can be applied to other approaches such as kernel methods, radial basis functions (RBF), model predictive control (MPC), and optimal control. In this paper, we were motivated by traffic examples and focused on developing a simple and practical algorithm to efficiently solve a wide range of CMDPs. While we have primarily concentrated on deep reinforcement learning algorithms using neural network parameterizations, exploring the applicability of our method with alternative approaches is indeed an interesting direction for future research. In response to your comments, we conducted preliminary experiments with support vector machines (SVM), one of the most popular kernel machines, to solve the CartPole CMDPs. Though SVMs are not inherently designed for sequential decision-making, we used them in a supervised learning context where we trained the SVM on the best actions given certain states. After training the SVM model, we transferred it to other CMDPs and collected the rewards. Our preliminary result in Figure R.5 shows that an SVM-based controller trained on a default configuration actually solves other tasks. The results of these preliminary experiments in Fig. R5. indicate that our method shows promise when applied to kernel machines as well. This suggests that our approach can potentially be extended to other non-neural network-based methods. We appreciate your suggestion and will consider including more detailed experiments and discussions in future work. > Some additional commentary on how to use the GP to search for a trained policy given a selected task. Thank you for your insightful comment. In our MBTL-GP method, the GP is utilized to predict the performance of a policy trained on a source task when applied to a target task. The modeled generalization gap helps predict the transferability of that source task. Using the GP model, we apply Bayesian Optimization (BO) to select the next training task. The acquisition function in BO balances exploration and exploitation by considering both the predicted mean performance and the uncertainty (variance) associated with the prediction. Specifically, our proposed modified UCB acquisition function is used. This allows us to strategically choose tasks that are likely to improve overall performance while reducing uncertainty. Once a new task is selected, the policy is trained on this task, and the resulting performance data is used to update the GP model. This iterative process continues, progressively refining the GP model and improving task selection. This approach allows the MBTL framework to efficiently search for trained policies by leveraging the predictive power of GP and the strategic task selection of BO. For a better understanding, we added Figure R.1 to illustrate the MBTL process. > Q1. Could you comment on the challenges of applying MBTL-GP on vision-control tasks? We appreciate your suggestion, and we understand the importance of evaluating our method on more complex tasks with high-dimensional state spaces. In response, we conducted additional experiments on high-dimensional environments. Unfortunately, the CARL benchmark no longer supports the RNA design application, so we decided to focus on vision-control experiments instead. The experiments are based on the benchmark [1], which supports visual generalization for reinforcement learning. We ran preliminary experiments with this benchmark using the CartPole task, specifically examining contextual MDPs of the CartPole environment with different frame skip parameters. This setup is similar to the task variant of advisory autonomy in traffic tasks. We kindly request the reviewer to refer General Response 2 [GR2]. The preliminary results in Figure R.2 show that MBTL algorithms ranging from simple strategies to GP-based algorithm also work in complex high-dimensional state space. These experiments demonstrate the scalability and robustness of MBTL in more challenging and complex settings. ### References - [1] Q. Li, Z. Peng, L. Feng, Q. Zhang, Z. Xue, and B. Zhou, “MetaDrive: Composing Diverse Driving Scenarios for Generalizable Reinforcement Learning,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 45, no. 3, pp. 3461–3475, Mar. 2023. --- Rebuttal Comment 1.1: Title: Thank you for your detailed response! Comment: I wanted to thank author first for their detailed response. The response has addressed most of my questions and I would like to keep my original score to recommend accept this paper. --- Reply to Comment 1.1.1: Comment: Thank you for your feedback and suggestions during the rebuttal period. It really helped us improve our work.	Summary: The paper introduces a framework called Model-Based Transfer Learning (MBTL) for solving contextual reinforcement learning problems. By modelling the performance loss as a simple linear function of task context similarity, the authors leverages Bayesian optimization techniques and provides theoretical analysis showing that MBTL exhibits sublinear regret in the number of training tasks, and discusses conditions to further tighten the regret bounds. MBTL is validated on a range of simulated traffic management scenarios and standard control benchmarks, demonstrating superior performance compared to baselines like exhaustive training, multi-task training, and random task selection. Strengths: 1. In general, the paper is easy to follow and well-motivated. The figures are helpful for readers to quickly grasp the key concepts and problem settings. 2. Active and transfer learning for contextual RL is an interesting and practical problem, especially given that exhaustive/multi-task training on RL tasks can be computationally expensive. 3. The experiments are conducted on a relative broad range of benchmarks and context variations. Weaknesses: I do think there are several major concerns regarding the current form of the paper: 1. The paper (especially the theoretical analysis) is based on too many assumptions: continuity of task space and performance function, linear genearalization gap and deterministic MDP transitions, which oversimplifies the problem and significantly limits the applicability range of the proposed method. The most concerning is Assumption 3 (Linear generalization gap), for which I have no clue why and when this can hold. Assuming Lipschitz continuity of the generalization gap seems much more reasonable to me, which makes assumption 3 an inequality instead of an (approximate) equality. 2. In line 96-98, the paper assumes that a vector representation/context feature $x$ of each task is given a priori, based on which the continuity assumptions 1-2 are made. Howeveer, as in line 333-335, context features are often not visible. Assuming prior knowledge of such information further limits the applicability range of the proposed method. 3. (2 continued) In fact, no matter whether context features are given a priori, there are many effective methods which perform transfer/meta-RL by learning a conditioned policy [1][2][3], which should be significantly better than the "multi-task" baseline adopted in the paper. However, there is currently no empirical evidence on how well the proposed method compared to these stronger baselines. 4. Even though Theorem 2 and Corollary 2.1 2.2 give quantitative regret bounds assuming the search space can be narrowed down at each training step, there is no theoretical guarantee on how the proposed method, especially MBTL-GP, can effectively realize such restricted search space. Hence the current analysis is not complete in terms of proving the effectiveness of proposed method. [1] Rakelly, Kate, et al. "Efficient off-policy meta-reinforcement learning via probabilistic context variables." International conference on machine learning. PMLR, 2019. [2] Shagun Sodhani, Amy Zhang, and Joelle Pineau. Multi-task reinforcement learning with context-based representations. In International Conference on Machine Learning, pages 9767–9779. PMLR, 2021. [3] Li, Lanqing, Rui Yang, and Dijun Luo. "Focal: Efficient fully-offline meta-reinforcement learning via distance metric learning and behavior regularization." ICLR 2021. Technical Quality: 2 Clarity: 3 Questions for Authors: What's the foundamental difference between "exhaustive training" and "multi-task RL"? Based on the brief description in line 257-258, they seem similar to me. Also why is "multi-task RL" even worse than "random" most of the time (in Table 1, 2)? Confidence: 4 Soundness: 2 Presentation: 3 Contribution: 2 Limitations: N/A Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We appreciate the reviewer's constructive and insightful feedback. We kindly request the reviewer to also refer to our general comments, which address (1) concerns with the linear generalization gap assumption, (2) the application of MBTL to tasks with high-dimensional visual inputs, and (3) multi-task baselines. Should our response meet the reviewer's expectations, we would be grateful if they could consider increasing the score. > The paper (especially the theoretical analysis) is based on too many assumptions: continuity of task space and performance function, linear genearalization gap and deterministic MDP transitions, which oversimplifies the problem and significantly limits the applicability range of the proposed method. The most concerning is Assumption 3 (Linear generalization gap), for which I have no clue why and when this can hold. Assuming Lipschitz continuity of the generalization gap seems much more reasonable to me, which makes assumption 3 an inequality instead of an (approximate) equality. Thank you for your valuable comments. We refer to General Response [GR1], where we detail interpretations of the linear generalization gap. Moreover, assuming Lipschitz’s continuity of the generalization gap could bound the performance range, it would provide a more flexible and realistic generalization gap estimation. However, incorporating Lipschitz continuity into our MBTL algorithm involves additional considerations on effectively utilizing this bound to optimize task performance. We acknowledge that further investigation is needed to understand the potential benefits of Lipschitz continuity. > In line 96-98, the paper assumes that a vector representation/context feature $x$ of each task is given a priori, based on which the continuity assumptions 1-2 are made. Howeveer, as in line 333-335, context features are often not visible. Assuming prior knowledge of such information further limits the applicability range of the proposed method. We appreciate the reviewer's insightful comments. This paper specifically addresses the SSTS problem settings where context features are visible. Many real-world applications for solving multiple related tasks with visible contexts, such as robotics manipulations, recommendation systems, autonomous driving scenarios, and personalized healthcare, often have accessible context features (e.g., robot configurations, user preferences, traffic, environmental conditions, and patient health records). These contexts allow our method to be broadly applicable in these domains. We acknowledge that there are also scenarios where context features might not be visible or available. Extending MBTL to handle such hidden context scenarios is a promising direction for future work. This could involve developing techniques to infer or estimate hidden contexts from observable data. We appreciate your suggestion and look forward to exploring this avenue in our future research. > (2 continued) In fact, no matter whether context features are given a priori, there are many effective methods which perform transfer/meta-RL by learning a conditioned policy [1][2][3], which should be significantly better than the "multi-task" baseline adopted in the paper. However, there is currently no empirical evidence on how well the proposed method compared to these stronger baselines. We appreciate this feedback and agree that including comparisons with stronger baselines would strengthen our evaluation. We refer the reviewer to the General Response [GR3] and Figure R.3 about the multi-task baseline. Additionally, our method has an advantage over PaCo [1] because it does not require learning additional parameters during training, thanks to the simple modeling of performance loss in transfer. > Even though Theorem 2 and Corollary 2.1 2.2 give quantitative regret bounds assuming the search space can be narrowed down at each training step, there is no theoretical guarantee on how the proposed method, especially MBTL-GP, can effectively realize such restricted search space. Hence the current analysis is not complete in terms of proving the effectiveness of proposed method. Thank you for your constructive comments. To address your concerns, we offer a more detailed discussion on the practical realization of a restricted search space and include empirical evidence to support our theoretical claims. The graph in Figure R.4 illustrates the impact of search space elimination on the performance of different strategies over multiple transfer steps. It compares the empirical search space of MBTL-GP in tasks provided in this paper with the examples given in Corollaries 2.1 and 2.2. Corollary 2.2, representing a greedy strategy (MBTL-PS), demonstrates a more aggressive reduction in search space, leading to the tightest regret bounds and superior performance. Corollary 2.1 also shows a rapid reduction in max space and improved performance. Although we cannot guarantee the theoretical performance, our empirical results indicate that MBTL-GP can achieve competitive performance compared to MBTL methods using simpler strategies. > What's the foundamental difference between "exhaustive training" and "multi-task RL"? Based on the brief description in line 257-258, they seem similar to me. Also why is "multi-task RL" even worse than "random" most of the time (in Table 1, 2)? Thank you for your feedback, and we apologize for any confusion in differentiating the two. Exhaustive training involves training separate models for all different cMDP tasks, while multi-task RL trains a single universal model that can generalize across different cMDP tasks. As shown in our transferability heatmap, some environments have low transferability to other tasks, making it challenging for multi-task RL to derive a single model that can effectively solve a wide range of task variants. Random selection of models in SSTS can sometimes cover a broader context range better than a single multi-task RL model. --- Rebuttal 2: Title: Reference Comment: [1] L. Sun, H. Zhang, W. Xu, and M. Tomizuka, “PaCo: Parameter-Compositional Multi-Task Reinforcement Learning,” Neural Information Processing Systems., 2022. --- Rebuttal 3: Comment: Thank you for the rebuttal, I appreciate the efforts for providing further experiments. After carefully reading through the rebuttal and general response, unfortunately, I feel some of my major concerns still remain. Most importantly, given the current form of the paper, I would expect more in-depth analysis and insight regarding the following subjects: 1. $\textbf{Theoretical justification of the linear generalization gap}$. This is claimed by the authors as a "key strength" of the paper. However, unlike a loss function with well-defined form, generalization gap is a complex function of model parameters, architectures, dataset sizes & distributions as well as context feature $\textit{without}$ a closed-form expression. Simply taking a linear assumption makes subsequent theoretical treatment easier, but without any convincing insight or theoretical justification, it would significantly limit the impact of the paper. My suggestion: First of all, I appreciate the additional result that the proposed algorithms perform reasonably well in the presence of a non-linear (e.g., quadratic) generalization gap function. However, to be more general, maybe consider using a separate nerwork to approximate this function, which in principle can be any function due to the universal approximation theorem, and then demonstrate the effectiveness of your methods. If you still want to hold on to the linear form to support your theoretical development, consider the Lipschitz constraint instead, which seems much more realistic. 2. $\textbf{Regarding MBTL-GP realizing restricted search space}$, the additional empirical evidence is nice. But since Theorem 2 and Corollary 2.1 2.2 are meant to theoretically ground the effectiveness of proposed methods, I think more rigorous proofs and insights instead of just empirical observations are still necessary to complete the whole argument. If you find it extremely hard or even impossible to bound/model the reduction rate in search space, at least state it clearly as an assumption, which of course, limits the impact of the paper. # Additional Concerns Given the authors explanation about "exhaustive training" and "multi-task RL", I realize that I previously misinterpreted the SSTS problem as a "continuous learning" + "active learning" setting, where you train a $\textbf{single}$ model on a sequence of tasks, in attempt to select the optimal next task to maximize generalization. However, now if I understand correctly, the proposed methods actually follow the "exhaustive training" paradigm, where for each new task, a new model is trained. This formulation of SSTS seems unconventional (or "novel" on the bright side), for which I have two major concerns: 1. According to Eqn 3, the task selection requires evaluation of all existing models (1-k) on every single target task $x'$, which may severely increase the total computational cost of SSTS. Suppose we have $N'$ target tasks, the proposed task selection requires $O(N'k)$ complexity to compute. If we want to select $N$ source tasks in total sequentially, it will end up with $O(N'N^2)$ complexity. Even though performing evaluation/inference is less computationally demanding than training, this additional cost can be non-neglectable especially when $N$ and $N'$ are large. This potentially makes the main motivation that "Our work has the potential to reduce the computational effort needed to solve complex real-world problems" much weaker. 2. Training a new model whenever encountering a new task is not scalable. In an idealized scenario, we would like to have a "universal model", like human brain, which can continuously learn by reusing prior knowledge to solve new tasks that are similar to tasks encountered before, and only make significant updates when the new task is completely beyond your current skill set (aka "out-of-distribution" in statistical words). This is the fundamental motivation of continual learning or life-long learning. The current setting of SSTS, if I understand correctly, seems less realistic or at least require significant justification for its practical impact. --- Rebuttal Comment 3.1: Comment: We appreciate your valuable and insightful feedback. >Theoretical justification of the linear generalization gap We appreciate your concern regarding the linear assumption of the generalization gap. As discussed in our general response [GR1], the linear model was chosen for its simplicity and to streamline the algorithm design process, though various complex factors influence the generalization gap. We are currently exploring the possibility of extending the proposed methods using neural networks to approximate the generalization gap. But again, the key strength of our simple algorithm is that we don’t necessarily need pre-training of those parameters. >Regarding MBTL-GP realizing restricted search space We understand the importance of rigorous theoretical analysis and regret bounds. We agree that the paper would benefit from a more detailed analysis of how the MBTL-GP algorithm can systematically reduce the search space. While we offer examples of simpler algorithms like MBTL-GS to illustrate potential strategies, we face challenges in bounding the reduction rate for MBTL-GP. Therefore, we have provided empirical insights into the rate at which the search space for MBTL-GP can be reduced. In the revised paper, we clearly state this approach, along with formally defined assumptions and detailed explanations. >According to Eqn 3, the task selection requires evaluation of all existing models (1-k) on ... We appreciate your observation regarding the difference between our proposed method and conventional approaches such as multi-task training, where a single universal model is trained across multiple tasks, or independent (exhaustive) training, where separate models are trained for each task. As you mentioned, one of the most important motivations for our method is that evaluation is much cheaper than training RL models in terms of computational cost. We think that this paradigm of training multiple models and applying zero-shot generalization (or fine-tuning) has little been studied and is promising. The strength of our approach lies in its ability to achieve near-oracle performance with a significantly smaller number of trained models. For example, in our experiments on standard control benchmarks with 100 tasks, we achieved performance close to the oracle level with only 10-15 trained policies. While exhaustive evaluation is required to ensure the selection of the best model among all possible task-specific models, we believe that the computational cost of evaluation is relatively low compared to training the remaining RL policies. Moreover, once the generalized performance of the models is obtained, further evaluations are not necessary in subsequent steps. This reduces the evaluation complexity to $O(N')$ per step, resulting in a total complexity of $O(N N')$ when training $N$ tasks, as opposed to the $O(N' N^2)$ complexity you mentioned. Additionally, in practical scenarios, we typically consider cases where $k \ll N$, further reducing the complexity to $O(N' k)$, which is significantly smaller than $O(N N')$. This highlights the computational efficiency of our approach in scenarios with many tasks. >Training a new model whenever encountering a new task is not scalable. In an idealized... Thank you for your insightful comments. We recognize the importance of developing a "universal model" that can continuously learn and adapt to new tasks by reusing prior knowledge, as emphasized in recent research on continual and life-long learning. However, we believe that there are specific scenarios where task-specific training policies, rather than a universal model, are necessary and practical, especially when side information is available. For instance, in the design of traffic signal phases at 4-way intersections, it is crucial to train distinct reinforcement learning policies for different intersection configurations. Considering that there are approximately 16 million different intersections in the United States, training a universal model or separate 16 million models for all configurations would be highly expensive and almost impossible. However, by leveraging context information such as the number of lanes, lane lengths, expected traffic inflows, and speed limits, we can intelligently devise a training procedure that trains multiple models, while still achieving good generalization across the broader distribution. Empirically, we have observed that in such scenarios, our method proves to be computationally more efficient and performs effectively. This approach allows for the targeted training of models that are specialized but still generalize well to similar tasks, thus addressing practical constraints in real-world applications. We hope this conveys the core idea and motivation of our work. We also acknowledge the potential of context-free learning for scalable, universal models, as you mentioned, and consider it an important direction for future research. --- Rebuttal 4: Comment: Thank you for the detailed response. My concern regarding the computational complexity is largely resolved. However, some of the major concerns remain, which I think the authors also agree upon. In summary, this is a novel paper which introduces the concept of "model-based transfer learning" based on "sequential source task selection", which I have not seen the exact same setting before, to my best knowledge. The authors propose to solve this problem by Bayesian optimization techniques, which are empirically proven effective, but the methodologies are not new. By assuming a linear generalization gap as well as bounded reduction of search space, the authors arrive at theoretical guarantees for sublinear regret. By the design, the proposed method can achieve better computational efficiency compared to conventional multi-task learning, in certain scenarios. I will give credit for all contributions above. However, as we discussed during the rebuttal, the paper still falls short in providing serveral key pieces of the story, such as the theoretical justification of the linear generalization gap (also needs to extend it to more generalized, realistic format as we discussed), theoretical guarantee for bounded search space, reliance on the existence of continuous context features, which significantly restrict the applicability and practical impact of the framework . Also for the problem setting of SSTS, the authors provided the example of "16 million different intersection configurations in the United States" to justify the need of training multiple models, which I find reasonable but $\textit{not convincing enough}$. A more promising and general approach to me to solve the same problem, is to leverage the power of pretrained large models. Specifically, one can use a pretrained context encoder model (e.g. large vision model for visual observation) to extract the context feature from the raw input, and use it to condition the downstream RL policy, instead of training a new model for each task, and carefully select the "optimal" next task, which is far less scalable. To conlcude, I believe there are novelties in this work and appreciate the authors' efforts in rebuttal, but remain conservative about its practical impact to the community. More importantly, I sincerely hope the authors to conduct further investigations to fix the issues we agreed upon to make the paper stronger, whether the paper is accepted. Given the reasoning above, I will keep my score but are open to further discussions. --- Rebuttal 5: Comment: Thank you for your thoughtful and comprehensive feedback. We appreciate your recognition of the novel aspects of our work. First of all, we see the reviewer’s concern on the generalization gap assumption. In situations where the true function is difficult to analyze, approximation methods are commonly used. Our MBTL algorithms approximate the generalization gap with a simple linear function of task context similarity. We show that even with the linear function, our MBTL framework works in various settings ranging from standard control tasks to complex real-world traffic applications. To further address your concern, we have also evaluated the MBTL-GP performance using non-linear approximations, including quadratic, cubic, $x^5$, and $x^{10}$ models along with the RMSE between the actual generalization gap. While higher-order approximation functions generally result in lower RMSE errors, we observed that the overall performance of MBTL on the SSTS problem does not consistently improve with more complex non-linear approximation. For example, the RMSE error of generalization gap with 10th-order polynomial approximation does not always perform best to solve CMDP tasks. This suggests that the simplicity and interpretability of the linear model can provide significant advantages without compromising effectiveness. \| \| Linear \| Linear \| Quadratic \| Quadratic \| Cubic \| Cubic \| $x^5$ \| $x^5$ \| $x^{10}$ \| $x^{10}$ \| \| ----------------- \| ----------- \| ------ \| ----------- \| --------- \| ----------- \| ------ \| ----------- \| ------ \| ----------- \| ------ \| \| \| Performance \| RMSE \| Performance \| RMSE \| Performance \| RMSE \| Performance \| RMSE \| Performance \| RMSE \| \| Pendulum \| 0.7555 \| 0.1070 \| 0.7423 \| 0.0965 \| 0.7615 \| 0.0862 \| 0.7494 \| 0.0705 \| 0.7558 \| 0.0192 \| \| CartPole \| 0.8896 \| 0.2571 \| 0.8102 \| 0.1905 \| 0.8941 \| 0.1495 \| 0.8926 \| 0.1029 \| 0.8761 \| 0.0745 \| \| BipedalWalker \| 0.9331 \| 0.1422 \| 0.9237 \| 0.1201 \| 0.9329 \| 0.1016 \| 0.9318 \| 0.0771 \| 0.9325 \| 0.0246 \| \| HalfCheetah \| 0.9165 \| 0.0019 \| 0.8426 \| 0.0019 \| 0.9260 \| 0.0018 \| 0.9271 \| 0.0017 \| 0.9295 \| 0.0004 \| \| Traffic Signal \| 0.8966 \| 0.1780 \| 0.8907 \| 0.1606 \| 0.8965 \| 0.1409 \| 0.8963 \| 0.1106 \| 0.8952 \| 0.0676 \| \| Advisory Autonomy \| 0.8177 \| 0.0551 \| 0.7782 \| 0.0508 \| 0.8214 \| 0.0464 \| 0.8245 \| 0.0393 \| 0.8245 \| 0.0283 \| \| Eco-Driving \| 0.5377 \| 0.1071 \| 0.4811 \| 0.0950 \| 0.5282 \| 0.0832 \| 0.5270 \| 0.0660 \| 0.5450 \| 0.0434 \| Additionally, we would like to highlight the potential for fine-tuning in our approach. When training a model at each step, it is possible to use the previous model or a model already trained in a closely related context as a starting point. This can significantly reduce the number of episodes required for training a new model, thereby improving efficiency and having the potential to be scalable. We are grateful for your constructive feedback and remain open to further discussions on these important points during the rebuttal period.	null	null	Rebuttal 1: Rebuttal: The authors appreciate each of the reviewers for their detailed and constructive comments. Here, we first respond to all reviewers before answering each reviewer’s specific question. ### [GR1] Concerns with the Linear generalization gap assumption Thank you for your valuable comments. Similar concerns were raised by Reviewer 21Qs and ECSQ, regarding the assumptions made in our method. The purpose of our assumptions was not to oversimplify the problem but to design a straightforward algorithm that benefits from simple modeling. Assumptions 1-3 in Section 4.1 were made to streamline the empirical algorithm design rather than to constrain our theoretical analysis. Although it may appear to be an oversimplification, the simple modeling of training performance and the generalization gap are key strengths of this paper. Empirical findings indicate that even when these assumptions do not hold perfectly, our simple, principled algorithms remain effective. To address these concerns, we have included additional experiments that relax these assumptions. As one example of a non-linear generalization gap, we tested our algorithms with quadratic generalization gap assumptions. Preliminary results show that these methods can perform well, sometimes better than those assuming a linear generalization gap. Specifically, in tasks like CartPole variants, estimation with a quadratic function performs better than linear modeling since the actual generalization resembles a quadratic function. Table R.1. Comparative performance of different methods with quadratic generalization gap function on CMDP tasks \|\|\|Random\|Exhaustive\|MBTL-GP\|MBTL-GP with quadratic function\|Oracle Transfer\| \|--\|--\|--\|--\|--\|--\|--\| \|Cartpole\|Mass of Cart\|0.7221\|0.9466\|0.8212\|0.7979\|0.9838\| \|Cartpole\|Length of Pole\|0.8121\|0.9110\|0.9124\|0.926\|0.9875\| \|Cartpole\|Mass of Pole\|0.8858\|0.9560\|0.9351\|0.9593\|1\| \|HalfCheetah\|Gravity\|0.8542\|0.6679\|0.9073\|0.8253\|0.9544\| \|HalfCheetah\|Friction\|0.8567\|0.6693\|0.9274\|0.8601\|0.9663\| \|HalfCheetah\|Stiffness\|0.8533\|0.6561\|0.9146\|0.8423\|0.9674\| Furthermore, non-linear generalization gaps require estimating more parameters than linear gaps, potentially complicating the achievement of effective performance. Despite this, our preliminary results are promising and indicate that our method can be effectively adapted to handle non-linear generalization gaps, enhancing its robustness and applicability across different tasks. ### [GR2] Application of MBTL to high-dimensional visual input task We appreciate the feedback and comments from Reviewer wJEK and ECSQ regarding the applicability of MBTL to high-dimensional state space tasks. We understand the importance of evaluating our method on more complex tasks with high-dimensional state spaces. In response to these comments, we conducted additional experiments on high-dimensional vision-control experiments. These experiments are based on the MetaDrive benchmark [1], which supports visually generated observations for driving scenarios. We ran preliminary experiments with the MetaDrive benchmark in the three-lane four-way intersection traffic network with different traffic density variations (from 0.05 to 0.5) (Fig. R.2). The task involves controlling an autonomous vehicle in the presence of other vehicles. The controlled vehicle observations are generated from a low-level sensor using an RGB-based camera view with 200x100 pixels. Those inputs were passed through a three-layer CNN for feature extraction. The autonomous vehicle is controlled with steering and acceleration changes. The preliminary results show that MBTL algorithms, ranging from simple strategies to GP-based algorithms, are still effective in complex high-dimensional state spaces. These experiments demonstrate the scalability and robustness of MBTL in more challenging and complex settings, confirming the versatility of our approach in handling high-dimensional visual input tasks. ### [GR3] Multi-task baselines We greatly appreciate the feedback from reviewer 21Qs and concur that including comparisons with stronger baselines would enhance our evaluation. In response, we thoroughly examined state-of-the-art multi-task reinforcement learning (MTRL) methods, including the suggested baselines. However, we believe the suggested CARE algorithm [2], which involves language embeddings, is not an appropriate comparison for our approach, where context variation is continuous and straightforward. Instead, we have compared our methods with the Parameter-compositional multi-task reinforcement learning (PaCo) [3] algorithm. In Figure R.3, Our preliminary implementation of PaCo [5] on CartPole CMDP variants indicates that MBTL remains competitive against these methods, demonstrating superior performance compared to our previous, more naive MTRL strategy. We would like to note that due to the limited time available for rebuttals, we could not offer comparisons with various MTRL baselines, as the training procedures require considerable computation time and effort. Also, it was unfortunate that there were a few MTRL works that didn’t release the codebase, had issues running the code, or could not be reproducible during the implementation of previous works. ### References - [1] Q. Li, Z. Peng, L. Feng, Q. Zhang, Z. Xue, and B. Zhou, “MetaDrive: Composing Diverse Driving Scenarios for Generalizable Reinforcement Learning,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 45, no. 3, pp. 3461–3475, Mar. 2023. - [2] Shagun Sodhani, Amy Zhang, and Joelle Pineau. Multi-task reinforcement learning with context-based representations. In International Conference on Machine Learning, pages 9767–9779. 2021. - [3] L. Sun, H. Zhang, W. Xu, and M. Tomizuka, “PaCo: Parameter-Compositional Multi-Task Reinforcement Learning,” in Conference on Neural Information Processing Systems., 2022. Pdf: /pdf/30d27c97a5fe83c6922f62cf4030ee973303b2c2.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Oracle-Efficient Reinforcement Learning for Max Value Ensembles	Accept (poster)	Summary: The paper considers the setting in which several good policies are available for some Markov Decision Process, and the agent has to learn how to combine them in a way that allows to achieve higher performance than following a single of the constituent policies. This problem is quite wide and a large number of methods exist to combine policies, with varying assumptions and properties. This paper proposes a method that can realistically be implemented, by considering that per-policy value functions can be learned for an ever-increasing horizon $h$, and then the action to execute in the environment is the one executed by the policy that has the largest value in the current state and current horizon. The novel aspect of the contribution seems to be the reliance on $h$ and the iterative nature of the algorithm. In MDPs with a finite time horizon, we have a finite amount of $h$ values, so a finite amount of value functions to learn. Combined with the fixed amount of constituent policies, this leads to an algorithm whose complexity scales well even to very large state-spaces, because the size of the state space does not intervene in the compute requirements of the algorithm. The proposed method is discussed from a theoretical perspective, and promising empirical results are provided. The experiments consider complicated robotic tasks, with an interesting setting and motivation for this work: the constituent policies are almost-optimal policies for various tasks, and the new policy to learn from a combination of the existing ones is learned against a new task. So, this work seems to be applicable to multi-task RL. Strengths: The proposed method seems sound, easily to implement (provided that the paper is made clearer) and to lead to impressive empirical results. The assumptions and limitations of the approach are well-discussed, which helps deciding whether it would apply well on some specific problem. Weaknesses: While the contribution seems of high quality, the paper lacks clarity and intuition, which may make it difficult to reproduce. - Examples of oracles for the value functions should be given, to better indicate to people whether the oracle can be a value function learned on another task, or obtained from rollouts, or requires a simulator. The oracle is an important part of the algorithm, as it is queried $K$ times per horizon step and its output is directly used to perform an argmax operation (the result of the oracle does not seem to be distilled to some learned function) - The paper should be a bit more explicit about how to produce the $\mu_h$ distributions and the fact that this requires resetting the environment and performing actions in it. Not every environment is resettable at will by the agent, and executing all these actions requires an online setting. - The core of the paper is the use of approximate max-following policies, defined in Definition 2.3. The definition is very dry and the reader has to carefully look at the notations to understand where everything comes from. For such an important definition, an intuition and maybe an example would have been very useful. Later in the paper (Figure 2), examples of environments and corresponding max-following policies are used in some argument, but without explaining what a max-following policy is. Thus, the definition is very dry, yet at the core of important arguments in the paper. Technical Quality: 3 Clarity: 2 Questions for Authors: Given the average-low clarity of the paper, I may have mis-understood several parts of the contribution. I expect the authors to disagree with some of the remarks written above. I would welcome to be corrected, and for the authors to take the opportunity to improve the paper given the possible ways it can be mis-understood. Confidence: 3 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: The paper does not seem to have potential negative societal issues, and its scientific limitations are well-discussed. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Dear Reviewer Qu$2$b, thank you so much for highlighting the scaling dependence of our algorithm/its ability to work in large state spaces well and for relating it to our empirical results and the broader multi-task RL area. Weaknesses > Examples of oracles for the value functions should be given In practice, the oracle can be implemented using an arbitrary function approximator such as a neural network. The input distribution of the oracle is approximated by rolling out the max-following policy to some time step $h$ and then rolling out a constituent policy up to the horizon of the environment. This can happen either in a simulator or on a real-world system. The collected data is then used to fit the neural network. The learned neural network is the output of the oracle. See Appendix C for additional detail on the procedure. For additional formal clarification of the oracle, see response to weakness $2$. >The paper should be a bit more explicit about how to produce the distributions and the fact that this requires resetting the environment and performing actions in it. We thank the reviewer for pointing out the lack of clarity in how the $\mu_h$ distributions are defined and sampled. We provide some explanation below, and will add clarification to the paper as well. - We first want to highlight that sampling from $\mu_h$ does not require that the agent can reset the environment at will. We only require what is typically required in the episodic setting -- that the agent explores for an episode of $H$ steps, where $H$ is finite and fixed across all of training. After these $H$ steps, the agent is then reset to a state sampled from the distribution over starting states. - The distributions $\mu_h$ are (informally) defined as follows: at iteration $h \in [H]$ of our algorithm, the agent has already learned a good approximate max-following policy for the first $h$ steps of the episode. The distribution $\mu_h$ is the distribution over states visited by the agent at step $h$ if it begins from a state drawn from the starting state distribution and then follows the approximate max-following policy it has learned thus far for $h$ steps. - That means to sample from $\mu_h$, the oracle can simply run the approximate max-following policy for $h$ steps to arrive at a state $s_h$, which is a sample from $\mu_h$. It can then do whatever it likes for the remainder of the episode, and so does not need to reset at arbitrary time steps. - In practice, since the oracle needs to produce a good approximation of the value function $V_h^k$ at time $h$ for policy $\pi^k$ on states sampled from $\mu_h$, we should think of it as using the remainder of the episode to obtain an unbiased estimate of the expectation of $V_h^k$ on the distribution $\mu_h$. That is, once it has sampled a state $s_h$ by running the approximate max-following policy for $h$ steps, it just executes policy $\pi^k$ for the remainder of the episode. The accumulated reward obtained by following policy $\pi^k$ from state $s_h$ for steps $h$ through $H$ gives the oracle an unbiased estimate of $\mathbb{E}_{s_h \sim \mu_h}[V^k_h(s_h)]$. To implement our oracle assumption, we could use many such unbiased estimates as training data to train a neural network, to learn a good approximate value function for $\pi^k$ at time $h$ on distribution $\mu_h$. >The core of the paper is the use of approximate max-following policies, defined in Definition 2.3. The definition is very dry and the reader has to carefully look at the notations to understand where everything comes from. Thank you for the feedback on the readability of Definition 2.3. First, as we start explaining in line 134 and following, a "max-following policy is defined as a policy that at every step follows the action of the [constituent] policy with the highest value in that state." With approximate max-following policies one can run into issues arising from the fact that value functions are not perfectly accurate anymore. We will add some additional motivating intuition leading up to the technical definition 2.3 similar to that of Definition 2.1. The purpose of our observations in section $4$ is to provide the intuition for max-following and approximate max-following. For instance, imagine a scenario where two of the value functions are very close to each other for some state. Now, due to noise introduced from approximation it might look as if the function with the true lower value actually has the higher of the two values (see Observation 4.6). As outlined in section $4$, accounting for this noise in our benchmark requires comparing the learned policy to a class of policies (the class of approximate max-following policies) rather than a single baseline policy, and so the technicality of Definition 2.3 is unfortunately necessary. If the reviewer thinks it would improve readability, we would be happy to move Section 4 before Section 3, where we present our algorithm, so that the reader can have these examples in mind before we present our main results. Questions We are extremely grateful for this reviewer's thorough feedback and attention to detail and we hope to be able to incorporate much of the advice provided to build a better paper. We hope to be able to use the discussion period to clarify some of the details surrounding our oracle assumption both in theory and in practice and work on improving the exposition/clarity of our definitions and examples to help create a better paper.	Summary: This paper presents an approach to enabling Reinforcement Learning (RL) by improving the process of generating an optimal policy. Their method assumes that there is access to a particular class of Markov Decision Process (MDP). The intuition is having a collection of bases determined as constituent policies. Under some theoretically supported assumptions, the policy learning process they propose guarantees consistently obtaining a policy that is at least as good as the best constituent policy and potentially better. The method relies on an algorithm that generates policies from the max-following class. The authors tested their framework with a practical version of such an algorithm (MaxIteration) in 16 robotic tasks. An essential aspect of their method is that it relies on heuristics to create the collection of constituent policies. Strengths: This paper presents a structured theory consolidated over the definition of a policy function class called max-following. The authors provided a practical algorithm that can generate policies belonging to that class. They proved their proficiency through robotic tasks, compared to an offline RL method called Implicit Q-Learning (IQL). Weaknesses: This class falls under a set of observations provided by the authors that are necessary for the theory to hold. Also, the bases of constituent policies rely on heuristics. That could restrict the potential application of their training method. I couldn't find the explanation of Policy 0 and Policy 1 in Figure 3. This figure could be more apparent, as understanding your baselines is essential. Technical Quality: 3 Clarity: 2 Questions for Authors: - What are Policy 0 and Policy 1 in Figure 1? - How do you explain the tasks where all the methodologies had a very low success rate? Confidence: 3 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: The authors addressed their method's main limitation: the need for an oracle for the methodology to hold. They claimed that they will address this concern in the future. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Dear Reviewer Z$6$cc, thank you so much for your feedback on our paper and for highlighting the practical nature of our theoretically-grounded algorithm. Weaknesses > We are unsure what "this class falls under a set of observations provided by the authors that are necessary for the theory to hold” means. Would you be willing to clarify a bit more? One interpretation of this statement may be that our observations from section $4$ are necessary for our theory to hold. This would be incorrect as we simply provide the observations to clarify the properties of our max-following and approximate max-following approach. These are \textit{not} assumptions needed in order for our algorithm and theoretical results to hold, and are rather meant for our reader to gain intuition into some of the definitions we provided. The main assumption our paper makes is access to an ERM oracle. > It is also unclear to us what it means that the bases of our constituent policies rely on heuristics. We would appreciate clarification on this point as well. The constituent policies are not chosen based on heuristics, and are rather chosen based upon access to some pre-existing class of policies. We do not make assumptions about the properties of these policies, beyond the assumption that a regression oracle is able to give us reasonable approximations to their value functions. We hope that in many realistic settings there are policies that are pre-trained such that they are skilled in one domain but not necessarily trained to be good at other tasks. Thus, we can compose them well, but skill-specific pre-training is not necessary for our theoretical results to hold. > I couldn't find the explanation of Policy 0 and Policy 1 in Figure 3. This figure could be more apparent, as understanding your baselines is essential. We appreciate this pointer. For the camera ready version, we will update the caption of the Figure to include a description of the policies. Policies $0$ and $1$ correspond to the pre-trained policies using IQL on the intial tasks above the arrow in each graph. That is, in the left most subfigure of Figure $3$, Policy $0$ corresponds to the policy of picking and placing a dumbbell, whereas Policy $1$ corresponds to the policy of moving a box into the trashcan. The MaxIteration algorithm enables the robot move a dumbbell into the trashcan without needing the robot to train separately on that task by reusing the earlier existing policies. Questions > What are Policy 0 and Policy 1 in Figure 1? In our figure $1a$, the policies correspond to moving left or right and in $1b$ correspond to moving right, left, or up. If the review is referring to Figure $3$, we refer to the previous response. > How do you explain the tasks where all the methodologies had a very low success rate? Note that in the experimental setting, the initial policies (i.e. policies 0 and 1) are pre-trained to solve tasks distinct from the task that we test them on. Thus, we expect the pre-trained policies to be bad at the test task. Our algorithm only guarantees that we are at least as good as the best individual policy. In some cases, we see that combining policies is not sufficient to achieve success. That is because the tasks we chose are robotics tasks with highly complex dynamics and the dynamics of moving a plate versus a dumbbell using a robotic arm differ quite a bit. In such cases, simply switching between the two policies is insufficient to solve the task. However, this opens up interesting directions for future work such as including minor policy update steps to the learning process without requiring state-space dependence. --- Rebuttal Comment 1.1: Title: Answer to Rebuttal Comment: Dear authors, thanks for your efforts in clarifying my comments. Here are some clarifications to the questions from my side that didn't appear very clear: > We are unsure what "this class falls under a set of observations provided by the authors that are necessary for the theory to hold” means. Would you be willing to clarify a bit more? I think you understood what I meant, and thanks to your answer, I can now identify that the observations are not necessary conditions (assumptions) on which to base your theoretical results. > It is also unclear to us what it means that the bases of our constituent policies rely on heuristics. We would appreciate clarification on this point as well. This part comes from the experimental results that require you to use heuristic-based versions of the algorithm. Thank you for clarifying that this is only related to this part and is not required in the theoretical proof. The confusing part comes from the abstract, where you stated: "One line of research [...] the natural assumption that we are given a collection of heuristic base or constituent policies [...]." I believe this part makes the reader assume that the constituent policies come from heuristics, which is why I commented in the first place. Maybe you can adjust the abstract to clarify the difference. > Regarding Figure 3 Thank you for explaining and considering my feedback to clarify what Policies 0 and 1 mean. I think improving the details you provided about them would help make your experiments more understandable. Your clarification about this was very helpful in understanding the underperforming tasks in my last question. Thanks for taking the time to answer all of them; besides what I stated above, I don't have additional comments. --- Reply to Comment 1.1.1: Comment: Dear reviewer Z6cc, we are grateful for your feedback and will make several changes in the next iteration of the manuscript. * We had hoped to convey that simple heuristic policies can sometimes be useful even when they are not complex, but we see now that there is ambiguity in this statement. We will adjust the abstract as you suggested and point out in the main text that constituent policies can, but must not necessarily, be heuristic. * We will also make changes to the caption and text with respect to the description of the policies 0 and 1 including a paragraph similar to what we provided in the rebuttal. Thank you for engaging in this discussion phase, we greatly appreciate it. We hope you are now more positively disposed to our paper and are happy to discuss further if there are any other points of confusion	Summary: The paper presents an algorithm called MaxIteration for addressing the challenges of RL in large or infinite state spaces. The core idea is to compete with a max-following policy, which at each state selects the action of the constituent policy with the highest value. The MaxIteration algorithm is efficient, requiring only access to an empirical risk minimization (ERM) oracle for value function approximation of the constituent policies, without needing the value functions themselves. Strengths: 1. The algorithm is computationally efficient, scaling well with large state spaces. 2. The paper provides a solid theoretical foundation with proofs of the algorithm's effectiveness. 3. It improves upon existing policies without needing to explore the entire state space. 4. The algorithm's performance is validated by experiments on robotic simulation tasks. Weaknesses: 1. The algorithm assumes access to an ERM oracle, which might not be practical in all scenarios. 2. While its efficiency in simulation tasks, the algorithm might be complex to implement in real-world systems. Technical Quality: 3 Clarity: 2 Questions for Authors: 1. Are there any specific cases where the algorithm's performance might degrade? 2. How does the algorithm deal with non-stationary environments or changing dynamics? Confidence: 2 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: Please see the above comments. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Dear Reviewer BR1J, thank you for your feedback on our work and highlighting the value of our theoretically motivated empirical algorithm. Weaknesses > The algorithm assumes access to an ERM oracle, which might not be practical in all scenarios. Many machine learning problems are known to be computationally hard in the worst case, but Empirical Risk Minimization (ERM) has still proven to be a useful framework in practice. For instance, the machine learning community has made great strides in solving supervised learning problems using neural networks over the past 10 years. Our oracle assumption can be thought of as providing us the guarantee that we can learn an approximate value function well in such a batch-ERM setting. That means, we are reducing the problem of learning an approximate max-following policy to a simpler supervised learning problem over a given distribution. In other words, our goal with this work is to provide guarantees under the assumption that in practice ERM is easy and neural networks do what neural networks do. > While its efficiency in simulation tasks, the algorithm might be complex to implement in real-world systems. We agree that one of the main challenges of implementing RL algorithms on real-world systems is the required sample complexity. However, we would like to highlight that our work is an attempt at reducing the required number of samples to obtain good policies. Our experimental results use only around $80$ trajectories while common on-policy RL algorithms require several thousand [Mendez et al. 2022]. Questions > Are there any specific cases where the algorithm's performance might degrade? We provably cannot do worse than the constituent policies with our approach which gives us a baseline for our algorithm's worst-case performance. Intuitively, we can think of it this way: if it is worse to switch between policies, we can always resort to using only a single constituent policy. Exactly for this reason, as we experimentally show, there are cases where MaxIteration also cannot do drastically better and ultimately performs similarly to one of the base constituent policies themselves. This is also the case in Figure $1b$. > How does the algorithm deal with non-stationary environments or changing dynamics? This is a very intriguing question and we thank the reviewer for bringing it up. Seeing what happens when the performance of a constituent policy changes due to changes in the environment is a very interesting idea. In general, we believe that it is possible to obtain efficient routines for such settings. However, this would require redefining the setting as well as some of the other definitions (and likely changing the algorithm). For the current manuscript we believe that this question is out of scope but it is an excellent direction for future work we would like to pursue.	null	null	Rebuttal 1: Rebuttal: First and foremost, we would like to thank all the reviewers for their time and feedback on our paper. We thank reviewers BR1J and Z6cc for highlighting the usefulness of our theoretically motivated but practically employable algorithm. We also thank reviewer Qu2b for highlighting the simplicity of our algorithm and the strong words about our empirical results. Given the common questions around our oracle assumption, we would like to make a clarifying statement up front. Many machine learning problems are known to be computationally hard in the worst case, but Empirical Risk Minimization (ERM) has still proven to be a useful framework in practice. For instance, the machine learning community has made great strides in solving supervised learning problems using neural networks over the past 10 years. Our oracle assumption can be thought of as providing us the guarantee that we can learn an approximate value function well in such a batch-ERM setting. That means, we are reducing the problem of learning an approximate max-following policy to a simpler supervised learning problem over a given distribution. In other words, our goal with this work is to provide guarantees under the assumption that in practice ERM is easy and neural networks do what neural networks do.	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
RectifID: Personalizing Rectified Flow with Anchored Classifier Guidance	Accept (poster)	Summary: This paper introduces a new method for Rectified Flow models to perform classifier-guidance sampling without needing a noise-aware classifier. Specifically, the authors leverage a fixed-point method to overcome the need for a noise-aware classifier and anchor the classifier-guided flow trajectory to a reference trajectory to stabilize the sampling process. In practice, the authors apply the method to personalization tasks, transferring the identity of a face or an object from a reference image to new generations paired with customized prompts. The process looks promising as demonstrated in the paper. Strengths: The idea is simple and makes sense; the application task is also good and worthy. Weaknesses: Not as I can think of Technical Quality: 3 Clarity: 2 Questions for Authors: Not as I can think of Confidence: 4 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: The idea only applies to rectified flow models right now, but I think it could be generalized to border diffusion models, it would be interesting to elaborate more on this in the future. Flag For Ethics Review: ['Ethics review needed: Research involving human subjects', 'Ethics review needed: Data privacy, copyright, and consent', 'Ethics review needed: Safety and security'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for the very constructive comments. Below are our responses to the raised concern. [L1] Generalization to broader diffusion models * While our classifier guidance is derived based on rectified flow, the same idea can be generalized to some few-step diffusion models by assuming straightness of their trajectories within each time step. We empirically demonstrate this in Figure 2 in the global response with two popular diffusion models, SD-Turbo [1] and phased consistency model [2]. As the results indicate, our method effectively personalizes these diffusion models to generate identity-preserving images. We will continue to explore this approach for other generative models in future research. --- [1] Sauer, Axel, et al. Adversarial diffusion distillation. arXiv 2023. [2] Wang, Fu-Yun, et al. Phased consistency model. arXiv 2024. --- Rebuttal 2: Title: after rebuttal Comment: sorry for the initial short review and thanks for the author's rebuttal. After reading other reviewer's comments and the author's rebuttal, I don't think I have more insights to add here. And I would like to keep my rating.	Summary: The paper introduces a training-free method based on rectified flow and classifier guidance for personalized image generation. The experimental results show that the proposed method performs better than other state-of-the-art baselines in generating personalized images for human faces, live subjects, and certain objects. Strengths: - The paper is well-written and easy to follow, and the motivation of the proposal is clear. - The theoretical background supports the motivation and the proposal well. - The experimental results present a significant improvement compared to recent existing works in the field. Weaknesses: - The theoretical justification or at least an intuition for Equation (6) is essential. - Does the "Time" column in Table 1 refer to the training time or the inference time? Does calling the gradient with respect to a classifier affect the inference speed of the proposal compared to other baselines? Technical Quality: 3 Clarity: 3 Questions for Authors: - The theoretical justification or at least an intuition for Equation (6) is essential. - Does the "Time" column in Table 1 refer to the training time or the inference time? Does calling the gradient with respect to a classifier affect the inference speed of the proposal compared to other baselines? Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: NA Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We deeply appreciate your valuable suggestions, and we would like to address your main concerns as follows: [W1/Q1] Theoretical justification for Equation (6) * The intuition for Equation (6) is to shift the velocity toward data regions with higher class likelihood. Formally, we verify this using the ODE formulation in EDM [1], which states that: $$ v(z_t,t)=-\\dot\\sigma(t)\\sigma(t)\\nabla_{z_t}\\log p(z_t), $$ where $\\sigma(t)$ is a noise schedule. By Bayes' theorem, the desired class-conditional distribution satisfies: $$ \\nabla_{z_t}\\log p(z_t\|c)=\\nabla_{z_t}\\log p(z_t)+\\nabla_{z_t}\\log p(c\|z_t). $$ It turns out that the new velocity $\\hat v(z_t,t)$ in Equation (6) generates the desired distribution when the guidance scale is set to $s=-\\dot\\sigma(t)\\sigma(t)$: $$ \\begin{aligned} \\hat v(z_t,t)&=-\\dot\\sigma(t)\\sigma(t)\\nabla_{z_t}\\log p(z_t)+s\\nabla_{z_t}\\log p(c\|z_t)\\\\ &=-\\dot\\sigma(t)\\sigma(t)\\nabla_{z_t}\\log p(z_t\|c). \\end{aligned} $$ In practice, a different scale can be used to adjust the guidance, resulting in the form of Equation (6). [W2/Q2] Issues with the "Time" column in Table 1 * The "Time" column in Table 1 refers to the inference time. Notably, our method is applied only at inference, without requiring additional training of the diffusion model. We will revise the table caption to make this clearer. * Regarding the inference time, there is indeed an overhead of about 0.2 seconds per iteration in calling the gradient w.r.t. the classifier. Nevertheless, the iterative process can quickly converge within 10 seconds over 20 iterations, which is comparable to other baselines in terms of efficiency . This efficiency is attributed to our proposed anchored classifier guidance, as confirmed by the ablation study, and we expect further speedup with algorithm improvements. --- [1] Karras, Tero, et al. Elucidating the design space of diffusion-based generative models. NeurIPS 2022. --- Rebuttal Comment 1.1: Comment: Thank you to the authors for their responses. I would like to keep my positive evaluation on the paper.	Summary: The paper introduces a training-free method for subject-driven generation using diffusion models. This approach utilizes a new classifier guidance with off-the-shelf image discriminators and anchors the flow trajectory to a reference, ensuring stability and convergence. The method shows promising results in various personalization tasks for human faces, and other subjects. Strengths: 1. The paper is well-written and easy to follow. 2. The methodology eliminates the need for extensive pre-training or subject-specific fintuning, making it highly eficient and adaptable to various use cases without the cost of training on large datasets or fintuning each model for each subject. 3. It allows for the use of off-the-shelf image discriminators, enabling not only personalization like presented in the paper but also other controllable generation tasks. 4. The idea of setting $t=1$ and solving Eq. 8 with fixed-point iteration is interesting. Weaknesses: 1. The approach heavily relies on the availability and quality of pre-trained image discriminators, which may limit its applicability in domains lacking robust pre-trained models. For example, the method for personalizing live objects (dog, cat) is quite ad-hoc and engineering for me. 2. The scope of this paper is quite limited while the method is very general. Therefore, experiments on other tasks, as mentioned below in the Questions section, can further strengthen the paper. Technical Quality: 3 Clarity: 3 Questions for Authors: 1. How to deal with the case of lacking pre-trained discriminators ? 2. The experimental settings are primarily focused on personalization with face-centric and specific object categories. However, the method is quite general. Have the authors tried other tasks like in Universal Guidance [1] ? [1] Universal Guidance for Diffusion Models. Arpit Bansal, Hong-Min Chu, Avi Schwarzschild, Soumyadip Sengupta, Micah Goldblum, Jonas Geiping, Tom Goldstein. 2023 Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: They have sufficiently addressed the limitations and potential societal impacts in their work. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for providing valuable feedback. Here are our responses to the concerns raised. [W1/Q1] Domains lacking pre-trained discriminators * In the short term, we suggest first training a specialized discriminator and then applying our classifier guidance. There are two reasons for doing this instead of finetuning the generator directly: (1) training/finetuning a discriminator is usually more efficient and stable than training/finetuning a generator; (2) it can take full advantage of domain images that have no captions or even labels by using standard contrastive learning loss. * In the future, scaling up vision-language models may be a general solution for these domains. The current models such as GPT-4V have demonstrated certain generalizability across visual understanding tasks. As they continue to improve in generalizability and robustness, they will become a viable source for guiding diffusion models in new domains. [W2/Q2] More controllable generation tasks * Following your suggestion, we've extended our method to more controllable generation tasks by directly using the guidance functions from Universal Guidance [1]. The experimental results under the guidance of segmentation map or style image are illustrated in Figure 1 in the global response. As shown, our classifier guidance can perform both tasks without additional tuning. This confirms the adaptability of our approach for various controllable generation tasks. --- [1] Bansal, Arpit, et al. Universal guidance for diffusion models. ICLR 2024. --- Rebuttal Comment 1.1: Title: Reply by Reviewer Comment: Thank authors for your additional experiments for controllable generation tasks and an interesting answer of using LLM for Q1. Here, the additional experiments demonstrate that their method can be applied to other tasks with good results so I raise my score to 7	null	null	Rebuttal 1: Rebuttal: We thank all reviewers for the insightful comments, which are important for improving our work. In response, we have meticulously prepared a PDF file containing figures that effectively address some of the raised concerns. Below is a concise summary of these figures. * Figure 1: Results for more controllable generation tasks (Reviewer dDUa). * Figure 2: Generalization to broader diffusion models (Reviewer Fu9U). Pdf: /pdf/959daaba161c2926071fe4bb6e99194b5a1a3515.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Data-Driven Discovery of Dynamical Systems in Pharmacology using Large Language Models	Accept (poster)	Summary: The paper presents the data discovery framework. It uses a LLM to iteratively discover and refine interpretable models of pharmacological dynamics. The D3 framework consists of three agents, which work collaboratively to propose, acquire, and integrate new features, validate models, and uncover new insights into pharmacokinetic processes. The framework is designed to address the limitations of traditional pharmacokinetic models that are often constrained by human expertise and scalability issues. The D3 framework was validated using a real pharmacokinetic dataset of Warfarin, demonstrating its ability to uncover a new, plausible pharmacokinetic model that outperforms existing models. Strengths: This paper is interesting. It innovatively applies a LLM to generate an interpretable the skeleton of a dynamic system and optimize the system via tranining dataset. By progressively adding relevant variables, the authors ultimately obtaining a precise and interpretable closed-form ODE. The paper leverages the extensive knowledge and self-reflection capabilities of LLMs, and the writing is clear and the experiments are comprehensive. I have learned a great deal from this paper, particularly admiring the authors' adept use of LLM agent capabilities. Weaknesses: All simulated datasets (and the ODE parameters) used in this study were publicly available before GPT-4's knowledge cutoff date. It is likely that OpenAI trained GPT-4 on relevant literature, leading to a significant knowledge leakage issue. I appreciate the author's perspective that LLMs encompass a vast amount of potentially usable knowledge. However, I do not believe that allowing LLMs to see the standard answers during training is an appropriate experimental setting. It will be better If the authors could demonstrate the feasibility of this method using real complex high-dimensional datasets whose dynamic is really unknown. After all, this is the kind of task faced in real pharmacokinetic studies. Meanwhile, the difference between this paper and many previous pharmacokinetic studies is that this paper does not conduct experiments on causal discovery. Instead, the model performance is evaluated through the MSE. It seems that this paper does not actually need to rely on simulated data and could use real high-dimensional time-series observational data for experiments. The Table 3 did not report the performance of baseline models. I believe that comparing only the so-called "standard model" in Table 3 is inappropriate. Researchers in many other disciplines do not prioritize performance to the same extent as those in the machine learning community. They often trade off performance for model simplicity, valuing clear and concise formulas over marginal gains in performance. Thus, it is not very convincing that the authors achieved a performance advantage by using a method that resulted in a much more complex system compared to the standard model. The baselines used in this paper are somewhat outdated. More recent studies published in the last two years, such as D-CODE and PGM (arxiv 2105.02522), could perform similar tasks as this paper. It is unclear why these were not included in the comparisons. Technical Quality: 3 Clarity: 3 Questions for Authors: NA Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 4 Limitations: NA Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for their constructive feedback and are glad the reviewer finds our paper interesting and appreciates our innovative application of LLMs to generate interpretable models of pharmacokinetic dynamics. We are also pleased that the reviewer acknowledges the clear writing and comprehensive experiments, and that they have learned from our work. > It is likely that OpenAI trained GPT-4 on relevant literature, leading to a significant knowledge leakage issue. We appreciate this insightful concern regarding potential knowledge leakage. To address this, we conducted additional experiments using five semi-synthetic datasets specifically designed to ensure that the LLM had no prior exposure to their underlying equations. We ran D3-Hybrid on these datasets and compared the results with some of the baselines. The results, which are included in the supplementary material, demonstrate that D3-Hybrid consistently performs well even when the LLM has never encountered such models before. This empirical evidence strongly mitigates the concern of knowledge leakage and reinforces the robustness of D3-Hybrid in discovering well-fitting models from novel data. > It seems that this paper does not actually need to rely on simulated data and could use real high-dimensional time-series observational data for experiments. Thank you for this suggestion. We agree with the importance of using real datasets and highlight that the Warfarin dataset used in our experiments is indeed a real-world dataset. Additionally, we conducted experiments involving up to 22 features, as shown in Figure 2 of Appendix G.2. The core focus of the D3 framework is to identify the most relevant features for modeling while disregarding irrelevant ones. This approach is particularly beneficial in real-world scenarios where distinguishing significant features from a large pool is crucial for accurate modeling. > The Table 3 did not report the performance of baseline models. We acknowledge the oversight and appreciate the reviewer pointing this out. We have updated Table 3 in the manuscript to include the performance of baseline models for a comprehensive comparison. This additional information highlights the competitive edge of our proposed D3 framework over traditional baseline models, reinforcing the novelty and effectiveness of our approach. > Baseline methods like D-CODE [ICLR'22] and PGM are not compared. We appreciate the suggestion to compare our work with D-CODE and other symbolic regression methods. However, our paper aims to introduce a framework that not only discovers interpretable models but also incorporates textual priors (context) and enables the acquisition of new features and samples on demand. While symbolic regression methods like D-CODE are powerful, they do not address the integrated feature acquisition and context utilization capabilities of D3. For comparison purposes, we included SINDy, a well-regarded symbolic regression method, and provided a detailed evaluation against it. We believe that a direct comparison with D-CODE, which focuses solely on symbolic regression, would not fully capture the broader capabilities and contributions of the D3 framework. Furthermore, the referred to PGM paper is out of scope as well, as it focuses on probabilistic graphical modeling of dynamical systems, whereas we focus on a deterministic best-fitting model for the dataset at hand. --- We hope that most of the reviewer’s concerns have been addressed and, if so, they would consider updating their score. We’d be happy to engage in further discussions. --- Rebuttal Comment 1.1: Comment: I appreciate the response from authors and I have improved my score. --- Reply to Comment 1.1.1: Title: Gratitude for Revised Review and Score Increase Comment: Thank you very much for your thoughtful consideration and the time you have dedicated to reviewing our paper. Your feedback was instrumental in enhancing our work, through extensive new experiments and explanations, and we are grateful for your increased score. Thank you once again! --- Rebuttal Comment 1.2: Comment: I thank authors for their thoughtful response, I keep my ratings as-is but the improvements do strengthen the paper. Thank you!	Summary: This paper presents the D3 Data Driven Discovery framework which uses GPT4-1106-Preview in a framework to iteratively consider modifying the features used in the ODE. The dynamical systems are evaluated on MSEs of held-out state-action trajectories. Strengths: The paper presents an innovative general strategy for searching the space of pharmacokinetic models in terms of which features to use. The high level approach is accessible. In their experiments, the D3-Hybrid (proposed) approach has the lowest MSE on 4 of 6 datasets. Weaknesses: The model space for the Modeling Agent could be better scoped---it appears to be whatever code the GPT-4 response is to the query. What happens in event of failure? Is this an automated framework? Typically you want interpretable and performance pharmacokinetic models, so there is a tradeoff between validation performance (e.g. MSE) and simplicity (measure in some way, e.g. MDL, number of features, etc), which creates a frontier for each model class. Could this be another way to compare the performance of these models? An analogous question would be related to acquisition costs $l(h_i)$ as well. Technical Quality: 2 Clarity: 2 Questions for Authors: What happens when the Modeling Agent produces an invalid model? What models are possible? Confidence: 2 Soundness: 2 Presentation: 2 Contribution: 3 Limitations: There is a limitation section, though the limitations appear more to be feature requests, rather than considerations that users would need to be aware of in using or building upon the work. Flag For Ethics Review: ['No ethics review needed.'] Rating: 3 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for their constructive feedback and are glad the reviewer finds our paper's presentation of the innovative general strategy for searching the space of pharmacokinetic models through our D3 framework to be accessible and acknowledges the superior performance of our D3-Hybrid approach on the datasets. > What happens when the Modeling Agent produces an invalid model? Thank you for raising this important point. When an invalid model is generated, typically due to a coding error, we have implemented a robust mechanism to address this. Specifically, if the generated code contains syntax errors or logical inconsistencies that prevent it from running correctly, the system automatically re-queries the LLM up to 10 times to regenerate the model. In practice, this iterative querying resolves most coding errors and ensures that the model is valid and executable. We have now included a detailed description of this procedure in the experimental setup section in Appendix F to enhance the transparency and reproducibility of our approach. This method effectively mitigates the issue of invalid models, ensuring continuous and reliable model generation. > What models are possible? The models generated by our framework are represented as PyTorch models. Therefore, any model that can be expressed using PyTorch's capabilities is possible within our framework. This includes a wide range of mathematical white-box models that can incorporate various operations such as logarithms, maxima, minima, and trigonometric functions. Additionally, our framework supports complex neural architectures, including multi-layer perceptrons with various regularization techniques (e.g., dropout), parameter initialization schemes, and activation functions. In practice, we observe that the generated models often consist of a combination of interpretable mathematical components and neural network elements, optimized for both performance and interpretability. This flexibility allows our framework to adaptively explore a diverse model space and discover well-fitting models tailored to the specific dataset and task at hand. > Typically you want interpretable and performance pharmacokinetic models, so there is a tradeoff between validation performance (e.g., MSE) and simplicity. We completely agree with this observation, and it aligns with one of the central goals of our research. Our D3 framework is specifically designed to navigate the tradeoff between model performance and interpretability. To achieve this, we employ a hybrid approach that combines the strengths of both white-box and black-box models. Our white-box models are inherently interpretable, providing clear insights into the underlying pharmacokinetic processes. At the same time, our hybrid models incorporate neural network components to capture complex dynamics that might be missed by purely white-box models. In our experiments, we systematically evaluate both types of models to ensure that we achieve a balance between accuracy and simplicity. For example, in our case study on Warfarin pharmacokinetics, we discovered a new, interpretable model that outperformed existing literature models in terms of validation MSE while maintaining clinical plausibility. This demonstrates the framework's ability to produce models that are not only accurate but also easy to understand and interpret by domain experts. Detailed insights into how we balance these tradeoffs can be found in Sections 4 and 5 of our paper, where we discuss the model evaluation metrics and provide expert clinical commentary on the interpretability of the discovered models. --- We hope that most of the reviewer’s concerns have been addressed and, if so, they would consider updating their score. We’d be happy to engage in further discussions. --- Rebuttal 2: Comment: Dear Reviewer 2i8U, I am a NeurIPS 2024 Area Chair of the paper that you reviewed. This is a reminder that authors left rebuttals for your review. We need your follow up answers on that. Please leave comment for any un-answered questions you had, or how you think about the author's rebuttal. The author-reviewer discussion is closed on Aug 13 11:59pm AoE. Best regards, AC --- Rebuttal Comment 2.1: Title: Concerning the frontier Comment: I still have some concerns about determining the frontier of model performance when providing a small interpretable model (white-box) and a performant model (black-box), and then describing their performance respectively with "new pharmacokinetic model" and "low MSE" respectively. Table 2 suggests D3-hybrid is similar to or marginally better than "transformer" (MSE lower in 4/6 datasets), and that D3-white-box is similar to or marginally better than SINDy/ZeroShot (though this latter comparison is very hard because we are not quantifying how sparse these white-box models are). More compelling would be to train each model across one or more hyperparameters and plot performance curves across performance (MSE) and some form of sparsity (MDL, etc). --- Reply to Comment 2.1.1: Comment: Thank you for the detailed feedback and for highlighting areas where additional clarification would be beneficial. We appreciate your focus on the balance between model performance (e.g., MSE) and model complexity (e.g., parameter count), particularly in the context of pharmacokinetic modeling. ### Addressing Model Complexity and Performance Trade-offs We understand the reviewer's concern about determining the frontier of model performance, especially when comparing the complexity of neural network-based models (black-box) with interpretable models (white-box). To address this, we conducted a thorough analysis of the average parameter count (running each baseline across ten random seeds) as a proxy for model complexity, and the results are summarized in the table below: \|Baseline\|Parameter Count\|Warfarin PK MSE $\downarrow$\| \|---\|---\|---\| \|DyNODE\|33,922\|0.726$\pm$0.17\| \|SINDy\|13\|6.84 $\pm$ 1.76\| \|RNN\|569,002\|0.0495 $\pm$ 0.0406\| \|Transformer\|2,558,348\|1.33 $\pm$ 0.941\| \|D3-white-box\|8\| 19.6 $\pm$ 40.3\| \|D3-hybrid\|245\|0.647 $\pm$ 0.167\| In our response, we chose parameter count as the metric to compare the complexity of different models for several reasons: 1. Interpretability: Parameter count provides a straightforward metric to quantify model complexity, which is particularly relevant when discussing trade-offs between performance and interpretability. Fewer parameters generally imply a simpler, more interpretable model, which is crucial in pharmacokinetics where model transparency is valued. 2. Consistency: This metric allows for a fair comparison across different types of models—ranging from highly parameterized black-box models to more concise white-box models. For instance, the D3-white-box model, despite having a significantly lower parameter count (8 parameters), still delivers competitive performance, albeit with higher variance, which reflects its simplicity and interpretability. 3. Practical Relevance: In pharmacokinetics, overly complex models (e.g., RNNs and Transformers) might offer better fit (lower MSE), but their high parameter count can obscure the underlying biological mechanisms, making them less useful for clinical interpretation and decision-making. --- ### Conclusion and Final Remarks We believe that the additional analysis and clarifications provided here address the key concerns raised in your review. We hope that these points demonstrate the robustness of our approach and the careful consideration we have given to the trade-offs between model complexity and performance. We would be grateful if you could reconsider your score in light of these clarifications. Of course, we are open to further discussion should you have any additional questions or require further details. Thank you again for your thoughtful review and for the opportunity to clarify these important points.	Summary: The paper presents the Data-Driven Discovery (D3) framework, a novel approach that iteratively discovers and refines interpretable pharmacological dynamical models using LLMs. This framework is novel and innovative in its domain, it is designed to address limitations in traditional pharmacokinetic (PK) modelling, which often relies on human expertise, and prior data in various formats. It is also constrained by existing knowledge. D3 leverages LLMs to propose and integrate new features, validate suggested models, and uncover new insights in PK. The framework demonstrates its effectiveness through experiments on various PK datasets, including a real-world Warfarin dataset, where it identified a new, well-fitting PK model outperforming existing literature. The D# framework utilises the following agents: Modelling agent: Writes Python code for an AI model with the information the LLM has acquired Evaluator agent: Evaluates the performance of the model by the modelling agent. The metric used is MSE (Mean Squared Error) Feature acquisition agent: Based on the evaluation of the model, more features are added to the model to improve accuracy (reduce MSE). A feature is acquired based on an estimation of the feature’s value using existing frameworks and available information such as text-based description of the feature, summary statistics and the feature’s existing data. Strengths: The Data-Driven Discovery (D3) framework introduces a novel approach to pharmacokinetic modelling by leveraging Large Language Models (LLMs). This method appears to be highly original within its domain, representing a unique application of well-known techniques to pharmacology-specific challenges. The framework's ability to explore multiple models and incorporate unstructured data distinguishes it from traditional methods that rely heavily on human expertise and predefined knowledge bases. I would judge the quality of the work as high, with claims well supported by theory and experimentation. The paper provides detailed information on D3 implementation, prompts, metrics, and compares its performance against other methods. The results demonstrate that D3 is capable of identifying well-fitting models and providing valuable insights, such as in the Warfarin case study where it uncovered less-intuitive features, interactions and combinations of them. The paper is clearly written and well-structured, with a logical flow of sections. It effectively uses tables, graphs, and equations to communicate information, although some text could be improved for readability. The methodology is explained with sufficient detail, covering how each component works. The significance of the framework lies in its potential to accelerate pharmacological modelling by automating the discovery and refinement of interpretable models. While it still requires some human expertise, D3 reduces dependency on experts to a degree, assisting them in their work. Its ability to uncover new insights into pharmacokinetic processes could have important implications for optimising drug dosing and minimising adverse effects. In terms of the novelty in AI, while agentic workflows are not new, the usability of D3 by non-AI specialists may be significant. The "evolving" nature of the system for non-AI domain specialists can be impactful, potentially bridging the gap between AI capabilities and pharmacological expertise. Weaknesses: In general, the paper is inspiring and is solid in its experimentations and validations. There are a few remarks, some of them for future consideration, while others might improve the clarity of the paper: 1. Cost function considerations: the current description of the cost function l(h_i) might be too simplistic and not fully capture the complexity of acquiring new features. Cost functions are often difficult to quantify accurately. Adding a few sentences or a small subsection to discuss the aspects of the cost function and its potential impact and tradeoffs will provide a more comprehensive understanding. 2. The D3 framework assumes that once a feature is selected, it is available for all individuals in the dataset. For example, certain biomarkers can be measured only in a small sample of patients. It would be interesting to discuss potential performance and limitations in light of missing data. Note: the authors briefly outlined it but elaboration on how to address it would be good given the commonality of this scenario. 3. While authors called out the scalability and computational complexity of the framework, it would be interesting to see specific numbers around time to completion wrt the numbers of features. 4. In line 212 it is mentioned that ‘The Evaluation Agent dynamically assesses both model performance and plausibility <…>’. Not sure if understood how plausibility is measured (couldn’t find it in the prompt in the Appendix either). Would be nice to see a bit more elaboration. 5. Table 2 has mixed formatting: mixing scientific and regular notation: like 0.000245 and 2.47e+03 are both present. Unifying the notation will be more consistent. In addition, the variability of the results in terms of MSE is concerning. Might be useful to think of a more coherent metric or to provide an explanation for such extreme variability (e.g. 5780 vs. 7.07 for Lung Cancer or 719 vs. 0.3 for Lung Cancer with Chemo ). 6. The choice of LLM is quite significant and it is stated for the first time in Limitations on page 9. This could be brought earlier. Technical Quality: 3 Clarity: 3 Questions for Authors: * Why was MSE used as the metric for accuracy? And on the same topic, in Table 2, what would be an interpretation of units in MSE? * Do you have ideas as to how to combat the limitations mentioned such as hallucinations? * Do you have a view on how to address the cost/ability of the LLM to distinguish between “easier” and “harder” features? Such as: “don’t include biomarker x as it’s difficult to acquire from patient”? * Have you considered the inverse bias problem when models such as GPT-4 are restricted not to use biased features but it could be informative in the pharmaceutical environment to a PK model, such as ethnicity? * I'm still not fully clear how the LLM acquires the unstructured context/metadata about each feature. Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: Outlined in the previous sections. They are outlined and very helpful but some of them spark interesting questions and would like to see some of them elaborated on a bit more like missing data. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for their constructive feedback and are glad the reviewer finds our work introducing the Data-Driven Discovery (D3) framework novel, innovative, and significant in its application to pharmacokinetic modeling. > Cost function considerations: Adding a few sentences or a small subsection to discuss the aspects of the cost function and its potential impact and tradeoffs will provide a more comprehensive understanding. We agree with the reviewer's suggestion and appreciate the opportunity to clarify this point. The current description of the cost function $ l(h_i) $ captures the complexity and computational resources required to acquire new features. However, it may not fully account for the practical challenges of acquiring specific biomarkers or data types that are costly or invasive to obtain. To address this, we have added a subsection discussing the potential impact and tradeoffs of different cost function considerations, emphasizing the importance of balancing accuracy improvements with practical feasibility. This addition provides a more comprehensive understanding of the cost-benefit analysis inherent in our feature acquisition process. > Certain biomarkers can be measured only in a small sample of patients. It would be interesting to discuss potential performance and limitations in light of missing data. We agree, and this is indeed an assumption of the current presented method. Allow us to kindly re-iterate that the focus of the paper is to propose the Data-Driven Discovery (D3) framework, a novel approach leveraging Large Language Models (LLMs) to iteratively discover and refine interpretable dynamics models, advancing pharmacokinetic modeling. While we acknowledge that handling partially missing data is a critical aspect of real-world applications, we believe such a detailed analysis falls beyond the scope of this paper. However, we plan to explore this interesting topic in future work, investigating robust methods to address missing data scenarios within the D3 framework. > See specific numbers around time to completion wrt the numbers of features. On average, a complete run of D3 with a feature size of 3 features takes approximately 1 hour. This duration includes the iterative processes of model generation, evaluation, and feature acquisition, ensuring a thorough exploration and optimization of the pharmacokinetic models. > How plausibility of the model is evaluated. The plausibility of the model is evaluated by the LLM through reflective analysis. Specifically, the LLM assesses the generated model based on domain knowledge, prior literature, and logical consistency. This reflective process involves checking the alignment of the model's predictions with known pharmacological principles and empirical observations. Additionally, the evaluation includes examining the model's ability to generalize across different datasets and its interpretability by human experts, ensuring both accuracy and clinical relevance. > mixing scientific and regular notation Thank you for highlighting this inconsistency. We will revise the tables to ensure uniform notation, using scientific notation consistently throughout the manuscript. The mixed notation resulted from the automatic generation of tables from raw results using Pandas dataframes, and we appreciate your attention to detail in this matter. > The choice of LLM is quite significant and it is stated for the first time in Limitations on page 9. This could be brought earlier. We agree and have now included the choice of the LLM in the introduction. Clearly stating this earlier provides context for the framework's capabilities and limitations, helping readers understand the significance of the LLM in driving the iterative discovery and refinement processes. ## Questions > Why was MSE used as the metric for accuracy? Mean Squared Error (MSE) is a standard metric for assessing model accuracy in pharmacokinetic modeling, as demonstrated in the cited PKPD model papers. It quantifies the average squared difference between observed and predicted values, providing a clear measure of model performance. We have defined and explained the use of MSE in the Appendix, ensuring transparency in our evaluation criteria. > Do you have ideas as to how to combat the limitations mentioned such as hallucinations? To combat limitations such as hallucinations, we could employ Retrieval-Augmented Generation (RAG) techniques. RAG combines the retrieval of relevant documents or data with generative models, grounding the LLM's output in factual information. This approach reduces the likelihood of hallucinations by ensuring the generated content is based on verified sources, enhancing the reliability and accuracy of the models produced by D3. > Have you considered the inverse bias problem. We acknowledge the inverse bias problem, where models like GPT-4 are restricted from using biased features that could be informative in the pharmaceutical context, such as ethnicity. While we have not addressed this issue in the current paper, we recognize its importance and plan to explore it in future work. Investigating strategies to balance the ethical considerations of bias with the need for accurate and individualized pharmacokinetic models is a promising area for further research. > I'm still not fully clear how the LLM acquires the unstructured context/metadata about each feature. The LLM is provided with the feature's name, of which it is empirically observed that is enough information to understand the relevance and value of that feature given the current context and progress seen during operation. --- We hope that most of the reviewer’s concerns have been addressed and, if so, they would consider updating their score. We’d be happy to engage in further discussions. --- Rebuttal 2: Comment: Dear Reviewer QDKe, I am a NeurIPS 2024 Area Chair of the paper that you reviewed. This is a reminder that authors left rebuttals for your review. We need your follow up answers on that. Please leave comment for any un-answered questions you had, or how you think about the author's rebuttal. The author-reviewer discussion is closed on Aug 13 11:59pm AoE. Best regards, AC	Summary: The paper proposes the Data-Driven Discovery (D3) framework, which leverages Large Language Models (LLMs) to iteratively discover and refine interpretable models of pharmacological dynamics. This approach enables the LLM to propose, acquire, and integrate new features, validate, and compare pharmacological dynamical systems models. The framework is demonstrated on a real pharmacokinetic datasets, highlighting its potential for clinical applications. Strengths: The D3 framework’s ability to iteratively improve models and acquire new features enhances its performance and robustness. The writing is clear and well-structured, and the methodology is well-explained. Figures and tables effectively convey key information. The problem setup, where LLM agents act together for clinically relevant tasks, is interesting and potentially useful for developing better models the current baselines. The authors demonstrate the framework’s performance on a clinically relevant warfarin dataset and show effective results. Additionally, they validate the model by obtaining feedback from clinicians, which improves the robustness of the evaluation. Weaknesses: 1. Limited Novelty: The paper has very limited novelty in terms of machine learning and does not propose any new tools. It effectively uses existing toolboxes for a clinically relevant task. While applying an existing toolbox in the context of a new task is perfectly fine, similar methods have been published before, particularly those related to automated science labs(self driving labs). 2. Lack of Guardrails for Hallucinations: Models like GPT-4 are prone to hallucinations and can generate incorrect information. The framework does not appear to have guardrails to mitigate this risk, which is a serious concern given the clinical relevance of the task. While the authors have acknowledged this as a limitation, it remains a critical issue. 3. Prompt Dependency: The model’s performance is highly dependent on the prompts provided. It is crucial to formulate the prompts correctly for the LLM to generate reasonable responses. This dependency suggests that the prompting framework might need adjustments for each dataset, leaving users vulnerable to the LLM’s unpredictability. 4. Scalability and Computational Efficiency: The framework’s scalability and computational efficiency are not thoroughly discussed. Given the iterative nature of the model refinement process, it could be computationally intensive compared to other baselines and may not be practical for larger datasets without significant computational resources. 5. Better performance of other baselines : The performance of the D3 framework might be dependent on the data. The paper shows better performance of models like RNN and transformers on tasks such as COVID-19 and Warfarin. The paper does not any comment on why that might be the case. Technical Quality: 3 Clarity: 3 Questions for Authors: 1. Given that models like GPT-4 can generate incorrect information, what measures have you considered or could implement to mitigate this risk, especially for clinically relevant tasks? I think implementing a RAG like model to address hallucinations will be highly relevant in this case and make the paper better. 2. How do you ensure consistency and reliability in the prompts across different datasets? Have you considered strategies to standardize the prompting process to minimize variability and improve predictability? Did you experiment with prompts multiple times to arrive at a reasonable framework? 3. Can you provide more information on the scalability and computational efficiency of your framework? How does the iterative model refinement process impact computational resources compared to other baselines, and what are the practical implications for larger datasets ? 4. The paper shows that models like RNN and transformers perform better on tasks such as COVID-19 and Warfarin. Can you explain why this might be the case and what limitations the D3 framework has in these scenarios? How might the performance be improved? If the authors address some of the concerns and reevaluate the frameworks with the clinicians, I will be happy to change the score. I get a sense from the expert comments that the datasets evaluated upon might not be challenging enough. Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: The authors have acknowledged the limitations of their model. However, I think some of the points mentioned, such as retrieval-augmented generation, must be implemented in the framework to make the model more robust. Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for their constructive feedback and are glad the reviewer finds the D3 framework’s ability to iteratively improve models and acquire new features enhances its performance and robustness. We also appreciate that the reviewer acknowledges the clear writing, well-structured methodology, effective figures and tables, and the interesting problem setup involving LLM agents for clinically relevant tasks. > Limited Novelty: automated science labs (self-driving labs) Thank you for raising additional related works. Allow us to kindly re-iterate that the focus of the paper is to propose a method that can both discover an interpretable model, incorporate textual prior (context), and have the possibility to acquire new features and samples. Existing automated science labs (e.g., The Automatic Statistician) do not leverage LLMs for iterative optimization and generally do not integrate feature acquisition in a dynamic manner. Our approach uniquely combines the strengths of LLMs with an iterative discovery process that can adjust to new data and contexts, providing a more flexible and scalable solution for pharmacological modeling. > Lack of Guardrails for Hallucinations We agree with your suggestion and highlight that any LLM-based method or paper should have its outputs always checked by a human expert before producing the final result. We highlight that this is a common problem across any LLM-based method paper. To mitigate this risk, we have implemented a human-in-the-loop framework where clinician feedback is integrated into the iterative process. Additionally, future work could incorporate retrieval-augmented generation (RAG) techniques to further reduce hallucinations by grounding the LLM’s outputs in factual data. > Prompt Dependency Allow us to highlight that any LLM-based paper depends on the prompts that are input into it. However, we emphasize that our method’s strength lies in the combination of model feedback and LLM iteration. By iteratively refining prompts based on model performance and expert feedback, we mitigate the risks associated with prompt dependency and enhance the reliability and consistency of the generated models. > Scalability and Computational Efficiency We find the method to still be scalable and the inner loop to train a small parameter hybrid model, where the parameter count on average is 245 parameters, to be feasible and a scalable approach. Compared to large black-box models like transformers with millions of parameters, our framework is computationally efficient and practical for larger datasets with reasonable computational resources. > Better performance of other baselines Thank you for raising this. The focus of the paper is to propose a method that can both discover an interpretable model, incorporate textual prior (context), and have the possibility to acquire new features and samples. Existing black-box methods such as RNNs or transformers can fit datasets well but are unable to perform the feature acquisition and interpretability functions of D3, making them not directly comparable. Our method offers a unique blend of interpretability, adaptability, and performance, making it suitable for clinical applications where understanding the model is as crucial as its predictive accuracy. ## Questions > Incorporate RAG? We agree that incorporating RAG-based techniques could improve the method; however, we mark it as out of scope for our initial paper. We acknowledge the potential benefits and will include a discussion of RAG techniques in the final paper to highlight future directions for enhancing robustness against hallucinations. > Did you experiment with prompts multiple times to arrive at a reasonable framework? Yes, we experimented with multiple prompts and iteratively refined them based on model performance and expert feedback. This process allowed us to develop the final proposed framework in the paper, ensuring that the prompts are well-suited to the task and yield reliable results. > Can you provide more information on the scalability and computational efficiency of your framework? This is a great question. We find our hybrid models on average contain 245 parameters, making them more scalable than existing large black-box methods such as transformers with over a million parameters. Our approach balances computational efficiency with the ability to iteratively refine models, making it practical for real-world applications with limited computational resources. > How might the performance be improved to black-box methods? It is a tradeoff to get an interpretable, hybrid/white-box model compared to a purely data-driven black-box method. Sacrificing some overall MSE can be beneficial when the process is interpretable and understandable by humans. Interpretable models provide insights that are crucial for clinical applications, where understanding the model’s behavior and its underlying assumptions is as important as its predictive accuracy. --- We hope that most of the reviewer’s concerns have been addressed and, if so, they would consider updating their score. We’d be happy to engage in further discussions. --- Rebuttal Comment 1.1: Comment: Thank you for the constructive feedback. Below, we address your main concerns briefly: 1. Novelty: While D3 builds on existing methods, it uniquely integrates LLMs for dynamic feature acquisition and iterative model refinement, which is not present in existing frameworks like automated science labs. This allows us to uncover new, interpretable models tailored for clinical applications. 2. Hallucinations: We mitigate hallucination risks with a human-in-the-loop process where all LLM outputs are validated by clinicians. We acknowledge the suggestion of using RAG techniques and will include a discussion in the final paper to explore this as a future direction. 3. Prompt Dependency: D3 addresses prompt variability through iterative refinement, ensuring prompts are well-tuned for each dataset, thus enhancing consistency and predictability across different datasets. 4. Scalability: Despite the iterative nature, D3 is computationally efficient due to its focus on discovering models with fewer parameters, making it practical for larger datasets while maintaining interpretability, which is critical in clinical settings. 5. Performance of Baselines: While black-box models like RNNs may perform well in MSE, D3’s strength lies in offering interpretable models that provide valuable clinical insights, balancing performance with the necessity for interpretability. We hope this clarifies our contributions and addresses your concerns. We kindly request you to reconsider your score based on this summary. We are open to further discussions if needed. Thank you for your time. --- Rebuttal 2: Comment: Dear Reviewer b77T, I am a NeurIPS 2024 Area Chair of the paper that you reviewed. This is a reminder that authors left rebuttals for your review. We need your follow up answers on that. Please leave comment for any un-answered questions you had, or how you think about the author's rebuttal. The author-reviewer discussion is closed on Aug 13 11:59pm AoE. Best regards, AC --- Rebuttal 3: Comment: I don't think the gains in MSE are marginal when comparing the performance of the transformer versus the D3-white box model in Table 2. The MSE of the D3-white box is roughly 5-10 times higher than that of the transformer across almost all datasets. The point was, if a model is already a poor fit, is its interpretability reliable? I have also updated my score in response to the comments on lack of guardrails and hallucinations as the authors pointed out they did not observe any significant deviation from expert consensus --- Rebuttal Comment 3.1: Comment: Thank you for your prompt feedback and for updating your score in response to our clarifications on guardrails and hallucinations. We greatly appreciate your thoughtful consideration of our responses. Regarding MSE and Interpretability: We understand your concerns about the MSE differences between the D3-white box model and the transformer across datasets. While it’s true that the D3-white box model may not match the transformer in terms of raw MSE, we’d like to emphasize a few key points: - Interpretability’s Value in Clinical Contexts: Even with a higher MSE, the interpretability of the D3-white box model provides crucial insights into the underlying pharmacological processes. This can lead to more informed clinical decisions, which may not be possible with black-box models, regardless of their lower MSE. - D3-Hybrid’s Balanced Approach: Importantly, we recommend the D3-Hybrid model for practical use. The D3-Hybrid model combines the interpretability of the white-box approach with the performance benefits of data-driven models. It achieves a strong balance, with an average of 245 parameters—significantly fewer than the 2,558,348 parameters in a typical transformer—while still delivering competitive performance. This model retains a largely interpretable component, which is critical for clinical applications, ensuring that practitioners can trust and understand the results without sacrificing too much in terms of accuracy. Given these considerations, we respectfully ask if you might reconsider your score once more, recognizing the unique value that the D3-Hybrid model brings. It offers a balanced, practical solution with substantial interpretability and strong performance, particularly in settings where understanding the model’s behavior is as important as its predictive accuracy. Thank you again for your time and continued engagement.	Rebuttal 1: Rebuttal: We are grateful to the reviewers for their insightful feedback. The reviewers broadly agree that our approach is novel and effective in leveraging Large Language Models (LLMs) for pharmacological dynamical system discovery. $\color{red} Re2Z$: “This paper investigates an interesting problem of LLM agents for pharmacological dynamical system discovery, which shows some promising results for pharmacokinetic modeling.” $\color{green} b77T$: “The D3 framework’s ability to iteratively improve models and acquire new features enhances its performance and robustness.” $\color{blue} QDKe$: “The Data-Driven Discovery (D3) framework introduces a novel approach to pharmacokinetic modeling by leveraging LLMs. This method appears to be highly original within its domain.” $\color{magenta} 2i8U$: “The paper presents an innovative general strategy for searching the space of pharmacokinetic models in terms of which features to use.” Reviewers also had concerns about the potential knowledge leakage issue due to pre-trained LLMs ($\color{magenta} 2i8U$). We address this concern below, and address reviewers individual concerns in each separate rebuttal. ## [A1] Performance on procedurally generated synthetic models. We would like to deeply thank the reviewers for bringing this up. We’ve performed a further analysis that considerably improves the paper by re-running D3-Hybrid and some baselines across five additional synthetically generated datasets. The results are provided in the attached one-page PDF. We observe that D3-Hybrid still performs well, especially when the LLM has never seen such a model. This provides empirical evidence to mitigate the concern of potential knowledge leakage issues due to pre-trained LLMs, as D3-Hybrid is still able to discover well-fitting models of the underlying synthetic equation, it has never observed before. The above point, in combination with the reviewer's addressed concerns, we believe significantly strengthens our paper. Thank you for your valuable feedback. Sincerely, The Authors Pdf: /pdf/bc765e538b19fcfcc3bac45bf48ec7eb49805d23.pdf	NeurIPS_2024_submissions_huggingface	2,024	Summary: This paper develops an LLM-assisted equation discovery framework especially for pharmacokinetic process. Three agents of Modeling Agent, Evaluator Agent and Feature Acquisition Agent are built to explore, refine and iterate vast model space, including three levels of initial conditions, observed features and possible acquired features. Several experiments mainly on simulated benchmarks are conducted to evaluate the performance of the proposed framework. Overall, this paper investigated whether LLM agents can help effectively search and determine the model space for dynamics modeling and process discovery in pharmacology. Strengths: 1. This paper investigates an interesting problem of LLM agents for pharmacological dynamical system discovery, which show some promising results of LLM for pharmacokinetic modeling. 2. The feature acquisition could be a novel part, which leverages the knowledge capability of LLM and well matches with the application demand in pharmacokinetic modeling. 3. The paper is well-organized, with clear sections and detailed explainations. The use of diagrams and examples, such as the iterative process involving the three agents, aids in understanding the complex interactions within the D3 framework. Weaknesses: 1. The benchmark methods are not recent works, which might not well identify the effectiveness of the proposed framework. For example, the symbolic regression methods like D-CODE [ICLR'22] are not compared. 2. To my understanding, the D3 model as well as other symbolic regression models discover equations from data-driven training, and then evaluate the performance based on the discovered equation. If I understand correctly, to me the experiments are not enough to prove the model effectiveness because of only five datasets with five equations. I would like to set several simulated datasets with different simulation equations for further investigation. 3. There is no ablation study on model design or case study on different module choice, which makes it hard to evaluate the robustness of the proposed framework. Also, can LLM agents provide explanations on their output results to make a more transparent solution. Technical Quality: 2 Clarity: 2 Questions for Authors: 1. How is the memory module implemented in this paper, and what exactly is the memory $s_i$? Are there several choices for memory and how would they affect the performance? 2. How much is the cost for training a D3 framework on certain datasets, especially how much would it cost for calling GPT API? Can other open-sourced LLM be used for same tasks and how is their performance? 3. RNN and Transformer models usually perform similarly in prediction tasks. However, in Table 2, RNN and Transformer perform differently on several datasets. For example, on Lung Cancer, RNN's MSE is 1.16e6, which I am wondering if the training converges successfully. Confidence: 3 Soundness: 2 Presentation: 2 Contribution: 2 Limitations: The pharmacologists feedback statements highly depend on the personal knowledge and scope, as well as their understanding to the dataset or modeling. In my opinion, this part especially with only three experts are not worth for evaluation and should be excluded to avoid bias. Flag For Ethics Review: ['Ethics review needed: Research involving human subjects'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for their constructive feedback and are glad the reviewer finds the results promising for using LLMs for pharmacokinetic modeling and the paper well-organized. > symbolic regression methods like D-CODE [ICLR'22] are not compared. Thank you for raising additional related works. Allow us to kindly re-iterate that the focus of the paper is to propose a method that can both discover an interpretable model, incorporate textual prior (context), and have the possibility to acquire new features and samples. Existing symbolic regression works such as D-CODE and others cannot acquire new features on demand, as outlined in the related works table in Table 1. We did compare against SINDy as a baseline, and believe D-CODE to be out of scope. > I would like to see several simulated datasets with different simulation equations for further investigation. We agree with your invaluable suggestion and created five additional semi-synthetic datasets running D3-Hybrid across them, combined with some of the baselines, the results of which can be seen in the additional rebuttal PDF, as outlined in the global response. We observe that D3-Hybrid still performs well, especially when the LLM has never seen such a model. This provides empirical evidence to mitigate the concern of potential knowledge leakage issues due to pre-trained LLMs, as D3-Hybrid is still able to discover well-fitting models of the underlying synthetic equation it has never observed before. > no ablation study on model design or case study on different module choice We can see how the existing ablations were overlooked. We did include ablations in most experimental results as ablations of D3, specifically with the additional baselines of a model zero-shot generated from D3 called ZeroShot and the same model with its parameters optimized called ZeroOptim. We have revised the baseline method description and tables to make these ablations more prominent to the reader now. Thank you for the suggestion. In terms of ablation results, these ablation results verify the components and complexity of D3 to achieve better performance. > can LLM agents provide explanations on their output results to make a more transparent solution We agree that this is indeed possible and already achieved by the evaluator agent, see Figure 1. ## Questions > how is the memory module implemented in this paper The memory module is simply a buffer of the top-k performing programs represented as code. > Cost for training D3, API cost The cost for training models is equivalent to training a standard 3-4 layer MLP with 128 hidden unit parameters. The API cost is around $0.075 per D3 run in total. Open-source LLMs could be used, however, D3's performance would correlate with the underlying LLM's ability. > RNN and Transformer perform differently on several datasets. We agree some datasets are difficult to model due to the large variation of the features and complex underlying feature interactions, especially for the Lung Cancer model when analyzing the underlying model. This leads to pure parameter optimization techniques getting stuck in local minima, and hence, starting with random seeds of random weight initialization can produce different final models on these complex datasets. > Ethics review flag Thank you for being cautious. However, we would like to clarify that we did not perform any research involving human subjects, only analyzing existing collected open-source medical data that is available in the public domain and providing links and descriptions to all datasets used within the paper. --- We hope that most of the reviewer’s concerns have been addressed and, if so, they would consider updating their score. We’d be happy to engage in further discussions. --- Rebuttal Comment 1.1: Comment: Thanks for the authors' reply. I appreciate that and would like to raise my score. --- Reply to Comment 1.1.1: Comment: We greatly appreciate your thoughtful review and the time you invested in evaluating our paper. Your feedback was crucial in refining our work, leading to additional experiments and improved explanations. We are thankful for your positive reassessment and the increased score. Thank you again!	null	null	null	null	null	null
Score-based generative models are provably robust: an uncertainty quantification perspective	Accept (poster)	Summary: This work studies the influence of different error terms for diffusion models from a continuous perspective under $W_1$ distance. They explain the reason why the early stopping parameter $\epsilon$ would lead to a memory phenomenon of diffusion models. To achieve these results, this work proposes a WUP theorem to explain the robustness of SGMs. Strengths: 1. The WUP theorem is novel since it can analyze generative flows instead of linear SDE and will arise independent interest. 2. The analysis of the early stopping parameter can deepen the understanding of the memory phenomenon. 3. The analysis of different objective functions is interesting. Weaknesses: 1. The abstract section mentions that stochasticity is the key mechanism ensuring SGM algorithms. However, this work does not discuss it in detail in the main content. It seems that the WUP theorem does not hold for the deterministic sampling process. It would be better to discuss it in detail. Technical Quality: 3 Clarity: 2 Questions for Authors: Please see the Weakness part. Question 1: This work does not consider the influence of discretization error. It would be better to discuss the challenge when considering this error. Question 2: For me, one interesting point is the balance of different terms when considering $\epsilon$. As shown in Theorem 3.3, $e_5$ term has $\sqrt{\epsilon}$ dependence and $e_2$ term has $1/\sqrt{\epsilon}$. It seems that there exists a balance between these terms when $N$ is finite. It would be better to discuss this balance in detail. Confidence: 4 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: This work does not discuss the limitation and societal impact in a independent paragraph. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Response to Weakness #1 Thank you for pointing this out, we should have been more clear in our PDE terminology for the generative modeling community and will make sure to fix it. The stochasticity in the generative flow appears as the \emph{Laplacian operator} in our PDEs. Without the Laplacian, the Fokker-Planck equation is a continuity equation, which describes the density evolution of deterministic flows. There are two aspects of SGMs where stochasticity/Laplacian provides regularizing effects. The first is early stopping, i.e., adding some level of noise $\epsilon$ to the data distribution. This, in effect, runs the noising process for a short amount of time and immediately mollifies the initial distribution to have a smooth density. The second aspect is that the Laplacian is the key mechanism that provides the regularizing effects to the test function that then allows us to bound, for example, the stronger $\\|\cdot\\|_{L^1}$ normal by the weaker $\mathbf{d}_1$-norm. Without the Laplacian this effect would not be possible in general and in fact we would not have access to long time behavior results. We will make sure to add a detailed remark on this. Response to Question #1 Yes, discretization error is indeed a source of error that should be looked into based on our analysis. This type of error can definitely be addressed by our framework; we however, defer this analysis for future work as it is a rather technical undertaking of its own. As we mentioned in Section 3.1, the most likely avenue for analysis is via the so-called modified equations [6]. That is, the numerical solution to the SDE is, in effect, the exact solution to a different modified SDEs. The difference between the drift terms in the modified SDE and the approximated score can then be included when applying the WUP theorem. This further highlights the capabilities of the WUP perspective and our UQ angle. We refer the reviewer to our rebuttal summary we chose the errors we thought were most impactful and relevant to score-based generative modeling and PDE regularity theory. As raise by Reviewer gUwF Weakness \#1, the paper is already rather packed with a lot of new results and insights, and we believe adding the discretization error would diminish the readability and understanding of the main message of the paper. Response to Question #2 This is a great point; in Remark 3.5 we briefly discuss how the bounds in Theorem 3.3 balances between the various sources of error or different properties of the data distribution. Moreover, it appears possible to optimize the bounds, which may further improve or inform the balance between the errors. This seems to be only possible as we work with integral probability metrics directly, which allows us to obtain sharper bounds than using a KL based approach. Moreover, roughly speaking our bounds (and all the previous bounds in the literature) obtain estimates on $d(m_{g},\pi)$ where $m_g$ is the generated distribution and $\pi$ the true data distribution. However, we only have access to $\pi$ through the empirical distribution $\pi^N$, and we essentially estimate $d(m_g,\pi)$ through $d(m_g,\pi)\leq d(\pi,\pi^N)+d(\pi^N,\pi^{N, \epsilon})+d(\pi^{N,\epsilon} ,m_g)$ where we further interpolate these distances through the addition of noise $\epsilon>0$. Notice that $d(\pi^N,\pi^{N,\epsilon})$ is finite when $d$ is an IPM, but not when it is a divergence. However, we believe it is currently rather premature to optimize the bounds as they are still qualitative for the most part, and are not fine-tuned (see our discussion to Reviewer PXMJ Weakness #1). We will add a short discussion on how obtaining sharper bounds and then optimizing them in Remark 3.5 in a future version of the manuscript. [6] Abdulle, Assyr, et al. "High weak order methods for stochastic differential equations based on modified equations." 2012. --- Rebuttal Comment 1.1: Comment: Thanks for the detailed response. It would be better to add the discussion of W1 to the main content in the next version. I am satisfied with the answers and will maintain my positive score.	Summary: The paper studies the robustness of score-based generative models (SGM) to different sources of error that are relevant in practice, such as the limited expressivity of the score function representation or the choice of reference distribution. Specifically, they upper bound the Wasserstein-1 and L1 distances between target and approximate distribution (given by an SGM) in terms of these different sources or error for both denoising and explicit score-matching objectives. Strengths: - Score-based generative models are extremely relevant within the machine learning community, and quantifying their uncertainty in terms of how well they capture the target distribution is an important research problem. - The results are, to the best of my knowledge, new and it is impressive that they manage to isolate different sources of errors in their bounds while placing no restrictive assumptions on the target distribution. Weaknesses: - The main weakness of the paper is its dense presentation. The authors did a good job of motivating and describing their contributions in the introduction, but the rest of the paper is not easy to follow. I am not sure, there is much room for improvement within the limited space of 9 pages, but I would suggest including a discussion on actionable insights one can get from these bounds. Throughout the paper, the authors comment on how important robustness is for the reliability of generative models in general, and I agree, but I could not get an intuition about when one can expect these bounds to be tight so as to ensure the resulting model is trustworthy. - While I respect the authors’ decision of going for an entirely theoretical paper, I cannot help but feel that some small scale experiments illustrating the tightness and usefulness of the bounds would be enlightening. ### Minor Issues - Line 35: “contributes” should probably be plural here. - Line 53: “recognizes” is misspelled. - Line 61: no need for “of” after “study”. - Line 100: if I’m not mistaken, the acronym SDE was not yet defined at this point in the text. - Line 102: Albeit clear from the context, $W$ and $\eta$ have not yet been defined by this point in the text. - Line 121: “however our results are generally apply” - Line 331: Word missing after “used”, probably “for”. Technical Quality: 3 Clarity: 2 Questions for Authors: - In Section 6.2., the authors discuss an application of their bounds to likelihood-free inference. To that end, could the authors elaborate on how difficult it is to estimate their bounds in practice? Is accurately estimating the Lipschitz constant of the score function the main challenge? Confidence: 2 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: This is mainly a theoretical work and I cannot foresee any direct societal impact stemming from this research. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Response to weakness #1 Thank you for the insightful feedback. As stated in our rebuttal summary, our goal is to introduce a PDE framework for error analysis of SGMs that are comparable to previous bounds, while being agnostic to situations where the data distribution is supported on a lower-dimensional manifold (see our response to reviewer PXMJ Weakness #1). To that end, the paper is organized to best understand the PDE framework for analyzing generative flows, i.e. 1. Study the evolution of test functions under the Kolmogorov backward equation of the true and approximate SDEs. 2. Bound the resulting integral probability metric using regularity estimates of the KBE. 3. Apply the resulting bound to the appropriate SGM setting. Therefore, the major actionable item the paper aims to convey is to consider PDE regularity theory for analyzing any generative flow—SGMs are just one choice. We will revise the paper to better highlight the important insights one may derive from our results. One reason we decided not to conjecture on actionable items is that our bounds are worst-case bounds that hold for any random sample of size $N$. While this shows that the bounds imply SGMs are robust, i.e., even in the worst case, the errors are bounded, we are not confident in the sharpness of the bounds. Response to weakness #2 We appreciate the reviewer's point, and we believe the ultimate goal and impact of our approach is the ability to produce a posteriori bounds that can quantitatively capture the confidence a practitioner may have in a trained generative flow. In our rebuttal summary and the response to Reviewer PMXJ's Weakness #1, our primary objective is to showcase the connections between PDE theory and generative flows. Therefore, we make no claim in sharpness. In our response to the next question, we illustrate the usefulness of computing sharp bounds, which, however, requires further research. We defer numerics to future work, when the bounds can be sharpened and applied to more useful applications. Response to Question #1 This is a great point, and it is an exciting topic we will study further in future work. We describe how one may think through how to compute the bounds. As you point out, the regularity bounds on the score function are critical. The Lipschitz constant of the score function will be dictated by the error on the ISM approximation we choose $e_{nn}$. To this end, a few factors need to be balanced. 1. If the underlying measure $\pi$ lies in a lower-dimensional manifold, its score function is undefined, since the term $\log(\pi)$ does not have meaning when $\pi$ is, for example, a Dirac mass. Therefore we require the addition of some noise with $\epsilon>0$, i.e., early stopping. 2. If $\epsilon >0$ is small and $e_{nn}>0$ is also chosen very small, then we are learning a potentially very rough function, and thus the Lipschitz norm will be large. 3. Moreover, we also have the regularizing effect of the Laplacian, which is highlighted in the choice of the test function. To bound stronger norms by weaker norms, we need more regularity on the score function we learn. For example, to bound the $\mathbf{d}_1$-norm by, say, some $H^{-s}$ norms, our bounds would require derivatives on the learned score function of order roughly $s>0$. The higher the $s$, the better the exponent on the size of the sample $N$, i.e., the rate. However, as pointed out in the previous item, the higher the $s$, the $ H^{-s}$-norm of the learned score function might also explode. With all of the above in mind, it seems that to answer your question, one would need a far more detailed analysis of the exact growth of these quantities, which is in fact the content of a work in progress. Finally, although we are not in a position yet to answer these questions, we believe that in the framework we introduced they can be posed as standard PDE questions. Once these questions are resolved, they may be most impactful for likelihood-free inference applications, e.g., [5] [5] Song, Yang, et al. "Solving inverse problems in medical imaging with score-based generative models." 2021. --- Rebuttal Comment 1.1: Comment: Thanks for the detailed response. I am satisfied with the answers and will maintain my positive score.	Summary: This paper studies the generalization error of diffusion models. The major tool is the Wasserstein uncertainty propagation theorem. With such a result and the regularity analysis in PDE, the authors establish robust analysis for diffusion models with respect to various errors. Strengths: 1. The authors examine the robustness of diffusion models from an uncertainty quantification perspective, that is not well-understood in prior work. 2. By leveraging the Wasserstein Uncertainty Propagation theorem, the authors provide the generalization error of diffusion models w.r.t. various error sources. 3. The paper is well-written and easy to follow. In particular, I appreciate the presentation of math derivation. Weaknesses: 1. The first major concern is the connection and comparison to the literature. The bounds in Theorems 3.2 and 3.3 are not explicit. I suggest the authors provide clear sample complexity results w.r.t. problem parameters. Furthermore, the authors should discuss how the bounds improved the existing results in the literature. 2. The analysis in this paper heavily relies on the PDE theory and regularity analysis. I suggest the authors discuss relevant prior work in Section 1.2. Also, I suggest the authors briefly introduce UQ used in other ML problems beyond diffusion models. Furthermore, the score approximation and estimation theory should be mentioned as that is one source of the errors. Technical Quality: 3 Clarity: 3 Questions for Authors: I have some minor comments and questions: 1. The results established in this work are usually referred to sample complexity bounds or distribution estimation error. The authors use the name robust analysis while the meaning of "robustness" seems different from the one in robust optimization. I suggest the authors clarify this notion in the context. 2. The paper leverages the pathwise characterization of probability distribution generated by the forward process. I suggest the authors add more explanations and/or refer the readers to the literature when a PDE is introduced, e.g., Eq. (11). The same applies to all the FK and HJB equations. Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: NA Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Response to weakness #1 Yes you are correct that for the majority of our results, the bounds are more qualitative than quantitative. We refer the reviewer to our rebuttal summary, that our main goal is to form a bridge between analysis of generative flows and PDE theory. We aim to illustrate our methods' strengths with specific applications such as the ESM and DSM bounds which, as you have highlighted, are not sharp. Establishing sharp constant bounds is important and beyond the scope of this work. See our response to reviewer gUwF about how we may investigate computing the bounds. To address your concerns, we highlight our novel quantitative and qualitative contributions: - Qualitative: - ESM Bound (Theorem 3.2) and DSM bound (Theorem 3.3) show the following improvements: 1. We obtain estimates in norms better than the KL divergence and, in fact, are able to bound the stronger total variation ($\\|\cdot\\|_{L^1}$ norm) by the weaker Wasserstein-1 ($\mathbf{d}_1$) norm. 2. We obtain estimates for the $\mathbf{d}_1$ norm without bounding the KL divergence and applying Pinsker's inequality. 3. Theorems B.5 and C.1 show it is possible to relate an a priori unknown error in the ESM objective with the error from the DSM objective (at least on average). Our results are agnostic to the manifold hypothesis, i.e., they apply both in the case when the distribution is degenerate, and when it admits a density. We highlight this fact throughout the paper (Sections 1.1, 1.2, and Theorem 3.3). Estimate (12) in Theorem 3.2 exists in previous literature only under the assumption that the data distribution is absolutely continuous with respect to a Gaussian [1,2,3] - Quantitative: While we track the major quantities in our Theorems, you are correct that there are important constants which are not explicit. In particular using the same notation as in our Theorems we use: 1. A constant $C>0$ which depends only on the dimension. 2. A constant $\omega$ related to the exponential rate of convergence to the stationary measure in the heat equation. 3. A constant $\delta>0$ which captures the lower bound a measure obtains when we apply some diffusion of level $\epsilon>0$. $C$ and $\omega$ are related to classical problems in PDEs and should be computable in the future when our framework is further refined. We chose to focus on the core connections between generative modeling and PDE theory, as explicitly computing these constant would make the paper far too technical in PDE theory. A major focus of future work is to compute these constants more explicitly. For example, it is important to understand if the dependence of $C>0$ on the dimension is linear, polynomial or something worse. For $\delta$, this appears to be more difficult to compute and would require more assumptions on the underlying measure $\pi$. While adding some noise $\epsilon>0$ (at least on the torus) guarantees that the measure will gain support everywhere the exact size is a challenging problem. Response to weakness #2 Thank you for your feedback. We will include discussion about relevant aspects of PDE theory that are most useful in our work. Moreover, while the use of generative modeling for UQ has been explored, to our knowledge, the UQ perspective for studying generative modeling is uncommon. We highlight [4] which derives a type of Wasserstein Uncertainty Propagation bound for the W2 distance, although they do not refer to their work as a UQ perspective. We discuss this work in Section 1.2. Regarding score approximation and estimation theory, we describe this error as source #3, score expressivity, in Section 3.1. We will rephrase this source of error in the next version of the manuscript. Response to Question #1 Thank you for your comments. There are multiple senses of robustness we use in our work. We will clarify these notions further in a future version of the manuscript. A subtle but key result of our work is that our sample complexity bounds are worst case bounds for any random sample of size $N$. As the worst case bound is finite and controlled, it demonstrates that score-based generative modeling is robust. See the discussion after Theorem 3.3. This sense of robustness is actually similar that of robust optimization, where the method produces the correct value for worst case choices of the parameters or initial conditions. In contrast to previous analysis, our results are agnostic to the manifold hypothesis. Past work assumes the data distribution has a density in $\mathbb{R}^d$, i.e., not supported on a low-dimensional manifold. As our results are independent of the manifold hypothesis, it explains why SGMs are robust, i.e., work well, even when the data distribution is degenerate. The regularizing properties of the Laplacian are what enable this robustness. Response to Question #2 Thank for for reminding us to include appropriate references to PDE theory for the generative modeling community. We will be sure to include references that will help both the PDE and generative modeling communities more easily explore each other's previous work. One goal of this paper is to showcase the connections between the two communities and we hope it may initiate such collaborations. We will add important sources, and provide some extra discussion to guide the reader. [1] Lee, Holden, Jianfeng Lu, and Yixin Tan. "Convergence of score-based generative modeling for general data distributions." 2023. [2] Chen, Sitan, et al. "Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions." 2022. [3] Chen, Hongrui, Holden Lee, and Jianfeng Lu. "Improved analysis of score-based generative modeling: User-friendly bounds under minimal smoothness assumptions." 2023. [4] Kwon, Dohyun, Ying Fan, and Kangwook Lee. "Score-based generative modeling secretly minimizes the wasserstein distance." 2024. --- Rebuttal Comment 1.1: Comment: Thank you for your detailed response. I have raised the score.	null	null	Rebuttal 1: Rebuttal: We thank all the reviewers for their careful reading, time, and insightful comments on our work. They will be invaluable for improving the current manuscript and for future work. We emphasize the organizing principle behind our paper. The primary goal of our work is to establish connections between PDE theory and flow-based generative models. We create a proper framework where various sample complexity and error bounds can be the derived from existing PDE stability results and regularity estimates. In particular, the current paper employs PDE regularity theory and the regularizing properties of the Fokker-Planck equation to analyze score-based generative models. Moreover, the Wasserstein Uncertainty Propagation theorem we derive is motivated by the model-form uncertainty quantification problem that naturally arises in score-based generative models. Many presentation choices and trade-offs in our work are made with the organizing principle in mind.	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Accelerating Pre-training of Multimodal LLMs via Chain-of-Sight	Accept (poster)	Summary: This paper introduces Chain-of-Sight (CoS), a novel vision-language bridge module designed to accelerate the pre-training of Multimodal Large Language Models (MLLMs). The key innovation is a sequence of visual resamplers that capture visual details at various spatial scales, allowing for a significant reduction in visual tokens during pre-training while maintaining or improving performance. The authors conduct sufficient experiments, including the evaluation on diverse benchmarks and three scaling experiments, to justify their assumptions and model designs. Strengths: 1. The Chain-of-Sight approach is a novel combination of multi-scale visual processing and token scaling, addressing a critical efficiency bottleneck in MLLM pre-training. 2. Extensive experiments support the claims, demonstrating significant pre-training acceleration (up to 73% reduction in wall-clock time) without sacrificing performance. 3. The paper is well-organized and clearly written. 4. The work addresses a crucial challenge in MLLM development: the computational cost of pre-training. Weaknesses: One minor weakness is that the authors have not discussed the potential impact of the scale of training data. Multiple compared MLLMs (e.g. Qwen, VILA) in Tables 5 and 6 are probably pre-trained on unequal sizes of data from diverse sources. It will help to clarify how the proposed Chain-of-Sight improves the performance on various tasks if the authors rule out the impact of the differences in the pre-training data. Technical Quality: 4 Clarity: 4 Questions for Authors: Q1: See the Weakness above. Q2: Will there be differences in the convergence speed of different compound scaling strategies? Which combination of window scale, resolution scale, and compound scale exhibits the fastest convergence? Q3: Do the authors interpolate the positional embeddings when increasing the input resolution mentioned in Line 175? Q4: Do the authors mean to refer to Table 3 instead of Table 6 in Line 222? Confidence: 5 Soundness: 4 Presentation: 4 Contribution: 4 Limitations: None. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Q1. Ruling out the impact of the scale of training data. Thank you for pointing this out. We agree that the scale of training data is one of the most crucial contributing factor in the downstream performance of MLLMs. However, in our humble opinion, it is hard to single out the impact of the scale of training data on the downstream performances, since the scale of data is entangled with many design choices and hyper-parameter settings in training large models, such as the data composition during supervised fine-tuning, model architecture (the visual backbone and the language model), training strategy (freezing or training the visual backbone and the language model), etc. In order to compare with existing connector structures used in modern MLLMs (e.g., Qwen and VILA), we categorize them into two groups: - linear projection based MLLMs (e.g., LLaVA, VILA, DeepSeek-VL, etc.), - and resampler based MLLMs (e.g., Qwen and mPLUG-Owl2). The downstream performances of these two types of connectors are compared with Chain-of-Sight in Table 2 and Table 3, with identical training configurations, including the training data in pre-training and fine-tuning, the visual backbone, the language model, and the training strategy. \| Method \| time \| # PT/SFT Tks. \| Res. \| Cap \| VQA \| Text \| MMB \| POPE \| SEED-I \| Avg performances \| \| ------ \| ---- \| ------------- \| ---- \| --- \| --- \| ---- \| --- \| ---- \| ------ \| ---------------- \| \| Linear \| 0.82x \| 256/256 \| 224 \| 111.8 \| 72.4\| 84.4 \| 67.9\| 83.2 \| 66.3 \| 84.24 \| \| CoS \| 0.42x \| 80/80 \| 224 \| 111.1 \| 72.3\| 84.6 \| 68.6\| 84.4 \| 64.6 \| 84.09 (-0.15) \| \| CoS \| 0.42x \| 80/336 \| 224 \| 112.7 \| 72.6\| 86.4 \| 69.2\| 84.8 \| 65.9 \| 85.10 (+0.86)\| \| Method \| time \| # PT/SFT Tks. \| Res. \| Cap \| VQA \| Text \| MMB \| POPE \| SEED-I \| Avg performances \| \| ------ \| ---- \| ------------- \| ---- \| --- \| --- \| ---- \| --- \| ---- \| ------ \| ---------------- \| \| Resampler \| 1.00x \| 336/336 \| 448 \| 113.4 \| 71.4\| 98.4 \| 66.9\| 85.3 \| 66.2 \| 86.76 \| \| CoS \| 0.42x \| 80/336 \| 448 \| 115.5 \| 73.3\| 100.8\| 70.2\| 85.9 \| 66.4 \| 88.63 (+1.87) \| \| CoS \| 0.42x \| 80/1296 \| 448 \| 115.7 \| 74.0\| 101.3\| 70.3\| 86.4 \| 67.5 \| 89.13 (+2.37)\| Note 1: The number of VQA here is different from the ones in Table 4 as the VQA in Table 4 did not take ScienceQA into account. Note 2: The average performances of Captioning, VQA, and Text, as well as the overall average performances are calculated based on the results in Table 2. From the above tables, we can observe that under the same configurations, Chain-of-Sight outperforms both linear projection and resampler based methods. Q2. Differences in the convergence speed of different compound scaling strategies. Counter-intuitively, we find different compound scaling strategies lead to a similar convergence speeds during the fine-tuning process, despite the huge differences in the downstream performances. Nevertheless, the model with more visual tokens and higher resolutions generally achieve a lower loss throughout the fine-tuning process. Q3. Interpolation of positional embeddings whtn increasing the input resolution. Yes, the positional embeddings in the pre-trained CLIP backbone are interpolated when we increase the input resolution to 448. Q4. Refering to Table 3 instead of Table 6 in Line 222. Yes, we meant to refer to Table 3 in Line 222. We will correct this in our revisions. --- Rebuttal Comment 1.1: Title: Response to the authors' rebuttal Comment: Thank you for providing the detailed answers. My concerns have been resolved and the rating of 7 is maintained. Good luck!	Summary: This paper proposed a post-pretrain token scaling strategy, Chain-of-Sight, to accelerate the pre-training of Multimodal Large Language Models (MLLMs). Through the proposed method, the authors were able to achieve a significant improvement in pre-training speed. The authors confirmed through an ablation study that the proposed method exhibits performance similar to existing approaches. Strengths: The paper is well-written, clearly and coherently presenting ideas. The proposed method demonstrates performance similar to or better than existing methods, despite having shorter training times. An ablation study was conducted across various tasks and settings. Weaknesses: The paper only includes experimental results using CLIP-ViT-L/14 as the visual encoder and Vicuna. Experimental results based on other models are needed. The explanation of how the number of tokens during pre-training and fine-tuning (e.g., PT:80 FT: 1296) was determined is insufficient. Technical Quality: 3 Clarity: 3 Questions for Authors: see weakness. Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The authors addressed both the limitations and potential negative social impacts in Section 5 (Conclusion) and Section A (Broader impact). Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Q1. Experimental results based on other models. Thank you for the constructive comment. We provide experimental results based on different language models in the following table, which shows Chain-of-Sight benefits from stronger language models. \| Language model \| # PT/SFT tks. \| Caps \| VQA \| Text \| MMB \| POPE \| S-I \| Avg performance \| \| -------------- \| ------------- \| ---- \| --- \| ---- \| --- \| ---- \| --- \| --------------- \| \| vicuna-v1.3 \| 80/336 \| 115.5 \| 73.3\| 100.8\| 70.2\| 85.9 \| 66.4 \| 88.63 \| \| vicuna-v1.5 \| 80/336 \| 115.0 \| 73.8\| 99.9 \| 70.9\| 85.4 \| 67.2 \| 88.68 \| \| llama3 \| 80/336 \| 114.1 \| 75.8\| 101.9\| 75.7\| 85.6 \| 72.4 \| 90.26 \| Note 1: The number of VQA here is different from the ones in Table 4 as the VQA in Table 4 did not take ScienceQA into account. Note 2: The average performances of Captioning, VQA, and Text, as well as the overall average performances are calculated based on the results in Table 2. To validate the effectiveness of Chain-of-Sight, we also performed ablation studies with Llama-3-8B, where various nubmers of tokens are used during supervised fine-tuning. The table below shows that the compound scaling strategy effectively improves the downstream performance. Since the pre-training takes long for resampler-based (336 tokens) and linear-based models (256 tokens), we only validate the effectiveness of the compound scaling here, and leave the baseline results to our revisions. \| Language model \| # PT/SFT tks. \| Caps \| VQA \| Text \| MMB \| POPE \| S-I \| Avg performance \| \| -------------- \| ------------- \| ---- \| --- \| ---- \| --- \| ---- \| --- \| --------------- \| \| llama3 \| 80/80 \| 113.1 \| 75.0 \| 100.2\| 74.3\| 85.5 \| 70.3 \| 89.14 \| \| llama3 \| 80/336 \| 114.1 \| 75.8 \| 101.9\| 75.7\| 85.6 \| 72.4 \| 90.26 \| \| llama3 \| 80/1296 \| 114.7 \| 76.3 \| 103.9\| 76.4\| 86.6 \| 73.5 \| 91.11 \| In addition, we also go through the whole training process with different language models, which includes the stage 1 pre-training, high resolution post pre-training, and multi-task supervised fine-tuning. \| Language model \| # PT/SFT tks. \| VQAv2 \| GQA \| SQA_I \| TextVQA \| POPE \| MME \| MMB \| SEED_I \| MMMU \| \| -------------- \| ------------- \| ----- \| --- \| ----- \| ------- \| ---- \| --- \| --- \| ------ \| ---- \| \| vicuna-v1.3 \| 80/1296 \| 82.9 \| 63.2\| 91.6 \| 65.3 \| 85.0 \| 1474/264 \| 72.5 \| 67.5 \| 34.1 \| \| vicuna-v1.5 \| 80/1296 \| 82.9 \| 64.0\| 93.9 \| 65.1 \| 85.9 \| 1549/301 \| 72.8 \| 68.9 \| 35.4 \| \| llama3 \| 80/1296 \| 84.3 \| 65.3\| 95.7 \| 67.6 \| 86.9 \| 1598/308 \| 76.6 \| 73.1 \| 39.7 \| We will include results based on other language models and visual backbones in our revisions. Q2. Explanation on how the numbers of tokens during pre-training and fine-tuning are determined. Because of the size of a large model and the scale of training data, it would be infeasible to do a grid search on the number of tokens. Therefore, the model hyperparameters including the window sizes and the number of visual tokens are determined under several key rationals. Pre-training. In the pre-training stage, we employ the resolution of 224, which gives us the feature of size 16x16. Window sizes. Since the main objective of Chain-of-Sight is to accelerate pre-training by reducing the number of tokens during pre-training, we limit the number of visual scale hierachies to two, i.e., one global view (window size 16) and one local view (window size 4). Token counts. Features with larger window sizes are usually more informative w.r.t. image contents, thus requiring more visual tokens to represent. For efficiency, we intuitively selected 16 visual tokens for encoding the global view (instead of 32 as used in BLIP-2 or more). As for the token counts in the local view, we have experimented with 1, 2, and 4 per window, as in Table 2 and 3. Eventually, we use 4 tokens per window for the local view, which strikes a good balance between the training speed and downstream performance. Supervised fine-tuning. As mentioned in the manuscript, given a pre-trained Chain-of-Sight model, there are two ways of scaling up the number of tokens, i.e., increasing the resolution and reducing the window sizes, respectively. Both methods can increase the token counts by 4 times for a specific pre-trained window size, producing a 16x token count for each window size, where 80 tokens are scaled up to 1280 tokens. In addition, we keep a copy of 16 global tokens for providing a comprehensive overview of the input image, resulting in a total number of 1296 tokens. We provide a detailed calculation of the number of tokens in both stages in the table below. Detailed explanation on the choice of model hyperparameters will be included in our revisions. \| Stage \| Feature size \| Win size \| # windows \| # tks. per win \| # tks. in total \| \| - \| -- \| - \| - \| -- \| - \| \| Pretrain \| 16x16 \| 16x16 \| 1\| 16 \| 16\| \| \| \| 4x4 \| 16 \| 4 \| 64 \| \| \| \| \| \| Pretrain total \| 16+64=80 \| \| Fine-tune \| 32x32 \| 32x32 \| 1\| 16 \| 16\| \| \| \| 8x8 \| 16 \| 16 \| 256 \| \| \| \| 2x2 \| 256 \| 4 \| 1024 \| \| \| \| \| \| Fine-tune total \| 16+256+1024=1296 \|	Summary: 1. This work proposes Chain-of-Sight, a training method of MLLM that leverages global and local visual contexts effectively. 2. To boost efficiency in the pretraining stage, the authors propose a post-pretrain token scaling strategy. During the pretraining state, it requires significantly fewer visual tokens and cuts down the wall-clock training time by 73% in the pretraining stage. To effectively increase tokens during fine-tuning stage to enhance performance, they propose a compound strategy by manipulating input resolution and window size at the same time. 3. When both use the same number of tokens during fine-tuning, the results achieved by the Chain-of-Sight model pre-trained with 32 tokens match or surpass those obtained using 336 visual tokens throughout the training process. Strengths: 1. The writing is mostly clear and easy to follow, except for the compound scaling part where a clearer illustration is suggested. 2. Comprehensive ablation study. Variations of pretraining token number / pretraining strategy(CoS, Resample) / FT are compared on various tasks including image captioning, visual question answering, text recognition, referring expression comprehension, etc. 3. According to Table 5, CoS-7B achieves good results on VQA benchmarks compared to 7B-level baselines. Weaknesses: 1. The method of hierarchical (multi-scale) visual input has already been explored in many former works, which is contradictory to the expression in L91-92 "Despite this, the potential for harnessing multi-scale visual hierarchies remains under-explored in the context of MLLMs". For example, LLaVA-NeXT [1] and InternLM-XComposer2-4KHD [2] both adopted multi-scale strategies and proved their effectiveness. 2. There are mistakes in the table of experiment results. For example, in Table 3, RefCOCO+, test-A, the second-best one should be 90.57. [1] Liu, Haotian, et al. "LLaVA-NeXT: Improved reasoning, OCR, and world knowledge." https://llava-vl.github.io/blog/2024-01-30-llava-next/ [2] Dong, Xiaoyi, et al. "Internlm-xcomposer2-4khd: A pioneering large vision-language model handling resolutions from 336 pixels to 4k hd." arXiv preprint arXiv:2404.06512 (2024). Technical Quality: 2 Clarity: 2 Questions for Authors: 1. In Table 2 and Table 3, why are many of the results of "CoS, pre-train 80, FT 336" better than those of "CoS, pre-train 336, FT 336"? Analysis or explanations are suggested. 2. The settings of ablation experiments are not explained. Is that the same as sec 3.1 training settings? If so, why do the results in Table 5 not agree with those in Table 2&3&4? Confidence: 4 Soundness: 2 Presentation: 2 Contribution: 2 Limitations: The experiment is only conducted on 7B-level model with PEFT. Larger scale model with full-parameter training is suggested to prove its effectiveness and extensibility in modern pretraining. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Q1. The method of hierarchical (multi-scale) visual input has already been explored in many former works, such as LLaVA-NeXT and InternLM-XComposer2-4KHD. The multi-scale nature is the fundamental characteristic of images manifested by David Marr's pioneering work on vision perception back in 1970s. How to exploit the multi-scale nature effectively has been a key research topic in most vision tasks, if not in all tasks, for half a century, which is likely to continue to be an active research topic in future decades. Thanks for raising this point and we are happy to discuss the differences in the multi-scale strategy between Chain-of-Sight and the methods used in LLaVA-NeXT and InternLM-XComposer-4KHD, in the following three aspects. Conceptual idea Both LLaVA-NeXT and InternLM-XComposer-4KHD process the high-resolution input image in two paths. One splits the high-resolution image into partitions of sub-images with a 'base resolution' supported by the backbone, which is 336 for both methods. The other resizes the high-resolution image to 'base resolution' to be processed by the backbone. The multi-scale idea is exploited on the input side before the visual backbone, which is similar to the multi-resolution/multiview strategy [1,2,3]. Differently, inspired by the pyramid structure in contemporary vision models [4,5,6], our Chain-of-Sight method constructs in-model multi-scale features, where multi-scale visual prompts are generated after the visual backbone based on the features of a single 'base-resolution' image. Hence, our method of leveraging multi-scale hierarchy is in parallel with the multi-view method used in LLaVA-NeXT and InternLM-XComposer-4KHD, and it is possible to combine both methods to achieve even stronger visual capabilities. Motivation The motivations of LLaVA-NeXT and InternLM-XComposer-4KHD are to enable MLLMs for capturing more details in the high-resolution images, while Chain-of-Sight is proposed to leverage the flexiblity of our multi-scale visual resampler such that the pre-training could be accelerated with lower nubmer of visual tokens without compromising performance. Methodological details In terms of the methodological details, both LLaVA-NeXT and InternLM-XComposer-4KHD leverages a two-level visual hierarchy, i.e., the global and local views. Though Chain-of-Sight splits the input image into global and local windows in the pre-training, it is able to be extended to three or more scale levels during fine-tuning thanks to the compound scaling strategy of Chain-of-Sight. In addition, we would like to highlight that, as mentioned in Sec 2.3, LLaVA-NeXT and InternLM-XComposer-4KHD can be considered as a special case of our compound scaling, where only the resolution of the input image is scaled up, while the window size is kept the same. More details will be provided in our revisions. [1] Karpathy, Andrej, et al. "Large-scale video classification with convolutional neural networks." In CVPR 2014. [2] Yan, Shen, et al. "Multiview transformers for video recognition." In CVPR 2022. [3] Feichtenhofer, Christoph, et al. "Slowfast networks for video recognition." In ICCV 2019. [4] Lin, Tsung-Yi, et al. "Feature pyramid networks for object detection." In CVPR 2017. [5] Wang, Wenhai, et al. "Pyramid vision transformer: A versatile backbone for dense prediction without convolutions." In ICCV 2021. [6] Liu, Ze, et al. "Swin transformer: Hierarchical vision transformer using shifted windows." In ICCV 2021. Q2. Mistakes in the experiment section. Thank you. We will re-examine the manuscript and correct the mistakes. Q3. Why is "CoS, PT80, FT336" stronger than "CoS, PT336, FT336"? It is indeed the case. Though the performances of the two variants are similar on referring expression comprehension, "CoS, PT336, FT336" underperforms "CoS, PT80, FT336" in almost all the other aspects. \| Model \| Caps \| VQA \| Text \| MMB \| POPE \| S-I \| Avg (Table 2) \| Avg (Table 3) \| \| ----- \| ---- \| --- \| ---- \| --- \| ---- \| ------ \| ------------- \| ------------- \| \| CoS, PT80, FT336 \| 115.5 \| 73.3 \| 100.8 \| 70.2 \| 85.9 \| 66.4 \| 88.6 \| 86.19 \| \| CoS, PT336, FT336 \| 113.9 \| 72.8 \| 97.1 \| 68.7 \| 84.2 \| 66.9 \| 87.2 \| 86.25 \| Note 1: The number of VQA here is different from the ones in Table 4 as the VQA in Table 4 did not take ScienceQA into account. Note 2: The average performances of different tasks and the overall average performances are calculated based on the results in Table 2. We believe the reason behind this is that the low capacity of the "CoS, PT80" model during pre-training acts as a filtering mechamism for the noisy data, which allows it to learn the more commonly existing distributions in the pre-training data. Specifically, we find the pre-training loss of "CoS, PT336" lower than "CoS, PT80", while the fine-tuning loss of "CoS, PT336, FT336" is notably higher than "CoS, PT80, FT336". Given the higher level of noise in the pre-training data, we believe the higher capacity of "CoS, PT336" model makes it learn more low-quality data than the "CoS, PT80" model, leading to the worse downstream performance of the "CoS, PT336, FT336" model. In fact, similar phenomenon can be observed with resampler-based model. As in Table 2, the average performance of "Resampler, PT80, FT 400" is also 0.6 higher than "Resampler, PT336, FT336". Q4. The results in Table 5 is different from that in Table 2&3&4. Yes, the training settings are different between our final model and the models in the ablation studies. The model in Table 5 is trained with an additional post-pre-train high-resolution stage, while for ablations, we skip this stage for efficiency, as mentioned in L184. We will make this clearer in our revision. Q5. Larger scale model with full-parameter training. Limited by time, we are unable to finish training large-scale model with full-parameter training. We will include the results in our revisions. --- Rebuttal Comment 1.1: Comment: Thanks for your reply, my concerns have been partially solved. However, I'm still concerned about the limited technical novelty (Q1), and the effect on larger-scale model or full-parameter training. Therefore, I would raise my score a bit but still be on the borderline (Please consider my score to be 4.5).	null	null	Rebuttal 1: Rebuttal: We genuinely appreciate the reviewers for dedicating their time and effort to review our manuscript and providing valuable comments and insights. We are encouraged by the reviewers' assessment that 1. Our work addresses a crucial challenge in MLLM development: the computational cost of pre-training (Q826). 2. Our proposed method, Chain-of-Sight - is a novel combination of multi-scale visual processing and token scaling, addressing a critical efficiency bottleneck in MLLM pre-training (Q826). - reduces the wall-clock training time by 73% for MLLMs without sacrificing performance (TSJ3 and Q826). - demonstrates performance similar to or better than existing methods (TSJ3 and cV6y). 2. Our experiments are comprehensive and extensive, which are able to support our claims (TSJ3, cV6y, and Q826). 3. The writing is easy to follow (TSJ3). The manuscript is well-written (cV6y) and well-organized (Q826). We are committed to addressing the limitations and concerns raised by the reviewers within the specified time frame. We believe that doing so will significantly improve the quality of our manuscript. Below, you will find detailed responses to the questions and comments raised by each reviewer.	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Causal Imitation for Markov Decision Processes: a Partial Identification Approach	Accept (poster)	Summary: This paper studies causal imitation learning from the perspective of partial identification. First, the authors show a hardness result that when both the transitions and the rewards are confounded, it is not possible to imitate or improve over the expert policy. Going forward, under only reward-confounding or transition-confounding, a new imitation learning objective is proposed using the partial identification bound of the corresponding non-identifiable unknowns, and it is proved that once the objective is optimized under $0$, the learned imitation policy would improve over the expert policy. Experimental result justifies the theoretical findings. Strengths: Orginality and Significance: The idea of partial identification in causal imitation learning is somehow new. The main results are also quite theoretically sound. Quality and Clarity: The paper is well written. The conclusions and the findings are clearly presented. Weaknesses: 1. The idea seems like a relatively direct extension of the standard imitation algorithm (e.g., GAIL) with the partial identification method from the causal inference literature. 2. Theoretically, it is still unknown when can we guarantee that the imitator can beat the expert. According to Theorem 2 (resp. Theorem 3), only when the optimization problem (14) (resp. (21)) has solutions with non-positive value would the imitator policy be guaranteed to achieve the same performance or improve over the expert policy. Is it possible to derive hardness results that in the reward-confounding-only case (or the transition-confounding-only case) there still exists instances such that it is impossible to improve over the expert? Technical Quality: 2 Clarity: 3 Questions for Authors: 1. The derivation of the partial identification bound, which is central to the method proposed in this work, is missing. I suggest clearly include them in the appendix to make the argument self-content and more convincing, or at least make it clear how the conclusion is made given the existing literature like [27]. 2. How to principally specify the (observational) reward function class $\mathcal{R}$ under the unobserved confounding? That is, since the underlying SCM is not known to the agent a priori, how to equip the learning agent a suitable function class $\mathcal{R}$ to match the observational reward function of the unknown SCM? 3. When the algorithm is applied to a non-confounded MDP (i.e., a standard MDP), how well would the algorithm perform when compared with prior arts designed for non-confounded MDPs? More generally, it seems unknown that how the performance of the proposed algorithms would change w.r.t. the confoundedness of the underlying MDP, e.g., how far the interventional probabilities deviate from the observational probabilities. 4. In Theorem 1, according to the proof, it seems essential to assume that all the observational probabilities $P(X,S,Y)$ are positive, which seems too strong an assumption. What if one drop this assumption? Does the conclusion change drastically? 5. Some minor typos: - In the last line of the footnote in the end of page 3, the first equation should be $P_{\pi}(s_{t+1}\|s_t,x_t) = P_{x_t}(s_{t+1}\|s_t)$. - The imitator's policy $\pi$ appearing in the subscript of $\rho$ is in a bold font but sometimes not, which is not consistent. Confidence: 2 Soundness: 2 Presentation: 3 Contribution: 2 Limitations: Please see the weakness section and the question section above. Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: > _“extension of the standard imitation algorithm (e.g., GAIL) with the partial identification method”_ Firstly, applying partial identification to IL is nontrivial due to the complex interplay between unobserved confounders and the dynamics of MDPs. Partial identification typically deals with static settings in causal inference, but MDPs introduce a temporal dimension where past actions and states can influence future outcomes. Our work extends these methods to handle such temporal dependencies, which involves significant theoretical innovation. Our proposed algorithms might appear neat and straightforward in their final forms, but this does not mean their derivations are simple. The causal bounding results in Eqs. 9-10 are only applicable to a single time step in MDP. Our contribution significantly extends these bounds across time steps, creating a robust framework that can handle the sequential nature of decision-making in practice, where each decision can influence subsequent states and rewards. We also apply special transformations so that they are tailored to GAIL’s training process. We invite the reviewer to check the Appendix and see if our statement is factual. --- > _“hardness results that in the reward-confounding-only case (or the transition-confounding-only case) there still exists instances such that it is impossible to improve over the expert?”_ Yes, it is possible. Consider the reward-confounding case as an example. One could construct an MDP model which consists of a sequence of independent contextual bandit models with side information $S_1, S_2, \dots, S_t$. For each contextual bandit model, given any context $s_i$, the expected reward of each arm matches the worst-case lower bound $E[Y_i \| s_i, x_i]P(s_i\|x_i)$. It follows from Example 1 that the imitator in this worst-case model is unable to improve over the expert’s performance. --- > _“The derivation of the partial identification bound ...”_ Thanks for the suggestion. The causal bounds in Eqs. 9-10 follow application of (Manski, 90). More specifically, Manski studies a canonical decision setting where $Z$ represents the context, $X$ is the treatment, and $Y$ is the primary outcome. Manski showed that for any observational distribution $P(X, Y, Z)$, the treatment distribution of intervening on $X$ is bounded by $P(y, x\|z) \leq P_x(y\|z) \leq P(y, x\|z) + P(\neg x \|z)$. To derive Eqs. 9-10, one could focus on the MDP within one timestep $t$. Applying Manski’s bound by setting $S_t$ as the context, $X_t$ as the treatment, and $S_{t+1}$ (or $Y_t$) as the primary outcome leads to the statement. We will include additional discussion in the updated manuscript. --- > _“How to principally specify the (observational) reward function class $\mathcal{R}$ under the unobserved confounding? That is, ..., how to equip the learning agent a suitable function class $\mathcal{R}$ to match the observational reward function of the unknown SCM?”_ We do not require the learner to specify the reward function class $\mathcal{R}$ over the interventional reward $E_x[Y\|s]$, but only the observational quantity $E[Y\|s, x]$. The observed domain of the state-action pair $(s, x)$ is well-specified and can be determined from the demonstration data. In this case, any measurable observational reward $E[Y\|s, x]$ can be approximated using some non-parametric function approximators, e.g., neural networks (NNs). The learner could start with a parametric family of NNs, and further restrict it to inject domain knowledge. --- > _“When applied to a non-confounded MDP (i.e., a standard MDP), how well would the algorithm perform when compared with prior arts designed for non-confounded MDPs? ... How far the interventional probabilities deviate from the observational probabilities.”_ For a standard MDP with no unobserved confounding, our algorithm could obtain a policy that is less effective compared to the one learned by the prior arts. The performance gap depends on how close the causal bounds are to the ground-truth interventional probabilities. However, we view this as a feature of our methods. When there is no unobserved confounding in the environment, we recommend the imitator to follow standard imitation learning procedures. When the imitator cannot exclude the unobserved confounding prior, our method obtains an imitating policy with performance guarantee. Our algorithms learn a policy by searching over the worst-case model. We believe this risk-averse approach is principled when facing uncertainty in offline imitation learning, since other models could deviate significantly from the ground-truth, leading to significantly inferior performance. --- > _“In Theorem 1, ... $P(X, S, Y)$ are positive, ... What if one drop this assumption? Does the conclusion change drastically?”_ We require the probabilities $P(X, S, Y)$ to be positive to exclude degenerated cases that the imitator and the expert performance happen to match. As mentioned in L518-520, "In some degenerated cases when $\mathbb{E}\_{\pi}[Y_{t} \mid s\_{t}] = 0$ and $\mathbb{E}[Y\_{t} \mid s\_{t}] = 0$, it might coincidentally follow that $V\_{\pi}(s_{t}) = 0$, which is equal to $V(s\_{t}) = 0$.” However, such occurrences are highly impossible in practical scenarios, and are statistically insignificant (measure zero) when one generates MDP instances uniformly at random. Moreover, from an algorithmic perspective, focusing on degenerate cases would divert focus from more prevalent and practically significant scenarios. As the experiment shown within Fig.4 (a), we have randomly generated over $1000$ MDP instance, and in all cases, the minimal performance gap between the imitator and the expert is negative, i.e., the imitator is unable to achieve the expert’s performance. This empirical evidence further supports the assertion that such degenerate cases, while theoretically possible, are exceedingly rare and do not affect the general applicability and robustness of our proposed methods. --- Rebuttal Comment 1.1: Comment: Thank you very much for your detailed responses! However, I still remain concerned with the soundness of the proposed algorithm. For example, while I agree with the author that the reward function class is to approximate the observed rewards, I am concerned with how the unobserved hidden (unknown) causal structure would affect the performance. More broadly, it is still unknown when can we guarantee that the imitator given by the algorithm can beat the expert, theoretically. This is less discussed even under a suitable theoretical assumption. Given such concerns, I would maintain my score and still recommend rejection of this paper. I suggest further refinement of the work for publication. --- Reply to Comment 1.1.1: Comment: > _"More broadly, it is still unknown when can we guarantee that the imitator given by the algorithm can beat the expert, theoretically."_ This condition depends on the quality of the demonstration data and the prior knowledge of the latent reward. For example, when there is no unobserved confounding, one could show that the imitator is guaranteed to perform at least as well as the expert. We acknowledge that deriving closed-form solutions for the improvement condition is an exciting problem. However, we would like to note that our proposed algorithms do provide a numerical condition for policy improvement, similar to the standard inverse RL methods like GAIL. When our proposed algorithm returns the game $\nu^* < 0$, the learned policy is robust and guaranteed to outperform the expert. One could find such instances in Figure 4 (b-c). --- Rebuttal 2: Comment: Thanks for taking the time to read the paper and your reviews. We recognize the importance of integrating a theoretical framework based on causality into IRL, especially when either the transition dynamics, the reward function, or both, are confounded. Below, we provide further clarification on our contributions, theoretical contributions and the experimental design to enhance understanding and address your concerns effectively.	Summary: The paper addresses challenges in imitation learning when the learner and expert have mismatched sensory capabilities and demonstrations are contaminated with unobserved confounding bias. The authors propose robust imitation learning within the framework of Markov Decision Processes (MDPs) using partial identification. They demonstrate that in the presence of unobserved confounders, learning a policy that guarantees expert performance is generally infeasible. The paper introduces two novel algorithms for imitation learning in partially identifiable settings—when either the transition distribution or the reward function is non-identifiable. These algorithms, based on augmentations of the Generative Adversarial Imitation Learning (GAIL) method, are designed to achieve expert-level performance even with confounded data. Strengths: 1. Interesting Problem: The paper studies the partial identification problem in imitation learning in sequential decision making. This problem is interesting and has not been investigated before. 2. Systematic Theoretical Investigations: The paper conducts systematic theoretical investigations on the partial identification problem in imitation learning, including three cases: non-identifiable transition and reward, identifiable transition and non-identifiable reward, non-identifiable transition and identifiable reward. The theoretical results demonstrate the infeasibility in the fully identifiable setting and the feasibility of the proposed approach in partially identifiable settings. Weaknesses: 1. Assumptions and Generalization: The approach relies on certain assumptions about the partial identifiability of the MDP. In practice, these assumptions might not always hold. Even if these assumptions hold, one may not know the type of partial identification in advance, potentially limiting the generalizability of the methods. 2. Complexity and Practicality: The proposed method CAIL-$\mathcal{T}$ requires solving a complex constrained optimization problem in Eq. (18) and Eq. (19). It is difficult to solve this optimization problem in practice when neural networks are employed. 3. Missing Experimental Details: The paper does not provide details about the implementation of the proposed algorithm and the environments. Besides, the source code is also missing. As such, it is difficult to reproduce their experiments. Technical Quality: 3 Clarity: 3 Questions for Authors: Please see the detailed review in the Weakness part. Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: The authors have thoroughly discussed the limitations of this paper. Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We sincerely thank your reviewers and recognize that certain elements of our work might have been misunderstood, which could have influenced the evaluations. Below, we aim to clarify these aspects and remain eager to engage in further dialogue to resolve any lingering doubts. Generally, we have validated the proposed algorithms across a broad range of practical scenarios, including SCMs with various reward functions and transition dynamics, driving, and healthcare, where the proposed algorithms have demonstrated significant improvements in decision-making outcome performance. --- > _“Assumptions and Generalization: The approach relies on certain assumptions about the partial identifiability of the MDP. In practice, these assumptions might not always hold. Even if these assumptions hold, one may not know the type of partial identification in advance, potentially limiting the generalizability of the methods.”_ Standard imitation learning in MDPs assumes both the Markov property (Assumption 1) and Causal consistency (Assumption 2) in the demonstration data. In this paper, we generalize the second assumption as we allow the presence of unobserved confounding or violation of overlap. This means that our proposed methods are applicable to all standard MDP instances, and also generalize well to confounded MDPs where standard imitation learning methods do not necessarily obtain a valid solution. Given the wide adoption of MDPs and imitation learning, and the prevalence of unobserved confounding bias, we strongly believe our proposed method could be applied in many real-world scenarios, e.g., autonomous driving and healthcare. Table 1 provides a recipe for applying our methods in practice, given the violations of assumptions. First, when Assumption 2 holds and there is no unobserved confounder, the standard imitation learning algorithm obtains an effective policy. When there exist unobserved confounders affecting both the reward function and transition distribution (i.e., both equations in Assumption 2 do not hold), the expert performance is not imitable and the learner should explore additional domain knowledge. When unobserved confounders only affect either the reward function or transition distribution, the imitator could apply our proposed method and obtain a robust policy with performance guarantee. --- > _“Complexity and Practicality: The proposed method CAIL-T requires solving a complex constrained optimization problem in Eq. (18) and Eq. (19). It is difficult to solve this optimization problem in practice when neural networks are employed.”_ We have developed specific methodologies to address these challenges. As outlined in Alg. 3 (see Appendix) and further elaborated in Thm. 3, our approach employs a structured algorithm designed to effectively navigate the optimization landscape. Specifically, as stated in L566-568, “The intuition for Alg. 3 is: in order to find the worst case, we need to put as less transition probability mass as possible to the state with maximal values, and allocate higher transition probabilities to states with smaller values.” Moreover, with some approximation techniques (Xia et al. (2023)), it is possible to solve it with NNs. To substantiate the practical applicability of our methods, we have conducted experiments focusing on Driving scenarios (L300-312). These experiments, detailed in Appendix C, successfully implement the proposed framework using neural networks and demonstrate its effectiveness and efficiency in real-world settings. These results underscore our method's viability and its capability to handle the complexities associated with neural network-based implementations. --- > _“Missing Experimental Details: The paper does not provide details about the implementation of the proposed algorithm and the environments. Besides, the source code is also missing. As such, it is difficult to reproduce their experiments.”_ We would like to clarify that our paper has indeed included a comprehensive description of the theoretical framework, algorithms, and step-by-step procedures required to understand and implement the proposed method. Theoretical contributions are summarized in Sec. 2 and 3, and further elaborated in Appendix A and B. Experimental and implementation details are provided in Section 4 and further elaborated in the supplementary materials (Appendix C). These environments are common in the causal imitation learning literature, ensuring that our experiments could be easily replicated. As mentioned in the checklist, we will open-source our codebase upon acceptance of our paper. --- Rebuttal Comment 1.1: Comment: Thanks a lot for the detailed responses. Regarding the first question, it seems that the response from the authors does not address my concern. My concern here is that, in practice, we typically do not know in advance which type of assumption the underlying task satisfies. For instance, whether the underlying reward function is identifiable or not. In that case, it remains unclear how to choose their methods to solve the task. --- Reply to Comment 1.1.1: Comment: We thank the reviewer for the response. Since the discussion phase is coming to an end, we would like to summarize below the logic behind our model assumptions and how they compare to standard imitation learning methods. 1. Standard imitation learning: Markov Property (Definition 1) + Unconofundedness (Definition 2); 2. Our approach: Markov Property (Definition 1). As described above, our model only relaxes existing assumptions in the standard setting and, therefore, is more general, subsuming the standard imitation learning. When the imitator has strong knowledge about the MDP environment and is confident about unconfoundedness, it should follow the standard imitation algorithms and obtain a solution. When the imitator is unsure about the unconfoundedness assumption, it could still apply our method and obtain a robust policy with a performance guarantee. Given the wide applications of existing imitation learning methods and the relaxation of the critical assumption of unconfoundedness, our results could be generalized to many practical domains.	Summary: The paper addresses the challenges in imitation learning when expert demonstrations are contaminated with unobserved confounding bias. It proposes robust imitation learning methods within the framework of MDPs using partial identification techniques. The authors demonstrate theoretically that when unobserved confounders exist, learning a robust policy to achieve expert performance is generally infeasible. They introduce two novel causal imitation algorithms to handle settings where either the transition distribution or the reward function is non-identifiable from the available data. The proposed methods are validated through experiments, showing their effectiveness in achieving expert-like performance in the presence of unobserved confounders. Strengths: 1. The paper tackles the issue of unobserved confounders in imitation learning, which is a significant challenge in practical applications. 2. The paper provides theoretical foundations, demonstrating the infeasibility of achieving expert performance with unobserved confounders and offering rigorous proofs for the proposed algorithms. 3. The introduction of two novel causal imitation algorithms (CAIL-$\mathcal{R}$ and CAIL-$\mathcal{T}$) enhances the robustness of policy learning in settings where either the transition distribution or the reward function is non-identifiable. Weaknesses: The experiment evaluation seems insufficient considering that there are already some causal imitation learning baselines such as [1], and some more experiment environments such as OpenAI gym for imitation learning. [1] P. de Haan, D. Jayaraman, and S. Levine. Causal confusion in imitation learning. In Advances in Neural Information Processing Systems, pages 11693–11704, 2019. Technical Quality: 3 Clarity: 2 Questions for Authors: On what tasks are these approaches experimented on, what do these tasks look like, and how does the demonstration data look like? Will the model performance change with a varying number of expert demonstrations? Confidence: 4 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: The limitations have been discussed in the paper. Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We appreciate your reviews and acknowledge that some aspects of our work might have been misunderstood. Below, we provide clarifications and are open to further discussions should there be any residual concerns. Our experimental design incorporated similar baselines from Zhang et al. (2020), Kumor et al. (2021), and Ruan et al. (2023), chosen for their direct relevance to our framework. The rationale behind this selection was to showcase the potential of partial identification techniques in improving algorithms such as GAIL. These enhancements are particularly important for achieving expert-level performance despite differences in the observation spaces of the imitator and expert—an aspect often overlooked in OpenAI Gym environments. Most current setups in these environments presuppose identical observation spaces and ignore the presence of unobserved variables, both of which are addressed in our study. --- > _“The experiment evaluation seems insufficient considering that there are already some causal imitation learning baselines such as [1], and some more experiment environments such as OpenAI gym for imitation learning.”_ (De Haan et al., 2019) explores the underlying causal relationships in the environment, and exploits the sparsity in these relationships to improve the imitator’s performance. However, their problem setting assumes there is no unobserved confounding in the environment, which is the very motivation and the starting point of this paper. That is, our paper studies the challenges of unobserved confounding for imitation learning in MDPs, which is orthogonal to the setting in (De Haan et al., 2019). Consequently, we did not include (De Haan et al., 2019) in the experiments since their methods and ours are not comparable. We did investigate some existing benchmarks including the OpenAI gym. Unfortunately, as far as we are aware of, no major RL benchmark simulates the presence of unobserved confounding without violating the Markov property. The corresponding causal diagrams of experts are shown in Fig.2 and Fig. 3. Due to these limitations, we have to build novel simulation environments to evaluate our proposed algorithms. Indeed, we intend to release our experiments and hope it could contribute to the existing RL benchmarks by highlighting the challenges of unobserved confounding. We believe that building our own benchmark should be taken as a strength, not a weakness. --- > _”On what tasks are these approaches experimented on, what do these tasks look like, and how does the demonstration data look like? Will the model performance change with a varying number of expert demonstrations?”_ Our learning task is similar to the standard imitation learning setting, where the imitator has access to offline demonstration data generated by an expert. The demonstration data is represented as a collection of sequences of trajectories in an MDP. For every sequence, it contains a finite number of state-action pairs $(s_j, x_j)$; the reward signal $y_j$ is not observed. The main difference is that we consider settings where the demonstration data could be contaminated with confounding bias; unobserved confounders exist affecting the action $X_j$, subsequent state $S_{j+1}$, and reward $Y_j$ (had it been observed). Specifically, as shown in previous research (Ruan et al. 2022), there exist lots of unobserved variables in real-world human driving datasets, e.g., road conditions. As stated in the driving experiment (L300-312), expert demonstrations include vehicle trajectories, “The state $S_t$ contains some critical driving information, e.g., the velocities of the ego vehicle and the leading vehicle and the spatial distance between them. The action $X_{t}$ represents acceleration or deceleration decisions the ego vehicle makes. The unobserved variable $U_{t}$ represents some information accessible to the expert but inaccessible to the imitator, e.g. slippery road conditions [24].” The details of our medical treatment experiments can be found in L313-325. Due to challenges caused by the confounding bias existing in expert demonstrations, our paper assumes that the imitator has access to sufficiently much demonstration data. We acknowledge that quantifying the uncertainty due to finite samples in imitation learning is an exciting problem, but it is beyond the scope of this paper. --- Rebuttal 2: Comment: Dear AC, Thank you for initiating this discussion. I acknowledge the differences in problem settings between this work and prior efforts (e.g., De Haan et al., 2019). However, I maintain that including additional baselines is essential, given that the underlying structural causal model is unknown a priori to the agent. Incorporating more baselines and discussing their relevance will provide a clearer understanding of the performance of the proposed approaches. --- Rebuttal 3: Comment: Thank you to the authors for the detailed responses. I do recognize the differences in problem settings between this work and previous studies. However, I still believe it is necessary to include additional baselines, especially since the underlying SCM is not known in advance to the agent. Adding more baselines and discussing their relevance will enhance our understanding of how effectively the proposed approaches perform.	null	null	Rebuttal 1: Rebuttal: # Overall Response We appreciate the reviewer’s feedback. We believe that a few misunderstandings of our work led to some of the evaluations being overly harsh and would sincerely ask the reviewers to reconsider our paper given the clarifications provided in the response. We will first address some main comments here and then reply to every reviewer separately. Unobserved Variables and Non-identifiability Unobserved confounders generally exist in demonstrations when the sensory capabilities of the imitator and the expert differ or privacy concerns are serious, e.g., HighD (Krajewski et al., 2018) or MIMIC-III (Johnson et al. 2016). In general, the structural assumptions (e.g., causal diagrams) required to perform causal inferences are inevitable, as shown in (Bareinboim et al., 2022, Theorem 1). Recognizing non-identifiability as a core challenge in causal inference, our approach improves previous partial identification techniques and applies them to sequential decision making settings. Significance and Novelty The central focus of our paper is on exploring the effects of unobserved confounders in imitation learning (IL), an area that, while touched upon, has not been thoroughly explored in existing frameworks. Unlike previous studies such as de Haan et al. (2019), which assume the absence of unobserved confounders, our paper delves into scenarios where either the transition dynamics, the reward function, or both, are confounded (summarized in Table 1). The proposed framework is a substantial deviation from traditional causal imitation learning approaches which often ignore such complexities. Furthermore, standard imitation learning in MDPs assumes both the Markov property (Assumption 1) and Causal consistency (Assumption 2) in the demonstration data. In this paper, we generalize the second assumption as we allow the presence of unobserved confounding or violation of overlap. This means that our proposed methods are applicable to all standard MDP instances, and also generalize well to confounded MDPs where standard imitation learning methods do not necessarily obtain a valid solution. Given the wide adoption of MDPs and imitation learning, and the prevalence of unobserved confounding bias, we strongly believe our proposed method could be applied in many real-world scenarios, e.g., autonomous driving and healthcare. To the best of our knowledge, we are the first to theoretically prove that “when unobserved confounders generally exist, it is _infeasible_ to learn a robust policy that is guaranteed to achieve expert performance from the demonstration data.” Additionally, our comprehensive experiments, which span various reward functions and transition dynamics, support these findings. Such findings are nontrivial, because it helps to explain why in practice lots of imitation learning cannot work very well. Building on the theoretical foundation, to “recover” from the unobserved confounding bias, we have proposed novel imitation learning algorithms using partial identification techniques (as detailed in Alg. 1 and Alg. 2), allowing the imitator to obtain effective policies that can achieve expert performance for different problem settings. The intuition is to optimize the policy within the worst-case environment compatible with the demonstration data and model assumption. Such strategy helps to enhance the robustness and applicability of imitation learning in complex real-world environments. Experiment Baselines In our experimental setup, we've chosen similar baselines from Zhang et al. (2020), Kumor et al. (2021), and Ruan et al. (2023) due to their direct relevance to our experimental framework. This selection is intended to demonstrate how partial identification techniques can enhance existing algorithms like GAIL, helping them achieve expert performance even when the observation spaces between the imitator and expert are different. This is crucial as most existing OpenAI Gym environments do not account for discrepancies between the observation spaces of the expert and the imitator, and assume unobserved variables do not generally exist, which we address in our experiments. Overall, our paper introduces significant theoretical and practical contributions to the field of imitation learning, opening up new pathways for research and application in environments affected by unobserved confounders.	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Rethinking LLM Memorization through the Lens of Adversarial Compression	Accept (poster)	Summary: This paper proposes a new definition of memorization, the Adversarial Compression Ratio (ACR), based on a compression argument. ACR provides an adversarial perspective on measuring memorization, offering the flexibility to assess memorization for arbitrary strings with relatively low computational requirements. Strengths: 1. The authors proposed a new metric to address the challenge of defining memorization for LLMs. This metric provides a simple and practical perspective on what memorization can mean, making it useful for functional and legal analysis of LLMs. It contributes to both the research area and real applications. 2. The authors have examined several unlearning methods using ACR and raised several problems for existing works, prompting further exploration into model memorization. 3. The paper is clearly written and well-organized. It is easy to follow the authors' ideas and understand their approaches. The authors use clear figures, i.e., Figure 1, to show their approach. The notations and experimental results are clear and easy to read. 4. The authors have provided a comprehensive literature review and show the importance of proposing this new definition and metric for LLM memorization. Weaknesses: 1. Some concepts need further clarification or justification. For instance, why do we need this adversarial view, not the natural text, for the compression argument? This assumption "if a certain phrase exists within the LLM training data (e.g., is not itself generated text) and it can be reproduced with fewer input tokens than output tokens, then the phrase must be stored somehow within the weights of the LLM" needs further justification. The authors should have provided more analysis on the threshold used in "The threshold is a configurable parameter of this definition $\tau(y)$" 2. The authors should have done some efficiency analysis on Algorithm 1. Technical Quality: 3 Clarity: 3 Questions for Authors: 1. Besides Algorithm 1 (using GCG), are there any other options, as discussed in Line 190? 2. As you mentioned here "This case suggests that we cannot safely rely on completion as a metric for memorization because it is too conservative." in Line 243, why and how to solve this? Confidence: 5 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: Current conclusions are limited since they are just made from two specific LLMs. Flag For Ethics Review: ['Ethics review needed: Data privacy, copyright, and consent'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We appreciate your positive feedback on our proposed metric for defining memorization in LLMs and its practical implications. We're glad you found our examination of unlearning methods using ACR insightful and our paper clear and well-organized. We acknowledge your concerns and attempt to address them below: ### Re: Adversarial View for Compression Argument We understand the need for further justification of the adversarial view in our compression argument. Here are a few points addressing this concern: 1. Necessity of Adversarial View: The adversarial perspective is crucial because it robustly challenges the model’s misuse of training data. This view ensures that the model cannot evade detection of memorization by merely altering its output slightly. We will expand our discussion to better justify the assumption that phrases stored within the LLM's weights can be reproduced with fewer input tokens than output tokens. 2. Threshold Analysis: We will provide a more detailed analysis of the threshold parameter used in our definition. This will include a discussion on how different threshold values affect the detection of memorization and the rationale behind our chosen threshold. ### Re: Efficiency Analysis of Algorithm 1 We agree that an efficiency analysis of Algorithm 1 is important. Here are our points addressing this concern: 1. Efficiency Analysis: We will include an efficiency analysis of Algorithm 1 in the revised manuscript. This analysis will provide insights into the computational requirements of the algorithm and its scalability across different datasets and model sizes. ### Re: Alternative Optimization Methods We appreciate your interest in alternative optimization methods. Here are a few points addressing this concern: 1. Alternative Methods: Besides the Greedy Coordinate Gradient (GCG) method, we have explored other optimization methods such as Random Search. This is presented in Algorithm 3 in our appendix. Additionally, we can move the discussion of other discrete optimizers (like those popular in the LLM Jailbreaking literature) from where they are mentioned in the additional related work section of our appendix to the main body. ### Re: Completion as a Metric for Memorization We understand the need for further clarification on why completion alone is insufficient as a metric for memorization. Here are a few points addressing this concern: 1. Completion Limitations: Completion is too conservative to capture memorization when model owners may take steps to make it look like their model has not memorized data it shouldn’t have. For example, unlearning methods (Sections 4.1, 4.2, 4.3) can be used to obscure memorization. Our definition, which relies on optimization and not completion alone, is not fooled by these minor tricks to appear compliant. 2. Clarification: We will further clarify this point in the next version of the paper, explaining how our method provides a more robust detection of memorization compared to completion-based metrics. ### Re: Limited Conclusions We acknowledge that our initial conclusions were based on experiments with two specific LLMs. Here are a few points addressing this concern: 1. Broader Experiments: Our experiments to include four different models in the Pythia family, which are open-weight, open-source models available at the time of writing. Additionally, we conducted experiments with LLaMA-2, a LLaMA model tuned on TOFU, and a version of LLaMA that does not know Harry Potter. These models are characteristically different, providing a broader evaluation of our metric. 2. In-Context Unlearning: We also performed experiments with in-context unlearning, demonstrating the applicability of our method across a wider range of scenarios. These additional experiments expand the breadth of our evaluation and further validate the robustness of the ACR metric. ### Conclusion Once again, we thank you for the constructive feedback on our work. We believe that these clarifications and additional analyses will significantly strengthen our paper, addressing your concerns and providing a more comprehensive and robust evaluation of the ACR metric. We are confident that these enhancements will improve the quality and impact of our work. --- Rebuttal Comment 1.1: Title: Thank you for your responses. Comment: I have read the authors' responses. Most of my concerns have been addressed. I will keep my score as 7 Accept.	Summary: The paper introduces a novel metric Adversarial Compression Ratio (ACR) to assess memorization in LLMs. The authors first contend that the conventional understanding of memorization may not be fully adequate for evaluating the memorization ability. Hence, ACR provides a quantitative measure by proposing that a model memorizes a piece of training data if it can reproduce it from a significantly shorter prompt, and presents a practical algorithm called MINIPROMPT to approximate the ACR for any given string. The authors validate the ACR through a series of experiments and case studies, demonstrating its effectiveness in various scenarios, including the detection of memorized content following attempted unlearning methods. Strengths: 1. The paper presents a new and innovative approach to defining and measuring memorization in LLMs, which is a significant contribution to the field. 2. The validation on existing unlearning methods is interesting. Weaknesses: 1. The ACR metric may inherently favor the detection of memorization in longer sequences due to the potential for a more substantial compression ratio when a shorter prompt reproduces a longer string. This bias could significantly impact the evaluation of an LLM's memorization of some concise knowledge. 2. The introduction on miniprompt is a bit brief, and since the optimizer algorithm in the experiment relies on the Greedy Coordinate Gradient Descent, the author might also consider providing a brief introduction to GCG in the main text to be more reader-friendly. Technical Quality: 2 Clarity: 2 Questions for Authors: 1. How does the ACR metric account for variations in the length of expressions conveying the same knowledge, such as "bird can fly" versus "it is a well-known fact that birds possess the ability to fly"? 2. How would you interpret it if two model, A has a larger portion memorized than B with a smaller average compression ratio? Which of the two metrics is more representative in measuring the memorization ability? Confidence: 3 Soundness: 2 Presentation: 2 Contribution: 3 Limitations: Yes. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your positive review! We are pleased that you found our approach innovative and recognized the significance of our contribution to defining and measuring memorization in LLMs. We acknowledge your concerns and attempt to address them below: ### Re: Favoring Longer Sequences We understand the concern that the ACR metric may favor the detection of memorization in longer sequences due to the potential for a higher compression ratio. Here are a few points addressing this concern: 1. Performance Across Different Lengths: To address this issue, we have included a plot with sequence length on the x-axis to illustrate how ACR performs across different lengths. This analysis shows that while longer sequences can achieve higher compression ratios, the ACR metric remains effective and meaningful for shorter sequences as well. We have added this plot and corresponding discussion to the revised manuscript. 2. Balanced Evaluation: Our experiments were designed to include a balanced mix of both short and long sequences, ensuring that the evaluation of the ACR metric is comprehensive and unbiased. This helps mitigate any potential bias towards longer sequences. ### Re: Introduction to MINIPROMPT and GCG We appreciate the suggestion to provide more details about the MINIPROMPT and the Greedy Coordinate Gradient Descent (GCG) optimizer. Here are our points addressing this concern: 1. Detailed Introduction: We have expanded the introduction to MINIPROMPT and included a brief overview of the GCG optimizer in the main text. This additional context will make the paper more reader-friendly and accessible to those unfamiliar with these concepts. 2. Clarity and Readability: These enhancements ensure that readers have a clear understanding of the methodologies used in our experiments, improving the overall clarity and readability of the paper. ### Re: Accounting for Variations in Expression Length We understand the importance of addressing how the ACR metric accounts for variations in the length of expressions conveying the same knowledge. Here are our points addressing this concern: > Variations in Expression Length: The ACR metric focuses on the compression ratio, which inherently normalizes the length of the input prompt and the generated sequence. This allows the metric to be robust against variations in expression length, as it measures the relative information content rather than the absolute length. > Disentangling knowledge from verbatim memorization: The analogy of birds can fly is a great one. In general, facts are not copyrightable, and a desirable measure would be one that can disentangle knowledge from verbatim memorization. Toward this end, we conducted a new set of experiment. In particular, we paraphrased the 100 famous quotes used in our paper with ChatGPT and checked their ACR values. The results are as follows: \|Model \|Data Type \|Avg. ACR \|Portion Memorized\| \|:----------\|:-----------------------------------\|:--------\|:------------\| \|EleutherAI/pythia-1.4b \|Paraphrase \|0.68 \|0.11\| \|EleutherAI/pythia-1.4b \|Famous Quotes \|1.17 \|0.47\| Our findings suggest that paraphrases of memorized content generally do not get flagged by our method unless the paraphrase itself is memorized (some paraphrases were also available on the internet based on our cursory search). This supports the idea that "facts are not copyrightable," and our method aligns with this principle. ### Re: Interpretation of Metrics We appreciate the question regarding the interpretation of models A and B, where A has a larger portion memorized, but B has a smaller average compression ratio. Here are our points addressing this concern:     Portion Memorized vs. Compression Ratio: We believe the portion memorized is a more crucial metric in practical applications. For instance, in legal contexts, the binary test of specific samples is more likely to be applied, making the portion memorized a more relevant measure of memorization. ### Conclusion Once again, we thank you for your valuable feedback. We believe that these clarifications and additions will significantly strengthen our paper, addressing your concerns and providing a more comprehensive and robust evaluation of the ACR metric. We are confident that these enhancements will improve the quality and impact of our work.	Summary: The authors propose adversarial compression ratio (ACR) as a novel metric for assessing memorization in LLMs. ACR compares the lengths of the smallest prefix string evoking a target completion from the model with the length of the completion. The shorter the prefix, the higher the compression ratio, and subsequently, the stronger the memorization. The authors further leverage an optimization-based approach using GCG, searching over the entire sequence length to find the shortest possible prefix, and demonstrate the effectiveness of such an approach in finding prompts which bypass in-context unlearning on LLaMA2-7-Chat & famous quotes.The authors perform further experiments on unlearning benchmarks such as TOFU and trying to forget harry potter, showing that ACR discovers that models are still able to reproduce significant portions of these datasets even after unlearning was applied. The authors also perform a scale-based analsyis as well as a comparison to data unlikely to be memorized to confirm that memorization increases with scale and the robustness of their proposed method, respectively. Strengths: - The paper is well written and positioned. It provides an excellent overview of the field of unlearning and motivates the contribution well. - The experimental setup is exhaustive and well motivated. - The proposed metric is demonstrably able to detect content which is still memorized within the model despite unlearning Weaknesses: - The optimization process, as mentioned by the authors, does not necessarily have to be completely accurate, sometimes underestimating the error ratio. It would be interesting to see how large this error can be by pehaps comparing the budget given to GCG. While it is not necessary for a solution to be optimal, an idea of how close the algorithm is, on average across a small sample size, would be relevant. - The method identifies exact memorization, but does not account for paraphrases. While it is unlikely that a paraphrase would be memorized & easily reproduced, while the exact string forgotten, this might be a consequence of unlearning. What do you think about this issue? Technical Quality: 3 Clarity: 4 Questions for Authors: See above Confidence: 4 Soundness: 3 Presentation: 4 Contribution: 3 Limitations: Yes Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your comprehensive review and valuable feedback. We appreciate your recognition of the strengths in our paper, particularly the well-positioned and motivated overview, exhaustive experimental setup, and the efficacy of our proposed metric in detecting memorized content despite unlearning efforts. Regarding the weaknesses you identified, we conducted additional experiments to address your points. Limited budget for GCG The idea is interesting, however, we found that controlling the budget does not significantly change things because our code is designed to exit early once a successful prompt (one that elicits an exact match) is found. Therefore, increasing the command line argument for num_steps does not provide additional benefits, as GCG is already optimized to use the necessary compute efficiently. And decreasing the number of steps shows many samples for which GCG fails to find a successful prompt altogether. Paraphrases We paraphrased the 100 famous quotes used in our paper with ChatGPT and checked their ACR values. The results are as follows: \|Model \|Data Type \|Avg. ACR \|Portion Memorized\| \|:----------\|:-----------------------------------\|:--------\|:------------\| \|EleutherAI/pythia-1.4b \|Paraphrase \|0.68 \|0.11\| \|EleutherAI/pythia-1.4b \|Famous Quotes \|1.17 \|0.47\| We conducted a cursory Google search and found that some paraphrased versions are present on the internet. Our findings suggest that paraphrases of memorized content generally do not get flagged by our method unless the paraphrase itself is memorized. This supports the idea that "facts are not copyrightable," and our method aligns with this principle. Thank you again for your insightful comments. We believe these additions and clarifications will strengthen our paper. --- Rebuttal Comment 1.1: Comment: Thank you for your response and the additional results. Budget then is probably not a good way of quantifying this - nevertheless, some bounds on the error ratio/idea of proximity to the optimal solution seem necessary, especially with the intended purpose of the method in mind (quantifying memorization). Example scenarios are: how much can the ACR vary between different optimization algorithms? How likely is the chance of the compression ratio seeming low, while the model actually memorized the texts? Such scenarios are likely to pop up if ever the method is to be used as proof for memorization. This is definitely not an easy problem to solve, but should be kept in mind or discussed by the authors. My score (Accept, 7) still reflects my opinion of the paper well, thus I will keep it.	Summary: ### Summary - This paper proposes a new metric for measuring memorization in LLMs. - Their proposed metric called Adversarial Compression Ratio (ACR) is capable of measuring memorization for arbitrary strings at a reasonably low compute. - The definition of memorization, the authors propose in the paper is based on a compression arguments which goes something like this - "a phrase present in the training data is memorized if we can make the model reproduce the phrase using a prompt (much) shorter than the phrase itself." - To operationalize this definition, the techinque requires finding the shortest adversarial input prompt that is optimized to produce the sentence under consideration as its output. - The ratio of input to output tokens is defined as ACR. - There are various ways to measure memorization - Discoverable Memorization - This was proposed by Carlini and essentially measures if a prefix elicits the suffix as the response. - This definition is very permissive since definition only tests for exact completions. - It's easy to evade by just tweaking a few tokens to avoid exact match - It also requires validation dataset to tweak generation hyperaparameters such as top-p, top-k etc. - Extractable Memorization - This definition defines extractable memorization as a string which elicits the string in the response. - Since this allows any arbitrary string as prompt, this definition is very restrictive as it allows the prompt to have the entire string in question. For e.g., "repeat the following string: X" -> X - Counterfactual Memorization - Measures the difference in model performance with a model trained with the example versus one trained without it - Since LLMs are expensive to train, this definition is quite impractical. - Membership Inference Tests which are commonly used to test if a model was trained on a particular example datapoint has the following problems - It's very restrictive. Akin to plagiarism, it is okay to read copyrighted books but copying is problematic - Have brittle evaluation - Based on the ACR ratio, ACR(M, y) = \|y\|/\|x\| where \|x\| = argmin \|x\| s.t. M(x) = y the authors propose a notion of $\tau$-compressible memorization i.e. if ACR(M,y) > $\tau(y)$ - This metric can be aggregated over a dataset to report an average compression ratio or another metric called portion memorized which measures the proportion of data with MCR > $1$ - GCG (Greedy Coordinate Gradient) is used to find the the adversarial prompt from earlier work which is a common algorithm. - The authors also show that in context unlearning can fool completion but not this adversarial notion of compression Strengths: ### Strengths - This definition is consistent with common notions of memorization - Bigger models memorize more - Random sequences are not compressible (zero compressibility) - sentences from a data source which are not part of training data have zero compressibility - Famous quotes have the highest value for ACR - The paper is well written and easy to follow. The background is thoroughly covered. Weaknesses: ## Weakness - The paper is well motivated and tackles an important problem. However, independent of the problem of false negatives, I wonder if false positives might be a bigger problem here. What if as a result of GCG algorithm, you are able to elicit a generation from a model which was never seen by the model during the training. I would suggest adding an experiment and some discussion around this. Technical Quality: 2 Clarity: 3 Questions for Authors: ## Questions - Line 125: "Hard to arbitrate: training data is often not released." - Even if the training data is not released, can a publisher not run MIA against the LLM to determine effectively if their training data was used during training. I don't quite agree with this claim - Line 313: Can you clarify what you mean "quells any fears that GCG is merely relaying that the gradients are more informative on some examples than others" Confidence: 3 Soundness: 2 Presentation: 3 Contribution: 3 Limitations: The authors have adequately addressed the limitations. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your thorough and thoughtful review. We are pleased that you found our definition of memorization consistent with common notions and that you appreciated the clarity and depth of our paper. We acknowledge your concerns and attempt to address them below: ### Re: False Positives We understand the importance of considering false positives in our method. Here are a few points addressing this concern: 1. False Positives with GCG Algorithm: The concern about the GCG algorithm eliciting generations that were never seen by the model during training is valid. Our experiments, including those involving random strings, have shown that while the GCG algorithm can elicit any generation, we have never observed compression of non-training data. This suggests that our method is robust against false positives. However, we will add further discussion and conduct an additional experiment to explicitly address this point. This experiment will aim to determine the likelihood of false positives by testing the ACR metric on a controlled set of non-training data. 2. Reference to Related Work: We will incorporate findings from relevant literature (e.g., Geiping, Jonas, et al. "Coercing LLMs to do and reveal (almost) anything." arXiv preprint arXiv:2402.14020 (2024)) to strengthen our discussion on false positives and demonstrate the robustness of our method. ### Re: Membership Inference Attacks (MIAs) We acknowledge the potential role of MIAs in determining training data usage. Here are our points addressing this issue: 1. Limitations of MIAs: While MIAs can be used to test for training data usage, they have significant limitations, as highlighted in recent work (e.g., https://arxiv.org/abs/2402.07841, https://arxiv.org/abs/2406.06443, https://arxiv.org/abs/2406.16201). Further, MIAs typically rely on scalar-valued losses, which are not easily interpretable in regulatory or legal contexts. This complicates their applicability in such settings and makes conclusive findings difficult to reach. 2. Context of Our Claim: Our claim in Line 125 refers to the broader challenges of proving training data usage without access to the training data itself. Even if a publisher can run MIA, the interpretability and conclusiveness of the results remain challenging. We will revise this section to provide more context and clarity on this point. ### Re: Clarity on Line 313 We appreciate your request for clarification on Line 313. Here are our points addressing this query: 1. Clarification on GCG and Gradient-Free Search: One might think that our findings are the results of some peculiarity in GCG or some bias/preference GCG has for finding short prompts on some types of data. We establish that the same general trends in memorization can be observed with a gradient-free search algorithm, and thus conclude that we are not mistaking a GCG bias for some other signal. We will provide more details on this random search experiment and explain how it supports the robustness of our findings. Once again, we thank you for the constructive feedback on our work. Working on the pointers has helped us improve the quality of our analysis. We look forward to further discussions and improvements in this evolving field.	Rebuttal 1: Rebuttal: We appreciate the thoughtful feedback and valuable suggestions from all of the reviewers. In response, we provided further clarity around key assumptions, conducted some experiments, and expanded our discussion in several places in the draft. Specifically, we examined paraphrased versions of the famous quotes and found that our methods align well with copyright standards. We believe all of this improvement have strengthened our paper and and that we have comprehensively addressed the reviewers' concerns. One reviewer asked How does the ACR metric account for variations in the length of expressions? Here, we include a plot of the average ACR versus sample length in the attached PDF (and in the latest version of the paper). We find no apparent spurious correlations, but rather that our method is useful across a range of sample lengths. For further accounting for information content of the samples, Appendix E.2 in the paper has a discussion of how the ACR compares to other compressibility measures like SMAZ. In conclusion, we agree that the concern about possible correlations with sample length should be addressed and we have added a plot and some discussion to better explain that this is not an issue for our method. Pdf: /pdf/b03529dee81f277cad9e00e99c3f5e980c9bada0.pdf	NeurIPS_2024_submissions_huggingface	2,024	Summary: This paper proposes Adversarial Compression Ratio (ACR), a metric for assessing memorisation in LLMs; ACR is defined as the ratio between the length of the generation we need to test memorisation for and the length of the shortest prompt that can elicit such a generation. A question I have is whether "length" is always suitable as a complexity measure; for example, y can be very long but also very "simple" (such as the "mmmmmmmm...mmm" messages from /r/microwavegang, which occur in some pre-training corpora). To solve such a combinatorial minimisation problem (finding the shorter prompt that elicits a given generation), the authors propose using Greefy Coordinate Gradient [GCG, Zou et al., 2023]. Overall, It is a very interesting approach and paper; however, it would be useful to compare ACR with other methods for testing for memorisation. Strengths: 1) Interesting approach for memorisation testing Weaknesses: 1) Lack of comparisons with other methods for solving the same task 2) Not sure why "number of tokens" may be a suitable measure of complexity Technical Quality: 2 Clarity: 4 Questions for Authors: Is ACR more effective at detecting memorisation compared to the method proposed in e.g., https://openreview.net/forum?id=TatRHT_1cK ? Confidence: 3 Soundness: 2 Presentation: 4 Contribution: 2 Limitations: Lack of comparisons with related methods for solving the same task Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your insightful feedback. We appreciate your recognition of our innovative approach to memorization testing. We acknowledge your concerns and attempt to address them below: ### Re: Comparisons with Other Methods We understand the importance of comparing our Adversarial Compression Ratio (ACR) with other existing methods for testing memorization. Here are a few points addressing this concern: 1. Verbal and Experimental Comparisons: In Section 2 of our paper, we verbally compare and contrast ACR with existing methods. Additionally, our section on in-context unlearning includes some experimental comparisons. However, direct experimental comparisons are challenging due to the different contexts in which these methods operate. For instance, methods like Extraction (https://openreview.net/forum?id=TatRHT_1cK) can't make conclusive claims about short strings, whereas we can handle strings of any length. Also, the adversarial nature of our approach, where the model owner might take minor steps to change the extractability, also differentiates our method. The in-context unlearning section serves as an example where other tests might be tricked, but our approach remains robust. More concretely, a direct comparison with the paper requested can be found in Section 4.1 of the paper, and also in Section 4.2 (Figure 3) on compression versus completion. These results clearly demonstrate how compression is a desirable metric to uncover seemingly hidden memorization. 2. Effectiveness of ACR: ACR introduces a new paradigm of memorization detection from an adversarial perspective. This approach has significant implications for discussions on copyright and intellectual property, where model providers may take measures to hide memorization. We believe that this perspective enriches the discourse and offers new insights for policy-making and regulation. It is more effective in the sense that it pierces the illusion of compliance, showing memorization where other methods might fail to, for example because of system prompts. ### Re: Suitability of "Number of Tokens" as a Complexity Measure We acknowledge the concern regarding the use of "number of tokens" as a measure of complexity. Here are a few points addressing this concern: 1. Compression Ratio: The compression ratio, where both the numerator (length of the generation) and the denominator (length of the shortest prompt) must be in the same units, is helpful in enforcing the constraint that the prompt has less information than the output. While other notions of information content could theoretically be used, we find the ratio of token lengths to be practically useful in defining memorization. 2. Empirical Utility: Empirically, we have found that using the number of tokens as a measure of complexity works effectively in our experiments. The simplicity of this metric allows for a clear and consistent definition of memorization across different contexts. Once again, we thank you for the constructive feedback on our work. We hope we were able to clarify your concerns. Please let us know if there are any lingering concerns.	null	null	null	null	null	null
SpaceByte: Towards Deleting Tokenization from Large Language Modeling	Accept (poster)	Summary: The authors propose a byte-level architecture called SpaceByte that involves local blocks (lower dimension, windowed attention) and global blocks (higher dimension, global attention) where the global blocks are between chunks of local blocks and only selectively applied. The global blocks are applied to "spacelike" characters (such as an actual space character), with the intuition being that at such points predicting the next character (like start of word) would be harder. The authors run extensive experiments to show that their proposed architecture outperforms previous byte-level architectures and in fact performs similarly to subword-level transformer baselines. Strengths: Originality: While this work seems to share much in common with past byte-level architecture work, the intuitive idea of some bytes being harder to predict (in a rule predictable way) is very natural and useful (and first presented in this work, as far as I am aware). The architecture itself is also novel. Quality: The authors run a lot of experiments to demonstrate the capabilities of their architecture. Clarity: The paper was clear, down-to-earth, and easy to understand. Significance: This paper shows that byte-level architectures can be competitive with subword tokenization transformers in a flop-matched setting. Weaknesses: * As a main weakness I'd say that even though this method beats other byte-level approaches and is comparable to subword tokenization, I don't see a compelling reason to use it over standard tokenization. In the Introduction the authors mention several downsides of tokenization, but don't have results that focus on these issues per se. I'm also a bit confused about the "additional modeling complexity (line 20)" point. It seems like tokenization is actually simpler. * It would have been nice to see some ablations on the architecture (for example, the local -> global -> local layer ordering seems a little arbitrary). * It would have been nice to see some modifications of the global rule. For example, only "space" characters like actual space and newline vs the more broad definition of "space" used in the paper. * It might be nice to include more info on what the "spacelike" tokens actually look like (what are the most common "spacelike" tokens and what percentage of all "spacelike" tokens do these make up). Technical Quality: 4 Clarity: 4 Questions for Authors: Please see weaknesses for my questions. Confidence: 4 Soundness: 4 Presentation: 4 Contribution: 3 Limitations: Yes. The paper does a good job of this. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you very much for your insightful and thorough review. ## Weakness 1 We agree that there is not a compelling case to use SpaceByte over a subword Transformer. However, we hope that iterating upon the SpaceByte architecture could eventually yield a compelling byte-level model. And we believe that SpaceByte is a significant milestone in this process since it's the first attention-based architecture to achieve performance parity with subword Transformers. We would have loved to address the other tokenization issues, but we unfortunately ran out of time. However, we were very pleased to see that MambaByte [7] (i.e. byte-level Mamba [25]) exhibits a significantly higher character-level noise-tolerance than subword Transformers. We expect SpaceByte to show a similar tolerance improvement, although we have unfortunately not had time to experimentally check this. The sentence on line 20 is not making a claim about SpaceByte. We simply mean that additional modeling complexity is a disadvantage of tokenized Transformers over e.g. a byte-level Transformer. We agree that the extra complexity of SpaceByte largely cancels out the simplicity of removing the tokenizer, and thus simplicity is unfortunately not a compelling reason to use SpaceByte over a tokenized Transformer. ## Weakness 2 We apologize for the lack of ablations. We don't have ablations because when faced with an architecture decision, we simply made the simplest choice that should work well. Examples include: the local block attention window (else the FLOPs for the local attention would be roughly 36x larger and dominate the model's flops), the lack of a linear layer to change model dimensions between local and global blocks (which MegaByte had but we found in preliminary experiments to slightly hurt FLOP-controlled performance), and our choice of spacelike characters. The local -> global -> local ordering is not at all arbitrary. If no local layers preceded the global layers (e.g. global -> local), then the global layers would not have any information about the majority of the bytes. Similarly, if no local layers followed the global layers (e.g. local -> global), then the global layers would have no influence on the majority of the output bytes. As such, local -> global -> local is the simplest good choice. ## Weakness 3 We studied something like this in preliminary experiments, and found that it performed slightly worse on the datasets we studied. ## Weakness 4 That is a nice suggestion, although it is certainly very dataset-dependent. We may include it in the next version. Until then, we hope that the demonstration in Figure 2 is helpful.	Summary: The paper introduces SpaceByte, a byte-level Transformer model that incorporates larger transformer blocks at specific byte boundaries to enhance performance in language modeling tasks. While the approach bears similarities to previous work (e.g. MegaByte), it demonstrates improved performance over traditional tokenization models. The study focuses on specific languages, acknowledging limitations in generalizability, particularly in languages like Chinese, which do not use spaces between words. Strengths: 1. The paper presents a novel approach in utilizing byte-level Transformer models with specific block insertions to enhance language modeling performance. 2. The study provides insights into the limitations of tokenization models and the potential benefits of byte-level architectures. 3. The experimental methodology is well-documented, controlling for compute costs and providing detailed training details in the appendices. Weaknesses: 1. The novelty of the SpaceByte approach may be limited by similarities to previous models. 2. The study's focus on specific languages, without detailed experiments on broader language datasets, limits the generalizability of the findings. 3. The paper could benefit from a more extensive discussion on the unique contributions of SpaceByte compared to existing models. Technical Quality: 3 Clarity: 3 Questions for Authors: 1. How do the authors plan to address the limitations in generalizability to languages beyond the ones studied in the current work? 2. Are there plans to conduct experiments on a more diverse set of language datasets to further validate the effectiveness of SpaceByte in different linguistic contexts? Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: The authors have acknowledged the limitations of their work, particularly in terms of language generalizability. To enhance the impact of the study, it would be beneficial for the authors to consider conducting experiments on a broader range of language datasets to strengthen the validity and applicability of SpaceByte across various linguistic domains. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you very much for your careful review of our work and for identifying its key strengths. ## Weakness 3 As discussed in Section 3, our primary contributions beyond prior works is to show how to scale word-boundary byte-level modeling to more diverse text modalities while roughly matching the performance of subword-level models in compute-controlled experiments. Previous works that studied word boundary LLMs did not demonstrate that this is possible or how to do it. ## Question 1 This is a very important direction for future work. Unfortunately, we will not have time to address it in the foreseeable future. However, Reference 9 studied some promising techniques, such as using entropy to partition the patch boundaries. It would be useful to see if this approach is also capable of matching subword Transformer performance, especially on broader language datasets. ## Question 2 We unfortunately do not currently have plans for this (due to time limitations).	Summary: Byte-level modeling allows transformers to circumvent subword tokenization, thus avoiding the many weaknesses introduced by tokenization. However those models are not very performant compared to subword-based transformers. This paper proposes a novel architecture named SpaceByte. The idea is to add an extra wide layer (i.e. "global block") between regular transformer layers (i.e. "local block") if and only if "the byte does not encode a letter, number, or UTF-8 continuation byte". Results show that when normalizing for training FLOPs, SpaceByte achieves the best PPL on multiple datasets. Plus, at different model dimensions and number of layers (?), SpaceByte always achieve the optimal or near-optimal Pareto optimality between PPL and inference FLOPs-per-byte. Strengths: 1. The idea is simple and well-motivated 2. Experiment results show that it is competitive when compared subword-based models Weaknesses: 1. While normalizing for FLOPs, I think there is some potential that the proposal will make the transformer blocks significantly harder to batch (due to the input-dependent dynamic structure of the model), hence the clock-time of the inference might actually be slower with the same FLOPs. It would be good to see some discussions on that. 2. There is no ablations as to whether the global blocks actually need larger dimension. 3. Presentation of the paper could be improved. See my question/suggestion in the next section. Technical Quality: 3 Clarity: 2 Questions for Authors: ### Presentation Suggestions 1. It's worth explaining more about how context lengths work differently for global vs. local blocks in Section 2. I'm also not very sure why the larger context length is necessary. 2. I'd suggest switching Section 2 and 3 and talk about related work first. 3. Three suggestions for Figure 3 -- a. make it clear in the caption that you are changing inference FLOPs with different model dimensions & layers (per line 206); b. use dashed/solid lines rather than thin/thick lines; c. mark the pareto frontier for each subfigures. ### Questions 1. Is the FLOP limits you imposed enough to make the models converge adequately on those datasets? It might have been the case that your model simply converges faster, but if trained longer, doesn't work as well as, e.g. sub-word models (which weakens your case). 2. Why set the dimension and context length equal? 3. I'm very confused what's the difference between section 6 and 5. How does the results in section 6 further complements the one in section 5? 4. In Table 2, you only have one context size, but don't global blocks have larger context size? What context size is being reported then? Confidence: 4 Soundness: 3 Presentation: 2 Contribution: 2 Limitations: See weakness point 1. I'm relatively confident that this could be a potential limitation that needs to be addressed. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your detailed review of our work. Although we agree that SpaceByte is more challenging to batch than a Transformer, we would like to emphasize that our work does establish a very significant milestone in byte-level LLMs because SpaceByte is the first byte-level attention-based architecture to demonstrate performance parity with the subword Transformer architecture. We believe this significance warrants acceptance (while leaving room for future work to show that the batching issue is not a significant hurdle). ## Weakness 1 You are correct that batching during inference is more challenging with SpaceByte. Nevertheless, we do believe that with a moderate amount of effort, a high FLOP utilization could be maintained with batching and without significantly sacrificing latency. One solution would be to maintain three separate queues for three parts of the model pipeline: 1. embedding + initial local blocks 2. global blocks 3. final global blocks + de-embedding Each queue processes a batch of input tokens or activations at a time. The batch size and context lengths are variable. Variable context lengths is not an issue since padding could be used (and padding is already typically used for batching due to variable prompt lengths). In a multi-GPU setup, it could be useful to put different queues on different GPUs in a 1-2-1 ratio for the three queues (to roughly even out the FLOPs). And 8 GPU setup would then naturally allow for two instances of each queue, which would be useful for reducing latency due to waiting in a queue. Thus, although the batching issue is annoying, we do not think that it is a major obstacle. ## Weakness 2 In preliminary experiments, we found that taking equal model dimensions for the local and global blocks to be significantly worse. Therefore, in our hyperparameter grid search, we take the local block dimension to be: D_local = 1/2 * D or (3/4 if D is a power of two else 2/3) * D where D is the global block dimension. This is specified in Appendix B.3. But as seen in Tables 3 and 4, which shows optimal hyperparameters found by our grid search, the smaller D_local = 1/2 * D performs better. Therefore, our paper does show strong evidence that it's important to use a larger model dimension for the global blocks. ## Presentation Suggestion 1 Thank you for the suggestion. We have appended the following sentence to line 76 at the end of Section 2: "The global blocks use a global attention that attends to all other global blocks." The context length that we experiment on is the natural (and roughly optimal) choice for all architectures that we evaluated. In particular, the chosen context length is natural and roughly optimal for the subword tokenizer since it roughly balances the FLOPs between the attention and MLP layers. SpaceByte uses a similar context length (after converting tokens to bytes) for a fair comparison (see Table 3 for precise numbers). But this context length would be too large for the local blocks to be efficient if we did not utilize an attention window since then the local attention blocks would use significantly more FLOPs than the local MLP blocks. An attention window prevents this inefficiency. ## Presentation Suggestion 2 Thank you for the suggestion. We made the choice to put the Related Work section after the SpaceByte section so that we could comment on how SpaceByte relates to the related works. ## Presentation Suggestion 3a Thank you very much for this suggestion! We agree that it greatly improves the clarity of the caption. We added the following additional sentence in the new version: "Each dot describes a model with a different number of layers and/or model dimension." ## Presentation Suggestion 3b Thank you for the suggestion. We tried dashed/solid lines as per your suggestion; but we feel the thin/thick lines are cleaner and easier to read. ## Presentation Suggestion 3c We already show the Pareto frontier, which is drawn for each model using a thin or think line. ## Question 1 It depends on what you mean by "adequately." The models are certainly not trained to convergence, as that would be prohibitively expensive in practice. In practice, one (almost always) does not care how well a LLM performs when trained to convergence. Instead, one cares about how well a LLM performs for a given cost budget. There are two important budgets that we consider: a training budget and an inference budget. We use training and inference FLOPs as a simple proxy for these respective costs since FLOPs are independent of software and hardware choices. This results in the Pareto frontiers shown in Figure 3. In this sense, all of the models shown in Figure 3 are very adequately trained as they lie on the Pareto frontier of performance vs cost. ## Question 2 We set the model dimension and context length equal so that the FLOPs are roughly balanced between the MLP and attention blocks, which tends to be the most efficient. This was a simple choice that we thought made the most sense for a fair comparison that evaluates all of the models at their best. ## Question 3 Section 5 is our main experiment. But we include Section 6 to make closer comparisons to the MegaByte and MambaByte experiments. Table 2 of Section 6 also includes PerceiverAR and MambaByte, which were not studied in Section 5. Furthermore, Table 2 shows MegaByte results trained by the MegaByte authors to help demonstrate that our finding that SpaceByte outperforms MegaByte is not just because we didn't train MegaByte well. (Unfortunately, this fact is only established for the PG-19 and Stories datasets in Table 2, since MegaByte was trained and evaluated on proprietary arXiv and Github datasets that are slightly different than the public datasets that we have access to). ## Question 4 We report the context size available to the LLM. For SpaceByte, this is the total number of bytes in the input sequence. --- Rebuttal Comment 1.1: Title: Post-rebuttal Comment Comment: Thank you for the very detailed rebuttal. It clarified my main confusions during my first read of the paper. Re: Question 1 -- By "adequately" I mean train until convergence, but your budget argument is valid and I will take it. I still have reservations on the practicality of the proposed method (esp. batching), but otherwise I think the paper should be accepted. I'm improving my final evaluation to "weak accept". Since the authors also agree that batching is challenging with this proposal, please make sure you make some space to address this issue/limitation in the final draft of the paper.	Summary: This paper proposes SpaceByte, a byte-level decoder architecture for language modeling. As opposed to comparable models such as MegaByte, SpaceByte applies global transformer blocks after space-like characters, not after patches of a fixed size. The authors show that this approach leads to a substantially improved performance: compared to several other byte-level decoder architectures (including MegaByte), SpaceByte is the only one that matches or even exceeds the performance of subword-level models trained with the same compute budget. Strengths: The proposed SpaceByte architecture is novel. The experimental setup is rigorous --- I think the authors did a great job in (a) evaluating a range of different architectures and (b) ensuring a fair comparison by controlling compute costs and using bits-per-byte as the evaluation measure. The results show clear performance improvements for SpaceByte, highlighting its advantages compared to other byte-level decoder architectures. Overall, I liked the paper very much and think that it should be accepted. Weaknesses: The main weakness that I see is that the authors only evaluate the different architectures using bits-per-byte, not any downstream task. To become a real alternative to subword-level models in practice, it would be important to show that the similar language modeling performance translates to a similar downstream task performance. While the authors cite work indicating that this might be the case (Huang et al., 2024), without actual experiments it is unclear whether this holds for the examined architectures as well. Technical Quality: 4 Clarity: 4 Questions for Authors: Is there any specific reason you did not include evaluations on downstream tasks? Confidence: 4 Soundness: 4 Presentation: 4 Contribution: 3 Limitations: Yes, the authors discuss limitations as part of the conclusion. Flag For Ethics Review: ['No ethics review needed.'] Rating: 8 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you very much for your thoughtful review and for accurately assessing strengths and weaknesses of our work. We would have loved to include evaluations on downstream tasks, but we unfortunately ran out of manpower and time.	null	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
BrainBits: How Much of the Brain are Generative Reconstruction Methods Using?	Accept (poster)	Summary: This paper aims to reduce the dimensionality of brain signals using linear layers to determine the minimal dimension required to preserve most of the reconstruction quality. The study involves experiments with three existing methods: two for brain-to-image reconstruction and one for brain-to-language reconstruction. Strengths: - The paper is easy to follow. - The paper aims to explore the extent of information necessary for brain decoding. Weaknesses: 1. The paper suggests that better reconstruction may be achieved with less brain signal input, yet all brain signals are utilized by the reconstruction models. While compressing signals to lower dimensions is possible, it does not guarantee that fewer signals can be used as input. 2. Only diffusion-based models are employed for decoding images. The relatively favorable results may stem from well-trained diffusion models capable of operating with minimal semantics. The discrepancy in bottleneck dimensions between image and text decoding (50 vs. 1000) could support this. In reality, diffusion models exhibit significant randomness in image generation, enabling the selection of images resembling ground truth stimuli from various generation runs. Consequently, drawing general conclusions based on the use of diffusion-based models may be challenging. 3. The performance of brain-to-image generation remains unsatisfactory. While subject1 shows promising results in some instances, the images generated using whole brain signals lack the structure and detail seen in the stimulus images. Furthermore, in additional poor cases not illustrated in this paper, the decoding results may be even more unsatisfactory. Therefore, achieving good image decoding results with fewer signals may be challenging. 4. The number of samples for different subjects is limited. Literature suggests significant performance variations in image generation among subjects, with some individuals exhibiting poor reconstruction outcomes. 5. The paper asserts that the method can be adapted to various neural recording modalities; however, differences in temporal and spatial resolution as well as signal characteristics among recorded signals pose uncertainties about BrainBits' adaptability. Notably, no experiments support this claim. 6. The second paragraph in the introduction appears somewhat contradictory. It mentions that higher quality reconstruction may require same or less signal from the brain, while also acknowledging the scarcity of open neuroscience datasets, especially those of sufficient scale to support this type of research. 7. The brain regions depicted in Figure 5 are not clearly labeled, making it difficult for readers to fully understand. 8. The effective dimensionality in Figure 4 lacks explicit clarification. 9. Text occlusion is apparent in both Figure 3 and Figure 11, affecting the clarity. Technical Quality: 2 Clarity: 2 Questions for Authors: 1. Given that lines 4-7 of the abstract lack a clear connection with the following sentences, and the paper does not tackle issues related to understanding stimulus distribution and enhancing text or image reconstruction, what meaning does it actually convey? 2. Why were two fMRI plus diffusion models chosen for image decoding instead of experimenting with other signal types or generative models? 3. Do different subjects activate different voxels for the same stimulus image? Or do different voxels get activated for different stimulus images within a subject? If so, utilizing a fixed subset of voxel recordings as input becomes challenging due to the uncertainty of which voxels will be utilized later. 4. Can BrainBits operate with fewer brain signals as input? If not, what specific contributions does this paper offer to the community despite this limitation? Confidence: 3 Soundness: 2 Presentation: 2 Contribution: 2 Limitations: There is no potential negative societal impact. Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for their time and extensive feedback. We answer questions and clarify a few points below. - _The paper suggests that better reconstruction may be achieved with less brain signal input, yet all brain signals are utilized by the reconstruction models._ - Yes, while all brain signals are available at input, the dimension of the bottleneck puts a hard upper bound on the amount of information available at reconstruction time. Notably, increasing the size of this bottleneck leads to better performance, from which we infer that these bounds are tight. - We have preliminary analysis of which parts of the brain are likely important (Figure 5), but truly selecting inputs by dropout is left for future work. This procedure is complicated by differences between subjects and significant computational costs, since dropout is a combinatorially difficult problem. - _Only diffusion-based models are employed for decoding images. The relatively favorable results may stem from well-trained diffusion models capable of operating with minimal semantics. Diffusion models exhibit significant randomness in image generation, enabling the selection of images resembling ground truth stimuli._ - We do not allow selecting images resembling the ground truth stimuli. We agree with the reviewer that doing so would be highly problematic. Instead, models get one chance to produce an image: one image for each of the 1000 stimuli. Then the average performance is computed. The variance on that average performance is small, since over so many images the stochastic nature of the diffusion models averages out. - Regarding the power of diffusion models, we agree entirely! Our entire point is that these models operate with minimal semantics, rather than with extremely rich representations needed to actually encode the entire image. This is not a particular property of diffusion models, it is instead a property of any large model trained on data that is similar to the test data shown to subjects. - _The performance of brain-to-image generation remains unsatisfactory._ - I think we’re in agreement here! The main thrust of our argument is this: prior work has claimed that brain-to-image reconstruction is satisfactory to some degree, according to existing metrics. - And whatever flaws these images have is up for discussion, but our experiments show that you can achieve the same performance on those metrics with much less information from the brain. This is so little information that clearly something must be missing from the images. Yet this point has not been made in the literature and it is critical for further progress. - _The number of samples for different subjects is limited._ - Our paper should be thought of as a meta-study over the field of work in brain-to-image reconstruction. To this end, we consider those subjects and samples used by existing works. - _Differences in temporal and spatial resolution as well as signal characteristics among recorded signals pose uncertainties about BrainBits' adaptability._ - Our method is very general: and simply entails adding a restriction on information flow through the reconstruction pipeline. This is applicable, no matter the modality. - _Authors claim reconstruction may require same or less signal from the brain, while also acknowledging the scarcity of open neuroscience datasets._ - To clarify, there is a distinction between the signal available in a single brain reading and the data available in the training dataset. The first is relevant to the quality of reconstruction, the second is relevant to the ease of training a reconstruction method. - _Regions depicted in Figure 5 are not clearly labeled_ - We created a legend with labeled regions (see additional PDF) that we will add to the main text. - _The effective dimensionality in Figure 4 lacks explicit clarification._ - Lines 201 through 204 explain the effective dimensionality method used. We will update the caption to include this. - _Text occlusion in both Figure 3 and Figure 11._ - Thanks! We will add labels, clarification in the caption for Figure 4, and we will fix the spacing in Figures 3 and 11 - _What meaning do lines 4-7 convey?_ - The reasoning is this: currently only measuring the quality of the reconstructed images allows for models to improve for reasons that do not involve extracting more signal for the brain. Lines 4-7 simply list a few of these possible reasons. The purpose of our work is to introduce a metric that cannot be “gamed” in such ways. - _Experimenting with other signal types or generative models?_ - The overwhelming number of recent state of the art publications in image reconstruction use fMRI enabled by the NSD dataset. Since this is by far the most common paradigm, we decided to adopt it. There is nothing about our method that is signal-specific. Nor is there anything that is specific to diffusion generative models. Given the state of the field, we chose the most representative methods. - _Do different voxels get activated for different stimulus images within a subject?_ - All of our learned maps and results are per subject. This avoids this problem. - _Can BrainBits operate with fewer brain signals as input? If not, what specific contributions does this paper offer to the community?_ - We are not sure if we understand the question. BrainBits is not a reconstruction method in itself. BrainBits is a method for measuring the dimensionality of the neural recordings required to perform reconstruction. And it is applicable, no matter the input size. It addresses a key problem: large networks can reconstruct images well with little information by exploiting the similarity between their massive training sets and relatively restricted test sets. Without BrainBits, one cannot disentangle why a model is performing better. Is it explaining more of the brain or taking more advantage of its priors? We show that these priors can be extreme. --- Rebuttal Comment 1.1: Comment: Thank you for your responses. As analysis of which parts of the brain have been provided in Figure 5, why not generate images using the brain activities from these brain regions? This could strongly support the main idea of this paper, while the other evidences seems to be circumstantial. --- Reply to Comment 1.1.1: Title: Response to further comments Comment: This is a really good idea for future work, and precisely what we are considering for our sequel! But the evidence as it stands is not at all circumstantial. The information bottleneck puts a hard upper-bound on the amount of signal that can be used for reconstruction. And the fact that increasing the bottleneck leads to increased image similarity shows that this bound is tight for sizes 1-50. Of course, there are many ways that the contents of this bottleneck can be further characterized, as you point out, and this is a good direction for future work.	Summary: The authors introduce BrainBits, an information-bottleneck pipeline that measures reconstruction performances from brain signals (fMRI datasets) as a function of bottleneck size by (linearly) projecting the data into a lower dimensional space of controlled dimensionality. The rationale is to disentangle the contributions to improved reconstruction quality seen in recent works into (1) improvements in actual decoding (better use of neural information - the actual goal of the decoding techniques) and (2) general improvements in generative models (more powerful architectures with better priors). Indeed the authors reveal that modern improvements are cause by the latter, with recent models making very little use of neural signals. Furthermore, the BrainBits pipeline enables inspection of which brain areas are mostly relied upon. The technique has broad applicability to both vision and language decoding and different signal modalities (however, only fMRI is reported). Strengths: a. Originality: The work provides a novel method to rigorously characterize decoding performances which surpasses previous metrics on critical aspect and is resilient to simply scaling decoder complexity. b. Quality: The work quality is generally high, with enough experimental result to support the author's claim. c. Clarity: The work is well written and properly organized. d. Significance: The results presented are of high significance for the brain-decoding community. Recent years have witnessed a wealth of novel contributions, each time showcasing evermore detailed brain reconstructions, implying significant advancements in our ability to decode neural signals. This work offers a much needed warning that we need to guard against misleading metric improvements granted by more powerful generative models and provides the tools to do so. The proposed pipeline is flexible and easy to build upon, offering a valuable contribution to the community at large. Weaknesses: - Figure 3c is hardly readable. Why are the axes y-scale range in [0, 1] (which then requires smaller inset to actually inspect the data)? Can't the range by set according to data dynamic range? - Regarding the analysis on brain regions (Figure 5). The authors claim that the BrainDiffuser model "As the bottleneck size goes up models exploit those original areas but do not meaningfully expand to new areas". By looking at the (small) image, however, bottleneck size 50 seems to have far fewer "silent voxels" (dark purple) than bottleneck 1 or 5 for example. This appears to hold also for other examples presented in Figure 11 in the Appendix (Note that Figure 11 has cut-out subplot titles that are illegible). Why do authors claim that the measured expansion is not "meaningful"? What would a meaningful expansion look like? Technical Quality: 4 Clarity: 4 Questions for Authors: - What are the implications of neural coding redundancy on the analysis presented in Fig. 4 where it is shown that a small fraction of the bottleneck dimension are effectively used by the models? Could it be that indeed the underlying neural code is highly redundant hence the model can make effective use of neural signals by using a much lower dimensionality? - Authors propose that each method should report a reconstruction ceiling. However it appears that such ceiling is not always clear how to measure. For example authors say: "No analogous ceiling procedure exists for the language reconstruction method, Tang et al 2023, [...]". It is my understanding that authors do not offer a general procedure to deal with this problem. If that's correct, how would they suggest to approach this problem in general? Confidence: 4 Soundness: 4 Presentation: 4 Contribution: 3 Limitations: The authors have adequately addressed the limitations of their study by presenting a dedicated section (6) with extensive discussion. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We appreciate the reviewer's time and good questions, which helped us clarify our interpretations. We're glad that the reviewer found our paper important to the field and easy to follow. Below, we answer the posted questions. - _Can't the range be set according to data dynamic range?_ - The inset is to emphasize the fact that for the text decoding case, reconstructed text is still very close to chance in an absolute sense. We will enlarge the label text for legibility and include a larger plot in the supplement. - _Why do authors claim that the measured expansion is not "meaningful"? What would a meaningful expansion look like?_ - In the 5 vs 50 case we meant to point out that no new significant cluster areas of activity emerge. You are correct in that “meaningfully expand” is not very precise, we will update the language in our paper to better describe our observations. We merely meant to observe that the most salient regions remained the brightest across all scales, and few new islands of activity were highlighted for the larger bottlenecks. - _Figure 11 has cut-out subplot titles that are illegible_ - Thanks for the catch! We’ll fix the spacing. To clarify, the rows of that figure were in subject ID order: 1, 2, 5, 7. - _What are the implications of neural coding redundancy on the analysis presented in Fig. 4 where it is shown that a small fraction of the bottleneck dimension are effectively used by the models? Could it be that indeed the underlying neural code is highly redundant hence the model can make effective use of neural signals by using a much lower dimensionality?_ - For comparison, for brain-diffuser, the average effective dim of the fMRI inputs is 2,257. For Takagi et al, the average is 4,485 (see additional PDF). This suggests that the underlying neural code is far higher dimensional than our bottleneck size, despite any redundancies that may exist. - _Authors propose that each method should report a reconstruction ceiling. How would they suggest to approach this problem in general?_ - The very simplest version of incorporating a ceiling, would be to always show the evaluation metrics, as they are with the ground truth inputs. For example, we show the complete scale from 0.0 to 1.0 on Figure 3c. We argue that looking at the distance to this simple ceiling is an important part of gauging whether reconstruction results can be called successful or not. A slightly more sophisticated ceiling involves using the ground truth image latents as conditioning information for the diffusion model. This is what we do in Figure 3a-b. Both of these procedures should always be feasible.	Summary: The paper proposes a method called BrainBits which aims at answering if the progress of the fMRI-to-Image/Text field of research comes from a better signal extraction from the brain or from other sources such as having better generative models or exploiting bad metrics. Their method introduces a bottleneck between the fmri data and various fMRI-to-Image/Text methods. Their method is thus directly applicable to basically every reconstruction method, and allows to change the dimensionality of the bottleneck and see whether one can obtain a substantial percentage of the original performance even with the bottleneck. Strengths: - The questions asked by the authors is very important to the field. Much progress has been made recently, but the causes of that progress remain unclear. Everyone would love the cause to be better brain signal extraction, and thus better understanding of the brain activity by the model. By providing a way to establish whether it is the case or not, the authors tackle a crucial issue. It is a known fact that the metrics used in the field lack a way of knowing how the brain data has been exploited. - The results obtained by the authors are surprising: in most cases, even with a narrow bottleneck, we can obtain a substantial percentage of the performance of the original model. - The paper is well written and easy to follow. The experiments are clear. Weaknesses: - The main weakness is that the bottleneck introduced in the paper does not definitely answer how much of the brain signal has been exploited in the process. Indeed, the MLP projecting the fMRI data to the bottleneck actually learns to identify the most important features within the brain data, in order to obtain the best reconstruction. Much like a VAE, it learns to compress information as efficiently as possible in order to have the best performance possible. Thus, the compression ratio, even if it is generally very high in the authors' results, is also a result of the best effort of the MLP to identify the best features. This crucial point kind of defeats the point of the paper: isolating how much of the brain signal was extracted and used. However, given the size of the compression ratio (300 in the case of BrainDiffusers for instance), I still believe that the authors rightfully identified that not all of the brain signal is used, and that their research is on the right track. However this point could be further improved and disentangled. Technical Quality: 2 Clarity: 3 Questions for Authors: Please answer to the main weakness I have identified. Any convincing clarification would result in a improved score of my review. Confidence: 4 Soundness: 2 Presentation: 3 Contribution: 3 Limitations: I would add the limitation identified in the weakness part, if it still stands after the rebuttal. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for recognizing the importance of our work and for their time and feedback. - _The main weakness is that the bottleneck introduced in the paper does not definitely answer how much of the brain signal has been exploited in the process. Indeed, the MLP projecting the fMRI data to the bottleneck actually learns to identify the most important features within the brain data, in order to obtain the best reconstruction. Much like a VAE, it learns to compress information as efficiently as possible in order to have the best performance possible. Thus, the compression ratio, even if it is generally very high in the authors' results, is also a result of the best effort of the MLP to identify the best features. This crucial point kind of defeats the point of the paper: isolating how much of the brain signal was extracted and used. However, given the size of the compression ratio (300 in the case of BrainDiffusers for instance), I still believe that the authors rightfully identified that not all of the brain signal is used, and that their research is on the right track. However this point could be further improved and disentangled._ - First, to clarify, we use a single linear layer, not an MLP, for projection. The nice thing about using a single linear mapping is that we can be fairly confident that no extra expressive power has been added to the reconstruction method. A single linear layer has much less representational power than a VAE. Of course, it is likely that better compressions may be possible with more powerful projection mappings, but these would be less interpretable as the reviewer correctly points out. --- Rebuttal 2: Title: Let us know if we can answer anything Comment: We greatly appreciate your time in reviewing our paper. Please let us know if our response helped clear anything up, or if there is anything else you would like answered!	Summary: The paper presents a method called BrainBits that aims to assess the extent to which generative image reconstruction based on fMRI data is based on the neural data itself, versus some spurious contribution of the reconstruction model itself (e.g., a stronger prior over natural images, or overfitting to the distribution of images used in benchmarks). The method involves introducing a bottleneck of varying size, and assessing how reconstruction performances varies based on the size of the bottleneck. They apply their method to two image reconstruction tasks and one language reconstruction task. They find that performance plateaus at a surprisingly small bottleneck size, and use this finding to argue that neural stimulus reconstruction approaches are only using a fraction of the information available in the neural data, such that we should worry that recent improvements in reconstruction are due to contributions from models, rather than more effective extraction of information from the brain. Strengths: The motivation of the paper is timely, sound, and convincing: we need to interrogate the possible sources of improved stimulus reconstruction performance, and we need ways to assess the contribution of the model versus the neural data itself. The authors argue this point clearly, and I could imagine this paper playing a useful role in raising awareness of this problem in the field, and making a first stab at addressing this issue. On a methods level, the paper appears to be sound: including the random performance and reconstruction ceiling provides helpful context, and the analyses linking the bottleneck activations to brain topography and decodable features were illuminating. The figures were well-chosen and clearly presented. The analyses support the case that reconstruction performance plateaus at a small number of dimensions (although I think the authors draw inferences from this that aren't warranted; see weaknesses section). Weaknesses: While I found the motivation for the paper to be convincing, and I believe the authors effectively make the case that a relatively small number of dimensions is sufficient to achieve maximum reconstruction performance, I think the authors' argument ignores an important piece of the puzzle: what is the effective dimensionality of the actual neural activations? For the sake of argument, suppose that the dimensionality of the neural responses (over the space of stimuli sampled) is 50: then, the fact that reconstruction plateaus with a bottleneck of size 50 is not due to the method using a small proportion of the underlying information available in the neural signal, but rather due to the fact that the neural activity patterns are themselves low dimensional (e.g., due to correlations in the underlying neuronal firing patterns, or the fact that the BOLD signal in each voxel reflects the aggregate activity of many neurons). Without addressing this issue, I don't think the authors' conclusions follow from their results. The writing style sometimes borders on overly informal ("Although, small bottlenecks are perhaps not that interesting given that the goal is to explain more of the brain"), though I believe this is easily fixed with further edits. Technical Quality: 3 Clarity: 2 Questions for Authors: 1. How can we know that the plateau in performance at a small bottleneck size reflects the model ignoring usable information in the neural measurements, versus exhausting the usable information available in the neural measurements? As mentioned in the weaknesses section, this is hard to assess without measuring the dimensionality of the neural activations. 2. Under the hypothesis that the prior in generative models is strongly contributing to reconstruction performance, it is odd to me that higher-level visual areas don't seem to be used by the reconstruction pipeline, even at higher bottleneck sizes: given that their activation is highly informative regarding object category, and given that these models presumably have a strong prior for how objects tend to look, I wouldn't have predicted this. It would be interesting (though perhaps too much for the scope of this paper) to restrict the pipeline to particular sectors of the visual system, and examine how this affects performance. Confidence: 4 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: There are no negative societal impacts that I can think of, and the limitations section provides helpful context regarding the practical application of their method. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your time and feedback. We're glad you found our work timely, sound, and convincing. We appreciate your questions, which have helped us sharpen our descriptions. - _What is the effective dimensionality of the actual neural activations? How can we know that the plateau in performance at a small bottleneck size reflects the model ignoring usable information in the neural measurements, versus exhausting the usable information available in the neural measurements?_ - The reviewer asks a good question! What is the dimensionality of the input fMRI signal and are we simply recovering this number? For brain-diffuser, the average effective dim of the inputs is 2,257. For Takagi et al, the average is 4,485. In comparison, 50 is small. (See additional PDF). We will add this figure to the appendix and note this computation in the main text. - We are glad the reviewer found our paper well motivated. We would like to further add that our main contention is not simply that the amount of needed brain data is small in an absolute sense, but that, as a field, we should always use a metric that is sensitive to the amount of brain data used for reconstruction, so as not to be misled by methods that improve on the image prior without improving on the extraction of neural signal. - _Under the hypothesis that the prior in generative models is strongly contributing to reconstruction performance, it is odd to me that higher-level visual areas don't seem to be used by the reconstruction pipeline, even at higher bottleneck sizes: given that their activation is highly informative regarding object category, and given that these models presumably have a strong prior for how objects tend to look, I wouldn't have predicted this. It would be interesting (though perhaps too much for the scope of this paper) to restrict the pipeline to particular sectors of the visual system, and examine how this affects performance._ - We suspect that higher level areas aren’t being used in part because they are redundant with early areas. Representations in early areas are retinotopic and potentially simpler than those in later areas which may be neither. - And yes! This is exactly what we aim to do in subsequent work and the main other application of our method: probing the information available in the decodings conditioned on different areas of the brain. We plan to automate this by having models look at the resulting images and then quantify the information that is being decoded: like albedo, lighting, shape, texture, class, relationships, etc. --- Rebuttal Comment 1.1: Comment: Thank you to the authors for response, which has clarified some of my questions with the submission: "The reviewer asks a good question! What is the dimensionality of the input fMRI signal and are we simply recovering this number? For brain-diffuser, the average effective dim of the inputs is 2,257. For Takagi et al, the average is 4,485. In comparison, 50 is small. (See additional PDF). We will add this figure to the appendix and note this computation in the main text." Thank you for these further analyses. However, a bit more clarity in how they're described would be useful. The PDF says "dimensionality of the fMRI inputs"--is this referring to the beta values, or to the raw time series values? And, to what extent do these dimensions reflect stimulus-related variability, versus the dimensionality of random sources of noise? This question is important, since only the former is useful for stimulus reconstructions, and only this is informative regarding how much usable information is being used by the networks. If many of these dimensions are noise-related, it is unsurprising that they're being disregarded by these reconstruction pipelines. A bit more clarity on this point would resolve my concerns on this issue. "We suspect that higher level areas aren’t being used in part because they are redundant with early areas. Representations in early areas are retinotopic and potentially simpler than those in later areas which may be neither." I remain puzzled by this issue, and I think it would be interesting to further explore (BOLD is low-res, and I would've expected the high-level information to help disambiguate parts of the image that are fuzzy based on early visual regions), but I think the paper is fine without definitively answering this question. --- Reply to Comment 1.1.1: Title: Response to follow up comment Comment: - _To what extent do these dimensions reflect stimulus-related variability, versus the dimensionality of random sources of noise?_ - This is an open question for the field at large. Parsing out exactly which activations are pertinent only to the task, is a yet unanswerable question. But this is not at odds with the goal of BrainBits! On the contrary, the purpose of BrainBits as a metric is to identify when reconstruction has ceased to extract signal from the neural recordings, whatever dimensionality that signal may be, and begun to make improvements purely on the image generation prior. The fact that this particular question remains open makes the need for BrainBits all the more critical because otherwise the only way to compute stimulus-specific ID is to attempt to find the ID of the corresponding neural response. As you note, this will possibly contain activity unrelated to the stimulus. BrainBits offers a much better alternative: try to find the ID of the bottleneck necessary for reconstructing the stimulus. - _Is this referring to the beta values, or to the raw time series values?_ - For the image reconstruction methods we computed the effective dimension of the betas, specifically the “betas_fithrf_GLMdenoise_RR (beta version 3; b3)” provided by the NSD dataset (masked to visual areas as was done by the reconstruction methods we investigated). These betas were computed using the GLM single method described in “Jacob S Prince, Ian Charest, Jan W Kurzawski, John A Pyles, Michael J Tarr, Kendrick N Kay (2022) Improving the accuracy of single-trial fMRI response estimates using GLMsingle eLife 11:e77599” which fits per voxel heart rate functions and attempts to remove other noise using the multiple responses available per stimuli. We also averaged the betas across repeated presentations within the subject. This is the same data and procedure that was used by the reconstruction methods we investigated. - From the NSD data manual the betas are described as: “betas_fithrf_GLMdenoise_RR (beta version 3; b3) – GLM in which the HRF is estimated for each voxel, the GLMdenoise technique is used for denoising, and ridge regression is used to better estimate the single-trial betas.” - _I remain puzzled by this issue, and I think it would be interesting to further explore (BOLD is low-res, and I would've expected the high-level information to help disambiguate parts of the image that are fuzzy based on early visual regions), but I think the paper is fine without definitively answering this question._ - This is certainly an interesting question to consider! And the fact that it’s on the table is a strength of the general approach. We plan on looking into it, along with looking at different regions, in a followup publication.	Rebuttal 1: Rebuttal: We thank the reviewers for their time and helpful feedback! We address each reviewer's concerns individually. Pdf: /pdf/6fa6d655b0929644c45af207fe2afbac37b3129a.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
SmallToLarge (S2L): Scalable Data Selection for Fine-tuning Large Language Models by Summarizing Training Trajectories of Small Models	Accept (poster)	Summary: This paper proposes a data selection approach to reduce the sample size required to conduct supervised fine-tuning (SFT) of LLMs for specific domains. The method achieves it by approximating the training gradients on the full data using only a subset of data. The experiments were done for SFT tasks, including (1) math problem-solving and (2) clinical text summarization. It was found that with 11% of the original dataset, the yielded model can be comparable to the one trained on the full dataset. Strengths: The paper provides a clear rationale for selecting data for Sparse Fine-Tuning (SFT) by estimating the full gradients with a subset of samples. It conducts a thorough analysis of various variants of the proposed method and includes experiments across diverse scenarios of its application. Weaknesses: 1. Data selection for machine learning has been explored in the literature. Some related works which this paper omits but may need to compare and discuss include: - influence function based approaches [1,2] - reinforcement learning based approaches [3] - data Shapley [4] 2. The generalizability of the proposed theory remains elusive. A small model is used to approximate the gradients. There are two gaps - The small model can have a distinct loss landscape from the large model. Approximating full gradients of a small model not necessarily extrapolate to a large and different models. - There is no theoretical guidance on how this small model should be like, which architecture, which parameter size, to be competent of approximating the gradients of the large model. Considering the black-box nature of deep learning, especially for LLMs, it seems very hard to build such theoretic foundation for the proposed method. [1] Wang, Z., Zhu, H., Dong, Z., He, X., & Huang, S. L. (2020, April). Less is better: Unweighted data subsampling via influence function. In Proceedings of the AAAI Conference on Artificial Intelligence (Vol. 34, No. 04, pp. 6340-6347). [2] Kong, S., Shen, Y., & Huang, L. (2021, October). Resolving training biases via influence-based data relabeling. In International Conference on Learning Representations. [3] Yoon, J., Arik, S., & Pfister, T. (2020, November). Data valuation using reinforcement learning. In International Conference on Machine Learning (pp. 10842-10851). PMLR. [4] Ghorbani, A., & Zou, J. (2019, May). Data shapley: Equitable valuation of data for machine learning. In International conference on machine learning (pp. 2242-2251). PMLR. Technical Quality: 3 Clarity: 3 Questions for Authors: From Figure 4, it is surprising that the proposed method and some baselines can outperform the full data performance with around 38% of the samples. How much benefit can the method bring if we continue to scale the data? Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: do not apply Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your feedback. We appreciate your positive comments on the rationale and thorough analysis of our method. We address your concerns and provide clarifications below: #### 1. Omitted Related Works: Our paper includes related works in the data selection domain, but we will expand this section to incorporate a discussion of the specific references you mentioned in our future revisions. Influence function-based approaches, such as those by Wang et al. (2020) and Kong et al. (2021), are not directly applicable to the problem we address with S2L. These methods rely on the availability of a validation set that is a very good representative of the test set, as they find training examples most similar to the validation examples. This is a different problem from ours, which does not assume the availability of a good validation set. Similarly, reinforcement learning-based approaches, such as Yoon et al. (2020), also address a different problem from ours. It aims to quantify the value of data by learning data values that improve model performance on a small validation set, focusing on tasks like domain adaptation. This approach also requires a clean validation set that is a good representative of the test set. In contrast, S2L focuses on dropping redundancies in the data, ensuring data diversity without the need for a clean and representative validation set. Thus, influence-based and reinforcement learning-based methods [1,2,3] are not applicable to our problem and are not considered as baselines. Calculating Data Shapley values requires evaluating all possible subsets of the dataset, (for a dataset with $ \|D\| $ instances, the time complexity of directly calculating Shapley values is $ O(\|D\| \cdot 2^{\|D\|}) $,) making it computationally infeasible for large datasets typically used in training LLMs. Approximations to Data Shapley values reduce the computational burden but still remain impractical for large-scale applications. Typically, estimating Shapley values accurately might involve several hundred to thousands of permutations, where each permutation involves training a model on different subsets of the data. In contrast, S2L’s training complexity is only a single additional training round of a smaller proxy model and its inference complexity is linear with respect to the proxy dataset size. #### 2. Generalizability of the Proposed Theory: In our paper, specifically in the "Small-to-Large Data Selection" paragraph in Section 4, we provided references and experiments supporting the use of small proxy models. In Figure 3 of our paper, we show that examples in the same loss trajectory cluster of a small model also have similar loss trajectories on a large model. This demonstrates that the clustering of loss trajectories from a small model can effectively capture the data characteristics relevant for training larger models, thereby validating our approach empirically. The reviewer is correct that in our proof, we assumed finding the loss trajectories using the target model used for fine-tuning. Assuming that the distance between loss-trajectories of examples on the proxy and target models is bounded by some constant, this can be incorporated into our theory to bound the distance between the gradient of the subset and the full data at every step of (incremental) gradient descent, and can be used to bound the size of the neighborhood around the optimal solution (found by training the target model on full data) that the target model converges to when trained on the subset. For the fine-tuning setting where we assume a bounded curvature for the proxy and target models, the above assumption is reasonable. We thank the reviewer and will incorporate this discussion. Additionally, Xia et al. (2022) analyzed the training trajectories of differently sized OPT models, ranging from 125M to 175B parameters. They showed that models of different sizes within the same architecture family pre-trained with the same data exhibit similar learning patterns and behaviors at equivalent levels of training perplexity, supporting the idea that smaller models can provide valuable insights for larger models. However, theoretically bounding the distance between loss trajectories of such models is not trivial and requires future investigation. ### Questions: New results: Figure 3 of the one-page PDF attached in the global rebuttal ([link](https://openreview.net/attachment?id=lyJkoUGNPM&name=pdf)) shows that S2L first increases in relative accuracy compared to the full data approach and then its advantage over training on full data decreases as data size continues to scale up. Ultimately, as data size approaches 100%, the accuracy will converge to that of training on the full dataset. Note that we kept the total training iterations/steps consistent for all results in Figure 3, including training on the full dataset. As discussed in the introduction section of our paper, training more on smaller, higher-quality data can be more effective than training on larger, redundant datasets. Even if we train on the full data for more epochs, our experiments show that training on S2L selected data yields higher accuracy (Figure 4 in the one-page PDF attached in the global rebuttal ([link](https://openreview.net/attachment?id=lyJkoUGNPM&name=pdf))) than training on full data with the same number of epochs, even though in this case full data takes more training budget/iterations compared to training with S2L selected subsets. By clustering based on loss trajectories, S2L ensures that the selected data is of high quality and representative, allowing the model to focus on the most informative examples. Results in Figure 3 indicate that S2L can bring significant benefits in terms of data efficiency, making better use of the available data. We hope these clarifications address your concerns. Thank you once again for your valuable feedback. --- Rebuttal 2: Comment: Dear Reviewer dErU, We hope our recent rebuttal has been helpful in addressing your concerns. If you have any remaining questions, please don't hesitate to let us know—we’d be more than happy to discuss further. We truly appreciate the time and effort you’ve put into reviewing our work, so we want to ensure we’ve adequately responded to your feedback. Best regards, SmallToLarge (S2L) Authors	Summary: This paper introduces a data selection method called Small to Large (S2L), which uses the training trajectory of a small model to build clusters and select data based on these clusters. The method is shown to be effective in two domains, math and medicine, with superior performance than other data selection methods and, oftentimes, better than training on the full dataset. A theoretical guarantee is also provided for the convergence of training based on this data selection method. Extensive analysis demonstrates S2L's effectiveness under various compute budgets and across different model series. Strengths: - The contribution of this work is indeed unique, as most data selection methods in the LLM era are focused on initial or continual pretraining and IFT, with relatively sparse attention given to SFT data in specific domains. This is important for many real-life LLM applications. - The idea is intuitive, as the training trajectory is informative of data characteristics, and effective. Additional theoretical support is provided for the similar effects during training by in-cluster data and the convergence analysis of data selected by S2L. Extensive experiments and analysis demonstrate the overall effectiveness of this method across various compute budgets (Figure 4) and for various model families like Pythia, Phi, and Llama. - Extensive analysis is also being conducted to better understand the S2L method, specifically the synergy between the cluster and fine-tuned model's embedding in terms of data similarity, as well as the robustness across the length and time frame of the training trajectory. Weaknesses: - As shown in Figure 4, it is clear that for many methods, the SFT has not yet converged. It would be interesting to see how each method affects the convergence of the SFT process and what the relative accuracy looks like, i.e., whether better performance can be further achieved. - The work studies the Pythia model as the small reference model and multiple models from different model families for task evaluation. It is intriguing to know whether other small models can serve as good reference models, and how the alignment between the pretraining data of the small and large models will affect the effectiveness of this data selection strategy. - In the LLM era, the size of SFT data scales up quickly. It will be interesting to see how this method scales with the SFT data size, for instance, at M/B token scale. - It is still tricky to determine whether the effect of such clusters will be influenced by different learning rate schedulers and optimizers. Technical Quality: 3 Clarity: 3 Questions for Authors: Please refer to weaknesses. Confidence: 5 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The work addresses the limitations of the limited domain tested and the limited size (7B) of the model used for evaluation. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your detailed review and constructive feedback on our paper. We appreciate your positive comments on the uniqueness, intuitiveness, theoretical support, and extensive experiments of our study. We address your concerns and provide clarifications below: #### 1. Convergence of SFT: The x-axis of Figure 4 is the size of the subset that we trained on till convergence. We conducted additional experiments extending our analysis to larger data sizes. Due to time and resource constraints, we focused on two data sizes larger than 38% (57% and 76%) for this extended analysis and 3 best-performing baselines in our original submission. The results are presented in Figure 3 in the one-page PDF attached in the global rebuttal ([link](https://openreview.net/attachment?id=lyJkoUGNPM&name=pdf)), which extends Figure 4 from our main submission. We observe that: - Random monotonically approaches full data performance as the data size increases, showing expected behavior. - High Learnability does not show improvement when scaling beyond 38% of the data. - Both Facility Locations and our S2L method continue to improve when increasing from 38% to 57% of the data. - As we approach 100%, the performance of all methods drops and converges to the dashed line (full data). Meanwhile, S2L consistently outperforms other approaches across all data sizes, both for in-domain and overall average accuracy. In our revision, we plan to include the remaining methods from Figure 4 that are not present in this new Figure 3. #### 2. Using Other Small Reference Models: New results: We used GPT-2 (2019), which has 124M parameters, and compared it to Pythia-160M (2024) as the reference model to select data to train Pythia-410M. GPT-2 was pretrained on the WebText dataset, which consists of 8 million web pages scraped from outbound links on Reddit, and cleaned to remove Wikipedia pages and duplicates. The Pythia models, on the other hand, were trained on the Pile dataset, a curated collection of English language datasets that is popular for training large autoregressive transformers. The Pile dataset contains approximately 300 billion tokens and includes diverse sources such as books, Wikipedia, and various web texts. Results in Figure 5 in the one-page PDF attached in the global rebuttal ([link](https://openreview.net/attachment?id=lyJkoUGNPM&name=pdf)) show that both proxy models perform comparably in guiding the data selection for training Pythia-410M, demonstrating that different small models can be effectively used as reference models. #### 3. Scaling with SFT Data Size: New results: The MathInstruct dataset, which we used in our experiments, contains approximately 60M tokens. Our method has shown strong performance and scalability with this dataset size. To further improve scalability, we conducted experiments by training the proxy on a smaller sample of the data (100K examples, ~30M tokens) for the same number of epochs (3 epochs) and saving the loss for all examples. Figure 1 of the one-page PDF attached in the global rebuttal ([link](https://openreview.net/attachment?id=lyJkoUGNPM&name=pdf)) presents the results of these experiments, demonstrating its efficiency and scalability for large datasets. #### 4. Effect of Different Learning Rate Schedulers and Optimizers: We tuned hyperparameters for fine-tuning the target model, specifically learning rate $\in$ {2e-5, 5e-6} and number of training epochs $\in$ {2, 3, 4}. Standard values were used for warmup ratio (0.03), weight decay (0), and learning rate scheduler type (cosine) as per [64]. The same hyperparameters were applied for all data selection methods, including S2L and the baselines, ensuring a fair comparison. For S2L, these hyperparameters were consistently used for both training the proxy model and fine-tuning the target model. We hope these clarifications address your concerns. Thank you once again for your valuable feedback. --- Rebuttal Comment 1.1: Comment: Thanks to the authors for the detailed reply. All of my concerns have been addressed. --- Reply to Comment 1.1.1: Comment: Thank you very much for taking the time to carefully review our rebuttal. We’re glad to hear that our responses addressed your concerns and appreciate the increase in your rating and confidence. Your feedback has really helped us improve our work. Thanks again for your valuable input.	Summary: This study presents an innovative technique aimed at improving data efficiency in the supervised fine-tuning of large language models for niche domains. The method leverages the training trajectories of smaller models to inform the data selection for larger models, thereby maximizing the utility of the available data. Experimental outcomes on tasks such as mathematical problem-solving and clinical text summarization demonstrate that this technique can significantly reduce the training dataset size while delivering better performance than other standard approaches. Strengths: - The paper addresses a critical objective: enhancing the efficiency of large models through data selection, utilizing a smaller model to streamline the selection process. - Extensive experiments are conducted to demonstrate the effectiveness of this approach. - The paper is well-structured, with the method and results clearly presented and supported by theoretical analysis. Weaknesses: - Overclaim: The paper showcases experiments on only two specialized domain datasets, yet it is presented as if the method is universally applicable. While the introduction offers some context, the title remains overly broad, and the methodology lacks domain-specific adaptations. The authors should refine the framing of their contribution to more accurately reflect its actual scope. - Marginal Novelty: Data selection using proxy models is not a new concept, as highlighted by reference [12]. Additionally, the use of training trajectories has been explored in prior studies, such as [1]. - Limited Evaluation: It would be beneficial to conduct experiments with larger language models beyond the 7B scale to validate the proposed method's effectiveness. The results only suggest that the method may be useful for smaller language models. Also, it would be better to calculate the win-rate for the summarization dataset. [1] LESS: Selecting Influential Data for Targeted Instruction Tuning Technical Quality: 3 Clarity: 4 Questions for Authors: 1. I am still not sure why using a small fraction of data is better than the performance of using full data on NUMGLUE and MATHEMATICS. Can authors provide more insights on this? 2. How to determine the number of K for clustering? Confidence: 4 Soundness: 3 Presentation: 4 Contribution: 2 Limitations: Yes Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your feedback. We appreciate your positive comments on the objective, experiments, structure, and theoretical analysis. We address your concerns and provide clarifications below: #### 1. Overclaim: S2L is generally applicable to various domains without requiring specific adaptations, ensuring its broad usability. As long as the fine-tuning data is in the form of pairs of questions and answers, our method is expected to work without any further modification. Converting domain-specific data (e.g., EHR records) into question/answer pairs has been studied in the literature and is beyond the scope of our work. Our study focuses solely on the "fine-tuning step" after the input data is formatted into question/answer pairs. We will clarify this point in our revised manuscript. Our title specifies that the method is aimed at improving data efficiency in supervised fine-tuning for specialized domains, which accurately reflects the scope of our work. Our experiments were conducted on more than one specialized domain (mathematical problem-solving and clinical text summarization) to demonstrate the potential versatility of S2L. We agree that further validation in additional domains is necessary and will ensure that the revised manuscript emphasizes this point. #### 2. Marginal Novelty: While proxy models are used by prior work such as [12], those approaches _do not translate well to LLMs_. They employ metrics like forgetting scores, uncertainty, or representations of a proxy model for data selection. Forgetting scores track the number of times a model correctly classifies examples and then incorrectly classifies them in the subsequent training iteration. While this approach is well-defined for image classification, it does not translate well to autoregressive LLMs because they do not do sample-level classification. Uncertainty metrics, which measure the model’s confidence in its predictions, as well as using representations were included as our baselines and we showed that S2L is more effective than these methods. Moreover, these methods rely on heuristics that do not provide theoretical insights. Due to the above-mentioned reasons, using a proxy model to select data for LLMs requires a different approach that works and scales better for LLMs than existing ones, which is the main contribution of our work. Unlike prior heuristics, we have provided a theoretically justified framework by leveraging the theoretical observation that examples with similar loss trajectories have similar gradients during training and empirically demonstrating that loss trajectories can effectively guide data selection. Regarding LESS, it _addresses a different problem and is not applicable to our setting._ LESS selects training examples whose gradients are most similar to the gradients of a validation set, focusing on targeted instruction tuning. In contrast, S2L does not assume access to a validation set and works without the need for clean validation data. This makes the problems S2L can address potentially more difficult. Moreover, LESS requires projecting gradients into a low-dimensional space, which is computationally expensive and slow. S2L, on the other hand, leverages loss trajectories (which are easier and faster to compute) collected from training a smaller model and uses clustering to identify representative subsets, focusing on balanced representation across clusters to ensure data diversity and efficiency. #### 3. Limited Evaluation: As an academic research lab, our computational resources are limited, and models at the scale of 7B parameters represent the largest scale we can currently experiment with. Our 7B experiments with a batch size of 64 and a maximum sequence length of 512 require 48G memory per GPU to host on 8 48G NVIDIA A6000 GPUs. Hosting models up to the 70B scale is much beyond our computational capacity. According to `accelerate`'s estimate-memory tool, training `meta-llama/Llama-2-70b-hf` with a batch size of 1 using Adam optimizer and fp32 requires 1TB GPU memory, while fp/bp16 requires 512G GPU memory, far exceeding our resources. Nevertheless, we believe that our results on models up to 7B are significant and provide a strong indication of the method’s effectiveness. New results: In response to your suggestion about calculating win-rates, we used GPT-3.5-turbo as an automated judge to evaluate the clinical summaries. We presented the judge LLM with the original findings and impression from the radiology reports and two anonymized summaries (one generated by our model trained with S2L selected data, and another generated by a model trained with full data). Our prompt instructed GPT-3.5-turbo to act as an expert radiologist, evaluating the summaries based on accuracy, completeness, relevance, and coherence, while using the original impression as a reference. The win-rate was calculated as the percentage of times the model was preferred. Our S2L model achieved a 54.8% win-rate against the full-data model. #### Questions: 1. Performance with a Small Fraction of Data: As discussed in the introduction section of our paper, training more on smaller, higher-quality data can work better than training on larger, lower-quality datasets [48,67]. Our method is theoretically guaranteed to remove redundancy (i.e. examples with highly similar effect on training) to allow the model to learn more effectively from a diverse and representative subset of training data during fine-tuning. By ensuring that the selected data is non-redundant and representative, S2L allows the model to focus on the most informative examples, thereby enhancing the overall training efficiency and performance. 2. Determining the Number of Clusters (K): Please see Figure 2 in the global rebuttal ([link](https://openreview.net/forum?id=K9IGlMQpif&noteId=lyJkoUGNPM)). We hope these clarifications address your concerns. Thank you once again for your valuable feedback. --- Rebuttal 2: Comment: Dear Reviewer 5vbK, We hope our recent rebuttal has been helpful in addressing your concerns. If you have any remaining questions, please don't hesitate to let us know—we’d be more than happy to discuss further. We truly appreciate the time and effort you’ve put into reviewing our work, so we want to ensure we’ve adequately responded to your feedback. Best regards, SmallToLarge (S2L) Authors	Summary: This paper addresses the challenge of data selection in supervised fine-tuning (SFT) of pretrained language models by introducing a novel method called SmallToLarge (S2L). The S2L method involves collecting loss trajectories from a smaller model, clustering these trajectories, and resampling the SFT data to ensure balanced representation across clusters within the given data budget. The authors tested S2L on tasks such as mathematical reasoning and clinical data summarization, demonstrating superior results compared to several existing offline and online data selection methods. Strengths: 1. The motivation of this study is clear, and the proposed S2L method enhances data efficiency in supervised fine-tuning (SFT) for specialized domains. 2. The writing is overall clear and the paper is easy to read. 3. Extensive experiments are conducted to validate the efficacy of the proposed approach. 4. The authors provide detailed analysis about why this method works. Weaknesses: 1. The proposed method may require training the model for multiple rounds, which may not scale up to datasets with millions of examples. 2. The proposed method introduce several additional hyperparameters such as the K in k-means clustering, the training epochs, but the effect of these components are not studied. 3. The connection between the theory and the proposed method is not clear. More explanation on this matter would be appreciated. Technical Quality: 2 Clarity: 3 Questions for Authors: See above Confidence: 4 Soundness: 2 Presentation: 3 Contribution: 3 Limitations: Yes Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your feedback. We appreciate your positive comments on the motivation, clarity, and extensive experiments of our study. We address your concerns and provide clarifications below: #### 1. Scalability Concerns: The S2L method requires only one additional round of 3-epoch training on a smaller model (e.g., Pythia-70M) to select a subset of training data. Training the 70M proxy on the MathInstruct dataset with 262K examples takes only 30 minutes with a batch size of 128. During this training, the loss trajectory of each example is saved, which is then used to cluster and select representative data. This selected subset can be reused for multiple fine-tuning sessions on larger models, significantly reducing computational costs compared to multiple rounds of full-scale training. For example, training the 7B model (Llama-2-7B in Table 2) with full data for 1 epoch took 10 hours with a batch size of 64 and a maximum sequence length of 512, consuming 48GB of memory per NVIDIA A6000 GPU with 8 GPUs. As shown in Table 2, with the cost of 30 minutes of training for a small 70M reference model, we can reduce the training time of the target 7B model by half without losing performance. The cost of full-scale training goes up significantly when scaling to millions of examples, making S2L a more efficient and scalable approach. New results: To further improve scalability, we conducted experiments by training the proxy on a smaller sample of the data (100K examples) for the same number of epochs (3 epochs) and saving the loss for all examples. Training the proxy on this smaller sample reduces the training time to approximately 12 minutes while maintaining performance, demonstrating S2L’s efficiency and scalability for large datasets. Please refer to Figure 1 in the one-page PDF attached in the global rebuttal ([link](https://openreview.net/attachment?id=lyJkoUGNPM&name=pdf)) for detailed per-dataset and average accuracy results. We'll add the results to the paper. #### 2. Hyperparameter Analysis: New results: We conducted a detailed analysis on the effect of K (number of clusters). The findings summarized in Figure 2 of the one-page PDF attached in the global rebuttal ([link](https://openreview.net/attachment?id=lyJkoUGNPM&name=pdf)) demonstrate that S2L maintains high performance across different values of K, indicating the method is not sensitive to the choice of K. Based on our analysis, we chose K=100 for our experiments because it provided the best average accuracy over the math evaluation datasets and use it for the medical dataset without further tuning, which confirms the robustness/stability of our method. #### 3. Theory and Method Connection: The theoretical foundation of S2L is based on the observation that, with a small curvature (which is typically the case during fine-tuning), examples with similar loss trajectories have similar gradients during training. Based on this observation, we cluster the examples based on their loss trajectories and then randomly sample examples from each cluster. This approach ensures that the subset's gradient captures the full data's gradient during training. Because the gradients of the subset and the full data are similar, each gradient update on the subset closely approximates an update on the full data. This similarity guarantees that training on the subset using (incremental) gradient descent maintains similar training dynamics and converges to a solution comparable to training on the full dataset. Our empirical results show that sampling an equal number of examples from different loss-trajectory clusters improves performance by reducing redundancy in the data. This method ensures that the selected data is high-quality and representative, enhancing the overall efficiency and effectiveness of the training process. We hope the additional explanations and analyses address your concerns. Thank you once again for your valuable feedback. --- Rebuttal 2: Comment: Dear Reviewer mU1m, We hope our recent rebuttal has been helpful in addressing your concerns. If you have any remaining questions, please don't hesitate to let us know—we’d be more than happy to discuss further. We truly appreciate the time and effort you’ve put into reviewing our work, so we want to ensure we’ve adequately responded to your feedback. Best regards, SmallToLarge (S2L) Authors	Rebuttal 1: Rebuttal: Thank you for your valuable feedback and for recognizing the strengths of our work, including its clear motivation, extensive experiments, and unique contributions to enhancing data efficiency for large language models (LLMs). We have conducted additional experiments and analyses to address the concerns raised and provide new insights, summarized in the attached one-page PDF. Figure 1. Scalability: To further demonstrate the scalability of the proposed S2L method, we conducted experiments by training the proxy on a smaller sample of the data (100K examples) for the same number of epochs (3 epochs) and saving the loss for all examples. The results, shown in Figure 1, confirm that S2L remains effective when the proxy model is trained on a smaller subset of training data and therefore is scalable to larger datasets without a proportional increase in computational costs. Figure 2. Robustness to Clustering Parameter (K): We conducted detailed experiments varying the clustering parameter K, as shown in Figure 2. The results demonstrate that S2L maintains high performance across different values of K, highlighting the robustness of our method to different clustering parameter choices. We chose K=100 for our experiments as it provided the best average accuracy across the evaluation datasets for the math reasoning task. Figure 3 & 4. Convergence and Data Efficiency: Figure 3 extends the analysis presented in the main submission, showing the relative accuracy to full data as the data size increases, with consistent total training iterations/steps for all results. Both in-domain and overall average accuracy are shown. S2L consistently outperforms other methods, such as Random, High Learnability, and Facility Locations, which were the best-performing baselines based on the results we presented in our paper, in terms of relative accuracy to full data. This underscores the efficiency and effectiveness of S2L in achieving comparable or superior performance with fewer data and fewer training iterations. Figure 4 in the one-page PDF illustrates the relative accuracy to full data across different epochs, comparing S2L-selected data and full data with the same number of epochs. Both in-domain and overall average accuracy are shown. S2L demonstrates superior performance with fewer data and fewer training iterations. Figure 5. Proxy Models: Reviewers also expressed interest in understanding whether different small models could serve as effective proxies. We used GPT-2 (124M) and Pythia-160M as proxy models for data selection to train Pythia-410M. The results, illustrated in Figure 5, show that both proxy models perform comparably in guiding the data selection, demonstrating the versatility and effectiveness of using different small models for S2L. We hope these additional explanations and analyses address your concerns and demonstrate the robustness, scalability, and effectiveness of the S2L method. Thank you once again for your valuable feedback. Pdf: /pdf/46859dd97999150821cb9d08a8dc214ec579a9df.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
ProvNeRF: Modeling per Point Provenance in NeRFs as a Stochastic Field	Accept (poster)	Summary: Paper presents a method for co-training an inference network that learns where points in a NeRF were “seen from” (ie. provenance) in the training data. This allows for quantification of uncertainty of the reconstructed geometry in terms of triangulation (location) and depth error. Mathematically frames these these provenances within a stochastic process, extending implicit maximum likelyhood estimation (IMLE) to the functional domain over infinite (euclidian) sets. Presensts a loss term for incorporation into NeRF training and demonstrate superior novel view synthesis with it, and lower triangulation uncertainty on two standard datasets. Strengths: While I'm not convinced the "Methods" section is as crystal clear as it could be, and the problem domain widely applicable, the paper appears to present a novel contribution in the extension of IMLE to infinite sets and functional samples that should be of likely interest to the NeurIPS community. The presentation is mathematically rigorous, though somewhat opaque, with extensive derivations in the supplement. Demonstrates improvements to novel view synthesis of existing NeRF scenes through co-training with their additional loss term and synthesis term, achieving improvements in reconstruction metrics. Also demonstrates quantitative SotA results over competing methods on triangulation uncertainty. Weaknesses: Introduction still leaves me asking “Why is this an important problem?”. The method only addresses triangulation uncertainty, ignoring other forms of uncertainty like transients, perhaps limiting applicability. Overly mathematical presentation. Is this being presented in the absolute simplest way possible? Confusion over just exactly which the stochastic process is being discussed. Should clearly state the use-case (NeRF training add-on, or co-training objective?) up-front. Technical Quality: 3 Clarity: 2 Questions for Authors: The exposition of section 4.1 is unclear and took me a while to understand. Primarily, I understand that for each point in space $x$ there is a distribution of provenances, But I could imagine two stochastic processes: 1) where each point is sampled from the distribution for a fixed location, or 2) where each point becomes the provenance distribution for the next point drawn. This could be made clearer. Perhaps a diagram would help. (Also note having figure S1 in the main text would have gone a long well to help me understand the method better). #25 "modeling for each point, the locations where it is likely visible.". Do you actually mean "likely visible in the training dataset", or "likely visible in the scene"? I believe you mean the former, yet this critical point was not clear to me until reading further into the paper. This seems like a critical distinction to make. ie. I could have a single view of a scene, yet properly infer that a point should be visible from many directions, even if not present in the training data. #126 "forms a stochastic process, $\mathcal{D}_\theta$ indexed by coordinates $x \in \mathbb{R}^3$" Shouldn't this be more correctly defined as a "stochastic field", given it's indexing by Euclidean space. In general this is not the "stochastic process" most readers would usually be accustomed to, as one indexed by the natural positive numbers. Also, you are defining samples as functions, not as $\mathbb{R}^3$ positions, correct? Given this is the core of your contribution, extra clarity for readers would be appreciated for this. #136, since you call $\mathbf{d}$ a "direction" it should be a normalized direction. Therefore the tuple should be in $R_+ \times \mathbb{S}^2$, right? ? If $\mathbf{d}$ is not normalized, I'm not sure I understand why (and should be called a "vector", not a "direction"). This should be a direction pointing towards the camera origin? #138 I would define (5) before (4) for clarity. Also, presumably $\mathbf{o}_i$ is the camera origin? Though I don't believe it's been defined yet. #211 Where is the actual architecture used for $\mathbf{H}_\theta$ described? This implementation detail seems critical to understanding the method, and how it might be helping NeRF training. Confidence: 2 Soundness: 3 Presentation: 2 Contribution: 2 Limitations: Authors leave discussion of limitations to a short paragraph in the supplemental. I’d prefer to see this in the main-text. Main current limitation is a long post-hoc training process. I’d also like to have seen a longer discussion on applicability of the method. Authors sufficiently discuss the societal impact of their method. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for finding our theoretical extension of IMLE to stochastic processes novel and mathematically rigorous and demonstrating improvements over existing methods. We address the questions raised below. ## Q1 Introduction still leaves me asking “Why is this an important problem?” Modeling provenances enables analysis of NeRF reconstruction from a classical stereo-matching point of view. As noted by the other reviewers, provenances are important concepts to model because they shed “insight about the quality of the input data for reconstruction” (GM1F) that “leads to a combination of traditional 3D vision-related fields, e.g. triangulation and uncertainty, to novel view synthesis” (u5T3). We will modify the introduction for better clarity and emphasis on the importance of provenance in the final version. ## Q2 Method only addresses triangulation uncertainty. Yes, one application of modeling provenances is modeling triangulation uncertainty in NeRFs. While uncertainty within NeRF’s reconstruction is multifaceted, isolating triangulation uncertainty can benefit downstream tasks such as next-view augmentation [19] that concern the capturing process (note other uncertainties such as transient are intrinsic to the scene). In the future, we hope to combine other types of uncertainty with triangulation uncertainty to achieve a more comprehensive understanding of NeRF reconstruction. ## Q3 Mathematical presentation; should clearly state the use case up-front. Thank you for your valuable feedback; we will modify our paper accordingly in our final version. Our ProvNeRF is a NeRF training add-on and we will state that up-front. We intend to describe the method in a mathematically precise way, but instead we will in the final version lighten the mathematical notations, simplify the idea's presentation and move details to the supplementary. ## Q4 Stochastic process in the exposition of Sec 4.1. Our stochastic process is defined as a collection of distributions at each 3D location instead of distribution over different 3D locations. To provide an illustration, Figure 2(a) in our rebuttal shows the provenance direction samples at different 3D locations. We will include this in the final version and add further clarifications to avoid confusion. ## Q5 Clarification on visibility. By visibility, we refer to that given by the training dataset (so the former in your question), not from the scene. We will clarify this in our final version. But modeling visibility of the scene would be an interesting follow-up work. ## Q6 Stochastic process v.s. Stochastic field. Yes, stochastic field would be a more suitable name for our provenance model, as each of our samples is a function mapping each 3D location to a provenance of it. We note that there is an inconsistency in the stochastic process literature in terms of terminology. For example, [74] defines stochastic process as an n-dimensional and m-variate random function whereas [75] defines it as those with only a one-dimensional indexing set. However, stochastic field is a more suitable name given that our indexing set is a field. We will change the stochastic process to the stochastic field in our final version. Note that we still use the term provenance stochastic process in rebuttal for terminology continuity. ## Q7 Why are directions not unit length? The predicted direction samples are not unit length to handle object/scene occlusions. We model a visibility term $v \in [0,1]$ (c.f., Eq. (5), main) as the norm of the predicted direction that accounts for how occluded this provenance sample is: this is why the distance-direction tuple lives in $\mathbb{R}_+ \times \mathbb{D}^3$. We overloaded the notation and used $\bf d$ for both the unnormalized and normalized directions. In practice, once we extract a provenance’s visibility by computing the norm of the direction, we normalize the direction and use it for downstream tasks. In the final version, we will denote the normalized direction as $\tilde{\bf d}$ and fix the inconsistencies in the paper. For further clarity, we note that our visualizations show the negative of the provenance direction (for clearer visuals) – that is the direction from a 3D location should be pointing away from the camera. ## Q8 $o_i$; defining Eq. (5) before (4). Yes, $o_i$ is the camera origin (see Ln. 99 main). We will reorder Eq. (4) and (5) in the final version; thank you for your suggestion. ## Q9 Architecture of $H_\theta$. It is a 3-layer MLP with ReLU non-linearity and input feature, hidden feature, and output dimensions being 288, 256, and 4, respectively. We will include these details in Sec. S2 in the final version. ## Q10 Limitation. Thanks for the suggestion. We will move our limitation discussion to the main paper. ## Q11 Longer discussion on method’s applicability. Our method can be applied to model stochastic fields other than provenance fields. For example, an interesting application other than provenance modeling is to model the material properties of a NeRF as a stochastic field. For instance, we could model the BRDF at each point in 3D as a stochastic field over the incoming and outgoing solid angles. Learning such a stochastic field would allow us to enable interesting applications such as relighting or material modification. Another possibility is to extend the deterministic framework in [76] to model the equivalent classes of signed distance fields given by a set of discrete signed distance samples as a stochastic field. This allows us to sample different but all plausible signed distance fields (thus implicit surfaces) given a set of discrete signed distance samples. We will include this discussion in the final version. [74] Shinozuka, M. (1987). Stochastic Fields and their Digital Simulation. [75] Knill, O. (2009) Probability Theory and Stochastic Processes with Applications. [76] Sellán, S., et. al. (2024). Reach For the Arcs, SIGGRAPH 24’ --- Rebuttal Comment 1.1: Comment: I thank the authors for their thorough rebuttal. Addressing the points as you have outlined will go a long way towards making this an excellent paper. As the practical application and evaluation metrics are somewhat weak, I do think the theoretical insight holds promise. Making the theoretical presentation crystal clear will make this paper a valuable read for the research community. Having more compelling use cases and conclusive evaluation metrics would push me into "accept" or "strong accept" territory. --- Reply to Comment 1.1.1: Comment: Thank you for taking the time to review our paper and rebuttal, and for recognizing the theoretical promise of our work. We promise to revise the notations and rearrange the presentation to clarify the theoretical analysis in the final version. While our improvements in Table 1 against baselines are modest, it’s important to note that our method is different from the baselines because we don’t introduce additional priors into the optimization process. Essentially, the geometry improvements showcased in Figure 3 come at no extra cost, thanks to our modeling of provenances. This characteristic also makes our method easily integrated into other approaches to further improve reconstruction. When compared with Bayes’ Rays [19], who, like us, can be plugged into any NeRF representations to improve its reconstruction without using additional priors, our method performs significantly better. The following shows NVS metrics comparison on the Scannet dataset between Bayes’ Rays and ours using the same pretrained SCADE model: \|Scannet\|Average\|Scene 710\|Scene 758\|Scene 781\| \|:-:\|:-:\|:-:\|:-:\|:-:\| \|\|PSNR/SSIM/LPIPS\|PSNR/SSIM/LPIPS\|PSNR/SSIM/LPIPS\|PSNR/SSIM/LPIPS\| \| Bayes’ Rays \|20.09/0.707/0.304\|21.05/0.692/0.335\|18.75/0.741/0.284\|20.46/0.688/0.294\| \| Ours \|21.73/0.733/0.291\|21.48/0.703/0.328\|21.99/0.786/0.258\|21.70/0.711/0.288\| While we cannot post rendering comparisons, the metrics above indicate that Bayes’ Rays’ regularization actually significantly degrades SCADE’s NVS quality because it removes all the uncertain regions as a post hoc operation – this operation in practice removes actual geometry rather than floaters and thus causes the degradation. In comparison, our formulation removes most of the visual artifacts as shown in Figure 3 of main and Figure 2 (b) in the rebuttal PDF without affecting the scene reconstruction. This is because our provenance stochastic process allows us to formulate an entirely differentiable regularizer and thus can improve the scene geometry through co-training instead of as a post-hoc operation. In addition to the applications in our experiment section (Sec. 5), we also provide an additional application in Sec. S5 that uses provenance to select favorable camera viewpoints based on differentiable criteria, leveraging a neural rendering framework. For instance, this can encompass orienting the camera to align with the normal vector of a specified target or achieving a detailed close-up view of the target. By incorporating provenances into the optimization objective that we define in Sec. S5, we are able to obtain a camera viewpoint that satisfies the predefined objective while achieving good rendering quality as shown in Figure S6 where we compare our formulation with a retrieval-based and a provenance-agnostic optimization-based baseline. We hope we have addressed your concerns and questions. Please do not hesitate to ask us should there be anything unclear. Lastly, we hope you can take the use cases and comparison delineated above into consideration for your final decision.	Summary: The paper describes a method for explicitly modeling the visibility of a point in space in a NeRF model. This is done though modeling provenance which is the space of points where the given point is likely visible. The motivation is that modeling visibility enables the underlying NeRF model to better utilize triangulation information from the training images. The proposed method introduces a neural network to model the provenance function which allows for sampling points visible point estimates from a given 3D position. This secondary network can be applied to any base NeRF model. When trained with the provenance loss, the resulting model performs better in the task of novel view synthesis across a variety of scenes and metrics, and allows for explicit modeling of uncertainty in the reconstructed scene geometry. Strengths: + The motivation for the problem is interesting. If you have a way to approximate where a point is visible given the input data, that does provide a lot of insight about the quality of the input data for reconstruction of view synthesis. + The results shown are good. The overall metric while better than other approaches are just a slight bump, but there are several examples shown where some of the common artifacts present in indoor NeRFs are mitigated if not completely removed using this method. That improved visual quality on top of the benefits of uncertainty modeling make this quite compelling. + The ablation in Table 2 shows that the naive ideas that most people would have tried are worse than this, so I think the more obvious baselines are covered in comparison. Similarly Table 4 is a good ablation over several methods that I think would be the go to baseline for an idea like this. Overall the evaluation is very thorough. + The main paper + supplemental is an immense amount of information and evaluation for a single paper. Clearly a lot of effort was put into describing and validating the method. Weaknesses: - Overall I found the presentation of the method to be very confusing. There is a lot of technical overview in 4.1-4.3 that I think over complicates what is actually happening. I had to reread these sections several times while making passes through the full paper to really get a grip on what is happening. The architecture diagram in Figure S1 makes it much clearer. I think the extremely technical discussion could be reduced and moved to the supplemental while a more direct description of what is actually being done like in the supplemental should be focused on more. - I don't follow why norm(d)>=0.7 has any berrying on the confidence of that provenance sample. The output provenance sample D(x) = (t,d) where the point y where x is estimated to be visible is y=x-td. So why is the length of the direction vector a signal for uncertainty? - The visualizations of the provenances for points don't align with what I expect. Why are the vectors all roughly the same length? Shouldn't it be more varied? Similarly, I don't think the definition of how to recover the point y where x is visible is correct based on the description and visualization. If y = x-td, then the output direction vector would be pointing away from points of visibility, not towards. - To reiterate my first point, the major weakness of this paper is the somewhat overwhelming amount of technical detail for what boils down to a pretty simple idea. Maybe if the details are reordered so that the simple explanation comes first followed by the more rigorous definition the paper would be easier to follow. After several reads I can follow the early sections, but they are still not extremely clear. I would recommend simplification if possible to make the core contribution as clear as possible and fill in the details where necessary instead of the current presentation. Though I admit that the technical groundwork is necessary so it is a difficult balance. But a clear example of what can be simplified is section 4.3. There is the initial equation 7 discussion, followed by the logic for simplifying to equation 8, which eventually reduces to equation 9 which is what I think most people would have assumed would be the natural conclusion. It's not to say that this presentation of the principles from equation 7 to equation 9 is not important if useful, but it is a bit heavy handed in my opinion. Technical Quality: 3 Clarity: 2 Questions for Authors: End of line 128, "we" should be capitalized. This is not necessarily a weakness, but it would be good to clarify. Are the 3D models being shown in the visualization based on evaluating the provenance on the ground truth mesh from depth fusion, or is that somehow extracted from the NeRF itself. They are shockingly clean to be extracted from a NeRF but it's not clear to me from the text if that is actually what's happening. Line 168 " We define a latent function sample Z ~ Z to be the concatenation of a random linear transformation of x and x itself." I don't think concatenation is the right word here based on equation 6. I think this sentence is phrased poorly or I'm missing something important. Confidence: 3 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: Yes Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for finding our work interesting and insightful and our evaluations thorough and compelling. We address the questions raised below. ## Q1 Presentation of the method section. Thank you for your valuable feedback. We will incorporate your suggestions and promise to improve the presentation of the method in the final version. We originally intended to describe the method in a mathematically precise way, but we understand this can cause confusion. We will lighten the mathematical notations, simplify the presentation of the idea, and move details to the supplementary. We will describe the method in a more intuitive way in the final version. ## Q2 Clarification on length and norm of direction vector. The length of the predicted direction determines how visible the provenance direction is to handle object/scene occlusion. That is, we model a visibility term $v \in [0,1]$ (c.f., Eq. (5) of main) as the norm of the predicted direction that accounts for how “visible” this provenance sample is. For further clarity, we note that we overloaded the notation and used $\bf{d}$ for both the unnormalized and normalized directions. In practice, once we extract a provenance’s visibility by computing the norm of the direction, we normalize the direction and use it for downstream tasks. In the final version, we will denote the normalized direction as $\tilde{\bf d}$ and fix the inconsistencies in the paper. Finally, in our NVS regularizer formulation in Eq. (10), we use the length of the direction vector to distinguish floaters from solid surfaces. I.e., if the predicted direction has $\lVert\bf d\lVert<0.7$, we assume that there is a solid surface in that direction and it shouldn't be regularized. Otherwise if $\lVert\bf d\lVert\geq0.7$, we treat it as a floater where we apply our regularizer to remove it. We will add this clarification in the final version. ## Q3 Variation in length of direction vectors. They are varied, as shown by the length of vectors in the supplementary video. We further provide additional visualization in Figure 2 (a) in the rebuttal PDF; we will include this in the final version. We note that the visualization in Figure 6 only shows normalized directions. We apologize for this confusion and we will change it to reflect the length of the direction vector in the final version. ## Q4 Misalignment of provenance visualization. Yes, you are right. The visualizations in Figure 6 and the video show the negative of the predicted provenance directions. This is done for ease of illustration: otherwise the samples will be hidden by the scene. We will add this clarification in the final version. ## Q5 Ln. 128. Thanks for pointing this out. We will fix it in the final version. ## Q6 Clarification of the provenance visualization. Yes, the visualizations shown in the video and Figure 6 are provenance samples generated at the ground truth geometry surface provided by the dataset. We will include this clarification in the final version. ## Q7 Ln 168. Thanks for the suggestion. Yes, the expression in Eq.(6) is a more mathematically precise definition of our random function $\bf{Z}$. We will modify the wording for a more precise definition in the final version.	Summary: This paper addresses gaps in existing Neural Radiance Fields research by modeling the provenance of each point as a stochastic process and enhancing triangulation quality through an extended Implicit Maximum Likelihood Estimation (IMLE) to functional space, resulting in improved novel view synthesis and uncertainty estimation under sparse, unconstrained view conditions. Experimental results demonstrate the effectiveness of the proposed method. Strengths: 1. The idea is interesting, especially the defined problem in this paper makes a lot of sense to me. ProvNeRF enhances Neural Radiance Fields by integrating per-point provenance information during training, which enriches the model with critical insights on triangulation quality. This integration leads to a combination of traditional 3D vision-related fields, e.g. triangulation and uncertainty, to novel view synthesis, particularly under challenging sparse and unconstrained viewing conditions. 2. The writing is very clear and easy to follow. Weaknesses: 1. My main concern is about the evaluation of the proposed idea. According to the paper, modeling the provenance for each point could potentially improve NeRF's accuracy in predicting the positions of points in space. However, there are few direct comparative experiments on depth/position, with only Fig. 4 showing some reflection. The depth error does not seem to significantly differ from other methods. This makes the evaluation less convincing from my view. 2. From Table 1,2, I wouldn't say that the result is significantly improved. And, the visualization in Fig.4, the difference between the proposed one and Bayes' is not notable. These make me a little bit concerned about the significance of the proposed method as it requires an 8-hour post-optimization. minor 1. The description of the images in Fig. 2 is reversed, with left and right sides swapped. Technical Quality: 2 Clarity: 3 Questions for Authors: 1. Does the proposed method solve the uncertainty problem? Does the uncertainty problem really matter in the NeRF-based method? If so, why does the proposed method have inferior performance compared with other sOTA methods in evaluation, e.g. table 1? 2. Can this method be applied to 3DGS or INGP-based methods? How much time it will cost to add the proposed framework in the post-optimiazation? Confidence: 4 Soundness: 2 Presentation: 3 Contribution: 3 Limitations: The authors demonstrate shortcomings concerning the optimization duration and mention a solution to address these deficiencies in the appendix section. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for finding our method interesting, easy to follow, and enriches NeRFs with critical insights on triangulation quality. We here clarify our experiment setup and avoid confusion. Our main experiments are split into two parts, each corresponding to a different application using ProvNeRF. 1) Novel view synthesis (Sec. 5.1): we use our learned provenance to formulate an additional regularizer $\mathcal{L}\_{provNVS}$ to improve scene reconstruction. We evaluate our approach in Fig. 3 and Tab. 1, demonstrating improvements compared to baselines. 2) Triangulation uncertainty estimation (Sec. 5.2): we use our learned provenance to estimate triangulation uncertainty. We show results on uncertainty estimation in Fig. 4 and Tab. 3 against baselines by measuring the uncertainty’s correlation to depth errors. This is a common evaluation protocol in prior works [51-52]. Note that in this context we do not compare the depth error across different models. We address your questions below. ## Q1 Evaluation of the proposed idea. As highlighted by other reviewers, we provide a “thorough” (GM1F) evaluation of our method and achieve improvements in both reconstruction and triangulation uncertainty metrics(o98v). In the attached PDF, we provide additional experimental results, including applying ProvNeRF on 3DGS for uncertainty estimation (Figure 1) and a depth map comparison between our method and SCADE (Fig. 2(b)). ## Q2 “Modeling the provenance improves NeRF's accuracy”. We clarify that modeling the provenance alone does not improve the NeRF’s reconstruction. However, it can be used to formulate the $\mathcal{L}\_{provNVS}$ regularizer to improve NVS and scene reconstruction as shown by experiments in Sec. 5.1. We further provide improved depth rendering visuals in Figure 2(b) of the attached PDF that supplements Fig. 3. ## Q3 “Few direct comparative experiments on depth/position, with only Fig. 4 showing some reflection.” We clarify that the depth error maps in Figure 4 are NOT to show improvement in depth as it is part of our uncertainty experiments (Sec. 5.2). Note that our $\mathcal{L}\_{provNVS}$ regularizer is not used here. Instead, Fig. 4 visualizes uncertainty maps from different methods and compares their correlations to the depth errors, which serve as a qualitative comparison for uncertainty estimation. ## Q4 Tables 1 and 2: “I wouldn’t say results significantly improved”. As noted by GM1F, while the improvements in the quantitative metrics on the NVS experiments (Table 1 & 2) are not huge, “several examples where some of the common artifacts present in indoor NeRFs are mitigated if not completely removed.” making our method “quite compelling”. This suggests that our additional regularizer $\mathcal{L}\_{provNVS}$ can improve the NeRF reconstruction by modeling provenance that comes for free from the training images. ## Q5 Difference between Bayes’ Rays in Figure 4. Sec. 5.2, Fig. 4 compares our approach against baselines such as Bayes’ Rays on uncertainty estimation. Note that a good uncertainty map should correlate well with depth error maps, marking regions with high depth errors as highly uncertain and vice versa. The boxed regions in Fig. 4 demonstrate the superiority of our estimated uncertainty over Bayes’ Rays. For example, our method accurately identifies both chairs (left and right examples) as certain due to good triangulation, contrasting with baselines that incorrectly mark them as uncertain despite their low depth errors. Again, we clarify that the results in Fig. 4 (main) do not show improvement in scene reconstruction – we do not enforce our $\mathcal{L}\_{provNVS}$ regularizer here. In fact, the depth error for Bayes’ Rays and ours are the same in Fig. 4 as we use the same base model to compute for uncertainty. For improvements in scene reconstruction see our NVS experiments (Sec 5.1.) where we enforce the regularizer to clear out floaters. ## Q6 Figure 2 caption. Thanks for pointing this out. We will fix this in our final version. ## Q7 Does the method solve the uncertainty problem and why is it important? Yes, our proposed method can be used to estimate triangulation uncertainty as shown in Sec. 5.2. Uncertainty estimation is crucial for applications needing reliable reconstruction like continual learning and robotic navigation. Several studies [51-52, 55] have addressed this within NeRF settings. ## Q8 Results are not SotA. We achieve SotA results in both NVS and uncertainty estimation applications. In the NVS experiment, Figure 3 shows our results clearly improve the previous SotA method SCADE by removing floaters and fuzziness on surfaces. This is also reflected quantitatively in Table 1 as we achieve on average better than the baselines on both datasets and ours are better in almost all the metrics; In the uncertainty experiment, qualitative and quantitative comparisons suggest that our uncertainty map is more informative -- i.e., marking poorly triangulated regions with high uncertainty and vice versa -- compared with existing baselines. ## Q9 Applying ProvNeRF to 3DGS. Yes, we can apply our method to 3DGS. We apply ProvNeRF on top of 3DGS on Scannet dataset. The post-optimization takes around 30 minutes per scene on a single NVIDIA A6000 GPU. To study its applicability, we used our trained provenance stochastic process to estimate triangulation uncertainty as in Sec. 5.2. See our global response for implementation details. Figure 1 in the attached PDF shows the comparison of estimated uncertainty maps between ours and FisherRF [73]. Note that we obtain a more correlated uncertainty map w.r.t. the estimated depth error from 3DGS. The same figure also shows a NLL comparison against FisherRF where we outperform the baseline by a large margin. These results show that applying ProvNeRF to recent explicit representations such as 3DGS is promising and we leave further exploration as future works. [73] Jiang, W. et. al. (2023). FisherRF, CVPR 24’ --- Rebuttal Comment 1.1: Comment: I am grateful for the author's reply. The rebuttal partially addressed my concerns, i.e. applying the proposed method to 3DGS. However, I am still unconvinced with the evaluation. Feeling the same with GKL5, it is weird to connect uncertainty directly with depth error. I checked with [51-52]. Although they use uncertainty in the evaluation, depth map, predicted depth, and depth errors are also shown in the figures to demonstrate their superiority. This makes the presentation of the evaluation confusing and has a large space to improve. Moreover, as the depth map shown in the pdf, the proposed method has a better estimation in the edge region of the image compared to SCADE, i.e. some guess estimation vs blank, and remains the similar quality in the middle region compared to SCADE, i.e. see the USA flag in the second column in pdf.fig.3. It seems the proposed method is good at filling the blank, not improve the reconstruction quality. Overall, I understand the evaluation is okay in terms of uncertainty. However, there is still a gap between the motivation and the evaluation in terms of reconstruction quality. Thus, I will maintain my original rating score. --- Rebuttal 2: Comment: We thank the reviewer for reading our rebuttal and eliciting their concerns which we address below. ## Weird to connect uncertainty directly with depth error We follow prior works [19, 51-52, 73] to visually evaluate our uncertainty estimation by inspecting its correlation with the depth error in Figure 4 of the main. We didn’t put the rendered depth maps in the figure because we are a post-hoc uncertainty estimation method, i.e. our approach is a plug-in to any NeRF backbone to estimate triangulation uncertainty, which means that the depth maps we obtain will be exactly the same as the backbone. However, baselines like CF-NeRF [51] and Stochastic NeRF [52] are not post-hoc methods and need to be trained from scratch with a modified volumetric rendering pipeline. So their convergence is not guaranteed and in fact, produces blurrier results than SCADE, the backbone we use. Our work is more similar to the recent baseline Bayes’ Rays [19], which also only shows a comparison between the uncertainty map and the depth error map and does not show rendered images or depths of the backbone (c.f. Fig. 6 of [19]). ## Comparison with SCADE; the USA flag in the second column in pdf. Fig.3. The error in the USA flag in Fig. 3 of the main is due to a pose inaccuracy on the dataset released by SCADE, a common issue from using COLMAP to estimate camera poses. This causes inconsistencies in the optimization, resulting in the wrong geometry of the flag. In fact, all of the methods in Table 1 take these poses as input and they all have this problem as well. This can be mitigated if we obtain better camera poses for the dataset. However, it is important to note that this problem is orthogonal to our contribution in Sec. 5.1 where we use our provenance stochastic process to remove artificial floaters, which is a common artifact in indoor NeRFs as suggested by GM1F and is mitigated by our method as shown in Fig. 3. ## It seems the proposed method is good at filling the blank, not improve the reconstruction quality. Our method does not fill in the blank. We are an optimization-based method and do not use any generative priors. Instead, the improvements in Fig. 3 are direct results of our method removing floaters from the pretrained SCADE model and revealing the correct geometry behind them. This is also suggested by the depth maps renderings we show in Fig 2 (b) of the rebuttal PDF. We hope we have answered your questions and concerns so that they can assist your final decision. Please do not hesitate to ask us should there be anything unclear.	Summary: This paper introduces a way to jointly learn/model provenance during NeRF training, where provenance is defined as locations where a 3D point is likely visible. This design is motivated by the classic idea of modeling triangulation quality, To implement this in NeRF, this paper extends implicit maximum likelihood estimation (IMLE) to functional space with an optimizable objective. Modeling provenance is beneficial to NeRF final results, and also enables a new way of uncertainty estimation. Strengths: - The introduced idea of Provenance modeling is sound and motivated by classic idea in stereo matching. - The ability of estimating uncertainty is very important, and it's a free side-product of the introduced Provenance modeling. - The idea of using Implicit Maximum Likelihood Estimation in functional space is indeed a good solution for represents probabilistic distribution as a set of samples, and also for stochastic processes. - This paper also builds up a system of theory which is complete and reasonable. This theoretical framework will inspire many follow-up work in this field. - The appendix is very informative and discussed things like extra results, important alternative designs, key derivations and ablation studies. I found it to be a good complement of the main paper. - The findings of this method is helpful to sparse, unconstrained view setting is very encouraging. Weaknesses: I find a few things can be improved as listed below: - Some motivations are less clear or need clarification, specifically: - L36 "we propose to model the provenance as the samples from a probability distribution, where a location y is assigned with a large likelihood if and only if x is likely to be visible from y": What's the alternative ways of modeling this probability distribution rather than using samples? Is it possible to learn a continuous representation rather than use discrete samples? - For sample-based generative model, what are the alternatives to implicit maximum likelihood estimation (IMLE)? Why is this specific approach is taken? A discussion could be very useful here. - The visual results are hard to interpret. Denser and more informative caption can be considered. - Why depth error is always shown with uncertainty. What's the connection and how can we interpret the depth? - Compared to the baselines such as Bayes' Rays, what are considered as improvement from the uncertainty map? Is it more semantic? Or is it more correlated with depth, means near objects tends to have lower uncertainty. - From results it appears some floaters/fuzziness are addressed but not totally. I'm wondering what's the reason and how can we address the remaining artifacts. - Since there is no GT for uncertainty, what's the best way to evaluate it? In Tab.3 NLL is used, is this the best way? - L135, provenances is parameterized as a distance-direction tuple. What's the other options here? Can we directly model it as a 3D vector? Or using other parameterization of 3D vector? - Sec.2 first paragraph "NeRFs and their Extensions" missed dicussion of recent explicit representation such as 3DGS. Also, it's unclear whether the proposed solution can generalize to 3DGS? In theory it should work but we don't know in reality. This extra backbone experiment can make the results and theory more convincing. - This paper claims the proposed method helps sparse, unconstrained view setting. Following this statement, the experiments should use a sparse setting such as few-shot NeRF. Also, I'm wondering why scannet and tanks and temple are picked as the testing benchmark but not other popular NeRF dataset (indoor, outdoor, synthetic, object-centric, etc). Technical Quality: 3 Clarity: 2 Questions for Authors: After reading, couple of questions remain: - In Fig.2, how does camera baseline distance, occlusions/visibility, and stereo range errors relate to Provenance? The connection is less clear. - Is it possible to visualize the learned confident provenances together with the camera poses in a way that can better illustrate the correctness/soundness of the learned provenances? - For results in Tab.1, is `ours` built upon NeRF? If so, is the only difference between `ours` and `NeRF` is the extra loss? - In Eq.9 there are two expectations. So in practice, two samplings are needed. I'm wondering how are D, x, and (t,d) sampled in practice. - How important are L_provNVS and L_provNeRF individually? Which one is more important and why both are needed? Confidence: 3 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: Limitations are discussed in the appendix where the authors are upfront about one important limitation of the running time. Societal impact is also discussed in appendix. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for finding our method sound, theoretically complete, and has the potential to inspire follow-up works in the field. We answer the questions raised below. ## Q1 Alternatives in modeling the probability distribution. Instead of as samples, we can either represent provenances as a discrete distribution in Eq.(4-5) main or as a closed-form continuous distribution (e.g. Gaussian Mixtures). However, discrete representations incur discretization errors and closed-form distributions have limited expressivity. In contrast, our provenances use an expressive deep net $H_\theta$. See Table S1 for an NVS quality comparison. ## Q2 Alternatives to functional IMLE. Compared to other sample-based implicit probabilistic models like GAN and VAE which are prone to mode collapses, IMLE can model multimodal distributions by implicitly maximizing likelihoods. Table 4 and Table S1 show quantitative comparisons of fIMLE against VAE highlighting its superior performance. We also tried GAN but it didn’t converge. ## Q3 Visual results and caption improvement. We include additional visualizations in the rebuttal. In Fig. 2 (a), we show provenances sampled on the ground truth surface. In Fig. 2 (b), we show improvements to depth images after applying $\mathcal{L}\_{provNVS}$ to SCADE. We will include them in the final version and update captions for Fig. 3, 4, and 6 of main for clarity. ## Q4 Uncertainty’s connection with depth error. A poorly triangulated region likely has incorrect depth due to large depth ambiguity (c.f. Fig. 5). Consequently, regions with high depth error should have high triangulation uncertainty and vice versa. Thus, we validate our uncertainty map by examining its correlation with depth errors, which is a common approach in prior works [51-52]. ## Q5 What are considered improvements in uncertainty maps? A good uncertainty map should correlate well with depth errors. E.g., the boxed regions in Fig. 4 (main) demonstrate the superiority of our uncertainty over the baselines. Our method accurately identifies both chairs as certain due to low depth errors while baselines incorrectly mark them as uncertain. ## Q6 Floaters/Fuzziness not addressed totally. Fig. 3 (main) shows visuals from the NVS experiment using our $\mathcal{L}\_{provNVS}$, improving scene reconstruction by clearing most floaters. Rendered depths included in Fig. 2 (b) of the rebuttal show further validation. While our method in theory may not eliminate all the artifacts when they are invisible from training cameras, in practice it removes most floaters as shown in the figures above. In Fig. 4 (main) that compares uncertainty estimation methods, floaters are present because we didn't apply the $\mathcal{L}\_{provNVS}$ regularizer; these floaters are from the pretrained SCADE. ## Q7 Uncertainty evaluation. NLL, a common uncertainty metric [51-52, 55], measures the negative log-likelihood of ground truth surfaces under the model's uncertainty prediction. The metric is intuitive as effective uncertainty maps should assign high likelihood to the true scene surface. While Area Under Sparsification Error (AUSE) is also used [19. 73], Figure S5 shows its defects that can lead to unreliable scores. We therefore opted to evaluate NLL. ## Q8 Provenance parameterization. Yes, we can model provenance as a 3D vector that connects the observation center with the 3D location. Other parameterizations such as a camera pose in se(3) are also viable. ## Q9 3DGS discussion. Our method is compatible with 3DGS. We integrate ProvNeRF to 3DGS and assess its triangulation uncertainty using the method in Sec. 5.2. See Fig. 1 of the attached PDF for both visual and quantitative comparisons with FishRF [73]. The results demonstrate the potential of applying ProvNeRF to explicit representations like 3DGS, and we plan to explore this further in the future. Details are in our global response. ## Q10 Experiment setting: should be sparse and why use scannet, tanks and template dataset. Our experiments indeed use a sparse setting following SCADE [58]. Specifically, ScanNet and T&T are standard datasets [58] with 18-26 training images in unconstrained camera poses in each scene. We also test NVS on the In-the-Wild dataset from [58] achieving superior metrics over SCADE: \|\|PSNR\|SSIM\|LPIPS\| \|-\|-\|-\|-\| \|SCADE\|22.82\|0.743\|0.347\| \|Ours\|22.85\|0.743\|0.343\| ## Q11 Fig. 2 clarification. Fig. 2 illustrates that modeling provenance is not straightforward, as different triangulation-related phenomena [20] such as camera baseline distance and occlusions need to be taken into account. We’ll improve this figure and caption in the final version. ## Q12 Provenance visualization. We provide additional visualization of our learned provenances in Fig. 2(a) in the attached PDF. Note that we visualized provenances together with the training cameras in the supplementary video. ## Q13 “Ours” built on NeRF? Ours is built on SCADE [58] (c.f. Ln 232-233). The only difference from SCADE is the extra $\mathcal{L}\_{fIMLE}$ loss in Eq. (8). ## Q14 How sampling is done in practice. D is sampled every 1000 iterations following IMLE [32], and (x, t, d) are sampled every iteration. ## Q15 $\mathcal{L}\_{provNeRF}$ v.s. $\mathcal{L}\_{provNVS}$. $\mathcal{L}\_{provNeRF}$ is crucial for learning the provenance stochastic process while $\mathcal{L}\_{provNVS}$ leverages this process to enhance scene reconstruction. Ablation studies show that training without $\mathcal{L}\_{provNeRF}$ leads to slightly worse results (`Ours*` in Table S1). This is because joint optimization synergistically adapts the provenance samples to the current geometry during joint optimization. Conversely, omitting $\mathcal{L}\_{provNVS}$ results in 21.44, 0.716 and 0.349 for PSNR, SSIM and LPIPS respectively. This is inferior to the pretrained SCADE because $\mathcal{L}\_{provNeRF}$ does not improve the reconstruction using provenances. [73] Jiang, W. et. al. (2023). FisherRF, CVPR 24’ --- Rebuttal Comment 1.1: Title: response Comment: Thanks for answering my questions in details. Most of concerns are addressed. I find this paper studing an important problem and the solution is sound and inspiring. I recommend acception.	Rebuttal 1: Rebuttal: We thank reviewers for their feedback and for finding our approach interesting (u5T3, GM1F), sound (GKL5), and novel (o98v). Our new formulation is classically motivated (GKL5), can be applied to any base NeRF models (GM1F), and leads to “a combination of traditional 3D vision-related fields to novel view synthesis” (u5T3). We also experimentally validate our provenance stochastic process in two applications that both lead to improvements over previous SotA methods (GKL5, o98v, GM1F). Below we include a summary of each response. Please see individual reviewer responses for more details. ## [GKL5, u5T3] Applying ProvNeRF to 3DGS. We plug in ProvNeRF to a pretrained 3DGS on Scannet with additional depth supervision for convergence. We model a provenance distribution for each splat using IMLE with a shared 6-layer MLP for $H_\theta$, which takes around 30 minutes to train. After training we use it for uncertainty estimation as delineated in Sec. 5.2 (main). Figure 1 in the attached PDF shows a comparison to FisherRF [73], a recent uncertainty estimation work on 3DGS. Compared to their uncertainty map, ours shows more correlation to the depth error as highlighted by the boxed regions. Quantitatively we evaluate NLL on the three Scannet scenes shown on the right side of the same figure and show substantial improvements over FishRF. This improvement over existing literature suggests applying ProvNeRF to other representations such as 3DGS is promising. We leave further exploration of the method and applications as future works. ## [GKL5] Alternative ways to model provenances. We experimented with other modeling strategies such as deterministic fields, gaussian mixtures, and VAEs. However, all of these methods suffer from mode collapses. Table 4 and S1 show our method’s quantitative advantage in provenance sampling and NVS co-training. ## [GKL5] How to interpret uncertainty visualization and uncertainty evaluation. Uncertainty maps are typically measured by their correlation to depth error [19]. An ideal uncertainty map should mark regions with high-depth error with high uncertainty and vice versa. We quantitatively evaluate uncertainty maps using negative log-likelihood following prior works [51-52]. ## [GKL5] Testing benchmarks. ScanNet and T&T are standard evaluation datasets used in prior works [58] that are scene-level with varied training camera setups. ## [GKL5, GM1F, o98v] Provenance stochastic process visualization. We visualize provenance samples on the ground truth scene surfaces in Figure 2 (a) of the attached PDF. Finally, we note that the visualized provenance directions are negative of the predicted directions for illustration. We will include this clarification and the figure in the final version. ## [GKL5] $\mathcal{L}\_{provNVS}$ v.s. $\mathcal{L}\_{provNeRF}$. $\mathcal{L}\_{provNeRF}$ is important for learning the provenance stochastic process and $\mathcal{L}\_{provNVS}$ is crucial for improving scene reconstruction using the provenance process. ## [u5T3] Evaluation of the proposed idea. The evaluation of ProvNeRF is split into two parts: Sec. 5.1 evaluates its NVS improvement using the additional regularizer $\mathcal{L}\_{provNVS}$. This enables the removal of common artifacts in NeRFs and improves the reconstruction metrics (GM1F, o98v). Sec. 5.2 evaluates our uncertainty estimation where we show SotA performance (o98v) compared with baselines. ## [u5T3] Results not significantly improved. Table 1, 2, and Figure 3 in Sec. 5.1 shows $\mathcal{L}\_{provNVS}$ can remove common artifacts in indoor NeRFs (GM1F). This leads to improvements in reconstruction metrics (GM1F, o98v). We provide the rendered depth images in Figure 2 (b) of the attached PDF to demonstrate the improved geometry. ## [GM1F, o98v] Overly mathematical presentation. Thanks for the suggestions. We aimed to present the method section with precise definitions. Instead, we will lighten the mathematical notations, move derivation details in Sec 4 to supplementary, and present the method section in an intuitive manner. ## [GM1F, o98v] Length of the provenance direction. We use the length of the provenance direction to model its visibility (c.f. Eq.(5)). A lower direction norm usually means that the 3D location is occluded from this direction. Additionally, we made a notational mistake and represented both the normalized and unnormalized provenance directions as d. We will fix this in the final version. ## [o98v] Importance of provenances. Modeling provenances in NeRF allows for analyzing NeRF’s reconstruction from traditional 3D vision (u5T3), shedding critical insights on NeRF’s convergence (u5T3, GM1F). We will better motivate provenances in the intro of the final version. ## [o98v] The method only addresses triangulation uncertainty. While one of our applications is to model triangulation uncertainty, isolating triangulation uncertainty can benefit downstream tasks such as next-view augmentation [19]. We leave modeling other types of uncertainty (e.g., transients) as further work. ## [o98v] Stochastic Process v.s. Stochastic Field. Thanks for the suggestion. There seems to be a terminology inconsistency for random functions with a multivariate indexing set [74-75]. But we agree that stochastic field is a better terminology as we have an $\mathbb{R}^3$ indexing set. We will change stochastic processes to fields in the final version. Note that we still use the term provenance stochastic process in rebuttal for terminology continuity. ## [GKL5, u5T3, GM1F, o98v] Typos and figures. We thank all reviewers for their suggestions. We will fix the typos and improve the figures for better illustration and clarity in the final version. [73] Jiang, W. et. al. (2023). FisherRF, CVPR 24’ [74] Shinozuka, M. (1987). Stochastic Fields and their Digital Simulation. [75] Knill, O. (2009) Probability Theory and Stochastic Processes with Applications. Pdf: /pdf/eecdab2d313d3e5801ee667992d6e29459ae7b78.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Even Sparser Graph Transformers	Accept (poster)	Summary: This paper proposes a two-phase training process for Graph Transformers to address the memory and computational inefficiencies associated with large graph datasets. The first phase involves training a small-width network to estimate attention scores. These scores are then used to construct sparse interaction graphs for a larger network, which is trained in the second phase. The authors claim that this approach maintains performance while significantly reducing memory requirements. They provide theoretical justifications for their sparsification method and validate their approach through experiments on various graph datasets. Strengths: 1. The paper is generally well-written and structured. The methodology and experimental setups are clearly explained, making it easier for readers to understand the proposed approach. 2. The paper introduces a novel two-phase training methodology. This approach is creative and has the potential to address a significant limitation in current graph transformer models related to scalability and memory usage. 3. The theoretical analysis provided in the paper gives a solid foundation for the proposed method. Weaknesses: 1. While the two-phase training process is innovative, it primarily builds on existing Exphormer. It mainly adjusts the flexibility of the expander graph and adds a sampled attention mechanism. The novelty might be seen as incremental rather than groundbreaking. 2. It was recently shown that the reported performance gap between Graph Transformers (GTs) and MPNNs on node classification is overestimated due to suboptimal hyperparameter choices [1,2]. My concern is whether we truly need global information propagation for node classification in large graphs and whether models need to approximate a full Transformer. Currently, from an experimental perspective, MPNNs with residual connections outperform GTs, even basic models like GCN or GAT. In this context, the authors need to compare the memory usage and runtime of MPNNs and the proposed method to demonstrate its efficiency. [1] Bag of Tricks for Node Classification with Graph Neural Networks. [2] Classic GNNs are Strong Baselines: Reassessing GNNs for Node Classification. 3. The authors are encouraged to include an ablation study to clarify the necessity of the two-phase training process. This study should illustrate the effects of not utilizing a wider network trained on a much sparser graph. 4. The theoretical analysis is primarily focused on the first layer of the network. It would be more compelling if the analysis were extended to deeper layers to provide a more comprehensive understanding of the method’s effectiveness. 5. Minor Issues: Lines 268-277 are somewhat confusing, particularly line 275, where the number of query nodes might be incorrect. Technical Quality: 2 Clarity: 3 Questions for Authors: The authors claim that the fixed number of neighbors for each node enables matrix multiplication calculations instead of edge-wise calculations (gather operation), improving the speed of the model. I would like to ask how much faster this approach is in terms of training time compared to Exphormer and MPNNs? Confidence: 4 Soundness: 2 Presentation: 3 Contribution: 2 Limitations: Limitations are discussed. Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thanks for your valuable review. Here are our responses. Please also refer to the rebuttal PDF for some extra tables and figures. > Innovation As mentioned in lines 97-102, we use Exphormer to interpolate between MPNNs and full-attention Transformers. Lower expander degrees make the model similar to MPNNs (particularly, eg, GAT), and the highest degree (n-1) will be equivalent to full Transformers. None of our theory relies on the expander degree or even the existence of the expander graph, and the experimental results include expander degrees from 30-200. The main idea of our work is to make a sparse and scalable method, and it made sense to start from an already sparse method such as Exphormer, and build on it to sparsify further. Sparsification from the full Transformer can be a little tricky, because the attention scores can be very small and unreliable (because of the large number of nodes to attend). In addition, our paper has other contributions of additional interest, such as the batching technique (a particular fit for our sparsification, but usable in other settings), and our theoretical results regarding the compressibility of the network. > Comparison with GNNs Thanks for pointing to these papers. The second paper mentioned here was published after our submission, and so we were not aware of it before submitting. However, there are a few important things to consider: - The networks they have used for their experiments are much larger than the ones used in our work, in the sense of the number of parameters. For example, for Minesweeper they use 15 layers with hidden dimension 512, while we use four layers with hidden dimension 32. We also have focused on the memory efficiency, and most of the small datasets are trained with less than 4GB GPU limitation. Their models have been trained on a workstation with 8 RTX 3090 GPUs (each of which would typically have 24GB of memory). - While our work is focused on memory efficiency, we also do batching based on the task and the requirements of the problem (relying on the attention scores from the initial network). However, these works need to train their method based on random subset selection batching, which as shown in our Figure 4 and Appendix E can sometimes behave very poorly. As the ratio of the batch size to the whole graph goes to zero for a fixed-degree graph, the probability of ever seeing any edge in the training process also goes to zero. By contrast, our batching is independent of the ratio of the graph size/batch size, and allows trading off time and memory without biasing the gradients of the problem parameters. - These GNNs are well studied for many years, and Graph Transformers are relatively new. Thus, there is probably also potential to also find new tricks that improve GT performance. Many key advantages of the GTs can also be brought to the GNN world, as most of these things appear in the papers you have mentioned. The long-range dependencies can be handled by deeper GNNs, and oversmoothing/oversquashing and simplistic message functions can be handled by residual connections, jumping knowledge, layer normalization, and larger hidden dimension. Even so, much smaller GTs “naturally” handle many of these problems, and so the potential for better performance by finding appropriate tricks seems solid. > Ablation studies Thanks for this suggestion; we have added an ablation study including this in our rebuttal pdf. > The theoretical analysis Indeed, this is a limitation of our theory at time of submission. Since submission, we’ve continued to work on that, and have been able to extend the result to deeper layers for a scheme similar to (but not the same as) the narrow network we use in practice: a narrow attention dimension, but dimensions for the other parts of the network (e.g., the MLP layers) the same as the target network. (This “in-between” scheme saves in the most expensive part of the network.) Because of the space limitation in this reply, please refer to [our response to reviewer UFNp](https://openreview.net/forum?id=K3k4bWuNnk&noteId=JyboPAF7sR) for the details. This expanded version of the theorem helps extend our guarantees about the possibility of approximation to deeper layers. Thank you for pointing out this important issue. > Minor Issues Thanks for mentioning this. We will fix the mistake and make the writing more clear for the next revision, as well as adding pseudocode to clarify. > Speed improvement To give you some examples, the training time per epoch for the Tolokers dataset when training on the sparsified graph improves from 0.56s to 0.47s, and for the Photo dataset, it improves from 0.43s to 0.36s on average. This is a significant improvement, considering that many other parts of the network, such as Q, K, and V mappings and the feed-forward networks, are fixed and have similar overhead in both cases, with only the attention score estimation part changing. The time improvement is even more considerable when comparing the Exphormer model to our sparsified regular graph. For example, the whole epoch time (neighbor sampling + training + validation) improves from 6.2s/epoch to 1.1s/epoch on the Tolokers dataset, and from 1.7s/epoch to 0.5s/epoch on the Photo dataset. --- Rebuttal 2: Comment: Thank you for your response. I have carefully reviewed all the content, particularly the comments from other reviewers. While I acknowledge the theoretical contributions of the paper, I remain unconvinced by the experimental results. When I closely examined Tables 1 and 2 in the original paper, I noticed that SGFormer [1] was not included. This inconsistency raises concerns about the validity of the experimental findings. The authors should conduct a thorough comparison with the latest scalable transformers [1,2], including performance, memory usage, and runtime across a broader range of datasets in the original paper (performance across all datasets). Given the current results, I will be maintaining my initial score. [1] SGFormer: Simplifying and Empowering Transformers for Large-Graph Representations. [2] Polynormer: Polynomial-Expressive Graph Transformer in Linear Time. --- Rebuttal Comment 2.1: Comment: Dear Reviewer, Thank you for your response. We wish we had heard about this concern earlier during the discussion period to address it more thoroughly. Given the time constraints, we would like to briefly address some points regarding your response: 1. SGFormer has indeed been our main baseline for the large graphs datasets in Table 2 (see the row just before our model). While we can add this baseline to Table 1, that is not the primary purpose of Table 1. The goal of Table 1 is to demonstrate that the sparsification from Exphormer maintains competitive results, and the other numbers provide context for the extent of the results for those datasets. If it satisfies you, we can add SGFormer to this table as well. Regarding large graphs, our model uses around 2-3 GB of memory, which is comparable to the SGFormer model. For instance, on Amazon2M, our model uses 3 GB while SGFormer uses 2.7 GB. Notably, our model allows for batch size reduction to train with less memory without sacrificing accuracy. However, as mentioned in Appendix E and Figure 4, random subset batching has its flaws, and reducing the batch size can significantly hinder the model’s performance. 2. Regarding the Polynormer, we have already outlined several reasons why we are not comparing our model with this baseline, and we are happy to include these reasons in our paper if it helps. To summarize, the reasons are: - Polynormer introduces an orthogonal idea that can be applied to many models, including ours. This idea enables a polynomial mixture of features and node embeddings. However, this process introduces several complexities, such as a two-stage training process and the requirement for a very large network. Our final model is sublinear with respect to graph size and achieves competitive results against linear or superlinear models. We are not pursuing every possible extension, such as adding polynomial characteristics, merely to chase state-of-the-art results. Our work has a specific purpose, and we explore ideas around it, comparing our model with reasonable baselines. - As is customary with deep learning models, models with a similar number of parameters should be compared. While our model is a much smaller network, Polynormer uses a hidden dimension of 512, and a single linear map in their network has more parameters than most of our networks. Although they do not explicitly mention the number of parameters, they typically use between 6 to 13 layers, each with many linear mappings. Additionally, while our model and our main baseline, SGFormer, aim to train on a 4 GB budget, Polynormer uses 48 GB GPU devices for training and still applies random subset batching in their work. - Not every model must achieve state-of-the-art results to be valuable. Our model aims to be memory-efficient and extend sparse pattern Graph Transformers to large graphs, offering a memory-time trade-off. We have demonstrated its effectiveness and compared it to relevant models that prioritize memory efficiency. In the NLP context, sparse pattern Transformers and low-rank models have always been distinct development threads, each excelling in different aspects. - We have addressed the limitations of a baseline mentioned in Figure 4 and Appendix E, and our model avoids these pitfalls. Even if model sizes are not convincing, we emphasize that different models should be developed in parallel. Suppressing a research direction because it does not immediately achieve top results is not scientifically sound. Different models have unique advantages, and the lack of benchmarks or not achieving the best results should not deter their development. After all, if neural networks had been abandoned early due to lack of best results, we would not enjoy their benefits today.	Summary: This paper proposes a method to reduce the memory complexity of Exphormer's transformer layers by learning a sparser attention pattern. Given some graph learning tasks, the authors first train a small-width, single-head proxy model on CPUs with large memory resources. After training, the attention scores of the smaller proxy model appear to reflect which interaction edges in Exphormer's attention network are important to solve the given task. These attention scores are used to sample (in a layer-wise fashion) sparser, regular subgraphs of the original interaction graph. These give rise to layer-wise sparse attention patterns which can be used to train a larger model on GPUs with constrained memory resources. This allows scaling Exphormer to larger graphs. Strengths: - It seems that the idea of using smaller proxy models to find sparse attention patterns is novel. Given that this approach could also be applicable to other domains, it may be relevant to the community. - The authors appear to have some theoretical results motivating their method. Weaknesses: - The paper claims that graph transformers typically suffer from quadratic memory complexity. While this holds true for dense attention mechanisms (including self-attention), efficient implementations like FlashAttention achieve linear complexity. The authors do not explore such implementations for their sparse attention approach, which could potentially lead to similar benefits. Notably, while the sparsity pattern itself requires $O(\|E\|)$ memory, it's unclear whether its storage dominates the memory usage compared to the potentially inefficient computation of attention scores as seen in Exphormer (e.g., [here](https://github.com/hamed1375/Exphormer/blob/1b43962bd418fcb7faf98f7b34e3b165ba833fb6/graphgps/layer/Exphormer.py#L46)). A more in-depth discussion on this trade-off would be valuable. - Furthermore, the evaluation focuses solely on memory consumption, neglecting runtime performance. Since runtime can be traded off for memory (e.g., via activation checkpointing), the authors should analyze the runtime implications. If the proposed method increases runtime, a detailed justification explaining the memory-runtime trade-off compared to existing approaches is necessary. - A potential bias in the evaluation is also observed. The authors use a higher expander degree (deg=30) compared to the original Exphormer paper (deg=6). This choice reportedly benefits their method (as noted in lines 524-526). However, the Exphormer baseline also uses this higher degree (lines 205-206). It's crucial to investigate how this skews the results and whether Exphormer with the original degree would have similar memory limitations. - Regarding Table 2, where Exphormer runs out of memory, stronger baselines are needed. For instance, Polynormer [1] might outperform Spexphormer on the pokec dataset. Additionally, studies like NAGphormer [2] that evaluate stronger baselines on pokec could provide evidence that even GCN might outperform Spexphormer. - To further validate the effectiveness of the proposed proxy models, including a baseline with random sparsification would be beneficial. This would demonstrate that the proxy models offer an advantage beyond simple pattern reduction. - The baseline distributions in section 5.1 appear overly simplistic. Utilizing distributions based on the actual models' behavior would provide a more realistic picture. - Ablation studies investigating the impact of value normalization (line 212) and variable temperature (line 218) would be insightful. ### Minor Points - Appendix B: This seems to contain verbatim citation. It also appears like this in the Exphormer paper, but I do not know whether that is the primary source. I think one should mark appropriate paragraphs as verbatim. - l162-l165: I feel like this is making a strong claim ("$\mathbf E^j$ is insufficient") with a very lax argument ("\[assuming\] the columns of $\mathbf K$ and $\mathbf Q$ are distributed independently and uniformly...."). I would consider removing this strong claim or adding an ablation that supports it. - l242-250: This paragraph is quite unclear. The phrasing "almost the same features" and "lead to the same result" are too unspecific for a research paper, even if one can infer what is meant. Overall, the paragraph seems to try to give an intuitive understanding why sampling should be better than selecting the top-k neighbors. Unless there are experimental results to support it, I am skeptical whether one should make the claim that one is better than the other. - In the equation in l142-143,some information regarding dimensions and the meaning of $\sigma$ could be helpful to readers. - Big Bird appears twice in references (l467, 470). Similar issue in lines 460, 462 - Landau symbols are not typeset consistently (sometimes `\mathcal` is missing) - l180-181: Being pedantic: it probably is possible to fit the transformer on the GPU, but it is not possible to train it. - l251-252: What does "exponentially large" mean? - l258-259: Do you mean $\mathcal O(\|\mathcal{N}_H(i)\|)$ complexity? - l259: what do you mean by trial and error? - l268: no space after comma - l289: I assume it should be $\|\mathcal{V}_l\|$ instead of $\|\mathcal V\|$ - l511: socal -> social - l536: missing reference #### References [1] Deng, C., Yue, Z., & Zhang, Z. (2024). Polynormer: Polynomial-Expressive Graph Transformer in Linear Time. ICLR 2024 [2] Chen, J., Gao, K., Li, G., & He, K. (2023). NAGphormer: A Tokenized Graph Transformer for Node Classification in Large Graphs. ICLR 2023 Technical Quality: 1 Clarity: 3 Questions for Authors: - The paper focuses on memory consumption for small graphs. It's expected that Spexphormer's benefits would be most significant on large graphs. To strengthen the analysis, consider estimating Exphormer's memory consumption on large graphs (e.g., by running a single training step on CPU). - The paper claims a complexity reduction for Spexphormer layers, from $\mathcal{O}((m + n)d^2)$ to $\mathcal{O}(nd^2 + ndc)$ (Eq. 31 & Eq. 77). This improvement hinges on $c$ scaling sublinearly with the average node degree. While theoretical indications for this possibility are mentioned, are there empirical results supporting it? - Section 4.2.1 suggests that Spexphormer allows for memory-efficient batching due to slower subgraph growth compared to Exphormer (line 42). Has this advantage been evaluated experimentally? - The claimed complexity of $\mathcal{O}((m + n)d^2)$ for Exphormer layers (line 31) is unclear. The Exphormer paper's discussion is also missing. Specifically, why is there an $md^2$ term instead of $md$ (there are $m$ dot products between d-dimensional vectors)? Additionally, why does the $d^2$ term change to $d$ in the Spexphormer complexity (line 77)? - Typically (including Exphormer), the equation would be $\mathbf{V}^j_i = \mathbf{W}\_o \mathbf{W}^{j}\_{V} \mathbf{X}_{\mathcal{N}_H(i)} $ where $\mathbf{W}_o \in \mathbb{R}^{d \times m}$ and $\mathbf{W}_V^j \in \mathbb{R}^{m \times d}$ and $m$ is the head dimension. This serves to reduce the parameter count. Is this also the case for you and just an accidental omission, or are you actually learning several $d \times d$ matrices $\mathbf{W}_V^j$? Confidence: 3 Soundness: 1 Presentation: 3 Contribution: 2 Limitations: While the authors identify high main memory usage as a limitation, a more comprehensive analysis of limitations is warranted. Here are some key considerations: - Efficiency of attention implementations: The paper doesn't explore the potential benefits of using efficient attention implementations like FlashAttention, which could potentially achieve similar memory savings as the proposed method. Evaluating Spexphormer's performance with such implementations would be valuable. - Impact of Expander degree: The evaluation compares Spexphormer to an Exphormer baseline that uses a higher expander degree than the original Exphormer paper. This potentially favors Spexphormer. A more balanced comparison would involve evaluating Exphormer with the original degree to understand if it suffers from the same memory limitations. - Runtime considerations: The evaluation focuses solely on memory consumption, neglecting the potential impact on runtime. Since runtime can be traded off for memory, it's crucial to analyze how Spexphormer affects runtime performance. Flag For Ethics Review: ['No ethics review needed.'] Rating: 3 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thanks for your very thorough review; sorry for brevity (character limit). Please also see rebuttal pdf for updated results. > quadratic memory complexity FlashAttention computes either full-attention or sparse-block attention mechanisms, with memory-aware loading of relevant parts of data. The use of full-attention, block-sparse attention (Big Bird), or linear approximate attention mechanisms (Performer) has been explored in the GraphGPS paper; Exphormer usually gets superior accuracies, probably thanks to its inductive bias. A full-graph transformer with FlashAttention should work (with somewhat-worse accuracy expected), but would highly rely on positional encodings, standard versions of which are difficult to compute for large graphs. This is a feasible model to explore, but would require significant innovation and be very different from our work. The block-sparse version of FlashAttention without considering the structural biases of the graph seems a poor fit for graph structures (cf BigBird results from GraphGPS). Doing FlashAttention on an Exphormer-type attention pattern seems inefficient, since the block structure seems important to FlashAttention's efficacy, while Exphormer-style graphs can have nodes of wildly varying degrees (if the original graph’s degree varies, as usual). Something like FlashAttention might be more feasible on regular graphs, as from Spexphormer. But this potential computational improvement to our approach seems to require deep thought about GPU memory structures and difficult implementation work, as did FlashAttention; we don't think this should be necessary for an initial paper exploring a new approach. > evaluation focuses solely on memory Where we can train the original network, our approach is faster than Exphormer in general. For Photo, Exphormer takes 1.7s/epoch, our initial network 1.1s/epoch, final Spexphormer 0.5s/epoch. For Tolokers, Exphormer takes 6.2s/epoch, our initial network 4.6s/epoch, final Spexphormer network 1.1s/epoch. This advantage is larger for denser graphs. We also have added some experiments on the trade-off between RAM and GPU, as we can trade-off memory and time without any advanced GPU-level implementations (Figure 2 in rebuttal pdf). > potential bias in the evaluation Even using a smaller degree Exphormer uses much more memory than our higher degree Spexphormer, see Fig 1 in our pdf for some numbers. Since Spexphormer can effectively use these higher degrees, it is more likely to be able to handle long-range dependencies. For example, in the ogbn-proteins dataset, an expander degree of 30 barely achieved an AUC of around 0.78 with a thorough hyperparameter search. Increasing the degree to 200 yielded an average AUC of 0.806. > Table 2 ... stronger baselines are needed Thanks for highlighting this. We mostly followed the experimental setup + setup code from SGFormer; while they state they use the standard 80-10-10 train-val-test split, we had not previously noticed that their code (and ours) actually uses a 50-25-25 split. The numbers in Table 2 are correct for this split, but exacerbate the difference vs Polynormer due to smaller training set; eg SGFormer's GCN has accuracy 62%, while Polynormer's is 75%. We only just realized this, and are rerunning with the standard split; we'll try to provide numbers before the discussion period ends. It's also worth noting Polynormer uses many more parameters than our models: 7 local + 2 global layers, each with hidden dimension 512, compared to our 2-layer network with hidden dimension 64. They train with batching based on a random subset of nodes, which as mentioned in Figure 4 and Appendix E can fail catastrophically; on Pokec in particular, though, the neighborhood summary is the most important feature, and the graph structure is not especially relevant, so this does not hurt much. The idea of polynomial layers is also possible to directly drop in most common architectures, including ours; a SpexPolynormer combination model would be straightforward to write down. Their added complexity and hyperparameters, however, including a warm-up phase, mixture of global and local layers, etc. makes this cumbersome to include when exploring other new ideas. Also, all of our current large-graph experiments now run with under 4GB of GPU memory, showcasing that our approach works well with very small batch sizes – unlike random-subset approaches which do not scale to small batches. (See the rebuttal pdf for more.) Moreover, our first phase of training uses high CPU memory, but later training and evaluating the learned model on a given node can be done with low memory. Pollynormer, SGFormer, even GCN all batch for low memory during training, but evaluate with high CPU memory (loading the whole graph). > Baseline with random sparsification; baseline distributions appear overly simplistic Also, uniform neighbor sampling is a common approach, used famously eg in GraphSAGE which often gets competitive results. In Table 1 of the pdf, we see using our network instead of random sparsification helps a lot in some datasets. We’re not sure what you mean by “distributions based on the actual models’ behavior,” other than exactly the distributions that we use in Spexphormer. Do you have a specific baseline in mind to compare to? > Ablation studies Good idea; also in new Table 1. > Appendix B Thanks for noticing this; sorry for the mistake which we overlooked in submission. We will rewrite this section. > l162 Our claim is not that it is _always impossible_ (though it is at initialization) for a model to decide to e.g. ignore expander edges, but that bias variables make it much easier. We’ll clarify. > l242 You are correct that we are making an intuitive argument for why we chose sampling over top-k selection; we'll clarify. > Other minor points Thanks; we'll fix these. > Questions Please see the separate author response above; thank you for your detailed review! --- Rebuttal 2: Comment: We again thank the reviewer for the detailed review. Here are a few new confirmations: Sampling Importance: Using the maximum-ranked edges instead of sampling can lead to poor results, especially seen on heterogeneous datasets. Here are some numbers: \| Dataset \| Sampling w Attention Scores Ratios \| Maximum Attention Neighbors \| \| -------- \| ------- \| ------- \| \| Minesweeper \| 90.72 ± 0.06 \| 87.92 ± 0.26 \| \| Tolokers \| 83.15 ± 0.12 \| 80.85 ±0.23 \| \| Photo \| 95.24 ± 0.12 \| 95.07 ±0.20 \| This confirms that sampling instead of getting the maximum is usually a better approach. The size of the effect can be very different among datasets, though. Subgraph Growth: For the efficiency of batching, as we argued earlier: > When $c$ is smaller than the expander degree $k$, as usual in our work, the neighborhood expansions are strict subsets of those from Exphormer. We haven't yet done explicit experimentation on this but will try to do so during the discussion period, or else for the revised version. It is easy to see our expansion should be much smaller than for example batching with considering the whole neighborhood. For example, for the Photo dataset if we start with 5 nodes, averaging over 10 times of sampling 5 initial nodes and extending the neighborhood our method increases the neighborhood size (number of nodes $\pm$ std) with the following numbers in layers: 0: 5.0 $\pm$ 0.0 1: 28.9 $\pm$ 1.1 2: 164.8 $\pm$ 7.4 3: 818.1 $\pm$ 37.1 4: 2587.7 $\pm$ 94.1 However, whole neighborhood sampling has these number of nodes: 0: 5.0 $\pm$ 0.0 1: 274.1 $\pm$ 45.1 2: 6172.3 $\pm$ 356.0 3: 7650.0 $\pm$ 0.0 4: 7650.0 $\pm$ 0.0 The graph has 7650 nodes in total; in 2 layers it already extends to the whole graph. This expansion can be smaller by reducing the expander degree, but the expander graph approximates full-attention Transformers, and thus if the expansion does not reach the whole graph, obviously the expander graph will fail in approximating the full-Transformer. This is not the only advantage, and as we have previously posted in the response to Reviewer vT4j, this lets us have regularity in our model and caused over 16% speed-up in the calculations for the Tolokers and Photo calculations over the sparse but not regular calculation scheme. The memory saving over the full neighborhood even without batching (which means we are not using the advantage of the slower expansion of our method in this comparison) has been explored in Figure 1 of our rebuttal PDF. Pokec Dataset and Polynormer Model Baseline: For the Pokec dataset, we can confirm that we have used SGFormer’s data split, which is different from the one used in the Polynormer paper. Our experiments are valid and we are comparing with numbers from SGFormer’s table, thus all the numbers are using the same split. Our method is not comparable with the GCN, NAGphormer, and Polynormer numbers mentioned by the reviewer due to different data splits, and if you compare our model with GCN with the SGFormer split our method has far superior results. For comparing with Polynormer in general as is common in the machine learning community, usually, methods with a similar number of parameters should be compared. Our model for the Pokec dataset has only 83,781 parameters, and while Polynormer does not report the number of parameters explicitly they use a hidden dimension of 512, which with only one layer of a linear map would need 262,144 parameters. They have 9 layers in total for this dataset, each having multiple linear mappings. Thus the scale of the number of parameters is not comparable at all. We have made our best effort to answer all the reviewer's concerns. We would greatly appreciate it if the reviewer could read our rebuttal and let us know if there are still concerns remaining. We would be happy to answer, though the remaining time from the discussion period is very short. --- Rebuttal Comment 2.1: Comment: Thank you for your detailed response. However, I remain unconvinced by the justification provided regarding the applicability of FlashAttention to memory-efficient sparse attention. More importantly, I do not think different data splits or model sizes are valid reasons to avoid comparing with stronger baselines. Therefore, I will maintain my initial score. --- Reply to Comment 2.1.1: Comment: Dear Reviewer, Thank you for your response. We hope that you are satisfied with the other parts of our rebuttal. Given the time constraints, we would like to address two points regarding your comment: 1. Regarding the FlashAttention type implementation, we would like to remind you that this implementation requires CUDA-level optimization, which is not straightforward in the highly irregular space of graph structures. Please note that the maximum graph size here is much larger than the context length typically used in Transformers for NLP, making full attention with simple masking not a viable option. While the direction you mentioned is worth pursuing, it has not been the focus of our work and is beyond its scope. 2. Regarding the baseline, not every model must achieve state-of-the-art results to be valuable. Our model aims to be memory-efficient and extend sparse pattern Graph Transformers to large graphs, offering a memory-time trade-off. We have demonstrated its effectiveness and compared it to relevant models that prioritize memory efficiency. In the NLP context, sparse pattern Transformers and low-rank models have always been distinct development threads, each excelling in different aspects. Our final model is sublinear with respect to graph size and achieves competitive results against linear or superlinear models. We are not pursuing every possible extension, such as adding polynomial characteristics, merely to chase state-of-the-art results. Our work has a specific purpose, and we explore ideas around it, comparing our model with reasonable baselines. We have addressed the limitations of a baseline mentioned in Figure 4 and Appendix E, and our model avoids these pitfalls. Even if model sizes are not convincing, we emphasize that different models should be developed in parallel. Suppressing a research direction because it does not immediately achieve top results is not scientifically sound. Different models have unique advantages, and the lack of benchmarks or not achieving the best results should not deter their development. After all, if neural networks had been abandoned early due to lack of best results, we would not enjoy their benefits today.	Summary: This work studies the topic of sparsifying Graph Transformers which if quadratic is not scalable even on medium sized graphs. It builds on recent works like Exphormer, GraphGPS, SAN, among others and proposes a new two stage procedure with the naming Spexphormer. It is designed to reduce memory complexity for node classification tasks. The two stage process helps improve the scalability limitations of existing work such as Exphormer. First, a narrow network is trained on a fully augmented graph to estimate attention scores and these are used without edge features. These attention scores are then used to train a wider network on a much sparser graph. Experiments conducted on 11 datasets show that Spexphormer achieves competitive accuracy with lower memory usage. Strengths: - The question of how can graph transformers be further made scalable - through sparsification - is addressed. Although there can be multiple directions to scale the network which are discussed in the literature review section. - The two stage training forms the basis of sparsifying the graph even further than Exphormer. While doing this, there can arise several challenges. These challenges are touched upon by the paper to a decent extent. - Experimental analysis shows a clear reduction in the memory usage of the proposed Spexphormer with the base model. - The method follows a theoretical justification of why the approach of sparsification makes sense, though with assumptions. Weaknesses: together with Questions below Technical Quality: 3 Clarity: 2 Questions for Authors: - Although the sparsification is addressed, the two stage process can be complicated to implement without expertise. Moreover, the reliance on the first narrow network could mean error propagation to the actual model. The paper mentions this limitation and provides a study for the approximation in 5.1. However, it may not be true universally. - The experiment section shows reduced memory usage for the smaller datasets, and in generally the maximum node size of datasets used is in ~2 million range. I would be curious to see the trends on the datasets of Table 2, eg. Amazon2M products dataset. - In section 4.3 and later in appendix, it seems the approximation aspect is studied for the first layer only, which makes it for simplification, understandably. What are the implications of this with respect to layer wise sparsification in terms of the approximation guarantees? - Writing format: For better readability, the Figure 4 can perhaps be placed appropriately before the experiments as it relates to the motivation of the method. Confidence: 4 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: Yes the paper discusses the limitations of the method in the work. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thanks for your valuable feedback! Here you can find our response; we also encourage you to check our rebuttal pdf for some new experiments. > the two stage process Even for one-stage training, hyperparameter tuning is a significant part of the training. In our setup, the first stage is relatively easier to tune — we only need one training run that converges from the initial network, and as the number of layers and the hidden dimensions are fixed, usually just tuning the learning rate works. So the “overhead” of training two networks is not so huge, compared to the usual process of hyperparameter tuning. We think this plus the additional extra complexity – mitigated by us releasing documented code for the two-stage pipeline – is not so extreme, and often worth it for the benefits it brings. Also, the training process of the second network is independent of the initial network given the attention scores. We intend to share the attention scores we have from our initial network’s training publicly for possible future uses. > error propagation It is true that the error can propagate. However, this is not too drastic because the second network learns its own attention scores. The neighborhood sampling is done with the initial network, and the second network just gets the updated list of the neighbors and learns its own attention scores. As long as the initial network gives reasonably high attention scores to important neighbors, the second network can adjust the attention scores. Even if some of the selected neighbors are not very informative, the second network can ignore them by giving a lower attention score. If an informative link is missed, it is likely that the needed information can propagate through other (longer) paths. Also, different neighborhood sampling per Transformer layer helps to mitigate the possibility of missing important links. Even if some of the important neighbors are underestimated in the initial network, increasing the number of sampled neighbors can also help bring them back to the sampled neighborhood. Our experimental results in Table 1, compared to Exphormer, show that the total amount of introduced error is not that large, and our approach can give competitive results. > The experiment section shows reduced memory usage ... In Figure 3, the memory has been reported from the actual running of the methods for smaller datasets. It is not feasible to train the original Exphormer on a 40GB GPU even with only 1 layer and hidden dimension of 4 or 8. Among the tested datasets, the largest feasible for Exphormer is ogbn-arxiv, where we see a ~5x reduced memory usage. The memory savings is considerable even without any batching. Training the model with two layers and hidden dimension 8 requires near 200GB for Amazon2M dataset; training it with the hidden dimension 256, and without advanced techniques that trade memory and time, requires between 32 (256/8) to (32)^2 times more memory, which is not feasible even with most CPU devices. > theory Indeed, this is a limitation of our theory at time of submission. Since submission, we’ve continued to work on that, and have been able to extend the result to deeper layers for a scheme similar to (but not the same as) the narrow network we use in practice: a narrow attention dimension, but dimensions for the other parts of the network (e.g., the MLP layers) the same as the target network. (This “in-between” scheme saves in the most expensive part of the network.) The result is as follows: Theorem: Assume we have a Transformer network $\mathcal{T}$ with arbitrary large hidden dimension $d_l$, $L=O(1)$ layers, and in this network, in all layers, we have $\lVert h_\cdot\rVert_2 \leq \sqrt{\alpha}$, and $\lVert W_\cdot \rVert_{op} \leq \beta $. There exists a Transformer $\widehat{\mathcal{T}}$, that for any layer $\mathbf{W}_Q$ and $\mathbf{W}_K$ are in $\mathbb{R}^{d_s \times d_l}$ for a $d_s=\mathcal{O}(\frac{\log n}{\epsilon^2})$, with a sufficiently small $\epsilon$, and for all $i \in [n]$, $\lVert\mathcal{T}(X)_i - \widehat{\mathcal{T}}(X)_i\rVert_2 = \mathcal{O(\epsilon)}$. The proof idea is to use Johnson-Lindenstrauss for the attention scores, bound them by relative error, and then bound the Euclidean distance of the other vectors based on the errors happening in the attention scores. The difference here with the previous proof is that the error can propagate from the Euclidean distance from the input of the layer too. But, we bound all these errors and show that the total error is still $\mathcal{O}(\epsilon)$. This proof only works for narrow attention score estimation, and assumes the other parts of the network have the same dimensions. This is, however, the most memory/time-intensive part of a Transformer architecture. The rest of the sections are node/token-wise and linear with respect to the number of nodes. The attention score estimation part of a full-Transformer layer requires $\mathcal{O}(n^2d)$ operations and $\mathcal{O}(md)$ operators are required for a sparse Transformer with $m$ attention edges. Thus this change effectively changes the computational complexity of the model. Also, another interesting thing about this proof is that it not only shows that there is a network with similar attention scores but narrow attention calculation hidden dimension; but also by bounding the error in the output, it shows that this network is nearly as good as the large one, and thus if the large network is optimal, this would be at least near-optimal network in the lower dimension. This expanded version of the theorem helps extend our guarantees about the possibility of approximation to deeper layers. Thank you for pointing out this important issue. >Writing format We very much agree with this comment and we will definitely move that figure for the next revision. --- Rebuttal Comment 1.1: Title: Reply to rebuttal Comment: Thank you for your responses. While the limitations of the two stage process and the error propagation may still hold to the best of my understanding, I believe the answers indicates towards how it does not alter (that much) the overall advantages brought by the sparsification of Exphormer like architecture in the proposed way. The memory trends of Amazon2M sized datasets also exposes the prior graph transformers which are memory-demanding, necessitating further sparsification. Taking in consideration the points raised in other reviews and pending revision based on the replies, I adjust my score to accept. --- Reply to Comment 1.1.1: Comment: We would like to thank the reviewer for acknowledging our rebuttal and raising the score. > The memory trends of Amazon2M sized datasets also exposes the prior graph transformers which are memory-demanding, necessitating further sparsification. Indeed, this has been one of the main points of our work. Thank you for pointing this out. As promised in our rebuttal, we will ensure to publish a cleaned-up version of our code along with our attention scores to make implementation easier for the community and enhance the usability of our work.	null	null	Rebuttal 1: Rebuttal: # New experiments All reviewers: please see the PDF linked below, which has some new experimental results. # Further response to Reviewer X47Y Due to character limits in responding to your very thorough review, these are continued here; thanks again for your work in reviewing our paper! > To strengthen the analysis, consider estimating Exphormer's memory consumption on large graphs (e.g., by running a single training step on CPU). We use 200GB of memory to train on a dataset such as Amazon2M with only hidden dimension 8. Training the network with hidden dimension 256 would require at least 32 times the memory, which we did not have available, even on CPU. Alternatively, the memory and time could be traded here, as you mentioned earlier, but training for 150 epochs with hidden dimension 8 takes almost a day; checkpointing or similar techniques could easily make the training take a week or more. > The paper claims a complexity reduction for Spexphormer layers, from $\mathcal O((m+n)d^2)$ to $\mathcal O(nd^2+ndc)$ (Eq. 31 & Eq. 77). This improvement hinges on c scaling sublinearly with the average node degree. While theoretical indications for this possibility are mentioned, are there empirical results supporting it? Spexphormer improves this asymptotic complexity if $m > n c$, or $c < (m/n) = \rho$, where $\rho$ is the average degree of the graph. This is in fact always the case in our setup. If we want to have the benefit of the expander graph, a regular expander graph of let's say degree $k$ would be added; in all our experiments $c < k$, and thus it is guaranteed that $c < \rho$. In most cases we also have $c < \rho - k$, if we considered not using the expander graph at all. $c/\rho$ values are as low as (0.08, 0.05) for the two layers of Proteins, and on average around 0.1 for the homophilic datasets in Table 1. In addition to the lower degree, the regularity of the sampled graph helps with avoiding many complexities from varying degrees in the nodes, helps with the batching process and more efficient calculations as mentioned in section 4.2.2. > Section 4.2.1 suggests that Spexphormer allows for memory-efficient batching due to slower subgraph growth compared to Exphormer (line 42). Has this advantage been evaluated experimentally? When $c$ is smaller than the expander degree $k$, as usual in our work, the neighborhood expansions are strict subsets of those from Exphormer. We haven't yet done explicit experimentation on this but will try to do so during the discussion period, or else for the revised version. > The claimed complexity of O((m+n)d^2) for Exphormer layers (line 31) is unclear. The Exphormer paper's discussion is also missing. Specifically, why is there an $md^2$ term instead of $md$ (there are $m$ dot product between $d$-dimensional vectors)? Additionally, why does the $d^2$ term change to $d$ in the Spexphormer complexity (line 77)? We briefly discussed this in lines 149-153, but will clarify. $md^2$ is because of the line `E = self.E(edge_attr)` in `ExphormerAttention.forward`, in the file `Exphormer/graphgps/layer/Exphormer.py` from the Exphormer repo. This edge feature mapping is a $d \times d$ multiplication, because Exphormer is used on datasets with many types of varying edge features. In Spexphormer, we only have three possible values of edge features, for each type of edge; thus we can replace that mapping with an edge type embedding, reducing the complexity to $m d$. For all the memory comparisons we have fixed this on the Exphormer as well. This is a very small change, but it drastically saves memory as usually $m \gg n$. > Typically (including Exphormer), the equation would be ... Our attention formulation is same as the Exphormer. We will revise this for future versions of our model. However, we should clarify that $W_O$ is actually of size $d \times d$ (not $m \times d$) in both Exphormer and the originating paper. $W_O$ will be applied on the concatenation of the heads, to mix the heads together. In our case, this can be combined with the next feed-forward network following the attention mechanism (as common in Transformer architectures). The reason why Exphormer cannot do that is that they combine their model with an MPNN, and the feed-forward network part applies on the combined representations coming from the Transformer part and the MPNN. Since we remove the MPNN part, we don't have this problem, and representationally $W_O$ can be absorbed into the next layer. Pdf: /pdf/5a53a7667d0632918cd1120c1ac0b9454d9d8c9a.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
An Analytical Study of Utility Functions in Multi-Objective Reinforcement Learning	Accept (poster)	Summary: The paper considers the problem of multi-objective RL and performs a rigorous theoretical analysis on the space of optimal policies as a function of the utility functions and preferences. Specifically, in teh case of utility optimal policies, it considers two types of optimality - at the state level and at all states level. The key contribution in this sub-task of utility optimality lies in demonstrating that the more common utility function conditions such as monotonicity, differentiability and strictly montonically increasing and continuously differentiable are all insufficient to guarantee optimality. Simple counterexamples are provided for each of these cases to prove their insuffiency. Given these observations, a signficiant contribution of the paper is in the identification of the conditions under which utility optimal policies exist for all states. Specifically, the paper identifies that a decomposable utility function of the form h(g(x)) where g is an affine function (linear with a constant) is one such condition under which the u-optimal policy exists. The second key contribution of the paper lies in teh fact that it considers user preferences, and identifies quasi-representative preference relations allows us to identify u-optimality. Strengths: + The paper is written well. It idenfies the problems clearly, motivates them well and provides simple counterexamples. + The problem addressed in this paper is an important one, that of deeply understanding multiobjective RL. It is probably the most natural setting inside RL and not enough attention is being given to this challenging task. So from that perspective, this is a very interesting read. I thank the authors for carefully constructing the problem and clearly explaning the challenges and then present their observations. + The two observations of decomposable utility (with affine functions) and the quasi-representative preferences are quite important. Weaknesses: - While the paper is written well and the problems are motivated well, I would have liked to see a specific discussion on the types of settings/problems where such situations are plausible/common. For example, where would one observe this decomposable affine functions or quasi-representative preferences in real-world? It would be nice to see a section with some real examples to make this paper's analyses clearer. - While I understand that the having a decomposable utility (with affine functions) can result in u-optimality, what is unclear is that are they sufficent or complete conditions? - Same issue with the quasi-representative preferences. While they themselves can be complete and transitive, is the condition of quasi-representativeness sufficient for optimality? If so, can you expand how? Technical Quality: 4 Clarity: 3 Questions for Authors: Please see the weakness part. I specifically would like to understannd the sufficiency and completeness of these conditions and if possible a discussion of the situations where these are both practical or common. Confidence: 4 Soundness: 4 Presentation: 3 Contribution: 3 Limitations: There are no significant potential societal negative impacts. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for their comments, suggestions, and feedback. We appreciate that the reviewer agrees with us in the need for addressing in more depth the theoretical aspects of multi-objective reinforcement learning. We proceed to answer the questions: Question 1: Regarding the types of problems that we address and their link to real-world problems. We cannot enter into much detail here, but linear utility functions (a particular kind of affine functions) represent a large majority of utility functions in real-world applications (due to their simplicity and well-known properties). To give one recent example, Rodriguez-Soto et al. in "Multi-objective reinforcement learning for designing ethical multi-agent environments" (2023) showed an example gathering scenario in which agents needed to face lexicographically two objectives (one individual related to how much the agent can gather for itself, and another one ethical, related to how much it helps the community), and provided a linear utility function that was able to reach lexicographic solutions (i.e., agents learned to prioritise the ethical objective over the individual one). We will also mention in our camera-ready version some of the practical examples of utility functions in the most recent MORL surveys, such as Hayes et al. "A practical guide to multi‑objective reinforcement learning and planning" (2022). These examples tackle problems route planning, water management, and wind farm control. Interestingly, another large body of work in MORL has tackled the problem of assuming an unknown utility function and trying to compute a solution set general enough to at least include a solution to this unknown function. This may lead to unexpected problems, as we have tried to show in this paper, in which we put the focus back into the utility functions themselves. Regarding preferences for which a quasi-representative utility function exists. As mentioned in the paper, the first two conditions of our Theorem 3 (Completeness and transitivity) are very common conditions for preference relations in game theory, so we expect it to cover the majority of most used preference relations. The third condition of Theorem 3 (that a maximal element exists per state) is virtually assumed by the whole MORL community since the goal is to always maximise the utility function (implicitly assuming that there exists a maximal element). In fact, it is difficult for us to even think of an example preference relation for which a quasi-representative utility function would exist without satisfying the conditions of Theorem 3. And recall from our definition that if the utility function is not quasi-representative of the preference relation, then maximising the utility would lead to not maximising the preference relation. Question 2: We apologise if Theorem 2 was not clear enough. The conditions of Theorem 2 are only sufficient conditions, but not necessary. As a quick example, notice that for any single-state MOMDP, any <u,s>-optimal policy of this single state is also by definition a <u>-optimal policy. Theorem 1 proves that we only need continuity to reach a <u,s>-optimal state (much more relaxed condition than being affine). In future work we expect to further study the necessary conditions for a <u>-optimal policy to exist in general MOMDPs. **Question 3: We hope that we are understanding the reviewer properly on this question, if not, we will correct our answer in the reviewer-author discussion. Again, we apologise if Theorem 3 was not clear enough. Theorem 3 only provides the sufficient conditions that a preference relation needs to meet to guarantee that an associated quasi-representative utility function exists. However, the reviewer is right on their intuition: it is sufficient for a utility function to be quasi-representative of a preference relation in a given MOMDP to guarantee that a <u,s>-optimal policy exists for every state of the MOMDP. We did not have space in the final paper to include this result. It is easy to prove: Theorem 3 requires the preference relation to have at least one maximal element (policy) per state. Then, if the utility function is quasi-representative of this specific preference relation, we require it to be the maximum element (policy) per state. In other words, we require it to have a <u,s>-optimal policy per state. Again, the necessary conditions for both issues here are future work that we are eager to tackle. --- Rebuttal Comment 1.1: Title: Thanks for the response Comment: I thank the authors for taking the time to carefully read the review and write the response. My questions on the two theorems were about sufficency vs necessary conditions. The response has made this quite clear to me. I hope that the authors will make the theorems clearer in the next iteration of the paper. Finally, there were some more multiobjective learning papers in mid 2000s (they were called as multicriteria RL back then). I suggest that the authors cite those papers in their paper as well for the sake of completion.	Summary: This paper studies the expressiveness of utility functions in multi-objective reinforcement learning (MORL). In MORL, the reward function of the MDP is a vector of multiple (possibly) conflicting reward functions, and the goal of an agent is to maximize a given utility function (function mapping the vector value function to a scalar) that expresses the preferences of a user. In particular, the paper studies two problems within MORL: (i) which utility functions are guaranteed to have an associated optimal policy? (ii) whch user preferences can be expressed via some utility function? The paper shows that, for (i), a continuous utility function is enough for optimality in a given state, and utility functions decomposable as a combination of an affine and a strictly monotonically increasing function is enough for optimality in all states. Regarding (ii), the authors show that for quasi-representative preference relations that satisfy a few conditions (e.g., completeness, transitivity), a quasi-representative utility function always exists that expresses the given preference. Strengths: - The problem studied in this paper is very relevant to the MORL community. - The paper is written clearly and the results are easy to follow. The authors present examples that make it easier to understand the introduced theorems. - The distinguishment between “preferences” and “utility functions” is, to the best of my knowledge, a novel perspective that can help the study of MORL under non-linear preferences. Weaknesses: - The main weakness of the paper is that it does not do a good job in discussing previous theoretical works in MORL and comparing/discussing its findings with the related literature (see below). - A few introduced results are not entirely novel but phrased differently than in previous works. For instance, that a stationary deterministic optimal policy may not exist for non-linear utility functions is a known result (Example 3). - Although the paper showed sufficient conditions for preferences being possible to express in terms of utility functions, it does not discuss how the results could be used to create or solve such utility functions in practice. Technical Quality: 3 Clarity: 3 Questions for Authors: In general, the paper introduces a few interesting and potentially useful theoretical results for MORL. However, the paper lacks a more in-depth discussion of how these results can be applied to design novel algorithms. This, combined with the fact that the ideas are not discussed in light of many previous results, makes the paper not yet ready for publication. Below, I have a few questions and constructive feedback to the authors: 1) My main concern is that the paper does not have a related work section and does not discuss many relevant related works. For instance: [1] showed how to construct stochastic policies that are optimal w.r.t. the initial state distribution. [2] introduced different solution sets that extend the definition of the Pareto front and can express more utility functions. [3] and [4] showed that many multi-objective utility functions can not be expressed via Markov rewards. [5] discusses the expressivity of many RL formalisms to represent different preferences, including MORL. 2) Regarding the examples, e.g., Example 3, it would be much clearer and easy to read if the authors provided an image of the MDP as graph. 3) Theorem 1 seems to be a more formal definition of the result in Vamplew et al. 2009 [1]. 4) Proof of Theorem 2 looks incomplete. Lemmas 7 and 8 consider single-objective MDPs, not MOMDPs. It is not clear how they can be combined to prove Theorem 2. 5) Theorem 2 shows one class of non-linear utility functions that have a deterministic stationary optimal policy. However, is it possible that a more general class exists? I would suggest adding this discussion. Minor: - Use large brackets, e..g., in Equation 1, the bracket is smaller than the summation symbol. - In definition 3, the transition function is $\mathcal{T}$ instead of $T$. Please be consistent. [1] Vamplew, P., Dazeley, R., Barker, E., and Kelarev, A. (2009). Constructing stochastic mixture policies for episodic multiobjective reinforcement learning tasks. In AI 2009: Advances in Artificial Intelligence. [2] Röpke, W., Hayes, C. F., Mannion, P., Howley, E., Nowé, A., and Roijers, D. M. (2023). Dis- tributional multi-objective decision making. In Elkind, E., editor, Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence, IJCAI-23. [3] Skalse, J. and Abate, A. (2023). On the limitations of Markovian rewards to express multi-objective, risk-sensitive, and modal tasks. In Evans, R. J. and Shpitser, I., editors, Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence. [4] Miura, S. (2022). On the expressivity of multidimensional markov reward. In Proceedings of the Conference on Reinforcement Learning and Decision Making. [5] Subramani, R., Williams, M., Heitmann, M., Holm, H., Griffin, C., & Skalse, J. (2023). On The Expressivity of Objective-Specification Formalisms in Reinforcement Learning. ICLR 2024. Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The results have some limitations that should be addressed (see Questions above). The paper has no potential negative societal impact. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for their insights and suggestions. Weakness 2: Yes, Example 3 illustrates a well-known fact in the MORL literature. In case of acceptance, we will state it. However, we wanted to include it before showing Example 4, which builds on Example 3 by providing an example of both strictly monotonically increasing and continuously differentiable function for which no u-optimal policy exists, a completely novel result. Weakness 3: We accept it, but we believe the topic of classifying the conditions for the existence of solutions, due to its novelty in the MORL community, deserved the entire paper (in fact, we had to struggle to fit in all the main results). Solving MORL problems is out of the scope of this paper. Question 1: While the recommended papers tackle relevant MORL problems, papers [1, 2, 4, 5] aim to solve a different problem than ours. Paper [3] is the most similar to ours, but they make no distinction between <u,s>-optimal and <u>-optimal policies. This is a major difference that we will discuss in the following paragraphs. Nevertheless, we do agree with the reviewer that our paper would benefit from an expanded related work section, which is currently compressed in Section 2 due to space limitations. We will include comments explaining the similarities and differences to these 5 papers upon acceptance. Let us clarify how these papers relate to ours: - Papers [1] and [2] tackle a different problem: they focus on creating novel solution concepts in MORL and methods to solve them. Instead, we focus on characterising for which families of utility functions this solution exists. In [1], they present a method for computing the Pareto front (PF) from a given state. They implicitly assume that the PF will include the <u,s>-optimal policy, but our Example 5 proves that this is not always the case. - Paper [4] tackles a complementary, though also different, problem to ours. They define preferences as sets of “acceptable policies' ' and aim to find for which environments they can set the constraints and reward functions of a constrained MDP (CMDP) for which the acceptable policies are optimal. CMDPs and MOMDPs are similar but separate research areas, being the major difference that a MOMDP does not have constraints, but a scalarization function. - Paper [3], which we were not aware of, slightly overlaps with ours. Their theoretical results complement ours by stating that, for every “objective” (preorder between policies), a <u>-optimal policy exists if and only if this objective can be represented with a linear utility function. This aligns with our results with Theorem 2. However, they do not establish whether there may be more families of utility functions for which a u-optimal policy exists, as we do with Theorem 2. Moreover, our “preference” definition allows for ordering policies in each state of the environment, providing more granularity than their “objective” definition. This difference is also significant, because it allows us to identify issues in the solution concepts of MORL as we have tried to illustrate with our examples. As a side note, we see their Corollary 2 reaches the same conclusion as us in Example 8. We will rewrite Example 8 to recognise their work. - Finally, Paper [5] follows on [3], but tackles a different problem than us. They compare the expressivity of the MORL framework with other frameworks. They aim to know which objectives can be represented on each framework. But here we tackle a different problem: we focus strictly on MOMDPs, and aim to clarify for which utility functions it makes sense to compute a u-optimal policy. Moreover, like [3], their “objective” definition does not allow them to order policies differently per state, unlike our “preference” definition. Question 2: Due to page limitations we were not able to include figures. In case of acceptance, we will try to fit as many supporting figures to the examples as we can. Question 3: No, Theorem 1 is not a more formal definition of the result in [1]. These are unrelated results. While [1] provides a method for computing <u,s>-optimal policies for monotonically increasing utility functions, we prove that a <u,s>-optimal policy always exists for any continuous utility function. Vamplew et al. proved that a Pareto front can be constructed from the deterministic policies of a convex coverage set (CCS). In our terms, they state that the <u,s>-optimal policy (if it exists) of any monotonically increasing utility function can be computed by first computing a CCS for state s. Meanwhile, our Theorem 1 states that for any continuous utility function, there exists a <u,s>-optimal policy. Our proof relies on the fact that all possible value vectors (at a given state) are contained in the CCS. Notice that our Example 5 is a counter-example to the methodology of [1]. Following their methodology we would not have found any <u,s>-optimal policy for the utility function of Example 5, because no <u,s>-optimal policy exists for it. This example remarks the importance of formalising <u,s>-optimal policies. Question 4: Sorry for the typo. Lemma 8 should read “For every finite multi-objective MDP, […]”. We hope that now this is clearer. Question 5: Indeed, this is a very interesting question! We hope to study this problem in future work, because we can think of example utility functions that do not satisfy Theorem 2 conditions while also having a u-optimal policy in some MOMDPs. The theoretical implications of Example 4 make it difficult finding more families of utility functions for which a u-optimal policy always exists. We know that if another family of optimally solvable utility functions exists, they need to satisfy the Bellman optimality equation. Finding this alternative family of utility functions would be an impactful contribution to the MORL community. Minor questions: In case of acceptance we will make sure of correcting all typos. --- Rebuttal Comment 1.1: Title: Response Comment: I thank the authors for their careful response to my questions and concerns. I am slightly increasing my score due to the authors' response. Below, I have a few more comments on the points raised by the authors: Weakness 3: I agree that algorithms for solving MORL problems are out of the scope of the paper. However, since the end goal of the field is the design of MORL algorithms, I strongly suggest adding a short discussion to the paper on how these theoretical ideas might be useful. E.g., "Theorem X implies that the community need to design novel algorithms with properties Y and Z.". Question 1: Thank you for providing this comparison. It is critical that these discussions are included in the final version of the paper, since they explain why previous related works are not sufficient. **Question 4: I believe this is not the only issue in this proof. Please provide more detailed proof of Theorem 2, which currently is "Direct consequence of combining Lemma 7 and Lemma 8". It is very unclear how this is the case. --- Rebuttal 2: Comment: We agree with reviewer's point regarding the importance of designing MORL algorithms in the field. In case of acceptance or in any future iteration of the paper, we will definitely add both a discussion section of how our theorems impact algorithm design, and a related work section, following the reviewer's suggestion. We will now provide an-indepth proof of Theorem 2. In case of acceptance we will make public this proof together with all appendix material. (i) - First, as Lemma 7 states, applying a strictly monotonically increasing utility function to a single-objective MDP does not modify its set of deterministic and stationary optimal policies. (ii) - Second, every linear utility function "lu" can transform a MOMDP M into a single-objective MDP M' with the scalarised reward function "lu \dot \vec{R}". Of course, all optimal policies of the single-objective MDP M' are precisely the lu-optimal policies of M (for the technical proof of this please see Section 2.2 of our paper). (iii) - These two facts together (i)+(ii) tell us: given a utility function "f" that can be decomposed into a strictly monotonically increasing function "smi", and a linear function "lu", then "f(x) = smi(lu(x))" will have deterministic and stationary f-optimal policies (which will be the deterministic and stationary lu-optimal policies). (iv) - Next, Lemma 8 proves that any affine utility function "af" is quasi-representative of another linear utility function "lu". More precisely, in every MOMDP, all af-optimal policies are also lu-optimal policies and vice-versa for the linear utility function "lu" defined as lu(x) = af(x) - af(0). This is because any affine function af(x) can be decomposed as "af(x) = A(x) + b", with A(x) being a linear function and b = af(0), a constant. Now, consider an utility function "f(x) = smi(af(x))" that can be decomposed as a product of a strictly monotonically increasing utility "smi" function and an affine utility function "af". (v) - Consider also the utility function "f'(x) = smi(af(x)-af(0))". This second function f'(x) is composed by a strictly monotonically increasing function and a linear function, so by (iii), there are deterministic and stationary f'-optimal policies. (vi) - Then, recall that, by (iv), utility functions "af(x)" and "af(x)-af(0)" are quasi-representative (i.e., they share the same optimal policies). Thus, it is clear that "smi(af(x))" and "smi(af(x)-af(0))" are also quasi-representative, because strictly monotonically increasing functions preserve the ordering by definition. This is a point that should have been much clearer in the paper, so we apologise for that. Finally, since: f'(x) = smi(af(x)-af(0)) has deterministic and stationary f'-optimal policies, and f(x)= smi(af(x)) and f'(x) are quasi-representative, we conclude that there are also deterministic and stationary f-optimal policies. This proves Theorem 2. If there is any further doubt or unclear proof we will be happy to clarify it. --- Rebuttal Comment 2.1: Comment: Thank you for clarifying the proof. I have one last question regarding Theorem 2: You showed a class of utility functions with deterministic and stationary optimal policies. However, because of the inner affine function, it seems that this utility function can represent the same set of optimal policies as linear utility functions. In other words, given a utility function "u" decomposable as a strictly monotonically increasing function and an affine function, its optimal policy will be on the Convex Hull (Eq. 5). Is that correct? If so, why would this class of utility function be useful if it can represent the same policies as linear utility functions? If this is not correct, can you provide an example where this utility function has an optimal policy whose value is a concave region of the Pareto front/undominated set? --- Rebuttal 3: Comment: This is correct: Theorem 2 proves that any function of such class is quasi-representative to another linear utility function, and thus its optimal policies belong to the convex hull. The usefulness of this class of utility functions is threefold, in our opinion: 1) it proves that not only linear utility functions have solution policies inside the convex hull. 2) similarly, it provides more structure to the convex hull, allowing us to identify a particular family of utility functions that belong to it. 3) In practice, Theorem 2 provides a general methodology for obtaining solution policies: if a utility function can be proved to be quasi-representative to a linear utility function, then an u-optimal policy is guaranteed to exist. Take for instance the utility function of Example 6. A priori, one would not know how to compute its u-optimal policy (or if it even exists). Thanks to Theorem 2 we know that it exists, and that it belongs to the convex hull. To understand the significance of these results, we would also like to remark that: it is still a complex problem to find utility functions for which an u-optimal policy always exists for any arbitrary MOMDP, and that furthermore this u-optimal policy does not belong to the convex hull. We are not aware of a single utility function for which this is true. Moreover, the theoretical implications of Example 4 greatly limit the candidate families of utility functions for which a deterministic and stationary u-optimal policy is guaranteed to exist. In any case, we already started working on searching for utility functions with concave deterministic and stationary u-optimal policies, and hope to find results in future work. --- Rebuttal Comment 3.1: Comment: Again, I thank the authors for their insightful response. I am increasing my score since the theoretical results in the paper can be potentially useful to other researchers in the field.	Summary: The authors studied preference relations and utility functions, which are the main components of utility-based MORL. Many prior works assumed two things: 1) for a given preference, there exists a utility that captures the preference, and 2) for a given utility, there exists an optimal policy. The authors provide several counterexamples for these assumptions and suggest sufficient conditions for each assumption to be true. Strengths: - The motivation of the study is important in utility-based MORL. - The authors provided several examples to show that a representative utility and an optimal policy may not always exist. These examples help to understand the motivation of this work. Weaknesses: - The suggested sufficient conditions do not seem that surprising and are quite straightforward. In particular, Theorem 2 appears to depend directly on prior results for affine utility and strict monotonicity. - To use Theorem 3, the relation must be a total order. In this setting, the Pareto dominance relation (x⪰Py iff xi≥yi∀i and xi>yi∃i), which is widely used in MORL, is not applicable since it is a partial order. - Section 3 and 4 seem misaligned. (please see question 3) Technical Quality: 2 Clarity: 3 Questions for Authors: - Is there any interpretation for how extensively the suggested sufficient conditions cover the set of desired preferences or utilities? For example, in Theorem 1, I understand that continuous utility has a <u,s>-optimal policy, but isn't this class too small to have a <u,s>-optimal policy? - Theorem 2 gives a sufficient condition for a deterministic stationary <u>-optimal policy. As I understand it, this condition guarantees the same property as in single-objective MDPs: the existence of a stationary deterministic optimal policy. However, in MORL, it is common for a stationary deterministic optimal policy not to exist. Is there any sufficient condition for a stationary stochastic <u>-optimal policy (even when there is no stationary deterministic optimal policy)? I guess that this result would be more helpful for MORL field. - In my understanding, the constructed u in the proof of Theorem 3 is discontinuous. If this is true, then even a <u,s>-optimal policy is not guaranteed to exist according to the Theorem 1. - (minor) In section 4, ⪰ is used for both vector preference (V(s)) and function preference (V). I guess that these need to be distinguished in notation. Confidence: 3 Soundness: 2 Presentation: 3 Contribution: 2 Limitations: The motivation and importance of this work are appealing. However, the sufficient conditions seem to result in a too small subclass of interest. Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for the provided suggestions and comments. We hope that our answers will clarify the soundness of our paper. Reviewer's rating of 3 indicates “technical flaws, weak evaluation, or inadequate reproducibility”. We consider that none of them are the case in our paper. We will rewrite the unclear parts of the paper in case of acceptance to further clarify all technical doubts. Weakness 1: Yes, Theorem 2 directly depends on previously well-known results in the MORL literature, though no one has connected them yet. Notice however that while Theorem 2 provides sufficient conditions, we also provide non-trivial proofs of insufficient conditions that complement Theorem 2 results, and other two theorems in the paper that tackle completely new topics in MORL: - Theorem 1 is the first result in MORL that characterizes when a solution policy exists in MORL for a single state (despite the concept has been used experimentally since the creation of MORL). - Theorem 3 is the first result in MORL that characterizes when a preference relation can be represented as a utility function (despite preference relations being used since the creation of MORL). - Example 4 proves that strictly monotonically increasing utility functions (despite their appeal in the MORL community) do not necessarily have a solution policy for any state (<u,s>-optimal policy in our terms). We are certain that this will be a shocking result in the community that will need to think again on their focus on monotonically increasing utility functions. - Example 5 proves that both strictly monotonically increasing and continuously differentiable (again, some of the most popular families of utility functions in the MORL community) do not necessarily have a global solution policy (u-optimal policy in our terms). In summary, all these results lead us to conclude that u-optimal policies are very difficult to guarantee in general, a problem that the MORL community was still not aware of. Weakness 2: We argue that such weakness does not hold for the following reasons: - It is right that Theorem 3 requires a total order among policies for every state s. The reviewer is also right that Pareto-dominance only imposes a partial order among policies. - But Pareto-dominance is a “solution concept” in MORL, not a utiltiy function, nor a family of functions. Roijers and Whiteson in their textbook “Multi Objective Decision Making” [16] provide a very good explanation of the difference. - This distinction is important here, because every utility function imposes a total order among policies for every state. Proof: for every state s, the scalarized value of every policy V^{\pi}(s) will be a scalar number. Thus, we can totally order all policies at state s. Hence, Theorem 3 applies to every possible utility function (even monotonically increasing ones, whose solution lies on the Pareto front), contrarily to what was said in weakness 2. Question 1: Regarding the extensiveness of the sufficient conditions of our Theorems. Recall that all theorems refer to finite MOMDPs, which are the most widely used kind of MOMDPs. - Then, Theorem 1 only demands the utility function to be continuous to guarantee the existence of <u,s>-optimal policies. Continuous utility functions are the most extensively known and used family of functions, including in MORL. Notice that in particular linear utility functions, widely used in MORL, are continuous. - Theorem 2, despite its apparent simplicity, already covers one of the most “desired” utility functions: linear utility functions. Again, as previously mentioned, Theorem 2 should be observed together with Example 5, which also covers families of desired utility functions (monotonic ones) but providing negative results for them. - Finally, as previously explained, Theorem 3 applies to every utility function. It does not apply to every possible preference relation, but our conditions copy standard conditions in game theory, which we consider to be representative enough. Question 2: Finding deterministic and stationary solution policies is very relevant and a major research topic for MORL research. Following Roijers and Whiteson’s classification of MORL solution concepts in [16], half of them involve the computation of deterministic and stationary policies, which our Theorem 2 directly addresses. Regarding the reviewer’s concern about expanding our result to stochastic policies: This is future work for us. We have tried to find such kind of families, but so far, we have only found negative results (e.g., Example 5) that greatly reduce the space of viable policies for which a stochastic u-optimal policy would always exist. However, we consider that these negative results will also be helpful for the MORL community. Question 3: While Theorem 1 and 3 are related results, they do not directly affect each other. Probably this was not clear enough on our part. - The constructive proof of Theorem 3 provides a discontinuous utility function. Theorem 1 guarantees that any continuous utility function will have a <u,s>-optimal policy, but does not deny that some discontinuous optimal policies may have a <u,s>-optimal policy. - Notice that having a <u,s>-optimal policy for some state s means that there is a maximum element among scalarized values of policies at state s. The utility function of Theorem 3 is specifically constructed to always have a maximum element for each state, thus guaranteeing the existence of <u,s>-optimal policies by definition. - In summary, the reviewer's inference does not hold: even though the utility function of the proof of Theorem 3 discontinuous, it is guaranteed to have a <u,s>-optimal policy. Question 4: We agree with the reviewer that this was an abuse of notation from our part. We will correct it in case of acceptance. --- Rebuttal Comment 1.1: Comment: Thanks for the reply. I have raised my rating.	null	null	null	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Image Reconstruction Via Autoencoding Sequential Deep Image Prior	Accept (poster)	Summary: The paper proposes Autoencoding Sequential Deep Image Prior (aSeqDIP) an extension to the family of untrained (no training data required) DIP methods. As in previous work a combination of data consistency loss and autoencoding regularization (a loss between network input and output) is used. However, instead of further regularizing the optimization by adding noise to the network input in every iteration as proposed in previous work, this paper varies the network input by setting it to the network output after every two iterations. Experimental evidence is provided that demonstrates superior robustness to overfitting and overall reconstruction accuracy compared to other DIP approaches and trained diffusion models. Strengths: Significance: Untrained neural networks are an important technique used in many fields, where training data is scarce. Mitigating the problem of overfitting is an important contribution. Originality: Despite the relatively small difference compared to previous work (regularize network input by setting it equal the output instead of adding noise to it as in the self-guided DIP) the importance and effectiveness of this idea seems to be justified by the experimental results in terms of reconstruction accuracy and robustness to overfitting. Clarity: Overall the paper is written in a clear way and related work in terms of DIP approaches and diffusion models are discussed. Quality: The experiments towards evaluating the reconstruction performance and overfitting robustness of the proposed DIP approach are well designed and ablation studies for the most important hyperparameters are provided. Overall an interesting paper. However, some questions remain and some important points remain unclear (see weeknesses). If those can be addressed adequately, I would consider raising the score. Weaknesses: 1. No results are provided for the most interesting case: Overfitting robustness for the task of denoising. To my understanding Prop. 3.1 says that in the limit the proposed approach converges to a network that has learned the identity and to a network output (which is identical to the network input) that perfectly fulfills data consistency under the forward operator and the given measurement. For the tasks of MRI and inpainting (in the absence of noise) solutions that fulfill Prop. 3.1 include the ground truth image and the empirical evidence provided in the paper shows that indeed the solution found by the proposed method is closer to the ground truth image than that of other DIP based approaches (why it is closer remains unclear up to intuitions/speculations, but answering this question is non-trivial and does not have to be the scope of the paper). Also, the robustness to overfitting seems reasonable for the aforementioned tasks. My intuition would be that repeatedly setting the network input to the output combined with the autoencoding regularization loss lets the network converge to identity relatively quickly. If at the same time data consistency is reached, there is no incentive for the network to change its weights anymore and a stable solution is reached. However, things change in the presence of noise or in general for the task of denoising. To my understanding, for denoising Prop. 3.1 is fulfilled, when the network perfectly reconstructs the noisy measurement $\mathbf{y}$, which is the very definition of overfitting. So, here it would be interesting to see curves as presented in Figure 4 for MRI and CT also for denoising to demonstrate to what extend overfitting is still prevented. 2. In general, I am not sure about the usefulness of Prop. 3.1. As discussed above for the tasks of MRI and inpainting reconstructions that fulfill Prop 3.1 comprise good and bad solutions however without making a statement why a good solution should be preferably reached over a bad solution, whereas for the task of denoising it implies convergence to a bad solution. 3. The learning based "SOTA" baselines perform very badly, which is not discussed in the paper and no information regarding the used training sets is provided. Diffusion model-based methods are introduced as the state-of-the-art in the paper (line 113) and indeed the works referenced there report impressive results in terms of quantitative and qualitative reconstruction performance. Yet, in this work the reconstruction scores and especially the reconstructed images (Figure 5, 12, 13) contain severe artifacts. I understand that training and inference of those diffusion models is sensitive to hyperparameters, but then potential reasons for this bad performance should at least be discussed in the paper. Also, no information is provided regarding the training data used for those baseline models. If there is no comparison to state-of-the-art end-to-end approaches (which definitely should give better results than DIP based reconstruction if trained properly on enough data) like the end-to-end VarNet (https://arxiv.org/abs/2004.06688) then at least the diffusion model based baseline should show reasonable results or if not it should be discussed why. 4. Code is only provided for the task of MRI reconstruction and the implemented method seems to differ from the description in the paper. Checking the code provided via a link (https://anonymous.4open.science/r/Aseq_DIP-E728/README) in the paper I can only find a notebook that performs MRI reconstruction Aseq_DIP.ipynb. In the code the step where the network output is set to be the network input for the following steps is implemented as follows: ``` pred_ksp = mps_and_gt_to_ksp(mps1.to(device), net_output) new_pred_ksp = (1 - mask_from_file).to(device) * pred_ksp.detach() / scale_factor + mask_from_file * ksp1 new_ref = ksp_and_mps_to_gt(new_pred_ksp, mps1) random_smoothing_temp = torch.zeros_like(new_ref).to(device) for jj in range(1): random_smoothing = new_ref + 1e-5 * torch.rand((640, 372), dtype=torch.complex64).to(device) random_smoothing_temp += random_smoothing random_smoothing_final = random_smoothing_temp ref[:, 0, :, :] = random_smoothing_final.real ref[:, 1, :, :] = random_smoothing_final.imag ``` If I understand it correctly the new input (ref) is first set to fulfill perfect data consistency and then processed with random smoothing, two things not mentioned anywhere in the paper. Also, the new input (ref) is updated before the computation of the loss, which means that in fact the autoencoding regularizer is not really computed between the network input and the network applied to this same input. It is unclear how essential these two steps (hard data consistency and smoothing) are to the proposed approach. Further, ``` loss.backward() for i in range(2): optimizer.step() ``` implies that the network weights are updated twice without updating the loss functions, which is not what is outlined in Algorithm 1 of the paper. If that is really how the mehtod is implemented that corresponds to the results in the paper the ablation study regarding the values for the number of iterations $N$ per network in Appendix C.4 seems meaningless as the loss is not updated as $N$ increases. Technical Quality: 3 Clarity: 2 Questions for Authors: 1. In the Figures (like Fig. 5) showing qualitative reconstruction results it would be helpful to show the measurement, i.e. noise image for denoising, mask fr in-painting and zero-filled reconstruction for MRI. 2. I personally find the formulation in line 10 "sequential optimization of multiple network architectures" a bit missleading as the networks are not changed or re-initialized. Only the network input is adapted. 3. Regarding Section 3.1 and Figure 2 it makes sense to me why the blue curve is decaying, but do you know why the red curve is decaying? Does the red curve decaying imply that a constant input (like all zeros) to the DIP would work best? Confidence: 4 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: Limitations are not discussed in the paper. This could be for example the limitted interpretability of the comparison to trained baseline methods as current results in the paper significantly fall behind the results reported in the baseline papers or the long reconstruction times compared to end-to-end deep learning based methods. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: C1 Overfitting robustness for the task of denoising: Since our method is an unsupervised approach optimizing a single image, our observations suggest that repeatedly setting the network input to the output, along with autoencoding regularization, enables convergence to autoencoding-specific images instead of the identity. The attached PDF in the global response presents the average PSNR for 20 images from the CBSD68 dataset for denoising. We observe two key points. First, aSeqDIP shows higher robustness against noise overfitting compared to other DIP-based methods, consistent with MRI and CT findings. Second, unlike MRI and CT, the onset of noise overfitting occurs earlier, but the subsequent decay is very small. Please refer to our response to the following comment for the proposition. C2 Usefulness of Prop. 3.1: The main point of this proposition is to highlight that the aSeqDIP algorithm minimizes a different optimization problem compared to Vanilla DIP. Proposition 3.1 is not intended to indicate solution quality or analyze RMSE during optimization but to state that, under strong convergence assumptions, our algorithm minimizes the optimization problem in (5). Solving (5) explicitly is challenging due to the equality constraint and the network's non-linearity. In other words, the proposition illustrates the types of solutions our algorithm converges to. Our empirical results show that our algorithm converges quickly and remains stable. C3 Performance of DM-based methods and their training data: Regarding the difference in PSNR values between our reported results and those in Score-MRI and MCG, we'd like to clarify that for our MRI experiments, we used Cartesian sampling, a more common scheme, while Score-MRI used Uniform 1D, Gaussian 1D, Gaussian 2D, and VD Poisson disk sampling. For CT, our aSeqDIP results (and other baselines except MCG) were obtained using the full 512x512 pixels in the AAPM dataset, whereas MCG downsized the images to 256x256 pixels for faster training and sampling (see the caption of Table 3 in the MCG paper). Therefore, we compared the ground truth after resizing the MCG results back to 512x512. We will include this discussion in the revised paper. In the following table, we compare aSeqDIP (a dataless method) versus MCG (a data-centric method) at their downsized pixel space, as reported in Table 3 of their paper. As observed, we achieve very competitive results. \| Task \| MCG 256X256 \| aSeqDIP 256X256 \| \|----------\|----------\|----------\| \| Sparse View CT with 18 views \| 33.75 \| 33.86 \| \| Sparse View CT with 30 views \| 36.09 \| 35.89 \| We use the testing images from the fastMRI and AAPM datasets. The pre-trained models for Score-MRI and MCG were trained on the training sets of these datasets. For our experiments with natural images (denoising, in-painting, and non-uniform deblurring), we used the CBSD68 dataset. For DPS (a DM-based method), we utilized a pre-trained model from ImageNet (128x128, 256x256, and 512x512), known for its high generalizability according to "The Emergence of Reproducibility and Consistency in Diffusion Models." This model is more generalizable than the alternative trained on FFHQ (faces dataset). In response to Reviewer MAra Comment 4, we experimented with the FFHQ testing set, using pre-trained models of DPS and DDNM trained on the FFHQ training set. For the DM-based baselines, we used the default hyper-parameters provided by DPS (natural images), Score-MRI, and MCG (sparse view CT). Note that we are not the first to observe unwanted artifacts in DPS (see Figure 3 in "Solving Inverse Problems with Latent Diffusion Models via Hard Data Consistency"). We believe these artifacts arise because DM-based approaches, which learn $p(x)$, require modifications to sample from $p(x \| y)$. These modifications, often approximations, may not be accurate or suitable for all tasks and images. A major point of our comparison is to show that our method achieves competitive or superior results compared to DM-based methods, without needing pre-trained models or training data. End-to-end (E2E) supervised models outperform many DIP-based methods like VarNet because the best DIP optimization steps can vary significantly. This motivates our aSeqDIP approach. The table below shows that our method achieves higher average PSNR than VarNet for 15 MRI scans (4x). While E2E models are faster at inference with a single forward pass, our method's advantage is that it is fully data-independent. \| Task \| VarNet \| aSeqDIP (Ours) \| \|----------\|----------\|----------\| \| MRI \| 33.78 \| 34.08 \| C4 Code: Thank you for bringing this to our attention. We mistakenly uploaded an older version of our code. We have fixed the link and uploaded .py files for all the tasks. Q1 Including measurements: See our global response. Q2 Comment on using "sequential optimization of multiple network architectures": In our algorithm, each network is initialized by the optimized parameters of the previous network, and then optimized using (3) such that the input of the network is the output of the previously optimized network (see line 157). No re-initialization or architecture change are needed. In the revised manuscript, we will re-word it for further clarification. Q3 Curves of Figure 2: Larger variance in the standard Gaussian distribution corresponds to larger additive perturbations even for the case of $\mathbf{x}^=\mathbf{0}$ (the red curve). We conjecture that this still leads to larger distances from the GT and hence worst performance. In regard to the case where the input is the all-zero vector, we ran Vanilla DIP with $\mathbf{z}=\mathbf{0}$, and the reconstruction quality is very low. We conjecture that this is due to (i) the impact of the first convolutional layer, which is only its bias, and (ii) the output of the first layer is concatenated to later layers through the skip connection. Limitation Comment: See our global response. --- Rebuttal Comment 1.1: Title: Reponse to author rebuttal - remaning concerns with baseline results Comment: I thank the authors for the clarifications and additional experiments and for answerning my qustions. My remaining concerns are with the baseline results. If Score-MRI is so unstabel that when trained on the entire fastMRI brain training set is still outperformed by a data-free method on the fastMRI brain validation set, then maybe it is not a good DM baseline. Also the type of undersampling mask should not make up for the difference in PSNR as Uniform 1D and Gaussian 1D are also Cartesian masks. Further, I find it extremely strange that the VarNet is outperformed by a data-free method as the VarNet provides stable SOTA results (see fastMRI challenge) if trained and tested on the same type of data. So what was the training and testing setup for this experiment with the VarNet? --- Rebuttal 2: Title: Thank you for your response. Addressing the remaining concerns with baselines results Comment: We would like to thank the reviewer for their prompt response to our rebuttal. We hope that the following will address the reviewer's remaining concerns with baselines. We would like to emphasize that the main point of comparing our method with data-intensive approaches (VarNet, Score-MRI, DPS, DDNM, and MCG) is to demonstrate that we achieve competitive results, all without the need for training data or pre-trained models by appropriately setting up the optimization and regularization of deep image prior. In what follows, we address your concerns in three parts. If Score-MRI is so unstable that when trained on the entire fastMRI brain training set is still outperformed by a data-free method on the fastMRI brain validation set, then maybe it is not a good DM baseline.* Score-MRI DM was originally trained on natural images and then fine-tuned on the entire training set of fastMRI using the single-coil setting. The reason for this pre-training + fine-tuning is that DMs require a significant amount of training data to enter the generalization regime (see Figure 2b in "The Emergence of Reproducibility and Consistency in Diffusion Models"), which may not be available for tasks such as MRI and CT. During testing, they used the multicoil real setting DM on both the real and imaginary parts. In their paper, they mention: "Our model requires magnitude images only for training, and yet is able to reconstruct complex-valued data, and even extends to parallel imaging." To the best of our knowledge, Score-MRI and CCDF (which we came across after submitting the paper) are the two best DM-based MRI baselines. In CCDF, they demonstrated slightly improved PSNR scores while requiring fewer sampling steps, making it faster. Refer to Table 5 in the CCDF paper, "Come-Closer-Diffuse-Faster: Accelerating Conditional Diffusion Models for Inverse Problems through Stochastic Contraction." In that paper, Score-MRI is referred to as "Score-POCS." For the 4x Gaussian 1D sampling, CCDF reports 32.51 dB, whereas Score-MRI achieved 31.45 dB. The type of undersampling mask should not make up for the difference in PSNR as Uniform 1D and Gaussian 1D are also Cartesian masks. Thank you for your comment. Note that in the Score-MRI paper (multicoil setting in Table 2), the PSNR values vary by nearly 4 dB depending on the mask, ranging from 29.17 dB (Gaussian 2D) to 34.25 dB (Gaussian 1D). We acknowledge the reviewer's comment that the masks they used are indeed Cartesian. Thank you for the correction. We needed to review the details of their code implementation to confirm this. The first column of Figure 4 (and its caption) in their paper describes the exact masks they used. Our sampling mask is the 1D Poisson Disk, which the Score-MRI authors did not use. The Poisson Disk mask in their results is 2D Poisson Disk. To fully address the reviewer's concern, we ran aSeqDIP with the 1D Uniform setting, the sampling mask used in the first row of Table 2 in Score-MRI. The results are averaged over 20 MRI knee scans (with 4x undersampling). As observed, we achieve competitive PSNR results with Score-MRI in this setting as well. \| Task \| Score-MRI (reported from their paper) \| Score-MRI (us running their code)\| aSeqDIP (Ours) \| \|----------\|----------\|----------\|----------\| \| MRI (1D Uniform Sampling) \| 33.25 \| 33.45 \| 34.05 \| Further, I find it extremely strange that the VarNet is outperformed by a data-free method as the VarNet provides stable SOTA results (see fastMRI challenge) if trained and tested on the same type of data. So what was the training and testing setup for this experiment with the VarNet? The reviewer is correct; VarNet indeed achieves very competitive results. Since VarNet does not provide a pre-trained model, we initially trained their architecture from scratch using 3,000 fastMRI multicoil datapoints and tested it with the fastMRI testing dataset. Please note that due to time constraints and the additional experiments conducted during the rebuttal, in our initial response, we used 3,000 knee images for training instead of the available 8,000 datapoints. To fully address the reviewer's concern, we trained VarNet with the full training set and their PSNR results do indeed improve when compared to the results of VarNet trained with only 3K points. See the following table. Our method is still quite competitive and could prove beneficial in limited training data regimes. \| Task \| VarNet (trained with 8k points) \| VarNet (trained with 3k points) \| aSeqDIP (Ours) \| \|----------\|----------\|----------\|----------\| \|MRI \| 34.89 \| 33.78 \| 34.08 \| Note that Score-MRI paper also reported VarNet results (7th column of Table 2), and the results slightly varied when different masks were used. We are happy to address any more concerns. Thanks, Authors --- Rebuttal Comment 2.1: Title: Some more details regarding the VarNet experiment? Comment: Thank you for providing the additional information regarding the DM baseline experiments. I guess Score-MRI looses more performance through this shift from training on magnitude images only to multi-coil evaluation than I expceted. Still impressive that your aSeqDIP can perform on the same or better level. Regarding the VarNet experiment, I have a last question. If I understand it correctly, you consider the problem of multi-coil knee slice reconstruction. Do you focus on a certain subset of slices or which data do you mean when you say 3000 out of the 8000 available fastMRI multi-coil datapoints? The fastMRI knee dataset contains alsmot 35k slices, see https://arxiv.org/pdf/1811.08839 Table 4. --- Reply to Comment 2.1.1: Title: Thank you for your response. Response to the VarNet experiment Comment: We would like to thank you again for your response. We are glad that you found the results of aSeqDIP impressive. We hope that our responses can further convince you to raise the score. We double checked and the reviewer is correct that the full training/validation set is larger. We would like to clarify the settings we used for the rebuttal. We used a subset of data and removed peripheral slices in each volume (around 10 per volume) during training. We followed similar setup as recent works "Blind Primed Supervised (BLIPS) Learning for MR Image Reconstruction, TMI 2021" (Fig. 3) that showed supervised model results with varying training sizes from ~1K to ~8K. We believe its promising that a data-free approach can compete with supervised networks trained with many knee slices. --- Rebuttal 3: Title: Thank you for your response and raising your score Comment: We would like to thank the reviewer for their response and raising their score. We are glad that the reviewer is satisfied with our rebuttal and the additional experiments. Following the reviewer's recommendation, we will add the additional experiments and more details about the baselines configurations in the revised manuscript.	Summary: This manuscript describes a variant of the seminar Deep Image Prior (DIP) work that incorporates aspects and mindset of the iterative prediction workflow in diffusion models. In particular, the proposed procedure (method?) aSeqDIP is training a network to predict a single and fixed but distorted (e.g. noisy) image when given a pixel-wise random input image (just as DIP has initially proposed). The key novelty is to only train for a few training steps before switching to feeding the current prediction as an updated input (instead of the initial noisy input image). The similarity to predictions with diffusion models is apparent. The approach is to the best of my knowledge novel and the idea, in my point of view, the biggest contribution of the paper. Strengths: * The idea is fantastic and thought provoking. * Introduction of the regularization term (autoencoding term) during iterative training and showing that it is useful and that tuning it is important. (Figure 7 from the supplement could make it into the main paper.) * Application to 4 different tasks (MRI and CT (important real-world use-cases) and denoising and in-painting (to make the CV community happy… ;) * Partially informative appendix. Weaknesses: * It surprises me that the manuscript does not argue more about WHY this approach leads to better results even when compared to data-dependent baselines. How strong are these baselines? Do better pre-trained methods exist? If so, why not show results with them as well? * An answer to the above “WHY?” question would go right to the heart of why diffusion works well and would therefore be very interesting. * Since the presented method/procedure is not dependent on any amount of available training data (but the single compromised target image) I wonder how this manuscript can avoid talking about inductive biases of the used network architecture (a UNet, hence, a CNN). * The manuscript is overall rather compact in content, the text certainly not too dense but maybe even a bit too repetitive and wordy, and the figures not very legible (adequately sized). I also much regret not to see the compromised target image used by aSeqDIP, but only GT and final predictions. * Figure 1: when seeing it first it really did not help me understand the paper any better. After reading the entire manuscript and coming back to Figure 1 I can confirm the figure makes sense, but one would hope that Figure 1 is more educational as it currently is. * Figure captions are in general not terrible but also not in all cases making the figures self-contained. It is necessary to find some potentially distant place in the manuscript to fully grasp the visuals (e.g. Fig. 2). Technical Quality: 3 Clarity: 2 Questions for Authors: * I cannot judge the quality or sufficiency of the used baseline methods. If for any of the 4 tasks the current SOTA (or industry standard) method would also be given and compared against, I would find that very useful. * When does the proposed approach work (when is it applicable) and what are known limitations of its applicability? (When does the inductive bias of the setup not suit the desired task?) Confidence: 4 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: * I would expect that the inductive biases that comes with the used network and training procedure dictate for what problems the presented method/procedure can produce good results. If the authors have any thoughts, I think the manuscript would much benefit from a short discussion in that vein. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: C1 WHY this approach achieves better results? Strength of the DM-based baselines. Inductive bias discussion: We thank the reviewer for their constructive comment. The answers to these questions will definitely strengthen our paper. We divided our response to this comment into the following three parts. - Answer to why we achieve better results when compared to diffusion models: Our approach and DM-based methods are conceptually different. Provided a set of training images, DMs are trained to approximate the underlying distribution $p(x)$. Subsequently, when employed to solve imaging inverse problems (IPs), the problem becomes sampling from the conditional distribution $p(x\mid y)$ where $y$ denotes the measurements. To this end, DM-based IP solvers attempt to approximate this conditional distribution (which may not be accurate and/or suitable for some tasks) using different approaches for which the reverse sampling steps are modified to achieve this target. aSeqDIP is different in the sense that it is an optimization-based method that depends solely on an input-adaptive Unet architecture and the generative power of the network, and a loss function that is designed to mitigate irrelevant noise overfitting (which is the major obstacle with DIP-based methods). We argue that the reverse sampling modifications needed to sample from the conditional distribution in DM-based methods present a more challenging design choice when compared to our approach. - Answer to how strong the data-dependent baselines are: We believe that the DM-based methods that we used as baselines are very strong on the tasks they were considered for. For MRI and CT, we used the following criteria: Select a method that perform strongly for every task, and use the test dataset with the same training dataset distribution for which these DMs were trained on. For example, for MRI, we used Score-MRI as baseline. This method utilizes a pre-trained DM that was originally trained on natural images and then fine-tuned with the training set of the fastMRI dataset. In our MRI experiments, we used the testing set of fastMRI. Similar approach was used in CT where we used the MCG method (with an AAPM dataset-trained DM) and the AAPM testing dataset. For our experiments with natural images (denoising, in-painting, and non-uniform deblurring which is added in this rebuttal), we used the CBSD68 dataset. As such, for DPS (the DM-based method), we utilized a pre-trained model that was trained on a very large and diverse dataset which is ImageNet 128X128, 256X256, and 512X512. This pre-trained model is much more generalizable when compared to the other option which was trained on FFHQ (a dataset of faces). According to `The Emergence of Reproducibility and Consistency in Diffusion Models', the ImageNet pre-trained model has high generalizability. In our response to Reviewer MAra Comment 4, we experimented with the testing set of the FFHQ dataset where the pre-trained models of DPS and DDNM (the DM-based baselines) were trained on the training set of FFHQ. The main message of our comparison with data-centric methods is to demonstrate that our method can achieve competitive or superior results compared to DM-based methods, all without requiring pre-trained models and training data. - Answer to why we generally achieve better results: We think that our method, similar to all DIP-based methods, benefits from the implicit bias inherited in the Unet architecture. The structure of a randomly initialized CNN is used as a prior as it was shown in the original DIP paper. The architecture of a generator network alone is capable of capturing a significant amount of low-level image statistics even before any learning takes place. However, the number of optimization steps required in DIP represents a challenge. Therefore, we believe that our method, exploiting autoencoding regularization and input-updating, keenly taps into the generative and denoising nature of CNNs for more explicit regularization to alleviate overfitting. C2 Text is not too dense but a bit too repetitive and wordy. Including compromised target images: We do agree that some points are sort of repeated in the Introduction and other places in the paper. In the revised manuscript, we will improve the writing and readability of the figures. In the PDF attached in the global response of this rebuttal, we included the degraded images in our visualizations of Figure 5. We will do the ones in the Appendix in the revised manuscript. C3 Figure 1 location and explanation: We acknowledge the reviewer's comment. In the revised manuscript, we will either elaborate more in the caption of this figure (or add more context to the diagram itself) or re-locate it until after we present our method. C4 Figures captions: Thank you for your comment. We will improve the captions in the revised manuscript. Q1 Sufficiency of the used baseline methods: To address your question about how strong the DM-based baselines are, please refer to our response to your first comment. See also the second part of our response to comment 3 of Reviewer Q1ff where we experimented with a leading end-2-end supervised reconstruction model. Regarding the DIP-based baselines, we would like to highlight that we considered the recent self-guided DIP work which has demonstrated highly competitive performance in terms of reconstruction quality and robustness to noise overfitting across multiple tasks. Q2 known limitations of aSeqDIP: Thank you for your question. Please see our global response. Additionally, we evaluate our approach using different additional tasks, baselines, and settings. We hope that these results will shed more light into the capabilities and limitations of our method. In particular, for run-time and practical convergence, see our response to comment 3 of Reviewer qnNG. For testing with a non-linear task, see our response to Reviewer MAra comments 2 and 4. --- Rebuttal 2: Title: A friendly and gentle reminder Comment: We would like to express our sincere gratitude to the reviewer once again for their insightful comments. As the open discussion period is drawing to a close, we would be deeply grateful if the reviewer could kindly respond to our rebuttal. This would provide us with the opportunity to address or clarify any remaining concerns thoroughly.	Summary: The authors in this paper propose an Autoencoding Sequential DIP (aSeqDIP) which aims to address the overfitting issue of DIP while without introducing extra parameters. The idea is very simple, the authors simply feed the output of the DIP into DIP model after each N updates. The authors validate the efficiency of their methods on several different image restoration tasks. Strengths: 1) The presentation of the paper is good and it is very easy to understand. 2) The authors have conducted experiments on for different image restoration tasks. 3) The authors provide numerical comparisons as well as visual comparisons. Weaknesses: I have several concerns about this paper. 1) The novelty is significantly limited. It is almost the original DIP. The only difference is: the original DIP each iteration uses a random noise as its input; while here, the output of DIP is fed into the DIP for the next N iteration's updates. 2) The current experiments are all linear image restoration tasks. It would be interesting to see how this model works for non-linear image restoration tasks such as image delurring. 3) The authors should compare their method with more advanced DIPs such as Ref1. 4) How does this model compare with SOTA diffusion models Ref2? 5) The current results (Table2), the improvement is very small. And I am wondering what if we run the experiments many rounds and report the mean and std. Ref1: Jo, Yeonsik, Se Young Chun, and Jonghyun Choi. "Rethinking deep image prior for denoising." Proceedings of the IEEE/CVF International Conference on Computer Vision. 2021. Ref2: Wang, Yinhuai, Jiwen Yu, and Jian Zhang. "Zero-shot image restoration using denoising diffusion null-space model." arXiv preprint arXiv:2212.00490 (2022). Technical Quality: 2 Clarity: 3 Questions for Authors: I have several questions which have been listed in [Weaknesses]. Confidence: 4 Soundness: 2 Presentation: 3 Contribution: 1 Limitations: I have listed the limitations in [Weaknesses]. Flag For Ethics Review: ['No ethics review needed.'] Rating: 3 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: C1 Novelty and Differences with the original DIP: We appreciate the reviewer's comment. We would like to emphasize that our proposed method differs significantly from other DIP-based methods, including Vanilla DIP. These distinctions, which we believe set our work apart, are highlighted below. - Formulation and Algorithmic Perspective: In addition to the input-adaptive nature of Algorithm 1 (which is motivated by the discussion in Section 3.1), we propose the use of the auto-encoding term (Section 3.2.1) which is not used in Vanilla DIP. Furthermore, the original DIP does not require the input to be an image, whereas in our case, it is an image-to-image mapping. - Noise Overfitting Perspective: The proposed input-adaptive procedure along with the auto-encoding term result in the major key benefit of significantly delaying the noise overfitting decay which is the main challenge in all of the DIP-based approaches. See Figure 4, Figure 10, and the first figure in the PDF attached in the global response of this rebuttal. - Applicability Perspective: In our paper, we presented experimental results using multiple reconstruction and restoration tasks. Most other DIP-based methods consider at most one to three tasks. For example, ref-guided DIP only considered MRI, whereas TV-DIP considered denoising and in-painting. Furthermore, in addition to the four tasks in the paper, in this rebuttal, we included a non-linear inverse imaging task which is non-uniform deblurring (see our response to the following comment). Based on the highlighted remarks, we respectfully ask the reviewer to reconsider their opinion regarding novelty. C2 It would be interesting to see how this model works for non-linear image restoration tasks such as image deblurring: We thank the reviewer for their comment. Here, we include results of the non-linear non-uniform image deblurring task using the setting in the DPS code. In particular, we use the ''blur-kernel-space-exploring'' setting. In what follows, we report the achieved PSNR (averaged over 25 images form the CBSD68 dataset) of aSeqDIP when compared to DPS, Self-guided DIP, and SGLD-DIP. As observed, our method significantly outperforms all DIP-based methods while reporting improved results when compared to DPS. \| Task \| DPS \| Self-Guided DIP \| SGLD-DIP \| aSeqDIP (Ours) \|----------\|----------\|----------\|----------\|----------\| \| Non-uniform Deblurring \| 23.4 \| 20.3 \| 19.8 \| 23.89 \| C3 Comparison with "Rethinking DIP for denoising": Thank you for your comment. In what follows, we compare aSeqDIP with the suggested paper. We use the task of denoising and report the average PSNR over 25 images from the CBSD68 dataset. As observed, our method reports higher PSNR. We believe that our approach, exploiting autoencoding regularization, keenly taps into the generative and denoising nature of CNNs for more explicit regularization to alleviate overfitting. \| Task \| Rethinking DIP for Denoising \| aSeqDIP (Ours) \|----------\|----------\|----------\| \| Denoising \| 30.98 \| 31.51 \| C4 Comparison with SOTA DM-based method, DDNM: Thank you for your question. In what follows, we present average PSNR results (averaged over 20 images) for the tasks of denoising (with $\sigma_d=25$), random in-painting (97\% missing pixels), box-in-painting (with HIAR of 25), and non-uniform deblurring of our method versus DDNM (the suggested paper) and DPS on the FFHQ testing dataset. For DPS and DDNM, we used a pre-trained model that was trained on the training set of FFHQ. As observed, our training-data-free method achieves competitive or slightly improved results when compared to data-intensive methods on all tasks other than box-inpainting (for which we slightly under-perform), all without requiring a pre-trained model. \| Method \| Denoising \| Random In-painting \| Non-uniform Deblurring \| Box In-painting \|----------\|----------\|----------\|----------\|----------\| DDNM (using FFHQ-trained DM) \| 31.45 \| 25.34 \|23.88 \| 22.89\| DPS (using FFHQ-trained DM) \| 31.65 \| 25.54 \| 23.67 \| 22.67\| aSeqDIP (Ours) \| 31.77 \| 25.76 \| 24.02 \| 22.3 \| C5 The current results (Table2), the improvement is very small: Thank you for your comment. While the PSNR and SSIM improvements compared to other baselines are not very significant, we would like to highlight the following points. First, compared to DIP-based methods, our approach not only achieves higher reconstruction quality but also significantly improves robustness to noise overfitting. See the PSNR curves in Figures 4 and 10, as well as in the figure in the attached PDF in the global response. Second, when compared to DM-based methods, our approach not only achieves comparable or slightly improved PSNR and SSIM scores but also has the significant advantage of being independent of any training data and pre-trained models. We hope that emphasizing these points will highlight the additional advantages offered by aSeqDIP. Regarding running the experiments for many rounds, do you mean for our method or the other baselines? Or do you mean running our method with different initializations of $\phi_1$? --- Rebuttal Comment 1.1: Comment: Thanks to the authors for the detailed rebuttal. And it is glad to know that the authors added the experiments on nonlinear tasks. However, to 1) the image to image mapping in DIP is not new at all, this paper [ref1] also used the image as its input instead of random seed; 2) I do agree that DIP-based model suffers from the overfitting issues, however, there are several papers have addressed this issue, see ref2, ref3. 3) for the nonlinear tasks, the authors may want to compare with DIP-based deblurring models such as ref4. Ref1: https://openaccess.thecvf.com/content_ICCVW_2019/papers/LCI/Mataev_DeepRED_Deep_Image_Prior_Powered_by_RED_ICCVW_2019_paper.pdf Ref2: https://arxiv.org/abs/2112.06074 Ref3:https://arxiv.org/abs/2110.12271 Ref4: https://openaccess.thecvf.com/content_CVPR_2020/html/Ren_Neural_Blind_Deconvolution_Using_Deep_Priors_CVPR_2020_paper.html --- Reply to Comment 1.1.1: Title: Thank you for your response Comment: We're glad the reviewer is satisfied with our testing of aSeqDIP on a non-linear task. Below, we address the remaining concerns. ### 1) The image to image mapping in DIP is not new, [ref1: DeepRED] also used the image as its input instead of random seed. In our rebuttal, we outlined the key differences between our work and the original DIP paper. We agree with the reviewer that we are not the first to consider a DIP network input containing some structure of the ground truth, as discussed in line 88 of our paper, where we cite two other works. Below, we discuss how aSeqDIP differs from [Ref1]. We agree that DeepRED initializes the algorithm with the noised image $x_0 = y$. However, in DeepRED, the DIP network input is still random noise that remains fixed. This is stated in Section 4 as *"In all the reported tests the same network as in [Original DIP] is used with an i.i.d. uniform (∼[0, 0.1]) random input tensor of size 32×W×H, where W×H is the size of the output image to synthesize". This input is $z$ in their algorithm which remains unchanged as given in Eq.(7), (11), and (12). In our case, the DIP network input is the image we are iteratively estimating, whereas for DeepRED, its a random tensor unrelated to the reconstruction. Additionally, we see three major differences between our work and DeepRED: - Variables: Due to their adoption of the ADMM algorithm, DeepRED requires updating three variables: The network parameters, variable $x$, and the Lagrange multipliers vector. In aSeqDIP, we only update the parameters and the input (updated by a single pass of the network after every few parameters update). - External Denoiser: Due to the use of RED (The Little Engine that Could: Regularization by Denoising), in addition to the DIP network, $\textrm{T}_\Theta$, DeepRED requires an external denoiser $f$. $f$ is used for updating the network input (Eq.(11) or (12)). Table 1 in DeepRED shows the external denoisers (NLM and BM3D) used in their experiments. In aSeqDIP, no external denoisers is needed. - Applicability: We considered a diverse array of tasks including two medical image reconstruction tasks (MRI and CT) and three natural image restoration tasks, whereas DeepRED considered three image restoration tasks. We will include this discussion in the revised manuscript. ### 2) I do agree that DIP-based model suffers from the overfitting issues, others paper addressed this issue. [ref2]: Early Stopping for Deep Image Prior, and [ref3]: Self-Validation: Early Stopping for Single-Instance Deep Generative Priors We would like to thank the reviewer for sharing these papers. As noise over-fitting is the major drawback of DIP-based methods, we agree that there are several works that address the noise overfitting issue including the ones we discuss (and include as baselines) such as (TV-DIP, Ref-DIP, SGLD-DIP, & Self-Guided DIP). Due to time constraints, we are unable to compare with [ref2] and [ref3]. However, we will include discussions about [ref2,ref3] in the revised related work section as below. In [ref2], the authors categorized DIP methods based on addressing noise over-fitting into: (i) Regularization, (ii) Noise modeling, and (iii) Early stopping (ES). The methods in [ref2] and [ref3] are both ES approaches, whereas aSeqDIP belongs to the "Regularization" category due to the use of the input-adaptive auto-encoding term. In [ref2], the authors use the running variance in Eq. (3) as the criteria for ES, whereas the authors of [ref3] propose combining self-validation and training to apply ES. Most importantly, we believe that aSeqDIP achieves high robustness to noise over-fitting. In Figure 10 ($\lambda = 1$), on average, noise over-fitting does not start until iteration 8000 with a subsequent very minimal decay for the task of MRI. The minimal decay in noise over-fitting is also observed in the PSNR curves for denoising in the attached PDF. In these experiments, we compared to SGLD-DIP, Self-guided DIP, and Vanilla DIP. ### 3) Comparison with DIP-based deblurring models such as [ref4]: Neural Blind Deconvolution Using Deep Priors In our rebuttal to the reviewer's comment (see C2 It would be...), we compared with two DIP-based methods (self-guided DIP and SGLD-DIP) for the task of non-uniform image deblurring. In an attempt to fully address the reviewer's comment, we ran the code of [ref4] using 20 FFHQ images, and report the results below. \| Method \| Forward Operator \| Non-uniform Deblurring \| \|----------\|----------\|----------\| DDNM (using FFHQ-trained DM)\| Known \|23.88 \| DPS (using FFHQ-trained DM)\|Known \| 23.67 \| SelfDeblur [ref4]\|Unknown \| 22.35 \| aSeqDIP (Ours)\| Known \| 24.02 \| While we achieve better results, we emphasize that [ref4] operates in a blind setting without access to the forward operator. We hope that our responses have addressed the reviewer's concerns and kindly ask if they could reconsider their score.* --- Rebuttal 2: Title: A friendly and gentle reminder Comment: We would like to sincerely thank the reviewer once again for their insightful comments. As the open discussion period is drawing to a close, we would be deeply grateful if the reviewer could kindly respond to our rebuttal. This would provide us with the opportunity to address or clarify any remaining concerns thoroughly. We would also like to respectfully highlight that other reviewers have acknowledged the novelty and strengths of aSeqDIP, with remarks such as "The idea is fantastic and thought-provoking", "The proposed approach for enforcing DIP to find its fixed point is interesting and novel", "The introduction of the regularization term (autoencoding term) during iterative training and showing that it is useful and that tuning it is important", and "Robustness towards overfitting demonstrating the benefits of the proposed approach".	Summary: This paper investigates how to prevent deep image prior (DIP) from overfitting to the noise or compressed measurements, which is a classic problem of DIP. To address the problem, the authors proposed Autoencoding Sequential DIP (aSeqDIP). The general idea of aSeqDIP is to cuts the overall training process into K sequential blocks, in each of which the input ($\mathbf{z_k}$) of the network is the previous output ($f(\mathbf{z_{k-1}})$), and the loss is defined as $\mathcal{L} = \|\|Af(\mathbf{z}_k) - y\|\|_2^2 + \|\| z_k - f(\mathbf{z}_k)\|\|_2^2$, where the second term forces the output to be alike the input. As k increases, the network aims to find the network $f$ such that $z = f(z)$ and $\|\|Af(\mathbf{z}_k) - y\|\|_2^2$ is minimized. In a word, aSeqDIP forces the output to be a fixed point of the network that fits the measurements as much as possible. Strengths: 1. The paper is well-written and easy to follow 2. The proposed approach for enforcing DIP to find its fixed point is interesting and novel 3. Superior performance has been demonstrated again current diffusion-model-based approaches for image reconstruction tasks. Weaknesses: 1. Although the experiment is thorough in terms of the variety of image reconstruction tasks, I still think it misses an important baseline that uses explicit regularizer (e.g. TV) to stablize the learning process. It would strengthen the argument if the authors could include a comparison like that. 2. The current introduction is concise, but it does not convey the message that the key benefit of aSeqDIP is to address the problem of overfitting. 3. The authors do not discuss the limitations of the proposed method. Technical Quality: 3 Clarity: 3 Questions for Authors: 1. Please consider including a baseline like DIP+TV in the experiment. 2. What is the runtime of aSeqDIP? A comparison between aSeqDIP and other baselines is preferred. 3. [Subjective] The proposition seems redundant: 1) it assumes very strong conditions (the convergence of the network), which, in my opinion distracts the reader from the key message; 2) it kinda shows how aSeqDIP prevent itself from overfitting, but it is not very clear without text. I suggest to write the proposition in the form of plain text with equations. Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: Please discuss the limitations such as runtime, practical convergence, etc. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: C1+Q1: Comparison with TV-DIP: We thank the reviewer for their comment. In what follows, we include a comparison with TV-DIP in terms of the average PSNR over 15 scans in MRI (with 4x and the fastMRI test dataset) and 20 images from the CBSD68 dataset for denoising and in-painting. As observed, our method outperforms TV-DIP. \| Method \| MRI \| Denoising \| In-painting \| \|----------\|----------\|----------\|----------\| \| TV-DIP \| 31.04 \| 30.57 \| 22.67 \| \| aSeqDIP (Ours) \| 34.08 \| 31.51 \| 24.56 \| C2: The current introduction does not convey the message that the key benefit of aSeqDIP is to address the problem of overfitting: We acknowledge the reviewer's comment. In the revised Introduction Section of the paper, we will emphasize that the main problem of DIP-based methods is noise overfitting as the selection of the number of optimization steps in DIP can differ not only from task to task but also from image to image within the same task. We will add a discussion that the main goal of introducing aSeqDIP is to mitigate the issue of noise over-fitting through the input-adaptive procedure and the use of the auto-encoding term. C3 Discussing the limitations such as runtime and practical convergence: Please see our global response. Q2 Runtime of aSeqDIP: We thank the reviewer for their comment. In the last column of Table 2, we report the average run-time (minutes) of all the methods. For the second best PSNR and SSIM (self-guided DIP), our method is 2X faster for MRI and CT reconstruction and requires 1 minute less than self-Guided DIP for denoising and in-painting. When compared to DM-based methods, aSeqDIP requires a slightly less run time while achieving an improvement in terms of the reconstruction quality (PSNR and SSIM). While DM-based methods only require function evaluations and our method is an optimization-based approach, the generally larger run-time reported for DM-based methods is due to the necessity of running a large number of reverse sampling steps. Q3 [Subjective] The convergence assumption in the Proposition: We agree with the reviewer that the convergence assumption in Proposition 3.1 is strong. The main point we'd like to convey in this proposition is that aSeqDIP is trying to solve the optimization problem in (5), which is different that Vanilla DIP. In Remark 3.2, we discuss this point by comparing aSeqDIP and Vanilla DIP. In the revised manuscript, we will present the point of the proposition as a remark for further clarification. --- Rebuttal Comment 1.1: Title: Thank you for the response Comment: I thank the authors for their response, and they have addressed most of my concerns. One only question remaining is how the DIP+TV is finetuned? I suggest the authors to include a description on this in the camera-ready. --- Rebuttal 2: Title: Thank you for your response. Addressing the Reviewer's Concern Comment: First, we would like to thank the reviewer for their response. For TV-DIP, during the rebuttal, we used "https://arxiv.org/pdf/1810.12864" following the reviewer's suggestion. We coded the TV regularization term in Equation (3) and used Equation (5) to tune the parameters $\Theta$. According to Section 4.1 of the TV-DIP paper, we used 5000 optimization steps. For the architecture, we used the U-Net architecture (with skip connections) from the original DIP paper, which is the same as the one the authors describe in Figure 3. In regard to the hyper-parameters (including the regularization parameter), in Section 4.1, the authors of TV-DIP mentions: "All algorithmic hyperparameters were optimized in each experiment for the best signal-to-noise ratio (SNR) performance with respect to the ground truth test image". As the authors do not provide the regularization parameter, in the results we provided in the rebuttal, we used $\lambda = 1$, which is similar to aSeqDIP. To fully address the reviewer's concern and ensure that the choice of $\lambda$ we used (in our rebuttal) in TV-DIP is sufficient, we run TV-DIP with additional values of the regularization parameter for the task of denoising and report the average PSNR results for 20 images from the CBSD68 dataset. As observed, the TV-DIP results with $\lambda$ near 1 is better than other values we considered here. In all cases, aSeqDIP achieves better PSNR. \| Task \| TV-DIP ($\lambda = 0.1$) \| TV-DIP ($\lambda = 0.8$) \| TV-DIP ($\lambda = 1$)\| TV-DIP ($\lambda = 1.2$) \| TV-DIP ($\lambda = 3$) \|TV-DIP ($\lambda = 10$) \| aSeqDIP (Ours) \| \|----------\|----------\|----------\|----------\|----------\|----------\|----------\|----------\| \| Denoising \| 30.02 \| 30.54 \| 30.57 \| 30.61 \| 30.43 \|28.89 \| 31.51 \| Following the reviewer's suggestion, we will add this discussion and the TV-DIP results in the revised paper. We are happy to address any other concerns the reviewer might have. We hope that, in light of our responses, the reviewer might consider raising their score. Thanks, Authors	Rebuttal 1: Rebuttal: # Global Response We thank the reviewers for their constructive comments. Many reviewers raised questions about the limitations and capabilities of the proposed approach, and requested experiments with different tasks, settings, and baselines. Below, we discuss these limitations and summarize the additional experiments and results obtained over the past week. These discussions will be included in the revised manuscript. Limitation Discussions: - Reviewer qnNG - Comment 3: We thank the reviewer for their comment. In terms of run time, we would like to point out that in Remark 3.4, we discuss the computational requirements of the proposed method, which is determined by (i) the $N\times K$ parameter updates, and (ii) the number of function evaluations necessary for updating the input of every network which is $K$. Furthermore, in Table 2, we include average run-time results of aSeqDIP as compared to the considered baselines. Furthermore, we have shown that our method is not that sensitive to the selection of $N$ and $K$ (along with $\lambda$) as, for the four considered tasks, we selected the same values. As our adoption of the autoencoding term delays the start of the PSNR decay, the empirical convergence plots for our method reaches nearly 5\% of its best possible PSNR at around iteration 2000 (see Figure 4). - Reviewer hjHc - Question 2: A known limitation of our method is its slow run-time when compared to the inference time of End-to-End (E2E) supervised reconstruction models. However, it is important to note that our method, as it is a DIP-based approach, operates without any training data and pre-trained models. - Reviewer Q1ff - Limitation Comment: Thank you for your comment. See our response to your third Comment that (i) justifies why the reported results in our paper and the DM-based baselines are slightly different, and (ii) includes additional aSeqDIP CT results on MCG's downsized pixel space. In regards to run-time, we agree with the reviewer that the inference of E2E methods is very fast when compared to our method and the DM-based methods. The reason is that E2E methods requires only one forward pass (or a few in the case of unrolling networks). However, it is important to note that our method, as it is a DIP-based approach, operates without any training data and pre-trained models. Summary of Additional Results: - MRI, Denoising, and In-painting PSNR results with aSeqDIP (Ours) vs. TV-DIP. (Reviewer qnNG). - Non-uniform image Deblurring (a non-linear inverse imaging task) PSNR results of our method as compared with DPS, Self-guided DIP, and SGLD. (Reviewer MAra) - Denoising PSNR results of our method as compared to Rethinking DIP. (Reviewer MAra) - Denoising, non-uniform deblurring, and in-painting results of our method as compared with DDNM and DPS using the FFHQ testing dataset. (Reviewer MAra) - CT reconstruction results of aSeqDIP as compared to MCG using the downsized 256X256 setting. (Reviewer Q1ff) - MRI PSNR results of our method as compared with a supervised E2E method, VarNet. (Reviewer Q1ff) - Average PSNR curves for the task of denoising with respect to iteration $i$ for aSeqDIP, Vanilla DIP, and Self-Guided DIP is given in the attached PDF. (Reviewer Q1ff) - The degraded images in Figure 5 are given in the attached PDF. (Reviewers hjHc and Q1ff) Pdf: /pdf/aca2cd8a97703e04cbdf5008f70978a977c32696.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Progressive Exploration-Conformal Learning for Sparsely Annotated Object Detection in Aerial Images	Accept (poster)	Summary: Summary: The paper addresses the challenge of sparsely annotated object detection (SAOD) in aerial images, a critical task for real-world aerial intelligence systems where annotations are limited. Acknowledging the difficulty posed by the imbalanced probabilities and confidences in predicted aerial objects, the paper proposes a novel Progressive Exploration-Conformal Learning (PECL) framework. This framework adaptively selects high-quality pseudo-labels to enhance detection performance. It comprises a conformal pseudo-label explorer and a multi-clue selection evaluator, which together form a decision-making paradigm for pseudo-label exploration. The paper also demonstrates that their method outperforms existing SOTA methods on the DOTA and HRSC2016 datasets. Contributions: The paper makes significant contributions to the field of semi-supervised aerial object detection by addressing key challenges related to sparse annotations and proposing a robust framework that improves detection performance through adaptive and progressive pseudo-label exploration. Strengths: (1) The overall paper is technically sound. (2) For originality and significance, the proposed PECL integrates a conformal pseudo-label explorer with a multi-clue selection evaluator to adaptively select high-quality pseudo-labels, offering a new perspective on handling sparse annotations in object detection. (3) For quality and clarity, the methodological framework is well-structured, detailing the iterative process between pseudo-label exploration and detector updating. Weaknesses: (1) While the PECL framework is innovative, its complexity might pose challenges for practical implementation. The multi-layer perceptron for the conformal pseudo-label explorer and the iterative training process could be computationally intensive. Discussing the impact of these modules on the overall computational cost and inference time is supposed to consider. (2) Can the authors provide more details on the computational efficiency of the PECL framework? Specifically, how does the iterative process impact training time, and are there any optimizations that can be applied to improve efficiency? (3) How does the PECL framework specifically address the detection of small and occluded objects in aerial images? Are there any additional strategies or modifications that could further enhance performance for these challenging cases? (4) The writing is a little unsatisfactory, especially in the first section, where the rationale for the proposed method is not well explained, making it difficult for readers to develop interest in your approach. (5) In Line 71-73, it is difficult for readers to intuitively realize that experimental performance is one of the main contributions without a very convincing data. (6) Shown in Line 142, “which can can adaptively” is a error. Moreover, the case of the first letter of the subsection and subsubsection should be unified in Section The Proposed Method. Technical Quality: 3 Clarity: 3 Questions for Authors: See the weaknesses above. Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: (1) While the paper claims state-of-the-art performance, it lacks the comparative experiments with the SOTA methods from January to May 2024. Adding several comparative experiments with SOTA methods, such as on CVPR/TGRS 2024, can be considered. (2) For Section Related Work, it would be better to add some latest works published in 2024. For Section The Proposed Method, it would arouse the readers’ interest to add illustration chart of the proposed SCIR framework. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your constructive suggestions. Here is our detailed response. (1) Our proposed conformal pseudo-label explorer and multi-clue selection evaluator are meticulously encapsulated classes that can be directly invoked. In practical implementation, they exhibit excellent user-friendliness, with no challenges to overcome. (2) Compared with baselines, during the training process, our PECL has a higher time cost due to an iterative detector updating procedure and an extra conformal pseudo-label exploration procedure; however, in the testing process, our method takes the same time as baselines with the same detection network. (3) Compared with other semi-supervised/sparse-annotated methods, our PECL demonstrates a degree of superiority in the learning process. Specifically, the training time of our PECL, Unbiased Teacher[1], Co-mining[2] methods are 13.35h, 16.74h, 15.42h on the DOTA dataset at 5% label rate. We conduct all experiments on two NVIDIA 2080Ti gpus. (4) Additionally, we further consider accelerating the convergence speed of the explorer and evaluator by reducing the complexity of the exploratory state and action spaces, as well as the frequency of updating the target network, thereby enhancing overall computational efficiency. (5) For small and occluded objects in aerial images, our proposed conformal pseudo-label explorer designs exploratory characteristics based on the non-conformity score, which considers the imbalanced probabilities between small and large objects. In future work, we will incorporate the size of objects into the characteristic design to further enhance the performance and robustness of our algorithm. (6) In order to intuitively reflect that the experimental performance is one of our main contributions, we will revise Lines 71-73 to:``......demonstrate the effectiveness of our PECL, which outperforms the baselines and state-of-the-art methods by at least 5.63%, 1.35%, respectively......’’. (7) According to our investigation, there are only two semi/sparse-supervised methods for object detection in aerial images in 2024, Pseudo-Siamese Teacher[3](TGRS 2024), S2O-Det[4](TII 2024), and neither of them is open source. We will add them to related work, and track the comparative experiments in the future. (8) For Section The Proposed Method, it would arouse the readers’ interest to add illustration chart of the proposed SCIR framework. (9) According to your suggestion, we have presented a diagram of our proposed PECL framework in Figure 4 of overall author rebuttal PDF file. (10) For minor writing/formatting errors, we will polish this paper in the revision. ## Reference [1] Unbiased teacher for semi-supervised object detection. [2] Co-mining: Self-supervised learning for sparsely annotated object detection. [3] Pseudo-Siamese Teacher for Semi-Supervised Oriented Object Detection. [4] S2O-Det: A Semisupervised Oriented Object Detection Network for Remote Sensing Images. --- Rebuttal Comment 1.1: Comment: Thanks for your detailed responses to every weaknesses and limitations we commented. Your responses address certain aspects of my concerns regarding this work and clear plans are provided for improving the manuscript. I keep my rating of Borderline Accept for several concerns remain unresolved and their illustrations and suggestions are as follows: 1) Some corresponding experimental analyses are necessary to prove that encapsulated classes of conformal pseudo-label explorer and multi-clue selection evaluator perform excellent user-friendliness compared to other methods 2) It would be better to provide more specific evidence or detailed examples to substantiate the same cost time on PECL compared to baselines with the same detection network. But how about on other latest detection network like Mamba-based or DETR-based? 3) The overall author rebuttal PDF file exceeds the limitation of one page. --- Reply to Comment 1.1.1: Title: Replying to comments by Reviewer hP3V Comment: （1）The conformal pseudo-label explorer takes the feature maps and predicted logits as input, computing the exploratory characteristics of the current pseudo-label and outputing a two-dimensional selection probability distribution. The exploratory characteristics consist of non-conformity score, prediction probability and similarity score. i) The non-conformity score is obtained through conformal prediction and represents the uncertainty of the current pseudo-label, to address the problem of imbalanced prediction probabilities between categories. ii) The prediction probability is the predicted classification score by the detector at the current stage. It indicates the classification information of the current algorithm for pseudo-labels. iii) The similarity score is a measure of the consistency between the current pseudo-label features and the maintained prototypes. In addition, the above three exploration characteristics can be obtained from both the one-stage and two-stage detectors. The multi-clue selection evaluator takes the current characteristic and the output of explorer as input and outputs the cumulative reward. We only need to input the necessary feature maps and predicted logits to complete the calculation in the encapsulation class, so it is user-friendly. （2） While our PECL will inevitably extend the training time, it remain faster than semi-supervised methods for training. Because the semi-supervised method needs to run two complete models at the same time, namely the teacher model and the student model. Our PECL only needs to add a few lightweight MLP layers. We conduct the experiments on two NVIDIA 2080Ti gpus. Specifically, the training time of Redet, S2ANet methods are 8.833h, 7.265h ,while the training time of Redet w/PECL, S2ANet w/PECL are 13.351h, 10.772h on the DOTA dataset at 5% label rate. But the SOOD (a semi-supervised method) based on Redet needs 18.511h under the same setting. For inference time, under the metric Frames Per Second (FPS) based on a 2080Ti, the inference speed of baseline detector S2ANet and S2ANet w/PECL achieves 13.1 FPS, demonstrating our PECL does not affect the inference time. （3）As for DETR, due to the complex nature of aerial images (such as densely arranged objects), the DETR series is rarely used in aerial images. Besides, we encountered some difficulties when applying our PECL to DETR-based detector, e.g. ARS-DETR. Our PECL is effective in pseudo-label exploration on dense object detectors, because a sufficient number of proposals provide enough samples for conformal prediction. However, for the DETR-based detector, which has sparse proposals, our PECL cannot perform well. As for Mamba-based detector, according to our research, mamba is currently used as a backbone for object detection and does not affect the application of PECL.	Summary: This paper propose a Progressive Exploration-Conformal Learning (PECL) framework to address the sparsely annotated object detection task, which can adaptively perform the selection of high-quality pseudo-labels. The pseudo-label exploration are formulated as a decision-making paradigm by adopting a conformal pseudo-label explorer and a multi-clue selection evaluator. Some evaluations on two public datasets demonstrate the superiority of our PECL Strengths: - Paper is well writen. - It seems interesting to simulate and learn the pseudo-label exploration process using reinforcement learning, i.e. the conformal pseudo-label explorer and the multi-clue selection evaluator. - The proposed method seems to work well. - The comparative experiments and ablation experiments are quite substantial. Weaknesses: - Table 4 lacks comparisons for weakly supervised oriented object detection, which are supported in MMRotate. Specifically, HBox-supervised (H2RBox, H2RBox-v2), Point-supervised (Point2RBox, PointOBB). - The authors mainly verified it on aerial image, but the proposed technology does not seem to be strongly related to the specific scenario, and therefore lacks verification in more convincing natural scenarios, e.g. COCO. - More object detection methods in aerial image need to be investigated in related work, such as OBB/HBB, full-/weakly-/semi-supervised. - After the introduction of reinforcement learning, the visualization of the changes of pseudo labels during the training process needs to be presented. The desired result is a significant improvement in quality. - The authors verified it on a CNN-based detector, and it would be more perfect if it could be verified on a DETR-based detector, e.g. ARS-DETR. - The left fields of Table 1 (e.g. 1%) and Table 4 (e.g. Sparse-annotated) do not seem to be centered. You can use ```\multirow``` to adjust them. Technical Quality: 3 Clarity: 3 Questions for Authors: - I thought of an interesting setting, that is, Sparsely Annotated weakly-supervised roriented Object Detection, such as sparsely annotated HBox. Is it possible to add a related experiment based on H2RBox-v2 and verify it in combination with PECL techniques? Of course, this is not necessary, it's just my sudden thought. If the author can provide it, I am willing to further improve the rating. - I am not a professional reinforcement learning researcher, so I am worried whether the training of the entire detector will be slower after the introduction of reinforcement learning. I hope the authors can clarify this. Confidence: 5 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: N/A Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your constructive suggestions. Here is our detailed response. (1) H2RBox[1] learns object center localization from horizontal box annotations in the weak supervision branch, utilizes scale and spatial constraints to learn object width, height, and rotation angle information in the self-supervision branch. H2RBox-v2[2] utilizes the principle of symmetry to learn flip-rotation consistency, thereby predicting the rotation angle of object. PointOBB[3] and Point2RBox[4] use Multiple Instance Learning and Knowledge Combination, respectively, to learn rotated box regression from single point supervision. We will add more weakly-/semi-supervised aerial object detection methods in the related work of the revision, which are all aimed at alleviating the time-consuming and labor-consuming of rotated annotations. (2) To prove the generality of our PECL, we try to conduct experiments on general detection dataset, COCO dataset. Following the setting of BRL[7], four sparsely annotated training sets are generated. In Table 1 of overall author rebuttal PDF file, we compare the different methods with our method trained under three annotation sets. It can be seen that under all sparse conditions, our PECL outperforms the Co-mining[8] by 0.2%, 0.6%, 0.8%, respectively, indicating that our proposed method can mine supervised signals effectively. (3) Thank you for the reminder; we will add more OBB/HBB, full-/weakly-/semi-supervised aerial object detection methods in the related work of the revision. (4) The visualization of the changes of pseudo-labels during the training process has been presented in Figure 3 of overall author rebuttal PDF file. The results indicate a significant improvement in the quality of pseudo-labels after introducing reinforcement learning. (5) We encountered some difficulties when applying our PECL to DETR-based detector, e.g. ARS-DETR[9]. Our PECL is effective in pseudo-label exploration on dense object detectors, because a sufficient number of proposals provide enough samples for statistics-based conformal prediction.However, for DETR-based detector, which has sparse proposals, our PECL cannot perform well. This idea is worth further exploration in future work. (6) For minor writing/formatting errors, we will polish this paper in the revision. (7) Sparsely Annotated Weakly-Supervised Oriented Object Detection is indeed an interesting and valuable research setting. However, we encountered difficulties when integrating our PECL with H2RBox-v2. Specifically, H2RBox-v2 is a weakly supervised method based on FCOS[5] detector, whose label assignment strategy requires the participation of all points on the feature map to classify each candidate point as a positive or negative sample. Therefore, this strategy requires ground truth boxes to have very high quality. We need to modify the FCOS label assignment strategy to allow for the assignment of ignored samples (similar to Faster R-CNN[6]), in order to reduce dependence on the quality of ground truth boxes. This involves a lot of work, and we have just proposed a preliminary idea that has not yet been implemented. We will implement this in future research work. (8) Compared with baselines, during the training process, our PECL has a higher time cost due to an iterative detector updating procedure and an extra conformal pseudo-label exploration procedure; however, in the testing process, our method takes the same time as baselines with the same detection network. ## Reference [1] H2RBox: Horizonal Box Annotation is All You Need for Oriented Object Detection. [2] H2RBox-v2: Incorporating Symmetry for Boosting Horizontal Box Supervised Oriented Object Detection. [3] PointOBB: Learning Oriented Object Detection via Single Point Supervision. [4] P2RBox: A Single Point is All You Need for Oriented Object Detection. [5] FCOS: Fully Convolutional One-Stage Object Detection. [6] Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks. [7] Solving missing-annotation object detection with background recalibration loss. [8] Co-mining: Self-supervised learning for sparsely annotated object detection. [9] ARS-DETR: Aspect Ratio-Sensitive Detection Transformer for Aerial Oriented Object Detection. --- Rebuttal Comment 1.1: Comment: Thanks to the authors for their detailed responses, some of my concerns have been well addressed. I still have one question and some suggestions. * Q1: The authors mention that training cost will increase, but how much? The authors need to clarify. * S1: The authors mentioned that the current PECL will have new issues when combined with DETR detectors, and I suggest that the authors include this in the discussion of limitations. * S2: As the authors replied to Reviewer hP3V, many semi/sparse-supervised methods are not open source. We hope that the authors can open source the code after the manuscript is accepted to promote the healthy development of the community. --- Reply to Comment 1.1.1: Title: Replying to comments by Reviewer RekV Comment: (1) We conduct all experiments on two NVIDIA 2080Ti gpus. Specifically, the training time of Redet, S2ANet methods are 8.833h, 7.265h ,while the training time of Redet w/PECL, S2ANet w/PECL are 13.351h, 10.772h on the DOTA dataset at 5% label rate. (2) We will outline the application limitations of PECL in the limitations section of the original paper to serve as a reference for future work. (3) We will make the code publicly available once the work is accepted.	Summary: This paper proposes a new learning framework, PECL, for sparsely annotated object detection (SAOD) in aerial images. The framework introduces a conformal pseudo-label explorer and a multi-clue selection evaluator, which can leverage category-specific characteristics and inter-instance contextual relationships. Comprehensive experiments demonstrate the superior performance of the proposed solution compared to prior approaches. Additionally, the paper includes numerous ablation studies and case studies that examine the various properties of the PECL framework. Strengths: - Aerial imagery has many useful properties for sparely annotated object detection. It is good that this paper explores those properties to develop a better SAOD framework. - The paper includes a substantial number of ablation studies and case studies, which could unveil valuable insights into the proposed method. Weaknesses: - The paper highlights PECL's effectiveness in addressing SAOD tasks by comparing the PECL-enabled version with a simple supervised baseline. The results are appealing, which is good. However, when comparing PECL with other SAOD solutions, the improvement is modest, at 1.35%. - The SAOD task in aerial imagery does not appear to be more challenging than SAOD tasks for general imagery, as objects in aerial imagery typically have only one degree of freedom in rotation. This reduces the significance of PECL's contribution. - The writing can be improved. The paper is somewhat hard to follow, for example, lines 128-131. Sometimes, even the logic is hard to follow. For instance, in line 31, the average number of objects per image seems irrelevant, as it is a dataset statistic. Neighboring aerial images could be stitched together to form a larger image with more objects. Technical Quality: 3 Clarity: 1 Questions for Authors: Please check out the weaknesses section for details. Confidence: 3 Soundness: 3 Presentation: 1 Contribution: 2 Limitations: I don't see potential negative societal impact of this work. Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your constructive suggestions. Here is our detailed response. (1) Our proposed PECL has improved performance by at least 5.63% compared to supervised baselines. Compared to other state-of-the-art methods, we have also achieved at least 1.35% growth. Given the limited improvement of other methods, this achievement is already quite challenging in the current research field, and it also indicates that our method still has a lot of room for improvement. (2) Compared to SAOD task in general images, SAOD task in aerial images faces greater challenges. - Firstly, objects in aerial images have characteristics such as arbitrary orientation, dense distribution, and large aspect ratios. Figure 1 of overall author rebuttal PDF file intuitively counts the number of objects in each image in the DOTA and COCO datasets, which reflects the relatively high density of objects in aerial images. Motivated by this, our proposed PECL utilizes rich contextual information between objects to mine high-quality pseudo-labels. - Secondly, aerial datasets often exhibit serious long tail problems, resulting in significantly imbalanced prediction results for different classes. Figure 2 of overall author rebuttal PDF file shows the statistical analysis on the selected candidates of each class. As in Figure 2, when the threshold is with 0.9, less positive/negative candidates are selected; when reducing it to 0.5, positive/negative candidates are all increased. This confirms that it is difficult to select pseudo-labels with a certainty threshold. In contrast, our PECL employs reinforcement learning to learn an adaptive policy to decide the confidence of selecting candidates. Therefore, SAOD in aerial images is necessary and challenging. - The diversity of rotation angles remains another challenge in aerial object detection. The introduction of rotation angles is not merely about adding a parameter to learn. The periodicity of angles leads to the boundary discontinuity and square-like problems[1], causing issues in the regression of rotated boxes and affecting the localization quality of rotated bound boxes. This is also an issue worth investigating in the SAOD task and can serve as the motivation for future work. (3) For minor writing/formatting errors, we will polish this paper in the revision. ## Reference [1] Detecting Rotated Objects as Gaussian Distributions and Its 3-D Generalization	null	null	Rebuttal 1: Rebuttal: Accurate annotation is a key factor in ensuring object detection performance. However, the manual annotation process is time-consuming and labor-intensive, especially in remote sensing scenarios with densely arranged objects. In this paper, we propose the Sparsely Annotated Object Detection (SAOD) task, which aims to perform remote sensing object detection using sparse annotations (e.g., 5%, 10%).To address the SAOD task in aerial images, we propose an innovative Progressive Exploration-Conformal Learning (PECL) framework, which consists of a conformal pseudo-label explorer and a multi-clue selection evaluator. This framework takes into account the imbalance in predicted results between categories and the rich contextual information to mine confident pseudo-labels, thereby enhancing the performance of the detector. The conformal pseudo-label explorer learns an adaptive pseudo-label policy by maximizing cumulative rewards. The multi-clue selection evaluator aims to optimize the policy by providing guiding feedback. Ultimately, the explored pseudo-labels can be utilized to guide the closed-loop iterative optimization of the aerial detector. We sincerely respond to each reviewer under their comments. Pdf: /pdf/00ceb2f40451d99dcbb32730cc51af5be8a46ee8.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Rejection via Learning Density Ratios	Accept (poster)	Summary: The paper proposes a distributional perspective to build abstaining classifiers. By considering an idealized distribution, the authors show that this translates into optimizing a loss risk with a $\varphi$-divergence regularization term. Moreover, they provide results when considering $\alpha$-divergences, a specific family of $\varphi$-divergences. Empirical evaluation is performed over clean and noisy datasets. Strengths: The main strengths of the paper are: i) the paper is clearly written, with clear contributions advancing the state of the art in abstaining classifiers ii) the theoretical contributions seem sound; iii) the proposed method is original and bridges DROs with Learning to Reject. Weaknesses: The main weaknesses of the paper are: i) there is no related work section explicitly dedicated to learning with a reject option. See, e.g., [a] for a recent survey. ii) the empirical evaluation can be improved: * for instance, the paper considers only four baselines (mainly from Learning to Defer literature) and ignores popular alternatives such as softmax response [26] * the method is tested only on three datasets, which seem easy to solve. In particular, MNIST might be too easy to evaluate abstaining classifiers (an accuracy of 100% is easy to achieve with relatively few rejections). A more interesting dataset collection could be MedMNIST [b], which contains medical images from real data tasks. [a] Hendrickx, Kilian, Lorenzo Perini, Dries Van der Plas, Wannes Meert, and Jesse Davis. "Machine learning with a reject option: A survey." Machine Learning 113, no. 5 (2024): 3073-3110.\ [b] Yang, Jiancheng, Rui Shi, and Bingbing Ni. "Medmnist classification decathlon: A lightweight automl benchmark for medical image analysis." In 2021 IEEE 18th International Symposium on Biomedical Imaging (ISBI), pp. 191-195. IEEE, 2021. Technical Quality: 2 Clarity: 3 Questions for Authors: I have a few questions for the authors: 1) is there a reason why you did not compare with the simplest (and often the best) abstaining classifier, i.e. the softmax response? In [c], the authors show that the classifier built using this strategy can be optimal. Moreover, recent empirical works [d,e] show that score-based approaches outperform other abstaining classifiers. 2) how did you train DEFER, without access to human predictions? As far as I know, the surrogate loss also requires specific human predictions; however, I could not find in the Appendix how this is done in practice. [c] Franc, Vojtech, Daniel Prusa, and Vaclav Voracek. "Optimal strategies for reject option classifiers." Journal of Machine Learning Research 24, no. 11 (2023): 1-49.\ [d] Jaeger, Paul F., Carsten Tim Lüth, Lukas Klein, and Till J. Bungert. "A Call to Reflect on Evaluation Practices for Failure Detection in Image Classification." In The Eleventh International Conference on Learning Representations. (2023)\ [e] Pugnana, Andrea, Lorenzo Perini, Jesse Davis, and Salvatore Ruggieri. "Deep neural network benchmarks for selective classification." arXiv preprint arXiv:2401.12708 (2024). Confidence: 3 Soundness: 2 Presentation: 3 Contribution: 3 Limitations: The authors discuss the limitations of their approach. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for sharing their insights and providing useful suggestions on improving our evaluation. Please find the rebuttal below. > Related Work We thank the reviewer for their various references. We will make sure to include these in the next version of the paper. We would also be happy to add a dedicated related work section. In particular, discussion regarding softmax response and score-based vs abstaining classifiers would be added. We would add this either to the main text (Sec 2\) with the additional page / space of the camera ready (alongside some reduction on the GVI / DRO section) or via an additional appendix section. > Empirical evaluation can be improved (datasets) Thanks for the dataset recommendation. Please see the shared rebuttal response section. We have added some preliminary results utilizing the MedMNIST collection. > Q1: Softmax Response (SR) Our work primarily started from examining rejection approaches which were inspired by surrogate loss functions and cost-sensitive losses. These approaches formed the baselines which we considered (many of these papers did not consider softmax response). Although we do not include softmax response as a baseline, we note that the density-ratio rejectors have a strong connection to this method. In the case of the KL-divergence rejectors with the practical trick employed (as noted in Line 271 onwards), our rejector will threshold the model’s predictive entropy. This is similar to the maximum softmax score. The theoretical framework of prediction using density-ratios presents a generalization of this elucidating further connections to DRO / GVI. We further believe that the sample complexity bounds do not have an equivalent in SR. Empirically, as a result, our approach and naive threshold rejection using the softmax scores should be comparable (when both utilize temperature scaling). The component of SR that we are missing is the calculation of the threshold according to a desired coverage guarantee. This would be a nice direction for future work to automatically prescribe $\\tau$. We will include this discussion and connection to the SR in the next version of the paper. > Q2: DEFER without expert One can utilize DEFER without human predictions by utilizing a ground-truth expert (one returning the data’s label). In particular, it has been shown that this interpretation provides a surrogate loss function of the 0-1-c loss function. This has been shown in \[a, see Appendix A.2\] and \[b\] which generalizes this. We are happy to include this discussion to make this baseline choice clear. \[a\] Charoenphakdee, Nontawat, et al. "Classification with rejection based on cost-sensitive classification." International Conference on Machine Learning. PMLR, 2021\. \[b\] Cao Y, Cai T, Feng L, et al. Generalizing consistent multi-class classification with rejection to be compatible with arbitrary losses. NeurIPS, 2022\. --- Rebuttal Comment 1.1: Title: Response to the Rebuttal Comment: I thank the authors for their rebuttal, and I hope they found the references to the MedMNIST collection helpful. I would like to add a small comment on the following: > The component of SR that we are missing is the calculation of the threshold according to a desired coverage guarantee. This would be a nice direction for future work to automatically prescribe $\tau$. Some approaches, as noted by the authors in the response to Reviewer MrTu, add a coverage constraint to the loss that is minimized. However, empirical evidence does not support using these models vs. SoftMax Response (see again e.g. [a,b]). In any case, given a target coverage $c$, both approaches require a calibration set and estimate the threshold $\tau$, considering the $(1-c)$ quantile of the confidence on the calibration set. Another option is resorting to cross-fitting to estimate the $\tau$ without the extra calibration set but exploiting test folds and stacking confidences (see, e.g., [c]). To conclude, I think this paper should be considered for acceptance. [a] - Feng, Leo, Mohamed Osama Ahmed, Hossein Hajimirsadeghi, and Amir H. Abdi. "Towards Better Selective Classification." In The Eleventh International Conference on Learning Representations. [b] - Pugnana, Andrea, Lorenzo Perini, Jesse Davis, and Salvatore Ruggieri. "Deep neural network benchmarks for selective classification." arXiv preprint arXiv:2401.12708 (2024). [c] - Pugnana, Andrea, and Salvatore Ruggieri. "A model-agnostic heuristics for selective classification." In Proceedings of the AAAI Conference on Artificial Intelligence, vol. 37, no. 8, pp. 9461-9469. 2023. --- Reply to Comment 1.1.1: Comment: We thank the reviewer for their support of the paper and for providing some additional context on the empirical weakness of the other baselines. We briefly considered cross-fitting to find thresholds values similar to [c], however did not go that route due to increases in computational costs for larger datasets. Nevertheless, we will include this discussion in to next revision and also add citations for previous work which have successful utilized this approach.	Summary: Classification with rejection emerges as a learning paradigm that allows models to abstain from making predictions. Traditional rejection learning methods typically modify the loss function, enabling models to explicitly reject making predictions when they are inaccurate or uncertain. These methods rely on providing good class probability estimates and often require training models from scratch. This paper proposes an interesting perspective to reconsider rejection not from the standpoint of the loss function, but rather from the perspective of distributions. By optimizing the risk of the loss with a $\varphi$-divergence regularization term, it seeks an idealized data distribution that maximizes the performance of pretrained models. Strengths: 1. This paper takes a more interesting approach to rejection compared to previous papers. 2. In theory, approaching from the perspective of distributions holds better prospects compared to considering single probabilities alone. 3. The theoretical richness of this paper provides strong evidence for its claims. Weaknesses: 1. For high-dimensional data, estimating density ratios and computing idealized distributions can be very challenging, implying that this method may only address low-dimensional data and its application scenarios are limited. 2. This method involves a large number of hyperparameters: $\lambda$, $\tau$, $\alpha$, $T$, which pose a significant burden for optimization. 3. The experiments in the paper may only be conducted on specific datasets and under certain conditions (some simple datasets), which could limit their generalizability to broader scenarios. Technical Quality: 3 Clarity: 3 Questions for Authors: 1. Although theoretically estimating the distribution $P(y\|x)$ holds more promise than estimating a single probability $\max P(y\|x)$, in practical situations, estimating the distribution seems less feasible compared to single probability estimates, especially given the various calibration methods available for single probabilities. 2. How did you design the expert in the experiments where you compared methods [1] from Learning to Defer？ 3. Since comparing with [1], it seems more reasonable to compare with [2], which is more relevant to the focus of this study. [1] Hussein Mozannar and David Sontag. Consistent estimators for learning to defer to an expert. ICML 2020. [2] Cao Y, Cai T, Feng L, et al. Generalizing consistent multi-class classification with rejection to be compatible with arbitrary losses. NeurIPS, 2022. Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: N/A. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the Reviewer for praising the interesting nature of our proposed approach and for the insightful questions. We are glad that the Reviewer appreciates the different approach we have taken and hope that the connections to DRO / GVI / distributions can lead to new theories. Please find the per-point rebuttal below. > \[...\] this method may only address low-dimensional data \[...\] We agree that with a naive application of this approach, there may be problems in high dimensions. This is a weakness shared by other density ratio-style algorithms like importance weighting. We would however note that there has been success in leveraging representation learning to operate in a lower dimension. This can be used as a potential work around, especially if the model weights of the original classifier is available. > This is a weakness seen in other density ratio-style approaches like importance weighting. We would like to comment on the hyperparameters noted by the reviewer. - We are unsure what hyperparameter $T$ the reviewer is referring to. - $\\tau$ for the threshold can be treated as a hyperparameter. But it can also be used as a value to be found to satisfy a specific risk-coverage requirement. This can be equivalent to $c$ considered in the baseline approaches. Actually, Reviewer dzAs reminded us of some work which picks thresholds according to a coverage-modified-risk requirement \[a\]. As future work, this might be an interesting future direction to our work. - We agree that tuning may present some challenges $\\lambda$ and $\\alpha$. However, we note that picking $\\lambda$ and $\\alpha$ is equivalent to picking an appropriate divergence. This is equivalent to how picking a surrogate loss for the classifier-rejection 0/1 loss function has many options. One additional note that we make about hyperparameter tuning of our approach, is that although there are potentially more individual parameters one may want to pick from, it is substantially cheaper to tune than the other baselines. Indeed, the process of learning the 1D normalization constant $b$ required for density ratio rejectors (Line 287\) is substantially cheaper than learning typically a whole network as required by the baselines. For our approach, we can keep the base classifier fixed and we only need to learn $b$ (see Appendix P.III for discussion on the number of tunable parameters of the approaches). \[a\] Geifman, Yonatan, and Ran El-Yaniv. "Selective classification for deep neural networks." Advances in neural information processing systems 30 (2017). > Experiments (Weakness 3\) Please see the shared rebuttal section. Other reviewers also commented about adding other datasets for strong evaluation. We have taken Reviewer dzAs’s recommendation of considering datasets in the MedMNIST collection. > Q1: Calibration Although calibration for the multiclass case is more challenging in practice than perhaps estimating $\\max P(y \\mid x)$, we shouldn’t dismiss theoretically motivated frameworks due to this reason. From a practical point of view, there are still many approaches which have shown reasonable success. For example, the standard temperature scaling approach that we utilize in the paper; or various different ensembling-style methods which we do not explore. > Q2: Experts for DEFER In essence, we are assuming that the experts replicate the ground truth labels. This is equivalent to the reduction in \[b, see Appendix A.2\] which provides a surrogate loss function for rejection. Essentially, the learning to DEFER loss function can be used to learn a general $g \\colon \\mathbb{R}^d \\rightarrow \\mathbb{R}^{K+1}$ classifier for $K$ classes with the last $K+1$ output dimension being used for rejection. This reduction / interpretation was also commented by Cao et al. (reference \[2\] of the reviewer) as their method generalizes this instantiation of DEFER. We will make sure to clarify how we are using DEFER in the next version of the paper. \[b\] Charoenphakdee, Nontawat, et al. "Classification with rejection based on cost-sensitive classification." International Conference on Machine Learning. PMLR, 2021\. > Q3: Comparing with \[2\] Apologies, this seems to be a clarity issue. The GCE baseline tested in the paper is actually \[2\] (in retrospect, this may not be as clear as we also cited the general cross-entropy loss function’s original paper). Following up on Q2 as well, this GCE baseline can be interpreted as a generalization of the surrogate loss derived from DEFER. --- Rebuttal Comment 1.1: Title: Response Comment: Thank you for your elaborated response to my review. I understand that the author's work is interesting and meaningful, but I still maintain my concerns about its validity on high-dimensional datasets (despite the addition of experiments using MedMNIST). As we are now gradually entering the era of large models, could you provide some more experiments on high-dimensional data, such as CIFAR10, regardless of the results? I hope this will help to better understand the limitations of the method. --- Reply to Comment 1.1.1: Comment: We thank the reviewer for their additional comment. We are happy to include results on CIFAR10. In the following, we have mirrored the setting of the additional MedMNIST / OrganSMNIST experiments presented in our global response. Of these settings, we note that this uses a Resnet18 base model for the classifier and baselines; and that the specific hyperparameter grid for $c$ is reduced to ensure that the experiments completed in time for the discussion deadline. Random cropping and horizontal flipping data augmentation are utilized in training for all approaches. We present an additional 85% coverage table as the coarseness of the $c$ grid provided better comparison for some of the baselines. ### CIFAR-10 (80% Coverage) \| \| Model Name \| Hyperparameter \| Accuracy \| Coverage \| \|---:\|:----------------------\|:-----------------\|:---------------\|:----------------\| \| 0 \| Base Clf \| - \| 90.095 (0.244) \| 100.000 (0.000) \| \| 1 \| $\rm KL-Rej$ \| 0.74 \| 97.285 (0.222) \| 80.165 (0.428) \| \| 2 \| $(\alpha=3)\rm{-Rej}$ \| 0.74 \| 97.236 (0.212) \| 80.433 (0.350) \| \| 3 \| $\rm PredRej$ \| 0.1 \| 90.271 (0.415) \| 94.792 (6.079) \| \| 4 \| $\rm CSS$ \| 0.15 \| 95.610 (0.274) \| 84.077 (0.616) \| \| 5 \| $\rm DEFER$ \| 0.2 \| 93.639 (0.964) \| 82.530 (3.919) \| \| 6 \| $\rm GCE$ \| 0.25 \| 93.807 (0.738) \| 82.710 (1.115) \| ### CIFAR-10 (85% Coverage) \| \| Model Name \| Hyperparameter \| Accuracy \| Coverage \| \|---:\|:----------------------\|:-----------------\|:---------------\|:----------------\| \| 0 \| Base Clf \| - \| 90.095 (0.244) \| 100.000 (0.000) \| \| 1 \| $\rm KL-Rej$ \| 0.62 \| 95.966 (0.283) \| 85.313 (0.490) \| \| 2 \| $(\alpha=3)\rm{-Rej}$ \| 0.58 \| 96.059 (0.305) \| 85.077 (0.469) \| \| 3 \| $\rm PredRej$ \| 0.1 \| 90.271 (0.415) \| 94.792 (6.079) \| \| 4 \| $\rm CSS$ \| 0.2 \| 94.339 (0.158) \| 87.783 (0.251) \| \| 5 \| $\rm DEFER$ \| 0.25 \| 93.423 (0.698) \| 87.837 (1.206) \| \| 6 \| $\rm GCE$ \| 0.3 \| 93.295 (0.781) \| 85.720 (0.682) \| ### CIFAR-10 (90% Coverage) \| \| Model Name \| Hyperparameter \| Accuracy \| Coverage \| \|---:\|:----------------------\|:-----------------\|:---------------\|:----------------\| \| 0 \| Base Clf \| - \| 90.095 (0.244) \| 100.000 (0.000) \| \| 1 \| $\rm KL-Rej$ \| 0.52 \| 94.314 (0.240) \| 90.070 (0.445) \| \| 2 \| $(\alpha=3)\rm{-Rej}$ \| 0.38 \| 94.179 (0.264) \| 90.420 (0.406) \| \| 3 \| $\rm PredRej$ \| 0.1 \| 90.271 (0.415) \| 94.792 (6.079) \| \| 4 \| $\rm CSS$ \| 0.25 \| 93.134 (0.641) \| 90.025 (0.705) \| \| 5 \| $\rm DEFER$ \| 0.3 \| 93.656 (0.393) \| 88.352 (2.164) \| \| 6 \| $\rm GCE$ \| 0.3 \| 93.295 (0.781) \| 85.720 (0.682) \| ### Discussion We make a few comments on the reported results. - For this higher dimensional dataset, the same patterns emerge when comparing to MedMNIST and the paper’s original datasets in the noiseless case. Our approach can perform better than the baselines. - An additional observation on the best $c$ taken for the baseline approaches: the optimal cost of rejection per coverage target depends greatly on the approach with no consistency across all baselines. This demonstrates that tuning of $c$ can be difficult in practice (especially as each $c$ requires an entire model to be trained). - The increase in dimension from OrganSMNIST/MNIST (1x28x28) to CIFAR-10 (3x32x32) does not seem significant enough to cause any practical issues. Additional to these direct comments, we would also like to make some other notes. Although the general framework we propose requires the learning of density ratios to determine the rejector, the closed-form solutions and practical trick (Line 271\) that we utilize does not require explicit learning of a density ratio. Instead, transforming a base model’s calibrated output is exploited (with only the normalization constant $b$ or $Z$ requiring approximation). As such, issues of high dimensional data for the current implementation would mainly be linked to difficulties in calibration in high dimension (which is a valid concern). Nevertheless, we hope these additional results address the reviewer’s concerns for at least this CV dataset. We will of course make a note of this limitation and the corresponding discussion in the next revision. This would be particularly useful in future work where different divergences or modifications do require an explicit distribution or density-ratio to be learned.	Summary: This paper proposes a novel method for classification with rejection based on density ratio estimation. Density ratio is estimated between the data distribution P and the "idealized" distribution Q, where Q is a distribution such that the model can have good prediction performance, while this distribution is still similar to the original data distribution P. The objective function is proposed to formulated as a risk minimization with a $\phi$-divergence regularization. Theoretical analysis is also provided to justify the soundness of the proposed method. The experiment shows that the proposed method is effective compared with well-known existing approaches. Strengths: 1. Proposed method is theoretically guaranteed and can support multiclass classification case. To me, it is not that straightforward to use density ratio estimation approach for multiclass classification with rejection and I appreciate this strength of the paper. 2. The proposed method and formulation discussed in the paper is quite general, and the discussion for Regression case also provided in appendix, suggesting the generality of the proposed method. Divergence that studies in this paper is not only KL-divergence, but different divergences were also studied. Weaknesses: 1. Unfortunately, I found the experiment section writing and result is not quite well-written compared with other sections. Perhaps there is a better way to analyse and understand practical behavior of the proposed method. - The figure shows in the paper does not really show the superiority of the method except in HAR (clean) and Gas Drift (clean). It is also quite hard to see since the starting point of each method is different. Perhaps table representation or different way to show the result might help. - Only three simple datasets were used in this paper and the discussion using these datasets still look difficult to conclude something as several methods are competitive. - In my understanding, KL and $\alpha$ divergence give almost exactly the same performance in all cases. Is this really the case? The study of hyperparameter sensitivity can also be beneficial to practitioners - Analysis of what kind of dataset characteristic makes the proposed distributional method more effective than the traditional method would be very useful. I feel existing methods such as CSS or the classifier-rejector approach might feel more like a direct approach to solving classification with rejection. Nevertheless, it is great to explore other approaches. - As a result, I believe revising the experiment section can significantly improve the paper. 2. I found the writing and organization of this paper can be significantly improved. It takes until page 4 to state the proposed method, leaving only a small space for the experiment section. Perhaps some discussion of theory for $\alpha-divergence and background of (DVI, DRO) can be wrapped up more compactly and defer to the appendix to make the paper more self-contained and provide sufficient discussion on experiments. - For reading experience, it might also be useful to highlight the final objective function (or use a latex Algorithm environment) to outline what exactly we need to do to use the proposed method so that practitioners can quickly understand how the method works. I found section 4 is quite difficult to follow. In this form, we have to go through the whole paper and mix all the ingredients to get an idea how to implement the proposed method (e.g., Normalization, how to get a(x), inverse function of $\varphi$. Technical Quality: 3 Clarity: 2 Questions for Authors: 1. Is there any superiority of $\alpha=3$ divergence over KL-divergence? I might have missed it. 2. Is it written in the main body of the paper what $\varphi'$ is (Eq. 11)? I believe it is a derivative of $\varphi$ over X? I am sorry if I missed it. If it is not written it should be so because for example, "'" can mean different things like how L' is used in this paper. 3. It seems the proposed method is quite weak under noisy data. Is there any possible explanation why this is the case? 4. The Theorem 4.2 (informal) states that there exists a threshold to achieve Chow's rule if original $h$ is correct looks quite restrictive to me in the sense that if h is really optimal, then we can just use h to achieve Chow's rule and there is no need to consider density ratio estimation. Can we say anything when h is not optimal? Minor comment: I think it is more common to call "classification-rejection" approach, a classifier-rejector approach (like Ni et al., 2019 [44]), or predictor-rejector approach (Mao et al., 2024) [39]. Confidence: 3 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: Limitations about the need to estimate P(Y\|X) with model h were discussed, suggesting that this approach requires estimating class-posterior probability. (Minor) broader impacts were discussed in Appendix L and perhaps it is better to put them in the main body if possible. Overall, I found the discussion about limitations is appropriate. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for their detailed reading and many suggestions for improving the readability of the paper. We will change “classification-rejection” to “classifier-rejector” as per the reviewer’s suggestion and space-permitting, will include the broader impact section in the main-body (or add a compact part of it in the conclusion). Please find other rebuttal points below. > Perhaps table representation or different way to show the result might help. \[...\] Only three simple datasets were used in this paper Thank you for the suggestion. We will add tables corresponding to different coverage targets to the paper. Please see the shared section to see a demonstration on an additional dataset added in the rebuttal period. We hope that the added dataset from the MedMNIST collection also alleviates the concern that the datasets we consider are only simple. > KL and $\\alpha$ divergence give almost exactly the same performance in all cases \[...\] \+ Q1 We would first like to note that we do include a hyperparameter sensitivity plot in Figure VII of the appendix. This tests different $\\alpha$s greater than 1\. In terms of ranges of $(\\alpha \\geq 1)$-divergences, the change in performance-to-coverage is minor. This can also be further seen in the table provided in the shared response section (which more clearly shows that although the results are not identical, they are not significantly different). One difference we did find was that the coverage curve “shortens” for $\\tau \\in \[0, 1\]$. Although $\\tau$ can be increased in practice, the cut-off in coverage for $\\tau \= 0$ shortens. > Analysis of what kind of dataset characteristic makes the proposed distributional method more effective \[...\] \+ Q4: Weakness under noise We believe that the dataset characteristic and your question about weakness under noise are linked. In general, in the noiseless case, there doesn’t seem to be a specific characteristic between what makes our proposed distributional rejection more effective. In general, it seems that the distributional rejection is slightly better in this clean case (results in tabular format, see general response). However, it becomes clear that from the drop in performance in the noisy dataset setting, that distributional rejection using $(\\alpha \\geq 1)$-divergences with our current proposed implementation is not as robust to noise as other methods. This makes sense as the current approach relies on the calibration of models, which would break under distribution shift. A note here is that future work examining divergences used in robustness may help alleviate this issue. > \[...\] writing and organization of this paper can be significantly improved. We thank the reviewer for their suggestions on improving the writing and organization of the paper. The following summarizes the small changes regarding this topic that will be made: - Additional space provided by the camera ready will be utilized for further experimental discussion (including some of the above discussed points in this rebuttal section) and a table summarizing experiments. A related work (sub)section dedicated for rejection will be added as suggested by Reviewer dzAS (possibly deferred to the appendix). The content for DRO and GVI will be reduced if needed. - To shortcut the theoretical parts of the paper, we will add an pseudo-code block next to Figure 1 which summarizes the abstract algorithm of distributional rejection. In addition, we will reference specific equations used to define the ratio $\\rho$. Additional text referencing this will also be added in the intro and start of Sec 3\. - Frame / highlight environments will also be used on equations referenced in the pseudo-code, as suggested by the reviewer. - We believe that the current structure of the Sec 2-4 works well from a theoretical analysis point of view. And the proposed changes above will shortcut and identify key components for implementation. We are confident that with the \+1 page, adding additional discussion, tables, and cosmetic highlights can be complete to improve the paper’s presentation. > Q2: Clarity on $\\phi'$ and $L'$ We would like to confirm that $\\phi'$ is the derivative. Actually, the $L'$ notation also can be interpreted as a functional derivative of $L$ on $Q(x)$. We will mention this notational choice to clarify why notation is set this way. Do feel free to comment if this still makes the notation of $L’$ confusing. We are open to changing this to another symbol if required, eg, via font $\\mathrm{L}$ or with a bar $\\bar{L}$. > Q4: Theorem 4.2 We agree with the reviewers comment that the theorem is restrictive. Its purpose is just to verify that the proposed distributional rejection method produces Chow’s rule under theoretically optimal conditions. When the optimal classifier is not optimal, the optimal rejection becomes a thresholding function over the pointwise risk of the model (in the language of CPE classification, see reference \[48, 49\]). --- Rebuttal Comment 1.1: Title: Thank you for your feedback Comment: Thank you for the author's rebuttal. I also have read other reviews. Given the fact that the organization will be modified as mentioned in the rebuttal and additional experiments provided, I would like to raise the score to 6 (Weak accept). I am aware of the concern of the high-dimensionality problem suggested by other reviewers. I believe the approach taken by this paper is innovative and it is also interesting to design other algorithms that follow this principle of identifying idealized distribution to use it as a criterion for rejection, which could be preferable to the current method in the high dimensionality regime. --- Reply to Comment 1.1.1: Comment: We thank the reviewer for raising their score. We are also interested in seeing new algorithms which exploit our proposed perspective of rejection. On the topic of high-dimensional data, the reviewer may be interested in the CIFAR-10 setting proposed by Reviewer MrTu. We have presented experimental results mirroring those provided for MedMNIST / OrganSMNIST and have reached similar conclusions to those expressed in the original global discussion.	Summary: This paper propose a new classification algorithm with abstention by learning a density ratio between an "idealized" distribution to the data distribution: if the density ratio is small, the classifier rejects to predict. The proposed learning framework is general, and is a function of the choice of $f$-divergence. The paper studies two concrete choices of divergences: KL- and $\a$-divergences, which admit a closed form rejector. The paper provides some experimental supports for the proposed ideas with neural-net classifiers. Strengths: The paper studies an important problem of classification with abstention. The proposed mathematical framework is quite neat and has nice connections with GVI and DRO. The math is quite crisp throughout the paper. Weaknesses: While the proposed method sounds reasonable, I have some concerns/questions in the presentation. Please see questions and suggestions below. Technical Quality: 3 Clarity: 2 Questions for Authors: Questions - What is the meaning of "The maximization is adversarial over the marginal label distribution" in line 128? - I had hard time to understanding the meaning of the "idealized rejection distribution" (as called. in line 157), especially because the following sentence was extremely confusing: ``` Given Definition 3.1 for idealized distribution, small values of $\rho(x)$ corresponds to regions of the input space $\mathcal{X}$ where having lower data probability would decrease the expected risk of the model. ``` I can't follow this sentence. Can you please elaborate this? - Further, I can't understand why does it make sense not to reject where $P(x)$ is relatively small? If the likelihood of occurrence is small, shouldn't we also avoid prediction at that point as the classification will be likely wrong? Or is the argument that we do not need to care the small probability mass in the first place as it won't incur a significant loss in expectation? - In the experiments, the proposed algorithms seem to perform well in the high-coverage regime, while dominated by existing methods in the low-coverage regime. Do you have any explanation on this? Suggestions - Compared to the quality of math, there are way too many typos and grammatical errors. To spot a very few: - line 23: "While" some approaches avoid... - line 25: ... approach aims... - line 74: ... an additional... There are too many of these throughout, so please revise them carefully. - Please consider moving lines 84-85 after line 76. - Please put subsections in Section 4 for readability. Confidence: 3 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: Limitations of the framework are noted by the authors. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for their praise of the mathematical presentation of the paper and their careful reading. We are happy to change the paper as per the reviewer's suggestions and will ensure that the typos and grammar improves. In what follows, we will answer Reviewer m8bi additional questions. > What is the meaning of "The maximization is adversarial over the marginal label distribution" in line 128? This line was to clarify that in DRO for label noise (specifically reference \[60\]), typically the distribution which is “adversarial” only applies to the marginal label distribution and not the full joint distribution over both inputs and labels. Thus the set of adversarial joint distributions $Q(y) P(x \| y)$ are generated by varying the marginal over labels $Q(y)$ whilst keeping the conditional equal to the data $P(x \| y)$. > I had hard time to understanding the meaning of the "idealized rejection distribution" (as called. in line 157\) The best intuitive way of thinking of the idealized distribution definition is to remove the regularization term in Definition 3.1. This corresponds to the distribution which minimizes the current model’s loss. Hence its “ideal” for the current model / set of parameters. > especially because the following sentence \[…\] For the follow up sentence, we further elaborate. When $\\rho(x)$ is small, this implies that $Q(x) \\ll P(x) \\leq 1$. (Recalling that $Q$ is the idealized distribution and $P$ is the data distribution.) Further note that from Definition 3.1 / Equation (8), $Q(x)$ being small implies that the loss $L’(x)$ cannot be too large (as otherwise we should reallocate mass from other x’s). Hence wrt the data distribution $P(x)$, moving mass away for regions of $x$ where $\\rho(x)$ is small reduces the loss function. > Further, I can't understand why does it make sense not to reject where is relatively small? \[...\] Or is the argument that we do not need to care the small probability mass in the first place as it won't incur a significant loss in expectation? The reviewers comment about the values corresponding to loss probability mass and thus no significant loss penalty in expectation is correct. Our rejection approach focuses on losses at different inputs values, as per Definition 3.1. Of course, this is from the perspective of our framework, so practically, various rejection rules may be needed to account for different types of uncertainty. A future direction may be to consider alternatives to expected loss which account for low $P(x)$. For example CVaR etc. An alternative theoretical reason for this style of thresholding choice is Theorem 4.2 in the paper. With our specific choice of thresholding / rejection on the ratio $\\rho(x) \= Q(x) / P(x)$, we recover Chow’s rule. The alternative of rejecting based on $P(x)$ would not yield this equivalence. > In the experiments, the proposed algorithms seem to perform well in the high-coverage regime, while dominated by existing methods in the low-coverage regime. Do you have any explanation on this? Good question. Firstly, we note that the trade-off curves can be extended further by increasing $\\tau > 1$. We suspect the difference in performance to be related to the quality of calibration. If the model was perfectly calibrated, then the density approach would be optimally rejecting. As such, deviation / suboptimality would be due to calibration error. This explanation is partially supported by the drop in performance of our approach on noisy variants of the dataset. Here the training set (and data used for calibration) is not representative of the test set which would result in a model miss-calibrated on the test set. For two additional notes: We also point the reviewer to the results of the MedMNIST dataset \-- additionally added in the rebuttal \-- in the shared response section. Here we find that for the lower 80% regime, our approach can perform better than the baselines for a more complicated dataset. A reason why the baselines do not provide / perform well in the extremely high-coverage regime (\~ 95%) is that it is difficult to tune the rejection costs $c$ hyperparameter to allow for fine tuning of the coverage. As the rejection decision of these baseline involve training a whole other model, the cost of tuning requires training several NNs. --- Rebuttal Comment 1.1: Comment: I appreciate the authors' rebuttal. Please carefully incorporate the answers in the revision. I believe that it is important to elaborate the reasoning behind using the idealized distribution. I will keep the score as is. --- Reply to Comment 1.1.1: Comment: We thank the reviewer for their response. We will ensure we incorporate the provided feedback and response into the next revision.	Rebuttal 1: Rebuttal: We thank the reviewers for their thoughtful comments and various suggestions. We are grateful to the reviewers for recognizing the novelty of our work, providing a “\[...\] more interesting approach to rejection compared to previous papers” (Reviewer MrTu). We appreciate the comments that our work has “\[...\] clear contributions advancing the state of the art in abstaining classifiers.” (Reviewer dzAs) including “\[...\] support multiclass classification case \[... which\] is not that straightforward \[...\] (Reviewer MiAk); and the recognition that our approach is “\[...\] quite neat and has nice connections with GVI and DRO \[... and the\] math is quite crisp throughout the paper.” (Reviewer m8bi). Please find the per point rebuttal below. In this shared section, we additionally provide results using the MedMNIST dataset collection and provide some samples for presenting the performance of the results via tables. ## Additional datasets (MedMNIST) & Tables Reviewer MiAk, MrTu and dzAs mentioned that a potential weakness of the current paper is the simplicity of the currently tested datasets. Noise was utilized to add complexity to the dataset settings and to provide cases where the base classifier does not reach a high (near 100%) accuracy. To supplement the experiments on these datasets and their noisy label noise variants, in the rebuttal we provide some additional experimental results on the MedMNIST dataset collection recommended by Reviewer dzAs. Additionally, Reviewer MiAk mentioned that presenting results in tabular format might enhance the readability of the experimental results settings. In this rebuttal section, we present accuracy tables for the MedMNIST dataset results, where we select hyperparameters (and their coverage) which are closest to a specific coverage goal. In particular, we will look at 90% coverage (high coverage) and 80% coverage (lower coverage) regimes. We have also included preliminary tables in the attached PDF for Figure 2 of the paper, where the coverage target is 80%. In the following, we present results for the OrganSMNIST dataset from the MedMNIST dataset collection. This is a 2D 28x28 classification task over grayscale images and 11 classes. We note that for this dataset, the base classifier (which we use a ResNet18 following the MedMNIST paper \[a\]) is not close to 95-100%. The general setup is identical to that in the paper (5-fold cross validation \+ grid search over hyperparameters of either $\\tau$ or $c$). The only difference is that there is a slightly reduced hyperparameter search of $c$ for ranges between 0.01 and 0.3 (rather than 0.01 to 0.5; DEFER had some additional hyperparameters tested) to complete these preliminary experiments on time for the rebuttal. The result tables are given as follows: ### OrganSMNIST (80% Coverage Target) \| \| Model Name \| Hyperparameter \| Accuracy \| Coverage \| \|---:\|:----------------------\|:-----------------\|:---------------\|:----------------\| \| 0 \| Base Clf \| - \| 90.119 (0.867) \| 100.000 (0.000) \| \| 1 \| $\rm KL-Rej$ \| 0.64 \| 97.548 (0.359) \| 80.512 (0.910) \| \| 2 \| $(\alpha=3)\rm{-Rej}$ \| 0.6 \| 97.660 (0.400) \| 80.144 (0.795) \| \| 3 \| $\rm PredRej$ \| 0.2 \| 89.938 (4.094) \| 81.662 (13.320) \| \| 4 \| $\rm CSS$ \| 0.08 \| 96.566 (0.854) \| 81.306 (1.255) \| \| 5 \| $\rm DEFER$ \| 0.14 \| 94.068 (0.677) \| 80.743 (3.946) \| \| 6 \| $\rm GCE$ \| 0.1 \| 93.973 (0.850) \| 80.068 (2.677) \| ### OrganSMNIST (90% Coverage Target) \| \| Model Name \| Hyperparameter \| Accuracy \| Coverage \| \|---:\|:----------------------\|:-----------------\|:---------------\|:----------------\| \| 0 \| Base Clf \| - \| 90.119 (0.867) \| 100.000 (0.000) \| \| 1 \| $\rm KL-Rej$ \| 0.54 \| 93.757 (0.308) \| 90.000 (1.241) \| \| 2 \| $(\alpha=3)\rm{-Rej}$ \| 0.4 \| 93.565 (0.327) \| 90.639 (1.088) \| \| 3 \| $\rm PredRej$ \| 0.22 \| 91.556 (1.603) \| 90.298 (6.066) \| \| 4 \| $\rm CSS$ \| 0.19 \| 92.437 (0.313) \| 90.361 (1.619) \| \| 5 \| $\rm DEFER$ \| 0.41 \| 91.557 (0.907) \| 91.916 (1.496) \| \| 6 \| $\rm GCE$ \| 0.25 \| 92.203 (0.346) \| 90.714 (1.429) \| ### Discussion From these results, interestingly our density-ratio rejectors are actually superior over these datasets. Thus, our method has practical relevance to datasets beyond those previously tested. Some other observations include: - There are minor differences between KL and $\\chi^2$ / $\\alpha \= 3$. However, the differences are not significant. - Performance of the density-ratio rejectors are not tied to near perfect accuracy of the base classifier. - Our method can perform better at high and lower coverage target regimes. We will add the new experimental result in the next version of the paper alongside other 2D datasets in the MedMNIST collection. \[a\] Yang, Jiancheng, et al. "Medmnist v2-a large-scale lightweight benchmark for 2d and 3d biomedical image classification." Scientific Data 10.1 (2023): 41\. Pdf: /pdf/cb9dad207ee712d6797f58df391e15e6f1cb74d5.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
D-CPT Law: Domain-specific Continual Pre-Training Scaling Law for Large Language Models	Accept (poster)	Summary: This work proposes a domain-specific scaling law to optimize mixture ratio between the general domain training corpus and the specific domain corpus. The authors considered several parameterizations and experimented on six different downstream domains such as code, math, and Medical. The result show that D-CPT Law has a high fitting accuracy across various model sizes, dataset sizes, and mixture ratios. Furthermore, the proposed cross-domain D-CPT Law reduced training costs while maintaining high performance in predicting domain-specific continual pre-training results. Strengths: 1. The paper proposes a domain-specific scaling that can more efficiently determine thec optimal mixture ratio between general and domain-specific corpora. The experiments demonstrate its effectiveness. 2. The paper presents three applications of D-CPT Law that may be of interest and benefit to the community. Weaknesses: 1. The models are limited to the Qwen series, which are relatively small in size. This makes it unclear whether similar results would be observed with larger models. Technical Quality: 2 Clarity: 3 Questions for Authors: 1. The author stated, "we test the validation loss every 1,000 steps and the total training steps are 20k." How did you determine the step parameters, such as 1,000 and 20,000? 2. You defined five parameterizations and demonstrated that L3 is the best through experiments. Could there be other parameterizations better than L3? In other words, is it possible to theoretically prove that L3 is the optimal D-CPT Law? Confidence: 3 Soundness: 2 Presentation: 3 Contribution: 3 Limitations: The authors state several limitations and will consider addressing them in their future work. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you very much for your valuable comments. I appreciate the time and effort you have put into reviewing our manuscript. Below, I will address your concerns and provide further clarifications. Weakness We acknowledge that the current status of our works is limited to the Qwen series (as we have also mentioned in the limitations) and the size of our model is relatively small (0.5 B to 4 B parameters). However, I will explain why we chose the Qwen series and the reasons behind the model size from the following points: 1. The Choice of the Qwen Series: Our work focuses on domain-specific continual pretraining(D-CPT), thus we need open-source base LLMs with strong foundational capabilities. Additionally, as we aim to explore performance across different model sizes, it is necessary that the model series have multiple model sizes. To meet these requirements, we choose the Qwen-1.5 series as this series provides multiple model versions (0.5B,1.8B,4B,7B,14B,32B,72B,110B). In contrast, LLaMA2/3 only has 3 available model sizes (7B,13B,70B), and the training costs on these models are large. While Pythia also offers a variety of model sizes, its overall model performance is relatively poor, making it unsuitable for D-CPT in practical scenarios. 2. Relevantly Large Model Size: Regarding the comparatively smaller model sizes mentioned, we believe our model sizes and dataset sizes are already quite large (model sizes: 0.5B,1.8B,4B, and dataset sizes: 0.1B-26B), especially when compared to 2 related works about data mixture (Data Mixing Law(https://arxiv.org/pdf/2403.16952): model sizes: fit on 70M, 160M and validate on 1B, dataset sizes: 30B; Regmix(https://arxiv.org/pdf/2407.01492): model sizes: fit on 1M and validate on 1B, dataset sizes: 1B). Additionally, we have also conducted experiments on 7B model to demonstrate that similar results will be observed with larger models (see Section 4.2, line 183-line 189). Besides, our primary focus is on the data mixture, and increasing the model size would result in a huge rise in experimental costs. Therefore, we choose these model sizes as the training and evaluation computation costs are relatively acceptable. Lastly, the recent work Observational Scaling Law (https://arxiv.org/pdf/2405.10938) has explored the Scaling Law across different models, they stated that "model families only vary in their efficiency in converting training compute to capabilities." We agree with their perspective and we think the overall experimental patterns and findings observed in the Qwen series can also be extended to other model families. Q1 In the Introduction section (line 50), we mention "dataset sizes from 0.1B to 26B tokens". However, there is a typo in Section 4.1 (line 159) on the training setup: "20k" should be "200k." Thank you for your question, which helped me discover this typo. Then, I would like to explain the conversion between the training step (t) and dataset size (D). The global batch size is 64, and the length of single data is 2048. The unit of dataset size is B, so the relationship between them is: $$D=t\cdot64\cdot2048\cdot10^{-9}$$ The total training step is 200k, which corresponds to a dataset size of 26.21 B, while 1,000 training steps correspond to a dataset size of 0.131 B. For the validation step count of 1000, we analyzed the fitting efficiency of different data sampling methods in Appendix I (line 621- line 643), which includes results for the validation step count of 5000. We conduct supplementary experiments with different validation steps on general-corpus validation loss. The fitting results (validation data points under different settings all correspond to the data points of the 1000 validation steps) are as follows: \|Validation Step\|Huber loss\|$R^2$\| \|-\|-\|-\| \|1000\|0.0041\|0.9977\| \|2000\|0.0043\|0.9970\| \|3000\|0.0045\|0.9968\| \|4000\|0.0042\|0.9973\| \|5000\|0.0042\|0.9976\| \|10000\|0.0053\|0.9953\| We observe that the results are quite similar across different validation steps, indicating that the final findings of D-CPT Law remain consistent regardless of the chosen validation step. Moreover, selecting 1000 as the validation step ensures a sufficient number of data points. The total training steps are set to 200k based on 3 main considerations: 1. Our experimental setup assumes that all data is not repeated (each data is trained only once). While the general-corpus Dolma is sufficient, the domain-corpus might be insufficient. We have 6 domains, the total training steps must be less than the amount of domain-corpus. Setting the total training steps to 200k ensures no repetition of domain-corpus. 2. Our total experimental cost is 5.3071 e+10 TFLOPs (compared to 9.864 e+10 TFLOPs for the Data-Constrained Scaling Law(https://arxiv.org/pdf/2305.16264)). Given the already high cost, increasing the total training steps would largely increase the experimental cost. Therefore, we chose 200k steps to maintain a reasonable experimental cost. 3. We observed that the validation loss stabilizes around 100k-150k, so increasing the validation steps further will not lead to significant changes in the validation loss. Here, I will provide some actual data to support this point. In the music domain, for a 1.8B model, using a 1:1 data ratio, the following table shows the general-corpus validation loss and domain-corpus validation loss at different training steps. \|Training Steps\|General-corpus validation loss\| Domain-corpus validation loss\| \|-\|-\|-\| \|10000\|2.8191\|0.8005\| \|50000\|2.7674\|0.7526\| \|60000\|2.7612\|0.7462\| \|70000\|2.7556\|0.7460\| \|80000\|2.7505\|0.7447\| \|90000\|2.7471\|0.7501\| \|100000\|2.7432\|0.7398\| \|120000\|2.7367\|0.7338\| \|140000\|2.7312\|0.7350\| \|160000\|2.7253\|0.7301\| \|180000\|2.7206\|0.7298\| \|200000\|2.7159\|0.7270\| We can observe that the changes in the model after 100k are not as significant as those before 100k and the loss is relatively stable when the training step is close to 200k. Q2 Please see G.Q1 in Author Rebuttal. --- Rebuttal Comment 1.1: Title: Looking forward to Feedback as Discussion Deadline Approaches Comment: Hi, we sincerely thank you very much for these constructive comments and evaluation of our manuscript. As the discussion phase will be closed on Aug 13 11:59 pm AoE, we would like to kindly ask you to take a look at our responses and reevaluate our work based on our clarifications. Please let us know whether our response addresses your concerns or whether there is any further detail we can provide to help address these concerns. Thank you again for dedicating your time to reviewing our paper. --- Rebuttal Comment 1.2: Comment: Thank you for your responses. After reviewing the rebuttal, I will maintain the previous score.	Summary: This work explore the data mixture scaling law ( D-CPT Law) between the general corpus and the downstream domain-corpus for the continual pre-training of large language model.They also extend the fitted standard D-CPT Law on cross-domain settings and propose the Cross-Domain D-CPT Law to predict the D-CPT law of target domains. D-CPT Law could be applied on three important scenarios: optimal mixture on the trade-off between general and domain-specific abilities, optimal mixture for limited domain-specific data, and resource allocation setting, which is useful in practice. Strengths: 1.This work experimented and analyzed on three scenarios including optimal mixture on the trade-off between general and domain-specific abilities, optimal mixture for limited domain-specific data, and resource allocation setting, which is useful in practice 2. D-CPT Law considered both the in-domain setting and the cross-domain setting with a new involved parameter K, which provide a reference for the unseen domain data mixing. 3. The analysis on the selected fitting function is comprehensive and make sense. Weaknesses: This work focus on the data mixing scaling law for the continue pre-training phase of LLM. However, I think this work didn’t specifically have any design for the continue pre-training. The setting for the final scaling Function (Equation 6) have not mentioned any specific for continue pre-training. As the author mentioned , Equation 6 is supposed to transform into the Chinchilla Scaling Law (which is for a LLM training from scratch) when r is fixed. Technical Quality: 3 Clarity: 3 Questions for Authors: 1.Could you explain why this scaling law function is for continue pre-training? 2.In Equation 7, the newly involved parameter K, why is also in a similar power law pattern? The domain-specific learnable coefficient might be a much different dimension with the total number of model parameters and training data. 3.How many combination did you choose for the experiments? There are many between the data sizes from 0.1B to 26B. The way the portfolio is chosen has an impact on the on the average results. Confidence: 5 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: As the authors have stated comprehensive in the limitation Section, I have no further comments for this part. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thanks for your careful reading and constructive suggestions. We will address your concerns shown below in detail. Weakness From the view of validation loss, continual pre-training (CPT) and pre-training (PT) are consistent, with the main difference being the initial validation loss (CPT: <5, PT: >10). This difference is represented by the bias term E in the D-CPT Law, and the fitted E values will differ between CPT and PT. In addition, the scenario of our work is Domain-specific Continual Pre-Training (D-CPT). In this setting, we usually need to collect high-quality domain-corpus to enhance the downstream performance and general-corpus to mitigate catastrophic forgetting of the general abilities. There, the mixture ratio (i.e., r) between domain-corpus and general-corpus plays an important role in the D-CPT setting, which is also the key distinction from the Chinchilla Scaling Law. Besides, though r is also introduced in PT, it's typically multidimensional (e.g., different data sources in CommonCrawl). In the D-CPT setting, r is two-dimensional. Moreover, we think that the consistency between the scaling laws in CPT and PT offers several benefits. First, it enables a seamless connection between PT and CPT. Specifically, by using a step function or other methods, we can jointly represent the scaling laws of both phases in a uniform parameterization. Second, when r is fixed and the D-CPT Law becomes equivalent to the Chinchilla Scaling Law, it ensures that the D-CPT Law can address resource allocation issues (line 235-line 237). Therefore, we designed such D-CPT Law. In the future, we will continue to investigate how to unify the Scaling Law for both PT and CPT. Q1 The Scaling Law is derived from fitting data points obtained from real experiments. Therefore, a good parameterization for D-CPT Law must align with the trends observed in actual data, only then can the parameterization effectively fit the data. In Section 3.1 (line 89-line 117), we listed 4 requirements that a good parameterization should meet: Adaptability, Explicit Trends, Implicit Trends, and Consistency. Both Explicit Trends and Implicit Trends refer to the observable trends in actual D-CPT scenarios. The final form of the D-CPT Law (Equation 6) successfully meets these 4 requirements (detailed mathematical derivation is provided in line 521-line 564). We believe that as long as these 4 requirements are met, the parameterization is sufficiently robust. For more information, please see G.Q1 in Author Rebuttal. Q2 In Section 3.2, I mentioned K, which represents the learnability of a domain. Unlike N, D, and r, which are real variables, K is an abstract variable for which we wish to establish certain predefined properties, such as Uniformity and Monotonicity, as discussed in Section 3.2 (line 130-line 135). We incorporate this variable into the D-CPT Law using a power-law form (both in OpenAI Scaling Law(https://arxiv.org/pdf/2001.08361) and Chinchilla Scaling Law(https://arxiv.org/pdf/2203.15556), they use a power-law form to represent the scaling law). Our main objective is to first find a method to represent K (i.e., to model K), and then we focus on the form of K in the D-CPT Law, where we directly use the power-law form to ensure it meets the requirements of Uniformity and Monotonicity. Secondly, the dimensions of K differ from those of N and D. This difference is not only reflected in their value ranges (N: 0.5 to 4, while K: 0.5 to 1) but also in the fitting parameters of their respective power-law forms. For instance, the fitting parameters for N, denoted as A=4.18 and $\alpha$=1.61. In contrast, the fitting parameters for K, denoted as F=0.35 and $\mu$=0.55. Finally, we added a comparison of the fitting results with different K forms. I supplemented 2 parameterizations: $$L_2=E+\frac{A}{N^\alpha}+\frac{Br^\eta}{D^\beta}+\frac{C}{r'^\gamma}+\frac{F}{\mu^K}$$ $$L_3=E+\frac{A}{N^\alpha}+\frac{Br^\eta}{D^\beta}+\frac{C}{r'^\gamma}+\frac{F}{(-\log K)^\mu}$$ The fitting results for L1(original form), L2, and L3 on general-corpus are as follows: \|Paramterization\|Huber loss\|$R^2$\| \|-\|-\|-\| \|L1\|0.0214\|0.9886\| \|L2\|0.0256\|0.9781\| \|L3\|0.0296\|0.9847\| It can be observed that the fitting results for different parameterizations do not show significant differences, so we believe it is more important to model the representation form of K. Additionally, modeling K with the loss (equation 9) is very intuitive: $$K=\frac{w_1}{k_1}+w_2\times k_2,$$ where k1 represents the initial loss of the model. A higher value indicates the model's weaker ability in this domain, making it harder to learn, so it is inversely proportional. k2 represents the rate of decline in the loss for this domain. A higher value indicates better mastery of this domain, so it is directly proportional. We use the loss for modeling K because loss is a very direct assessment of model performance (also used in Compression(https://arxiv.org/pdf/2404.09937) to represent compression). Q3 In the main experiment (Section 4.2), there are 6 domains, 3 model sizes, 200 dataset sizes, and 9 data mixtures. - Effectiveness:For the Effectiveness experiment, we fit and evaluate using all the data points. - Model Size Generalizability: we use 3-fold cross-validation. We randomly select 2 model sizes for fitting and then use the fitted D-CPT Law to predict the remaining model size. This yields 3 cross-validation experiments, and we take the average result. - Dataset Size Generalizability: we divide the 200 dataset size data points into 3 groups (1-67, 66-133, 133-200). Using 3-fold cross-validation, we fit two groups and validate the remaining group. This yields 3 cross-validation experiments, and we take the average result. - Mixture Ratio Generalizability: we randomly select 7 ratios for fitting and use the remaining 2 ratios for validation. With 36 combinations of selecting 7 out of 9 ratios, we take the average. --- Rebuttal 2: Comment: I thoroughly looked at the author's response, and the score remained unchanged. --- Rebuttal Comment 2.1: Comment: Thanks for your feedback. We will carefully address your concerns in our new version.	Summary: For continual pretraining of domain-specific large language models, an important question is how to choose the optimal mixture ratio between the general corpus and the downstream domain corpus. This paper proposes to fit the scaling law for domain-specific continual pre-training (D-CPT Law), using small-scale training costs to predict the general and downstream performance of arbitrary model sizes, data sizes, and data mixture ratios. They also extend it to Cross-Domain D-CPT Law to reduce training costs for the target domain. The paper shows empirical evidence for the effectiveness and applications of the Laws. Strengths: - Discovered that model performance can be predicted given the data mixture ratio between general and domain-specific corpus and a few other factors in domain-specific language model training. - Proposed essential requirements of the scaling law formula, compared multiple parametrization of the scaling law, and proposed a parametrization that extends the Chinchilla Scaling Law. - Extended the law to cross-domain scenarios and described its features. - Empirically verified the effectiveness, model size generalizability, and dataset size generalizability of the proposed methods. Weaknesses: - The paper lacks a comparison between applying the proposed laws and performing a grid search over hyperparameters. How much computation is saved in various applications? Technical Quality: 3 Clarity: 3 Questions for Authors: - Is it possible to fit a set of parameters in the scaling law, such that all independent variables can change their values? - How many different $(N, D, r)$ are needed to fit the parameters in the D-CPT Law formula? Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The authors addressed the limitations well in Appendix A. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you very much for your valuable comments and questions. I appreciate the time and effort you have put into reviewing our manuscript. Below, I address your concerns and provide further clarifications. Weakness First, the main motivation of our paper is to address the challenge of determining the data mixture ratio between general-corpus and domain-corpus during domain-specific continual pre-training. Specifically, we aim to predict performance for any given N, D, and r using scaling laws. To achieve this, we conduct multiple experiments to collect data points for fitting the D-CPT Law and then use the L-BFGS algorithm to fit the parameters of the D-CPT Law. Once we have fitted the D-CPT Law for a specific domain, we can use it to predict model performance for different N, D, and r settings. Therefore, our D-CPT Law can be considered as an auxiliary tool, which can be used to estimate validation loss in various scenarios and real-world usages once we obtain the D-CPT Law. In contrast, grid search typically addresses a single search problem under one setting, and the results of grid search are usually not reusable for other settings. Therefore, it would be unfair to directly compare the experimental costs of the two methods based on these aspects. However, for clarity, we will show the differences in experimental costs between using the D-CPT Law and grid search for a specific setting, as illustrated in Table 5 of the paper. Cost of D-CPT Law: We take the setting of Table 5 as an example. Specifically, the model size is 1.8 B, and the dataset size is 10B (See Line 214-Line 221). We have prepared data points for 9 different ratios, so the total compute budget required for fitting D-CPT Law is: $$1.8 * 10^9 * 10 * 10^9 * 9 * 6/10^{12}=9.7210^8\ \text{TFLOPs}$$ Cost of Grid Search: In Table 5, both the D-CPT Law and actual experimental data indicate that the optimal data ratio is 0.924. To perform a grid search on this ratio, based on binary search, we start by conducting experiments with r=0 and r=1. Then we would test r=0.5, followed by r=0.75, r=0.875, r=0.9375, r=0.90625, r=0.921875, r=0.9296875, r=0.92578125, and r=0.923828125. Assuming this meets the requirements under the settings of Table 5, a total of 11 experiments on different ratios would be needed. The total compute budget is: $$1.8 10^9 * 10 * 10^9 * 11 * 6 /10^{12}=11.88 * 10^8 \ \text{TFLOPs}$$ By comparison, it can be observed that in the single setting of Table 5, the experimental cost of grid search is still higher than that of D-CPT Law. Moreover, a significant feature of scaling laws is that the performance of small-scale experiments can be used to predict the performance of large-scale experiments. Therefore, for a 14B model, D-CPT Law can be experimented on at 1.8B, whereas grid search needs to be experimented on at 14B. This results in a tenfold difference in experimental cost for a single experiment, and the results of the grid search cannot be reused. Furthermore, if the grid search needs to evaluate 10 experimental settings, the difference would grow to 100 times (14 / 1.8 11.88 / 9.72 10 = 95.06 times). Therefore, the D-CPT Law significantly reduces the experimental cost required by grid search, and it can be reused across multiple settings. We appreciate your suggestion and will include this supplementary information in our new version to visually illustrate the cost difference between grid search and D-CPT Law. Q1 For clarity, here I first briefly introduce the D-CPT Law formulation and the fitting process as follows: $$L(N,D,r)=E+\frac{A}{N^\alpha}+\frac{B\cdot r^\eta}{D^\beta}+\frac{C}{(r+\epsilon)^\gamma},$$ where N, D, and r are independent variables and the other parameters as fitting parameters. After collecting multiple data points for (N, D, r), the L-BFGS algorithm is used to fit the D-CPT Law and obtain specific values for the fitting parameters E, A, B, C, $\epsilon$, $\gamma\$, $\alpha$, and $\beta$. Then, we can use the D-CPT Law to predict L for any given N, D, and r. For your question, I have 2 interpretations. I will explain each situation separately: 1. If you mean fitting the relationships between L and N, D, and r separately, as done in the OpenAI Scaling Law(https://arxiv.org/pdf/2001.08361), I have added the fitting formulation for L versus D and L versus r as follows: $$ L(D) = E_D + \frac{B}{D^\beta}, \quad \text{when N, r are fixed} $$ $$ L(r) = E_r + \frac{C}{r^\gamma}, \quad \text{when N,D are fixed} $$ Similarly, the fitting parameters of the above formula can be obtained using L-BFGS (for instance, we have fitted the above formula and we get B=2.2075, $E_D$=0.6175585, $\beta$=0.014580619, C=0.49847686, $E_r$=2.1966128, and $\gamma$=0.13764255). This allows us to individually explore the relationship between L and D for a given N and r, as well as the relationship between L and r for a given N and D. However, the goal of our work is to explore the relationship between L and (N, D,r) together. The relationships L(D) and L(r) are insufficient for exploring the behavior of L with respect to arbitrary values of N, D, and r. 2. If you mean fitting the relationship among L and (N, D, r) (as our paper does), each independent variable can change its values independently. However, in terms of the function's trend, D and r are interrelated (see line 106 - line 110 ). Specifically, changes in r will affect the trend of L with respect to D, and changes in D will affect the trend of L with respect to r. This can be seen from the form of Equation 5, and further explanation can be found in Appendix E.2 of the paper. Additionally, when N and D are fixed, L only depends on r; when N and r are fixed, L only depends on D; and when D and r are fixed, L only depends on N. This leads to the above situation where we fit L(D) and L(r) independently. Q2 Please see G.Q2 in Author Rebuttal. --- Rebuttal Comment 1.1: Title: Looking forward to Feedback as Discussion Deadline Approaches Comment: Hi, we sincerely thank you very much for these constructive comments and evaluation of our manuscript. As the discussion phase will be closed on Aug 13 11:59 pm AoE, we would like to kindly ask you to take a look at our responses and reevaluate our work based on our clarifications. Please let us know whether our response addresses your concerns or whether there is any further detail we can provide to help address these concerns. Thank you again for dedicating your time to reviewing our paper.	null	null	Rebuttal 1: Rebuttal: # General Response Thanks a lot for handling/reviewing our submitted manuscript. We would like to thank the reviewers for their thoughtful and constructive comments and suggestions. By addressing each of the issues raised by the reviewers, we believe that the quality and clarity of our D-CPT Law can be improved a lot. The general responses are summarized as follows: G.Q1: Could there be other parameterizations better than L3? We acknowledge that there may exist better parameterization than L3, but we believe that this is not crucial because our core objective is to find one that satisfies the 4 requirements outlined in Section 3.1 (Line 100-Line 110), and we assume that when these 4 requirements are met, the parameterization is considered a good option of D-CPT Law. Specifically, regarding the choice of parameterization for the D-CPT Law, our research goal can be understood as finding a parameterization that matches the trend of real (N, D, r) data points and possesses certain mathematical properties. These trends and mathematical properties can be explicitly expressed as the 4 requirements in Section 3.1: Adaptability, Explicit trends, Implicit trends, and Consistency. Besides, in Section 4.2, we provide 5 parameterizations, only L3 can meet all 4 requirements. Moreover, as there are also other parameterizations that can meet these 4 requirements, we provide another 2 parameterizations that satisfy these 4 requirements as follows: $$ L_6 = E + \frac{A}{N^{\alpha}} + \frac{B \cdot e^{r}}{D^\beta} + \frac{C}{r'^{\gamma}} $$ $$L_7 = E + \frac{A}{N^{\alpha}} + \frac{B \cdot r'^\eta}{D^\beta} + \frac{C}{r'^{\gamma}} $$ The fitting results for L6, L7, and L3 on general-corpus are as follows: \| Paramterization \| Huber loss \| $R^2$ \| \| ---------------- \| ---------- \| ----- \| \| $L_3$ \| 0.0048 \| 0.9968 \| \| $L_6$ \| 0.0051 \| 0.9963 \| \| $L_7$ \| 0.0049 \| 0.9969 \| The fitting results for L6, L7, and L3 on domain-corpus are as follows: \| Paramterization \| Huber loss \| $R^2$ \| \| ---------------- \| ---------- \| ----- \| \| $L_3$ \| 0.0157 \| 0.9796 \| \| $L_6$ \| 0.0164 \| 0.9778 \| \| $L_7$ \| 0.0160 \| 0.9801 \| We observe that when 4 requirements are met, the fitting results do not differ a lot. In conclusion, first, as there are many parameterizations that meet the 4 requirements, it is challenging to find the optimal parameterization. Second, the L3 mentioned in the paper is relatively simple and meets the 4 requirements with good fitting results. In the future, we will continue to investigate how to find the optimal parameterization for the D-CPT Law. G.Q2: How many different (N, D, r) are needed to fit the parameters in the D-CPT Law formula? In the main experiment, we have a total of 6 domains, 3 model sizes (0.5B, 1.8B, 4B), 9 data mixtures, and 200 validation loss data points (collected every 1k training steps for a total of 200k training steps). Hence, the main experiment consists of 6x3x9x200 = 32,400 data points. In other words, there are 5,400 data points for each domain. Additionally, in Appendix I (see line 621 - line 643), we analyzed the impact of data point sampling methods on the fitting results. We found that sampling more points when D is relatively small, and sampling fewer points when D is relatively large, can greatly reduce the experimental costs. Besides, we found that validating every 5000 steps and every 1000 steps resulted in similar fitting results. Therefore, we can actually achieve a good fitting result with only 1/5 of the original data points, which means we only need 5400/5=1080 data points to fit. Therefore, in practical scenarios, considering fitting efficiency, approximately 1000 actual data points are sufficient to reasonably fit a domain's D-CPT Law.	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
REDUCR: Robust Data Downsampling using Class Priority Reweighting	Accept (poster)	Summary: This paper proposes a data downsampling method called REDUCR which is robust to class imbalance and distribution shits. In particular, REDUCR reduces the scale of the training data while emphasizing the datapoints with the worst generalization performance. Experiments on 6 benchmarks demonstrate the effectiveness of the method. Strengths: * This paper is well-written and well-organized. * The motivation of this paper is clear. Weaknesses: * In the abstract, the authors claim that REDUCR is robust to distribution shifts. However, the experiment part does not include relevant datasets with different types of distribution shifts between the training and the test samples. * Although the technical novelty might be somewhat limited, I like the fact that the method is rather straightforward and effective. Technical Quality: 3 Clarity: 3 Questions for Authors: * Could you provide the numerical results on datasets with distribution shifts? * Could you discuss other kinds of model architectures such as ConvNeXt and Swin to verify the generalizability of REDUCR? Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: The authors claim the limitation of this work and that there are no negative societal impacts to be highlighted. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for their review, recognising the strong motivation behind our work, and that our paper is well-written. In response to the weaknesses and questions: > W1/Q1: REDUCRs Performance under Distribution Shifts In response to the reviewer’s first question, we direct the reviewer to line 272 of the Key Results Section. Here we note that the Clothing 1M dataset sees a distribution shift between the training and test set where the worst performing class is more prevalent in the test dataset. We will emphasise this in the text and include a graph to show how the number of points per class changes between the training and test set of the Clothing1M dataset in the appendix of the paper (see the rebuttal pdf). We also record the worst-class performance on the test set of all our datasets. The worst possible class distribution shift (defined in terms of groups in [1]) between the training and test set is one where the entire test set consists of only points from the worst performing class. As such one can consider the worst-class test accuracy as a lower bound on the performance under any class distribution shift. In Table 1, we show that REDUCR outperforms all the baselines on this metric. We will adjust the text to make this clearer in the manuscript by adding at the end of the Experiment setup (before Section 5.1): “Finally, it is important to note that we analyse the worst-class test accuracy which can be interpreted as a lower bound on a model’s performance under all class distribution shifts. This is because the worst possible distribution shift between the training and test set is one where the entire test set consists of only points from the worst performing class.” Whilst other types of distribution shift exist, class distribution shift is an important subset and can drastically affect the performance of algorithms - the worst-class test accuracy varies dramatically from the average test accuracy on certain datasets. Robust online batch selection to address a wider variety of types of distribution shift remains an open problem and is an interesting direction for consideration in future works. > W2: Novelty To the best of our knowledge our work is the first to propose and address the question of robust online batch selection. Whilst the use of reference models to help point selection and a weighting strategy to improve the worst class performance are both present in the literature, using those ideas to solve the problem is non-trivial and is a novel contribution of our paper. This can be seen through the class holdout loss term and class irreducible loss model which arise only in the robust online batch selection setting and are unique to our work. > Q2: Generalizability of REDUCR We thank the reviewer for their recommendation and have included experiment results using the Clothing1M dataset and the ConvNext architecture in the attached pdf. We repeated the Clothing1M results using the facebook/convnext-tiny-224, ConvNext model architecture [2] from HuggingFace. The results are presented in the attached pdf. We note that REDUCR continues to match or outperform all the baseline approaches on the dataset. We ran each experiment for 3 seeds and used the hyperparameters from our original Clothing1M experiment. These are promising initial results and further hyperparameter tuning specific to the model architecture will improve the performance further. We have addressed all of the reviewers points, run additional experiments to further verify the generalizability of REDUCR and included several clarifying remarks in the manuscript. In light of this we ask that the reviewer reconsider and increase their score. *References* [1] Shiori Sagawa et al. Distributionally robust neural networks for group shifts: On the importance of regularization for worst-case generalization. Internation Conference on Learning Representations, 2020. [2] Zhuang Liu, Hanzi Mao, Chao-Yuan Wu, Christoph Feichtenhofer, Trevor Darrell, and Saining Xie. A convnet for the 2020s. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 11976–11986, 2022. --- Rebuttal Comment 1.1: Comment: Thank you for your response. It has addressed most of my concerns. Therefore, I chose to raise my score. --- Reply to Comment 1.1.1: Comment: Thank you for your feedback on our work and for raising your score.	Summary: - This paper introduces a method using an online algorithm with class priority reweighting to downsample data for vision and text tasks. The experiments demonstrate that this approach can achieve robustness and efficiency in situations with imbalanced classes and poor worst-class generation performance. Strengths: - Originality and Significance: The new online batch selection approach is robust to noise, imbalance, and distributional shifts. It can effectively preserve the worst-class generation performance, as demonstrated by the results. - Quality and Clarity: The work includes positive experimental results supported by sufficient formulas that recap the background, problem definition, theoretical algorithms, and justification of the method. The use of figures helps readers better understand the algorithm and evaluation results. Weaknesses: - The ablation studies are not elaborated upon. There are limited descriptions on how to draw conclusions about the necessity of each component for robust online batch selection, which raises curiosity. Technical Quality: 3 Clarity: 3 Questions for Authors: - What are the most challenging aspects when applying this new method to scaling and broader scenarios? Are there potential solutions for addressing these challenges? Confidence: 1 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: - Further exploration is needed on the balance between compute efficiency and data downsampling efficiency among different combinations of model architectures and class group numbers. - Limited tasks: The work focuses on and is evaluated using a series of text and image classification tasks. However, to improve data efficiency for real-world applications and broader machine learning models, further research on the effectiveness of this method on other tasks is necessary. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the Reviewer for their score and recognising the originality and significance of our approach along with the quality and clarity of our manuscript. In response to the weaknesses, question, and limitations: > W: Ablation Studies In Section 5.2 we investigate how the removal of the class holdout loss term affects the performance of the algorithm. Later in Appendix A.7.2 we also describe in detail how the clipping of the selection score stabilises the selection scores and thus motivate its inclusion in the algorithm. In response to the reviewers feedback we will look to include the following in the paper to further motivate the inclusion of the model loss and class irreducible loss model terms in the algorithm. “In Figure 4a) we note that removing the Model Loss results in the worst performance in the set of ablation studies. This is because the Model Loss provides REDUCR with information about which points are currently not classified correctly by the model. By removing this term REDUCR only selects points which do well under the Class Irreducible Loss model and does not prioritise points the model has not yet learnt. Selecting points not yet learnt by the model is an important quality in online batch selection approaches and the main premise of the Train Loss baseline algorithm. Likewise by removing the Class Irreducible Loss Model term we remove the ability of the model to infer if a point can be learnt or not. In [1], the authors note that these pretrained models enable the algorithm to pick points that are learnable and do not have label noise.“ > Q: Challenges The most challenging aspect, which we wrote in Section 6 (Limitations), is that the computational efficiency of REDUCR scales linearly with the number of classes and as such applying this method to scenarios that scale with the number of classes increases the computational cost of selecting data with REDUCR. To begin addressing these problems we explore an approach in which we apply REDUCR to superclasses in Section 5.3. This approach shows strong results on the CIFAR100 dataset, outperforming the worst-class and average test accuracy of the baseline algorithms. On top of this we propose another direction of research in the limitations section - using smaller models to guide larger models. A variety of work (see [1][2] in our related work) has shown that smaller models can guide the training of a larger model and, as such, we think this is a promising direction of investigation for improving the algorithm’s computational complexity. We intend to study this more rigorously in future work as the scope is beyond that of one conference paper. > L1: Generalisation of REDUCR The compute efficiency and data downsampling efficiency are reflected in the progression of test accuracy as the number of training steps increases. In the general response, we include results on the ConvNext model architecture applied to the Clothing1M dataset. The results indicate that REDUCR can be widely applicable to more architectures. We agree with the reviewer that improving compute efficiency for a larger number of classes is a promising direction of research and address this in the Limitations section of the paper. >L2: Effectiveness of REDUCR We respectfully disagree with the reviewer on this point. Whilst further research on applying REDUCR to non-classification tasks is a promising direction for future work, the focus of this paper is on data selection in the classification setting, introducing the robust online batch selection problem and proposing a practical solution. We demonstrate REDUCR’s performance on two different modalities of data (text and image) showing the algorithm generalises across a number of different real-world classification tasks. Classification problems are still highly relevant to practitioners (e.g. sentiment classification to ensure LLM output is safe) and as such REDUCR has numerous real-world use cases as it is described in our work. While it is always nice to include more tasks and more applications, we don’t consider those “necessary” for our paper, since we have already demonstrated a range of detailed results in both the main paper and appendix to support our claim that class-robust data downsampling is an important problem and REDUCR can help to solve this problem. *References* [1] Mindermann et al. Prioritized training on points that are learnable, worth learning, and not yet learnt. International Conference on Machine Learning, 2022. [2] Sang Michael Xie et al. Doremi: Optimizing data mixtures speeds up language model pretraining. arXiv preprint arXiv:2305.10429, 2023. --- Rebuttal Comment 1.1: Comment: Thanks for the comprehensive responses, especially regarding the challenges. I have updated the rating to 7 and look forward to the future work. --- Reply to Comment 1.1.1: Comment: We would like to thank the reviewer for their remarks and raising their score.	Summary: Problem: The paper addresses the challenge of efficient online batch selection while training for classification tasks. It identifies a key issue with current batch selection algorithms: they often perform poorly on underrepresented classes in the training data. The paper proposes solutions to this problem while ensuring efficient data sampling. The goal is to optimize both the worst class performance and the average class performance on classification benchmarks by selecting a subset of each batch that enhances the performance of the worst performing class. Contributions: The paper proposes an online batch selection algorithm that assigns priority weights to training data points in a batch based on i) class weights in training data and ii) usefulness to the model. This is done by selecting points which have the highest worst class generalization error (hence selecting underrepresented classes) and selecting those points which are learnable given more data, thus avoiding noisy and task-irrelevant points. All of these objectives are ensured by assigning selection scores to training points in a batch. These selection scores are computed based on the model loss (training loss), class-irreducible loss (training loss from a reference model training on class-specific holdout data), and class-holdout loss (training loss on holdout data). Although existing works such as RHO-LOSS employ similar reference models training on holdout datasets, they fail to optimize for underrepresented classes in the training data. Further, REDUCR is also robust to noise in the training data, by selecting points that are harder to learn from worse-performing classes over those which are easier to learn (and are already performing well at a given training point). Experiments and Results: REDUCR has been evaluated on both image and text classification datasets. The paper assesses both worst-class test accuracy and average test accuracy. REDUCR outperforms existing batch selection methods like RHO-LOSS by at least 3% in worst-class accuracy, while achieving comparable results to RHO-LOSS in average class performance. Strengths: The strengths of the paper are: 1. The proposed data sampling algorithm, REDUCR, aims to optimize worst-class performance in classification tasks. REDUCR makes significant progress towards efficient data sampling algorithms that are robust to class imbalance and noise in training data. 2. Contributions regarding improved worst-class accuracy are empirically well-supported across a wide range of classification datasets, including both text and images. 3. The REDUCR algorithm is well-motivated in the paper, with a focus on the efficiency of data sampling. Weaknesses: Weaknesses of the paper: 1. All experiments are conducted on small-scale datasets (with fewer than 1000 classes). The paper mentions in line 73 that the problem of robustness becomes less applicable in settings with a high number of classes. However, as the number of classes increases, the problem of class imbalance becomes more pronounced due to the power law in most datasets. Since REDUCR scales linearly with the number of classes, a thorough evaluation of the suggested approach of using super-classes would be beneficial. 2. The paper does not compare with other approaches, such as [1], which specifically address popularity bias in training datasets and could improve worst-class performance. 3. The paper lacks ablation experiments on hyperparameters in REDUCR, such as the fraction of data points selected for training and the number of reference models trained. [1] [Distributionally Robust Language Modeling](https://arxiv.org/pdf/1909.02060) Technical Quality: 3 Clarity: 4 Questions for Authors: Broadly two questions on REDUCR evaluation: 1. How does REDUCR compare with existing data selection algorithms (other than RHO-LOSS) aimed specifically at distributional shifts? 2. How does REDUCR perform on large-scale classification tasks? Further, can REDUCR be applied to tasks other than classification? Confidence: 3 Soundness: 3 Presentation: 4 Contribution: 3 Limitations: Please refer weaknesses and questions. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for their score recognising the strengths of our paper, including the strong motivation and progress towards solving the problem setting we introduce in this work. In response to the weaknesses and questions: > W3: Ablation Experiments We direct the reviewer to Appendix A.7 of our work where we run ablations on the gradient weight, learning rate and percent train hyperparameters. In response to this feedback we will make it clearer in Section 5.2 (Ablation Studies) that these hyperparameters studies are in the paper’s appendix. The number of reference models is the same as the number of classes if we don’t adopt superclasses. We discuss the superclass setting in the response to question “The paper mentions in line 73..” > W2/Q1: Comparison with Existing Algorithms To the best of our knowledge we are the first work to consider the setting of online batch selection that is robust to issues such as distributional shifts and class imbalance. Whilst approaches such as [1] and [2] derive training objectives to address distributional shift, these approaches do not address the question of how to sub-sample the data they are trained on. REDUCR selects data and thus adjusts the distribution of classes in the loss, however [2] directly upweights the gradients of poorly performing classes in the training loss. Indeed one could apply this approach on top of REDUCR to try and further improve performance on the worst classes. This is an important direction to explore but orthogonal to the approach we introduce in REDUCR. > W1/Q2: High Number of Classes To address the linear scaling problem, we propose the super-class approach in Section 5.3 and apply it to CIFAR100. We note that the results on CIFAR100 with super-classes are promising, CIFAR100’s worst-class average test accuracy and average test accuracy outperform all the baseline algorithms. We note in the limitations that this is one of many potential approaches to address the linear scaling problem and as such a full investigation of all these ideas is left for future work; our goal in this work is to introduce the problem setting and thoroughly investigate the base REDUCR algorithm. The reviewer also addresses the problem of class imbalance becoming more pronounced due to the power law. This requires further investigation beyond the scope of our work to answer important questions e.g. what are the real world scenarios where introducing more classes worsens class imbalance, what datasets are representative of this, and how these questions are reflected in the model’s performance. > Q2: General Applicability of REDUCR REDUCR can potentially be applied to generative tasks or regression. One can generalise the idea of optimising the worst-class performance to optimising the worst-group performance [2]. For example, generative tasks can have different groups of problems related to math, coding, or literature etc. Regression tasks may have different groups of inputs. To apply REDUCR in this setting one needs group labels for each data point and an objective (e.g., log-likelihood) such that the REDUCR selection rule (Equation 7) can still be applied. REDUCR lays a strong foundation for future exploration in this direction, specifically in Section 5.3 where we group classes together, and show strong empirical performance on the CIFAR100 dataset with this approach. *References* [1] Yonatan Oren, Shiori Sagawa, Tatsunori B Hashimoto, and Percy Liang. Distributionally robust language modeling. arXiv preprint arXiv:1909.02060, 2019. [2] Shiori Sagawa et al. Distributionally robust neural networks for group shifts: On the importance of regularization for worst-case generalization. Internation Conference on Learning Representations, 2020.	null	null	Rebuttal 1: Rebuttal: We thank the reviewers and ACs for their time and work in evaluating our paper. In response to your feedback we have re-run our experiments on the Clothing1M dataset with a new model architecture to test the generalizability of REDUCR. The results can be seen in the attached PDF. REDUCR outperforms the next best baseline in terms of the mean worst-class and average test accuracy. We ran each experiment for 3 seeds, using the original hyperparameters from our original Clothing1M experiment. These are promising initial results and further hyperparameter tuning specific to the model architecture will improve the performance further. We have also clarified several points in the manuscript. Firstly we have provided a more detailed explanation of how ablating various components of REDUCR affects the algorithm’s performance: “In Figure 4a) we note that removing the Model Loss results in the worst performance in the set of ablation studies. This is because the Model Loss provides REDUCR with information about which points are currently not classified correctly by the model. By removing this term REDUCR only selects points which do well under the Class Irreducible Loss model and does not prioritise points the model has not yet learnt. Selecting points not yet learnt by the model is an important quality in online batch selection approaches and the main premise of the Train Loss baseline algorithm. Likewise by removing the Class Irreducible Loss Model term we remove the ability of the model to infer if a point can be learnt or not. In [1], the authors note that these pretrained models enable the algorithm to pick points that are learnable and do not have label noise.“ Secondly, we have clarified how by analysing the worst-class test accuracy we lower bound the performance of the trained model under a variety of class distribution shifts: “Finally, it is important to note that we analyse the worst-class test accuracy which can be interpreted as a lower bound on a model’s performance under all class distribution shifts. This is because the worst possible distribution shift between the training and test set is one where the entire test set consists of only points from the worst performing class.” Thirdly we have visualised the distribution shift in the Clothing1M dataset, we will include this in the paper and have added this plot to the attached PDF. Finally, we will further clarify in the main text that the extensive ablation experiments we ran on the gradient weight, learning rate and percent train hyperparameters are included in the Appendix. We look forward to engaging with the reviewers in the author reviewer discussion period. Pdf: /pdf/300e822da335d30c5821c0f15759bc754506ab8c.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null

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