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title string	paper_decision string	review_1 string	rebuttals_1 string	review_2 string	rebuttals_2 string	review_3 string	rebuttals_3 string	review_4 string	rebuttals_4 string	global_rebuttals string	dataset_source string	conference_year int64	review_5 string	rebuttals_5 string	review_6 string	rebuttals_6 string	review_7 string	rebuttals_7 string	review_8 string	rebuttals_8 string
Distributionally Robust Reinforcement Learning with Interactive Data Collection: Fundamental Hardness and Near-Optimal Algorithms	Accept (poster)	Summary: This work deal with sample complexity of Robust MDPs. The major improvement is that, contrary to previous research that relies on generative models or pre-collected datasets, this paper focuses on RMDPs learning through interactive data collection, addressing two key challenges: distributional robustness and balancing exploration and exploitation. Three main contributions are : 1) Explaining that sample-efficient learning is unachievable without additional assumptions due to the curse of support shift, where training and testing environments may have non-overlapping distributions. 2) Introducing of the vanishing minimal value assumption for Robust Markov Decision Processes (RMDPs) with a total-variation distance robust set, assuming the minimal value of the optimal robust value function is zero, leading to a tractable case. 3) Proposing an algorithm with a provable sample complexity guarantee under this framework. Strengths: The strengths of this paper are : 1) The paper is clearly written and ideas are well exposed. 2) Authors derive a nice lower bound with counterexample on the sample complexity of RMDPs in an online setting, and tight upper bound using extra assumptions such that vanishing minimal value assumption where TV uncertainty set can be rewritten using Radon-Nikodym derivatives. 3) The proof seems correct for me. 4) Algorithm is quite classic but make sense to derive robust policy while balancing exploration and exploitation. Weaknesses: 5) It would also be interesting to extend results for $s$- rectangular case. 6) There is no lower bound with vanishing minimal assumption to ensure that the upper bound under these assumptions is tight. 7) It would be nice to add the range of $\epsilon$ for the upper bound where sample complexity is valid or give a condition on K rather than saying "lower order term in K" 8) I think it would be interesting to gives more intuition on vanishing minimal assumption. Technical Quality: 3 Clarity: 3 Questions for Authors: 9) Do you think that vanishing minimal assumption is restrictive to derive Deep Robust RL algorithm ? 10) Do you think it would be possible to adapt Proposition 4.2 to other norms such as $L_p$ ? 11) To clarify thing, the main difference between generative model setting and online setting in RMDPs is to deal with support shift of kernel ? 12) I understand that KL and $\chi^2$ is a slightly different problem, does vanishing minimal assumption for KL or $\chi^2$ divergences RMDPs make sense as the definition of these divergences already impose bounded support shift of transition kernel ? 13) From a practical point of view, would the idea that sample complexity of RMDPS is smaller than MDPs (both in online and generative model setting) could lead to more sample efficient algorithms ? Confidence: 4 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: Q1: It is interesting to extend to $\mathcal{S}$-rectangular case. A1: Thanks, we appreciate your suggestions! But still, we would like to emphasize that our work is the first one on robust RL with interactive data collection that proves the hardness result and provides the algorithm with sharp sample complexity under suitable assumptions. We leave possible extensions to a broader range of cases to future work. Q2: About the lower bound under the vanishing minimal value assumption. A2: Thank you for this question! The prior work [1] derived a lower bound of $\Omega(\min\{H_\gamma,1/\rho\}H_\gamma^2SA/\varepsilon^2)$ for discounted RMDPs with generative model, where $H_\gamma = 1/(1-\gamma)$ is the effective horizon. After examining the proof, we find this lower bound can be extended to finite-horizon RMDPs, giving an $\Omega(\min\{H,1/\rho\}H^2SA/\varepsilon^2)$ lower bound. This applies to both the generative model setting and the online interactive learning setting, as the latter is considered more challenging. However, we acknowledge that the hardness instance given by [1] does not satisfy the vanishing minimal value assumption and requires some modifications. We conjecture that this lower bound still holds with the vanishing minimal value assumption and we will attempt to provide a rigorous proof in the revision. Q3: On lower order terms in $K$ and the range of $\varepsilon$ s.t. the sample complexity is valid. A3: Thanks for pointing this out! For the lower order terms in $K$ of the online regret, we actually included them clearly in the proof (see Appendix E.1, Line 999). Correspondingly, the sample complexity of Algorithm 1 is $\widetilde{O}(\min\{H,1/\rho\}H^2SA/\varepsilon^2 + H^3SA/\varepsilon)$ for any $\varepsilon>0$. Thus Corollary 4.4 holds for $\varepsilon\in(0,c\cdot\min\{1, 1/(H\rho)\}]$ with $c$ being an absolute constant. We will make this clear in the revision. Q4: About intuitions on the vanishing minimal value assumption. A4: As we concluded in the paper, the main difficulty of robust RL with interactive data collection is from the curse of support shift. By looking into the duality representation of the robust value functions, once the minimal values vanishes, the robust set is then equivalent to a new type of robust set without explicit support shift, thus combatting the original difficulty (Proposition 4.2). We also refer to the discussions after Proposition 4.2 for more explanations (Lines 259-265). Q5: Is the vanishing minimal value assumption restrictive for deep robust RL? A5: Thank you for asking! The vanishing minimal value assumption is a general, not restrictive, assumption for deep reinforcement learning in real-world applications. One sufficient condition for this assumption is the fail-state assumption, which is common in practice. For example, in robotics scenarios where a "destroyed robotics" state is absorbing and yields a minimum zero reward, it satisfies both the fail-state assumption and the more general vanishing minimal value assumption. Q6: Is it possible to adapt Proposition 4.2 to other norms such as $L_p$? A6: Thanks for the interesting direction! We do notice that previous works e.g., [2] (and references therein) considered the general $L_p$-norm, but in a different learning setup than ours. However, the general $L_p$-norm robust set gives a complicated duality representation for the robust Bellman operator (Lemma B.5 in [2]), and the vanishing minimal value assumption alone does not provide similar equivalence results like Proposition 4.2 to combat the curse of support shift. This assumption does rely on $p=1$. Therefore, a direct extension of Proposition 4.2 to $L_p$-norm is hard. However, we appreciate this question. It definitely serves as an exciting direction to study when robust RL with interactive data collection is possible under general $L_p$-norm robust set. Q7: Is the difference between generative model and the online setting to deal with support shift? A7: Yes! More specifically: For generative model setting, since the learner can query each state-action pair for the next state, there is no curse of support shift in estimating the nominal transition. In contrast, in the online setting, the agent collects data by interacting with the training environment, and there could exist hard-to-reach states which are important for generalizing to testing environments (support shift happens). Q8: Does vanishing minimal value assumption for KL or $\chi^2$ divergences make sense? A8: As we have already mentioned in Q4 and Q6, this assumption is tailored for the TV robust set. It is not a suit for KL or $\chi^2$ divergences RMDPs. However, we note that even though there is no explicit support shift for KL and $\chi^2$, we an still build hard instances where the probability of reaching certain states that appear in the test environment is extremely low in the training environment (a broader understanding of support shift, see Appendix B.3). Thus it is unknown whether robust RL is possible with interactive data collection for these types of robust sets even with suitable assumptions. We leave this question as future work. Q9: Would that the sample complexity of RMDPs is smaller than MDPs leads to more sample efficient algorithms? A9: We remark that RMDPs and MDPs use different performance metrics. The former seeks the optimal robust value function while the latter finds the optimal standard value. Therefore, it is reasonable that deep robust RL algorithms find robust optimal policy using less samples than standard RL algorithms to find a standard optimal policy. References: [1] Shi, Laixi, et al. "The curious price of distributional robustness in reinforcement learning with a generative model." NeurIPS 2023. [2] Clavier, Pierre, et al. "Towards minimax optimality of model-based robust reinforcement learning." arXiv preprint 2023. --- Rebuttal Comment 1.1: Comment: Thank you for your detailed answers. I maintain my score and advocate for acceptance. --- Reply to Comment 1.1.1: Comment: Thank you for your efforts reviewing our paper and your support! We will further improve our paper following your suggestions during revision.	Summary: This paper studies the learnability of the optimal policy for robust Markov decision process (RMDP) under the interactive data setting. The paper first show a fundamental hardness results which necessitates identifying a subclass of RMDPs which is actually solvable. The authors propose an algorithm whose sample complexity and regret are analyzed. Strengths: 1. The paper is well-organized and well-written. 2. The setting is meaningful and motivated. 3. The analysis is thorough. 4. The comparisons with existing works are very detailed, making the paper easy to follow. Weaknesses: I am not aware of notable weaknesses. Technical Quality: 3 Clarity: 3 Questions for Authors: 1. In my understanding, this is the first value-based online/interactive data collection DRRL algorithm. Can authors confirm this is the case? 2. I am aware of Dong et al., 2022, and I am also aware that their proof has fatal flaws. I would like to mention that there is another actor-critic method for DRRL, Zhou et al., 2023 [1]. I believe this can also handle online interaction with the nominal model and learn a robust policy. Can the authors compare it with your work, especially about their robust critic component. 3. Assumption 4.1 is a sufficient condition for any RMDP to be solvable. Can the authors share some insights about the "gap" between this sufficient condition and a could-be necessary condition. Reference [1] ZHOU, R., LIU, T., CHENG, M., KALATHIL, D., KUMAR, P. and TIAN, C. (2023). Natural actor-560 critic for robust reinforcement learning with function approximation. In Thirty-seventh Conference561 on Neural Information Processing Systems. Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: No other limitations I would like to bring up. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Q1: Whether our work is the first value-based interactive data collection DRRL algorithm? A1: Thanks for pointing this out! But we want to clarify that our algorithm is model-based since it necessitates an explicit estimation of the training environment transition kernel, denoted by $\widehat{P}$. We will make this conceptual point clearer in the revision. Q2: Comparison with the previous work [1]. A2: Thanks for pointing out this interesting work [1]! We have also cited and mentioned this work in the paper. [1] proposes a novel robust natural actor-critic algorithm under function approximation to solve robust RL with interactive data collection, also with certain theoretical guarantees. The key difference between the theory in [1] and our work is in the data assumptions and thus the subsequent techniques required to design and analysis the respective algorithms. Regarding the data assumptions, [1] relies on interacting with a nominal environment that satisfies several concentrability and mixing assumptions (Assumptions 1, 3, 6 in [1]), and thus [1] does not explicitly address the problem of exploration where the agent needs to adaptively use interactive data collection to explore and robustify its policy. In contrast, our work does not make any assumption regarding the concentrability or mixing properties of the underlying nominal MDP. Instead, we use algorithmic design to incentivize the agent to explore automatically. Besides, regarding the comparison to the robust critic component, since our algorithm is not in the actor-critic style, a direct comparison is hard. But still, we maintain a robust value function estimation during training, which is similar to a robust critic. The key difference is that, in order to address the fundamental challenge of exploration during interactive data collection, our robust value estimator features a carefully designed optimistic bonus that encourages the agent to explore the nominal environment sample-efficiently. This is different from the design idea of the robust critic in [1]. Q3: About the "gap" between the sufficient condition (Assumption 4.1) and other potentially necessary conditions. A3: While we have established a worst-case hardness result without the vanishing minimal value assumption, we acknowledge that more general sufficient or even necessary conditions for sample-efficient learning with interactive data collection may exist. We agree with the reviewer that this is an interesting and challenging direction to explore, as our vanishing minimal value assumption is currently the most general sufficient condition enabling sample-efficient learning to the best of our knowledge. We will include further discussions on this topic in our revision and will consider it for future research. References: [1] Zhou, Ruida, et al. "Natural actor-critic for robust reinforcement learning with function approximation." Advances in neural information processing systems 36 (2023). --- Rebuttal Comment 1.1: Comment: Dear authors, Thank you for responding to my questions. I will maintain my rating. Good luck. --- Reply to Comment 1.1.1: Comment: Thank you very much for your efforts reviewing our paper and we appreciate your support! We will further improve our paper following your suggestions during revision.	Summary: This paper studies robust RL in a finite-horizon RMDP through interactive data collection. They give both a fundamental hardness result in the general case and a sample-efficient algorithm within tractable settings. Strengths: 1. Unlike previous work, which relies on a generative model or a pre-collected offline dataset enjoying good coverage of the deployment environment, this paper tackles robust RL via interactive data collection. 2. This paper introduces the vanishing minimal value assumption to RMDPs with a TV-distance robust set, postulating that the minimal value of the optimal robust value function is zero, which eliminates the support shift issue for RMDPs. 3. This paper proposes an algorithm with sharp sample complexity. Weaknesses: 1. This paper is purely theoretical. Although I understand the focus of this paper, but I still want to see some empirical results or even some simulations to get more insight. Moreover, an algorithm is given in this article, thus some numerical studies are required. 2. I am not sure if the Interactive Data Collection design is feasible in practice especially in some real-world problems. 3. Some more detailed discussion about the comparison between the proposed method and the baseline methods are required especially when they are designed for different cases. So maybe some numerical results are helpful. Technical Quality: 3 Clarity: 3 Questions for Authors: Please see the weakness part. Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: No Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Q1: This paper is purely theoretical. Although the reviewer understands the focus of this paper, but still want to see some empirical results to get more insight. Moreover, since an algorithm is given in this article, some numerical studies and comparisons are required. (Weakness 1&3) A1: Thank you for recognizing that our work focuses on theoretical study. We appreciate your suggestion to add experimental results. We will consider including them in the revision. Q2: About the feasibility of the interactive data collection setup. (Weakness 2) A2: Thanks for the question! Yes, this setup is indeed possible and is even a common practice in certain real-world problems. For examples, in robust RL for robotics, e.g., [1, 2, 3, 4], the agent is usually trained in a simulated environment (corresponding to the training environment in our theoretical setup) through trial and error, which is interactive data collection since the algorithm does not use pre-collected offline data or a generative model (we remark that in the theoretical literature a generative model means that the algorithm has the access to directly query the next state given any state-action pair). The goal is to ensure that the robot still functions well even if the environment changes (corresponding to the testing environment in the theoretical setup), e.g., when the coefficient of friction differs or the weight of the robot changes. Thus the interactive data collection setup is indeed feasible in real-world problems. References: [1] Pinto, Lerrel, James Davidson, Rahul Sukthankar, and Abhinav Gupta. "Robust adversarial reinforcement learning." In International conference on machine learning, pp. 2817-2826. PMLR, 2017. [2] Tessler, Chen, Yonathan Efroni, and Shie Mannor. "Action robust reinforcement learning and applications in continuous control." In International Conference on Machine Learning, pp. 6215-6224. PMLR, 2019. [3] Zhao, Wenshuai, Jorge Peña Queralta, and Tomi Westerlund. "Sim-to-real transfer in deep reinforcement learning for robotics: a survey." 2020 IEEE symposium series on computational intelligence (SSCI). IEEE, 2020. [4] Brunke L, Greeff M, Hall A W, et al. Safe learning in robotics: From learning-based control to safe reinforcement learning[J]. Annual Review of Control, Robotics, and Autonomous Systems, 2022, 5(1): 411-444. --- Rebuttal Comment 1.1: Title: Engage with authors Comment: Dear Reviewer, Please engage with the authors. This is the last day a back and forth discussion is possible. The AC --- Rebuttal Comment 1.2: Comment: Hope you can include some numerical studies in the final version, as you mentioned that the setup in this paper 'is indeed possible and is even a common practice in certain real-world problems.' --- Reply to Comment 1.2.1: Comment: Thank you for your valuable time reviewing our work and thanks for your support! We appreciate your suggestions on adding numerical experiments in the revision. We will include that and further improve our paper following your suggestion during revision.	Summary: The paper addresses the challenges in distributionally robust reinforcement learning (DRRL), particularly focusing on robust Markov decision processes (RMDPs) under the framework of interactive data collection. Unlike previous work that depends on generative models or pre-collected datasets, this study emphasizes interactive data collection where the learner refines policies through interaction with the training environment. The main contributions include identifying fundamental challenges that for total variation (TV) distance, there exists a hard RMDP that all algorithms at least need $O(KH)$ regret. In addition, by introducing a vanishing minimal value assumption to mitigate these challenges, this work proposes a sample-efficient algorithm (OPROVI-TV) with regret $O(\sqrt{\min\{H, 1/\rho\}H^2 SAK } after $K$ trajectories, which matches the results from the state-of-the-art non-robust MDP online learning and also robust MDP with generative model. Strengths: 1. This work focuses on interactive data collection for robust RL, addressing practical challenges and moving beyond reliance on generative models or pre-collected datasets, which is an underdeveloped open direction. 2. The proposed OPROVI-TV algorithm balances exploration and exploitation, providing strong guarantees for online regret and sample complexity for such robust RL problems with online settings. Weaknesses: 1. The main assumption (Assumption 4.1) that this work mainly depends on is interesting, but will such assumptions make the problems (robust MDPs with TV uncertainty set ) not a suitable and meaningful robust RL problems for those tasks? Specifically, no matter Assumption 4.1 or the fail-state assumption from [1] indeed implies that for all policy, $ \min_{s\inS} V_{h}^{\pi}(s) = 0 $ for all $h=1,2,\cdots, H$ if the reviewer does not miss something. The main concern from the reviewer is that (actually the author already discuss about this in Appendix B.4.1): For those tasks under such assumptions, if we consider robust MDPs using TV distance, will those robust MDPs directly equivalent to some non-robust MDPs but with a discounted reward (non-robust MDP with reward function $r<1-\rho/2)$. * So in such cases, will the robust RL problem using TV to construct the uncertainty set be meaningful? I think those robust formulations will reduce back to non-robust MDPs. So maybe some uncertainty set with support control (the adversarial can't make the transition kernel to be out of the support of the nominal transition kernel) will be more suitable to use in such tasks. * In addition, the reviewer believe that under Assumption 4.1, the regret of this problem can be improved to $O(\sqrt{\min\\{H, 1/\rho\\}^3 SAK}?$ Since the maximum value of the robust value function will be $\min\\{ H, 1/\rho\\}$ but not $H$ in the non-robust value function anymore. [1]Panaganti, Kishan, and Dileep Kalathil. "Sample complexity of robust reinforcement learning with a generative model." International Conference on Artificial Intelligence and Statistics. PMLR, 2022. Technical Quality: 3 Clarity: 3 Questions for Authors: 1. In the introduction "Given that all the existing52 literature on robust RL theory relies on a generative model or pre-collected data" Not all the existing works are using generative model or offline dataset? Such as [1]. If so, please check [1] Dong, Jing, et al. "Online policy optimization for robust mdp." arXiv preprint arXiv:2209.13841 (2022). Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: Well-answered Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Q1: About whether Assumption 4.1 reduces our problem setup to a non-robust RL problem. (Weakness 1&2) A1: Here we clarify that Assumption 4.1 does not reduce the problem to its non-robust counterpart. It is a misinterpretation of the discussions in Appendix B.4.1 that Assumption 4.1 reduces the problem to non-robust RL. In fact, Appendix B.4.1 clearly states that (Lines 706-709) under Assumption 4.1, the TV-robust MDP is equivalent to a discounted robust MDP with another formulation of robust set (bounded transition probability ratio w.r.t. the nominal model, see Proposition 4.2). Thus, under Assumption 4.1, our problem setup is still in the regime of robust RL and is fundamentally different from doing non-robust RL. Regarding robust sets where one explicitly assumes that the adversarial can't change the support, again thanks to the equivalent result in Proposition 4.2, we can actually solve robust RL with interactive data collection for discounted robust MDPs with robust set containing transitions that have bounded ratio to the nominal model (and thus the support does not change) by using a variant of our Algorithm 1 (see discussions in Appendix B.4.3). It is an interesting future work to consider other (perhaps more general) types of robust set where the adversarial can't change the support. Q2: Whether the regret is further improvable to $\widetilde{O}(\sqrt{\min\{H, 1/\rho\}^3SAK})$ given that the maximum value of the robust value function is $\min\{H, 1/\rho\}$? (Weakness 3) A2: We first want to point out that achieving the regret bound $\widetilde{O}(\sqrt{\min\{H, 1/\rho\}^3SAK})$ seems impossible. Specifically, even for MDPs with $V_{\text{MAX}} = R$, the lower bound still scales with $\Omega(\sqrt{R^2HSAK})$. The intuition is that when we consider the inhomogeneous setting where the transition kernel $\{P_h^{\star}\}_{h\in H}$ varies in the $H$ time steps (as we considered in this paper), the factor $\sqrt{H}$ is inevitable. We believe that the dependence on $H$ instead of $\min\{H, 1/\rho\}$ is inherent to the problem and cannot be further improved. In addition, we need to point out that, actually the proof of the current result has already utilized the fact that the upper bound and the variance of the robust value functions are controlled by terms related to $\min\{H, 1/\rho\}$, as is observed by the reviewer. More specifically, in the proofs of Lemma C.2 (showing that the robust value estimators are optimistic/pessimistic, see Eq (C.15)) and Lemma C.5 (controlling the summation of robust value functions over time horizons and episodes, see Eq (C.22)), we have utilized the fact that the robust value function is bounded by $\min\{H, 1/\rho\}$ to make the sharpest of our result. Given all that, we are still the first work that provides the algorithm with sharp sample complexity bound in the interactive data collection regime. We leave it as a future work to further figure out the sample complexity lower bound under assumptions that can make interactive data collecting robust RL feasible. Q3: About the previous work [1] on robust RL with interactive data collection. A3: We do agree that this work also considers robust RL that relies on interactive data collection, and we actually cited and discussed this work in our paper (see Appendix B.1, Lines 649 to 653). However, as we pointed out in Appendix B.1, this work exhibits an essential flaw (misuse of Lemma 12 therein) in the proof of their main result (online regret). This error invalidates their theoretical results, as Reviewer sH9q has also recognized. Thus, even though [1] works on the setup of interactive data collection, they actually did not answer the question that "Can we design a provably sample-efficient robust RL algorithm that relies on interactive data collection in the training environment?". In contrast, we are the first work that proves the hardness result in the general case and provides the algorithm with sharp sample complexity bound in the interactive data collection regime under suitable assumptions. We would make this comparison clearer in the main part of our paper during revision. References: [1] Dong, Jing, et al. "Online Policy Optimization for Robust MDP." arXiv preprint arXiv:2209.13841 (2022). --- Rebuttal Comment 1.1: Title: Engagement with authors Comment: Dear Reviewer, Please engage with the authors. This is the last day a back and forth discussion is possible. The AC	null	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Generalizability of experimental studies	Reject	Summary: The paper tries to formalize the concept of generalizability in experimental studies in machine learning research. It relies on three different types of kernels in order to quantify difference between the rankings in an experiment output. A core contribution is the development of an algorithm for estimating the number of experimental studies needed in order to generalize the results at a desired level. Strengths: - The topic is interesting and worthwhile. - The paper is clearly written. - The formalization of generalizability is well-defined and nicely parameterized through the use of kernels. - The practical usefulness of the algorithm is somewhat unclear to me. Weaknesses: - There is no discussion on the computational costs of the algorithm (except for a vague statement that it is very fast in the checklist). - The empirical evidence for the algorithm's effectiveness appears somewhat weak to me (see respective item in _Questions_). - The python package is not properly configured I think. I see this after having installed the package into a virtual environment with the correct python version and using `pip install . -r requirements.txt`: ```python In [1]: import genexpy --------------------------------------------------------------------------- ImportError Traceback (most recent call last) Cell In[1], line 1 ----> 1 import genexpy File ~/.pyenv/versions/genexpy/lib/python3.11/site-packages/genexpy/__init__.py:4 2 from .src import lower_bounds 3 from .src import mmd ----> 4 from .src import probability_distributions 5 from .src import rankings_utils 6 from .src import relation_utils File ~/.pyenv/versions/genexpy/lib/python3.11/site-packages/genexpy/src/probability_distributions.py :11 8 from typing import Literal 10 from genexpy import kernels as ku ---> 11 from genexpy import rankings_utils as ru 12 from genexpy import relation_utils as rlu 15 def sample_from_sphere(na: int, n: int, rng: np.random.Generator) -> np.ndarray[float]: ImportError: cannot import name 'rankings_utils' from partially initialized module 'genexpy' (most l ikely due to a circular import) (/home/<anonymous_reviewer>/.pyenv/versions/genexpy/lib/python3.11/site-packages /genexpy/__init__.py) Technical Quality: 3 Clarity: 3 Questions for Authors: ### Questions - To me it feels like the evidence for why the algorithm works is somewhat circular. If I am not mistaken, the case studies in 5.1 and 5.2 just show the output of the algorithm, which is really just an example of what your method outputs and doesn't really help show how well your method performs. And as far as the result in section 5.3 goes, how can this can be generalized to other problems? As far as I am able to tell, there is no reason to assume that even $N=50$ should be sufficient for $g_1$ in the general case? How do I know how to trust $n^$? Maybe I'm missing something here. ### Suggestions - The captions for your figures are too brief. They should at least describe what is shown in the plots. Please be more detailed. At least describe the variables shown. - Put conclusions before limitations and future work in section 6. - Please include a discussion on the computational costs of the algorithm. - L19: It's hard to tell what this is a reference too. Be more explicit. - L46: I'm nitpicking, but large language models shouldn't be in title case, I think. - L53: Consider replacing "motivation" by "problem". - L60: Consider replacing "conclusions" by "hypotheses". - L101: This sentence is phrased oddly. Please revise it. Maybe "are" should be removed? - L111: Incorrect hyper-reference (??). - L215: Remove "the" in front of "Maximum". - L232: "exist" should be "exists". - L260: It should be "the one-hot encoder". - L513: "Altohugh" should be "Although". Confidence: 2 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: Some of the limitations are discussed but I still think the paper could be more self-critical of for instance $n^$. Possible computational costs are also not discussed. There are no potential negative societal impacts of this work. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We are thankful to the reviewer you for their insightful remarks and for testing our module. There is no discussion on the computational costs of the algorithm (except for a vague statement that it is very fast in the checklist). Thank you for your remark, we have addressed it by adding, in Sections 5.1 and 5.2, the respective run times of 20 and 2 minutes respectively (on a Lenovo ThinkPad with AMD Ryzen 7 with 8 cores, 1700 Mhz). However, we do not treat the time complexity, as we deem estimating generalizability necessary and no competing methodology exists. [Python module not working] We are sorry for the inconvenience, after the submission we updated the repository with a new script to generate synthetic distributions of rankings, which caused the circular import you have observed. We have now fixed this problem and updated the faulty script as well as the instructions to install our module. ## Questions *To me it feels like the evidence for why the algorithm works is somewhat circular. If I am not mistaken, the case studies in 5.1 and 5.2 just show the output of the algorithm, which is really just an example of what your method outputs and doesn't really help show how well your method performs. And as far as the result in section 5.3 goes, how can this can be generalized to other problems? As far as I am able to tell, there is no reason to assume that even $N=50$ should be sufficient for $g_1$ in the general case? How do I know how to trust $n^\$? Maybe I'm missing something here.** Thank you for raising this important concern. The results in Section 5.3 show that our algorithms outputs predictions for $n^$ that are comparable to $n^_{50}$ even with lower sample size. To further prove our points that our estimates 1. are converging 2. to the correct $n^$, we performed additional experiments on synthetic data. Synthetic data is necessary because we do not have enough data available to obtain the true value of $n^$ for hundreds of studies. Recall that $ n^* = \min \{n\in\mathbb N_0: \text{Gen}\(\mathbb P; \varepsilon^, n) \geq \alpha^\}. $ The experiment goes as follows: 1. Uniformly generate 1000 rankings of 4 alternatives ($\|\mathcal R_4\| = 75$, as described in footnote 2, on page 6 of the manuscript). 2. Compute generalizability of the sample for increasing $n$, get $n^$ satisfying the equation above. 3. For $N=10, 20, 40, 80$, predict $n^_N$. 4. Compute the relative error $(n^* - n^_N) / n^$. 5. Repeat steps 1. to 4. 100 times. The results are shown in Figure 2 of the attached pdf. In particular, we remark that even 10 preliminary experiments are sufficient to get within 20\% of the correct $n^$ on 50\% of the tries. We added the code necessary to reproduce this analysis to the repository, under `demos/Synthetic data/demo1\_estimate\_nstar.py`. Performing this experiment required 40 minutes. We will add a dedicated subsection to Section 5 detailing these results as well as additional experiments on other synthetic distributions. ## Suggestions The captions for your figures are too brief. They should at least describe what is shown in the plots. Please be more detailed. At least describe the variables shown.* We have expanded the captions to be more descriptive. Put conclusions before limitations and future work in section 6. We have swapped limitations and conclusions in Section 6. Please include a discussion on the computational costs of the algorithm. We have added the relevant discussion, as described above. L19: It's hard to tell what this is a reference too. Be more explicit. We updated L19: "For instance, one expects that the best encoders of categorical features identified in [41] are likely to outperform their competitors on datasets not considered in the study." L101: This sentence is phrased oddly. Please revise it. Maybe "are" should be removed? We have made L101 clearer: "Design factors are chosen by the experimenter; e.g., whether and how to tune the hyperparameters, quality metrics, and number of shots.". Remove "the" in front of "Maximum". to the best of our knowledge, the usage of "the" in front of MMD is accepted in the literature. Refer for instance to [1]. We have consequently updated all the other usages of the word and its abbreviation in the paper. "exist" should be "exists". We deem ``exist'' correct, as it refers to both $\beta_0$ and $\beta_1$. To make it clearer, we updated L232 to "$\forall\alpha^$, there exist $\beta_0 \geq 0$ and $\beta_1 \leq 0$ s.t.". L46, L53, L60, L111, L260, L513* We have updated the paper accordingly. --- [1] Gretton, Arthur, et al. "A kernel two-sample test." The Journal of Machine Learning Research 13.1 (2012): 723-773. --- Rebuttal Comment 1.1: Comment: Thanks for the additional information, discussion, and experiments. I have improved my score accordingly.	Summary: This paper deals with experimental studies. After providing a mathematical formalization, it focuses on the generalizability of these studies. The main contribution is a quantitative estimate of the the size of the study to obtain generalizable results. Experiments on LLMs are conducted. Strengths: - [mathematical formulation] It is nice to have a solid formulation of experimental studies, this is quite relevant to the community. Weaknesses: - [train / test split] A concrete problem in machine learning practical experimentation is that of train / test split, and more particularly its absence (that is, training on the test). I do not see this issue discussed in the paper. Can it be incorporated in the setting? Is it possible to clarify whether the paper assumes that the training is done on a training set without calibration on a validation set or is this hidden somewhere? What would then be the influence on the number of experiments? - [testing between rankings] If I understand correctly, the paper proposes (in Section 4.1) to check whether rankings are consistent by performing kernel two-sample test, with adapted kernels. This does not seem standard to me: there exists some ad-hoc statistical tests (e.g., Kendall's \tau, Spearman's \rho, etc.). Why not use them directly? Is there an advantage to using MMD? - [minor comments]: - missing ref line 111 - repeated word ('of') line 300 Technical Quality: 3 Clarity: 3 Questions for Authors: see weaknesses 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: [train / test split] A concrete problem in machine learning practical experimentation is that of train / test split, and more particularly its absence (that is, training on the test). I do not see this issue discussed in the paper. Can it be incorporated in the setting? Is it possible to clarify whether the paper assumes that the training is done on a training set without calibration on a validation set or is this hidden somewhere? What would then be the influence on the number of experiments? Thank you for your question. You may be confused by the fact that when an ML model performs well on unseen (test) data, it is often said that it "generalizes" well to new data. Our methodology addresses a completely different kind of generalizability, which has to do with experimental studies (line 164). We assume a sufficient background of an experimenter and let them decide if a train-test split is necessary in their particular experiments (it may be redundant in a benchmark of, say, clustering algorithms). For clarification, we will add a separate section to our paper. See the global rebuttal for details. [testing between rankings] If I understand correctly, the paper proposes (in Section 4.1) to check whether rankings are consistent by performing kernel two-sample test, with adapted kernels. This does not seem standard to me: there exists some ad-hoc statistical tests (e.g., Kendall's $\tau$, Spearman's $\rho$, etc.). Why not use them directly? Is there an advantage to using MMD? You are correct in saying that we are using kernel two sample tests, but we are afraid there is a subtle difference. While we are approximating the distribution of the null for the kernel two sample test (line 238), we are not actually performing any test. Although not a standard procedure, we rely on it because the standard ones do not give answers to the problem of whether the results are consistently the same if a study is performed multiple times, Or, equivalently, if two samples of results are similar, hence the two sample testing. Tests of correlation based on $\tau$ and $\rho$ test whether two variables (i.e., two rankings) are highly correlated or not. Thus, they cannot be used directly to compute generalizability as usually understood in this context (line 163), as this requires to compare samples of results rather than single rankings. Other statistical tests, for instance posthoc tests such as Nemenyi and Conover-Iman, instead compare whether two specific alternatives are ranked consistently with respect to one another. Again, these are not directly applicable to our use case as they do not compare samples of results but instead work "within" a given sample. Finally, we use the MMD to compare samples of results because it considers the goal of a study, it handles well sparse distributions, and it has a solid theory backing it (lines 241--220). missing ref line 111, repeated word ('of') line 300 Sorry for the inconveniences, we fixed the reference to Section 3.2 on line 111 and removed the extra 'of'.	Summary: The paper tries to formalise the notion of an experimental study by considering the sampling process of acquiring a dataset. It then uses this notion to argue about generalisability. Strengths: The problem of understanding the performance of machine learning when tested on new data is a very important problem. The authors use some technically sophisticate methods to tackle this problem. Weaknesses: For me the authors model of an experiment is too simplistic and does not capture the problems faced by machine learning. If we collect medical data then that data is likely to vary depending on the equipment used, the clinicians running the equipment and population where the data comes from. These kinds of variations are the bugbear for machine learning, but not captured at all by the model. Another issue is that a lot of data is non-stationary. Even in the much used example of checkmate in one. If a machine learns this very well, then players against the machine are likely to learn their mistake and alter their play. Thus, I am not convinced that the model being proposed is particularly interesting. Technical Quality: 3 Clarity: 2 Questions for Authors: What kind of variations in datasets does your model capture? Where does this push the field beyond the current statistical learning theory? Confidence: 4 Soundness: 3 Presentation: 2 Contribution: 2 Limitations: This is fine. Flag For Ethics Review: ['No ethics review needed.'] Rating: 3 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for their comments, which allowed us to improve on the clarity of our paper. The problem of understanding the performance of machine learning when tested on new data is a very important problem. The authors use some technically sophisticate methods to tackle this problem. We are afraid this is a misunderstanding of our contribution. Our methodology is not intended to help understand the performance of machine learning methods when tested on new data. Instead, it helps assessing the trustworthiness of the results of an experimental study. Indeed, we quantify generalizability as the probability with which two studies with the same scope (i.e., compared methods, experimental conditions, and goals) yield similar results (lines 163--171). Furthermore, our methodology is not limited to changes in the data used to evaluate the methods, but we can consider any experimental factor (lines 106, 257, 285). For me the authors model of an experiment is too simplistic and does not capture the problems faced by machine learning. If we collect medical data then that data is likely to vary depending on the equipment used, the clinicians running the equipment and population where the data comes from. These kinds of variations are the bugbear for machine learning, but not captured at all by the model. This claim is not true. Contrary to your statement, our methodology aims to, and does, capture the variation of all experimental factors, which are arbitrary variables identified by the experimenter (line 97). We call it "generalizability" rather than just "replicability" (lines 21--22) precisely because we can deal with any factor. For instance, "equipment" (as well as "clinician" and "population") can be modeled as categorical factors. First, one assesses what pieces of equipment are necessary for the various experiments. Second, one decides how to identify the pieces, for example with their serial number. The identifiers are the levels of factor "equipment" (line 98). If one wants to check whether the results are consistently the same despite changes in the equipment, they can flag "equipment" as an allowed-to-vary factor and proceed as in sections 5.1 and 5.2. The `genexpy` module, linked on page 2, allows to replicate this analysis with a few changes to the `config.yaml` file. Another issue is that a lot of data is non-stationary. Even in the much used example of checkmate in one. If a machine learns this very well, then players against the machine are likely to learn their mistake and alter their play. Thus, I am not convinced that the model being proposed is particularly interesting. We are investigating the generalizability of experimental studies (also known as benchmarks). If your claim is that the results of published benchmarks are not useful because of the inherent non-stationarity of the experimental conditions, we point to the success of the NeurIPS track "Datasets and Benchmarks", which publishes several high-quality benchmark studies every year. In any case, the lack of stationarity does not affect our methodology, because time can be accounted for as another experimental factor. As discussed in the global rebuttal, we assume that the experimental study is properly designed. If needed, for instance, by taking time into account. What kind of variations in datasets does your model capture? To clarify, our methodology captures any variation caused by changes in the allowed-to-vary factors (line 82). The specific kind of variation one is interested in is specified in the scope of the study, by choosing appropriate levels for the experimental factors (lines 98, 109). For example, let's say an experimenter is evaluating on binary classifiers on tabular datasets. Then, by choosing what datasets to consider in the analysis, the experimenter can investigate the generalizability of their results on different kinds of variation in datasets. If they include only datasets with similar numbers of rows but wildly different numbers of columns, they can test whether their results depend on the number of columns. If, on the other hand, they do not specify any condition on the datasets, they can test whether their results depend on the choice of datasets in general. We added a sentence to line 99 to further clarify this point. Where does this push the field beyond the current statistical learning theory? Our method does not advance statistical learning theory directly. We provide researchers with a tool for estimating the generalizability (trustworthiness) of their results, which is a well-known problem of existing studies (cf. Section 2). --- Rebuttal Comment 1.1: Title: Acknowledgement of rebuttal Comment: Thank you for your detailed rebuttal. I will reread the paper and see whether your arguments convince me.	Summary: The authors provide a formalism for the generalizability of experimental studies in ML. Strengths: Anything pushing to get better practices in evaluation of ML is very important. Weaknesses: I could quibble with some of the setup, which is a bit confusing to me: design factors being properties of the context rather than of the alternative, for example, is kind of odd, but I don't think this is very important. The big problem is that there is a huge literature on a very similar problem and I have very little sense of how this work connects to it: starting with the Neyman-Pearson lemma and going down through the standard corpus of decision theory, we have a lot of statistical tools for thinking about this problem in very broad strokes. After reading this paper, I have a sense that you're trying to solve a very similar problem (given a sample from some population, what can I say about the reliability of my estimate? How many samples would I need to be sure that it's reliable?) Section 4.3 seems to be rederiving some form of power analysis. Looking at A.3.3, it appears that the procedure is essentially the following: (1) [the inner loop from 1...n_rep] construct a null hypothesis at a given sample size, find the upper alpha quantile of that null hypothesis (2) Repeat this at a variety of sample sizes (3) Estimate a power-law relationship between sample size and the upper-alpha quantiles (4) Predict the sample size which would have such an upper-alpha quantile This procedure is an empirical version of power analysis where the null distribution is not known but simulated and extrapolated. If I know the type-I error rate, type-II error rate and a distribution under the null and under the alternative, deriving the required sample size is straightforward. Indeed, we have a CLT for MMD (at least under some kernels) [1], so these distributions are known asymptotically, which is likely plenty for the purposes of sample size determination. Do \alpha^* and \delta^* map onto concepts from Neyman-Pearson? It's entirely possible. This is an important question because decision theory has very well established results on things like uniformly most powerful tests. When we just invent a new framework rather than relying on well-trod ones, we are likely to derive suboptimal procedures unless we compare very carefully to these existing procedures. There's no similarly sophisticated discussion of error properties in this paper, which would be reasonable if this were truly the first paper in its vein, but I don't think that's the case. Further, it's not clear to me why these similarities between rankings should be the target of inference. Rather, shouldn't I care about whether, based on the sample of allowed-to-vary factors I've used, alternative A is preferred to alternative B? This is an extremely standard matter of decision theory as far as I can tell. By moving to these more complicated research questions about rankings it clouds this fact, but I'm not sure it needs to. If the target of inference were instead to be a rank of K alternatives, I believe a decision theorist would take a somewhat similar approach to what you've done here: define a similarity metric based on the research question. An example solution to a problem like this would be [2], [3]. I just don't see why we need this new framework to accomplish a task I think we already have the tools for. It's entirely possible that there's a contribution here, but it can't just be "this is a new task". We have methods from decision theory that have been designed for a wide range of decision tasks, and its incumbent upon the authors to demonstrate why those existing tools do not fit the task in front of them. [1] https://www.jmlr.org/papers/volume24/22-1136/22-1136.pdf [2] https://onlinelibrary.wiley.com/doi/abs/10.1002/mcda.313 [3] https://www.sciencedirect.com/science/article/abs/pii/S0377221715008048 Technical Quality: 3 Clarity: 3 Questions for Authors: see above Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 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 the very helpful comments. I could quibble with some of the setup, which is a bit confusing to me: design factors being properties of the context rather than of the alternative, for example, is kind of odd, but I don't think this is very important. We follow a factorial design, in which the factors define the context under which an experiment happens [1, ch.5]. As in the standard setting, varying the level of a factor causes a change in the observed response (in our case, rankings of the alternatives). To make it clearer in the paper, we have rewritten lines 97--98 as: "As in the standard factorial setting [1, ch.5], an experimental factor is anything that might affect the result of an experiment." This procedure is an empirical version of power analysis where the null distribution is not known but simulated and extrapolated. [...] It's entirely possible. We would be grateful if you could clarify the following open points. You mention that deriving the necessary sample size is straightforward under certain assumptions, which we do not find obvious for our case. Could you please provide us with more information and/or references on how to derive said sample size? Moreover, even if this was indeed straightforward, we are unsure whether the assumptions hold in our case. In particular, we are not aware of any method to derive the distribution of the MMD under the alternative hypothesis that the distributions differ. Thank you for hinting us at the CLT for the MMD. This results could indeed prove useful in the future to derive an asymptotic theory of generalizability. The methodology we propose in this paper, however, has to work on small sample sizes, as the typical number of levels of allowed-to-vary factors is usually limited in real-world benchmark studies. For instance, [2] "only" consider 50 datasets, implying that we can only compute generalizability up to $n=25$ (algorithm in A.3.3). In light of this, we are not convinced whether an asymptotic theory, although appealing in principle, would be useful in practice. We have added the following sentence to the future work (line 333): "Finally, one could investigate applying the central limit theorem for MMD~[1] to derive an asymptotic theory of generalizability." This is an important question [...] There's no similarly sophisticated discussion of error properties in this paper, which would be reasonable if this were truly the first paper in its vein, but I don't think that's the case. Could you please clarify what you mean by suboptimal in this context, and what kind of error properties you deem are missing from our paper? Further, it's not clear to me why these similarities between rankings should be the target of inference. [...] It's entirely possible that there's a contribution here, but it can't just be "this is a new task". We have methods from decision theory that have been designed for a wide range of decision tasks, and its incumbent upon the authors to demonstrate why those existing tools do not fit the task in front of them. We agree that there are many methods for testing whether A is better than B on a sample of results. For instance, there exist posthoc tests such as Nemenyi and Conover-Iman or consensus ranking aggregation (of which Kemeny-Young aggregation is one of many possibilities). However, these methodologies do not directly translate to generalizability, as we now discuss. First, to the best of our knowledge, these tests work within a given sample of results. In other terms, they are applied to the experimental results to see how significantly the hypothesis holds within that sample. Similarly, consensus ranking aggregation is commonly used to draw some conclusion from the results. By design, these methods do not take into account that varying the experimental conditions can lead to very different results --- which is what the concept of generalizability captures. Measuring generalizability (line 163) requires comparing the results between any two samples, to understand how strongly different choices of experimental factors influence the result. Regardless of how significantly the hypothesis "A is better than B" holds within any of the samples involved. A strong example of this can be found in [2], where they report that previous studies on encoders reached very different and contrasting conclusions. To the best of our knowledge, we propose the first principled approach to quantify generalizability. Nonetheless, investigating the non-trivial relation between generalizability, significance of tests, and consensus ranking aggregation is an interesting direction for future work. We have thus added this point in our conclusions. Second, "A is better than B" is not the only goal a study could have, especially if the study is a large scale evaluation with more alternatives . As you acknowledge in your comment, a decision theorist would define an appropriate similarity metric based on the research question. Our framework provides this flexibility in defining research questions not limited to "A is better than B". See Section 4.1 where we discuss in detail how an experimenter can incorporate a given research question in our framework. To show that our framework also supports the "A is better than B" goal, we added the following sentence on line 205: "Additionally, one can use it [the Mallows kernel] to test whether an alternative $a_1$ is consistently better than another alternative $a_2$ by restricting the rankings to $a_1$ and $a_2$ and using the Mallows kernel." --- [1] Montgomery, Douglas C. Design and analysis of experiments. John wiley & sons, 2017. [2] Matteucci, Federico, Vadim Arzamasov, and Klemens Böhm. "A benchmark of categorical encoders for binary classification." Advances in Neural Information Processing Systems 36 (2024). --- Rebuttal Comment 1.1: Comment: I thank the authors for their engagement. To clarify a few points: > You mention that deriving the necessary sample size is straightforward under certain assumptions, which we do not find obvious for our case. Could you please provide us with more information and/or references on how to derive said sample size? > Could you please clarify what you mean by suboptimal in this context, and what kind of error properties you deem are missing from our paper? Both of these relate to the Neyman-Peason Lemma. The suboptimality in question is the fact that NPL shows that the likelihood ratio statistic is (subject to certain restrictions) the uniformly most powerful test. Other tests, meanwhile, would be suboptimal according to their Type I and II error properties. Under standard a standard NP framework, power analysis follows straightforwardly once distributions of test statistics are known. In some cases it may be possible to express these quantities directly (e.g. if you look under the hood of power.t.test in R or a similar function), but the more general approach is to simulate from the relevant distributions. I'm not claiming that the approach you have proposed is not useful, but rather that the mathematical scaffolding you've created for it doesn't seem strictly necessary, since simulating these distributions is a common part of existing statistical practice, and this is associated with reliable theory justifying it. This theory would be in standard theoretical statistical texts like [1] or [2]. The central question I still don't understand the answer to is why the NP framework is not sufficient for your goals? > First, to the best of our knowledge, these tests work within a given sample of results. This is not an accurate description of standard NP statistical inference. Indeed, drawing from the original [3], the authors say "observed facts are described as 'samples,' and the hypotheses concern the 'populations' from which the samples have been drawn". As far as I can tell, this accords with your "generalizability" goal: you want to know about the "population" of _all_ datasets rather than only the specific sample of datasets on which evaluations were performed. [1] Lehmann, Erich 1959 Testing Statistical Hypotheses [2] Casella and Berger 1990 Statistical Inference [3] Neyman Jerzy and Pearson Egon Sharpe 1933IX. On the problem of the most efficient tests of statistical hypotheses Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character 231: 289–337 http://doi.org/10.1098/rsta.1933.0009 --- Reply to Comment 1.1.1: Comment: We thank again the reviewer for their engagement and their clarifying comment. For the sake of clarity, please allow us to state again the setting we are dealing with. 1. We have observed a sample of results --- as mentioned in the global rebuttal, not necessarily of rankings. 2. We want to compute the generalizability of our results, i.e., the probability that repeating the experiments under other experimental conditions (e.g., the datasets) does not change the distribution of results "too much". Among other, we want to find the minimum sample size yielding generalizable results, $n^$. 3. As we do not observe other samples, we infer $n^$ from smaller subsamples. In step 2, we use a statistical distance (the MMD) to compare the distributions of the samples. Incidentally, the MMD can and has been used for non-parametric two-sample testing by deriving appropriate distribution-free upper bounds [1], which we use to prove Proposition 4.2. The test proved, however, too conservative to be useful for our use-case, as mentioned in Appendix A.3.2. > The central question I still don't understand the answer to is why the NP framework is not sufficient for your goals? We can now discuss your comment, based mainly on the sources you kindly provided. First and foremost, the NP framework cannot be directly applied to our use case. As we understand it, the likelihood ratio test can only test whether a sample is more likely to follow a certain candidate distribution rather than another one. Moreover, these two distributions are usually assumed to come from the same parametrized family. In our scenario, however, we do not have any information on the underlying distribution. Therefore, we do not have any candidate distributions, and we can only compare two samples and test whether they come from the same distribution with two-sample tests such as the MMD. We are not aware of any similar formulation of the NPL for two-sample testing. Second, the NP framework works with real-valued distributions, while experimental results are might not be real vectors. Although some variants might handle probability distributions on arbitrary sets, we are not aware of any such variant. Third, as we discuss and you acknowledge in your first comment, one needs to be able to account for the different goals a study could have, as the results might be generalizable wrt. one goal but not another. We hypothesize that any test flexible enough to account for these will necessarily not always be optimal in terms of type I and II errors. Indeed, if the goals are modeled with, let's say, different kernels, then all of the tests based on different kernels will have different rejection regions. In conclusion, although we recognize the importance of optimality of the tests involved and we will look into integrating our methodology within the NP framework, we (1) do not see any straight-forward way to do so, and (2) if it is possible, the loss of flexibility might hinder the flexibility and practical usefulness of our methodology. We will make the points above clearer in the paper. --- [1] Gretton, Arthur, et al. "A kernel two-sample test." The Journal of Machine Learning Research 13.1 (2012): 723-773.	Rebuttal 1: Rebuttal: We sincerely thank all reviewers for their work. We have noticed that in some cases there has been misunderstanding of our contribution. Therefore, we would like to address these points here and add the corresponding sections to the manuscript. ## The experimental pipeline and the role of generalizability Here we describe the experimental pipeline, some of the choices made by the experimenter, and the gap that our methodology fills. Consider an algorithm benchmark study. First, the experimenter defines the scope of the study, which comprises the tested algorithms (e.g., binary classifiers), the experimental conditions (e.g., datasets for binary classification), and the hypothesis under scrutiny (e.g., one classifier is consistently the best one). Second, the experimenter runs the planned experiments to evaluate the algorithms under the different conditions, obtaining a sample of results. Third, the experimenter analyzes the sample of results, ranks the alternatives (if necessary), and determines whether their hypothesis is validated. Finally, the experimenter tries to assess 1. whether their results are generalizable, i.e., whether another study on similar conditions would obtain similar results, and 2. whether additional experiments are needed. Despite the relevance of this final step (cf. Section 2), there is still no established methodology to tackle it. Our methodology addresses specifically the last step of the pipeline; thus, it can be used independently of the choices made in the previous steps. In particular, it leaves the experimenter free to choose, according to best practices, how to evaluate the algorithms and how to obtain the rankings from the results. For example, one can use an out-of-sample evaluation (e.g., train/test split) for supervised classifiers, but not for unsupervised methods. Moreover, one can rank the algorithms according to their average performance, to the result of pairwise comparisons with corrected t-tests [1, 2], or taking the magnitude into account with methods from Bayesian statistics [3]. ## Why rankings? We chose rankings for the following reasons: 1. They are already used for non-parametric tests such as Friedman, Nemenyi, and Conover-Iman [1, 4]. 2. They do not suffer from experimental-condition-fixed effects, such as a chess position being inherently easier to solve than another one. There are multiple ways of adapting raw performances to handle these (for instance, by standardizing the performance of alternatives for a fixed experimental condition). The lack of a preferred procedure is an open problem closely related to obtaining a consensus ranking from the results [5, 6]. 3. One can define kernels for rankings that model the goals of a study, as discussed in Section 4.1. Our framework, relying on the MMD to compare the results of studies, does not need the results to be rankings. Instead, one can model the experimental results to be elements of an arbitrary probability space $X$, provided that 1. one can define a kernel on $X$, and 2. the kernel models the goals of the study. For instance, one can use the raw performance of the algorithms as the result and the Gaussian kernel to compare them. In this case, however, it is unclear what the goal of the corresponding study would be. --- [1] Demšar, Janez. "Statistical comparisons of classifiers over multiple data sets." The Journal of Machine learning research 7 (2006): 1-30. [2] Nadeau, Claude, and Yoshua Bengio. "Inference for the generalization error." Advances in neural information processing systems 12 (1999). [3] Benavoli, Alessio, et al. "Time for a change: a tutorial for comparing multiple classifiers through Bayesian analysis." Journal of Machine Learning Research 18.77 (2017): 1-36. [4] Conover, William J., and Ronald L. Iman. "Analysis of covariance using the rank transformation." Biometrics (1982): 715-724. [5] Matteucci, Federico, Vadim Arzamasov, and Klemens Böhm. "A benchmark of categorical encoders for binary classification." Advances in Neural Information Processing Systems 36 (2024). [6] Nießl, Christina, et al. "Over‐optimism in benchmark studies and the multiplicity of design and analysis options when interpreting their results." Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery 12.2 (2022): e1441. Pdf: /pdf/193bb4d9e3a8d5b451a7358ad94a5f4c29b51562.pdf	NeurIPS_2024_submissions_huggingface	2,024	Summary: The authors propose a new mathematical framework and a corresponding new algorithm to evaluate the generalizability of published experimental studies, by adapting Montgomery's classification of experimental factors [44]. They demonstrate the efficacy of this framework in evaluating the generalizability of two popular published experimental studies. Strengths: 1. The paper appears to be theoretical strong. It goes beyond the standard notion of reproducibility of an experimental study and comes up a definition of generalizability of an experimental study. Morever, Proposition 4.2 provides a theoretical result on the sample size $n$ necessary to obtained a desired generalizability $\alpha^$ for a desired similarity $\epsilon^$, and the authors also provide an algorithm (A.3.3) to compute this sample size. Since the similarity $\epsilon^$ is hard to specify, they make it a function of the kernelized distance between rankings $\delta^$. 2. The empirical evaluation in Fig. 2 and Fig. 3, on the categorical encoder comparison from [41] or the BIG-bench framework for LLM comparison from [55], respectively, demonstrates the practical utility of the proposed approach in determining sample sizes to guarantee generalizability. Weaknesses: 1. The clarity in the writing can be significantly improved: 1.A. Symbols are used before defining them, typos exist, and symbols are not used consistently: 1.A.a. On line 118, the symbol $\mathcal{R}_{n_a}$ is mentioned, but the relation of this symbol to the ranking on alternatives only becomes clear later in Definition 3.1. 1.A.b. The Section number is missing on line 111. 1.A.c. The symbol $m$, is defined as the number of shots, on line 115, whereas line 114 uses the symbol $n$ rather than $m$. Moreover, on line 88, $n$ is defined as the number of shots. 1.A.d. In contrast to 1.A.c, in eq. (1), after line 170, the symbol $n$ is now used without providing a definition. It now appears to be the size of any study, in a general definition, rather than the number of shots, as defined on line 88. 1.A.e. On Sec. 5.3, line 315, $N$ is defined as the number of preliminary experiments, whereas on line 154, it is defined as the size of the sample of valid experimental conditions. Do these mean the same thing ? 1.B. Sec. 3.1 defines a ranking of alternatives as the primary result of an experimental study. However, the effect size, i.e., the magnitude and sign of the difference between two alternatives, can be important in certain experiments. The MMD kernel, used in Sec. 4.2, actually allows measuring this effect size, as discussed in [27], but the limitations imposed by the usage of this MMD kernel within the author's generalizability framework, are not clear despite the somewhat cryptic discussion in Sec. 6. 2. The experimental evaluation is limited to a comparison of ranking differences between alternatives, and does not include a measurement of the practical differences between alternatives, or the significance of these differences. Technical Quality: 3 Clarity: 2 Questions for Authors: 1. The experimental evaluation seems to depend strongly on the choice of kernel, and its parameters. In Sec. 5.1, (g2), or Sec. 5.2, (g2), for example, what would happen if the Jaccard kernel hyper-parameter $k$ were varied ? 2. Please refer to the question under weakness 1.A.e. Confidence: 4 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: Please refer to the potential limitation underlying weakness #2. Is it possible to quantify the magnitude of differences between alternatives using the generalizability framework provided by the authors ? The authors mention this limitation in Sec. 6, but it is not clear why the MMD kernel cannot quantify magnitude of differences. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for noticing these inconsistencies, we did the necessary fixes as follows: - 1.A.a. On line 118, the symbol Rna is mentioned, but the relation of this symbol to the ranking on alternatives only becomes clear later in Definition 3.1. - We moved definition 3.1 to line 116. - 1.A.b. The Section number is missing on line 111. - We fixed the reference to Section 3.2. - 1.A.c. The symbol m is defined as the number of shots, on line 115, whereas line 114 uses the symbol n rather than m. Moreover, on line 88, n is defined as the number of shots. - 1.A.d. In contrast to 1.A.c, in eq. (1), after line 170, the symbol n is now used without providing a definition. It now appears to be the size of any study, in a general definition, rather than the number of shots, as defined on line 88. - We replaced $n$ with $m$ on lines 88 and 114. - 1.A.e. On Sec. 5.3, line 315, N is defined as the number of preliminary experiments, whereas on line 154, it is defined as the size of the sample of valid experimental conditions. Do these mean the same thing ? - These numbers do indeed refer to the same concept, as we treat the preliminary experiments (line 315) as an empirical study. The details are in our answer to Question 2. - 1.B. Sec. 3.1 defines a ranking of alternatives as the primary result of an experimental study. However, the effect size, i.e., the magnitude and sign of the difference between two alternatives, can be important in certain experiments. The MMD kernel, used in Sec. 4.2, actually allows measuring this effect size, as discussed in [27], but the limitations imposed by the usage of this MMD kernel within the author's generalizability framework, are not clear despite the somewhat cryptic discussion in Sec. 6. - 2. The experimental evaluation is limited to a comparison of ranking differences between alternatives, and does not include a measurement of the practical differences between alternatives, or the significance of these differences. - 1.B, 2 Magnitude, sign, statistical significance, and related concepts can be incorporated when defining the rankings, for instance with statistical tests or a "rope" [1]. We include more details in the global rebuttal. Please, however, note that the MMD is not a kernel, but a distance between distributions. To make this clearer, we replaced line 217 with "First, the MMD takes into consideration the goal of a study, as it requires a kernel --- such as the ones described in Section 4.1." ## Questions The experimental evaluation seems to depend strongly on the choice of kernel, and its parameters. In Sec. 5.1, (g2), or Sec. 5.2, (g2), for example, what would happen if the Jaccard kernel hyper-parameter k were varied? For a given experimental study, some claims are generalizable whereas others are not. The exact claim defines the kernel as well as its parameters. For instance, one might claim that "the top-performing $k$ alternatives are consistently the same" and thus use $\kappa_j^k$. Figure 1 in the attached pdf shows how generalizability depends on $k$. As expected, perfect generalizability is achieved with $k$=32, because 32 is the total number of alternatives. To summarize, this dependence on the kernel and its parameters refers to one of our contributions and highlights the universality of our framework, which allows for testing the generalizability of a variety of claims. Please refer to the question under weakness 1.A.e. The two $N$'s do indeed refer to the same concept, as a preliminary study is an empirical study. On line 154, $N$ is the size of a sample of valid experimental conditions and, equivalently, the size of an empirical study performed on that sample of conditions (line 155). The second $N$, on line 315, refers to the size of a preliminary study, performed on a (supposed) random sample of valid experimental conditions. Such a preliminary study satisfies the definition of empirical study (line 155). Hence, in both cases, we use $N$ to refer to the size of an empirical study. To make it clearer, we added the following to line 312: "This section evaluates the influence of the number of preliminary experiments $N$ on $n^*$. The preliminary experiments are an empirical study of size $N$." --- [1] Benavoli, Alessio, et al. "Time for a change: a tutorial for comparing multiple classifiers through Bayesian analysis." Journal of Machine Learning Research 18.77 (2017): 1-36. --- Rebuttal Comment 1.1: Title: Thank you ! Comment: I wish to thank the authors for all the responses and clarifications (especially regarding my incorrect usage of the term "MMD kernel") in their rebuttal, and the proposed related modifications to the paper. I have also read the rebuttals to other reviewers. My positive rating (5) on this paper remains unchanged.	null	null	null	null	null	null
Mind the Gap: A Causal Perspective on Bias Amplification in Prediction & Decision-Making	Accept (poster)	Summary: This paper studies the impact of downstream thresholding operations on continuous (and possibly fair) prediction scores. The paper argues that inappropriate thresholding can amplify or ameliorate the disparity in predictive performance across groups defined by the protected attribute. Using a causal framework, the paper provides a methodology to separate the disparities in the original predictive score from the disparities introduced due to thresholding. Strengths: 1. One of the motivations of the paper is to understand the downstream utility of fair predictions. In that regard, I appreciate the more practical focus on investigating the barriers faced by popular fairness during real-world implementations.  2. The disentanglement of different kinds of business necessity requirements seems interesting by itself and allows for potentially meaningful connections between legal and empirical notions of fairness (although I do have some questions on it that are noted later). Weaknesses: 1. The writing and presentation are often hard to follow and various parts of the analysis seem under-explained, which makes evaluating the paper’s claims difficult. For example, Definition 1 defines $M$ using a generic $t$-value, whereas the proof of Theorem 1 in the appendix, if I understand correctly, directly uses $t=1/2$. If the theorem is based on a specific $t$ value, then that should be made clear in the theorem and the surrounding text in the main body.\   Similarly, when discussing “strong business necessity”, there’s very little explanation of what it means for a causal pathway to be “unconstrained”. With a lack of a clear explanation of this concept, I am not totally sure about the difference between weak and strong BN.  2. Related to thresholding, the paper never goes into the details of how a certain threshold is chosen. Again, seems like Theorem 1’s proof and Example 1 use $t=1/2$, but that is not the only possible choice of threshold that can be used in practice. In fact, if all the claims in the paper are based on the explicit assumption that $t=1/2$, then I don’t see the claims being generalizable to other threshold classifiers and also not applicable to various kinds of classifiers used in practice.   3. Additionally, there is a wide post-processing fairness literature that essentially proposes methods to choose group-specific thresholds so that the biases from training data and prediction scores do not propagate to the final binary predictions (e.g., Hardt et al. 2016 and related papers). I would strongly recommend an expanded discussion on this related work, especially comparing the proposed approach to other prior fairness works on choosing appropriate thresholds to guarantee outcome fairness.  4. Minor points and typos.\ a. Potential missing word in Line 73 around “…ramifications more”.\ b. In Example 1, seems like the outcome should be 0 and 1, and not $y_0$ and $y_1$.\ c. Line 138, function $pa$ is not defined. I am assuming it means “parent variable” but needs to be properly introduced and described. Technical Quality: 2 Clarity: 1 Questions for Authors: The main questions I have are related to the above points. 1. Does the paper primarily focus on $t=1/2$ or are the results applicable for other threshold values as well? 2. Do the issues associated with margin complement persist even when after using post-processing approaches to achieve outcome fairness (like those introduced in Hardt et al. 2016)? 3. What’s meant by a causal pathway being “unconstrained” when defining strong BN? Confidence: 2 Soundness: 2 Presentation: 1 Contribution: 2 Limitations: Some limitations are acknowledged but the paper could do a better job of expanding on the limitations related to the full knowledge of structural causal models. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Authors: We thank the reviewer for the time spent on our submission. We would like to state clearly that the results of the paper are not at all constrained to the $t = 1/2$ setting and work for any value of $t$. We therefore hope the reviewer can reconsider the contributions in light of this. (W1: threshold $t$ value) Thank you for giving us the opportunity to clarify this point. The proof of Theorem 1 was stated for $t=1/2$, but $t=1/2$ can be replaced with an arbitrary threshold $t$, which is now done in the manuscript. In other words, the method can be used for classifiers with arbitrary thresholds. Here, the reviewer is correctly noting that the notion of margin complement changes. We are no longer computing the margin complement with respect to 1/2, but with respect to an arbitrary threshold t. However, the proof remains the same for the arbitrary threshold, and the interpretation of the decomposition remains very similar. (W2: Limited generality) Considering (W1) above, we note that the concern raised by the reviewer is not a limitation of the proposed method and the method can be used in general. Furthermore, we also note that our goal is not to suggest how to choose a specific threshold, but to provide a diagnostic tool for an arbitrary choice of the threshold. Please also note that in the experimental section, in the MIMIC-IV example, we are using a threshold different from 1/2. In particular, we are using a threshold that is the median of the predicted probabilities, which is about 0.15 in the data. Still, the analysis yields important insights even in this case, highlighting the generality of the method in practice. We hope that this addresses the key concern of the reviewer. (W3: post-processing methods) Thanks for asking this, this is a really good question. First, we wish to note that (Hardt et. al., 2016) are attempting to provide a post-processing method to satisfy equality of odds (i.e., constructing fair predictions). In our work, we are trying to offer a diagnostic tool, that quantifies the impact of thresholding on the causal fairness measures. In other words, we are solving a slightly different problem (which would be called bias detection/quantification). Having said that, the reviewer raises an excellent point. Our analysis is based on classifiers with a single threshold, whereas (Hardt et. al., 2016) and many other methods use two thresholds, one for each group. In the paper, we now added an appendix that handles the following question: is it possible to adapt the diagnostic tool in this paper to a thresholded classifier in which the threshold $t$ depends on $X$, i.e., $t_x$? The answer to this is yes! Please refer to point (P2) of the main response for an updated decomposition of the TV measure in case of group-specific thresholds. In this new decomposition, we see that group-specific thresholds change only the direct effect of $X$ on the predictor while the indirect and spurious effects remain invariant. There is a new explicit term that quantifies the direct effect of using a group-specific threshold (see (P2) of main response for the exact expression). We also remark that this gives the first result establishing that, causally, post-processing methods with group-specific thresholds change only the direct effect of $X$ on the predictor, and gives an explicit expression for this direct effect. We think this makes the paper substantially stronger, and thank the reviewer for pointing us in the right direction! Our method can now handle the post-processing approach in (Hardt et. al, 2016) and many other similar methods in the literature. (W4: typos) Thanks a lot for catching this. We have now fixed all of them! (Q1: t=1/2 or not?) The paper can handle an arbitrary threshold $t$, please see responses (W1), (W2). (Q2: post-processing relationship) Please see (W3) for an answer. (Q3: Unconstrained in Strong BN) Thanks for asking this, we have now clarified it in the text accordingly. By unconstrained we mean that the causal effect $x\\text{-CE}(m)$ can take an arbitrary value $c$, instead of being constrained to $0$ like in the weak BN setting. We hope this clarification in the writing helps address the question. Please let us know! --- Rebuttal Comment 1.1: Comment: Thanks for the detailed response and clarifications! I am satisfied with the response on the ability to handle arbitrary thresholds and will increase my score. I also appreciate the response on group-specific thresholds, but agree with Reviewer bCLY that the discussion on prior related work needs to be expanded and more thorough. --- Reply to Comment 1.1.1: Title: Thank you for constructive feedback Comment: We wish to thank the reviewer for the opportunity to engage and provide important clarifications on the manuscript. We also appreciate you sharing constructive suggestions, which we took very seriously, and which helped to improve our manuscript and led us to a new result. Related to the discussion on previous literature, as we mentioned to Reviewer bCLY, we already revised the discussion of related literature in fair decision-making. We added the suggested references within this context, and expanded the discussion on related works accordingly. We once again thank the reviewer for the constructive review process.	Summary: The paper studies how much thresholding a predictor affects the disparity in the decisions according to sensitive attributes and formalizes new notions of business necessity based on the causal graph of features, outcome and prediction function. Strengths: - Understanding the amplification of bias along the machine learning and decision making pipeline is an important topic. - There are some very interesting ideas that could have benefited from better execution in the paper. Having some technical definition of business necessity makes claims of BN testable in the real world, and could have policy impact. - A relatively comprehensive attempt to study the topic. Results include decomposition, identification, with proofs, as well as examples/experiments. With some significant improvements, it will be a nice contribution. Weaknesses: - Technical writing needs improvement and some key definitions are clearly wrong. (1) Looking at Definition 3, weak BN implies strong BN according to this definition. Why is the condition for weak BN stronger than for strong BN? I was also unable to make sense of the rest of this definition, e.g. part 1. (2) some quantities/notation are not properly defined. E.g. in definition 3, what are s, x'', m, x', y, and where are they defined? There should be no reasonable doubt about what these letters refer to. Same comment holds for Theorem 1 (what is m, s?), Theorem 2 and corollary 2. (3) Please use the notation :=, or similar, to denote definitional equivalence (rather than an equality _claim_). - Theorem 1 and 2 appear to be basic, as far as I can tell from the definitions and the proof. I'm not sure why the decomposition, which follows from definition, needs to be presented as a main theorem. The main novelty appears to be the definition. If this is the case, you might consider making this clear to the reader instead of presenting something as more complex that it needs to be. If this is not the case, is there a way you can make the technical contribution clearer in the proof and writing? - Example 1 is not a reasonable example. In this case (where you ONLY have gender on which to make a definition, and there is practically no signal from it), there would be no reason to use a predictor at all. -Related work: The discussion of closely related work is sparse. The connection with the causal fairness literature is relegated to a few sentences in the introduction, and there is no meaningful discussion of the contributions of prior work. Please elaborate on the connection between your definitions of business need and causal fairness? Lack of citations and discussion of prior work. The paper states "Most of the literature in fair machine learning 4 focuses on defining and achieving fairness criteria in the context of prediction, 5 while not explicitly focusing on how these predictions may be used later on in 6 the pipeline." This is an inaccurate representation of the literature. Even one of the cited works Chouldechoulva (2016) has an entire section on how scores impact decisions. Minimizing prior work on fairness in decision making is at best unhelpful to the reader, and at worst, misinforms. For prior work on fairness in decision making (indeed, how predictions are used later in the pipeline), also see the following and the cited works within: Liu, L. T., Dean, S., Rolf, E., Simchowitz, M., & Hardt, M. (2018, July). Delayed impact of fair machine learning. In International Conference on Machine Learning (pp. 3150-3158). PMLR. Chouldechova, Alexandra, and Aaron Roth. "The frontiers of fairness in machine learning." arXiv preprint arXiv:1810.08810 (2018). Dwork, Cynthia, Christina Ilvento, and Meena Jagadeesan. "Individual fairness in pipelines." arXiv preprint arXiv:2004.05167 (2020). Technical Quality: 2 Clarity: 2 Questions for Authors: 1. What is the key technical contribution in Theorem 1 and 2, other than the novelty of the definitions (which allows you to write TV in a new, "human interpretable" way)? 2. What is the connection between your definitions of business need and counterfactual fairness (e.g. Kusner at al 2017)? 3. Please explain the corrected version of Definition 3 and what is the intended use case for each of the three definitions? 4. What is the potential negative societal impact of using the weak and strong business need definitions in a regulatory context? Confidence: 3 Soundness: 2 Presentation: 2 Contribution: 3 Limitations: Incompletely addressed impact of weak and strong business need definitions. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Authors: We thank the reviewer for the detailed review. We would like to draw the attention of the reviewer to some misunderstandings. The tone of the review seems much harsher than what we are used to in a venue such as NeurIPS and also how we perform our own reviews, always very respectfully. For instance, calling a definition “clearly wrong”, whereas the definition is correct, calling a theorem basic, saying that an example is not reasonable, comes across as harsh and discouraging. Even if there is a suspected mistake, it may be better to point it out politely, since the authors (including us) are always trying their best when writing. Thus, we hope that the reviewer can reconsider the assessment of the paper based on our detailed response below, especially because the reviewer seems to appreciate some genuine novelty in the paper, and we believe the response below clarifies the existing misunderstandings. (W1: Technical writing) Definition 3 is correct and “Weak business necessity” is indeed a special case of “Strong business necessity”. The concept of BN allows the predictor designer more flexibility in designing the predictor (fewer constraints). Therefore, strong BN (or stronger/higher flexibility) is indeed a more broad concept than weak BN (or weak/lower flexibility). More concretely, a predictor designer given the freedom to choose any arbitrary value for the $x-CE(m)$ effect, could choose to set this value to $0$ (and thus satisfy the weak BN requirement). However, under strong BN, they do not have to do so necessarily. We hope this clarifies a core confusion. Furthermore, we would like to clarify some of the notation. Indeed, in Definition 3, we now explicitly state that $x, x’$ are two distinct values of $X$, whereas $x^{’’}$ is an arbitrary value of $X$. We thank the reviewer for pointing this shortcoming out, which is now corrected. Regarding $y, m, s$ notation: here, we are following the common notation in the graphical approach to causality. The small letters indicate the random variable which is integrated out, in line with the previous works on causal fairness and the causality textbook (Pearl, 2000). (W2: Theorems are “basic”) We do not see the mentioned theorems as basic, and view this as a harsh assessment. While the definitions are important, it is apriori not clear that these definitions interact in such a nice & non-parametric way with the decomposition of the TV measure (Theorem 1). Furthermore, Theorem 2 requires replacing the true outcome $Y$ with $S$ in the causal diagram. This, even conceptually, is a non-trivial step that has not been done before, and requires specific causal assumptions (such as the SFM), and may not always hold. We invite the reviewer to check the counterfactual graph in Figure 5(b), and then re-assess whether the claim is trivial. Thus, we believe the results are non-trivial. Furthermore, we also do not think we made any attempt to present the results as more complex than they are. The statements and proofs are stated as clearly and concisely as possible. To draw a parallel with some well-known results, think about the Pearl’s decomposition of the total effect (TE) into natural direct and indirect effects (NDE, NIE). While this decomposition is a consequence of the definitions of NDE, NIE, it is by no means trivial, and required almost a decade to appear after the first notions of direct and indirect effects were considered. (W3: Example 1 is not reasonable) Example 1 is used to illustrate the core concept of the paper in the simplest possible, two-variable case. We now explicitly state this in the introduction. A data scientist who has access to just these two variables (and perhaps does not even know the meaning of $X$), may simply implement a predictor without checking the predictive value, right? Once again, we are not trying to argue that the example reflects real-world practice (now stated explicitly before the example), but rather illustrate the concepts in the simplest form. Please see the Experiments section for more realistic, practical examples. (W4: Related work) Thanks for the suggested references. We have now expanded the part on related work, and reference the works you have shared, referring to “notable exceptions investigating the decision-making aspects of fairness”. However, we do believe it is true that most of the literature looks at prediction, which is also noted in the second reference that you shared. To be clear, our goal is certainly not to diminish any of the contributions in this area, but rather to argue that more works are needed in this direction. We hope that the addition of the suggested references, and the better placement of the work in a broader context helps address this concern. Please let us know. --- (Q1: Key technical contribution) Please see (W2) for a detailed response. (Q2: Connection with counterfactual fairness) This is a great question! It has been shown in the causal fairness literature that counterfactual fairness is simply a notion that constrains the _total (causal) effect)_ of $X$ on $Y$. When doing so, counterfactual fairness does not distinguish between, for instance, direct and indirect effects. As a consequence, counterfactual fairness inherently does not have the flexibility to model business necessity requirements, since it considers a single pathway (total causal effect). We hope this answers the question. (Q3: Definition 3) Please check the response (W1), the definition is correct. Regarding the intended use cases, please see details in global review response (P3). (Q4: Societal impact) This is another great question. In terms of negative consequences, one may argue that imposing weak BN or no BN constraints may harm the utility of the classifier, which may cause harm in specific applications. However, this represents a trade-off between utility and fairness, which is acknowledged in the literature. We now added an explicit discussion on this in the paper. --- Rebuttal 2: Comment: Dear Reviewer bCLY, In the spirit of the constructive discussion period we usually have at NeurIPS, we would like to double-check if there are any issues that were not sufficiently addressed in our rebuttal. We would be happy to engage and elaborate further on any questions that you may have. Thank you again for the time spent reading our work, Authors of paper #3972	Summary: The paper investigates how thresholding the score of a predictive model as a decision rule influences the fairness of the final decisions. In particular, the authors consider binary decisions or predictions of a true binary outcome in presence of a sensitive binary attribute. In that context, the authors show that the fairness measure of the total variation depends on the direct, indirect and spurious effects due to the true outcome and due the margin complement; a measure introduced by the authors expressing the difference between the predicted score and the final prediction after thresholding. Under this new measure, the authors also introduce the notions of weak and strong business necessity (BN); under weak BN, disparities due to the true outcome are considered fair, while disparities due to the thresholding rule are not tolerated—zero marginal complement; under weak BN disparities due to both the outcome and the thresholding rule are tolerated. Strengths: The paper is well organized, has a clear structure and seem appropriately placed into contemporary literature. The technical contributions appear strong, well motivated and clearly presented. The examples do help the reader to understand the intuition and follow the technical results. The problem of potential bias amplification due to applying a thresholding rule on predicted scores appears quite interesting and seems directly relevant and applicable in high stakes domains as the authors demonstrate through the real world data examples. Weaknesses: The abstract appears somewhat convoluted and confusing providing low level technical details, especially in lines 12-21. It might have been more helpful to explain the contribution at a higher level, while focusing more on the intuition. Technical Quality: 3 Clarity: 2 Questions for Authors: The causal decomposition of the TV measure are on the optimal 0/1 predictor. How this decomposition would change for a sub-optimal (e.g. near optimal) predictor? Confidence: 2 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: The authors very briefly refer to the limitations due to the assumptions on the standard fairness model. It would be useful perhaps to elaborate concretely on some of these assumptions; e.g., on how the notion of the margin complement could be extended assuming that the protected attribute takes values in a discrete set or a continuous range. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Authors: We thank the reviewer for the time and effort in reviewing our paper. We are quite glad that the reviewer appreciated the ideas appearing in the paper, and considered the technical contributions strong, well motivated, and clearly presented. Below we address the main questions/concerns. (W1: Abstract) Thank you for this suggestion. Your point is indeed valid, it may be quite difficult to understand some of the technical detail that is mentioned in the abstract. This is now updated, and we provide a more high-level explanation of the developments. (Q1: Suboptimal predictors) This is a great question, and we thank the reviewer for raising this. In fact, this leads to an important result, which we add to the appendix (see also (P1) of the general response). Firstly, we note that Theorem 1 holds for any thresholded predictor $\tilde Y$ based on a score $\tilde S$. In other words, Theorem 1 is not true just for the optimal 0/1 predictor. Crucially, however, Theorem 2 no longer holds for a suboptimal predictor. We can clearly see that if $\tilde S$ is suboptimal, $E[\tilde S] = E[Y]$ is not expected to hold, which means that the causal effects of $X$ on $\tilde S$ need not equal those of $X$ on $Y$. Having said that, the suboptimality of $\tilde S$ can be remedied in a very nice way. In Corollary 3, we have a two-way decomposition along each causal path with contributions: (i) coming from the true $Y$; (ii) coming from the margin complement $M$. When instead of the optimal $S$, we are thresholding a suboptimal $\tilde S$, this results in three-way decomposition along each path with contributions: (i) coming from the original $Y$, (ii) contribution of the suboptimality (difference along the causal path resulting from using $\tilde S$ instead of $S$), and (iii) contribution of $M$. We invite the reviewer to check this interesting result in (P1) of the main review response. Thanks once again for pointing us in the right direction! --- Rebuttal Comment 1.1: Comment: I would like to thank the authors for their reply that has sufficiently addressed my question. The authors should consider adding the discussion and results in (P1) in the revised version of their paper.	null	null	Rebuttal 1: Rebuttal: We thank the reviewers for their thoughtful reviews. We would like to mention three exciting updates to the paper that come as a result of some great questions from the reviewers. We believe these updates substantially improve the scope of the tools described in the paper: (P1) (Reviewer 1zLn, Q1) We now introduce a new causal decomposition, which is a variation of Theorem 1 and Corollary 3. This decomposition handles threshold predictors that are based on arbitrary prediction scores $\tilde S$ (and not just the optimal predictor). The new decomposition is as follows: $$ \\begin{align} \\text{TV}_{x_0, x_1}(\\tilde y) &= {x\\text{-DE}\_{x_0, x_1}(y\\mid x_0)} + (x\\text{-DE}\_{x_0, x_1}(\\tilde s\\mid x_0) - x\\text{-DE}\_{x_0, x_1}(s\\mid x_0)) + {x\\text{-DE}\_{x_0, x_1}(\\tilde m\\mid x_0)} \\\\ &\\quad - \\big( {x\\text{-IE}\_{x_1, x_0}(y\\mid x_0)} + (x\\text{-IE}\_{x_1, x_0}(\\tilde s \\mid x_0) - x\\text{-IE}\_{x_1, x_0}(s\\mid x_0)) + {x\\text{-IE}\_{x_1, x_0}(\\tilde m\\mid x_0)} \\big)\\\\ &\\quad- \\big( {x\\text{-SE}\_{x_1, x_0}(y)} + ({x\\text{-SE}\_{x_1, x_0}(s)} - {x\\text{-SE}\_{x_1, x_0}(\\tilde s)}) + {x\\text{-SE}\_{x_1, x_0}(m)} \\big). \\end{align} $$ As the expression indicates, there is an explicit term measuring how much the suboptimality of the prediction score $\tilde S$ contributes to the overall difference along the pathway. This is quantified by comparing the difference of the effect of $X$ on $\tilde S$ (the predictor being analyzed) vs. the effect of $X$ on $S$ (the optimal predictor). (P2) (Reviewer ZV8n, W3) The reviewer raised the question of handling post-processing methods that use separate thresholds for different groups. As it turns out, our tools can be adapted to this setting as well. Suppose that $\tilde Y$ is a predictor using group-specific thresholds. In particular, a new TV decomposition can be written as follows: $$ \\begin{align} \\text{TV}\_{x_0, x_1}(\\tilde y) &= x\\text{-DE}^{\\mathrm{GST}}\_{x_0, x_1}(\\tilde y \\mid x_0) + {x\\text{-DE}\_{x_0, x_1}(\\tilde s\\mid x_0)} + {x\\text{-DE}\_{x_0, x_1}(\\tilde m\\mid x_0)} \\\\ &\\quad - \\big( {x\\text{-IE}\_{x_1, x_0}(\\tilde s\\mid x_0)} + {x\\text{-IE}\_{x_1, x_0}(\\tilde m\\mid x_0)} \\big)\\\\ &\\quad- \\big( {x\\text{-SE}\_{x_1, x_0}(\\tilde s)} + {x\\text{-SE}\_{x_1, x_0}(\\tilde m)} \\big). \\end{align} $$ In this new decomposition, we see that group-specific thresholds change only the direct effect of $X$ on $\tilde Y$ while the indirect and spurious effects remain the same. The term $x\text{-DE}^{\mathrm{GST}}_{x_0, x_1}(\tilde y \mid x_0)$ is given by $$ \\begin{align} E [ \\mathbb{1} ( \\tilde S_{x_1, W_{x_0}} (u) \\geq t_{x_1} ) - \\mathbb{1} ( \tilde S_{x_1, W_{x_0}} (u) \\geq t_{x_0} ) \\mid X = x_0 ] \\end{align} $$ and measures the direct effect of using a group-specific threshold. With this new decomposition, a whole class of methods in the fair ML literature can be analyzed, including reject-option classification (Kamiran & Calders, 2012) and post-processing for equality of odds (Hardt et. al., 2016), among many other methods. (P3) (Reviewer bCLY, Q3 & Bounded Strong BN) The reviewer asked about different possible use cases for the notions of business necessity in Definition 3. Regarding the intended use cases, we provide the following explanations: (i) No BN is used for pathways that are considered discriminatory, and when we wish to have no causal effect transmitted along the pathway. (ii) Weak BN is used for cases where a pathway is important for the utility of the predictor designer, while there is still a need to avoid any kind of bias amplification compared to the current world. (iii) Strong BN is intended for cases where the utility of the decision-maker along the causal pathway is so important that we are willing to accept even amplification of disparities as a result of improving this utility. We remark that something in between Weak and Strong BN can be proposed, such as Bounded-Strong BN, where the contribution of the margin complement cannot be arbitrary but has to be bounded by some value $\alpha$. Therefore, we introduce the concept of $\alpha$-bounded Strong BN into the manuscript, which is discussed after Definition 3. We thank the reviewer for raising this question!	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Learning 3D Equivariant Implicit Function with Patch-Level Pose-Invariant Representation	Accept (poster)	Summary: The paper addresses 3D surface reconstruction from point clouds. It proposes a patchwise rotation equivariant neural network to map query points to their 3D displacement to the surface. The local rotation equivariance allows weight-sharing between similar patches at different orientation, and displacement fields have been shown to outperform occupancy and distance fields. Experiments show the method outperforms the baselines on several datasets. Strengths: S1) Using equivariant models to promote better use of model capacity is a great idea. Point clouds often present patches that are similar up to rotation so this design choice makes a lot of sense. S2) Results are strong and seems state-of-the-art on surface reconstruction from point clouds. Weaknesses: W1) As far as I understand, the ideas in the paper are not novel, so the contributions are around combining existing ideas. a) NVF [1] introduced the idea of using vector instead of distance fields, b) E-GraphONet [2] uses the idea of rotation-equivariant models for implicit surface representation, c) Zhao et al [3] uses the particular way of achieving equivariance through SVD on point sets. This might not be a deal-breaker since the results are good but more novel ideas would make for a stronger submission. W2) I think the PCA-based alignment is not very robust. While it is perfectly rotation equivariant given the exact same point cloud patch on a different orientation, I think in practice we would see slightly different patches so the alignment is not guaranteed. Moreover, the way the ambiguity on the axis orientation is resolved seems to rely on the furthest point position so a moving a single point slightly might change the orientation drastically. There are other methods that are use equivariant layers which seem more appropriate such as Vector-Neurons [4] and SE(3)-transformers [5], why weren't they considered? W3) Given W2 I found the design decision of using the PCA-alignment quite arbitrary. Given that the most related works are NVF and E-GraphONet, I believe a more natural choice would be to modify E-GraphONet to predict vector fields instead of occupancy fields, would it perform better than the proposed method? If the goal is to show that the PCA-alignment can be better than equivariant layers, a comparison against E-GraphONet on occupancy field prediction should have been performed. ## References: [1] Yang et al, "Neural Vector Fields: Implicit Representation by Explicit Learning", CVPR'23. [2] Chen et al, "3D Equivariant Graph Implicit Functions", ECCV'22. [3] Zhao, "Rotation invariant point cloud classification: where local geometry meets global topology.", 2021. [4] Deng et al, "Vector neurons: A general framework for so (3)-equivariant networks", ICCV'21. [5] Fuchs et al, "SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks", NeurIPS'20. Technical Quality: 3 Clarity: 3 Questions for Authors: Q1) Poisson surface reconstruction [6] is a classical method for surface reconstruction that is quite robust, how does the proposed method compare to it and similar follow-up works? ## Typos: L123: P -> P_i L48, L77: PEFI -> PEIF ## References: [6] Kazhdan et al, "Poisson Surface Reconstruction.", SGP'06. Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: The limitation regarding robustness of PCA-alignment should be addressed more clearly (see W2). Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thanks for the questions and comments. Please see the following responses. Q1: Novelty and relevant methods discussion. Thanks for this question. The major novelty of our approach is to learn the equivariant implicit vector fields for 3D reconstruction. Our novelty lies in the motivation and idea to design the patch-based intrinsic feature learning network. Our framework is inspired by the observation that local patches of 3D shapes repeatedly appear on 3D surfaces if removing the poses, we thus conduct pose normalization, and design the patch feature learning and learnable memory bank for learning the intrinsic patch geometry features. With them, the learned implicit vector fields are equivariant. These designs enable us to achieve state-of-the-art reconstruction results while being robust to the rotations of input points, as shown in the experiments. Compared with [1], our approach achieves equivariance for the vector field prediction. Compared with [2], our model is equivariant by proposing intrinsic patch geometric feature learning, instead of using vector neurons in [2]. Compared with [3], we tackle different tasks (classification vs. 3D reconstruction), and the model designs are significantly different. We will more clearly discuss the relation and novel contributions compared with these related works in the paper. Q2: The Robustness of PCA-based alignment and comparison with other alternatives, such as Vector-Neurons[4] and SE(3)-transformers [5]. Thanks for this good question. In our approach, we compute the PCA over local patches of local points. As suggested, we conduct experiments to test the robustness of PCA-based alignment, and compare with other alternatives using Vector-Neurons[4] and SE(3)-transformers [5]. (1) To test the robustness of PCA, when computing the PCA over patches, we randomly perturbed the patch point coordinates by Gaussian noises with $\sigma=0.001$ (the average distance from knn points to patch center point is about 0.004), resulting in perturbed PCA matrices. The results on the ABC dataset in Table R4-1 show the robustness of PEIF to PCA perturbations. Table R4-1. Comparison of results for random perturbations of rotation matrices. Methods\|CD↓\|EMD↓\|NC↑\|F-Score↑ -\|-\|-\|-\|- w/ perturbation\|0.250\|2.680\|0.960\|0.990 w/o perturbation\|0.241\|2.672\|0.969\|0.998 (2) Using the same GPU, we substitute the layers of our network with the Vector-Neurons[4]-based layers, and set hyper-parameters fitting the GPU memory. The results are in Table R4-2. Table R4-3 provides the hyper-parameters and resource consumption of our model and Vector-Neurons[4]-based implementation. Table R4-2. The results of PEIF with Vector-Neurons [4] equivariant layers. Methods\|CD↓\|EMD↓\|NC↑\|F-Score↑ -\|-\|-\|-\|- Vector-Neurons\|0.379\|2.769\|0.895\|0.955 Table R4-3. The hyper-parameter comparison of Vector-Neurons [4] and Pose-normalization based PEIF on ABC dataset with a single NVIDIA 4090 GPU. Cost\|Vector-Neurons [4]\|PCA-based -\|-\|- Feature dim\|64\|128 Hidden feature dim\|32\|256 Para (M)\|0.71\|7.65 Training time (s, per epoch)\|283.59\|34.56 Training memory (G)\|15.97\|17.75 Testing time (s, per shape)\|664.96\|40.98 Testing memory (G)\|3.54\|1.56 (3) We also attempt to use the SE(3)-transformers [5] to replace the patch feature extraction (SRM, PFEM) in our model. Using the same GPU, even by setting the batch size to 1 and the feature dimension of 64, we experienced out-of-memory issues when training the SE(3)-transformer based implementation. As a summary, the PCA-based patch pose normalization enables us to design a light-weight network achieving equivariant implicit function learning, and achieves sota results shown in experiments. Q3: Further comparison with E-GraphONet [2]. For a fair comparison, we tried to use PEIF to predict the occupancy field (OF) by only changing its loss to regress OF. In such a setting, we use the same training/test dataset as E-GraphONet. The reconstruction results are reported in Table R4-4. We also trained E-GraphONet to predict the vector field, we tried our best but the learned model cannot reasonably reconstruct object surfaces. The integration of training based on both occupancy and vector field prediction deserves us to try in the future. Table R4-4. The reconstruction results of PEIF predicting occupancy field on ABC dataset. Methods\|CD↓\|EMD↓\|NC↑\|F-Score↑ -\|-\|-\|-\|- PEIF (OF)\|0.874\|4.7199\|0.709\|0.675 Q4: Comparison of PSR [6] and similar follow-up works on the ABC dataset. As suggested, we compare with PSR [6], OccNet [7], and SAP [8] on the ABC dataset in Table R4-5. Our PEIF achieves the best results. Table R4-5. The reconstruction results on ABC dataset. Methods\|CD↓\|EMD↓\|NC↑\|F-Score↑ -\|-\|-\|-\|- PSR [6]\|1.207\|4.137\|0.535\|0.584 OccNet [7]\|0.691\|3.261\|0.797\|0.636 SAP [8]\|0.376\|2.765\|0.946\|0.962 PEIF (Ours)\|0.241\|2.672\|0.969\|0.998 Q5: Typos. Thanks and we will fix these typos. [1] Yang et al. Neural vector fields: Implicit representation by explicit learning. CVPR. 2023. \ [2] Chen et al. 3D Equivariant Graph Implicit Functions. ECCV. 2022. \ [3] Zhao et al. Rotation invariant point cloud classification: where local geometry meets global topology. Pattern Recognition. 2021. \ [4] Deng et al. Vector neurons: A general framework for so (3)-equivariant networks. ICCV. 2021. \ [5] Fuchs et al. SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks, NeurIPS. 2020. \ [6] Kazhdan et al. Poisson surface reconstruction. Proceedings of the fourth Eurographics symposium on Geometry processing. 2006. \ [7] Mescheder et al. Occupancy networks: Learning 3d reconstruction in function space. CVPR. 2019. \ [8] Peng et al. Shape as points: A differentiable poisson solver. NeurIPS. 2021. --- Rebuttal Comment 1.1: Comment: Dear reviewer FF8y, Thanks for your questions and suggestions. Considering your insightful comments, we have carefully responded to your questions and will include these revisions in our paper. According to your comments, we have made the following responses. (1) Novelty and relevant methods discussion. (2) The robustness of PCA-based alignment. (3) Implementing our network with Vector-Neurons/SE(3)-transformer for equivariance, resulting in decreased performance/increased memory and computing cost. (4) Further comparison with E-GraphONet by predicting occupancy using our model. We hope these responses addressed your concerns, and we expect to discuss with you in this author-reviewer discussion phase if you have additional questions. Kind regards, All authors --- Rebuttal 2: Comment: Thank you for the positive feedback on our rebuttal, and the additional comments/questions. We further respond to these questions as follows. (1) Vector neuron-based method constructs equivariant neural layers by extending neurons from 1D scalars to 3D vectors, thereby ensuring equivariance when implementing SO(3) actions in vector-based feature space. This higher-dimensional vector-based representation requires higher momery cost, more matrix operations and vector transformations to maintain geometric properties and rotation invariance, and consumes more computational cost. As suggested by the reviewer, we will analyze and discuss the computational cost considering the other computationally expensive equivariant alternatives, and clarify the motivation on using PCA for patch pose normalization, as a simple yet effective strategy for learning equivariant implicit function, while yielding good experimental results. (2) Thanks for the question on the comparison of expressiveness of PCA-alignment and VN-based representation. We think that the current experiments can hardly disentangle the effects of PCA/VN from the network design and conclude on the expressiveness comparison between them. In our model, the design of PCA-normalization at patch level is tied with our specific network design. By removing the poses of local patches using PCA-alignment, we propose the modules of "patch feature extraction module" , "intrinsic patch geometry extractor" for learning the patch-level intrinsic geometric features, as well as the "spatial relation module" encoding the off-set-based features between query point coordinate to its neighboring patch (kNN). These designs are integrated with the PCA-alignment for achieving the off-set vector field estimation. The comparative analysis between the PCA-alignment and VN is an interesting topic, and we are interested to design experiments that can disentangle the effects of PCA/VN from the specific network designs to compare them. Due to the limited time, we will consider this in the future work. Title: Thanks for the positive recommendation	Summary: This paper studies a simple task: input dense point cloud and output the implicit surface reconstruction of the geometry. To achieve this goal, the model uses an "equivariant" network to predict the displacement field. Since the input point cloud is dense, this paper crops the nearest patch on the surface point cloud to the query space point and uses PCA to canonicalize the patch. Once aligned, a transformer will predict the query points displacement vector to the surface. Since the PCA canonicalization is known, the displacement can be transformed back. This simple task is evaluated on shape and scene data. Strengths: - The insight of reusing elementary shapes with different poses is good. - This paper, although straightforward, considers using equivariance to model such elementary shapes/local intrinsic patterns. Weaknesses: - Heuristic baseline: I have a feeling that the model may depend very much on the dense KNN queries of the surface point cloud, in other words, the network is learning a potentially too easy task, just find the nearest point (or interpolate the nearest point) in the patch and compute a displacement to it if the point patch is too dense. A heuristic baseline could be just fitting a small parametric (polynomial, or even plane) to the nearest patch, and analytically computing, or directly finding the nearest point to produce the displacement vector. - Noise/Sparse/Partial data? The task might be too easy in the current literature. Since the input is a completely dense point cloud, the geometry is almost given, and this work still depends on the surface point KNN queries to do the canonicalization, so what happens if the input observation is partial, sparse, or noisy? Technical Quality: 3 Clarity: 2 Questions for Authors: Please see weakness Confidence: 4 Soundness: 3 Presentation: 2 Contribution: 2 Limitations: Some limitations are discussed in the end. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thanks for the valuable comments and suggestions. Please see below for the responses. Q1: A heuristic baseline. We aim to learn the equivariant implicit function that outputs the vector of each query point to its nearest point on the unknown continuous 3D surface. Since only discrete points on the surface are observed, it is challenging to infer the vector of the query point to the continuous 3D surface based on these discrete points. Instead of using local knn points to regress a local surface function (e.g., polynomial functions) for each query point, our neural network-based approach infers the vector of the query point to the surface by learning the intrinsic geometry feature of the local patch to estimate the vector of each query point. We also design and take advantage of the rotation-invariant patch features for achieving equivariant implicit function learning. This design enables us to achieve sota performance for 3D reconstruction. In Q2, we also evaluate the performance of the degradations of input point clouds. Q2: The performance of PEIF on sparse/noisy/partial data. As suggested, we evaluate the performance of our PEIF on different data degradations (sparse, noisy, and partial) on the ABC dataset. In the following experiments, the test input point clouds with different degradations, and the results are reported in Tables R3-1 to R3-3. In Tables 1-3 of the uploaded PDF file in “general response”, we also report the results when both the training and test point clouds are degraded. (1) Sparse point cloud. In experiments of the original submission, all the compared methods use the same number of input points (10k) for each shape in testing, as NVF. We randomly select a subset of input points as input, and the results are in Table R3-1. Table R3-1. The reconstruction results of sparse data on the ABC dataset. Methods\|$N$\|CD↓\|EMD↓\|NC↑\|F-Score↑ -\|-\|-\|-\|-\|- NVF\|5k\|0.297\|2.706\|0.935\|0.979 GeoUDF\|5k\|0.306\|2.726\|0.940\|0.985 GridFormer\|5k\|0.292\|2.694\|0.952\|0.982 PEIF (Ours)\|5k\|0.269\|2.679\|0.945\|0.988 -----\|-----\|-----\|-----\|-----\|-----\|----- NVF\|2k\|0.409\|2.725\|0.932\|0.946 GeoUDF\|2k\|0.399\|2.711\|0.935\|0.952 GridFormer\|2k\|0.369\|2.703\|0.945\|0.956 PEIF (Ours)\|2k\|0.360\|2.685\|0.938\|0.960 (2) Noisy point cloud. We plugged Gaussian noise with standard deviation ($\sigma$) as 0.005 and 0.01 to the input points. Table R3-2. The reconstruction results from noisy input on the ABC dataset. Methods\|$\sigma$\|CD↓\|EMD↓\|NC↑\|F-Score↑ -\|-\|-\|-\|-\|- NVF\|0.005\|0.512\|3.257\|0.712\|0.924 GeoUDF\|0.005\|0.496\|3.268\|0.732\|0.911 GridFormer\|0.005\|0.839\|3.321\|0.793\|0.805 PEIF (Ours)\|0.005\|0.480\|3.132\|0.745\| 0.952 -----\|-----\|-----\|-----\|-----\|-----\|----- NVF\|0.01\|0.792\|3.687\|0.723\|0.693 GeoUDF\|0.01\|0.785\|3.428\|0.710\|0.655 GridFormer\|0.01\|1.132\|3.379\|0.759\|0.510 PEIF (Ours)\|0.01\|0.773\|3.358\|0.715\|0.702 (3) Partial point cloud. We remove a fraction (with ratio $p$) of the input points to form a partial point cloud. Specifically, we use the farthest point sampling to select a set of center points and remove their K-NN points to ensure the sampling fraction. Table R3-3. The reconstruction results from partial points on the ABC dataset. Methods\|$p$\|CD↓\|EMD↓\|NC↑\|F-Score↑ -\|-\|-\|-\|-\|- NVF\|10%\|0.264\|2.697\|0.943\|0.992 GeoUDF\|10%\|0.268\|2.695\|0.959\|0.994 GridFormer\|10%\|0.267\|2.706\|0.964\|0.982 PEIF (Ours)\|10%\|0.246\|2.692\|0.960\|0.996 -----\|-----\|-----\|-----\|-----\|-----\|----- NVF\|20%\|0.274\|2.710\|0.940\|0.990 GeoUDF\|20%\|0.275\|2.745\|0.947\|0.991 GridFormer\|20%\|0.298\|2.746\|0.946\|0.987 PEIF (Ours)\|20%\|0.249\|2.697\|0.956\|0.995 --- Rebuttal Comment 1.1: Title: Keep my original positive recommendation Comment: After reading the reviews and rebuttals, I appreciate the author's effort in additional experimental results. The partial/noisy data experiments are convincing. I keep my original positive recommendation. --- Reply to Comment 1.1.1: Title: Thanks for the positive recommendation Comment: Thanks for your inspiring questions and positive comments on our work. We will include these additional results and revisions in the paper (main body or appendix).	Summary: The authors introduce the 3D Patch-level Equivariant Implicit Function (PEIF), leveraging a 3D Patch-level Pose-Invariant Representation (PPIR) to address the surface reconstruction task. To overcome the limitation that existing Implicit Neural Representations (INRs) are not equivariant to 3D rotation, they develop PEIF to encode both equivariant and invariant information, thereby enhancing generalization to unseen 3D rotations. The SE(3)-equivariant implicit function is optimized using displacement optimization loss and patch discrimination loss with ground-truth 3D models. Experimental results on surface reconstruction datasets validate the effectiveness of PEIF. Strengths: 1. Motivation: The study is well-motivated, addressing the redundancy in existing INR-based methods concerning local orientation-normalized patches. Moreover, the current methods are weak against unseen rotations of local shapes. 2. Technical Novelty and Soundness: The introduction of local pose-invariant representation for SE(3) equivariant implicit function is novel for 3D surface reconstruction. Patch-based pose normalization facilitates efficient training without the need for rotation augmentation. 3. Verification of Rotational Robustness: The authors demonstrate the rotational robustness of the proposed method, as shown in Table 4. 4. Performance Improvement: The proposed PEIF achieves superior performance compared to both equivariant and non-equivariant surface reconstruction methods on the ShapeNet, ABC, and SyntheticRooms datasets, as indicated in Tables 1 and 2. Weaknesses: 1. Rotational Robustness: Further clarification is needed regarding the experimental settings in Table 4. Specifically, it is unclear whether "w/o rotation" and "w/ rotation" refer to rotation augmentation during training or testing. 1. Missing Citations: A similar approach exists in 2D pixel-level correspondence, as detailed in the work by Lee et al. (CVPR 2023). This study also utilizes local-level dominant orientation from rotation-equivariant features and normalizes the equivariant feature using the dominant orientation for an invariant descriptor. It would be beneficial to cite this work and discuss the similarities and differences.  [A] Learning Rotation-Equivariant Features for Visual Correspondence (Lee et al., CVPR 2023) 1. Computational Cost: There is a lack of discussion regarding the computational cost of the proposed PEIF. Information on computation time and memory consumption, and a comparison with E-GraphONet would be valuable. Technical Quality: 4 Clarity: 3 Questions for Authors: Further Research Direction: The concept introduced could potentially be extended to few-shot training scenarios, where the local embedding might capture various types of 3D rotations. Did the authors explore this direction? Confidence: 3 Soundness: 4 Presentation: 3 Contribution: 3 Limitations: I recommend a weak accept score for this paper due to its strong motivation and technical novelty in addressing the limitations of existing INRs with respect to 3D rotation equivariance. The introduction of the 3D Patch-level Equivariant Implicit Function (PEIF) and its verification of rotational robustness demonstrate a significant advancement in 3D surface reconstruction, achieving state-of-the-art performance on multiple datasets. However, there are some limitations that should be addressed. The experimental settings regarding rotational robustness need further clarification. Additionally, the paper lacks citations to related works in 2D pixel-level correspondence that employ similar techniques, which would strengthen the discussion of novelty and prior art. Finally, the computational cost of PEIF, in terms of computation time and memory consumption, is not discussed, leaving questions about its practical applicability compared to existing methods. Addressing these points would enhance the overall contribution and clarity 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 the positive comment that our approach is well-motivated and novel. Please see below for responses. Q1: The experimental settings of "w/o rotation" and "w/ rotation" in Table 4. In Table 4, "w/ rotation" and "w/o rotation" represent that the testing input point cloud is with and without arbitrary rotation respectively. This will be clarified in paper. Q2: Missing citations of related works in 2D pixel-level. Thanks for this comment. RELF [1] uses group equivariant CNNs to extract discriminative rotation-invariant descriptors for 2D images. Differently, our framework is designed for 3D reconstruction, and we design equivariant implicit function learning for 3D reconstruction. We will include the reference of equivariant network in 2D and discussion of RELF [1] in our paper. Q3: Computational cost. We report the computational cost, including the training time per epoch, training memory, testing time per 3D shape, and testing memory cost on the ABC dataset, in Table R2-1. Methods of GeoUDF and GridFormer include two stages of upsampling/reconstruction and reconstruction/refinement. We report the computation cost of them in each table cell with two values (denoted as · + ·), respectively representing the costs for each stage. We will include these details in the appendix. Table R2-1. The comparison of computational cost. Cost\|Training Time (s)\|Training Mem (G)\|Testing Time (s)\|Testing Mem (G) \|-\|-\|-\|-\|-\| NVF\|28.06\|6.70\|73.9\|0.66 GeoUDF\|61.20+58.78\|14.99+14.99\|124.73\|2.27 GridFormer\|26.48+26.78\|6.59+6.59\|13.32\|0.31 E-GraphONet\|37.82\|16.11\|1.92\|1.49 PEIF (Ours)\|34.56\|17.75\|40.98\|1.56 Q4: Further research direction. It is a good suggestion to extend our approach to few-shot training scenarios. Along this direction, our patch-based pose invariant representation can be taken as a foundation network for pre-training, followed by fine-tuning on few-shot examples. In the pre-training step, we may learn a general representation of intrinsic 3D patch features, and the fine-tuning may adapt these representations to the given few-shot examples. We will include this direction as a future work in the conclusion section. [1] Lee et al. Learning rotation-equivariant features for visual correspondence. CVPR. 2023. --- Rebuttal Comment 1.1: Comment: Dear reviewer 6vbf, Thanks for the valuable questions/suggestions and the overall positive comments on the motivation and novelty. We have carefully responded to your questions and will include these revisions in our paper. In the rebuttal phase, we have responded in the following aspects. (1) The setting of w/o or w/ rotation. (2) Missing citation and the corresponding discussion. (3) More details on the computational cost. (4) The suggested future research direction. If you have additional questions, we expect to discuss them with you in this author-reviewer discussion phase. Kind regards, All authors --- Rebuttal 2: Comment: Thank you for the valuable questions and the positive feedback. As suggested, we will discuss the related work of equivariant/invariant mapping in 2D image matching [1] in the final revision. Title: Thanks for the positive recommendation	Summary: In this paper, the authors address the task of surface reconstruction. They propose a patch-level pose-invariant representation of 3D objects, which is employed in the design of a patch-level equivariant implicit function. The proposed PEIF framework is composed of three modules: the spatial relation module, the patch feature extraction module, and the intrinsic patch geometry extractor. They authors demonstrate the effectiveness of the proposed framework for the surface reconstruction task through comprehensive experimental evaluations. Strengths: - The authors introduce a novel pose normalization scheme and a displacement predictor that employs the proposed pose normalization scheme, accompanied by rigorous proofs - The proposed method shows the state-of-the-art performance in the surface reconstruction task, surpassing other equivariant method (i.e. E-GraphONet) - The proposed method shows the state-of-the-art performance in the cross-domain evaluation setting Weaknesses: - The proposed method exhibits a significantly longer inference time compared to other equivariant methods (E-GraphONet). It appears that the majority of thie increased inference time results from the computation of the SVD. A detailed analysis of the inference time would be beneficial for a more comprehensive understanding of the proposed method - The proposed method shows comparable performance compared to GeoUDF (which is not an equivariant method). This raises questions about the necessity of using an equivariant method for the surface reconstruction task - The authors claim that the proposed pose-invariant property is intended to enhance the cross-domain generalization ability. To validate this, the cross-domain experiment should include the result of E-GraphONet (which is also pose-invariant) - In table 4, it seems that other algorithms also quite robust to rotation changes. The authors are encouraged to provide further explanation on this observation. - An ablation study concerning the three modules (i.e., the spatial relation module, the patch feature extraction module, and the intrinsic patch geometry extractor) is not provided. The inclusion of such a study would be valuable. Technical Quality: 2 Clarity: 3 Questions for Authors: - Could the authors provide a visualization of the learned memory bank? This would aid in comprehending the proposed intrinsic patch geometry extractor. - What value of K is used in the MGN experiments? - Minor comments - L57: 3D construction -> 3D reconstruction - L62: introduces Transformer -> introduces transformer - Figure2: displacement Predictor -> displacement predictor - L180: multi-head memory bank index starts from 1, but it starts from 0 in Figure 3 - L191: displacement estimate -> displacement estimation - L234: distance(CD -> distance (CD Confidence: 3 Soundness: 2 Presentation: 3 Contribution: 2 Limitations: The authors have adequately addressed the limitations and societal impact in the main paper. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thanks for these comments. We address the concerns and questions as follows. Q1: The visualization of the learned memory bank. We provided two approaches for visualizations of the learned memory bank. Please refer to Figure 1 in the attached PDF file uploaded in the top “general response”. (1) We visualize the set of point patches with the highest weights to the corresponding element of the memory bank (the weights are computed by Eqn. (12)). These patches are highlighted by colors in these examples. It shows that the patches with high weights to each element of memory have similar geometry structures. (2) We further visualize (by t-SNE) the features of point patches with the highest weights (Eqn. (12)) to different elements of the learned memory, rendered by different colors. It shows that the patches with high weights assigned to different elements of learned memory have clustered features in the feature space. We will include these visualizations in the appendix of our paper. Q2: What value of $K$ is used in the MGN experiments? $K$ is set to 54 in testing on the MNG dataset, using the trained model with $K=54$ on Synthetic Rooms dataset. As shown in Table R1-1, when changing $K$ to 48 and 32 on the Synthetic Rooms in training, the test results using the corresponding $K$ on MGN are stable. We also presented the ablation studies on $K$ in Table 5 of the manuscript. Table R1-1. The impact of $K$ when training on Synthetic Rooms and testing on MGN. K\|CD↓\|EMD↓\|NC↑\|F-Score↑ -\|-\|-\|-\|- 48\|0.247\|2.724\|0.961\|0.998 32\|0.252\|2.735\|0.959\|0.991 Q3: Minor comments on typos. Thanks and we will correct them. Q4: A detailed analysis of the inference time. In Table R1-2, we report the time consumption of each operator in PEIF to process 10,000 query points. Specifically, the operations include SVD (Singular Value Decomposition), PE (Point-wise Feature Extraction), SRM (Spatial Relation Module), PFEM (Patch Feature Extraction Module), IPGE (Intrinsic Patch Geometry Extractor) and Others (other Conv layers). Table R1-2. The time to process 10,000 points on the ABC dataset using one NVIDIA 4090 GPU. Operator\|SVD\|FE\|SRM\|PFEM\|IPGE\|Others\|Total -\|-\|-\|-\|-\|-\|-\|- Time (s)\|0.4473\|0.1773\|0.0297\|0.0004\|0.0008\|0.02\|0.6688 We will add them in the main body or appendix of our paper. Q5: Comparison with GeoUDF and necessity of equivariance. As shown in Tables 1, 2 of the manuscript and Tables R3-1 to R3-3 in response to Reviewer H6Ua, our results are better than GeoUF, especially for degraded data. Moreover, Table R2-1 in response to Reviewer 6vbf shows that our time/memory cost is lower than GeoUDF. (1) Learning the equivariant implicit representation ensures that the reconstructed surfaces are robust to the rotation of the input points. Figure 2 of the uploaded PDF in “general response” shows that GeoUDF generated 3D surfaces with some noise artifacts after rotation. While our results are more smooth and stable to rotations. (2) The equivariance/invariance is important to our model's performance. We learn the equivariant implicit vector field based on patch intrinsic geometric features by removing patch poses. It is inspired by the observation that local patches are repetitively appearing on 3D shapes if removing patch poses. This novel idea is essential for achieving improved reconstruction accuracy, while robust to rotations. As shown in Table 5, if removing the equivariance design (i.e., w/o pose normalization), the 3D reconstruction accuracy apparently decreases. Q6: The comparison of cross-domain generalization ability with E-GraphONet. As suggested, we compare with E-GraphONet in the cross-domain experiment as reported in Table R1-3. Our PEIF achieves better quantitative results on the MGN dataset. These results will be included in Table 3 of our paper. Table R1-3. The cross-domain evaluation on the real MGN dataset, where the model is pre-trained on the Synthetic Room dataset. Method\|CD↓\|EMD↓\|NC↑\|F-Score↑ -\|-\|-\|-\|- E-GraphONet\|0.433\|3.817\|0.863\|0.920 PEIF (Ours)\|0.241\|2.672\|0.969\|0.998 Q7: Further clarification on the robustness of the competed algorithms to rotation changes. Thanks for the question. We have further evaluated the rotation robustness of the methods in Table 4 to different rotation angles, which is reported in Table R1-4. Figures 2, 3 of the uploaded PDF in "general response" demonstrate that NVF and GeoUDF exhibit noise and holes after rotation, while our results are more smooth and robust to rotations. In Q5, we also discussed the importance of equivalence/invariance of vector field/patch features to our model for achieving good performance. Table R1-4. The results for different rotation angles (0/90/180/270) on the ABC dataset. Method\|CD↓\|EMD↓\|NC↑\|F-Score↑ -\|-\|-\|-\|- NVF\|0.245/0.260/0.263/0.262\|2.685/2.683/2.685/2.687\|0.963/0.950/0.944/0.952\|0.996/0.994/0.993/0.993 GeoUDF\|0.245/0.256/0.253/0.263\|2.688/2.691/2.698/2.683\|0.9640.956/0.958/0.966\|0.997/0.993/0.996/0.994 E-GraphONet\|0.432/0.441/0.436/0.445\|2.688/2.696/2.702/2.690\|0.910/0.906/0.906/0.897\|0.906/0.896/0.909/0.906 PEIF(Ours)\|0.241/0.249/0.247/0.243\|2.672/2.675/2.678/2.676\|0.969/0.966/0.964/0.968\|0.998/0.996/0.998/0.998 Q8: An ablation study of the three modules. We conduct an ablation study of the three modules (e.g., SRM, PFEM, IPGE) in our PEIF on the ABC dataset. Table R1-5 reports the quantitative measures of our PEIF without these modules. The results show that the intrinsic patch geometry extractor (IPGE) contributes more to the performance of PEIF. Table R1-5. Ablation study of the three main modules proposed in PEIF. Setting\|CD↓\|EMD↓\|NC↑\|F-Score↑ -\|-\|-\|-\|- w/o SRM\|0.243\|2.686\|0.962\|0.997 w/o PFEM\|0.244\|2.699\|0.961\|0.996 w/o IPGE\|0.276\|2.715\|0.959\|0.992 PEIF (Full)\|0.241\|2.672\|0.969\|0.998 --- Rebuttal 2: Comment: Dear reviewer dfBj, Thanks for your inspiring suggestions and questions. We have carefully considered your questions/concerns, and responded in the following aspects. (1) We have provided the visualization of the learned memory bank, showing that the elements of the memory bank represent patch-level 3D geometric patterns. (2) We have presented more details on the inference time, the setting of K, etc. (3) We have provided additional experiments on the justification of the necessity of equivariance and robustness to the rotations. (4) We have conducted ablation studies on the key modules and the cross-domain comparison with E-GraphONet. Due to the limited remaining time for authors-reviewer discussion, we are expecting to have further discussion with you if there are any additional concerns. Kind regards, All authors --- Rebuttal Comment 2.1: Comment: I appreciate the authors' effort in providing additional results. The rebuttal effectively clarified and addressed the key issues I had with the paper. I lean towards acceptance. --- Rebuttal 3: Comment: Thank you for the positive feedback. We will incorporate the corresponding revisions into our paper. Title: Thanks for the positive recommendation	Rebuttal 1: Rebuttal: # General Response We appreciate the reviewers' positive comments on the novelty (especially Reviewers dfBj, 6vbf, H6Ua), motivation (especially Reviewers 6vbf, FF8y, H6Ua), and performance gain (especially Reviewers 6vbf, H6Ua, FF8y). We have responded to these questions/suggestions of reviewers, and will incorporate the corresponding revisions into our paper's main body or appendix. Following this general response, we uploaded a PDF file containing the figures/additional tables, referred to in the responses to each reviewer's comments. Pdf: /pdf/2aa6db274c42b962299f7fc1d8b12564cbf5081a.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
CNCA: Toward Customizable and Natural Generation of Adversarial Camouflage for Vehicle Detectors	Accept (poster)	Summary: This paper presents a novel method CNCA for generating customizable and natural adversarial camouflage of fooling vehicle detectors. This work is an interesting contribution in the field of adversarial attacks, especially improving the naturalness of the camouflage while maintaining high attack performance. Strengths: It is interesting to apply diffusion models to physical adversarial attacks to generate natural camouflage for the first time, and it is also of practical value to generate natural adversarial camouflage with customizable styles based on text prompts. Weaknesses: The clipping strategy lacks innovation; it has been used in PGD for a long time, and it is not worth spending too much space on it. Technical Quality: 2 Clarity: 3 Questions for Authors: 1. Why is there no comparison with baselines in the physical world? 2. Whether other detection models can be used as white-box to generate adversarial textures to verify the transferability of CNCA. 3. Only use the subjective evaluation may not be convincing for experimental verification, and visual observation does not seem to be more natural than previous methods. Is there a more convincing scoring rule to evaluate naturalness? Confidence: 5 Soundness: 2 Presentation: 3 Contribution: 3 Limitations: The experimental results are insignificant. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: W1: The clipping strategy lacks innovation; it has been used in PGD for a long time, and it is not worth spending too much space on it. The core contribution of our work is introducing the diffusion model to enable the customizable and natural generation of physical adversarial camouflage. The clipping strategy from PGD itself is not novel, but our contribution is adapting it to regulate the perturbation level of the diffusion model. We describe the details of clipping ( in only 3 lines) because we want to make our method clear to readers who are not familiar it. Q1: Why is there no comparison with baselines in the physical world? For our physical world evaluation, we follow the setting from the previous state-of-the-art works of DTA and ACTIVE, which only compares the performance between the normal and the generated camouflage. For the completeness of the evaluation, we extend the physical evaluation with previous baselines and both indoor and outdoor environments. The results are as shown in the table below: \| Methods \| YOLOv3 \| YOLOX \| SSD \| CenterNet \| RetinaNet \| Total \| \|-------------\|--------\|-------\|------\|-----------\|-----------\|-------\| \| Normal \| 0.778 \| 0.936 \| 0.890\| 0.916 \| 0.981 \| 0.900 \| \| DAS \| 0.734 \| 0.878 \| 0.847\| 0.873 \| 0.955 \| 0.857 \| \| FCA \| 0.560 \| 0.770 \| 0.767\| 0.798 \| 0.921 \| 0.763 \| \| DTA \| 0.566 \| 0.689 \| 0.786\| 0.854 \| 0.886 \| 0.756 \| \| ACTIVE \| 0.518 \| 0.563 \| 0.574\| 0.743 \| 0.735 \| 0.627 \| \| CNCA \| 0.439 \| 0.464 \| 0.557 \| 0.698 \| 0.780 \| 0.588 \| The results demonstrate that our method achieves comparable performance with previous baselines in the real world, which matches the results from the digital world evaluation. The details of the extended physical evaluation can be found in the G2 section of the global rebuttal. The physical examples can be found in Figure 1 in the attached PDF. Q2: Whether other detection models can be used as white-box to generate adversarial textures to verify the transferability of CNCA. Yes, they can. We currently use YOLOv3 to generate adversarial camouflage for a fair comparison with previous methods (FCA, DTA, and ACTIVE), which also use this detector to generate camouflage. To validate the transferability, we use YOLOv5 as the attacked white-box detector to generate camouflage. We keep the other experiment settings the same, such as input prompt (yellow black graffiti) and clipping threshold (value is 1). We report the attack and naturalness performance using the average of car AP@0.5 over 5 different detectors and human evaluation. The results are as follows: \| Attack Detector \| YOLOv3 \| YOLOv5 \| \|----------------\|--------\|--------\| \| Averaged AP@0.5 \| 0.522 \| 0.518 \| \| Natural Score \| 3.33 \| 4.00 \| The results demonstrate that CNCA has similar attack performance regardless of the white-box models in the CNCA framework, which verifies its transferability. Q3: Subjective evaluation may not be convincing for experimental verification, and visual observation does not seem to be more natural than previous methods. Is there a more convincing scoring rule to evaluate naturalness? Evaluating the naturalness of physical adversarial attacks is a challenging task. We have surveyed the existing work related to this task. Among these works, S. Li et al. [1] is the most relevant one because they evaluate the naturalness of the physical attack for vehicle detection. They trained an evalution model with vehicle images and the corresponding human ratings. However, we found the trained model shows a bias of low scoring towards the full-covered painting vehicle image, even if the vehicle painting is designed by humans and looks very natural. As a result, all the full-cover baselines receive low scores. We believe it is caused by the training dataset's lack of full-cover painting vehicle images. To avoid this bias, we decide to follow the work of [2] and conduct a subjective survey to directly evaluate the naturalness by considering full-cover painting vehicles (for instance, racing cars with banners and logos) still natural. To maintain the fairness of the survey, we invited 45 participants from different ages, backgrounds, and genders, which is twice the number in [3] ( which is 24). [1] S. Li et al., “Towards Benchmarking and Assessing Visual Naturalness of Physical World Adversarial Attacks,” In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2023, pp. 12324–12333, May 2023. [2] Hu, Yu-Chih-Tuan, et al. "Naturalistic physical adversarial patch for object detectors." Proceedings of the IEEE/CVF International Conference on Computer Vision. 2021. L1: The experimental results are insignificant. Our primary goal is to improve naturalness and enable customization of the physical adversarial camouflage. It is challenging to achieve this goal while maintaining competitive attack performance. We leverage the pre-trained diffusion model to generate adversarial texture images with input prompts to tackle this. Besides, we introduce adversarial features so that the adversarial gradient from the detector can guide the camouflage generation. Finally, we adapt the clipping strategy to balance the trade-off between attack performance and naturalness. Experimental results show that our attack performance is close to the state-of-the-art method (ACTIVE), but our method's naturalness score is 54% higher, which is a significant improvement. While our work isn't perfect, it represents a significant initial effort towards customizable and natural camouflage generation. We believe it will draw increased research attention to this field. --- Rebuttal 2: Title: Reply to Reviewer oknY Comment: Dear Reviewer oknY, Thank you for your time and effort in reviewing our work and rebuttal. Your feedback has helped us improve. We are grateful that you raised the rating for our work after we provided the clarifications in the rebuttal! Best Regards， Authors of Submission 17110	Summary: The paper introduces a interesting idea and also a novel method called Customizable and Natural Camouflage Attack (CNCA) to generate adversarial camouflage against vehicle detectors, leveraging a pre-trained diffusion model. This approach allows the generation of natural-looking and user-customizable adversarial patterns that maintain robust attack performance across various digital and physical settings. The paper's contributions include a unique application of diffusion models to adversarial camouflage, introduction of adversarial features for gradient-based generation, and a clipping strategy to balance naturalness with attack performance. Extensive experiments and user studies demonstrate the effectiveness of CNCA in producing more natural-looking camouflage with competitive attack performance. Strengths: - The paper proposes an interesting and useful application direction, namely natural and customized adversarial camouflage. The research motivation has substantial practical significance, and the proposed method appears intuitively reasonable. - This study is the first to apply diffusion models for natural adversarial camouflage generation. It is also the first to generate various 52 styles of adversarial camouflage against vehicle detectors. - The experiments are thorough, and the results are statistically significant, indicating high-quality research. - The code is provided. Weaknesses: - Some expressions are not clear, making it difficult for those unfamiliar with the field to understand. For example, lines 32 to 35. It would be better and easier to understand if some visual evidence were provided regarding these limits. - Figure 1 is not correctly referenced. - The experimental section would be more convincing if the effectiveness of the proposed components and methods were demonstrated through ablation experiments. - Concerning anonymity: Some comments in the provided code reveal personal information. Please be aware of this! Technical Quality: 3 Clarity: 2 Questions for Authors: - I am curious about its complexity. The method involves multiple components and parameters (e.g., adversarial features, clipping strategy), which might complicate its deployment in practical applications without substantial customization and tuning. - It would be more helpful if more ablation experiments were added to individually demonstrate the functions of each component. Confidence: 2 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: Refer to the “Questions” section. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: W1: lines 32-35 are not clear to understand. Provide visual evidence to illustrate. We would like to clarify that lines 32-35 explain the two reasons why the previous camouflage methods lack naturalness. Firstly, these methods lack prior knowledge of naturalness to guide the camouflage generation. Secondly, these methods optimize the adversarial texture at a pixel level, making it difficult to form a natural-looking texture pattern. For instance, the previous state-of-the-art methods like FCA, DTA, and ACTIVE generate suspicious and attention-grabbing patterns, resulting in a low-score performance in naturalness, as shown in Table 4 in our paper. W2: Figure 1 is not correctly referenced. We will correct it in future versions of our paper. W3: The experimental section would be more convincing if the effectiveness of the proposed components and methods were demonstrated through ablation experiments. \| Pipeline \| No Diff. \| Diff. \| Diff. + Adv. \| Diff. + Adv. + Clip \| Diff. + Adv. + Clip + Reorder \| \|-----------------------------\|----------\|-------\|--------------\|---------------------\|------------------------------\| \| AP@0.5 \| 0.619 \| 0.553 \| 0.520 \| 0.494 \| 0.479 \| \| Natural Score \| 1.00 \| 3.37 \| 1.71 \| 2.75 \| 3.33 \| The above table shows the results of the ablation studies for each component of the pipeline. During the ablation study, we gradually add the components individually to see their contribution to attack performance and naturalness. All the test pipelines with the diffusion model use the same input text prompt: "yellow black graffiti." The description for each test pipeline is the following: - No Diff. directly optimizes the texture image of the vehicle at a pixel level, resulting in an unnatural texture; - Diff. introduces the diffusion model to generate texture image compared to No Diff., which improves the naturalness score; - Diff.+Adv. introduces the adversarial feature compared to Diff.. The attack performance improves but compromises the naturalness; - Diff.+Adv.+Clip introduces the clipping strategy compared. to Diff.+Adv., which improves the naturalness; - Diff.+Adv.+Clip+Reorder is our final pipeline, which uses a reordered texture map compared to Diff.+Adv.+Clip, which further improves the attack performance and naturalness. No Diff. optimizes the texture image of the vehicle with no prior knowledge of naturalness at a pixel level, which results in an unnatural texture image. To improve naturalness, Diff. leverages the prior knowledge from the diffusion model. Diff.+Adv. introduces the adversarial feature, which enables the texture image generation guided by the adversarial gradient from the detector. It improves the attack performance but compromises the naturalness. Diff.+Adv.+Clip introduces the clipping strategy to regulate the perturbation level of diffusion, which improves the naturalness. Our final pipeline Diff.+Adv.+Clip+Reorder uses a reorder texture map to keep more natural patterns generated by the diffusion model, further improving the attack performance and naturalness. To summarize, the ablation studies demonstrate that all the components of our pipeline contribute to improving the camouflage's attack performance and naturalness. Please find the above table and corresponding generated texture images in Table 1 from the attached PDF. W4: Concerning anonymity: Some comments in the provided code reveal personal information. We have made the necessary modifications to remove the personal information in the code. Q1: The complexity during its deployment in practical applications without substantial customization and tuning. In the early stage of our experiment, we indeed spent some effort manually tuning the clipping threshold to generate the adversarial camouflage for a certain prompt. To amend this, we propose an automatic tunning method to adjust the clipping threshold dynamically. We calculate the relevance score between the input prompt and the generated image. If the relevance score is high above the pre-defined threshold, the clip threshold will use a larger value, allowing more exploration of the adversarial feature. If the relevance score is lower than the threshold, which means the generated images cannot match the input prompt, the clipping threshold will use a smaller value to constrain the adversarial feature. To calculate the relevance score, we leverage the CLIP[1] model, an effective pre-trained model that learns the relevance between visual images and text captions. To validate this idea, we conducted an ablation study on manual and automatic tunning under the same input prompt ("yellow black graffiti") and detection model (YOLOv3) settings, showing that they achieve comparable attack and naturalness performance measured by AP@0.5 and naturalness score, as shown in the table below. \| Tuning Method \| Manual Tuning \| Automatic Tuning \| \|--------------------\|---------------\|------------------\| \| AP@0.5\| 0.479 \| 0.509 \| \| Natural Score \| 3.33 \| 3.28 \| [1] Radford, Alec, et al. "Learning transferable visual models from natural language supervision." International conference on machine learning. PMLR, 2021. Q2: Add more ablation experiments to demonstrate the functions of each component individually. Please refer to the reply to W3. --- Rebuttal 2: Title: Friendly Reminder: Follow-Up on Rebuttal for Submission 17110 Comment: Dear Reviewer MuNz, We are writing to follow up on the rebuttal we submitted regarding your review comments for our paper. We appreciate your time and effort in reviewing our work and providing valuable feedback. We have made a sincere effort to address each of your comments and questions in the rebuttal. We believe the clarifications and improvements we made in response to your suggestions have strengthened the paper significantly. We kindly request that you review our rebuttal as soon as possible ( today is the final day for discussion ) and consider increasing your rating for our paper with the provided changes and clarifications. Thank you again for your dedication to the review process; we look forward to hearing from you! Best Regards， Authors of Submission 17110 --- Rebuttal Comment 2.1: Comment: The author addressed most of my concerns, I will rise the score.	Summary: The manuscript presents a novel approach to generating physical adversarial camouflage against vehicle detectors, leveraging a pre-trained diffusion model. The proposed method, called Customizable and Natural Camouflage Attack (CNCA), aims to produce adversarial camouflage that is both natural-looking and customizable via user-specific text prompts. This approach addresses the limitations of previous methods that produced conspicuous and unnatural camouflage, maintaining effectiveness in adversarial attacks while enhancing the camouflage's appearance to blend seamlessly into its surroundings. Strengths: CNCA introduces a novel application of diffusion models for generating physical adversarial camouflage, a significant shift from the traditional pixel-level optimization methods. The method allows for the generation of camouflage that is not only effective in evading detection but also customizable and more natural-looking, meeting specific user requirements. The manuscript provides a comprehensive evaluation of the CNCA approach, including both digital and physical world tests and user studies, demonstrating its effectiveness and practical applicability. Weaknesses: The approach involves complex integration of diffusion models with adversarial attack frameworks, which may increase the computational overhead and complexity compared to more straightforward adversarial techniques. Although the manuscript includes extensive testing, the evaluations focus primarily on vehicle detection in controlled settings. The performance and practicality of CNCA in more varied or less controlled environments remain to be fully explored. Technical Quality: 3 Clarity: 3 Questions for Authors: See strength and weakness above. Confidence: 5 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: No. While the paper discusses potential positive impacts, such as improving AI robustness, the technique could also be used maliciously to evade surveillance, posing ethical and security concerns. Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: W1: Integration of Diffusion models with adversarial attack frameworks may increase computational overhead and complexity. We have discussed this weakness in the section on Limitations & Societal Impact. We would like to clarify that our work's novelty enables the naturalness and customizability of the physical adversarial attack. Integration with diffusion models is the key to achieving this. Despite its higher computational cost, camouflage can be generated offline at a one-time cost. The generated camouflage can be used to attack a wide range of detectors. In summary, introducing diffusion models is still valuable, although it increases the computation cost. W2: The evaluations focus primarily on vehicle detection in controlled settings. The performance and practicality of CNCA remain to be fully explored in more varied or less controlled environments . Vehicle detection is crucial in autonomous driving and traffic monitoring. Therefore, many previous methods chose to research the physical attack on this task setting. Our work follows this research direction. We agree that we need to validate our method's performance and practicability in more varied environments. Therefore, we extend our physical evaluation to both indoor and outdoor environments, as shown in Figure 1 in the attached PDF. The results demonstrate that our method is transferable in varied real-world environments. L1: The technique could also be used maliciously to evade surveillance, posing ethical and security concerns. We have discussed this in the section of Limitations & Societal Impact. We acknowledge the potential malicious usage of our technique. However, although our method generates physical attack examples, these examples can be used for the research of defense methods, such as adversarial training, adversarial testing, and adversarial example detection. The research of defense can ultimately safeguard AI systems. --- Rebuttal Comment 1.1: Comment: The author's response addressed some of my questions and I decided to keep my rating. --- Rebuttal 2: Title: Request for a higher Rating from Reviewer guSy Comment: Dear Reviewer guSy, Thanks for taking the time to review and reply to our rebuttal. We are grateful for your feedback, which has helped us to improve our work. We understand and respect your decision to maintain your current rating. However, we kindly ask you to consider whether our clarifications justify a higher rating. We believe the enhancements made during the rebuttal, specifically the extended ablation studies for each component in our pipeline and both indoor and outdoor physical evaluations with previous methods, have strengthened the quality and clarity of our work. We appreciate your understanding and consideration of this request. We would like to provide further clarification if there are any issues you would like us to address. Thanks again for your time and effort in reviewing our paper! Best Regards， Authors of Submission 17110	Summary: The paper introduces a novel framework, CNCA, for generating customizable and natural adversarial camouflage for vehicle detectors using a diffusion model. This work addresses critical limitations in current adversarial camouflage techniques by focusing on naturalness and customizability, which are often neglected in favor of attack performance. While the paper presents a significant advancement in adversarial camouflage, several areas require improvement to enhance rigor and presentation. The proposed CNCA framework holds substantial promise, but further validation and detailed comparison are essential to establish its superiority and practical relevance. Strengths: 1. The use of a diffusion model for generating natural and customizable adversarial camouflage is novel. 2. The extensive experiments, including both digital and physical settings, provide strong evidence of the method's effectiveness. Weaknesses: 1. The explanation of the adversarial feature generation and its integration with the diffusion model is somewhat convoluted. Quantitatively define the evaluation indicators of naturalness and attack performance, or provide relevant references. 2. The evaluation in the physical world is limited to small-scale models and specific conditions. Extend the evaluation to a broader range of vehicle detection models and datasets, including those used in autonomous driving (e.g., KITTI, Waymo Open Dataset). Assess the scalability of CNCA by testing on larger, more complex scenes and different environmental conditions to validate its general applicability. 3. The paper lacks ablation studies to isolate the impact of different components of the proposed framework. Conduct ablation studies to demonstrate the contribution of each component (e.g., the diffusion model, adversarial feature clipping) to the overall performance. Technical Quality: 4 Clarity: 3 Questions for Authors: Experimental Statistical Significance: The authors recruited 45 participants to subjectively evaluate the naturalness of different camouflages, reporting the mean scores and standard deviations (SD) for naturalness of each type of camouflage. While this is good, merely reporting the mean scores and SD does not statistically demonstrate whether the differences in mean scores are significant. It would be more convincing to conduct t-tests or ANOVA (preferably repeated measures ANOVA with post hoc tests, based on the current experimental design) and report the relevant statistics (e.g., t and F values, as well as p values). Physical World Evaluation: In the physical world evaluation, the paper only compared two models, one for a normal and another for the generated camouflage. Have the authors considered including models with other adversarial camouflage methods for comparisons, as the authors did in the digital world? Confidence: 4 Soundness: 4 Presentation: 3 Contribution: 4 Limitations: Perform a thorough comparison with state-of-the-art methods like AdvCam and UAPs that are known for their effectiveness. Discuss the differences in performance metrics such as attack success rate, naturalness, and computational efficiency. Highlight the advantages and limitations of CNCA relative to these methods. Flag For Ethics Review: ['Ethics review needed: Research involving human subjects'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: W1: The explanation of the adversarial feature generation and its integration with the diffusion model is convoluted. Quantitatively define the evaluation indicators of naturalness and attack performance or provide relevant references. During the normal T2I diffusion model inference process, the text prompt is encoded to a text feature vector with the shape of (N, W) to guide the denoising process. N is the number of tokens, and W is the feature dimension of the token embedding. Our method introduces an adversarial feature vector with the shape of (M, W). M is a hyperparameter that defines the size of adversarial information. During the adversarial camouflage generation, the clipping strategy regulates the adversarial feature vector. Then, it is concatenated with the text embedding feature to form the combined feature vector with the shape of (M+N, W) as input to the diffusion model. The diffusion generates vehicle texture, and the detector processes the camouflaged vehicle image. The adversarial feature is optimized by the detector's adversarial loss. The quantitative measurement of attack effectiveness used in our paper is car AP@0.5. This metric is computed based on the precision-and-recall curve for the car category. It's a popular performance metric for object detection, whose definition can be found in[1]. Previous state-of-the-art methods like DTA and ACTIVE have used this metric to evaluate their attack performance. The most relevant previous work on quantitative measuring of naturalness is S. Li et al. [2]. They collected vehicle images and human rating data to train a model to assess the naturalness automatically. We try to use their trained model in our case. However, we found a bias of low scoring towards vehicles with full-covered paintings, even if the painting is human-designed and looks natural. All the baselines except DAS receive low scores. We suspect it is because the dataset lacks full-cover painting vehicle images. As a result, we follow the previous work of Hu et al. [3] to conduct a subjective survey to evaluate the naturalness directly. To maintain the fairness of the survey, we invited 45 participants from different ages, backgrounds, and genders, which is twice the number (24) in [3]. [1] Everingham, Mark, et al. "The Pascal visual object classes (VOC) challenge." International journal of computer vision 88 (2010): 303-338. [2] S. Li et al., “Towards Benchmarking and Assessing Visual Naturalness of Physical World Adversarial Attacks,” In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2023, pp. 12324–12333, May 2023. [3] Hu, Yu-Chih-Tuan, et al. "Naturalistic physical adversarial patch for object detectors." Proceedings of the IEEE/CVF International Conference on Computer Vision. 2021. W2: Assess the scalability of CNCA by testing on larger, more complex scenes and different environmental conditions to validate its general applicability. The camouflage generated by our work needs to be deployed on a 3D model in the simulator or on a real vehicle model to get test data. Our generated camouflage cannot extend to the KITTI and Waymo datasets, which only contain 2D videos and images of vehicles. We try to extend our physical evaluation in indoor and outdoor scenarios and compare our method with previous baselines, as shown in Table 2 and Figure 1 in the attached PDF. The results show that our methods can achieve competitive attack performance among previous baselines. We acknowledge that our current evaluation is limited in scale and conditions due to our limited resources and budget. We agree that the road test evaluation for our method is essential, especially for autonomous driving. But due to its high time and labor cost, we plan to explore this in our future work. W3: The paper lacks ablation studies to isolate the impact of different components of the proposed framework. We have added extra ablation studies to demonstrate the contribution of each component, including the diffusion model, adversarial feature, clipping strategy, and mask reordering. Due to the word limits, please find the details of the ablation study in G1 section the global Author Rebuttal. Q1: Experimental Statistical Significance: conduct t-test and ANOVA test to prove the significance of the naturalness survey data. Thanks for your suggestion. We conduct a t-test and ANOVA with a post-hoc Tukey HSD test on our data. The results of the t-test are: \| Compare Method \| t Value \| p Value \| \|----------------\|---------\|-----------\| \| Normal \| 8.72 \| < .00001 \| \| DAS \| -3.18 \| 0.00108 \| \| FCA \| -2.77 \| 0.00358 \| \| DTA \| -4.04 \| 0.00007 \| \| ACTIVE \| -4.13 \| 0.00005 \| The results of the ANOVA with post-hoc test are: \| Compare Method \| Q Value \| p Value \| \|----------------\|---------\|---------\| \| Normal \| 11.18 \| 0.001 \| \| DAS \| 4.77 \| 0.011 \| \| FCA \| 4.44 \| 0.023 \| \| DTA \| 5.91 \| 0.001 \| \| ACTIVE \| 6.08 \| 0.001 \| The p values of the t-test and ANOVA test are lower than 0.05. Hence, we can conclude that the differences between the baselines and CNCA in the naturalness evaluation are significant. Q2: Include models with other adversarial camouflage methods for comparisons in the physical world evaluation. Please refer to the reply to W2. L1: Compare CNCA with methods like AdvCam and UAPs. Methods like AdvCam and UAPs can generate natural and effective physical adversarial examples based on one 2D image of the object. However, these physical adversarial examples are not robust against diverse viewing angles because they are typically optimized for a fixed viewing angle. As a result, these methods are not competent for our task because the attack needs to be effective at various viewing angles and distances. Therefore, we did not compare these methods with CNCA. --- Rebuttal Comment 1.1: Comment: The authors provided thorough explanations and additional experiments to address concerns. The integration of adversarial features has been clarified with the diffusion model and provided relevant metrics for naturalness and attack performance. Additional studies were conducted, isolating the impact of each component in the framework. The authors extended their evaluation to more complex scenarios, though they acknowledge limitations due to resource constraints. The authors have mentioned that this paper need larger-scale evaluations in future work, with more immediate tests in varied environments. --- Rebuttal 2: Title: Response to Reviewer TBRf Comment: Dear Reviewer TBRf, We sincerely appreciate your time and effort in reviewing our work and rebuttal. We kindly ask you to consider whether our improvements might justify a higher rating. We believe the extended ablation studies for each component in our pipeline and both indoor and outdoor physical evaluations with previous methods have strengthened the quality of our work. We would be happy to provide further clarifications if you have further questions. Thanks again for your time and effort in reviewing our paper! Best Regards， Authors of Submission 17110	Rebuttal 1: Rebuttal: We want to thank all the reviewers for their insightful comments on our work. Most reviewers mention the ablation studies of CNCA pipeline components and comparisons with the previous baselines in the physical world. Hence, we have extended the ablation study and physical evaluation as suggested, which are discussed in the following sections. G1. Ablation studies for each CNCA pipeline component. \| Pipeline \| No Diff. \| Diff. \| Diff. + Adv. \| Diff. + Adv. + Clip \| Diff. + Adv. + Clip + Reorder \| \|-----------------------------\|----------\|-------\|--------------\|---------------------\|------------------------------\| \| AP@0.5 \| 0.619 \| 0.553 \| 0.520 \| 0.494 \| 0.479 \| \| Natural Score \| 1.00 \| 3.37 \| 1.71 \| 2.75 \| 3.33 \| The above table shows the results of the ablation studies for each component of the pipeline. During the ablation study, we gradually add each component to see their contribution to attack performance and naturalness. All the test pipelines with the diffusion model use the same input text prompt: "yellow black graffiti." The description for each test pipeline is the following: - No Diff. directly optimizes the texture image of the vehicle at a pixel level, resulting in an unnatural texture; - Diff. introduces the diffusion model to generate the texture image compared to No Diff., which improves the naturalness score; - Diff.+Adv. introduces the adversarial feature compared to Diff.. This enables the texture image generation guided by the adversarial gradient from the detector. With this component, the attack performance is improved, but the naturalness is compromised; - Diff.+Adv.+Clip introduces the clipping strategy compared. to Diff.+Adv., which improves the naturalness; - Diff.+Adv.+Clip+Reorder is our final pipeline, which uses a reordered texture map compared to Diff.+Adv.+Clip, which further improves the attack performance and naturalness. To summarize, the ablation studies demonstrate that all the components of our pipeline contribute to improving the camouflage's attack performance and naturalness. Please refer to Table 1 in the attached PDF for the above table and the corresponding generated texture images. G2. Comparison with the previous baselines in the physical world. We implement four previous baseline camouflages in the physical world for comparison and add more physical world testing scenarios. To be specific, our latest physical experiments are conducted in both indoor and outdoor scenarios. In each scenario, we choose two distances and two elevation angles. We also choose 24 azimuth angles for the outdoor scenario and 27 azimuth angles for the indoor scenario. The physical test set contains 204 images for each method. In the attached PDF, the comparison of the methods is shown in Table 2; examples of indoor and outdoor environments are shown in Figure 1. The results show that our method still achieves comparable attack performance with previous baselines in the physical world. Pdf: /pdf/aba84eb5a1fa8e2e9b18b0db0b07f88033631cce.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
CA-SSLR: Condition-Aware Self-Supervised Learning Representation for Generalized Speech Processing	Accept (poster)	Summary: This work proposes a method to automatically condition a (frozen) speech foundation model to a particular language and/or speaker. This method consists of 2 parts; they use an ECAPA-TDDN model to compute speaker or language embeddings from a set interval of intermediate layers of the SSL model, and a conditioning layer which uses those embeddings to modify subsequent layer outputs of the SSL model. The authors conduct experiments with the multilingual SUPERB benchmark (for language identification and ASR) and VoxCeleb1 dataset (for speaker recognition). Edit Rebuttal: Houlsby adapter was addressed, presentation style was addressed but cannot be judged. Updated score from reject to borderline reject. Strengths: This work tackles the difficult problem of using a single model to perform ASR on 123 languages, with only 1 hour of training data for each language. They show that, during inference on the test set, making use of a ground-truth language label significantly improves the character error-rate, indicating that baseline models like wav2vec2-xlsr do not adequately activate the representations of a specific language. The authors propose a method where a model can learn to condition itself during inference on a specific target domain. Weaknesses: The presentation of this paper is, in my opinion, subpar to what is expected for NeurIPS. Most importantly, I found it difficult to grasp the proposed method from the methodology section. Line 123-131 are copied from the related work section. Line 133 introduces a “hierarchy” of conditioners, but hierarchy is never explained. Then line 140 assumes the reader is very familiar with TCAC while it has not been explained yet. Line 141 to 146 mention a lot of different configurations related to SV and LID decoders, this could be streamlined into a single “standard” setup, while the experimental section could ablate on different settings. Moreover, I think that the speaker decoder story only distracts from the interesting results of this paper (e.g., Table 1, Table 2, Figure 2 do not make use of the speaker decoder at all, so why make the method section hard to understand by including it?). Furthermore, I cannot implement the conditioner (TCAC) from the description in line 156-170. Also, line 221-222 should be in the method section. In the experiment section, references to the appendix should be made to guide the reader to relevant information regarding experimental details. I cannot judge whether the current experimental setup is fair. Furthermore, I think some relevant literature and methodology is missing: [1] Houlsby, Neil, et al. "Parameter-efficient transfer learning for NLP." International conference on machine learning. PMLR, 2019. [2] Thomas, Bethan, Samuel Kessler, and Salah Karout. "Efficient adapter transfer of self-supervised speech models for automatic speech recognition." ICASSP 2022-2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2022. [3] Otake, Shinta, Rei Kawakami, and Nakamasa Inoue. "Parameter efficient transfer learning for various speech processing tasks." ICASSP 2023-2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2023. [4] Peng, Junyi, et al. "Parameter-efficient transfer learning of pre-trained transformer models for speaker verification using adapters." ICASSP 2023-2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2023. I think a comparison with the standard adapter from [1] is required. To keep things as simple as possible, instead of the proposed TCAC, the adapter from [1] could potentially use the ECAPA-TDNN langauge/speaker embedding as a second input. I’ll end with listing minor (formatting) issues: * Line 20: inconsistent citation style * Line 34: word ‘ControlNet’ missing * Line 37: this challenge instead of these challenges (labeling data is a solution, not a challenge) * Line 44,52: CA-SSLR instead of CA-SSL * Line 76,78,80,84: hyperbolic language * Line 84-86: This sentence does not make sense to me * Line 87: inconsistent citation style * Figure 1: “Condition-aware” instead of “conditioned-aware" * Multiple instances where an abbreviation is explained while it has been used previously, e.g. CER in line 249, * Figure 2 is unreadable in black and white print, using a different marker for each hue could alleviate this problem. * Line 199: inconsistent citation style * Line 280: requires instead of required * Line 280: Real-Time Factors * Most justifications in the paper checklist contain a spelling mistake, are missing, or do not refer correctly. Also, the instruction block was not deleted. Technical Quality: 2 Clarity: 1 Questions for Authors: I do not understand the time-channel attention conditioner. Given formula 1, what are \alpha, \gamma, and \beta? Are they a function? In line 164, they are defined as vectors? In line 166, you mention a linear layer to compute attention scores? How are these attention scores used? Do you not use a self-attention layer? It is unclear to me how exactly the time-channel attention conditioner is used within the SSL model. Given formula 1, I assume the conditioner is inserted between each wav2vec 2.0 transformer layer? In section 5.1, does the LID-FT experiment imply 2 fine-tunings, first on LID (with what data?), and then on ASR (with what data?), where the first fine-tuning updates the SSL model, and the second only the ASR decoder? In section 5.1, what hyperparameters were used for these experiments? Is there a more comprehensive learning rate scan for the LID-TCAC setting compared to the XLSR-R baseline and LID-FT setting? Are they conducted with the same amount of update steps? In section 5.1, line 236, it states “only TCAC layers are updated”, while I assume the ECAPA-TDNDN language ID decoder was also trained? In section 5.2, Table 2 states ASR adapted, but aren’t the models adapted to language ID? In section 5.2, how do you condition using the ground-truth language ID labels? In the same context, how are hard-predicted and soft-predicted language labels used for conditioning, and where do they come from? In section 5.2, second paragraph, are the results shown in Figure 2 all your experiments? Regardless, how did you ensure a fair comparison (learning rate scan, number of updates)? Why did you choose to compare with LoRA? You mention that Chen et. al. [2023b] shows marginal improvements for LoRA, but this paper shows that AdapterBias and Houlsby are more effective for ASR? Confidence: 3 Soundness: 2 Presentation: 1 Contribution: 3 Limitations: While the proposed method improves performance for the specific condition of the ML-SUPERB benchmark, it might not work as well with unbalanced datasets (e.g., 100 hours of english data language, 1 hour of spanish and mandarin data). Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your detailed comments, which have helped us improve our manuscript. Below are our clarifications: Speaker Decoder and Generalization Ability: We respectfully disagree that the speaker decoder detracts from the results. We intend to show that integrating conditioning in the SSL improves unseen tasks. In Table 1, CA-SSLR conditioners/LID-decoder are trained on LID loss, then frozen, and the ASR decoder is trained on top. Thus, no component in the CA-SSLR encoder is trained for ASR but obtains improvements w.r.t. Baseline. In the same manner, CA-SSLR$^L$ models improve SV by 20% while the CA-SSLR$^L$ encoder conditioners were adapted on ASR and LID losses, not SV. Therefore, the speaker decoder is essential for demonstrating the generalization ability of our condition-aware approach and showing that CA-SSLR$^L$ is a generalist encoder. Comparison with Houlsby Adapter ([1], Chen et al. [2023b]): CA-SSLR not only offers parameter-efficient fine-tuning (PEFT), but its principal contribution lies in incorporating dynamic adaptation to the language and speaker of the input, thereby improving generalizability, as noted by Reviewers iiaB and Jsg6. We performed additional experiments using the Houlsby adapter, as shown in Table A of the rebuttal PDF. Our ASR-CA-SSLR approach outperforms the ASR-Houlsby adapter, achieving WER of 18.6% and 31.6% compared to 20.3% and 34.6%, respectively. In SV, CA-SSLR improves EER from 1.29 to 1.15, while the Houlsby adapter worsens it from 1.29 to 1.37 compared to the XLS-R baseline. These results suggest that standard adaptation methods lack the enhanced generalization capabilities inherent to CA-SSLR. We appreciate the suggestions and plan to explore integrating our conditioner into the Houlsby adapter in future work. Unbalanced Dataset and Performance It's important to highlight that ML-SUPERB includes 20 few-shot languages with only five utterances each for ASR to evaluate performance on unbalanced datasets. Improvement in few-shot CERs is documented in Tables 1 to 3, Figure 2, Appendix Table 8, and additional Table A. These results demonstrate CA-SSLR's robustness in unbalanced scenarios. Fair Comparison and Hyperparameter Search: We confirm that the model parameters, learning rates, and batch size for ASR training are consistent with those in the ML-SUPERB benchmark paper. Parameters specific to the LID and SV decoders, such as dropout rates and hidden channels, were set using frozen SSLR settings to ensure a fair experimental setup. We added a reference in Section 4.2 to Appendix A.1 for clarification. Enhancements in Presentation: - Removed the duplicated content in Lines 121-131. This duplication was inadvertently introduced by one of the authors who didn’t notice that this content had been moved to another section. - Revised the hierarchical writing with Figure A. - Moved TCAC explanation before line 140 and substituted text with precise equations to assure reproducibility. - Consolidated SV and LID configurations in lines 141-146 into a standard setup, relocated to the experimental section. - Moved the information in 221-222 to the methods section. - Included suggested parameter-efficient transfer learning references [1~4] in the related work and fixed the minor formatting issues. We add the following equations for TCAC Implementation: The TCAC module process latent representations at layer $l$, $\mathbf{S}^{(l)}\in\mathbb{R}^{C\times T}$, and the latest estimate of the conditioning features $\mathbf{z}\in\mathbb{R}^R$ and generates modulated latent representations $\mathbf{\tilde{S}}^{(l)}$ as $$\mathbf{\tilde{S}} _{t,c}^{(l)} = \text{TCAC}(S _{t,c}^{(l)}, \mathbf{z}) = \tilde{\gamma} _{t,c}^{(l)}(\mathbf{z}, S^{(l)})S _{t,c}^{(l)}+ \tilde{\beta} _{t,c}^{(l)} (\mathbf{z}, S^{(l)})$$ Thus, the latent features are modulated by time-channel dependent scales $\tilde{\gamma} _{t,c}^{(l)}$ and biases $\tilde{\beta} _{t,c}^{(l)}$, obtained by: $\tilde{\gamma}_{t,c}^{(l)} (\mathbf{z}, \mathbf{S}^{(l)})=\alpha_t^{(l)}(\mathbf{z}, \mathbf{S}^{(l)})\times \gamma_c^{(l)}(\mathbf{z})$ $\tilde{\beta}_{t,c}^{(l)} (\mathbf{z}, \mathbf{S}^{(l)})=\alpha_t^{(l)} (\mathbf{z}, \mathbf{S}^{(l)}) \times \beta_c^{(l)}(\mathbf{z})$ where channel-dependent $\gamma^{(l)},\beta^{(l)}\in \mathbb{R}^C$ are obtained as $\gamma^{(l)}(\mathbf{z})=\mathbf{W}_\gamma^{(l)}\mathbf{z}+\mathbf{b} _\gamma^{(l)}$ $\beta^{(l)}(\mathbf{z}) = \mathbf{W}_\beta^{(l)} \mathbf{z} + \mathbf{b} _\beta^{(l)}$ The time-dependent scales $\alpha^{(l)} \in \mathbb{R}^T$ are obtained with an additive attention mechanism as $\alpha^{(l)} _t(\mathbf{z}, \mathbf{S}^{(l)}) = \mathbf{v}^T _\alpha f(\mathbf{W} _\alpha^{(l)} [\mathbf{S} _t^{(l)T} \mathbf{z}^T]^T$+ $\mathbf{b} _a^{(l)})$ where $f(.)$ is a ReLU non-linearity, $\mathbf{W} _\alpha^{(l)}\in \mathbb{R}^{C'\times (C+R)}$, $\mathbf{b} _\alpha^{(l)}\in\mathbb{R}^{C'}$, and $\mathbf{v _\alpha}\in\mathbb{R}^{C'}$. We obtained the conditioning features $\mathbf{z}$ from the hard decisions or internal embedding layer $\mathbf{e}\in\mathbb{R}^E$ of the intermediate decoders, by $\mathbf{z} = \mathrm{LayerNorm}(\mathbf{W} \mathbf{e} + \mathbf{b})$, where the affine transform parameters $\mathbf{W}$, $\mathbf{b}$ are shared across TCAC layers. Additional Clarifications: - Alpha, beta, and gamma are functions that predict vectors, in parts of the text the dependency on (z,S) is dropped to keep the notation uncluttered. - The conditioning feature can be derived from the decoder's second last layer (embedding layer) or decoder output (either as hard or soft labels). - The LID decoder was updated with the pre-trained, frozen SSLR model but remained frozen during TCAC training, as shown in Figure A. - "ASR-adapted" refers to training CC/TCAC with ASR loss only. - TCAC is integrated within wav2vec 2.0 layers after the self-attention module. These details are included in the model architecture section. --- Rebuttal Comment 1.1: Comment: Thanks for these clarifications and new experiments. I've raised my score, incorporating the new experiments comparing to Houlsby, and the inability to grok the updated presentation style fully (due to no fault of your own). --- Reply to Comment 1.1.1: Comment: Thank you for considering our clarifications and new experiments. We appreciate your adjusted score and will work to further improve the clarity of our presentation.	Summary: This paper employs multi-task learning with hierarchical conditioning to adapt pre-trained speech SSL models. By utilizing lightweight task-related auxiliary decoders repeatedly at various positions, the method gradually tailors the SSL representations. A time-channel-dependent conditioner is introduced to facilitate the fusion process. By incorporating LID and Speaker SV decoders, the proposed approach achieves significant improvements in multi-lingual ASR, LID, and SV. Strengths: - The method is novel in reusing the decoders multiple times for incremental conditioning. - The framework is general for various sets of speech tasks. One could change the conditioning decoder(s) according to the target tasks. - Relatively strong results in adapting SSL models for multi-lingual ASR, which may inspire more SSL-based methods in multi-lingual scenarios. Weaknesses: Although the authors refer to the proposed model as "generalist", it still requires proper selection of conditioning/auxiliary decoders according to the target tasks. In the paper, the major task is multi-lingual ASR and the initial conditioning decoder is a language identifier, which are closely related. As illustrated in Table 4, further incorporating the SV conditioner leads to less performance gain. A terming issue: the "Time-wise Attention" seems time-dependent scaling rather than an "attention mechanism". In Eq. (2), $\alpha_t^{(l)}(\textbf{z}, \textbf{S}^{(l)}) \in \mathbb{R}^T$ is computed frame-wise with a linear projection, and it scales the SSL features at different timesteps without interactions among frames/timesteps. Technical Quality: 4 Clarity: 3 Questions for Authors: (Line 144-145) It states "... the TCAC, SV, and LID decoders are trained...". But in Figure 1, the two decoders look frozen and the caption confirms this. Which is the actual setting? (Line 163) It states that the output projection layers of conditioners are all shared. But as stated at line 221, each auxiliary decoder, at different points, takes the previous SSL representations using a weight average. Are those weights and input projection layers partially shared across positions, or totally position-dependent? (Line 188) What augmentation is leveraged in the "Extended Few-shot condition"? (Line 236) Which model does "the pre-trained and fixed SSLR model" refer to? If it refers to "XLS-R" in Table 1, then it is a bit confusing because a prediction head is added and the SSLR model is not purely pre-trained. (Line 251) The conditioner takes $z \in \mathbb{R}^{C_E}$ as input, then how is it adpted to consume LID labels? Some illustrations here would avoid confusion. (Table 4) Why is $\text{CA-SSLR}^{L,S}(\text{TCAC})$ not compared? As Eq. (3) mentions the adaptation method of this "full configuration", it is surprising that it does not appear in the final comparison. Some personal suggestions/concerns regarding the presentation: - Line 145: "ASR,a" -> "ASR," - Line 163 implies the re-estimation is conducted every three layers for both LID and SV, which conflicts with the actual setting. - Table 4: the results are derived by jointly optimization for all three tasks, including system "+ FT", but this operation is not explicitly mentioned in the experiment setting, which could be confusing at first. Confidence: 4 Soundness: 4 Presentation: 3 Contribution: 3 Limitations: The authors have adequately addressed the limitations and potential negative societal impact of their work. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thanks for the comment. Here are some clarifications. Regarding the generalist model concern, we want to emphasize that CA-SSLR is considered a generalist model because it maintains the base model's integrity while improving performance on previously unseen tasks. In Table 1, CA-SSLR conditioners/LID-decoder are trained on LID loss, then frozen, and the ASR decoder is trained on top. Thus, no component in the CA-SSLR encoder is trained for ASR but obtains improvements w.r.t. Baseline. In the same manner, CA-SSLR$^L$ models improve SV by 20% while the CA-SSLR$^L$ encoder conditioners were adapted on ASR and LID losses, not SV, showing that CA-SSLR$^L$ is a generalist encoder. We acknowledge the concern about using the term "Time-wise Attention." Although it seems like time-dependent scaling, it fits the concept of additive attention, without normalizing weights to sum up to one with softmax. We observed that removing the softmax provided better results. Our approach involves using a linear projection to compute $\alpha _t^{(l)}(z, S^{(l)} _{t,c}) \in \mathbb{R}^T$ by concatenating a single feature vector $\mathbf{z}$ with $S^{(l)} _{t,c}$ at each timestep, similar to the method used in [A]. This process assigns different weights to each timestep, allowing us to scale $S^{(l)} _{t,c}$ accordingly. Even though there are no direct interactions between timesteps, the dynamic assignment of weights based on features aligns with the principles of attention, as the approach applied in [B]. In Table 4, we have updated CA-SSLR$^{L,S}$ TCAC results for comparison with XLS-R, achieving the best results in LID and ASR and ranking second in SV, showing strong adaptation capabilities while maintaining competitive generalization ability. \| Model \| LID (10min) \| ASR \| EER \| CDF \| LID (1h) \| ASR \| EER \| CDF \|------------------------------------------\|----------\|----------\|----------\|----------\|----------\|----------\|----------\|----------\| \| XLS-R \| 89.0 \| 29.0 \| 1.29 \| 0.093 \| 90.9 \| 22.7 \| 1.29 \| 0.093 \| \| + CA-SSLR$^{L,S}$ (CC) \| 89.1 \| 18.8 \| 1.04 \| 0.075\| 88.1 \| 15.0 \| 0.94 \| 0.073\| \| + CA-SSLR$^{L,S}$(TCAC) \| 89.0 \| 18.3 \| 1.11 \| 0.086 \| 93.5 \| 14.4 \| 1.01 \| 0.077 \| Regarding the confusion about frozen and trainable parameters, first, we train the LID decoder on the pre-trained SSL model. The decoder gets a weighted average of the SSL encoder layers. Afterward, this LID decoder is then frozen and used to get the conditioning features that are fed to the LID TCAC conditioners. In this case the LID decoder gets a weighted average of the CA-SSLR encoder layers computed up to that point, and the conditioning feature is recomputed every three CA-SSLR layers. Here, we only train the linear projection before the LID decoder and the LID TCAC parameters to the LID-conditioned CA-SSLR encoder, termed CA-SSLR$^L$. Similarly, the SV decoder is trained on top of the CA-SSLR$^L$ then frozen. Then, we just train the SV TCAC parameters to get the CA-SSLR$^{L,S}$. The adaptation training has been detailed in Figure A of the rebuttal PDF and will be added to Sec. 3. We also update lines 144 and 145 to avoid confusion. Regarding parameter sharing, the only layer-dependent features used for calculating the condition feature z are the linear projections for the decoders and the weights used for the weighted sum of the SSL layers before the linear predictions, as shown in Figure A of the rebuttal PDF. All other decoder parameters are shared. For the extended few-shot condition, the original ML-SUPERB settings include "normal languages" with 10 minutes to 1 hour of data per language and "few-shot languages" with only 5 utterances each. In the "extended few-shot condition," we incorporate the language labels from these few-shot data for LID training but continue using only 5 utterances with transcriptions for ASR training. This is because language labels are more accessible to obtain than transcriptions. We will add this table to the appendix to clarify these settings. \| Data Per Language \| Language Type \| LID Training \| ASR Training \| \|-------------------------\|----------------------\|---------------------------------------\|------------------------------------------\| \| Original Settings \| Normal \| 10 min - 1 hr \| 10 min - 1 hr with transcription \| \| \| Few-shot \| Not used for LID \| 5 utts with transcriptions \| \| Extended Few-shot \| Extended Few-shot \| 10 min - 1 hr \| 5 utts with transcriptions \| Regarding whether the "pre-trained and fixed SSLR model" refers to XLS-R, Yes, it does refer to the frozen pre-trained XLS-R model with a trained decoder head. We will update the sentence to "frozen XLS-R model with ASR decoder" for clarity. Regarding the condition feature z, we have updated the sentence in L163 for clarity: "We re-estimate the condition feature 𝑧 from the updated language or speaker embedding every three layers using a linear projection and layer normalization, which are shared across layers.” This has been revised to “As shown in Figure A, 𝑧 is derived from the updated language or speaker embedding through a linear projection layer or an embedding layer for hard LID/SV labels.” [A] Luong, M. T., Pham, H., & Manning, C. D. (2015, September). Effective Approaches to Attention-based Neural Machine Translation. In Proceedings of the 2015 Conference on Empirical Methods in Natural Language Processing (pp. 1412-1421). [B]Lin, Z., Feng, M., dos Santos, C. N., Yu, M., Xiang, B., Zhou, B., & Bengio, Y. (2022, July). A STRUCTURED SELF-ATTENTIVE SENTENCE EMBEDDING. In International Conference on Learning Representations. --- Rebuttal Comment 1.1: Comment: Dear Reviewer 4eyk, As the discussion between the reviewers and authors is coming to an end, could you please respond to the authors to confirm whether your concerns have been addressed? Thanks! AC	Summary: This paper introduced a framework, CA-SSLR, that integrates conditioning into pre-trained Self-Supervised Learning (SSL) models by adapting only the trainable conditioner. Through a hierarchical self-conditioning mechanism, CA-SSLR can match or achieve better the performance of single-task fully fine-tuned models and benefit from more efficient model tuning. CA-SSLR offers a versatile and efficient approach to integrating conditioning information into pre-trained models. Strengths: The strengths of the paper are: 1. Good presentation of the proposed framework. 2. Strong results on different tasks and different scenarios. Weaknesses: The weaknesses of the papers are that the overall system might be complicated because of performing multiple tasks and some tasks would be dependent on the output of other tasks. As a result, the inference cost would be increased for the subsequent tasks. Technical Quality: 3 Clarity: 3 Questions for Authors: Here are some minor concerns to the paper: 1. Is it necessary to provide the rel RTF in Table 3 and 4? I feel like the absolute value would be enough though. 2. It is intuitive that the multilingual ASR model can be improved by using LID as the condition. Is there a cascaded baseline doing LID + ASR that the pretrained model is not fused? The results can help us understand the real effectiveness of the proposed framework. 3. Since the proposed framework achieves better parameter efficient finetuning, is there a training speed or peak memory usage comparison between the proposed method and full finetuning? How about its efficiency compared to other PEFT methods, like LoRA? Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The advantage of the paper is to use less resources than full finetuning but achieve similar performance. However, the inference cost is increased. This can be problematic when the method is used in real applications. The inference cost might weigh more than the training cost when the training cost is affordable. Another limitation is that the framework cannot be used for streaming purposes as mentioned by the authors. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for the insightful comment. Here are some clarifications. Regarding inference cost, the encoder parameters are shared among all three tasks, which helps to minimize expenses. The LID decoder is lightweight, with an RTF of less than 0.001, so it doesn't significantly add to the computational load of the ASR task. While the ASR and SSL models are more complex, with single-pass RTFs of 0.004 and 0.016, respectively, they may need multiple inferences based on the decoding algorithm. As shown in Tables 9 and 10, the CA-SSLR system achieves 30 to 45% faster RTF than multi-task baselines across different components and scenarios. Concerning the cascaded baseline, we examined the cascading baseline for LID + ASR in Table 2 and Figure 2. In this method, we train the LID decoder with a pre-trained SSL model and use another SSL model with TCAC components to train the ASR decoder. Our findings indicate that the TCAC can achieve performance comparable to a fully fine-tuned approach for languages with abundant resources and surpasses the fully fine-tuned approach in few-shot ASR languages. To assess training speed and peak memory usage, we compared the CA-SSLR approach with the additional baseline, Houlsby Adapter, and a fully fine-tuning approach (the results comparing the Houlsby Adapter and CA-SSLR$^{L}$ are detailed in Table A of the rebuttal PDF). We evaluate the training speech for 10k iterations with batch size 8, and the results are shown in the following table: \| Method \| Bottleneck Dims. \| Training Speed \| Peak Memory Usage \| \|---------------\|------\|---------------------------------------------\|-----------------------\| \| Houslby Adapter \| 256 \| 76 mins \| 58B \| \| CA-SSLR$^{L}$(3L) \| 256 \| 120 mins \| 68B \| \| FT \| - \| 135 mins \| 79B \| we found that the CA-SSLR approach ranks second compared to the Houlsby Adapter and a fully fine-tuning approach in speed and memory usage. However, CA-SSLR surpasses the Houlsby Adapter in adaptation effectiveness, as shown in Table A(b) of the rebuttal PDF. It also demonstrates the best generalization ability among the three methods, detailed in Tables 1, 4, and A. Additionally, we acknowledge that the current implementation is not yet optimal and are committed to further improvements. --- Rebuttal Comment 1.1: Title: Reply to the rebuttal Comment: Thanks for the rebuttal. My concerns have been addressed. If the explanations can be included in the revised version, I am willing to raise my score to 6. --- Reply to Comment 1.1.1: Comment: Thank you for your feedback. We’re glad to hear that your concerns have been addressed. We will definitely include the explanations in the revised version.	Summary: The paper introduces a method named CA-SSLR, a versatile model for various speech-processing tasks that integrates language and speaker embeddings from earlier layers to reduce reliance on input audio features while preserving the base model's integrity. More specifically, both LID and SID conditioning features are integrated as additional inputs for the SSL model. The proposed approach shows advantages in improving the downstream speech tasks. ML-SUPERB dataset is used in the evaluation, which shows superior performance over the conventional SSL models. Strengths: - The paper is well-written and easy to follow. The topic is interesting, and the proposed idea is simple yet effective. - The experiments are thorough and convincing. Weaknesses: - There is no comparison between the proposed approach and the SOTA numbers on ML-SUPERB. Readers would likely be interested in understanding the gap between the proposed approach and the SOTA numbers. - It is somewhat unclear when to use the proposed TCAC, as sometimes using CC (without attention) seems sufficient, as shown in Table 2 and Table 4. More analysis should be provided to explain these results, rather than just mentioning them. Technical Quality: 3 Clarity: 3 Questions for Authors: 1. The first question relates to the second point in the weaknesses: when is attention necessary? Can we visualize the attention using one or two examples? 2. Which layers are helpful in generating the embeddings? 3L and 4L are reported in the tables; are the shallow layers sufficient? Confidence: 5 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: See the Weaknesses. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for the helpful comments. Here are some clarifications. First, for the generalist model without fine-tuning, the SOTA results for pre-trained SSLR models can be found in the paper ML-SUPERB challenge [A], where the MMS-1b model performs the best with 1hr ASR WER 18.1% and LID accuracy 86.1% respectively (see the table below). However, we used XLS-R 300M to make our experiments feasible. Second, with fine-tuning, the single-task SOTA results can be found in Table 1 and Figure 2, with 90.1% LID accuracy and 17.3% ASR CERs. \| SSL Model \| Model size \| 10mins LID \| 10mins ASR \| 10mins ASR \| 1hr LID \| 1hr ASR \| 1hr ASR \| \|-------------\|-----------------\|------------------------\|-----------------\|-----------------\|----------------------\|-----------------\|-----------------\| \| \| \| Normal \| Normal \| Few-shots \| Normal \| Normal \| Few-shots \| \| XLS-R~\citep{shi2023ml} \| 0.3B \| 66.9 \| 29.2 \| 40.9 \| 87.9 \| 22.0 \| 39.3 \| \| MMS-1b ~\citep{shi2023findings} \| 1B \| 84.8 \| 21.3 \| 30.2 \| 86.1 \| 18.1 \| 30.8 \| \| XLS-R (Ours) \| 0.3B \| 89.0 \| 29.0 \| 39.0 \| 90.9 \| 22.7 \| 36.9 \| \| + Embed TCAC^{L} \| 0.3B \| 89.0 \| 17.8 \| 31.8 \| 90.9 \| 13.5 \| 31.4 \| \| + CA-SSLR^{L} (TCAC, 3L) \| 0.3B \| 88.6 \| 18.6 \| 31.6 \| 93.4 \| 15.1 \| 29.6 \| We found that compared with the MMS-1b baseline, the proposed system achieves better results in Normal languages and comparable results in few-shots languages than the model with three times more parameters (300M vs. 1B). We will add these results in Table 3. Regarding the concern about using shallow layers, we would like to clarify that the CA-SSLR system recomputes the embeddings every 3 or 4 layers rather than predicting only once in the initial layers, as shown in Table A in the rebuttal PDF. From the SSL feature weights utilized by the LID and SV decoders, we observe that LID weights are evenly distributed, while SV weights are more concentrated in the earlier layers. Consequently, incorporating predictions from higher LID layers can enhance LID accuracy and improve conditioning features. Conversely, for SV, using only the first 6 or 12 layers of XLS-R might be sufficient. We will further explore this in future work. While CC applies the same transformation to all time frames, we added the attention module in TCAC to be able to emphasize different time-frames of the encoded features within the SSLR layers. When deciding between TCAC and CC, our experiments indicate that TCAC provides better results for LID and ASR. However, as shown in Table 4, CC currently yields slightly better results for SV. Overall, relative improvements of TCAC in ASR and LID are larger than relative degradation in SV. We plan to conduct further investigations to enhance the SV performance of TCAC. In the updated version, we will provide visualizations of the attention mechanism for the TCAC module using one or two examples. We will further provide a more detailed analysis of our results in the revised version. [A] Shi, J., Chen, W., Berrebbi, D., Wang, H. H., Huang, W. P., Hu, E. P., ... & Watanabe, S. (2023, December). Findings of the 2023 ml-superb challenge: Pre-training and evaluation over more languages and beyond. In 2023 IEEE Automatic Speech Recognition and Understanding Workshop (ASRU) (pp. 1-8). IEEE. --- Rebuttal Comment 1.1: Comment: Thanks for the answers. I'm suggesting putting the previous SOTA results (with some descriptions) in the paper as a reference for the readers. I'll keep my rating of the paper. --- Reply to Comment 1.1.1: Comment: Thank you for your positive feedback and suggestion. We will add the SOTA results along with descriptions to the paper.	Rebuttal 1: Rebuttal: Dear Reviewers, We thank the reviewers for their insightful and positive feedback! We are encouraged that they appreciate various aspects of CA-SSLR, including the novelty (Reviewers Jsg6, 4eyk), the clarity and presentation of our writing (Reviewers iiaB, mDev), and the impressive experimental results (Reviewers Jsg6, iiaB, mDev, 4eyk) that demonstrate the benefits and general applicability of our CA-SSLR across multiple tasks and scenarios. Your time and effort dedicated to improving our work are truly appreciated. We have answered all your questions and addressed the issues in detail in our rebuttal and the latest revision. These revisions include additional explanations, paragraphs, and equations to help readers understand the proposed method and additional experiments to highlight its advantages. Most importantly, we have added new results from the Houlsby adapter experiments further to illustrate CA-SSLR's impact on adaptation and generalization abilities (Reviewer xgMo), as well as results for the MMS-1b SSL model to update the current SOTA baseline (Reviewer iiaB). This response offers a high-level overview of these revisions for the convenience of reviewers and future readers. Major revisions include: - New Experiment Results in Sec. 5.2 and Sec. 5.4: A new experimental study of the Houlsby adapter model (Reviewer xgMo). - New Experiment Results in Sec. 5.3 and Sec. 5.4: A new SOTA baseline of the MMS-1b SSL model and CA-SSLRL,S$^{L,S}$(TCAC) (Reviewers iiaB, 4eyk). - Improved Writing in Sec. 3: Added system figure and equations for TCAC and removed duplicate sentences (Reviewers Jsg6, xgMo). Minor revisions include: - A detailed table of the extended few-shot settings is included in the appendix (Reviewer 4eyk). - An analysis of training speed and peak memory usage was added in the appendix (Reviewer mDeV). We hope these revisions address your concerns and improve the overall quality of our paper. Thank you again for your review! Best regards, Authors Pdf: /pdf/c91a9c24ff273ffe588f58854a7301b2701525e3.pdf	NeurIPS_2024_submissions_huggingface	2,024	Summary: This paper introduces conditioning into self-supervised learning of speech representations. In particular, a hierarchical self-conditioning mechanism is introduced where intermediate language and speaker embeddings are used to condition upper layers. The proposed approach is used together with XSLR and mHubert models and several experiments are conducted using the SUPERB benchmark. Strengths: - Multiple experiments are conducted demonstrating the benefits of the proposed method. - A novel conditioning method is introduced for learning speech representations in a self-supervised way. Weaknesses: I think the main weakness of the paper is that it is too dense. Too much information is presented which makes several sections of the paper hard to follow. For example, it's not very easy to follow section 3. It would help if additional equations are added or a more detailed figure is included. Fig. 1 is too high-level and it's not very informative. In addition, some sentences from sections 1 and 2 are literally copied and pasted in section 3. For example, the following sentence can be found both in sections 2 and 3 "Unfortunately, this results in employing a distinct encoder per task, leading to a large increase in computational load that scales linearly with the number of tasks to be assessed.". It would good if the authors rephrase such sentences. There are a few more such examples. Technical Quality: 3 Clarity: 2 Questions for Authors: Please see above. Confidence: 3 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: Limitations have been addressed. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thanks for the insightful comments. We have included additional equations and figures to improve the clarity and address the writing in Sec. 3. Regarding additional figures, we add Figure A in the rebuttal PDF to clarify our system as the elaboration for the original Figure 1. Regarding additional equations, we further add details equations to clarify the Time-Channel Attention Conditioner to form a separate subsection of Sec 3.2 to improve the readability: "As depicted in Fig.1b, the TCAC module ingests the latent representations of the CA-SSLR at layer $l$, $\mathbf{S}^{(l)}\in\mathbb{R}^{C\times T}$, and the latest estimate of the conditioning features $\mathbf{z}\in\mathbb{R}^R$ and generates modulated latent representations $\mathbf{\tilde{S}}^{(l)}$ as $$\mathbf{\tilde{S}} _{t,c}^{(l)} = \text{TCAC}(S _{t,c}^{(l)}, \mathbf{z}) = \tilde{\gamma} _{t,c}^{(l)}(\mathbf{z}, S^{(l)})S _{t,c}^{(l)}+ \tilde{\beta} _{t,c}^{(l)} (\mathbf{z}, S^{(l)})$$ where $t$, $c$, and $l$ represent time, channel, and layer indices, respectively. Thus, the latent features are modulated by time-channel dependent scales $\tilde{\gamma} _{t,c}^{(l)}$ and biases $\tilde{\beta} _{t,c}^{(l)}$. These are obtained as the products: $\tilde{\gamma} _{t,c}^{(l)} (\mathbf{z}, \mathbf{S}^{(l)})=\alpha _t^{(l)}(\mathbf{z}, \mathbf{S}^{(l)})\times \gamma _c^{(l)}(\mathbf{z})$ $\tilde{\beta}_{t,c}^{(l)} (\mathbf{z}, \mathbf{S}^{(l)})=\alpha_t^{(l)} (\mathbf{z}, \mathbf{S}^{(l)}) \times \beta_c^{(l)}(\mathbf{z})$ where channel-dependent $\gamma^{(l)},\beta^{(l)}\in \mathbb{R}^C$ are obtained as $\gamma^{(l)}(\mathbf{z})=\mathbf{W}_\gamma^{(l)}\mathbf{z}+\mathbf{b} _\gamma^{(l)}$ $\beta^{(l)}(\mathbf{z}) = \mathbf{W}_\beta^{(l)} \mathbf{z} + \mathbf{b} _\beta^{(l)}$ The time-dependent scales $\alpha^{(l)} \in \mathbb{R}^T$ are obtained with an additive attention mechanism as $\alpha^{(l)} _t(\mathbf{z}, \mathbf{S}^{(l)}) = \mathbf{v}^T _\alpha f(\mathbf{W} _\alpha^{(l)} [\mathbf{S} _t^{(l)T} \mathbf{z}^T]^T$+ $\mathbf{b} _a^{(l)})$ where $f(.)$ is a ReLU non-linearity, $\mathbf{W} _\alpha^{(l)}\in \mathbb{R}^{C'\times (C+R)}$, $\mathbf{b} _\alpha^{(l)}\in\mathbb{R}^{C'}$, and $\mathbf{v _\alpha}\in\mathbb{R}^{C'}$. We obtained the conditioning features $\mathbf{z}$ from the hard decisions or internal layer (embedding layer) $\mathbf{e}\in\mathbb{R}^E$ of the intermediate decoders, by $\mathbf{z} = \mathrm{LayerNorm}(\mathbf{W} \mathbf{e} + \mathbf{b})$, where the affine transform parameters $\mathbf{W}$, $\mathbf{b}$ are shared across TCAC layers. Thus, TCAC enables the model to dynamically adjust its behavior to the input audio in response to the provided conditioning features." Also, for the Condition-Aware Learning Mechanism, we remove Lines 121-131 to eliminate duplication and focus the section on our unique contribution. This duplication was inadvertently introduced by one of the authors who didn’t notice that this content had been moved to another section. Following are the revisions of the second and third paragraphs in Sec. 3.1: “The proposed CA-SSLR model improves the efficiency of evaluating multiple tasks by introducing a hierarchy of conditioners within the pre-trained SSL encoder layers. It utilizes intermediate predictions from the language identification (LID) and speaker verification (SV) decoders as conditions to recursively adapt subsequent layers, as shown in Figure A. This hierarchical approach structures the SSL encoder layers so that each layer refines its output based on the predictions of the preceding layers. Early layers produce embeddings that capture the essential language and speaker characteristics, which are then used to inform scaling and bias adjustments in later layers. We propose a novel mechanism, the Time-Channel Attention Conditioner (TCAC), which modulates the encoder's hidden representations using time-channel-dependent scales and biases. This approach enables the SSL encoder to dynamically adjust to varying tasks and input conditions. The inputs to these conditioners are embeddings derived from intermediate evaluations of the LID and SV decoders." --- Rebuttal Comment 1.1: Comment: Dear Reviewer Jsg6, As the discussion between the reviewers and authors is coming to an end, could you please respond to the authors to confirm whether your concerns have been addressed? Thanks! AC --- Rebuttal Comment 1.2: Comment: I have read the rebuttal and based on it and I have increased my score from 5 to 6. --- Reply to Comment 1.2.1: Comment: Thank you for reviewing our rebuttal and for increasing your score. We appreciate your feedback on the writing and will continue to refine it to ensure clarity and quality.	null	null	null	null	null	null
Unified Covariate Adjustment for Causal Inference	Accept (poster)	Summary: The paper introduces a new framework for identifying causal estimands, referred to as Unified Covariate Adjustment (UCA). It demonstrates that the UCA-expressible class (a class of causal estimands identifiable by UCA) is extensive, encompassing estimands identified by the (sequential) back-door adjustment, front-door adjustment, and Tian’s adjustment. Furthermore, the paper proposes an estimation strategy for the UCA-expressible class using machine learning methods and analyzes the error of such estimators. Notably, the proposed estimator is scalable and achieves the double robustness property. Strengths: 1. The paper provides good examples to illustrate the relationship between the UCA-expressible class and other classes of estimands identified by different adjustments. 2. It offers comprehensive identification and estimation strategies, thereby presenting a complete causal inference methodology. 3. The theoretical analysis of the estimator's scalability and error characterization is solid. Weaknesses: 1. While the paper provides sufficient conditions for an estimand being not UCA-expressible (i.e., necessary conditions for an estimand being UCA-expressible), it lacks necessary conditions for an estimand being not UCA-expressible (i.e., sufficient conditions for an estimand being UCA-expressible). However, addressing this issue might be beyond the scope of this paper. 2. In the presence of unmeasured confounders, causal estimands (e.g., average treatment effects) may not be identifiable by UCA since identification requires bridge functions and a specifically designed ID algorithm (e.g., Shpitser et al. 2023, JMLR, The Proximal ID Algorithm). It may be worth mentioning these points at the end of Section 2, along with the "napkin" estimand. 3. The authors claimed the estimator is doubly robust (page 8, line 307) under certain conditions, which includes $n^{-1/4}$ convergence rate for $\widehat{\mu}^i$. However, I believe this condition may not be achievable, as the error tends to accumulate for large $i$; see Question below. Technical Quality: 4 Clarity: 3 Questions for Authors: page 2, Table 1: Can the authors clarify or provide examples of why UCA does not cover the functionals identified by obsID/gID? page 3, line 94: There are double commas. page 4, line 145: Given that the probability is at most 1, does this mean that $r_i$ is discrete? If so, can the authors explain why $r_i$ has to be discrete? Section 3.1: - Estimation of $\mu$: I think the error $\\| \widehat{\mu}^i - \mu_0^i \\|$ is not only affected by the estimation errors from the $i$th stage, but also by the estimation errors from the previous stages. In other words, the estimation error of $\mu$ accumulates as the index $i$ increases. Can the authors provide some comments on this error accumulation? - Bias structure: The bias structure $R_2$ in Theorem 3 consists of [error of $\mu^i$]$\times$[error of $\pi^i$] and [error of $\mu^i$]$\times$[error of $\pi^{i-1}$]. The second cross-$i$ product term seems non-trivial. Can the authors provide an example of causal estimands that only has the bias structure of [error of $\mu^i$]$\times$[error of $\pi^i$] without cross-$i$ product terms? Sections F.1.4 and F.1.5: Typo: textttnormal Confidence: 3 Soundness: 4 Presentation: 3 Contribution: 4 Limitations: Limitations are not explicitly discussed in the paper. The authors might consider including the weaknesses mentioned above as limitations. 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 valuable feedback, and appreciate the positive assessment of our work. --- > While the paper provides sufficient conditions for an estimand being not UCA-expressible (i.e., necessary conditions for an estimand being UCA-expressible), it lacks necessary conditions for an estimand being not UCA-expressible (i.e., sufficient conditions for an estimand being UCA-expressible). However, addressing this issue might be beyond the scope of this paper. As mentioned, developing necessary conditions is challenging and beyond the scope of this paper. We believe this question has the potential to open a new direction for enhancing the proposed method. Thank you for the insightful question. --- > In the presence of unmeasured confounders, causal estimands (e.g., average treatment effects) may not be identifiable by UCA since identification requires bridge functions and a specifically designed ID algorithm (e.g., Shpitser et al. 2023, JMLR, The Proximal ID Algorithm). It may be worth mentioning these points at the end of Section 2, along with the "napkin" estimand. In Table 1, we provide the coverage of the UCA, which states that not all obsID/gID functions are identified. We will further mention this point as suggested at the end of Section 2. --- > The authors claimed the estimator is doubly robust (page 8, line 307) under certain conditions, which includes $n^{-1/4}$ convergence rate for $\hat{\mu}^i$. However, I believe this condition may not be achievable, as the error tends to accumulate for large $i$; see Question below. > Estimation of $\mu$: I think the error $\\|\hat{\mu}^i - \mu^i_0 \\|$ is not only affected by the estimation errors from the $i$th stage, but also by the estimation errors from the previous stages. In other words, the estimation error of $\mu$ accumulates as the index $i$ increases. Can the authors provide some comments on this error accumulation? Good point. Due to the nature of nested expectation (and nested regression), the error of the nuisances can accumulate as $i$ decreases from $m$ to $1$. The term $\\|\hat{\mu}^i - \mu^i_0 \\|$ indeed represents the accumulated error of $\hat{\mu}^i$. Even with this accumulation, the error decomposes into the product of the errors of the nuisances; i.e., $\text{[error of DML]} = \sum_{i=1}^{m} \text{[error of $\mu^i$]} \times \text{[error of $\pi^i$]}$ still holds. As long as $\hat{\mu}^i$ converges to $\mu^i_0$ (which is likely in practice with flexible ML models), even if errors accumulate, the rate of convergence of the DML estimator outperforms that of competing estimators (OM, PW). On the other hand, we note that $n^{-1/4}$ is used to exemplify the debiasedness property because it’s the fastest rate that a neural network can achieve [1] . [1] Györfi, László, et al. “A distribution-free theory of nonparametric regression” (2002) --- > page 2, Table 1: Can the authors clarify or provide examples of why UCA does not cover the functionals identified by obsID/gID? UCA does not cover all the functionals identified by obsID/gID. We provide an example called Napkin estimand in lines 202-204, with a causal diagram in Figure 1c. The identification estimand is given as $\frac{ \sum_{w}P(x,y \mid r,w)P(w) }{ \sum_{w}P(x \mid r,w)P(w) }$. The UCA cannot handle cases where the functional is given as a ratio of two functions. A detailed discussion on the coverage of the UCA is provided in Section C.3. > page 4, line 145: Given that the probability is at most 1, does this mean that $r_i$ is discrete? If so, can the authors explain why $r_i$ has to be discrete? No, it means that the value of $R_i$ is governed by the probabilistic measure $\sigma^i$. Whether $R_i$ is continuous or discrete depends on the choice of $\sigma^i$. For example, if $\sigma^i$ is a uniform distribution over $[a,b]$, then $R_i$ can be any real number within $[a,b]$. However, if $\sigma^i$ is a Bernoulli distribution, then $R_i$ is a $\{0,1\}$ binary variable. --- > Bias structure: The bias structure $R_2$ in Theorem 3 consists of [error of $\mu^i$] $\times$ [error of $\pi^{i}$] and [error of $\mu^i$] $\times$ [error of $\pi^{i-1}$]. The second cross-$i$ product term seems non-trivial. Can the authors provide an example of causal estimands that only has the bias structure of [error of $\mu^i$] $\times$ [error of $\pi^i$] without cross-$i$ product terms? Consider the back-door adjustment where $i=1$. Since the error term only contains [error of $\mu\^i$] $\times$ [error of $\pi\^i$], the second cross-term doesn’t exist when $i=1$. --- > Sections F.1.4 and F.1.5: Typo: textttnormal > page 3, line 94: There are double commas. Thank you for catching the typo. These will be fixed. --- > The authors might consider including the weaknesses mentioned above as limitations. We will discuss more about the limitations based on provided feedback. Thanks. --- Rebuttal Comment 1.1: Comment: Thank you for your response. I believe the paper is well-prepared for acceptance, so I will keep my score as is. --- Reply to Comment 1.1.1: Title: Response Comment: Thank you for taking the time and effort to provide constructive feedback.	Summary: This paper describes the estimand framework "unified covariate adjustment (UCA)" and discusses its coverage with multiple examples (Front-door, Verma's equation, Counterfactual directed effect and most importantly Tian's adjustment). Then it develops an estimator for this function class and shows that it is scalable. Lastly the authors run experiments on simulated data to empirically demonstrate the robustness and the scalability of their estimator. Strengths: * This work is original as it introduces - to the best of my knowledge - the only scalable estimator for many functions classes. It makes a lot of novel causal inference results applicable in real applications. * The overall quality of this work is very good, the results are provided as theoretically sound theorems and empirically confirmed through simulated data experiments. * This paper is clear, the contributions are clearly stated and the paper is well structured with some useful examples. Weaknesses: * All the proofs are provided in the supplementary material and the intuition for the proofs are not provided in the main paper. * Some further experiments could be interesting even they are not necessary. For example: how does DML compare to prior scalable estimators on BD/SBD? In figure 2a,b,c how much can the dimenion of the summed variables grow before the running time of DML reaches unreasonable values (eg. 2000)? Similar question for figure2d,f how little can thee sample size be before the errors of DML reaches unreasonable values? * UCA could be more thoroughly delimited. It is well defined and the authors give examples of scenarios that are included, how they do not clearly discuss which type Ctf-ID are covered and which are not (This is also true for obsID/gID and transportability). Furthermore, there is no discussions concerning non-covered function classes and what difficulties prevent estimation in those cases. * Some intuition regarding the meaning of the mathematical objects would have been appreciated (eg. what are the sets $\bm{C}_i$ and $\bm{R}_i$ in Def 1)? * While pseudo-code is provided, giving access to the code is always appreciated. Technical Quality: 4 Clarity: 3 Questions for Authors: * Could you give intuition concerning the meaning of the $\bm{C}_i$ and $\bm{R}_i$ and $\bm{S}_i$ in Def 1 as well as $\bm{\mu}$ and $\bm{\pi}$ for non experts. * Could you discuss the limits of DML, ie. when the dimension grows and when the sample size shrinks. * Concerning the experiments, each point corresponds to the average of 100 simulations. Could you provide the variances as well? Confidence: 3 Soundness: 4 Presentation: 3 Contribution: 3 Limitations: * The authors do not discuss which function classe are not covered by UCA. Moreover, they do not discuss the limits of their estimator DML when the dimension grows and when the sample size shrinks. 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 valuable feedback, and appreciate the positive assessment of our work. --- > Some further experiments could be interesting even they are not necessary. For example: how does DML compare to prior scalable estimators on BD/SBD? In figure 2a,b,c how much can the dimenion of the summed variables grow before the running time of DML reaches unreasonable values (eg. 2000)? Similar question for figure2d,f how little can thee sample size be before the errors of DML reaches unreasonable values? We have provided a set of experimental results in the attached pdf file. --- > UCA could be more thoroughly delimited. It is well defined and the authors give examples of scenarios that are included, how they do not clearly discuss which type Ctf-ID are covered and which are not (This is also true for obsID/gID and transportability). Furthermore, there is no discussions concerning non-covered function classes and what difficulties prevent estimation in those cases. Some cases where the target estimand cannot be expressed through UCA are discussed in Appendix C.3. A summary of this discussion will be provided in the main paper. --- > Some intuition regarding the meaning of the mathematical objects would have been appreciated (eg. what are the sets $C_i$ and $R_i$ in Def 1)? > Could you give intuition concerning the meaning of the $C_i$ and $R_i$ and $S_i$ in Def 1 as well as $\mu$ and $\pi$ for non experts. The meaning of $C_i$, $R_i$, and $S_i$ depends on specific cases. In all examples, we specified what $C_i$, $R_i$, and $S_i$ meant. For the BD/SBD, we can view $C_i$ as a set of covariates, $R_i$ as a treatment, and $S_i$ as predecessors of $C_{i+1}$. $\mu$ is a (nested-) expectation functional representing the UCA estimand, and $\pi$ is the probability-weighting-based functional representing the UCA estimand. We will provide more explanation to give an intuition about these mathematical objects in the paper. Thank you. --- > While pseudo-code is provided, giving access to the code is always appreciated. We will make the code available after the revision. Thank you. --- > Could you discuss the limits of DML, ie. when the dimension grows and when the sample size shrinks. As shown in the experiment in the PDF of the global response, the proposed DML estimator remains scalable when the dimension is high. When the sample size shrinks, it’s possible that the error of the DML estimator is amplified because its error decomposes into the product of the errors of nuisances; i.e., $\text{[error of DML]} = \sum_{i=1}^{m} \text{[error of } \mu^i \text{]} \times \text{[error of } \pi^i \text{]}$. If the sample is small so that the errors of nuisances become large, the resulting DML estimator may have a larger error since the error is multiplied. However, as the sample size grows, the DML estimator is guaranteed to converge faster whenever nuisances are converging to the truth. --- > Concerning the experiments, each point corresponds to the average of 100 simulations. Could you provide the variances as well? In all plots in Figure 2, the confidence intervals of the error with $\alpha = 0.05$ are shown as error bars. --- > The authors do not discuss which function classe are not covered by UCA. Some function classes where the target estimand cannot be expressed through UCA are discussed in Appendix C.3. We will add a sufficient criterion to determine which estimands can be represented as a UCA estimand in the revision of the paper. The idea behind the criterion is as follows: If 1. The target estimand is expressed as the mean of the product of conditional distributions over $(\mathbf{C}_1, \mathbf{R}_1, \cdots, \mathbf{C}_m, \mathbf{R}_m)$; and 2. The variables that are marginalized and fixed simultaneously (e.g., $X$ in the front-door adjustment) only appear in $\mathbf{C}_1$, the proposed methods can be applied. These conditions are sufficient for applying the empirical bifurcation technique (Def 2) that allows scalable estimation. --- Rebuttal Comment 1.1: Title: Response to author's rebuttal Comment: Thank you for all the clarifications. After reading other reviews, I still think it is an interesting paper and I maintain my score. --- Reply to Comment 1.1.1: Title: Response Comment: Thank you for spending the time reading our paper and the positive assessment.	Summary: The paper presents a class of adjustment formulas called unified covariate adjustment (UCA) which is shown to be able to express many classes of adjustments known in the existing literature. A scalable and doubly robust estimator for UCA is also presented along with some experimental results. Strengths: The proposed UCA estimator seems to be very expressive and is able to model many existing estimators in the literature. Examples were given to show how existing estimators can be expressed as a UCA estimator. The paper also proposes a doubly robust method to obtain UCA estimates. Weaknesses: - It is of my personal opinion that the paper lacks polish. There are many instances of technical notations being used without first properly defining them, making it hard to understand and follow the discussion (see the Questions section for some of them). The reader should not be expected to guess the meaning of certain notations by cross-referencing across subsequent pages (at best check the preliminaries/notation section) or even across other paper references. - The paper claims on Lines 57-58 that "while these estimators are designed to achieve a wide coverage of functionals, they lack scalability due to the necessity of summing over high-dimensional variables" but the general definition of UCA in equation (1) also involves summing over potentially many variable values in $c \cup r$. Please explain clearly why UCA avoids scalability issues. - Line 302-304: It is not true that only asymptotic analyses were known for all these estimators. For example, [1] gives non-asymptotic finite sample guarantees for the Tian-Pearl adjustment. The paper would benefit from a comparison against such prior works and illustrate how DML-UCA adjustments are indeed more sample efficient as compared to existing estimators. - Why is there no experiments against the Tian-Pearl adjustment? - No code was released (though some parameters were given the appendix). [1] Arnab Bhattacharyya, Sutanu Gayen, Saravanan Kandasamy, Vedant Raval, Vinodchandran N. Variyam Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, PMLR 151:7531-7549, 2022. Technical Quality: 2 Clarity: 1 Questions for Authors: - How are the symbols in Table 1 determined? "scalable" is defined to be "evaluable in polynomial time relative to number of covariates and capable in the presence of mixed discrete and continuous covariates", but about "coverage"? - Consider rephrasing the awkward-sounding sentence "Our work strives maximizing coverage..." on Line 73-76? - $S^b_{i-1}$ first appears in Line 141. How is this defined? How does it differ from $S_{i-1}$? - In Line 144, $S_0, C_0, R_0$ are referenced but how are they defined? Also, how do the $S_i$s relate to the variable set $V$? Is $S_i$ the c-component of the $i^{th}$ vertex? - Equation (4): The notation $v^{(i−1)}$ is undefined. Is $v^{(i−1)} = \\{v_1, \ldots, v_i\\}$ as in the Tian-Pearl 2002 paper? - Line 312: What is $O_{P^{i+1}}$? How does it differ from just the usual big-O notation? Also, how do the errors in the estimation scale with the number of samples? Lines 307-309 only say "if the terms converge at a rate of $n^{-1/4}$, then DML-UCA coverges at a rate of $n^{-1/2}$". Why do those terms converge at a rate of $n^{-1/4}$? - Given a general causal graph and causal query, how does one find a suitable and valid UCA expression? What is the procedure? Potential typos: - Double comma on Line 94 - Extra ) on Line 153 Confidence: 3 Soundness: 2 Presentation: 1 Contribution: 3 Limitations: Nil Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your feedback and for the opportunity to provide further elaboration. --- > technical notations being used without first properly defining them We will further proofread the paper and the preliminaries. --- > Please explain clearly why UCA avoids scalability issues. Existing BD/SBD estimators avoid scalability issues by replacing marginalization with nested expectation. However, when a variable is both marginalized and fixed simultaneously (e.g., FD: $\sum_{x’,c}E[ Y \| z,x’,c] P(z \| x, c) P(x’,c)$, where $X$ is fixed to $x$ in $P(z \| x,c)$ and marginalized by $\sum_{x’}$ in other components), representing the marginalization operator as a nested expectation is non-trivial. These challenges lead to potential scalability issues for previous FD estimators (Fulcher et al., 2019; Guo et al., 2023), which have a complexity of $O(n2^m + T(n,m))$ ($m$: the dimension of variables, $T(n,m)$: time complexity of learning nuisances). In contrast, the newly proposed UCA estimator uses empirical bifurcation to replace marginalization with nested expectation, achieving $O(n + T(n,m))$ by leveraging the empirical bifurcation method. --- > [1] gives non-asymptotic finite sample guarantees for the Tian-Pearl adjustment. We will cite all the referred papers. Please note that lines 302-304 discuss DML-style estimators, while the mentioned paper provides finite sample guarantees for a basic plug-in estimator under the discrete random variable setting. --- > Why is there no experiments against the Tian-Pearl adjustment? Figure 2(b,e) shows the experimental results for Verma's graph (Figure 1b), which is an example instance of the Tian-Pearl adjustment. --- > No code was released (though some parameters were given the appendix). We will make the code available after the revision. Thank you. --- > How are the symbols in Table 1 determined? "scalable" is defined to be "evaluable in polynomial time relative to number of covariates and capable in the presence of mixed discrete and continuous covariates", but about "coverage"? Coverage indicates whether established estimators exist. For obsID/gID classes, estimators like those by Jung et al. (2021a, 2023a), Xia et al. (2021, 2022), and Bhattacharya et al. (2022) are marked in the "Prior" column. The UCA, covering Tian's adjustment, is checked in its respective column. --- > Consider rephrasing the awkward-sounding sentence "Our work strives maximizing coverage..." on Line 73-76? Thank you. We will rephrase as follows: “Our work aims to maximize coverage, enabling the effective development of scalable estimators with the doubly robust property.” --- > $S^b_{i-1}$ first appears in Line 141. How is this defined? How does it differ from $S_{i-1}$? $\mathbf{S}^b_{i-1}$ represents a set of variables fixed to $\mathbf{s}^b_{i-1}$ in a conditional distribution $P^i(\mathbf{V}) = Q^i(\mathbf{V} \mid \mathbf{S}^b_{i-1} = \mathbf{s}^b_{i-1})$ (e.g., $\mathbf{S}^b_1 = \{X\}$ with $\mathbf{s}^b_1 = \{x\}$ in FD, Example 1). Meanwhile, $\mathbf{S}_{i-1}$ is a subset of the union of $\mathbf{C}^{(i-1)}$ and $\mathbf{R}^{(i-1)}$, excluding the fixed set. --- > $S_0, C_0, R_0$ are referenced but how are they defined? Also, how do the $S_i$s relate to the variable set $V$? Is $S_i$ the c-component of the $i$th vertex? 1. $S_0$, $C_0$, and $R_0$ are all defined as the empty set. We will add this in the preliminaries. 2. We define $\mathbf{S}\_{i-1} := (\mathbf{C}\^{(i-1)} \cup \mathbf{R\}^{(i-1)} ) \setminus \mathbf{S}\^{b}\_{i-1}$ in line 144. This is a subset of the variable set $\mathbf{V}$. 3. Thank you for the good question. $\mathbf{S}_i$ is not a c-component. We only used $\mathbf{S}\_{X}$ to denote the c-component containing $\{X\}$. We will improve the notation to distinguish them more explicitly. --- > Equation (4): The notation $v^{(i-1)}$ is undefined. Is $v^{(i-1)} = \{v_1,\cdots,v_i\}$ as in the Tian-Pearl 2002 paper? Yes, it's defined in line 98. --- > Line 312: What is $O_{P^{i+1}}$? How does it differ from just the usual big-O notation? Also, how do the errors in the estimation scale with the number of samples? > Why do those terms converge at a rate of $n^{-1/4}$? 1. As written in line 104, $O_P$ is a stochastic boundedness called the big-O in probability [van der Vaart, "Asymptotic Statistics."] (1998). The expression $f(\mathbf{V}) = O_{P^{i+1}}(n^{-1/4})$ means that $n^{1/4} \times f(\mathbf{V})$ will be bounded even when $n$ increases to infinity. This indicates that $f(\mathbf{V})$ decreases at least as fast as $n^{1/4}$. If the error term is $O_{P^{i+1}}(n^{-1/4})$, then it decreases at the rate of $n^{1/4}$. 2. Theorem 3 and Corollary 3 show that when nuisances converge at the rate of $n^{-\alpha}$ ($\forall \alpha \in (0,1)$), the estimator can converge at the double rate: $n^{-2\alpha}$. We demonstrate this with $\alpha = 1/4$, since $n^{-1/4}$ is the fastest convergence rate for modern ML models like neural networks [1]. [1] Györfi, László, et al. “A distribution-free theory of nonparametric regression” (2002) --- > how does one find a suitable and valid UCA expression? Some causal queries that satisfy known graphical criteria (e.g. BD/SBD, FD, or Tian’s adjustment) can be represented as an UCA. On the other hand, we have further developed the sufficient criterion to determine if a given estimand can be represented as a valid UCA expression. The idea behind the criterion is as follows: If 1. The target estimand is expressed as the mean of the product of conditional distributions over $(\mathbf{C}\_1, \mathbf{R}\_1, \cdots, \mathbf{C}\_m, \mathbf{R}\_m)$; and 2. The variables that are marginalized and fixed simultaneously (e.g., $X$ in the front-door adjustment) only appear in $\mathbf{C}_1$, the proposed methods can be applied. This criterion will be added in the revised version of the paper. --- > Double comma on Line 94, Extra ) on Line 153 We will fix the typos, thank you. --- Rebuttal Comment 1.1: Comment: Thank you for the detailed responses. They have addressed my concerns. I look forward to these being incorporated nicely in a future revision. I will increase my score upwards. --- Reply to Comment 1.1.1: Title: Response Comment: We appreciate your constructive input. Thank you for the positive feedback.	Summary: The paper introduces a novel framework, unified covariate adjustment (UCA), which covers a broad class of sum-product causal estimands and additionally develops a scalable estimator (via DML-UCA) that ensures double robustness. Strengths: * The paper presents a well-developed theoretical framework with clear assumptions and derivations. The motivation to extend existing estimands is well-articulated, and the comparisons with prior work are thoroughly examined. * The paper is well-written and clearly presents the motivation, methodology, and contributions. * It is interesting to revisit the coverage and scalability of previous studies and provide comprehensive evaluations. Weaknesses: * The proposed method is based on structural causal models, which have been extensively studied. UCA-class is an extension of the sequential back-door adjustment (SBD), and there are already existing studies that address similar questions * The authors mention in Example 1 that the Front-Door adjustment (FD) can be represented using the UCA framework. Are there any assumptions required to validate this representation? Similarly, to represent the Verma constraints as UCA in Example 2, are there any criteria that could be followed to verify the representation in practice? What are the requirements and limitations for implementing these representations to ensure the reliability and validity of the estimation in general? Technical Quality: 3 Clarity: 3 Questions for Authors: See Weaknesses Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: yes Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for sharing your thoughts and feedback! > UCA-class is an extension of the sequential back-door adjustment (SBD), and there are already existing studies that address similar questions Indeed, UCA is an extension of the SBD, and we have appreciated and cited papers regarding estimating the SBD estimand. However, naively applying the SBD estimators to the UCA-class (e.g., FD, Verma) may lead to biased estimators whenever the value of SBD estimand and the UCA estimand don't match. Also, modifying the existing SBD estimators to the UCA-class is non-trivial since variables that are fixed and marginalized at the same time (e.g., ‘X’ in FD) are not properly treated in the SBD estimators. A special method (such as the empirical bifurcation in Def. 6) is required to develop an estimator. Furthermore, for Tian’s adjustment, the weighting nuisances $\pi^{i}_0$ do not have the same form as those in SBD. In summary, developing doubly robust estimators for the UCA class is a novel and non-trivial task. --- > Are there any assumptions required to validate this representation? Similarly, to represent the Verma constraints as UCA in Example 2, are there any criteria that could be followed to verify the representation in practice? What are the requirements and limitations for implementing these representations to ensure the reliability and validity of the estimation in general? Some causal queries that satisfy known graphical criteria (e.g. BD/SBD, FD, or Tian’s adjustment) can be represented as an UCA. Recall that representing the Tian's adjustment through the UCA estimand is demonstrated in the paper. On the other hand, we have further developed the sufficient criterion to determine if a given estimand can be represented as a valid UCA expression. The idea behind the criterion is as follows: If 1. The target estimand is expressed as the mean of the product of conditional distributions over $(\mathbf{C}_1, \mathbf{R}_1, \cdots, \mathbf{C}_m, \mathbf{R}_m)$; and 2. The variables that are marginalized and fixed simultaneously (e.g., $X$ in the front-door adjustment) only appear in $\mathbf{C}_1$ (that is, $\mathbf{S}^{b}\_{i-1} \cap \mathbf{C}\^{\geq 2} = \emptyset$), then the proposed methods can be applied. These conditions are sufficient for applying the empirical bifurcation technique (Def 2) that allows scalable estimation. --- Rebuttal Comment 1.1: Comment: Thanks for the detailed responses, I will maintain my score. --- Reply to Comment 1.1.1: Title: Response Comment: Thank you for your positive assessment of our paper.	Rebuttal 1: Rebuttal: We attached a PDF to report the experimental results in respond to the following questions from Reviewer ZBfF: 1. > In figure 2a,b,c how much can the dimenion of the summed variables grow before the running time of DML reaches unreasonable values (eg. 2000)? 2. > how little can thee sample size be before the errors of DML reaches unreasonable values? In summary, the proposed DML-UCA estimator can be evaluated under a high-dimensional setting where $d = 50000$. The estimator can also be evaluated under a small sample size setting, with samples varying from 10 to 100. Pdf: /pdf/661860ba31aac74664f8665943757667f2210a30.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Learning to grok: Emergence of in-context learning and skill composition in modular arithmetic tasks	Accept (oral)	Summary: The paper studies the emergence of the in-context ability of the GPT-style transformer model trained using autoregressive loss and arithmetic modular datasets. It analyzes the influence of the number of tasks, number of in-context examples, model capacity, etc., on the ICL capability of an appropriately trained model (i.e., using early stopping). It also provides a persuasive “task decomposition hypothesis”, which is well supported by the ablation study and various experiments. The white-box analysis on the attention heads provides convincing evidence of the proposed explanation. Although there is a gap between the grokking settings (i.e., small model and toy dataset) and practical systems, the paper does a good job of explaining many important trends and concepts related to the emergence of compositional in-context ability. I enjoy reading this paper and suggest an acceptance. Strengths: - The paper is easy to follow. Good presentation! - The experiments are well-designed, providing compelling support for the claims. - The results in Figure 5 are cool. - The skill decomposition discussed in section 5 is great. The clear pattern in attention heads verifies it very well. (The hypotheses could be further verified if the author can link the values of $c_1, c_2$ to some weights in the network, see the question part.) Weaknesses: - The emergent ability (or grokking) usually refers to a phenomenon in the model “got stuck” in a non-generalization region and suddenly gained the generalization ability. Hence some discussion about the learning dynamics, i.e., how the accuracy, loss, representation, ability, attention pattern, etc., gradually evolve during training would make the paper stronger. - The task and batch sample selection in this paper have many constraints (e.g., the rectangular rule, the balanced number of samples in each batch, etc.). However, the practical systems usually cannot strictly satisfy all these assumptions. Hence a more detailed analysis of how these assumptions influence the generalization ability would provide more insights to practical systems. Technical Quality: 3 Clarity: 4 Questions for Authors: - The paper claims in line 147 that “As the o.o.d. performance increases, the pre-training performance simultaneously degrades “. However, it is hard to read this information from Figure 3-a panel 1. Maybe a different color mapping or adding numbers on these patches would be helpful. - Equation 2 is a bit hard to understand. How does it correlate to $z = ax+by$ ? (Although, from the latter explanations, I know the model relies on $c_1z_1^t + c_2z_2^t$ to get $z$, but it might be helpful to claim how it is derived.) - Better to define $GF(p)$, i.e., the Galois field, before using it. - Are the results in Figure 6 coming from $d=2$ or $d=4$? I can find the figure for all 8 attention heads for $d=2$ in the appendix, what about the $d=4$ case? It might be helpful to see if the pattern in later layers (i.e., attention focusing on different $z_i$) exists in shallow layers, and vice versa. - In line 264, the paper claims that the pattern depends on $(a,b)$, but it is hard to read that from Figure 6b. - As also mentioned in the strength part, is it possible to find some specific value in the weight space (e.g., attention weights, readout layers, etc.) that is highly correlated to $c_1, c_2$? If so, the hypothesis that the model first learns skill 2 (scale each example) and then skill 3 (weighted combine different examples) would be further verified. - The OOD settings studied in grokking or emergent ability setting are quite related to the compositional generalization and systematic generalization. It would be helpful to discuss them in the related works, here are some of them: [1] Schott, Lukas, et al. "Visual representation learning does not generalize strongly within the same domain." ICLR 2022 [2] Xu, Zhenlin, Marc Niethammer, and Colin A. Raffel. "Compositional generalization in unsupervised compositional representation learning: A study on disentanglement and emergent language." NeurIPS 2022 [3] Ren, Yi, et al. "Improving compositional generalization using iterated learning and simplicial embeddings." NeurIPS 2023 Confidence: 4 Soundness: 3 Presentation: 4 Contribution: 3 Limitations: Discussions on how the findings help the practical system. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for the encouraging feedback and incisive questions. ## Weaknesses Emergent abilities / Grokking: The loss and accuracy curves are already presented in Figure 3 of the current version of the paper. We agree that the gradual emergence of useful representations as a function of training time are useful results to showcase. In the final version of the paper, we will also include the feature analysis (similar to Figures 5,6) for intermediate checkpoints during training -- as suggested by the reviewer. (Note that we have not included these plots in the PDF of the Global Rebuttal due to space constraints.) We also note that we exercise a broader take on emergent ability than only learning dynamics. Emergent behaviours [1] are characterized by qualitative changes in model capabilities upon scaling-up (i) model size, (ii) dataset size, (ii) training duration, (iii) task-diversity etc. While the transition with training duration is an interesting aspect of the literature on Grokking, it is only one part of the emergent phenomena in deep learning. Moreover, careful initialization and optimization have been known to mitigate such effects [2]. However, the transition in capabilities with respect to dataset and model sizes are known to be more robust. Pre-training task and batch selection: The structured selection of tasks (rectangular rule) and balanced batches largely serve the purpose of making the pre-training more stable. Our intuition for using the specific setup was to reduce batch noise, as the training itself is challenging for this task. We strongly believe that scaling up the batch-size and model sizes will alleviate these constraints. We did not explore this avenue due to compute restrictions. ## Questions o.o.d. vs pre-training performance: The performance trade-off between o.o.d. and pre-training is more clear in the $d=2$ and $d=4$ models, shown in Figure 4. We will update line 147 and add a reference to the phase diagrams in Figure 4. Equation 2: Following the reviewer's suggestion, we will modify Equation (2) to read as follows: $$c_1 (x_1, \\; y_1 ) + c_2 (x_2, \\; y_2 ) = (x, \\; y) \\; \mathrm{mod} \\; p \qquad \xrightarrow{\text{find} \\; c_1, c_2} \qquad z = c_1 z_1^t + c_2 z_2^t \\; \mathrm{mod} \\; p \\; \qquad\qquad (2)$$ For completion, we provide an explanation of the algorithm here: The model finds the right way to "linearly combine" $(x_1, y_1)$ and $(x_2, y_2)$ to equal $(x,y)$. The re-scaling factors $c_1, c_2$ in this linear combination can then be used to get the correct answer: $z = c_1 z_1^t + c_2 z_2^t$. Here is an intuitive way to think about the algorithm: Instead of directly solving for the unknowns $(a, b)$, the model treats the in-context examples $(x_1, y_1, z_1)$ and $(x_2, y_2, z_2)$ as vectors. The task then becomes to fill in the last component of a new vector $(x, y, ?)$. By aligning the first two components using coefficients $c_1$ and $c_2$: $c_1 (x_1, y_1) + c_2 (x_2, y_2) = (x, y)$ mod $p$, the model naturally finds out the correct way of aligning $z_1$ and $z_2$ with $?$, given the fact that they are constructed with a same underlying linear relation $a x + b y$ mod $p$. We will add a version of this explanation to the final version of the paper to enhance clarity. Galois Field: We thank the reviewer for pointing out the missing definition of Galois Field. We will include that in the final version. Figure 6 and attention heads: The results in Figure 6 are for $d=2$. We will specify that in the caption as well as the main text in the final version. In the Appendix of the final version of the paper, we will extend Figure 11 to include all the attention heads from the $d=4$ model. Unfortunately we cannot show them in the Global Rebuttal PDF due to space constraints. Task dependence of Figure 6(b): In Figure G.2 of the attached PDF (Global Rebuttal) we present the PCA of attention heads for multiple tasks. Taking a close look at the first column in the layer 2, head 2 case, we see that the attention pattern is different for the two different tasks. % (Note that the layer 2, head 2 plots may seem denser than Figure 6(b). This is because we have included all the points here -- in Figure 6(b) we had only included points with even $x$ values, to keep the figure clean and interpretable.) Re-scaling coefficients $\mathbf{c_1, c_2}$: We tried using linear probing to extract information of $c_1, c_2$ from the residual stream, but the result is inconclusive. Please see the Global Rebuttal for more details. Compositional and systematic generalization: We thank the reviewer for pointing out the relevant references. We will include their relation to our work in the final version of the paper. [1] Wei et al.; "Emergent Abilities of Large Language Models"; arXiv:2206.07682 (2022) [2] Kumar et al.; "Grokking as the transition from lazy to rich training dynamics"; ICLR 2024 --- Rebuttal Comment 1.1: Comment: Thanks very much for the author's response. The new results are quite interesting. All of my concerns are well resolved. I confirm my evaluation and hope to see its new version.	Summary: * The authors propose a synthetic sequence learning problem that I would call 'in-context modular regression', an elegant generalisation of prior work studying modular addition and in-context linear regression. * Using carefully constructed batches the authors are able to train transformer models to perform regression for a subset of tasks (weights) and a subset of inputs. * The authors show that under some conditions on the data distribution and model architecture, the transformers not only achieve good performance on tasks and inputs included during training, but they also generalise to new tasks and/or new inputs. The authors document the conditions governing these generalisation capabilities in detail including showing phase plots and observing that in larger models, the generalisation properties are transient (they appear and then disappear across the training process). * The authors postulate a breakdown of skills required to correctly perform the task. They effectively isolate and examine the abilities of their models to perform each component task. They also inspect the activations of each head and identify patterns suggestive of partial mechanisms underlying the generalising behaviour of the models. Strengths: I thank the authors for submitting their excellent work which stands to have a substantial impact in the science of deep learning. * The work makes a meaningful contribution to an exceptionally important and interesting topic of the emergence of capabilities and internal mechanisms in deep learning. * The setting and experiments neatly isolate and clearly demonstrate several interesting phenomena of emergence of capabilities and shifting in the solutions found by deep networks throughout training, contributing to the field's developing catalogue of examples of these phenomena. * Moreover, the proposed synthetic problem is both rich and elegant. I expect this framework will become a fruitful test-best for follow-up work studying emergence phenomena, helping the field to improve our empirical and theoretical understanding of these phenomena. * The authors also offer a partial behavioural and mechanistic analysis which is a solid starting point for a more detailed understanding of the learned structures that emerge in this setting. * While some elements of the analysis are complex, the authors have done an exceptional job of clearly presenting their findings. I feel careful study of each section and figure in the main text was rewarded since there was no question that occurred to me that was not addressed in the authors' clear descriptions or figures. * The authors have acknowledged all of the related work that I am aware of. Weaknesses: I have not noticed any weaknesses in the paper that would temper my overall recommendation to accept. However, I note the following weaknesses, some of which the authors have already acknowledged, and others which they may like to take into consideration if they are interested to improve the paper further. 1. Delicate training set-up. The authors explain that training transformers on multiple modular addition tasks crucially relies on following a delicately balanced batch construction methodology. I am left wondering if this batch construction methodology, as a further departure from the standard language modelling setting, has any other implications for the learning process that may affect the generality of the results. Note: This weakness is not decisive because the authors clearly document their training methodology and it's not that artificial anyway. 2. The mechanistic analysis is only partial. The authors admit that they have not been able to identify an end-to-end mechanistic model of how the trained transformers perform the task. This leaves their posited skill decomposition and partial mechanistic analysis open to the possibility that they are incomplete. Note: I think the contribution the authors have given in terms of the setting, the generalisation phenomena, and the partial skill decomposition and mechanistic analysis are already significant. 3. Relationship to prior work. The related work section does a good job of summarising the contributions of prior work in in-context linear regression and modular arithmetic in the context of transformer models. However, I feel that this section could be improved if the authors attempted to offer greater insight into the relationship between these prior works and the present work. For example, the authors have an opportunity here to informally describe the in-context linear regression and the modular addition problem settings that the newly proposed setting generalises. 4. I noticed some minor text errors as follows, which I expect the authors can easily correct. * Line 94: The notation $[1, p^2]$ to me suggests a closed continuous interval, whereas you appear to mean $\lbrace1, \ldots, p^2\rbrace$, also in some cases denoted $[p^2]$. * It seems that equation 2 should read $\ldots = (z_1^t, z_2^2) \mod p$ and the equation on line 203 should read $c_1x + c_2y \mod p$. That is, $x$ and $y$ should swap places with $z_1^t$ and $z_2^t$. Is this indeed a mistake, or am I missing something? * In figure 6 (top row) there is a typo: "Qeury" on the vertical axis. * In line 445 there is a broken link. I have not studied all appendices in detail. Technical Quality: 4 Clarity: 4 Questions for Authors: 1. Why is the title 'learning to grok'? * Is this meant in the sense that the grokking of a modular addition task is occurring in-context? If so, this seems a little inaccurate, since the phenomenon analogous to 'grokking' seems to still be occurring during pre-training. * To be honest this part of the title has puzzled me since I first looked at the paper. Even if my understanding above is wrong and the title has an accurate interpretation, that I have failed to notice it might be one data point suggesting that if you are going for a title that is both short and informative, this might not be the right choice. 2. In the figure 1 caption, is it possible to offer a clearer summary of the difference between in-distribution generalisation and out-of-distribution memorisation? On my first read through, treating the figure and caption as an overview of the work's main results, I had trouble distinguishing these two concepts. Confidence: 4 Soundness: 4 Presentation: 4 Contribution: 4 Limitations: The authors transparently acknowledge all of the limitations I was able to identify within the paper itself. Flag For Ethics Review: ['No ethics review needed.'] Rating: 8 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for the encouraging feedback and valuable comments. ## Weaknesses 1. Delicate training set-up: The structured selection of tasks (rectangular rule) and balanced batches largely serve the purpose of making the pre-training more stable. Our intuition for using the specific setup was to reduce batch noise, as the training itself is challenging for this task. We strongly believe that scaling up the batch-size and model sizes will alleviate these constraints. We did not explore this avenue due to compute restrictions. We will add this clarification to the final version of the paper. 2. The mechanistic analysis is only partial: We have included additional results in the Global Rebuttal and the attached PDF, further strengthening our analysis. Notably, this includes highly structured neuronal activation patterns (Figure G.1). However, the end-to-end algorithm still remains an open question. 3. Relationship to prior work: We will incorporate the reviewer's suggestion into the camera-ready version of our paper. 4. Minor Text Errors: We have addressed all the minor errors pointed out by the reviewer, except one, which is not an error. Specifically, equation (2) and line 203 are not typographical errors. The algorithm we propose differs from the conventional method humans use to solve linear systems of equations, which involves explicitly computing the coefficients $(a,b)$ from the in-context examples. Instead of finding the unknowns $(a,b)$, the model finds the right way to "linearly combine" $(x_1, y_1)$ and $(x_2, y_2)$ to equal $(x,y)$. The re-scaling factors $c_1, c_2$ in this linear combination can then be used to get the correct answer: $z = c_1 z_1^t + c_2 z_2^t$. To emphasize this point, we have modified Equation (2), which now reads: $$c_1 (x_1, \\; y_1 ) + c_2 (x_2, \\; y_2 ) = (x, \\; y) \\; \mathrm{mod} \\; p \qquad \xrightarrow{\text{find} \\; c_1, c_2} \qquad z = c_1 z_1^t + c_2 z_2^t \\;\mathrm{mod} \\; p \\; \qquad\qquad (2)$$ Here is an intuitive way to think about the algorithm: Instead of directly solving for the unknowns $(a, b)$, the model treats the in-context examples $(x_1, y_1, z_1)$ and $(x_2, y_2, z_2)$ as vectors. The task then becomes to fill in the last component of a new vector $(x, y, ?)$. By aligning the first two components using coefficients $c_1$ and $c_2$: $c_1 (x_1, y_1) + c_2 (x_2, y_2) = (x, y)$ mod $p$, the model naturally finds out the correct way of aligning $z_1$ and $z_2$ with $?$, given the fact that they are constructed with a same underlying linear relation $a x + b y$ mod $p$. We will add a version of this explanation to the final version of the paper to enhance clarity. ## Questions 1. On the origin of the title: The authors have always been of the opinion that the central theme in grokking is the formation of highly structured representations at the end of training. In fact, these representations can be viewed as a 1st order phase transition (in the proper statistical mechanics sense as explained in https://arxiv.org/abs/2310.03789). If we take this perspective then in the present work grokking happens in _two_ qualitatively different ways: (i) _as optimization time passes_ the model learns to solve the task in-distribution (and sometimes o.o.d.), which requires highly structured representations, and (ii) _as the number of in-context examples increases during inference_ the model performance steadily improves; completely solving the arithmetic problem with enough in-context examples. It is crucial that the predictions are conditioned on the sequence of in-context examples and this conditioning is _emergent_. A more accurate name could be "grokking grokking", but we decided to opt for a milder version. 2. We thank the reviewer for pointing out the cumbersome phrasing. We have edited the part of the caption in Figure 1 that distinguishes various phases to make it clearer. The part of the caption now reads: > (b) Phase diagram for a six-layer model. We find four different phases. (1) in-distribution memorization: The model only performs well on tasks $(a,b)$ and examples $(x,y)$ from the training set -- it does not generalize on unseen examples or tasks. (2) in-distribution generalization: model generalizes on unseen examples $(x,y)$ but not on unseen tasks $(a,b)$. (3) out-of-distribution memorization: model generalizes on unseen tasks $(a,b)$ but only for examples $(x,y)$ it has seen during training. (4) out-of-distribution generalization: model generalizes on unseen tasks $(a,b)$ for seen as well as unseen examples $(x,y)$. We focus on investigating phase (4) in more detail. Additionally, we will add a table clarifying the performance on the sets $S_{train}^{i.d.}, S_{test}^{i.d.}, S_{train}^{o.o.d.}, S_{test}^{o.o.d.}$ in the four different phases, on page 4 of the main text. We hope that this will help avoiding any possible confusion in the definition of the phases. --- Rebuttal Comment 1.1: Title: Thanks for clarifying and for your proposed improvements to an already strong paper Comment: Thank you for clarifying especially my confusion around the proposed vector scaling approach to solving the task. The proposed revisions and the additional experiments will further improve an already strong paper. I maintain my confident recommendation that this paper should be accepted.	Summary: This paper studies the emergence of in context learning and skill composition in autoregressive models. They create an algorithmic dataset to probe how autoregressive models use tasks learned during training to solve new tasks. They find that more training tasks lead to a generalizing / algorithmic approach instead of memorization. Strengths: - This work introduces a new algorithmic dataset (with modular arithmetic tasks) that force models to learn a variety of tasks. The work finds that when the number of tasks goes from small to large, the model transitions from memorization to generalization. - This work has many interesting experiments. I found Section 5.2 (Attention Heads Implement Essential Skills) pretty interesting. Weaknesses: - The definition of task diversity is not well defined. Is the number of pretraining tasks truly indicative of task diversity? I think the paper could benefit from some justification of this assumption. - The paper claims that for larger models, early stopping is necessary (line 52). While I appreciate that the authors used GPT-like architectures to reflect realistic settings, the architectures in the experiments are not that large. Even amongst popular open source models, the smallest are usually around 7B parameters. - Many works in the continual learning and meta learning literature suggest that training on multiple tasks at once leads to better generalization. Perhaps it is worth including brief discussion on the connections between this point and the model’s ability to generalize ood which is predominantly determined by the number of pre-training tasks. Technical Quality: 3 Clarity: 3 Questions for Authors: Since multiplication can be viewed as repeated addition, isn’t skill 2 an extension of skill 3 (or can even be viewed as skill 3 composed with itself multiple times)? Is hierarchy of skills important here? Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: As acknowledged by the authors, this work is limited to particular algorithmic datasets. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for their insightful comments. ## Weaknesses Task Diversity: Our definition of task diversity follows the existing works on in-context learning with linear regression, with a key difference: since our tasks are defined over a finite field, the total number of possible tasks (labeled by the task vectors $(a, b)$) is _finite_ and equals $p^2$. This differs from commonly discussed cases of linear regression, where the set of tasks is infinite (and, in fact, _continuous_). Consequently, the number of pre-training tasks (as a fraction of the total tasks $p^2$) is a natural measure of task diversity. There is a subtlety in that tasks may not be completely independent from each other, and a true definition of task diversity should include a reference to independence. However, it is not clear to what extent the model leverages this possible redundancy -- and similar point is also omitted in the works on linear regression. We decided to not go down that rabbit hole and defined task diversity in a naive way. That being said, we acknowledge that different ways of sampling the task sequences could also influence o.o.d. generalization. To address this, one might construct a phase diagram with an additional axis representing task sampling. However, this would require an order of magnitude more computations and a detailed multi-page discussion, making it impractical for our current study. Early Stopping and Larger Models: We appreciate the reviewer raising this point. First, we would like to clarify that the "larger model" mentioned in line 52 refers to the comparison between the $d=6$ model and the $d=2,4$ models used throughout the paper. Notably, these settings are sufficient to demonstrate our point, as the model's scale should be measured relative to the dataset size. The SoTA LLMs are pretrained on corpora much larger and diverse than the arithmetic tasks that we study in this work. We agree that larger-scale experiments would be necessary to transfer the insights gained from our study to modern LLMs. However, such experiments are far beyond our current capabilities due to limited GPU resources. Finally, the purpose of including details such as early stopping is to aid reproducibility of our results -- we do hope that the community will explore and generalize our setting. Relation to meta-learning and continual learning: We thank the reviewer for pointing out this interesting connection. It is indeed possible that some of the insights from our work finds connections to these areas. In the current version, we have cited one work [1] related to meta-learning. In the camera-ready version, we will include a more elaborate discussion with more references. We welcome suggestions for specific resources about continue learning that the reviewer has in mind relevant to our study. ## Question The reviewer raises an interesting point about the hierarchy of skills, and is correct in pointing out that multiplication can indeed be constructed from repeated additions. However, it is important to think from the model's perspective. We believe that efficient implementation of finite field operations by the model requires separate components to perform addition and multiplication. One intuitive way to think about this is that the models do not have sufficient depth to perform arbitrary repeated additions to construct multiplication. Instead, the models build correct representations to implement multiplication. Consequently, it is better to think of the numbers on a finite field $\mathrm{GF}(p)$, with distinct operations of addition and multiplication. [1] Louis Kirsch, James Harrison, Jascha Sohl-Dickstein, and Luke Metz; "General-purpose in-context learning by meta-learning transformers"; https://arxiv.org/abs/2212.04458 (2022) --- Rebuttal Comment 1.1: Comment: Thank you for the detailed response. I have increased my score 6 --> 7.	Summary: This paper develops novel insights into in-context learning and how it works in Transformers. To this end, the authors propose a generalization of the modular arithmetic task explored in several prior works on grokking. Unlike those works, the structure of the defined task is more rich, enabling an analysis of both in-distribution generalization (standard test evaluation) and out-of-distribution generalization (which is itself broken down into two variants). Strengths: The paper is fairly well written and clear. Going beyond the standard linear regression task to study ICL was great to see as well. The main selling point for me are the empirics though---I really like the results! The visualization of how the model represents concepts relevant to this paper's setup is quite beautiful: the circle of circles was fascinating to look at and, arguably, not something I expected. In retrospect, I can rationalize this as making sense---we get circular embeddings in grokking, so circle of circles is the logical geometrical extension here. Results on scaling are interesting in their own right as well. Weaknesses: I do not have any major apprehensions, except for the related work, which I think is relatively sparse. - Related Work. At this point, the topic this paper is focused on has a rather rich literature and I think a more detailed related work is warranted (perhaps in the appendix if space is an issue). For example, the results by Kirsch et al. (which is cited) are very similar to what authors show, especially results on scaling effects. The main different is width scaling in that paper and no geometric analysis, but nonetheless the relationship warranted more emphasis and discussion. Similarly, several recent works have explored OOD generalization of toy ICL tasks defined in prior works (e.g., see Ahuja and Lopez-Paz [1] for work on linear regression tasks and Ramesh et al. [2] for group arithmetic tasks). Regarding grokking, there are several works exploring the phase transition-y nature of this task. For example, see Kumar et al. [3]. The transient nature of ICL also has negative results (see Reddy [4]), which are worth discussion since they are the primary conclusion in depth scaling as I see it. [1] https://arxiv.org/abs/2305.16704 [2] https://arxiv.org/abs/2311.12997 [3] https://arxiv.org/abs/2310.06110 [4] https://openreview.net/forum?id=aN4Jf6Cx69 Technical Quality: 3 Clarity: 3 Questions for Authors: A few questions below that I would like to see answered. - PCA variance. Given this is a rather rich geometry in 2-D, I'm slightly surprised to see PCA captured it. Did you have to do some preprocessing? How much variance is explained by the two projected components? If there are other components that are not shown but have a large variance, what do those components encode---can you try 3D plots? - What does the MLP do? Given the mechinterp focused on attention solely, it is unclear what role MLPs played. Two experiments to try here are: (i) train attention only models to see if MLPs are even necessary, and (ii) perform the PCA analysis to uncover representations' geometry at the level of attentions and MLPs at each block in the model. Experiment (i) may require retraining models, so I understand if the authors are unable to conduct it, but my expectation will be that you will see that model "internalizes" task vectors and records them in MLPs. Attention only models can solve the task, but I expect the representations' geometry will be quite different. For experiment (ii) however, I expect that's easy to run and is merely repeating the plotting script on intermediate representations as a forward pass occurs through the model. If the geometry is primarily formed at attention layers, we'll see that in this experiment; vice versa, if it forms via MLPs, we'll see it explicitly. Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: Limitations are fairly discussed. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for the encouraging feedback and helpful suggestions. ## Weakness We thank the reviewer for pointing out the highly relevant references. We will add the citations and utilize the additional page allowance in the final version to discuss their relation to our work. ## Questions PCA Analysis: We conducted PCA without any preprocessing. As per the reviewer's suggestion, we expanded upon Figure 6 from the original manuscript by plotting higher order PCA components. The results are presented in Figure G.2 of the attached PDF and discussed in the Global Rebuttal. We analysed the top-4 components, and found highly structured features. The top-4 PCA components account for a significant portion of the PCA variance. (Note that we present 2d slices instead of 3d plots of PCA because sparse 3d plots shown in 2d are difficult to comprehend.) Furthermore, following the suggestion of the reviewer rwBm, we plot similar features with a different task vector $(a,b)$ and a different number of shots. These results serve as evidence for the claims made in Figure 6 caption. Specifically, the PCA constructed from the first layer's head remains unchanged across different task vectors (up to a negative sign along certain directions). In contrast, the PCA derived from the second layer's head changes with the choice of task vector. PCA of Attention outputs: As per the suggestion of the reviewer, we present the PCA analysis of Attention outputs (as opposed to individual heads) in the top row of Figure G.3 of the attached PDF. We find highly structured top-4 PCA patterns in Layer 1, which also account for a significant fraction of PCA variance. Layer 2 exhibits less structured organization and the contribution of the top-4 PCA components is diminished. Analysis of MLP features: In the attached PDF, we have added two main results concering MLPs. 1. We extended our analysis to include PCA Multi-Layer Perceptron (MLP) features, as shown in the bottom row of Figure G.3 of the attached PDF. The results demonstrate: - Layer 1: Highly structured patterns are evident in MLP features. The top-4 components contribute substantially to the overall PCA variance. - Layer 2: Features exhibit less structured organization, and the significance of the top-4 components is diminished compared to Layer 1. 2. Additionally, in Figure G.1 of the attached PDF, we have shown the post-ReLU neuronal activations from various layers as functions of $x,y$. We find highly structured activation patterns across layers, especially in Layer 3 of $d=4$ model. For a detailed account of the MLP results, please refer to the Global Rebuttal. We will discuss these new results in the additional page allowance of the final version. We believe that in a future work, our analysis of the attention heads as well as MLP activations can be tied together to infer an end-to-end algorithm for our setting. --- Rebuttal Comment 1.1: Comment: Thank you for the response. I really like the new results and hope they'll be included in the final paper. I'll maintain my original score.	Rebuttal 1: Rebuttal: # Global Rebuttal We included three new figures in the attached one-page PDF. These new results address questions raised by one or more of the reviewers. Especially, the results about MLP layers are relevant to multiple reviews. ## Figure G.1 We examined how individual neurons (post-ReLU) are activated for different inputs $(x,y)$. We discovered that each neuron only gets activated for highly specific inputs. This can be interpreted as a further skill composition at the neuron level, although the exact role of each neuron remains to be discovered. Notably, in Layer 3 of the $d=4$ model we find that neuronal activations follow the re-scaling relation $x = k y$. The layer contains all such re-scalings, forming a complete basis. Layer 2 of the $d=4$ model show a periodic pattern wrt $(x,y)$, while Layer 1 neurons only get activated only for specific $x$ values. Neurons in the $d=2$ model appear to be superposed/compressed versions of those found in the $d=4$ model. This is likely due to $d=2$ model not having enough layers. We observe that the neurons from Layer 1 of the $d=2$ model contains patters similar to Layer 1 and 2 of the $d=4$ model. Neurons from Layer 2 of the $d=2$ model appear to be superpositions of various re-scaling patterns from Layer 3 of $d=4$ model. ## Figure G.2 We expanded upon the PCA plots of the $d=2$ model presented in Figure 6 of the original manuscript. In this extension, we included a different task vector $(a, b)$ and plotted the results using a different shot (16-shot). We see that The top-3,4 components of PCA of layer 1, head 3 also forms circle of circles, albeit with a different pattern from that of top-1,2 components. In this case, we find pairs of coinciding circles, where the $x$ corresponding to the coinciding circles differ by $(p-1)/2 = 14$. In layer 2, head 2 we can see that the PCA pattern changes for different tasks. This is in contrast to the layer 1 PCA patterns, which remain unchanged. (as claimed in the main text) ## Figure G.3 We performed PCA on both (i) Attention output (as opposed to individual heads) and (ii) MLP output of the $d=2$ model. In the Attention output of Layer 1, we observe a circle-of-circle structure. The other components also exhibit some structure -- notably, the top-3,4 components in layer 1 form 4 clusters corresponding to even/odd $X$ and $y$ values. ## Additional Experiments In addition to these results, we also ran a few more experiments. Due to space constraints, we could not include them in the one-page PDF. We describe these experiments and results in words here -- we will include them in the camera-ready version of the paper. 1. Linear probing of $c_1$ and $c_2$: We extracted the feature from the residual stream after each transformer block; attached a new linear layer and fine-tuned it to predict the correct re-scaling coefficients. We simplified the experiment to the $1$-shot case, where the sequences are simply $(x_1, y_1, z_1, x, y, ?)$. The fine-tuned linear layer was used to predict the correct coefficients $c_1$ such that $x_1 \cdot c_1 = x$ mod $p$ (alternatively $y_1 \cdot c_1 = y$ can be used). We observed $15 \\% - 20 \\%$ accuracy across all the layers for both $d=2$ and $d=4$ models. Despite the accuracy being above random guessing ($3\%$), we believe this result to be inconclusive. 2. Linear probing of (a,b): We also ran similar experiments with full sequences ($1$-shot to $31$-shots) and tried to predict the task vector $(a, b)$ along the sequence. We found random performance on the o.o.d. generalization set, suggesting that the model does not explicitly compute the task vector. Note that this is in agreement with our proposed algorithm. 3. Pruning / Activation Patching [1]: In this experiment, we replaced the output of each attention head with its averaged output over pre-training sequences. The average was taken over all the pre-training tasks, and $512$ sequences from each task. We found that: - For both $d=2$ and $ d=4$ models, pruning the circle-of-circle head immediately brings the model to random guessing. This can be understood as an average over sequences collapsing the circle down to a point, which destroys the feature completely. - For the $d=2$ model, pruning any other head causes some performance drop. This is to be expected since the model does not have enough capacity even before patching. - The $d=4$ model is significantly more robust to pruning. We can patch all heads except for (i) the three shown in Figure 11 of the manuscript and (ii) the heads in the last layer, with almost no impact on the performance (less than a $5\\%$ performance drop). [1] Fred Zhang, Neel Nanda; "Towards Best Practices of Activation Patching in Language Models: Metrics and Methods"; https://arxiv.org/abs/2309.16042 Pdf: /pdf/dd22b9962d4d90f2262b68359c6dd7a071c6859c.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
4+3 Phases of Compute-Optimal Neural Scaling Laws	Accept (spotlight)	Summary: The authors consider a simple scaling model and derive scaling laws for one pass SGD in an asymptotic limit. From the scaling laws they identify several phases and subphases where certain components of the loss dominate and the compute-optimal model parameter count is affected. The loss components are related to the model capacity, SGD noise, and feature embedding. Detailed calculations are performed to completely characterize the behaviors in different regimes and are accompanied by simulations to give supporting evidence. Interestingly large regions of the phase space result in a "universal scaling" independent of the problem parameters. Strengths: Understanding scaling behavior of learning models is of great theoretical and practical importance. This work provides a very thorough and comprehensive analysis of the simplest, non-trivial model. Despite the simplicity of the model a rich variety of behavior is observed which requires effort to analyze and catalogue. The observations of universality and effects of finite size are interesting and potentially relevant to more realistic settings. Weaknesses: 1. It is unclear how novel the mathematical techniques are and how general purpose they are, some discussion would be helpful. 2. It is unclear how related the simple model is to observations about more realistic models so some more commentary could be useful. Technical Quality: 4 Clarity: 3 Questions for Authors: 1. Is there potential for a more general explanation for universality since the same scaling appears to hold in the Chinchilla scaling law? 2. Can any of the techniques be extended to analyze more complex models? 3. Are there any lessons for practical LLM scaling? Confidence: 3 Soundness: 4 Presentation: 3 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 their insightful comments and suggestions which were very helpful. We address these below. 1. *Novelty of Techniques.* * Analysis of learning rates via Volterra equations in concert with random matrix theory has appeared before (say \[10\]/\[11\] in the paper). Volterra analysis is not widespread, and it remains to be seen how general purpose they are. For precise risk curve analysis of stochastic algorithms, they seem useful, including momentum methods \[1\]. A more general point of view is needed for analysis of non-quadratic problems, but there is an equivalent system of ODEs reminiscent of mean field theory (this is equivalent to the Volterra description in the least-squares case) which has been used as well \[2\]. Generalizing the type of results in this paper to a non-linear setting would require understanding how these systems of ODEs evolve without appealing to convolution-Volterra-theory; these look quite similar for the linear and nonlinear cases, so I would be cautiously optimistic that the risk curve analysis could be adapted to nonlinear PLRF \[1\] Paquette et al. Dynamics of stochastic momentum methods. 2021 \[2\] Collins-Woodfin et al. Hitting the high-dimensional notes: An ODE for SGD learning dynamics on GLMs and multi-index models. 2023\. * Random matrix theory analyses of generalization errors in random features models are now pretty well-developed, and this paper certainly fits within that tradition. The majority of the technical work and mathematical novelty in this paper is the analysis of the PLRF resolvent, which is a pure random matrix theory question. After that, there’s a fair bit of asymptotic analysis which is needed, which will probably be common to all analyses of power-law scaling law problems. 2. *Regarding applications to realistic models.* We’ve also been asking ourselves this question. Probably the quantitative predictions of this model will be impossible to fit to anything like Chinchilla; one would need to have a way to estimate both $\\alpha$ and $\\beta$, which is approaching science fiction. Now on the other hand, it is possible (as in Chinchilla) to measure the resulting scaling laws. One may attempt to vary parameters that could influence $(\\alpha,\\beta)$, and see if the scaling laws respond in the way one would expect from this paper. One might also look for a phase plane of LLM parameters in which the optimal scaling $d^\* \= \\sqrt{f}$ with $f = $flops changes; we saw that this is possible in some parts of the $(\\alpha, \\beta)$ plane. Another possible complexity is that adaptive and preconditioned methods are all but necessary for training LLMs, and so some effort should be made to establish to what extent the phase diagram we described is affected by different optimizers. Responses to Questions: 1. **(Deeper pattern to where $d^\ \= \\sqrt{f}$).*** This is a great question and perhaps one of the biggest mysteries of the phase diagram, given that it appears in 3 distinct regimes. I can share some possible speculations, but I don’t really know. * One possible answer is that real-life is closest to $\\alpha=\\beta$ (or perhaps autoregressive problems are always somewhere close to $\\alpha=\\beta$), and along this line it just so happens $d^\= \\sqrt{f}$. Potentially, regimes where $d^\* \= \\sqrt{f}$ are not optimal are a reflection of the algorithm ‘failing’ in some sense, and one should be looking to improve it. Conversely, existing work suggests that Phase Ia might be algorithmically unimprovable – see the discussion above. 2. *(Extensions to more complex models).* Of course the proof will be \`\`in the pudding,’’ but we would guess that the answer is yes – nonlinear power-law-random-features, anisotropic weight matrices, models with some level of feature learning in mean-field scaling. Existing work on random features regression and 2-layer networks strongly suggests that the extension to the nonlinear case should be solvable. The case of anisotropic weight matrices should be quite similar mathematically to this work (it mostly comes to mind as a way to better understand the effect of using preconditioned algorithms on scaling laws). 3. *(Practical lessons for LLM scaling).* We have a few possible lessons: * We give some further evidence that $d^{\\star} \= f^{½}$ is justified. * The ‘functional form’ of the scaling laws of the risk curves which is empirically fit to scaling laws should be updated to be $Risk(n,d) \= c \+ a\_1 n^{-b\_1} \+ a\_2 d^{-b\_2} \+ a\_3 d^{-b\_2} n^{-b\_3}.$. The last term looks like $F\_{ac}$, and is usually dropped. But it is needed even in this simple setting to get the correct scaling law behavior (in our setting $b\_2$ is always $1$). * Finite-dimensional effects in size of parameters (d) exist and potentially have a huge impact on the compute optimal exponents. We see even in our simple model (see Fig. 4). If one is doing empirical scaling laws, then one can easily see measured exponents that change by something like $0.05$ as one increases the FLOP-budget by a factor of $10^9$. In LLM scaling, this $0.05$ is the same order of magnitude as the observed scaling law itself, and it is not (per se) related to a breakdown of the scaling laws. * Speculatively: with some hypotheses about which phase one is in, one may be able to determine what is the dominant feature of the loss curve ($F\_{ac}$ dominated, $F\_{pp}$ dominated, $K\_{pp}$ dominated). This could allow one to determine if in future training runs, how to increase parameter counts or compute. (Roughly $F\_{ac}$ is expensive from a compute point of view, and it is cost efficient to increase scale – or reserve compute for other parts of the model when one enters this regime). Of course, this heuristic is just a hypothesis, based on the work here and needs to be tested. --- Rebuttal Comment 1.1: Comment: Thank you for the detailed responses. I will maintain my score.	Summary: This submission studies the Power Law Random Feature (PLRF) that depends on three parameters: data complexity, target complexity, and model parameter count. They derive a deterministic closed expression for the dynamics of SGD using a clever mapping to Volterra equations. They are able to determine the compute-optimal frontier for different learning scenarios. The theoretical claims are supported by extensive numerical simulations. Strengths: The main strength of this paper stands clearly in being both theoretically and numerically exhaustive. The numerical illustrations and details backing up the theoretical claims are explored in detail both in the main and appendices. Moreover, the questions addressed are of great interest to the theoretical machine learning community. Weaknesses: The strong weakness of this submission is the presentation. It is challenging for a non-expert reader to navigate the related literature with only thirtheen references and eleven lines devoted to the related works. Technical Quality: 2 Clarity: 1 Questions for Authors: As mentioned above, a large part of my concerns resides in the presentation of the results and the framing of the present submission in terms of the related literature. See below for some examples of needed citations/explanations. - Deterministic equivalent at page 2, what is it and how is it used in machine learning theory? Cite reference for this, e.g., [1]. - What is a "neural scaling model". This appears in the first line of the abstract. - When introducing PLRF there is no mention to what classical RF looks like [2]. Many works could be cited that use also Random Matrix Theory tools to connect at the previously described deterministic equivalent, e.g. [3] among many others. - [4,5] are two papers that drew phase diagrams for the training dynamics of SGD. Although they do not seem related to the present submission, they deal with the optimal tuning of SGD from a theoretical point of view. The setting presented in the manuscript has many limitations-- which is completely acceptable for a primarily theoretical work. However, the technical challenges that the authors would face if they were to lift them are never discussed. For example, square loss, lack of non-linearity in the PLRF, deterministic teacher vector $b$, need for $v>d$, etc. All these assumptions are reasonable, but must be compared to related works on the subject and why it is difficult to lift them. ### Minor points - Explain in deeper detail footnote number 6. Why is this the case? - The mapping to Volterra equations is nice and I believe it would deserve more space in the main body. - Different subfigures might have different aspect ratios (see e.g. Figures 2 and 3). ### References - [1] Random Matrix Methods for Machine Learning. Coulliet & Liao 2022, Cambridge University Press. - [2] Random Features for Large-Scale Kernel Machines. Rahimi & Recht. NeurIPS 2007. - [3] The generalization error of random features regression: Precise asymptotics and double descent curve. Mei & Montanari. Communications on Pure and Applied Mathematics 2021. - [4] Online Learning and Information Exponents: On The Importance of Batch size, and Time/Complexity Tradeoffs. Arnaboldi et al. ICML 2024. - [5] Dissecting the effects of SGD noise in distinct regimes of deep learning. Sclocchi et al. ICML 2023. Confidence: 2 Soundness: 2 Presentation: 1 Contribution: 2 Limitations: The suggestions for improving the description of the theoretical limitations are given above. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Responses to Weaknesses and questions: Thank you for your comments. We will definitely add a more thorough evaluation of related works. Great catch about Footnote number 6 – it’s actually not true – we’ve removed it. We’d be very happy to hear any other comments about the content of the paper – time allowing, we will add some discussion in the appendix about batch size, which was a not-fully-explored thread of this paper. Regarding the questions (square loss, lack of non-linearity in PLRF, deterministic teacher vector $b$, need for $v \> d$). \`\`All these assumptions are reasonable, but must be compared to related works on the subject and why it is difficult to lift them.’’ 1. Extending to square loss and adding a nonlinearity are both very interesting directions of future research, and it would certainly be reasonable to do them after considering the square loss – linear case\! 2. The deterministic teacher vector could be replaced by a random one with neither an increase in complexity, but also no change in phenomenology (if it has the same behavior as $b$). Perhaps we can add: the goal here isn’t really theory-building, in the sense of covering as wide a class of kernel regression problems as possible. The goal is to map out as much phenomenology as possible. So generalizations of the problem-setup which are not expected to change this phenomenology were not prioritized. 3. The case of $v\>d$ is for simplicity and also because we broadly believe it aligns with what one sees in neural scaling laws. Indeed you can consider another phase when ($2\\alpha \+ 2\\beta \< 1$) with $v \< d$, but we suspect it is another ‘Phase I’. The same comment goes for negative $\\beta$. We agree with the reviewer that more references and a more thorough discussion of background and related work would improve the accessibility of this paper. For that reason we have included 32 references and proposed changes to the related work and background sections (see the general response). In light of these changes, we hope the reviewer will reconsider their score. --- Rebuttal Comment 1.1: Title: Thank you for your rebuttal Comment: I thank the authors for their rebuttal. I carefully read it along with the other reviewers’ comments and I would like to increase my score to 6. As I mentioned in my first review, the outstanding weakness of this paper was the presentation, and I believe the proposed changes will greatly improve the quality of the submission. --- Rebuttal 2: Comment: Hi reviewer, in the response you wrote that you would like to increase their score from a 4$\rightarrow$6. However seems the system not actually change their score. If you want to increase your score, may you implement this to the openreview system? Thanks. Your AC	Summary: The paper studies a linear random feature model trained on power law data under online SGD. By using a Volterra approach and leveraging deterministic equivalence, they characterize the loss in the high dimensional limit. From this, they extract scaling laws for this model, that determine compute optimality. The show that depending on the spectral decay of the covariates and the task vector, SGD noise as well as finite width effects can effect the scaling of the loss curves with time. A consequence of this is that the optimal allocation of compute can change. By systematically studying finite width and time effects, the authors characterize the scaling laws one should expect in this model. Strengths: The paper investigates an important problem. The reviewer has checked much of the math in the (extensive) appendix. The derivations are technically sound. The conclusions of this paper certainly add meaningfully to the present machine learning literature and our understanding of the role of the optimizer on neural scaling laws. The experiments are beautifully done and add meaningfully to the presentation of the paper. I commend the authors on the care put into the experiments and encourage them to make the code public. Weaknesses: There are two primary weakness: 1. The paucity of citations in this work is stunning Many authors have studied random feature models before and concurrently with the Maloney paper. The set of random feature model papers that deserve a citation are many, and I leave it to the authors to do a thorough review. Certainly Mei and Montanari https://arxiv.org/abs/1908.05355, as well as Bach's paper that also derives the same scalings as Maloney: https://epubs.siam.org/doi/abs/10.1137/23M1558781 Before all of this, Hastie et al in their original paper studied random projections on structured data as well: https://arxiv.org/abs/1903.08560 Although not explicitly calculated, the results of Mel and Pennington give as a special case the generalization error formula in Maloney et al and was published much earlier. They just didn't calculate the scaling law exponents. https://openreview.net/forum?id=JfaWawZ8BmX Similar models were studied and exactly solved by Loureiro and colleagues in several papers, for example https://arxiv.org/abs/2102.08127 Moreover, although I have not read all of the Bordelon paper due to lack of familiarity with DMFT, I can see that they explicitly treat the case of SGD noise. Given the substantial overlap in model and problem studied I think it is worth clarifying sharply what this paper puts forward beyond the initial studies of that one. I think this work is important. Putting it in the context of works that came before is also important. The authors are hurting the reception of their paper in the broader community by citing so sparsely. 2. Although the readability of this paper in the main text is reasonable, the accessibility of the appendix is quite poor. The first section deriving the Volterra equation is written quite clearly and accessibly. From there forward, it becomes increasingly impossible to read. By hopping around the theorems and propositions one can eventually recover your bounds on the forcing function and the kernel function. I strongly recommend restructuring the order of your theorems and propositions. I also strongly encourage an "overview of proofs" to start the appendix off so that a reader can navigate the dense math more carefully. The contour presented in Figure 7 comes out of nowhere. Even after reading most of this paper several times over I still have no idea how the authors arrived at it. I've managed to reproduce most of the results and I don't need this type of analytic contour argument at all. If these two concerns can be addressed, I will be happy to raise my score. Specifically, I would like the authors to list all of the relevant papers that they will cite in the revised draft, and I would strongly encourage them to follow through. Technical Quality: 4 Clarity: 2 Questions for Authors: 1. It is not obvious without going deep into the appendix why these terms are called $K_{pp}$, $F_{ac}$, etc. It would be much better if you explained this sooner rather than later. 2. If I am not mistaken, the limit that isn't high-dimensional, $2 \alpha < 1$, would never be encountered for a kernel trained on natural data. Although there do indeed seem to be interesting phenomena below that line, I am wondering why the authors have decided to so carefully study this? Is is purely out of a desire to characterize the entire $\alpha, \beta$ plane? 3. Further, $\beta > 1$ corresponds to tasks that are ``in the Hilbert space'' of the original $v$ dimensional space. Again, this is never the case for natural data, where the spectral decay is much much slower. If anything this paper seems to tell us that SGD has very little effect on the scaling laws on realistic data. Please let me know if I am incorrect in this characterization. Otherwise, given the discussion of scaling laws, there will likely be some practitioners that read this paper who are confused about how to interpret $\alpha$ and $\beta$. I think the authors would do well to state clearly the relationship between the regions in the $\alpha$ and $\beta$ plane and the values one would expect in real datasets. 4. Why are you using the term `SGD frustrated'? In the statistical physics literature this is taken to mean something else entirely. 5. As a smaller comment, the notation for the exponents is quite different from other works. In linear regression its standard to report things in terms of the "source and capacity" exponents, where $\alpha$ is the decay exponent of the spectrum. Of course the authors don't need to change their notation but a table comparing notations with other works would be very useful and go a long way. Confidence: 4 Soundness: 4 Presentation: 2 Contribution: 3 Limitations: Given that this is a toy model of neural scaling laws, I do not expect major societal implications. However, the principled understanding of such scaling properties may well have important impacts on the future of the field. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for their insightful comments and suggestions. We address below questions and concerns raised by the reviewer. Because there was a lot of depth in the questions raised, we needed additional characters to respond adequately so below is the first part of the response. There will be an additional “Official Comment” with the remaining response. Responses to Weaknesses: 1. (Related Work) We are very happy to add discussion regarding random feature generalization (especially the relations to generalization error bounds which were developed for source/capacity conditions) and SGD complexity on power-law problems, which are absolutely related to this work. See response to the ‘General Reviewers’ and the attached pdf for comparison of our notation to source/capacity conditions. 2. (Accessibility) * We will add an introduction to the appendix to guide how the proofs are done. * The contour is \`what works.’ We do not believe the contour is absolutely necessary to proving the result; it is a nice technical tool, but not essential. Indeed – we heuristically derived all the arguments long before we found the contour in the process of formulating the proof. The origin of the contour is solving the fixed point equation for $m$. The ‘kink’ in the contour occurs at real-part $x \\approx d^{-\\alpha}$. This corresponds to a point of transition in the spectrum of the PLRF matrix: for smaller scales, the self-consistent spectrum forms a spectral bulk. For larger scales, the self-consistent spectra forms outliers, roughly located at $j^{-2\\alpha}$ for integer $j$. In the self-consistent spectra, these outliers actually have densities of width approximately $O(1/sqrt(d))$. Now the contour is basically chosen as the closest contour to this axis that makes this transition invisible, which means the imaginary part of the contour is just a bit larger than the inter-eigenvalue spacing, and it means we see a clean power-law everywhere along the contour. One could instead not put the kink, but then would have an absolutely continuous part and an \`\`approximately’’ pure point part of the spectrum, which is more annoying than anything (mostly because the m function undergoes some relatively high-frequency changes near each outlier, and all this high-frequency excitement turns out to be completely invisible and unimportant to the larger picture). The method we use to approximate the m is fundamentally perturbative, so matching all the high-frequency changes in m is super-hard; so it’s easier to change the contour and then have a good, smooth ansatz for m. 3. (Comparison with Bordelon et al. \[1\]) We highlight below the main differences between our work and Bordelon et. al \[1\]: * Bordelon et. al assumes the functional form for the loss is $n^{-\\tau} \+ d^{-\\sigma}$ (see Appendix N, Eq. (153)). Then they use DMFT to find the exponents $\\tau$ and $\\sigma$. We prove that the functional form for the loss of power-law random features is $$ P(n,d) \\asymp \\underbrace{n^{-\sigma\_1}}\_{F\_{pp}} \+ \\underbrace{n^{-\sigma\_2}}\_{K\_{pp}} \+ \\underbrace{d^{-\tau\_1}}\_{F\_0} \+ \\underbrace{ d^{-\tau\_2} n^{-\sigma\_3}}\_{F\_{ac}} $$ Note the cross-term $\\underbrace{ d^{-\tau\_2} n^{-\sigma\_3}}\_{F\_{ac}}$ which is missing from the functional form for Bordelon and plays an important role in Phase II and III for the compute-optimal curves. Additionally, Bordelon et. al. do not consider phase III, and the impact of the SGD algorithm through the term $K\_{pp}$. * Our work holds for any $\\alpha$ and $\\beta$ and Bordelon et. al. only work for the trace class setting, i.e., $2 \\alpha \> 1$. Moreover Bordelon et. al. compute-optimal result agrees with our compute-optimal exponents when $2\\beta \< 1$. This is consistent since the loss curves in Phase Ia only depend on $F\_{pp}$ and $F\_0$. The cross term $F\_{ac}$ and the impact of SGD $K\_{pp}$ do not appear until Phase II-IV. Comparison of $(a,b)$ and $(\\alpha, \\beta)$ between the two papers ---------------------------------- Bordelon, et. al. \| This paper ---------------------------------- b \| $2\alpha$ a \| $2\beta + 2\alpha$ We will add a comparison to the text (see also Table 1 in attached pdf of revision). \[1\] B. Bordelon, A. Atanasov, and C. Pehlevan. A Dynamical Model of Neural Scaling Laws. arXiv preprint arXiv:2402.01092, 2024\. --- Rebuttal Comment 1.1: Title: (Response to questions) Comment: Response to Reviewer Questions 1. (Moving up definition of $K\_{pp}$ and $F\_{ac}$): We agree with the reviewer and we will move the explanations of $K\_{pp}$ and $F\_{ac}$ earlier in the text. Actually, we didn’t explain the names because the notation was grandfathered in from earlier parts of the project (which featured such abominations as $K\_{ac}$ and $F\_{bulk}$ and which all turned out to be irrelevant), and this notation turned out to not be well-aligned with what the terms mean. We plan to change the names. 2. (Below the line $2 \\alpha \< 1$ and $\\beta \> 1$): We do not view this work as motivated by kernel regression, which perhaps explains the philosophical divide. The random features model here with $d$ parameters is a toy model of non-linear optimization problems with $d$ parameters, e.g. LLM training problems of growing parameter count. We can imagine approximating these optimization problems by kernel problems, which would lead to a sequence of kernels, one for each $d$. To make a nice limit theory these kernels would need to converge weakly – but they certainly don’t have to converge to a trace-class operator. So any eigenvalue decay/growth rate could be realized this way. For example, if the NTKs performed some type of ‘whitening’ operation on some underlying data, one would expect long stretches of eigenvalues with very slow (or almost no) decay. (Which $\\alpha, \\beta$ are important:) By the same token, even with a fixed target, if you have a sequence of kernels you could have basically anything for the target decay rate. As for $\\beta$ in various phases being more “real” than others – I’m curious to know if you have any in-depth study. My guess is that $\\beta=\\alpha$ is actually super common, especially in autoregressive tasks or in classification tasks which are well–approximated (spectrally) to the nearest-neighbor function. The exponents we see in LLMs scalings \[1\] are really small so this would suggest that there is some practical merit to considering what happens below the high-dimensional line. For LLMs scaling, which is the motivation of this work, estimating $\\alpha, \\beta$ is hard. \[1\] Hoffmann et. al. Training Compute-Optimal Large Language Models. 2022 3. (SGD frustrated): We are not married to this terminology and can change it. In Phase III, the optimization trajectory is slowed primarily due to the rate of SGD noise production, which is sufficiently fast that the underlying problem is solved faster than SGD can solve for its own mistakes. In other words, geometrically the gradients produced by SGD are sufficiently randomly orientated that they themselves are the slowdown to the algorithm (and this overwhelms the difficulty of finding the signal). So this looks a little like frustration, even if the usage is not the same as in spin systems. But to avoid confusion we will adopt other terminology, perhaps ‘SGD limited’. 4. (source/capacity): We have provided a table with the comparisons in the attached pdf to “All Reviewers”. --- Rebuttal 2: Title: Response to Reviewer Comments Comment: I thank the reviewers for compiling a more proper bibliography for this quality of work. I also thank them for explaining in detail the differences between this work and the prior works, especially of Bordelon et al. I looked at the supplementary note, comparing notations and especially Table 3 comparing this work with others. I think this is a very nice table, that will be important and useful for the community, and I encourage them to either start the appendix with this table or to even consider putting it in the main text. I definitely hope that the related work section on page two can be expanded beyond just five sentences to highlight some these facts and point the reader to the table. It makes it much more clear what this paper contributes over prior work. Lastly, given that the contour is indeed just "what works" I strongly encourage the authors to state that clearly in the appendix. I found the appendix relatively readable until this contour came out of nowhere. Even just an idea of what motivated the authors to consider it would go a long way. As promised, I have raised my score. --- Rebuttal Comment 2.1: Title: Thoughts on Studies of the High Dimensional Line Comment: The authors raise an interesting question in point 2. To my knowledge, extensive study of $\alpha$ and $\beta$ has not been performed but it certainly can be done so in principle. In Fig 12 of the Bordelon paper I see that they measure $\alpha$ for image datasets for the NTK of a resnet and find throughout the course of training that the effective $\alpha$ remains above the high dimensional line. The other paper I am familiar with is one of Steinhardt and Wei: https://arxiv.org/pdf/2203.06176 see especially Fig 5 and Table 3. There, for a variety of architectures on basic vision tasks they find that both the initial and final kernels have spectral decay that keeps the kernel trace class. I have a strong belief that this will remain true for virtually all vision datasets, even at much higher resolutions. For text data I do not have strong intuition, but would believe as with images that $\alpha$ remains above $1/2$ and only $\beta$ is small. Our differing intuitions are indeed interesting and I would be very excited to see an empirical paper study this!	Summary: This submission studies the generalization error dynamics of one-pass SGD in a sketched linear regression setting, where the data and target signal are distributed according to certain power laws, and SGD optimizes a linear model on top of a Gaussian random projection. Using random matrix theoretical tools, the authors precisely computed the asymptotic generalization error of the SGD iterates in high dimensions; this reveals various scaling laws and allows the authors to characterize the compute (flop) optimal frontier. Strengths: This is an emergency review, so I shall simply state that this is probably the most interesting submission in my batch and should be accepted. Weaknesses: My main concern is that the authors do not adequately discuss the overlap with prior results. 1. Generalization error of the random features model under various source and capacity conditions has been extensively studied. For instance, (Rudi and Rosasco 2016) derived scaling laws of random features regression with respect to the model width and number of training data, and this result is later extended to SGD in (Carratino et al. 2018), taking into account the scaling of iteration number. The authors should explain the similarity and differences in the findings to highlight the advantage of a precise analysis. * (Rudi and Rosasco 2016) Generalization Properties of Learning with Random Features. * (Carratino et al. 2018) Learning with SGD and Random Features. 2. If we do not take optimization into account, then neural scaling laws in the form of $(\text{data}^{-\beta} + \text{param}^{-\gamma})$ have been established in many prior works on nonparametric regression (Schmidt-Hieber 2017) (Suzuki 2018) -- these are rigorous versions of the hand-wavy arguments in (Bahri et al. 2021) which the authors cited. If we interpret the number of training data to be the same as the iteration number, can we obtain similar plots on the compute-optimal front as reported in Figure 2(a)(b)? * (Schmidt-Hieber 2017) Nonparametric regression using deep neural networks with ReLU activation function. * (Suzuki 2018) Adaptivity of deep ReLU network for learning in Besov and mixed smooth Besov spaces: optimal rate and curse of dimensionality. Some additional questions: 1. In light of empirical findings that training small models for a longer time can be beneficial, can the authors comment on the possibility of extending this analysis to the multiple-pass setting? In the kernel regression literature, it is known that multi-pass SGD has statistical superiority (Pillaud-Vivien et al. 2018). * (Pillaud-Vivien et al. 2018) Statistical Optimality of Stochastic Gradient Descent on Hard Learning Problems through Multiple Passes. 2. Does the sample size scaling match the minimax optimal rate in (Caponnetto and de Vito 2007) in certain regimes? * (Caponnetto and de Vito 2007) Optimal rates for regularized least-squares algorithm. 3. What are the technical challenges to show the asymptotic equivalence between the SGD dynamics and the deterministic equivalent description that the authors analyze? 4. Can the authors comment on the restriction to proportional $v,d$? Why is there a sharp transition at $2\alpha=1$ that decides the scaling of $d$? Technical Quality: 3 Clarity: 3 Questions for Authors: See Weaknesses. Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: See Weaknesses. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for their comments which were very helpful. We address these below. Because there was a lot of depth in the questions raised, we needed additional characters to respond adequately so below is the first part of the response. There will be an additional “Official Comment” with the remaining response. Response to weakness: Yes we agree, the comparison to existing work should be expanded. We will include a more detailed discussion of existing work and how it compares. We will also include a section detailing how these SGD-generalization bounds compare to optimized non-algorithmic bounds (especially to optimal ridge regression). The suggestions for references are super helpful – thank you – and we have made an attempt to integrate them. We’ll outline the results of our attempt to answer your question in the points below. We’re happy to have feedback if you believe the works considered are still inappropriate. Regarding the specific suggestions, thanks, many are new to us. We will formulate our response partly based upon the concurrent article \[1\], which features a sharp analysis of ridge regression on a problem with the capacity/source conditions and which improves over Rudi-Rosasco. Note the source/capacity conditions are not meaningful for $2\\alpha \< 1$, so we restrict the discussion to phases Ia/II/III ($2\\alpha \> 1$). Directly addressing the points you have made below: 1. *Ridge regression comparison.* The bounds for ridge regression agree with SGD in phases Ia/II, which is to say that if one takes ridge regression with r-samples, computes the generalization error with the ridge estimator with a O(1) ridge parameter; then the SGD risk curve we compute agrees with the generalization error and the ridge error agree up to constants. (Using Corollary 4.1 of \[1\]). To match notation with the source/capacity literature, we'll use our $\alpha$ parameter (so the capacity is $2\alpha$) and we'll use the source parameter $r = (\\alpha+\\beta-0.5)/(2\\alpha)$; see also Table 1 in the pdf attached to OpenReview. We note that phases Ia/II/III correspond to previously observed hardness regimes ($r \\in (0,0.5), (0.5,1.0), (1.0, \\infty)$) A few comments about this: from \[1\], one recovers that the ridge-generalization-error equals the SGD-generalization-error in Phase 1a/II, at all points in the risk curve. In Phase III, ridge regularization with O(1) ridge has better generalization error than SGD. The comparison to the Rudi-Rosasco bounds can be seen in (48) of \[1\]. They match the generalization errors in Phase Ia, but are not optimal in Phase II/Phase III. The Carratino et al. bounds (Corollary 1 of that paper) match the minimax-optimal rates attained by kernel ridge regression, and they effectively show that there are parameter choices for one-pass SGD which match those rates. We discuss below minimax optimal rates. 2. *Regarding non-parametric regression: thanks for these references. Bahri et al. and Maloney et al are indeed not mathematics papers. We still believe they are quite valuable scientifically to this paper. We’re happy to clarify how we view their contributions. Regarding your main question Figure 2, it is not possible to get this figure by identifying steps with samples. It’s super important to plot the x-axis of the curve in FLOPs, or there is no compute-optimal frontier (i.e. each iteration has a cost which is d-dependent). So without choosing an algorithm which attains the regression bounds in the papers you list and assigning them a computational cost, the problem is not well-posed. Now if we are talking about ridge regression with $O(1)$ ridge, then we could assign a computational cost of ($n \\times d$), for example using conjugate gradient (CG) (up to log factors). One could also do this by considering vanishing ridge parameter, but then (since the condition numbers of these matrices grow like $d^{2\\alpha}$), the computational cost of computing using CG will increase to $n \\times d \\times (\\min\\{ d^{\\alpha}, \\sqrt{1/ridge}\\})$. Let’s suppose we continue with ridge parameter $O(1)$, which is morally comparable to one-pass SGD, in that they use the same amount of compute – it’s also comparable in the sense that a non-optimized algorithm like gradient descent on the ell2-regularized-least-square objective will be similar in complexity (and vanilla SGD is surely a non-optimized algorithm). In Phase Ia/II, the optimal ridge estimates in \[1\] (which agree with Rudi-Rosasco in Phase 1a but not in II) would indeed yield the same curves, treating computational complexity as $n \times d$ (with $n$ the number of samples and $d$ the dimension). In Phase Ia, you get the same loss curves as SGD with O(1) ridge regularization, and so you get the same compute-optimal frontiers for CG+O(1)-ridge as SGD. Incidentally, here you gain nothing by increasing the amount of ridge regularization. In Phase III, CG+O(1)-ridge performs better than SGD for small sample counts. However, if you run SGD to the stopping criteria for which it is compute optimal, it performs the same as CG+O(1)-ridge with the same choices of parameters/sample counts. Now, on the other hand, it could be (and should be) that using CG+O(1)-ridge there is a different compute-optimal frontier curve. We’re very happy to add the details (and some of the computations) of the comparison of SGD and ridge regression in an appendix, showing how these curves agree/do not agree. We will also improve the discussion surrounding how compute plays a role, and link it to kernel regression literature. \[1\] Defillips, Loureiro, Misiakiewicz. Dimension-free deterministic equivalents for random feature regression. arXiv: May, 2024 --- Rebuttal Comment 1.1: Title: (Response to reviewer questions) Comment: Response to Reviewer Questions: 1. *(Extension to multipass.)* Yes this is a super interesting question. We believe lots of the technology is in place, but there will also need to be a substantial mathematical effort, as the theory needs to be pushed. Regarding the Pillaud-Vivien et al. reference, they identify two phases: “easy”, “hard”. Hard is further divided into “improved” and “multipass optimal”. The phase boundary of easy/hard is $\beta \= 0$ (so all of phases Ia/II/III are easy). And if my reading of Pillaud-Vivien et al is correct, it should be anticipated that multipass SGD does nothing across the whole phase plane. On the other hand (if I understand correctly) \`\`easy’’ is made in comparison to the Rosasco-Rudi upper bound (showing SGD attains it), and this upper bound is not optimal for our problem. We have some simulations that suggest multipass SGD improves the sample complexity in Phases II/III. The paper \[2\] shows that it is possible to derive risk curves in the form of convolutional Volterra equations, much like we have here. \[2\] only proves them below the high-dimensional line ($2\\alpha \< 1$), but we expect that they generalize to the case $2\\alpha \> 1$ up to errors that should not affect the scaling laws (this is the case for the one-pass case). The random matrix theory requires an extension as well, as one needs to study Gram matrices built atop samples of the random vectors we use in the paper under review. This is another application of the Marchenko-Pastur map and so it requires another analysis. It could introduce additional technical complexities and/or qualitative phenomena which need to be handled, but the path is certainly clear. 2. *(Sample size complexity of Caponnetto and de Vito)* No, the rates do not match minimax optimal rates (over problems classes with ‘source/capacity’ conditions). The minimax optimal rates are $n^{-\\frac{2\\alpha+2\\beta-1}{2\\alpha+2\\beta}}$ for $r \\leq 1$ (which can be attained with small stepsize one-pass SGD by Dieuleveut and Bach; this is also used as a baseline by Pillaud-Vivien et al.). In comparison the rates here are given by (Phases Ia/II) are $n^{-\\frac{2\\alpha+2\\beta-1}{2\\alpha}}$ in the $F\_{pp}$-dominated part of the loss curve. This is no contradiction – we are studying a single problem with the source/capacity class, for which the performance can be better. We further use a stepsize which is much larger than what is used in Dieuleveut-Bach. See Table 2 & 3 in the attached pdf “All Reviewers” comment. 3. *(What are the technical challenges)* There are three components of the proof, broadly. * The first is establishing a convolutional Volterra representation of the expected risk of the Gaussian streaming SGD. This uses Gaussianity and is a relatively simple computation, but to our knowledge is new; previous Volterra equation analyses of SGD were done for non-Gaussian problems but required $2\\alpha \< 1$. This is also relatively simple, and we do not really view this as a major contribution. * The second component is an approximation of the solution of the convolutional Volterra equation in which we keep 1 convolutional power of the bias and variance terms – similar approximations have been developed in the branching process literature and are expected in power-law risk curves. This part is probably not new, but the precise formulation we needed was not readily available, so we proved the relevant approximations (pointing to related work). * The third part is the analysis of the self-consistent equation for the PLRF resolvent. This part, to our knowledge, is absolutely new (if the referees know otherwise, please let us know). This is also the vast majority of the technical challenges, in part because the PLRF spectrum exhibits a transition at $d^{-\\alpha}$ (from absolutely continuous to pure point) and in part because we need to know the spectrum at all scales to get the whole loss curve. This part represents the largest component of the technical challenges. 4. *(Proportional v/d).* For the regime $2\\alpha \> 1$, it’s not important for $v/d$ to be linear, and indeed $v=\\infty$ works fine, consistent with all the kernel literature. For $2\\alpha \< 1$, $v=\\infty$ is actually meaningless, and in fact there is a transition that occurs when $v \\gg d^{1/(2\\alpha)}$ (the whole problem setup becomes trivial as the target becomes orthogonal to the span of the model). So for simplicity we fixed a scaling of how $v$ grows with $d$. With a more sophisticated analysis, one could change the problem setup, releasing $v$ to the meta-optimizer and then optimizing over $d$ with respect to $v$. It would be very interesting if it turns out that $d^\* \\ll v$. \[2\] C. Paquette, E. Paquette, B. Adlam, J. Pennington. Homogenization of SGD in high-dimensions: exact dynamics and generalization properties. arXiv 2022	Rebuttal 1: Rebuttal: We thank the reviewers for all the constructive comments and suggestions for comparison. All the reviewers requested additional discussion of related work. We will do the following. 1. Expand our discussion of related work and background in the main text and add a section in the Appendix. A draft of some of these additions is visible here on OpenReview. See the “Official Comment” below. 2. Add an appendix with quantitative comparisons of the risk curves we derive and related risk curves from the random features literature (Table 2/3 in attached pdf), including a table bridging the notation (Table 1 attached in pdf). We have responded to each of you with a discussion of the points that you have raised. Novelty/Comparison to existing work. * We emphasize that the motivation of the work is not kernel/random features regression, but rather explaining compute scaling laws. This is why we consider the full $\\alpha, \\beta$-plane. * When this work is compared to sample-complexity bounds, it is important to also remember that the estimator has an algorithmic cost. This algorithmic compute cost is what we are capturing in this work. Some works on sample-complexity are not explicit about their algorithm and so some additional work is needed to produce compute scaling laws. In response to Reviewer ahLt, we have done this comparison for ridge regression. We plan to add an appendix containing these comparisons. See attached pdf * While it may not be true in general, for this work the compute scaling laws happen to be corollaries of precise risk curves as a function of samples. Many of our risk curves are new; they cannot be derived from existing estimates on SGD. We discuss these in the response to Reviewer ahLt (in re Caponetto et al.), the improved works-cited (see new Related Work section in 'Official Comment to All Reviewers' below), and included a table of comparisons in the PDF. * From a mathematical point of view, this paper also contains new random matrix theory: we analyze the (long-established) self-consistent equations for the resolvent of the power-law-random-features covariance matrix. This has to be done for spectral parameters (the argument of the resolvent) all throughout the spectrum; in contrast, ridge regression requires negative spectral parameters, and this leads to different challenges. (See also discussion to Reviewer 9ixz) We will add an additional "Official Comment" with the new proposed related work section. Pdf: /pdf/357f14773fbfdcf1e263a58a440acafef898076b.pdf	NeurIPS_2024_submissions_huggingface	2,024	Summary: This paper studied a solvable neural scaling law model (the power-law random features, PLRF) that involve three parameters (data complexity: $\alpha$, target complexity: $\beta$ and the number of parameters: $d$). The PLRF model here is trained by applying the stochastic gradient descent (SGD) algorithm to the mean-squared loss. For different choices of the parameters $\alpha$ and $\beta$, the optimal number of parameters $d$ is solved by minimizing the expected loss. A corresponding phase diagram is drawn with respect to $(\alpha,\beta)$. An extensive set of numerical experiments is also conducted to justify the main theoretical results. Strengths: 1. This is a technically solid paper with rigorous mathematical proof. For each of the transition boundaries in the phase diagram, an intuitive explanation is provided to help the readers understand the key idea behind. 2. An extensive set of numerical experiments are included to justify the theoretical results. Weaknesses: One possible drawback of the current version of this paper is that the list of references is incomplete. It seems to the reviewer that the discussion on related work is incomplete and ignores many recent and concurrent work on the theoretical aspects of neural scaling law. See for instance [1,2]. Technical Quality: 3 Clarity: 3 Questions for Authors: Overall, the reviewer enjoyed reading both the proof and the experiments presented in the paper a lot. One possible broad question that the reviewer is interested in is how the theoretical results presented here can be linked to previous work on the learning of timescales in two-layer neural networks [3] (In general, the key question is also to address which features get learned at which stage). Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: It seems that the authors didn't perform experiments on large-scale language models (LLMs). One possible way to make the work more impactful is to do some empirical investigation on LLMs to see if certain parts of the theoretical results still hold when the model complexity drastically increases. References: [1] Jain, A., Montanari, A., & Sasoglu, E. (2024). Scaling laws for learning with real and surrogate data. arXiv preprint arXiv:2402.04376. [2] Lin, L., Wu, J., Kakade, S. M., Bartlett, P. L., & Lee, J. D. (2024). Scaling Laws in Linear Regression: Compute, Parameters, and Data. arXiv preprint arXiv:2406.08466. [3] Berthier, R., Montanari, A., & Zhou, K. (2023). Learning time-scales in two-layers neural networks. arXiv preprint arXiv:2303.00055. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for their report, for their comments on directions of improvement, and for the questions. Response to weakness: Yes we agree, the comparison to existing work should be expanded. We will include a more detailed discussion of existing work and how it compares (see comments to all reviewers). The suggestions for references are helpful – thank you – and we have made an attempt to integrate them (see the proposed related works section). We’re happy to have feedback if you believe the works considered are still inappropriate. We provided a comparison with the concurrent work \[2\] (see Table attached in pdf) which was released after NeurIPS submission. Response to question (2-layer Neural Network): With regards to the question, the reference \[3\] is very interesting. It is the first time this author is reading it, but it’s very close to my interests and I will dig back into it after NeurIPS. In \[3\], if one takes the single-index model to have a suitable decay rate of its Hermite expansion (which I believe is power-law decay of its Hermite coefficients), the gradient flow loss curve would have power-law decay. That seems like it should open the door to an analysis of one-pass SGD that exhibits similar phenomenology to what we’ve done. I’m not bold enough to speculate how similar it would be to what we’ve done, because I don’t have a good picture of what the SGD-noise looks like in this setup. If the SGD noise behaves similarly to the quadratic problem we study, then it could fit naturally as a line through our phase diagram parameterized by the exponent $\\beta$ (which would come from the decay rate of the target function). That would be a beautiful theorem\! \[2\] Lin, L., Wu, J., Kakade, S. M., Bartlett, P.L., & Lee, J.D. (2024) Scaling laws for learning with real and surrogate data. arXiv preprint arXiv:2402.04376. \[3\] Berthier, R., Montanari, A., & Zhou, K. (2023) Learning time-scales in two-layers neural networks. arXiv preprint arXiv:2303.00055. Response to limitation: A deeper empirical investigation of LLMs would also interest this author, who hopes it can be done. This is certainly a limitation; also estimating the alpha (and worse) estimating beta are serious obstructions in using the results of this paper quantitatively to do optimal model-parameter decision making. However, as a matter of better understanding the training and optimization of LLMS, we agree this is an important direction of investigation. --- Rebuttal Comment 1.1: Title: Response to authors' rebuttal Comment: Dear authors, Thank you so much for your response, which have addressed my questions. Just as pointed out by the other reviewers, the theoretical results are pretty interesting, but please include a separate section to compare the result and proof techniques presented in your paper with the missing references listed in your global response above. Also, it would be a good idea to include what you wrote in your rebuttal as part of the future work as well. Best regards, Reviewer HQ3F	null	null	null	null	null	null
Evaluating the World Model Implicit in a Generative Model	Accept (spotlight)	Summary: This paper aims to develop new metrics for assessing a model’s ability to recover a world model. The key idea is to test coherence with respect to the world, guided by the Myhill-Nerode theorem for deterministic finite automata (DFA). Specifically, if the true world model is a DFA, the learned world model should meet two requirements: (1) sequences leading to the same DFA state must have the same continuations, and (2) sequences leading to distinct DFA states should have distinct continuations. Based on these principles, the authors proposed three new metrics: compression precision, distinction precision, and distinction recall. To test these metrics, they trained a GPT model on New York City taxi rides, hoping the GPT would learn a map of NYC. They found that the trained transformer model performed nearly perfectly using classical methods for testing world models, such as next-token prediction and state probe. However, under their three proposed metrics, the trained model appeared not to learn the world model at all, suggesting that these new metrics might be a valuable alternative for evaluation. Strengths: This work is well-motivated and well-written. The proposed metrics are interesting, and the authors have supplemented the study with detailed ablation studies on the training data, which is commendable. Weaknesses: 1. Generalizability of the proposed metrics The main concern I have with the proposed metrics is their generalizability. The metrics are strictly applicable when the true world model is a DFA. While this might be suitable for the New York City map and the Othello game, it is not directly applicable to Logic Puzzles. The issue is that Logic Puzzles are prompted using natural language (see Fig. 22), and natural language texts cannot be accurately modeled as DFAs. Although one could argue that the same state is reached via different prompts at the latent concept level, language models do not operate directly on this latent concept space. Instead, they work on the token level, which cannot be represented as a DFA. This limitation significantly restricts the scenarios in which the proposed metrics can be applied. In contrast, the two existing metrics (next-token prediction and state probe) are applicable regardless of the true world model. This fundamental limitation could impact the overall significance and applicability of the study. 2. Inter-metric consistency problem Despite the limitations of the proposed metrics, they would still be valuable if they performed well under the DFA assumption in indicating world model recovery. However, there is a lack of inter-metric consistency. In Table 1 (Random Walks row), almost all metrics, except for the proposed Compression Precision metric, indicate that the model perfectly captures the world model. This inconsistency raises questions: What is the correct conclusion when two out of three metrics suggest the presence of a world model, while the other does not? How can these metrics be relied upon if there are substantial internal inconsistencies based on the statistics motivated by the Myhill-Nerode theorem? Resolving this issue in practice may be challenging. It appears that the three proposed metrics have low false negatives (i.e., they perform well when the model does not learn the true world model, similar to existing metrics). However, they seem to have high false positives (i.e., the statistics struggle to detect if a model has actually learned the world model). Resolving this issue may be difficult because it likely requires substantial knowledge of the true world model to develop the appropriate statistical corrections for sampling two sequences that reach the same DFA state. Technical Quality: 3 Clarity: 3 Questions for Authors: What was the context length for your GPT model? This is crucial, as a context length that is too short for the type of data presented to the model will negatively impact its performance. Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: The main text lacks an explicit section on Limitations and Future Research. However, the authors acknowledged in the Conclusion that their primary limitation was the focus on deterministic finite automata. Minor comments: Line 76: “our evaluation metrics are based sequences” —> “our evaluation metrics are based [on] sequences” Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your insightful review. We're glad you found our proposed metrics interesting and ablation studies compelling. We appreciate your comments on the clarity of our paper. > _Inter-metric consistency problem... What is the correct conclusion when two out of three metrics suggest the presence of a world model, while the other does not?_ You raise a great question. If a model has the true world model, all metrics will score 100%. Conversely, if any metric is less than 100%, it won't have a perfect world model. As you note, once the metrics aren't perfect, some can be worse than others. This is similar to supervised learning: AUC, accuracy, F1, etc. are all the same when we have a perfect classifier. It's only when we have an imperfect model that these metrics reach different conclusions. This is why having multiple metrics is important: they tell you where a model is failing. For example, Table 1 shows that while the random walks model is able to differentiate between states, this comes at the expense of failing to capture that the same state can be reached by different sequences. There is a tradeoff between metrics: it's easy to ace compression (by saying every sequence has the same continuations) but then distinction suffers. > _It appears that the three proposed metrics have low false negatives [and]... high false positives_ This fantastic comment helped us clarify the discernment properties of our proposed metrics. A model with the true world model will not fail when detours are introduced to sequences. In our original submission, we used detours to validate our metrics on the navigation exercise; detour performance correlated with our metrics (Table 2). We perform the same exercise below to validate our metrics' discernment of Othello models: Existing metrics imply that both OthelloGPT models from [1] ("Championship" and "Synthetic") are close to having the true world model. Our metrics reveal a more complex picture: while Synthetic recovers the true world model, Championship fails by our metrics. Crucially, we can validate this discernment with an additional "detour" exercise: with probability p, we replace a model's top predicted move with another valid move and assess whether it completes the game validly. While the Synthetic model produces near-perfect games regardless of detours, the Championship model fails immediately. A model that recovers the true world model will succeed regardless of detours. There is a clear distinction between Championship and Synthetic models, but this is only captured by our metrics; existing metrics would lead us to conclude that both have world models. Random detours \|Model\|0%\|1%\|10%\|25%\|50%\| \|-\|-\|-\|-\|-\|-\| \|Championship\|1.00 (0.00)\|0.66 (0.05)\|0.05 (0.02)\|0.01 (0.01)\|0.01 (0.01)\| \|Synthetic\|1.00 (0.00)\|0.99 (0.01)\|0.97 (0.02)\|0.97 (0.02)\|0.99 (0.01)\| Adversarial detours \|Model\|0%\|1%\|10%\|25%\|50%\| \|-\|-\|-\|-\|-\|-\| \|Championship\|1.00 (0.00)\|0.70 (0.05)\|0.01 (0.01)\|0.01 (0.01)\|0.00 (0.00)\| \|Synthetic\|1.00 (0.00)\|0.98 (0.01)\|0.99 (0.01)\|0.96 (0.02)\|0.97 (0.02)\| > _The main concern I have with the proposed metrics is their generalizability. The metrics are strictly applicable when the true world model is a DFA. While this might be suitable for the New York City map and the Othello game, it is not directly applicable to Logic Puzzles_ You bring up an important point to clarify on logic puzzles. Constant-sized logic puzzles are canonical examples of DFAs [2]. Because each puzzle corresponds to a true state, we can assess the different ways state is reflected by a model; this is why [3] use logic puzzles to probe a model's representations for state, and it's why we can study token-level outcomes to assess whether a model's behavior is consistent with state. While it may seem like the model is performing badly on our test because we're translating logic into natural language that can confuse LLMs, the input space of possible sequences is relatively simple (21 possible statements). LLMs perform poorly on our metrics despite this simplicity. We agree that adding richer language would create more realism; still if a model performs poorly with the simple language, it's informative for their understanding of more complex problems. Generally, we focus on DFAs because they're common in real-world phenomena: we focus on game-playing, logic, and navigation, and they also arise in search engines, control systems, and genetics [3]. Papers that study world model recovery have also focused on DFAs, even if they don't explicitly mention it [4, 5, 6]. DFAs are also important to study as testbed problems: What can we say about an LLM’s world model if it can’t recover a map? Finally, the requirements for our evaluation metrics fall in line with existing metrics in this literature: sampling from a model, seeing its predictions, and comparing them to the set of allowed predictions. These are the same requirements as the next-token test, and are similar to the probe test, which additionally requires access to a model's internal representations. > _What was the context length for your GPT model?_ The maximum navigation length during training was 100 tokens so we used a context length of 100. Across all tests, we were careful to only evaluate models using the context length they were trained on, e.g. when we sample sequences for navigating from A to B we made sure there was a valid route with at most 100 moves (see lines 299-300 and 508-510). We did the same thing for Othello (which was trained on up to 60 tokens since games have <=60 moves). Thanks again for your review. If we've addressed your comments, we hope you'd consider raising your score. [1] https://arxiv.org/abs/2210.13382 [2] https://link.springer.com/chapter/10.1007/978-3-642-59126-6_7 [3] https://www.cs.ucdavis.edu/~rogaway/classes/120/spring13/eric-dfa.pdf [4] https://arxiv.org/abs/2106.00737 [5] https://arxiv.org/abs/2210.13382 [6] https://arxiv.org/abs/2102.13249 --- Rebuttal Comment 1.1: Comment: Thank you for the rebuttal. While some of my concerns were addressed, I remain concerned about the applicability of the developed metric. It appears that this metric is effective primarily when the true world model has been fully learned. In cases where the world model is imperfectly learned, the metric may not be reliable, as it does not provide directly comparable scores among imperfect models. Although achieving 100% on all metrics indicates that the true DFA has been learned, scores below 100% only confirm that the model is imperfect, without offering a clear measure of the degree of imperfection. --- Reply to Comment 1.1.1: Comment: Thank you for engaging with our paper. We're glad our rebuttal addressed some of your concerns. Here we attempt to answer your remaining questions: - We want to clarify a potential confusion: while it's correct that any metric less than 100% implies there is no world model, the metrics can also be directly compared to one another. This is again similar to supervised learning: while there's a tradeoff between false positive rate and false negative rate, if one model always has a better false positive rate and false negative rate, it is doing better than another model, even if it's imperfect. Our metrics are not arbitrary scores; they are grounded in a theoretically-based formulation of what it means to learn the structure of a world model. We also validate this empirically: for each model (across maps and Othello), a model's ranking on our metric is exactly its ranking on the detours exercise (for all three metrics and both kinds of detour exercises). - Our results would still be interesting even if our metrics only captured whether there is a world model or not. This is because prior metrics would lead us to conclude that all models we test across maps and Othello do have world models. Our metrics are capturing something new, and this is not only motivated theoretically but also validated empirically on 1) map reconstruction and 2) detour exercises on Othello and maps.	Summary: This paper proposes a new metric to assess the implicit world model of generative models, such as neural LMs. Inspired by the Myhill-Nerode theorem, this metric evaluates whether a model can determine if pairs of sequences are equivalent in terms of their underlying state. The author presents two specific metrics: sequence compression (SC) and sequence distinction (SD). For a pair of sequences (e.g., natural text, destination trajectories, or game scripts) that correspond to the same state, SC measures whether neural LMs accept the same set of continuations. Conversely, SD assesses whether neural LMs can accurately distinguish between sets of continuations that are uniquely permissible for one sequence but not for the other. The paper assumes that the model under test is a Deterministic Finite Automaton (DFA), and hence the model can directly determine whether a sequence is accepted. However, since neural LMs lack this capability, the author suggests using a token-level threshold as a proxy: $\forall t P_\theta(x_t\|x_{1:t-1})> \epsilon$. Experiments conducted across three datasets with various neural LMs (small-scale Transformers & LLMs) indicate that these models score significantly lower on SC&SD compared to existing metrics. Based on these findings, the authors claims that SC&SD are more faithful. Strengths: 1. This work proposes a new metric that measures the coherence of the implicit world model of neural LMs, which is novel perspective in this field. 2. The paper is overall well-written and easy to follow. 3. The authors conduct extensive evaluation on a wide range of base models (LLMs & Transformers) and three datasets, and the results are consistent. Weaknesses: 1. The authors inaccurately summarize existing work and consequently address a non-existent flaw. >... Toshniwal et al. and Li et al. assess world models by measuring the percent of top model predictions that are valid in the underlying DFA. (L112-113) This is not true. Li et al. [1] do not solely rely on the validity of the top model predictions to assess the implicit world model. Instead, they directly probe the internal world state from the model, which has been the common practice of existing work ([2], [3]). 2. There are two fundamental flaws of the proposed metric * accountability issue: Poor performance according to the metric could stem from an bad transformation of actions from the world state, rather than a bad implicit world model. * It's challenging to ascertain whether a neural LM "accepts" a sequence, which makes it hard for the theoretical guarantees of SC and SD hold in practice. The proposed metric relies heavily on the deterministic nature of the DFA, which directly indicates sentence acceptance. In contrast, neural LMs model distributions over tokens or sentences without a clear mechanism for determining sentence acceptance. The author proposes using a token-level probability threshold as a workaround, yet this approach has several flaws: * A top-$k$ predicted sequence may include tokens with low likelihood. * Conversely, a sequence satisfying the criteria might not appear in the top-$k$ predictions. * Additional confounding variables can affect the metric's value. For example, LMs with higher entropy typically have a larger set of "accepted" sequences. This entropy can be influenced by the hyperparameters of decoding algorithms, training, and fine-tuning methods of the LMs, etc. 3. Lack of empirical evidence that proves the faithfulness of the proposed metric. * Considering the loose approximation of the DFA-style acceptance, I expect the author to provide empirical justification of the proposed metric, which is notably missing in the paper. The only evidence presented is the poor performance of existing LLMs on this metric. However, this is insufficient since the lower performance on the metric could be simply because the methods are unfairly penalized. * Also, there is a concerning indication of the metric's questionable faithfulness: the conclusions drawn from the Othello experiments in this paper contradict those of Li et al. [1]. Li et al. convincingly probes Transformer's internal representation of the board state and demonstrates that it can causally influence the Transformers' predictions. [1] Li, Kenneth, et al. "Emergent world representations: Exploring a sequence model trained on a synthetic task." ICLR 2022. [2] Yun, Tian, et al. "Emergence of Abstract State Representations in Embodied Sequence Modeling." Proceedings of the 2023 Conference on Empirical Methods in Natural Language Processing. 2023. [3] Karvonen, Adam. "Emergent world models and latent variable estimation in chess-playing language models." arXiv preprint arXiv:2403.15498 (2024). Technical Quality: 2 Clarity: 3 Questions for Authors: 1. Did you try other acceptance criteria that go beyonds manipulation of threshold value, e.g. sequence-level probability/rank? Confidence: 5 Soundness: 2 Presentation: 3 Contribution: 2 Limitations: The author doesn't address the limitations discussed above in the paper. Flag For Ethics Review: ['No ethics review needed.'] Rating: 3 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your review. Your review makes several helpful points that will improve our paper. However our rebuttal clarifies a couple of important points of your review: one involving an incorrect statement of what is in our paper (we do describe and empirically test probes), and another is a clarification of the value of having multiple metrics. We'll make these more clear in our revision. > _The authors inaccurately summarize existing work... Li et al. [1] do not solely rely on the validity of the top model predictions_ Your review states that we ignore the probe test of Li et. al [1]. We agree probes are important and this paper would be incomplete without them. However, we not only describe the state probe in the Li et al. paper and the larger literature in the related work section (lines 74-78) but also perform probing experiments for our maps setting (Table 1 and lines 240-242). We agree that the sentence you point out could do more to foreshadow these results/discussion, so we'll update it in the revision and cite the two additional papers you mention. > _The conclusions drawn from the Othello experiments in this paper contradict those of Li et al._ Our tests measure different outcomes than Li et al [1]. If a model's world model is perfect, all metrics will score 100%. Conversely, if any metric is less than 100%, it won't have a world model. This is similar to supervised learning: AUC, accuracy, F1, etc. are all the same for perfect classifiers. But having multiple metrics tells us _how_ an imperfect model is failing. We validated our metrics in the original submission by showing 1) they capture behavior other metrics don't and 2) they correlate with detour performance for the taxi exercise (Table 2). We now include additional validation for Othello using detours. Results from [1] imply that both OthelloGPT models ("Championship" and "Synthetic") are close to having true world models. Our metrics reveal a more complex picture: while Synthetic recovers the true world model, Championship fails by our metrics. Crucially, we can validate this differentiation. We do this with an additional "detour" exercise: with probability p, we replace a model's top predicted move with another valid move and assess whether it completes the game validly. While the Synthetic model produces near-perfect games regardless of detours, the Championship model fails immediately. There is a clear distinction between Championship and Synthetic models, but this is only captured by our metrics; existing metrics would lead us to conclude that both have world models. Random detours \|Model\|0%\|1%\|10%\|25%\|50%\| \|-\|-\|-\|-\|-\|-\| \|Championship\|1.00\|0.66\|0.05\|0.01\|0.01\| \|Synthetic\|1.00\|0.99\|0.97\|0.97\|0.99\| See the PDF for similar results on adversarial detours. > _Poor performance according to the metric could stem from an bad transformation of actions from the world state, rather than a bad implicit world model._ Our metrics test a model's outputs while probes test a model's internal state. Both metrics are important because they measure different things: our metrics find inconsistencies not revealed by probes (see Tables 1, 2, 6, and the Othello detours above). Further, the reliability of probes is far from settled. Ongoing debate [2] includes issues like proper baselines [3, 4], classifier complexity [5, 6], and faithfulness [7, 8]. Even for OthelloGPT, probes are sensitive to specification: linear and nonlinear probes have very different error rates [1], and different encodings reach different conclusions [9]. Moreover, should probe labels reflect each tile individually (as [1] considers) or the full board (all 64 tiles)? The championship Othello probe has 91% accuracy for each tile individually [1], but accuracy falls to 0.2% when the label is the full board. We think probes are valuable tools, but they don't yet provide conclusive results given these open questions. > _Neural LMs model distributions over tokens or sentences without a clear mechanism for determining sentence acceptance._ We agree that focusing on a single threshold alone provides an incomplete picture. This is why we include ablations across multiple thresholds (Table 3). All thresholds result in incorrect world models. Common decoding strategies _do_ provide mechanisms for determining sequence acceptance, like top-k, top-p, and threshold-based sampling (i.e. epsilon sampling) [10, 11, 12]. While our paper focuses on epsilon sampling [12], different choices can easily be made within our framework. Below we include additional results for top-p and top-k sampling (more ablations in the PDF), which are very similar to the original results. The paper will be stronger thanks to your suggestion to add these. Top-p (p=0.99) \|Model\|Compression precision\|Distinction precision\|Distinction recall\| \|-\|-\|-\|-\| \|Shortest paths\|0.22\|0.39\|0.21\| \|Noisy shortest paths\|0.03\|0.39\|0.24\| \|Random walks\|0.54\|1.00\|1.00\| Top-k (k=2) \|Model\|Compression precision\|Distinction precision\|Distinction recall\| \|-\|-\|-\|-\| \|Shortest paths\|0.21\|0.32\|0.17\| \|Noisy shortest paths\|0.07\|0.31\|0.23\| \|Random walks\|0.21\|0.93\|0.73\| Thanks again for your review. We think these edits will make the paper stronger. If we have addressed your comments, we hope you'd consider raising your score. [1] https://arxiv.org/abs/2210.13382 [2] https://arxiv.org/abs/2102.12452 [3] https://arxiv.org/abs/1805.01070 [4] https://arxiv.org/abs/2004.03061 [5] https://arxiv.org/abs/1610.01644 [6] https://arxiv.org/abs/2104.03514 [7] https://arxiv.org/abs/1812.08951 [8] https://arxiv.org/abs/2004.14975 [9] https://arxiv.org/abs/2309.00941 [10] https://arxiv.org/abs/1904.09751 [11] https://arxiv.org/abs/1805.04833 [12] https://arxiv.org/abs/2210.15191 --- Rebuttal 2: Comment: Thank you for your rebuttal and the updated results. My responses are below. ## Summary of existing work ``` Your review states that we ignore the probe test of Li et. al [1]. ``` No, it doesn't. My criticism that "The authors inaccurately summarize existing work and consequently address a non-existent flaw" is directly related to the specific statement I referenced from your manuscript: "Toshniwal et al. and Li et al. assess world models by measuring…". Given that your proposed metrics are motivated by the shortcomings of existing work, it is essential to faithfully represent those work and to identify actual, rather than imagined, flaws. Nonetheless, I consider this to be a relatively minor issue, one that can be addressed through some clarification, particularly when weighed against the validity of the proposed metrics. ## Validity of the metrics ``` We validated our metrics in the original submission by showing 1) they capture behavior other metrics don't and 2) they correlate with detour performance for the taxi exercise (Table 2). We now include additional validation for Othello using detours. ``` It's good to have multiple metrics, but it's also crucial that each one holds validity. I find it somewhat unclear how detour performance serves as a valid indicator in this context. Specifically, how can we be certain that the performance is solely influenced by the world model? For instance, could you clarify why $\text{Synthetic}$ appears to possess a near-perfect world model, whereas $\text{Championship}$ doesn't? To me, it's a typical phenomenon of exposure bias rather than a specific issue of implicit world model. $\text{Championship}$ is trained on expert data, where the prefix trajectories fall within a rather limited distribution. In contrast, $\text{Synthetic}$ is trained on randomly generated legal trajectories, which are distributed more evenly. As a result, the disparity between training and testing is significantly smaller for $\text{Synthetic}$ than for $\text{Championship}$. ``` Common decoding strategies do provide mechanisms for determining sequence acceptance, like top-k, top-p, and threshold-based sampling (i.e. epsilon sampling) ``` I respectfully disagree. It seems there might be some conflation of concepts here. DFA are designed to accept or reject sequences through checking transition rules. In contrast, auto-regressive generative models don't have such mechanisms. All they have are token-level distributions and they are not trained to accept all "legal" sequences. Although it's possible to implement post-processing functions to pull an acceptance label out of it, such functions can influence metric scores, potentially weakening the soundness of the evaluation. Particularly, it's well known that the commonly used sampling-based decoding methods, e.g. top-p sampling, tend to select sequences that diverge significantly from the generative models' modes. I'm looking at Table 2 (top-k sampling) in the new pdf. With k=1, the scores for $\text{Random walks}$ are 0.40, 0.69, and 0.30, respectively. However, when k=4, these values rise to 0.64, 0.98, and 0.51. The disparity is quite pronounced to me. When it comes to Table 3 (top-p sampling), the compression precision for $\text{Random walks}$ is 0.16 when p=0.9 but 0.73 when p=0.99. The results somehow confirm my concerns. --- Rebuttal Comment 2.1: Comment: Thank you for engaging with our paper. See our responses below. > _Summary of existing work_ Thank you for clarifying your initial comment: _“Li et al. [1] do not solely rely on the validity of the top model predictions to assess the implicit world model. Instead, they directly probe the internal world state from the model, which has been the common practice of existing work ([2], [3]).”_ We're glad it's clear that our paper not only describes the probe test of Li et al. [1] but also devotes empirical work to it. > _I find it somewhat unclear how detour performance serves as a valid indicator in this context. Specifically, how can we be certain that the performance is solely influenced by the world model?_ This is a good question. We'd like to clarify a potential confusion about our paper: our metrics assess whether a model has a world model by assessing the _outputs_ of the model. In contrast, tests like the probe test do not test world models via their outputs, only their mechanisms (e.g. whether a representation encodes state and/or how a model uses this representation). This is why we and Li et al [1] include both kinds of metrics. The detours exercise assesses the outputs of a model. A model whose output is consistent with the true world model will perform well on detours; the detours exercise passes valid inputs to the model and sees if it can complete them successfully. In practice, we find that the detours exercise amplifies world model errors. The Championship Othello accuracy falls to 1% when detours are common, behavior that is not consistent with a model with the true world model. Our hypothesis as to why the Championship Othello doesn't have the correct world model is similar to your intuition -- that the way it's trained prevents it from differentiating between invalid moves and very bad moves. But our paper is focused on measuring whether a model behaves like the true world model rather than the reason as to why or why not. > _DFA are designed to accept or reject sequences through checking transition rules. In contrast, auto-regressive generative models don't have such mechanisms._ Our metrics test whether a model's behavior obeys ground-truth rules. To implement these metrics, we need to define what it means for a model to accept or reject a sequence. This isn't unique to our setting; one way that Li et al [1] and Toshniwal et al. [2] test world models is by looking at whether the top-ranked prediction of a model is legal. Of course, a model generates more than one top-ranked token, and our different metrics and ablations provide different specifications. The results you point out are not contradictory. If a model has the true world model, all metrics (compression precision and distinction precision/recall) will score 100%. Conversely, if any metric is less than 100%, it won't have a perfect world model. As you note, once the metrics aren't perfect, their performance can differ and vary with a threshold parameter. To give a simple example: it's easy to ace compression (by saying every sequence has the same continuations) but then distinction suffers. This is similar to supervised learning: sensitivity and recall are all the same for a perfect classifier, but can differ for imperfect models in ways that vary with a thresholding parameter. The dependence on a thresholding parameter is not a weakness; it's crucial for decomposing error into precision and recall and measuring AUC. And our results across thresholding parameters and sampling mechanisms point to the same final conclusions. Thanks again for engaging with our paper. We'll update the paper in the revision to make these points more clear. [1] https://arxiv.org/abs/2210.13382 [2] https://arxiv.org/abs/2102.13249 --- Rebuttal 3: Comment: Thank you for your follow-up response. It helped me sort out some disagreements between us. I believe the root cause is this: "our metrics assess whether a model has a world model by assessing the outputs of the model. " While you state that you're evaluating the "implicit world model" of generative models, it seems to me that the outputs—and therefore the metrics—are influenced by various factors (such as the entropy of the learned distribution, decoding hyper-parameters, and algorithms) beyond just the implicit world model. ``` The detours exercise assesses the outputs of a model. A model whose output is consistent with the true world model will perform well on detours ``` I agree. But I'm not sure the model performs poorly on detours/proposed metrics if and only if it's inconsistent with the true world model. Even if there is some inconsistency, it might be exaggerated—or maybe even minimized; I'm not sure. The new results you presented earlier clearly confirm this concern. ``` And our results across thresholding parameters and sampling mechanisms point to the same final conclusions. ``` To be frank, I'm not sure I fully understand your point. If you're suggesting that the relative ranking of Random-walks > Shortest-paths > Noisy-shortest-paths is consistent across different decoding methods/hyperparameters, that's accurate. However, since you're proposing evaluation metrics, they should be applicable to more realistic models, not just those trained artificially. What happens if two models are trained on the same dataset, and their performance gap is much smaller? How can we ensure their relative ranking will still hold? This level of hyperparameter sensitivity raises concerns about the reliability of these metrics. On a related note, I have another question: why does Shortest-paths outperform Noisy-shortest-paths? If I understood correctly, Noisy-shortest-paths should involve more random exploration during training compared to Shortest-paths. ``` Our hypothesis as to why the Championship Othello doesn't have the correct world model is similar to your intuition -- that the way it's trained prevents it from differentiating between invalid moves and very bad moves ``` Indeed the gap between Championship and Othello in terms of differentiating between invalid moves and very bad moves are captured by the probe tests in Li et al. (2022). As shown in their Table 2, the error rate with Synthetic is significantly lower than with Championship. ``` To implement these metrics, we need to define what it means for a model to accept or reject a sequence. This isn't unique to our setting; one way that Li et al [1] and Toshniwal et al. [2] test world models is by looking at whether the top-ranked prediction of a model is legal. ``` Your setting is indeed unique. Sequence generation models are typically trained to maximize the probability of ground-truth sequences, making the selection of the top-ranked prediction—essentially MAP estimation—consistent with their training. While it's possible to use heuristics to sample multiple sequences from the distribution and argue that these sequences are "accepted" by the distribution (though what it means for a sample to be "accepted" by a distribution is unclear to me), this approach of inference differs from how the models are trained. This inconsistency arises due to the evaluation method, so it's questionable to blame the models if they don't perform well under these conditions. Moreover, if the top-1 prediction is typically used for reasoning tasks that rely on underlying world models, why should we be concerned with the consistency of top-$k$ predictions? ``` The dependence on a thresholding parameter is not a weakness; it's crucial for decomposing error into precision and recall and measuring AUC. ``` I'm not quite sure how those decoding hyperparameters function similarly to a classification threshold. With classification thresholds, it's easy to predict how adjusting them will affect precision and recall, making it a useful tool for balancing the precision-recall tradeoff. But when it comes to those hyperparameters and decoding algorithms, how exactly do they influence the metric values? For example, why does top-p decoding (p=0.999) result in a higher metric value for Random-walks compared to top-k decoding (k=4), yet performs worse for Shortest-path? --- Rebuttal 4: Comment: Thanks for continuing to engage with our paper. We appreciate your feedback and will clarify our paper. > _I believe the root cause is this: "our metrics assess whether a model has a world model by assessing the outputs of the model."_ We think a helpful comparison for our metrics is the next-token test performed by Li et al [1] and Toshniwal et al. [2]. Like our metrics, this test seeks to evaluate world models by the _behavior of their outputs_. Once we've established that a model behaves like it has the true world model, we can ask questions about the mechanism for why it behaves like that (e.g. via probing). For example, only after showing that OthelloGPT performs well on the next-token test do Li et al. [1] perform probing tests. The goal of our metrics is to test whether a model, when using common decoding schemes (we evaluate three different schemes), behaves like it has the true world model. For both our metrics and the next-token test, if a model's generations are influenced by factors like entropy, it would show up when practitioners decode from the model, and is therefore crucial for incorporating into metrics that assess world model behavior. At a high level, we believe that metrics which evaluate a model in a black-box manner, just based on observing their generative behavior, are vitally important and qualitatively distinct from those which rely on a certain implementation and/or internal parameters (we agree these are also useful). Several of the benefits of black-box metrics are the following - They directly measure the quality of the actual thing we care about: the sequences generated by the model. - They can be applied to any language generator, regardless of implementation. This also means that humans can be evaluated by the same measurements to get a baseline to compare models against. - They provide a definition of what it means to have recovered a world model which is generic. We believe that the question “does a language model have an implicit world model?” can and should be evaluated by metrics that look only at the outputs of the model. Prior works [1, 2] introduced the ingenious idea of testing this question on rules-based systems (i.e. games and other types of DFAs) where we know the true world model. Our interpretation of having a world model corresponds to recovering the state space of the system. Automata theory tells us that this is the correct way of understanding these systems. Recovering the true states of the world corresponds to an intuitive notion of capturing the world model. The key idea is using this connection to automata theory to understand how well states are captured just by looking at sequences. We believe this connection as well as the extensive evaluation on new and standard tasks for interrogating world models contributes an important contribution to this line of work. >_I agree. But I'm not sure the model performs poorly on detours/proposed metrics if and only if it's inconsistent with the true world model. Even if there is some inconsistency, it might be exaggerated—or maybe even minimized_ We're glad you agree that models whose outputs are consistent with the true world model will perform well on detours. Then we have the following: - If a model performs poorly on detours it doesn't behave like the true world model - Models like Synthetic Othello perform poorly on detours - This means they don't behave like the true world models - Previously proposed metrics suggest that all models we consider (including Synthetic Othello) do behave like correct world models - Our metrics correctly measure that they don't. This is a contribution of our work: we not only show that previously proposed metrics can lead to incorrect conclusions about world models, we also propose and validate new ones. We'd be happy to discuss any aspects of this further if you have questions or would like additional clarification. We agree that while poor performance on detours implies an incorrect world model, an incorrect world model can still perform well on detours. This is why it's important to have metrics that fully measure world model structure, like the ones we propose. Our detours exercise serves as one-way validation, which is the direction of disagreement between our proposed metrics and existing ones. --- Rebuttal 5: Comment: > _However, since you're proposing evaluation metrics, they should be applicable to more realistic models, not just those trained artificially. What happens if two models are trained on the same dataset, and their performance gap is much smaller?_ Like other papers about world model metrics [1, 2], we validate our metrics on models trained on artificial data. It is theoretically possible for model performance to depend on the decoding mechanism. It could imply that the models are so close in the amount of world model structure they capture that their performance depends on the decoding mechanism. You're correct that noisy shortest paths would involve more random exploration during training compared to shortest paths. It's a good question why it performs worse. One possibility is that it reaches a middle ground between random and constrained exploration that means it can't reap the benefits of either extreme. While we focus on world model metrics, it's important for future work to assess _why_ some models have world models and others do not > _Indeed the gap between Championship and Othello in terms of differentiating between invalid moves and very bad moves are captured by the probe tests in Li et al. (2022). As shown in their Table 2, the error rate with Synthetic is significantly lower than with Championship._ The best probe accuracy for the Championship model from Li et al. [1] is indeed lower than the best accuracy for the Synthetic model (90.6% vs 98.3%). However a challenge of probing tests is the difficulty of distinguishing between two high scores [3, 4, 5] (Li et al [1] make no difference in their conclusions for each model's world modeling capabilities). In contrast, our metrics clearly differentiate the two Othello models (e.g. 0.98 compression precision for Synthetic and 0.00 for Championship) which is validated on detours (e.g. 99% accuracy for Synthetic with 0.50 detours compared to 1% accuracy for Championship). > _Sequence generation models are typically trained to maximize the probability of ground-truth sequences, making the selection of the top-ranked prediction—essentially MAP estimation—consistent with their training_ Note that this is defining an acceptance criterion: top-k with k=1. Our metrics apply to this setting and we included experiments based on them. We also tested multiple ablations and two other sampling mechanisms to capture the diversity of ways in which it is possible to decode from LLMs. We believe it is important to consider various settings instead of constrain ourselves to a single one. > _Moreover, if the top-1 prediction is typically used for reasoning tasks that rely on underlying world models, why should we be concerned with the consistency of top-k predictions?_ We performed multiple top-k ablations because of your suggestion to consider top-k sampling. This was a great suggestion: Even if top-1 predictions are typically used for reasoning, it certainly isn't the only sampling mechanism, and our experiments show the robustness to sampling mechanisms. > _But when it comes to those hyperparameters and decoding algorithms, how exactly do they influence the metric values? For example, why does top-p decoding (p=0.999) result in a higher metric value for Random-walks compared to top-k decoding (k=4), yet performs worse for Shortest-path?_ There are patterns for how performance varies with threshold. For example, compression precision will typically increase as more sequences are accepted. This is because as more sequences are accepted, it is more likely that a model will accept a suffix for two prefixes that lead to the same state. While it's not an exact 1-1 mapping, we find this to be true for almost all models we consider. While we included top-k with the k=4 ablation for completeness, it is not an especially useful decoding mechanism for navigation. This is because there are only 8 possible cardinal directions, not all of which will be legal moves, and so decoding with top-k (k=4) can force the model to select sequences that aren't legal. [1] https://arxiv.org/abs/2210.13382 [2] https://arxiv.org/abs/2102.13249 [3] https://arxiv.org/abs/2102.12452 [4] https://arxiv.org/abs/1805.01070 [5] https://arxiv.org/abs/2004.03061 --- Rebuttal 6: Comment: Dear author, I have some quick questions. > The best probe accuracy for the Championship model from Li et al. [1] is indeed lower than the best accuracy for the Synthetic model (90.6% vs 98.3%). Could you direct me to the specific paragraph or section where this result is reported? > While we included top-k with the k=4 ablation for completeness, it is not an especially useful decoding mechanism for navigation. But nearly all models achieve their best metric scores in this setting. No? I will reply to other responses later. --- Rebuttal Comment 6.1: Comment: Thank you for continuing to engage with our paper. We appreciate the continued discussion. > _Could you direct me to the specific paragraph or section where this result is reported?_ These results are from Table 2 in [1]. The lowest probe error is 9.4% for Championship (layer 4 representation) and 1.7% for Synthetic (layer 7 representation). This corresponds to 90.6% accuracy for Championship and 98.3% for Synthetic. > _But nearly all models achieve their best metric scores in this setting. No?_ Most models have better precision metrics when k=4 than lower k because of the intuition described in the last response: as more sequences are accepted, a model will accept more suffixes, meaning that precision typically improves. Recall has the opposite intuition. Note these are not strict 1-1 mappings, e.g. the recall for the Random Walks model gets worse for k=4 but better for the Shortest Paths model. We implemented the top-k metrics thanks to your suggestion and think they're useful to include in the paper, but the sensitivity of top-k metrics to the number of legal moves is why we prefer epsilon-based and top-p sampling. > _I will reply to other responses later._ Thanks again for your engagement. Please let us know if you have any other questions. [1] https://arxiv.org/abs/2210.13382	Summary: This article proposes an evaluation framework for understanding whether or not transformers have learned an implicit world model. Existing metrics focus on next-token prediction and state probes, while this article proposes metrics inspired by the Myhill-Nerode theorem: Whether the network treats two action sequences arriving at the same state as having the same continuations, and whether the network properly distinguishes whether two states differ in allowable subsequent action sequences. They find that across large models trained on taxi data, Othello moves, and logic puzzles, these new metrics reveal far more weaknesses than previous metrics. Strengths: This is a brilliant article. Given the influence of LLMs, the question of whether strong next-token prediction leads to neural networks with emergent, implicit world models is open and very important. In my view, this article is the most convincing evidence yet with regards to this question. I can see this article having major impact. Particular strengths include - Excellent writing and presentation - Choice of Taxi example - Extensions to Othello and Logic puzzle domains - Overwhelmingly clear results Weaknesses: I don't see real weaknesses. I have a couple minor suggestions for clarification: - Figure 2 is a clever illustration but it could use some more detail in the caption, and I'm not sure I fully understand it. For the compression test, why are the only errors under the pink line, as opposed to covering other nodes in the graph on one side of the boundary? I have a similar question for the right hand side. - Ideally the metrics in the tables, "Compression precision", "Distinction precision", "Distinction recall", would be more clearly defined somewhere in bold, like other terms in the article. Technical Quality: 4 Clarity: 4 Questions for Authors: - I'm a little puzzled why the models have low distinction precision/recall. If the two states they are meant to distinguish are sampled randomly, why would the model confuse their continuations? Some more intuition here--especially providing example errors-- would be helpful. - How much training was provided to the models? Confidence: 4 Soundness: 4 Presentation: 4 Contribution: 4 Limitations: I see no issues here. Flag For Ethics Review: ['No ethics review needed.'] Rating: 9 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your thorough and insightful review of our paper. We appreciate your enthusiasm for the work and your remarks on the quality and significance of our paper. > _Figure 2 is a clever illustration but it could use some more detail in the caption, and I'm not sure I fully understand it. For the compression test, why are the only errors under the pink line, as opposed to covering other nodes in the graph on one side of the boundary? I have a similar question for the right hand side._ This is a good point. We apologize for the confusion. The figure was intended to illustrate boundary errors, but you're right that examples to the side of the boundary are also errors. We've updated the figure and caption to make more clear that we're just showing boundary errors and we've also made a few stylistic updates as well (see the shared PDF response). > _Ideally the metrics in the tables, "Compression precision", "Distinction precision", "Distinction recall", would be more clearly defined somewhere in bold, like other terms in the article._ Thank you for the suggestion. We'll add these definitions in bold in the main text. > _I'm a little puzzled why the models have low distinction precision/recall. If the two states they are meant to distinguish are sampled randomly, why would the model confuse their continuations? Some more intuition here--especially providing example errors-- would be helpful._ This is a good question. Your intuition for the distinction metric is right. An important point is that the distinction metric tests both whether the states are correctly distinguished and whether a model produces the correct difference in continuations. In other words, to perform well at the distinction test, a model needs to know the exact set of continuations that are legal in one state but not the other. One reason this could be hard is if the Myhill-Nerode boundary between states is large; then models need to correctly differentiate potentially long-range and complex continuations. In the navigation setting, we found two kinds of interpretable distinction errors. One is that intersections that are geographically close to each other are confused for one another. Another is that intersections on streets with the same traffic patterns (e.g. the intersecting streets are one-way in the same directions) are also confused for each other. We found other kinds of distinction errors as well that were harder to interpret; an interesting research question is understanding why models fail to distinguish states that humans can distinguish easily. We'll add qualitative examples to our updated revision and we thank you for suggesting them -- they'll make the paper stronger. > _How much training was provided to the models?_ Training sizes: - Shortest paths: 2.9M sequences (120M tokens) - Noisy shortest paths: 31M sequences (1.7B tokens) - Random walks: 91M sequences (4.7B tokens) We trained models until the validation loss increased or stopped improving. This ranged from ~12 hours for the smallest models and datasets (shortest paths) and 48 hours for the largest models (random walks) on 8 A100 GPUs. We'll update the paper to make these training details more clear. --- Rebuttal Comment 1.1: Comment: Thanks for your reply. I reaffirm my very positive assessment of the work!	Summary: This paper proposes new evaluation metrics to assess whether a learnt world model is indeed learning the underlying dynamics or logical reasoning required to fully decipher a new domain. The paper sheds light into how world models should be evaluated, compared to what is being done in the literature currently and finds that current metrics can lead to instability or lacks enough evidence that a true underlying world model of the domain is indeed learnt. Strengths: The core idea of the work seems interesting; but unfortunately as a review I do not have the necessary background to fully or properly assess this work. This work tries to address an important question for how current world models should be evaluated, and uses literature from automation theory to propose new metrics to see if the underlying logic of the domain can indeed be learnt by the world model. My assessment of the work is rather high level with not enough technical background to assess the core contributions of this work; however, if this wiork is technically sound and can be made addressable with enough intuitions to general audience not familiar with automata theory, this work can indeed be quite significant and important to the community. Weaknesses: My only comment would be that the paper should perhaps provide more background and intuition from automata theory, to justify the tools that are introduced to be able to fully understand this work. The core idea seems interesting but the experimental and contributions of the work, if it can be explianed more generally, would perhaps be more useful. Technical Quality: 3 Clarity: 3 Questions for Authors: ... Confidence: 1 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: .... Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your careful and insightful review of our paper. We're glad that you think the paper is addressing an important question and that it has the potential to be "quite significant and important to the community". > _My only comment would be that the paper should perhaps provide more background and intuition from automata theory, to justify the tools that are introduced to be able to fully understand this work. The core idea seems interesting but the experimental and contributions of the work, if it can be explained more generally, would perhaps be more useful._ You bring up a great point. We'll use the extra space available to us in the camera-ready revision to move the definition of DFAs from the appendix to the main text. We'll also provide the following high-level explainer: At a high level, a DFA is a collection of states and a set of rules that govern how states are related to each other. For example, consider the game of Othello. This is a DFA where each state is essentially a different board position. The rules are similar to the rules of Othello; they tell you not only which moves are legal, but also how playing a particular move at a given board takes you to a new board. While we use Othello here as an illustrative example, DFAs are general: for example, navigation is a DFA (where the true state is which intersection you're at). They're common in other application areas, such as search engines, control systems, and genetics. DFAs are commonly used to study world models because they let us compare a model's predictions to the true rules [1, 2, 3, 4]. One popular method is the next-token test: given a sequence that corresponds to a true state, is the model's top-predicted next token valid under the rules of the DFA at that state? For example, given a sequence of Othello moves (encoded as tiles, e.g. "34 12 30 23 26"), is a transformer's prediction of the next tile a legal move? Our paper shows this next-token test can be misleading; models that are very far from having the true world model can perform very well at this test. A classic result -- the Myhill Nerode theorem -- provides intuition as to why: states aren't only defined by which individual next actions are legal, but rather by which (potentially long) sequences of actions are legal. For example, there are many Othello boards that have the same set of legal next moves, but the _sequences_ of legal moves differ when we consider longer sequences. As a result, testing whether the true world model has been recovered requires going beyond next-token tests. This motivates two new properties a model must satisfy if it has recovered the true world model recovery: - Sequence compression: if two sequences lead to the same state, a model shouldn't distinguish them. - Sequence distinction: if two sequences lead to distinct states, a model should distinguish them. Our metrics directly measure these properties. Sequence compression is evaluated by sampling two sequence prefixes that lead to the same state and making sure a model's predicted continuations of those sequences are similar. For Othello, this corresponds to checking whether a model's outputs are similar for two move sequences that result in the same board. Our measure of sequence distinction is similar: it's evaluated by sampling two sequence prefixes that lead to different states and making sure that a model's predicted continuations reflect the differences in the continuations. In other words, this metric tests how well a model captures how different board positions are different. Empirically, these metrics capture important aspects of world model recovery that other metrics do not. In the taxi example, prior metrics for assessing world models would lead us to conclude that transformers trained on taxi rides have world models. But our metrics come to a different conclusion: these models are far from recovering the true world model. We validate this by recovering the implicit map of NYC and showing it's nonsensical, along with showing that each model's navigation performance breaks down when detours are introduced. Our metrics also discern between two different types of Othello models: the model trained on Synthetic games has a world model, while the model trained on Championship games does not by our metrics. We validate this with a similar detours exercise (see the PDF for more details), where the Synthetic model produces near-perfect games regardless of detours and the Championship model fails immediately. There is a clear distinction between Championship and Synthetic models, but this is only captured by our metrics; existing metrics would lead us to conclude that both have world models. We hope this is helpful. We've also included more motivation for including DFAs in our response to Reviewer S5LR. Please let us know if anything is unclear. If these comments have addressed your concerns, we hope you'd consider raising your score. [1] https://arxiv.org/abs/2106.00737 [2] https://arxiv.org/abs/2210.13382 [3] https://arxiv.org/abs/2102.13249 [4] https://arxiv.org/abs/2310.07582 --- Rebuttal Comment 1.1: Comment: Thank you again for taking the time to review our paper. We appreciate your comments and believe the paper will be stronger because of them. We were wondering if you had any more questions our review didn’t address. Since the discussion period ends tomorrow we want to make sure we have time to address your points. If you don’t have any more questions, we hope you’d consider changing your score.	Rebuttal 1: Rebuttal: We thank the reviewers for their careful evaluation and feedback. We're glad you found our paper "brilliant" (7KXV) and offering a "novel perspective" (RjHx), with the potential to be "quite significant and important to the community" (YkfB) and to have "major impact" (7KXV). Moreover we appreciated your comments on the strength of the empirical evidence (7KXV, RjHx, S5LR) and quality of the writing (7KXV, RjHX, S5LR). In response to the reviewers’ suggestions, we've included updated results in the attached PDF with: - Additional validation results: Our original submission validated our metrics empirically using maps and detours for the navigation data. We now include a similar empirical validation for Othello. In our original submission, we showed that while existing metrics conclude that both Synthetic and Championship Othello models recover the true world models, our metrics find that only the Synthetic model recovers the true world. We include an additional "detour" exercise (where a model's predicted move is replaced with another legal one) to validate this discernment for Othello. While the Synthetic model produces near-perfect games regardless of detours, the Championship model fails immediately. A model that recovers the true world model will succeed regardless of detours. There is a clear distinction between Championship and Synthetic models, but this is only captured by our metrics; existing metrics would lead us to conclude that both have world models. - Additional acceptance criteria: While our submission considered fixed probability thresholds to define transformer acceptance, an advantage of our framework is that it can be implemented with different acceptance criteria. In response to Reviewer RjHx's suggestion, we've also added results for top-p and top-k sampling (along with ablations of p and k). These come to the same conclusions as our original criterion, which, along with the ablations in Table 3 of our submission, show the robustness of our metrics to acceptance criteria. - Updated figure: In response to Reviewer 7KXV's suggestion, we've updated Figure 2 from our original submission to make the interpretation more clear. These results will make the paper stronger, and we thank you for suggesting them. We’ve also included more details about these results in our individual responses to each reviewer. Pdf: /pdf/ec7851b70c69c9b4ae903c05ccd93394adc7a909.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
MotionTTT: 2D Test-Time-Training Motion Estimation for 3D Motion Corrected MRI	Accept (poster)	Summary: This work proposes a novel deep learning-based framework for recovering high-quality 3D MR images from undersampled and motion-corrupted k-data. The proposed approach is well motivated and technically sound. The authors perform extensive experiments on simulated and real MR datasets, which confirm the effectiveness of the proposed framework. Strengths: Motivation and significance Motion correction is an important issue in the field of MR imaging. The proposed method removes the reliance on motion simulation by training a neural network that reconstructs high-quality MR image from under-sampled k-data in advance. This new paradigm significantly improves the robustness of the reconstructed images. Technical solid In the steps 2 of test-time training for motion estimation, the MRI acquisition knowledge, such as forward model, sampling trajectory, are effectively integrated into the framework, which improve the reliability of the reconstruction. Clarity and organization This submission is well-written and easy to follow. Experimental evaluation The authors perform experimental evaluations on simulation and real-world datasets. I am pleased to see the experiments based on the real-world dataset. I think it greatly improves this paper. Weaknesses: For this submission, I have a few minor suggestions as follows. Various types of rigid motion In line 205, the authors show that random rigid motions ($M_\text{max}=[2,5,10]$) are simulated. However, the rigid motion in the real world could follow some patterns, such as involuntary motion and abrupt motion. I think it is better to test these different movements. Compared methods For supervised methods, only U-net is used as a baseline. Advanced supervised models [1][2] are not discussed. Furthermore, motion correction methods [3] based on diffusion models are not compared. > [1] Han Y, Yoo J, Kim H H, et al. Deep learning with domain adaptation for accelerated projection‐reconstruction MR[J]. Magnetic resonance in medicine, 2018, 80(3): 1189-1205. > [2] Liu J, Kocak M, Supanich M, et al. Motion artifacts reduction in brain MRI by means of a deep residual network with densely connected multi-resolution blocks (DRN-DCMB)[J]. Magnetic resonance imaging, 2020, 71: 69-79. > [3] B. Levac, A. Jalal, and J. I. Tamir. “Accelerated Motion Correction for MRI Using Score-Based 388 Generative Models”. ISBI 2023. Some typos For example, the symbol $\mathcal{E}$ in Eq. 3 is not defined. Technical Quality: 3 Clarity: 3 Questions for Authors: See the section of Strengths and Weaknesses, please. Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The authors mention enough limitations of their work. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for the feedback and the positive evaluation of our work. In the following we address the weaknesses in the order as pointed out by the reviewer. - Weakness 1, various types of rigid motion: We agree that in practice motion can be categorized into different types. However, the range of different motions is large varying with patient population and condition. Also we are not aware of good available models of the different types of motion based on real measurements in the literature. Hence, it is common to evaluate with randomly simulated motion (see line 202 for examples). Note that for the experiments in Figure 3 we simulated a total of 100 different motion trajectories with up to 10 randomly generated motion events per trajectory covering a wide range of possible motions. In general, we expect our method to work well for different types of motion as different to previous deep learning based approaches it was not trained on a particular type of simulated motion. - Weakness 2, compared methods: [1] proposes a domain adaptation method for reconstructing radial MRI in a limited data regime, but does not discuss motion correction. [2] proposes a novel network architecture for end-to-end motion artifact reduction but only in 2D and in general it has been found that end-to-end methods, while being significantly faster, result in inferior reconstruction quality compared to reconstruction based on previously estimated motion parameters like ours. See e.g. Fig. 3 in [4] and Fig. 7 in [5]. While diffusion model based motion correction is an interesting direction, the reason why we do not compare to [3] is that the proposed method can only operate 2D motion, while we investigate motion estimation in 3D. Directly extending the method to 3D requires training a diffusion model on entire 3D volumes, which is computational difficult and would require much larger 3D datasets. At the same time it is unclear how to use a 2D diffusion model to estimate motion in 3D. - Weakness 3, some typos: Thanks, we fixed it. [4] Haskell et al. “Network Accelerated Motion Estimation and Reduction (NAMER): Convolutional Neural Network Guided Retrospective Motion Correction Using a Separable Motion Model”. In: Magnetic Resonance in Medicine (2019). [5] Hossbach et al. “Deep Learning-Based Motion Quantification from k-Space for Fast Model-Based Magnetic Resonance Imaging Motion Correction”. In: Medical Physics (2023). --- Rebuttal Comment 1.1: Comment: Thank you for the detailed response. I have also reviewed the comments from other reviewers. While I believe this paper makes a significant contribution to 3D motion correction in MRI, there are some limitations, such as the limited comparison of methods. Therefore, I recommend a weak acceptance for this submission. --- Reply to Comment 1.1.1: Comment: Thanks for noting that our paper makes a significant contribution to 3D motion correction, and many thanks for the reply. Regarding comparing to more methods, we would have been happy to compare to more methods, but found no suitable 3D methods other than the one we compare to (alternating minimization). Please not that all methods you mentioned are for 2D motion correction, and they do not extend to 3D in a straightforward manner. We think it can’t be expected to extend other work significantly in order to generate new baselines, this would be independent contributions. Motion estimation and correction in 3D is extremely difficult, this is testified by the fact that the vast majority or papers only studies 2D motion reconstruction, even though motion in MRI always occurs in 3D space. Please let us know if you have any baseline in mind that has been applied to 3D motion estimation or correction by the papers that proposed the method.	Summary: This paper proposes a motion correction MRI reconstruction algorithm for 3D brain MRI. The proposed technique consists in a deep learning-based estimation of rigid motion parameters, which allows to correct the k-space before a final reconstruction. Estimation of motion parameters are based on a single optimization step freezing the reconstruction UNet parameters, and assuming loss will only (or mainly) be influenced by motion. Strengths: The paper addresses an important problem, namely motion correction, using a fully data-driven approach. Moreover, the originality of the approach lies in tackling this problem directly on the 3D frequency (or k-)space , when most deep-learning techniques are focusing on 2D acquisitions. Weaknesses: The overall structure of the paper is quite confusing, which makes it hard to follow. Experiments and alternative techniques seem to be presented throughout the result section. A proper ablation study seems required, in order to assess the added-value of each step. Proper baseline also seems necessary especially regarding the reconstruction step or the removal of motion artifacted lines, as more recent techniques could have been used as SOTA. The overall motion estimation relies on a first 2D reconstruction pipeline however the performance of the technique seems to be lower than a standard L1 reconstruction technique. If so, how could the authors be sure that motion parameters are not biased or affected by the low performance of the 2D reconstruction pipeline. Why did the authors not try to directly reconstruct from the 3D k-space domain, in order to estimate motion parameters in 3D? Moreover, I believe the authors should also provide further details on they are switching back and forth from 3D k-space domains to 2D, as a simple slicing in a given direction of the 3D k-space is not appropriate. Technical Quality: 2 Clarity: 1 Questions for Authors: Could the authors find another database of 3D data in order to train a 3D reconstruction UNet directly? Given the proposed technique aims also at suppressing corrupted k-spaces lines, would it be sensible to train a reconstruction technique with higher a acceleration factor? Would the proposed technique be applicable for other sampling strategies, especially would it be possible to apply on stack of stars acquisitions or other 3D sampling strategy. Why did the authors not apply other reconstruction (standard L1) reconstruction for the real dataset for comparison? Especially since it was outperforming the UNet approach on simulated motion data. Confidence: 3 Soundness: 2 Presentation: 1 Contribution: 2 Limitations: The authors should discuss the risks of hallucinations and bias of the proposed technique. Flag For Ethics Review: ['No ethics review needed.'] Rating: 3 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thanks for the feedback. In the following we address the concerns and questions in the order as pointed out by the reviewer. - Weakness 1, experiments and alternative techniques seem to be presented throughout the result section: Thanks for the feedback. We will make sure to describe all methods that we compare in the main Figure 3 at the end of the setup Section 5.1 before the results section. - Weakness 2, a proper ablation study seems required, in order to assess the added-value of each step: In fact, Figure 3 already shows the performances during all steps of MotionTTT. L1 indicates the performance without any motion correction (before applying MotionTTT), MotionTTT-L1 the performance after motion estimation and MotionTTT-L1+Th after motion estimation plus data consistency loss thresholding. - Weakness 3, baselines regarding the reconstruction step or the removal of motion artifacted lines: Regarding the reconstruction step, our method is agnostic to the method used for reconstruction based on the estimated motion parameters. Hence we do not expect any new insights from trying additional reconstruction methods as a better reconstruction method would lead to a better performance for any motion estimation method.   Regarding baselines for the removal of motion artifacted lines, we are not sure to which method the reviewer would like to see a comparison. Our method estimates motion parameters with a high accuracy and hence will outperform any method that only detects and then removes motion corrupted lines. Only in the presence of severe motion we remove lines that exhibit a large data consistency loss indicating inaccurate estimation of motion parameters, a feature that comes for free with the proposed method. However, also in the most severe cases typically not more than 5% have to be discarded. - Weakness 4, effect of the low reconstruction performance of the U-net on motion estimation: It is not clear if a better reconstruction performance of the U-net due to an increased amount of training data would further improve the ability to estimate motion parameters especially as our experimental results show, the current reconstruction performance of the U-net already achieves highly accurate motion parameter estimation across a wide range of simulated motion and significantly improved image quality in case of prospectively acquired real motion-corrupted data. Nevertheless, we will investigate if even further improvements can be achieved by training on additional data sources like e.g. 2D brain data. - Weakness 5, why did the authors not try to directly reconstruct from the 3D k-space domain, in order to estimate motion parameters in 3D: Training 3D models on entire 3D volumes is infeasible in terms of memory and compute requirements. However, we agree that instead of chunking the volume slice-by-slice as we do, one could also train a 3D model on 3D chunks and perform chunk-by-chunk reconstruction. We decided to build on the well-established 2D convolutional U-net as it enabled highly accurate motion estimation combined with fast reconstruction and a low network parameter count, which is important as the entire volume has to be reconstructed in every iteration. In the future, this also enables enlarging the training set with 2D data in order to overcome the limited availability of 3D dataset. - Weakness 6, regarding switching between 2D and 3D: As the reviewer pointed out correctly, slicing the k-space in arbitrary directions is not appropriate. Hence, we only slice the zero-filled reconstruction in the image domain at the network input and add slices together at the network output before applying the 3D fourier transform to obtain the reconstructed k-space data. We will emphasize this more clearly in the Section 4, step 2: Test-time-training for motion estimation. - Question 1, existence of another database of 3D data to train a 3D reconstruction UNet directly: To the best of our knowledge the used dataset is the largest 3D brain dataset containing the original k-space measurements publicly available. While other smaller ones exist, we do not believe that even if compute would not be a problem the amount of training examples would suffice to train a 3D model on entire volumes. - Question 2, training a reconstruction technique with higher acceleration factor to compensate for thresholding: We only threshold a relatively small number of lines, typically not more than 5% of the acquired lines even under the most severe motion. Nevertheless, there is a discrepancy between the undersampling mask the U-net was trained on in the absence of motion and the undersampling of the motion-corrected network inputs due to rotations in the k-space as discussed in the paper in Section 5.2. However, both changes in the mask due to thresholding and rotations are motion specific and hence difficult to train on without simulating motion. Hence, in the paper we use L1-minimization for reconstruction, which is mostly independent of changes in the mask. - Question 3, application to other 3D sampling strategies (stack of stars): See author rebuttal point 1. - Question 4, missing L1 reconstruction for the real-motion data: We do show the results for MotionTTT+Th-L1 in Figure 6. - Limitation, risks of hallucinations and bias: As currently the final reconstruction results of our method are based on L1-minimization no learning based hallucinations can occur. If the motion parameter estimation is off, the result will be a reconstruction with motion artifacts similar to when no motion correction is applied. We are not sure what type of bias the reviewer is referring to. We hope those responses address the reviewer's concerns and the reviewer considered raising their score.	Summary: This paper proposes a method for estimating the motion of patients, such that accurate motion-corrected images could be reconstructed. The key idea is that a neural network trained for motion-free reconstruction has a small loss if there is no motion, thus optimizing over motion parameters passed through the reconstruction network enables estimation of the motion. Strengths: - The estimation of motion of patients is important in MRI measurement. This paper is a good trial to address this problem. Weaknesses: - There is no technical novelty in this work. It introduces some existing modules to address the proposed problem. - The experiments are weak to demonstrate the efficacy of the proposed method. 1）There lacks strong baselines and there are no compared methods. Although according to the authors, there are no other methods designed for 3D rigid motion estimation for 3D motion-corrected MRI, there should be some methods that could reconstruct the images. 2) The data are little for evaluating the methods, and more averaged quantitative results are suggested to report. Technical Quality: 2 Clarity: 2 Questions for Authors: See the weaknesses. Confidence: 2 Soundness: 2 Presentation: 2 Contribution: 2 Limitations: Yes, limitations are discussed. Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for the feedback. In the following we address the concerns in the order as pointed out by the reviewer. - Weakness 1, introduction of existing modules and lack of novelty: We would like to point out that combining a 2D reconstruction network trained on motion-free data with test-time-training for motion estimation in 3D has not been proposed before, neither a closely related method. Our work is the first that enables efficient motion estimation in 3D based on a 2D network trained on motion-free measurements. As discussed in our related work section, previous work on deep learning based motion estimation has exclusively focused on the 2D case and methods that are required to simulate motion during training and hence are specific to the type of motion used during training. Thus the work contains significant technical novelty. - Weakness 2 part 1, lack of further baselines in particular motion corrupted image reconstruction networks: While we are not aware of any deep learning based baselines for 3D motion estimation, there are indeed methods for 3D end-to-end reconstruction from motion corrupted volumes as discussed in our related work section, second paragraph. As we note there, this class of methods is well known to perform poorly relative to methods that perform motion estimation and then reconstruct, like our method. See Fig. 3 in [1] and Fig. 7 in [2]. - Weakness 2 part 2, average quantitative results over more test examples: For a given method each result in Fig. 3 in the paper is averaged over 5 test examples with each 2 independent motion trajectories. As we consider 10 different levels of motion, we evaluate in total over 100 different motion trajectories each consisting of up to 10 randomly generated motion events. Regarding the required number of test examples, for image reconstructions tasks this number is typically lower than in other ML domains like computer vision as one test image contains already many different structures and details that the method needs to recover in order to achieve a high image quality score. Especially, in 3D the amount of data per test volume is large and comparatively small test sets are often used (e.g. 7 volumes used in [3]). We hope this addresses the reviewer's concerns and if yes, that the reviewer considers raising their score. [1] Haskell et al. “Network Accelerated Motion Estimation and Reduction (NAMER): Convolutional Neural Network Guided Retrospective Motion Correction Using a Separable Motion Model”. In: Magnetic Resonance in Medicine (2019). [2] Hossbach et al. “Deep Learning-Based Motion Quantification from k-Space for Fast Model-Based Magnetic Resonance Imaging Motion Correction”. In: Medical Physics (2023). [3] Johnson and Drangova. “Conditional Generative Adversarial Network for 3D Rigid-Body Motion Correction in MRI”. In: Magnetic Resonance in Medicine (2019). --- Rebuttal Comment 1.1: Comment: Thanks to the authors for the rebuttals. Some of the concerns are addressed but some remain. After reading the comments of all reviewers, I keep my original rating. --- Reply to Comment 1.1.1: Comment: Can you be specific which concerns remain? You point out that “this paper is a good trial to address this problem” but at the same time argue that the work lacks novelty and that there “should be other methods”, without pointing to any specific work in the literature. If you have any concrete concerns that remain, we would be happy to clarify.	Summary: The paper presents MotionTTT, a deep learning-based method for estimating and correcting rigid motion in 3D MRI images. The approach leverages a neural network pre-trained for 2D motion-free image reconstruction and employs test-time-training (TTT) to estimate motion parameters from motion-corrupted 3D measurements. The effectiveness of the method is demonstrated through evaluations on both simulated and real datasets. Strengths: The paper proposed a novel approach for 3D rigid motion estimation using a neural network trained on 2D motion-free images and TTT for motion parameter estimation. The application of test-time-training for motion estimation is a novel contribution that effectively addresses motion artifacts in 3D MRI images, and outperformed classical alternating optimization methods in terms of speed and accuracy, especially under severe motion conditions. Weaknesses: The theoretical foundations of MotionTTT are generally robust, but there are notable gaps. The method builds on existing neural networks for 2D image reconstruction, extending them to handle 3D rigid motion estimation. During the pre-training step, $f_\theta$ is trained to map under-sampled k-space data back to fully sampled k-space data. The authors show that under-sampled k-space data with motion (where certain regions of the k-space undergo rotation and phase shifting) results in higher reconstruction loss for $f_\theta$. However, this indirect optimization lacks theoretical proof and needs more robust experimental validation. For instance, the performance of this method may heavily depend on the under-sampling pattern of the k-space (such as the undersampling factor and the linear sampling trajectory) and the specific regions in k-space that are affected by motion. However, in the experiments, the setup of the undersampling of the k-space was fixed. A more thorough theoretical and experimental investigation into why this optimization works and under what conditions it is most effective would strengthen the soundness of the method. Technical Quality: 2 Clarity: 3 Questions for Authors: 1. The idea behind minimizing loss (4) is not intuitive and clear. How do you prove the effectiveness of using loss (4) to recover and remove the motion corruption? Will the effectiveness be affected by the undersampling factor and trajectory? What if you have a higher or lower factor? or maybe a spiral trajectory? Can you find the optimal factor for your method? 2. Based on the assumption that rigid motion leads to rotation and phase shift in k-space, is the linear trajectory the optimal undersampling trajectory? 3. Do you really need the fully sampled k-space data to learn $f_\theta$? Confidence: 4 Soundness: 2 Presentation: 3 Contribution: 3 Limitations: The indirect TTT optimization method lacks theoretical justification. The authors should investigate both theoretically and experimentally why this approach works and under what conditions it is most effective. The performance of MotionTTT may be heavily dependent on the under-sampling pattern of the k-space and the specific regions affected by motion. The method’s effectiveness might vary significantly with different sampling patterns and motion artifacts. The method relies on a pre-trained network using fully-sampled data, which may not always be available in practice. Flag For Ethics Review: ['Ethics review needed: Research involving human subjects'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thanks for the feedback and for acknowledging the novelty of our work. In the following we address the weaknesses (W), questions (Q) and limitations in the order as raised by the reviewer. - W 1, lack of theoretical investigation of why the optimization works: To get an understanding on why the proposed optimization works, we developed the following theory for a (very) simplified setup that models our approach. This setup also helps to understand the necessity of defining a learning rate schedule that in the presence of motion explores the loss landscape with an initially large learning rate before gradually decaying it. We will include this result and discussion in the revised version of our paper.   We consider the signal $\mathbf{x} \in \mathbb{R}^n$ that lies in a $d$ dimensional subspace, i.e., the signal is generated as $\mathbf{x} = \mathbf{U} \mathbf{c}$ with orthonormal $\mathbf{U} \in \mathbb{R}^{n \times d}$ and Gaussian vector $\mathbf{c}$.   Let $\mathbf{F}_\mathcal{T}$ be the Fourier matrix with rows chosen in the set $\mathcal{T}$. We assume a measurement model, where the signal $\mathbf{x}$ takes on $N_s$ motion states defined by the unknown translations $t _1^\ast,\ldots,t _ {N _ s}^\ast$, and for each translated version of the signal, a set of measurements is collected according to $$\mathbf{y _ s} = \mathbf{D} _ {t _ s^\ast, \mathcal{T} _ s} \mathbf{F} _ {\mathcal{T} _ s} \mathbf{x}, \tag{1}$$ where $\mathbf{D} _ {t _ s^\ast, \mathcal{T} _ s} $ is a diagonal matrix with $e^{i 2 \pi t_s^\ast l / n}, l\in \mathcal{T} _ s$ on its diagonal. Here, we use that a circular shift by $t_s^\ast$ in the spatial domain is a multiplication with a complex exponential in the frequency domain. We write the acquisition of the entire measurements $\mathbf{y} \in \mathbb{R}^k$ from all motion states as $ \mathbf{y} = \mathbf{D} _ \mathbf{t^\ast} \mathbf{F} _ \mathcal{T} \mathbf{x}.$ For simplicity we assume the fully sampled case, i.e., $k=n$.   Next, we define a network $f( \mathbf{x}^\dagger) = \mathbf{U} \mathbf{U}^T \mathbf{x}^\dagger$, for which it is straightforward to see that if all motion parameters $\mathbf{t}^\ast$ are known we have that $$f( (\mathbf{D} _ {\mathbf{t}^\ast} \mathbf{F})^\dagger \mathbf{y} ) = \mathbf{x}, \tag{2}$$ i.e., the network reconstructs the signal perfectly. The loss function used in the paper for this setting is $$\mathcal{L} _ {\text{TTT}} (\mathbf{t}) = \|\| \mathbf{D} _ {\mathbf{t}} \mathbf{F} _ {\mathcal{T}} f( (\mathbf{D} _ {\mathbf{t}} \mathbf{F} _ \mathcal{T})^\dagger \mathbf{y} ) - \mathbf{y} \|\| _ 2^2, \tag{3}$$ on which we can perform test-time-training with gradient descent with respect to the motion parameters $\mathbf{t}$.   Assuming that $\mathbf{U}$ is a random subspace and that $\mathbf{c}$ is drawn from a Gaussian with identity covariance matrix, it can be shown that the objective function concentrates around $$\mathcal{\tilde L} (\mathbf{t}) = \|\| \mathbf{D} _ \mathbf{t} - \mathbf{D} _ {\mathbf{t}^\ast} \tag{4} \|\|^2_F.$$ This expected objective function has a unique minimizer at $\mathbf{t} = \mathbf{t}^\ast$ and is convex in a small region around $\mathbf{t}^\ast$, but not globally.   For setting the number of motion states $N_s=1$ we obtain a simple one-dimensional optimization problem and can inspect the behavior of the loss function graphically. Without loss of generality we set $t^\ast = 0$ and plot the loss $\mathcal{L} _ {\text{TTT}} (t)$ in PDF Fig. 4. As we can see the loss exhibits a global minimum at $t=t^\ast$, but also local minima for $t \neq t^\ast$.   In order to minimize such a function in practice, we defining a learning rate schedule (see Appendix B.2 in the paper), where from the start we explore the loss landscape with a large learning rate if the initial loss is large as this indicates the presence of strong motion and initializing all motion parameters with zero might constitute to a large distance to the true motion parameters. Then, the learning rate is reduced gradually. Also once estimated motion parameters approach the true parameters, we did not observe significant deviations from this solution indicating the existence of a global minimum (or a good local one) in practice. - W 2, experimental investigation under what conditions the method is most effective in terms of undersampling factor and sampling trajectory: See author rebuttal. - Q 1, why and under what conditions does the method work: See Weakness 1 and 2. - Q 2, is the linear trajectory the optimal undersampling trajectory: See author rebuttal. In short, a linear trajectory is not the best choice for motion estimation with our method, an interleaved or random order is better. - Q 3, do you need the fully sampled k-space data to learn $f_\theta$: We do not, as discussed in Section 6, our method can leverage recent advances in self-supervised training of MRI reconstruction networks. This is a strength of our method, other proposed deep learning based method for (2D) motion correction in MRI rely on simulated motion artifacts during training which require fully sampled k-space data. - Limitations, the method’s effectiveness might vary significantly with different sampling patterns and motion artifacts: Regarding the role of the sampling pattern see author rebuttal. Regarding the role of motion artifacts we evaluated our method on motion events occurring at random time points with different amplitudes and frequencies resulting in different motion artifacts achieving good performance for all of them. In general, we expect our method to work well for different types of motion as it was not trained on a particular type of simulated motion. Remaining limitations have been discussed above. We hope the provided theory as well as the additional simulations and clarifications address the concerns of the reviewer and if yes, that the reviewer considers raising their score.	Rebuttal 1: Rebuttal: Thanks for the reviews! We would like to start by emphasizing that our work is the first that enables efficient motion estimation in 3D based on a 2D neural network trained on motion-free measurements. We show that our method can reliably predict motion and that this yields significant improvements in image quality. We provide extensive numerical results, including for simulated motion, as well based on real motion in an MRI scan that we specifically collected for this project. Most existing works for motion estimation and correction are for 2D and do not contain results on real motion in an MRI scanner. In the following, we address two concerns raised by reviewers fV1o and H96H regarding the role of the sampling trajectory and undersampling factor for the success of our proposed motion estimation method. To address those concerns, we provide additional experimental results in the attached single-page PDF. 1. The sampling order is important as it is difficult to estimate motion parameters for a batch of k-space measurements that contain only high-frequency components. Reviewer fV1o and H96H asked if the effectiveness of MotionTTT is affected by the sampling trajectory (e.g. Cartesian vs. spiral or stack of stars). Up to trajectory specific additional sources of artifacts like B0 field inhomogeneities that needed to be modeled, the problem of motion estimation does not change with the sampling trajectory, and as our forward model is implemented via the non-linear FFT, our method can process any k-space geometry. However, the sampling order is important, as we show with an additional experiment. We investigate three different sampling orders for a Cartesian trajectory: We fix the undersampling mask and change the order at which k-space lines are acquired between interleaved, linear (both have been used already in the paper) and random (see PDF, Fig. 3 c,d,e for a visualization of sampling orders). For motion severity level 5 we obtain the average (8 instances) reconstruction performance in PSNR for reconstruction based on motion parameters estimated by our MotionTTT vs. ground truth motion as 35.98vs.36.00, 36.27vs.36.28 and 33.16vs.36.99 for interleaved, random and linear sampling orders. Interleaved and random orders achieve perfect motion estimation, while the linear order leads to a significant gap of almost 3dB. For a given test example PDF Fig. 1 a,b shows the data consistency (DC) loss of MotionTTT at the first and final iteration. For the random and interleaved order motion states are estimated accurately resulting in a final DC loss well below our defined DC loss threshold. For the linear order first and last motion states, pertaining to shots that contain only high-frequency, i.e., low-energy components, maintain a high final DC loss and the corresponding estimated motion parameters are off as exemplified with the estimated translation parameter in $k_y$ direction in PDF Fig. 1 c. We attribute this finding to the U-net used during MotionTTT reconstructing high-frequency components not as faithfully as low-frequency components. Finally, we would like to note that the sampling order of a Cartesian trajectory can be customized without affecting any other sequence parameters like the shape of the undersampling mask, and hence choosing a, e.g., random order does not limit the generality of our method in the context of Cartesian sampling, which is still most commonly used in practical 3D MRI. 2. The acceleration factor influences the performance of MotionTTT as a smaller factor leads to overall higher reconstruction performance but also to a more difficult optimization problem as more shots are acquired translating to more unknown motion states to be estimated. Reviewer fV1o requested a more robust experimental validation of the conditions in terms of sampling trajectory (see above) and undersampling factor under which MotionTTT works. To this end, we conducted the following experiment, where we re-train the U-net on two additional Cartesian undersampling masks with acceleration factors R=2,8 in addition to the existing results with R=4 (see PDF Fig. 3 a,b,c for the masks). PDF Fig. 2 shows the reconstruction performance in PSNR based on motion parameters estimated by our MotionTTT compared to ground truth motion over three levels of motion severity and the three acceleration factors. As expected, the overall performance decays with increasing acceleration factors and motion severities. For mild and moderate motion, MotionTTT achieves highly accurate motion estimation for all acceleration factors indicated by the vanishing performance gap to using ground truth motion. For strong motion, the best performance is still achieved for the lowest acceleration factor, but an increasing performance gap exists for decreasing acceleration factors due to incorrectly estimated motion states that are then discarded from the final reconstruction via DC loss thresholding. In fact, under severe motion an average of 20.7/100, 2.6/50 and 0.6/25 shots have to be discarded for acceleration factors 2,4 and 8. We attribute the increasing numbers of incorrectly estimated motion states to the increasing complexity of the optimization problem as the number of unknown motion states to be estimated increases linearly in the number of acquired shots. We will include those results in the revised version of our paper. We hope that you find the additional experiments helpful and are happy to discuss further. Pdf: /pdf/1e3eedf818c0abff8f5c03ee4fc0b36097dc0548.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
SureMap: Simultaneous mean estimation for single-task and multi-task disaggregated evaluation	Accept (poster)	Summary: The paper proposed SureMap, a promising method for solving multi-task disaggregated evaluation problem. The key innovation of SureMap lies on transforming the problem into structured simultaneous Gaussian mean estimation and incorporating external data, e.g. from the AI system creator or from their other clients. Experiments on disaggregated evaluation tasks in multiple domains show the promising performance. Strengths: 1) Well motivated. 2) Introduce several datasets for disaggregated evaluation and propose method that uses SURE to tune the parameters of a well-chosen Gaussian prior before applying MAP estimation. 3) Experiments are promising. Competitive in both single task and multi-task evaluation. Weaknesses: As analyzed in Section 2.4: 1) Gaussian assumption may result in underperformance on heavy-tailed data. 2) Incorporating data from multiple clients may be costly. Technical Quality: 3 Clarity: 3 Questions for Authors: 1) Can the authors provide some analysis or insights when the data contradicts with Gaussian assumption? 2) Can the authors visualize/show the cost when incorporating data from clients? Confidence: 2 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: I don't think there are any negative societal impacts of this work. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your detailed review! We address your concerns and questions below: 1. [Can the authors provide some analysis or insights when the data contradicts with Gaussian assumption?] a. Please see our discussion of this issue in the general response (Issue 1: Assumption). 2. [Can the authors visualize/show the cost when incorporating data from clients?] a. Please see our discussion of efficiency in the general response (Issue 2: Computation) and in particular Rebuttal Figure 2. We will include this analysis and visualization in the revision. --- Rebuttal Comment 1.1: Title: Thanks for the rebuttal Comment: Thanks for the rebuttal. I don't have further questions.	Summary: This paper studies disaggregated evaluation, which aims to estimate the performance of models on various subpopulations. This problem is challenging due to small sample sizes in subpopulations, thus leading to inaccurate performance estimates. This issue is magnified when multiple clients use the same AI model and require individualized evaluations, which is referred to as multi-task disaggregated evaluation. This paper designs a method that transforms the problem into a structured simultaneous Gaussian mean estimation problem. The method is comprised of two components: first, conduct maximum a posteriori (MAP) estimation for Gaussian mean estimation and then apply cross-validation-free tuning using Stein’s unbiased risk estimate (SURE). Furthermore, the method employs an additive intersectional effect prior for capturing relationships between subpopulations with a limited number of hyperparameters. The method, namely SureMap, is evaluated on various disaggregated evaluation tasks across different domains, including automated speech recognition (ASR) and tabular census data. The method shows high estimation accuracy for both single-task and multi-task settings over naive estimation, pooled estimation, and Bock estimation. Moreover, the method improves performance estimation even in data-poor regimes. Strengths: - This paper presents a novel method, SureMap, designed to improve the accuracy of performance estimation for models on various subpopulations. This is crucial for assessing the fairness and robustness of machine learning models, especially when subpopulations are small or data is scarce. - Across tabular census data and automated speech recognition datasets in both single task and multitask settings, the proposed method outperforms previous estimation approaches by up to 50%. The results are consistent for various sampling rates and task numbers up to 50. Weaknesses: - The efficiency discussion of the method needs to be expanded. It would be better to list the complexity of the proposed method with existing methods and report the actual runtime. - There are certain cases that the proposed method performs worse than the pooled estimation, such as in Figure 2. It would be better to analyze the reasons behind such results. Technical Quality: 3 Clarity: 3 Questions for Authors: - For subpopulations with few samples, how does this paper compute their ground truth and evaluate the estimation? - It would be better to clarify the pooled estimator. For example, what does the notation $h$ in Equation 3? - It would be better to explain the working of the baselines, such as the Bock method. Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: This work has discussed its limitations in the setup of Gaussian distribution. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your detailed review! We address your concerns and questions below: 1. [The efficiency discussion of the method needs to be expanded. It would be better to list the complexity of the proposed method with existing methods and report the actual runtime.] a. Please see our discussion of efficiency in the general response (Issue 2: Computation). We will include this analysis in the revision. 2. [There are certain cases that the proposed method performs worse than the pooled estimation, such as in Figure 2. It would be better to analyze the reasons behind such results.] a. In Figure 2, pooling outperforms our approach at extremely low data regimes where the typical number of samples per group is 1. In this extreme regime, there may not be enough information to estimate group-level performance well and so the best thing to report is the overall mean (which is what the pooled estimator does). 3. [For subpopulations with few samples, how does this paper compute their ground truth and evaluate the estimation?] a. As noted in the first paragraph of Section 5, we exclude subpopulations with fewer than twenty samples, as we cannot obtain a reasonable ground truth for them. 4. [It would be better to clarify the pooled estimator. For example, what does the notation $h$ in Equation 3?] a. The pooled estimator just takes the average across all data samples, or equivalently a weighted average across the average performance on each subpopulation, with weights corresponding to the number of samples on each subpopulation. Equation 3 makes the latter explicit, and uses $h$ to index each subpopulation. 5. [It would be better to explain the working of the baselines, such as the Bock method.] a. The Bock estimator is described in Section 3.1, and specified explicitly in Equation 6. All other baselines are also specified in Equations 2, 3, and 5. We will make this clearer in the paper.	Summary: The author developed a disggregated evaluation method called SureMap, which has high estimation accuracy for both multi-task and single-task disggregated evaluations. SureMap transforms the problem into structured simultaneous Gaussian mean estimatio, incorporating external data. This method further combines Maximum A Posteriori (MAP) estimation and cross-validation-free tuning via Stein's risk estimate (SURE). Significant improvements in accuracy were observed in disggregated evaluation tasks. Strengths: 1. The author introduces a new method, SureMap, which tunes the parameters of the selected Gaussian prior using SURE before applying MAP estimation. Only linear parameters are needed to recover several natural baselines for disggregated evaluation. 2. The author introduces disggregated evaluation datasets for both single-task and multi-task settings. 3. SureMap shows good results in both single-task and multi-task settings. Weaknesses: 1. I would like to know if there are any rules that need to be followed in the selection of disaggregated evaluation datasets to ensure fairness, as well as the reason why the disaggregated evaluation goal is set as the mean 0-1 error. 2. The fairness assessment is an application biased towards real-world scenarios. Does using Gaussian distribution as a prior align with real-world evaluations？ Technical Quality: 3 Clarity: 3 Questions for Authors: Disaggregated evaluation is a core task in the fairness assessment of AI systems. This paper provides a possible solution and gives the corresponding analysis. I would like to point out that my expertise does not directly align with the specific field of this article. Nevertheless, I have carefully read the paper several times, attempting to provide constructive feedback. I look forward to reading the insights of other reviewers, whose expertise is more closely related to the subject, to further inform my final score. Confidence: 2 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: see the weaknesses and questions above Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your detailed review! We address your concerns and questions below: 1. [I would like to know if there are any rules that need to be followed in the selection of disaggregated evaluation datasets to ensure fairness, as well as the reason why the disaggregated evaluation goal is set as the mean 0-1 error.] a. The goal of disaggregated evaluation is to evaluate fairness and thus help surface any fairness issues that need to be addressed. The question of selecting the right dataset and metric for disaggregated evaluation is an active area of research but beyond the scope of this paper. Some considerations include how well the data represents the intended uses of the AI system and how well the metric captures potential harms / benefits; see Barocas et al. (2021) for an in-depth discussion. In our case, for dataset selection we simply use all the available data, while for the performance metric note that 0-1 error is just one possible measure among many that our method can be applied to, including MAE, MSE, WER, AUC, and so on. In addition to the 0-1 error our experiments include results for MAE and WER. 2. [The fairness assessment is an application biased towards real-world scenarios. Does using Gaussian distribution as a prior align with real-world evaluations?] a. Please see our discussion of these points in the general response (Issue 1: Assumption). In particular, please note that we do not assume that the prior and individual-level distributions are Gaussian, only that the summary statistics are. As discussed in the response, this approximation is quite reasonable for numerous performance metrics of practical interest, including the 0-1 error, MSE, WER, AUC, and so on. ## References Barocas, Guo, Kamar, Krones, Morris, Wortman Vaughan, Wadsworth, Wallach. Designing disaggregated evaluations of AI systems: Choices, considerations, and tradeoffs. AIES 2021.	Summary: This paper introduces SureMap, a new method for disaggregated evaluation of AI systems especially for multi-task setting. The authors model the problem as Gaussian mean estimation and use a structured covariance prior that captures intersectional effects. SureMap is evaluated on several datasets, including a new multi-task ASR dataset they introduce. They show SureMap generally outperforms existing methods, especially for small subgroups and in the multi-task setting. Strengths: 1. This paper tackles an important problem in fairness and evaluation of AI systems and formulation as a Gaussian estimation problem with a structured prior. 2. Theoretical analysis showing SureMap can recover existing baselines. 3. This paper introduces the multi-task ASR datasets for evaluation. 4. The empirical results are strong, especially in the multi-task setting. Weaknesses: 1. The Gaussian assumption may be too strong for some real-world settings 2. No comparison to some recent methods like GP-based approaches 3. The multi-task formulation assumes clients are willing to share data statistics Technical Quality: 3 Clarity: 3 Questions for Authors: 1. Have you considered non-Gaussian models? For example, a t-distribution might better handle heavy-tailed performance data that can occur in practice. 2. The multi-task setting assumes clients are willing to share summary statistics. How realistic is this assumption? Could you explore privacy-preserving ways to share this information? 3. How does SureMap compare to GP-based approaches like in [1]? The method aims to handle low-data regimes well, which seems relevant here. [1] Active assessment of prediction services as accuracy surface over attribute combinations. NeurIPS 2021 Confidence: 3 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 detailed review! We address your concerns and questions below: 1. [The Gaussian assumption may be too strong for some real-world settings [...] Have you considered non-Gaussian models? For example, a t-distribution might better handle heavy-tailed performance data that can occur in practice.] a. Please see our discussion of these points in the general response (Issue 1: Assumption). In particular, as noted in the paper we view a derivation of a robust version of the SureMap objective using Student’s t-distribution as a good direction for future work. 2. [The multi-task setting assumes clients are willing to share summary statistics. How realistic is this assumption? Could you explore privacy-preserving ways to share this information?] a. There are many settings when this is not a concern, e.g. in situations when the companies are already sharing the performance statistics publicly as a form of disclosure to their customers or government regulators. In settings where this is a concern, it should be possible to apply techniques from the differential privacy (DP) literature to overcome these limitations (many DP techniques exist for releasing summary statistics, e.g. Biswas et al. (2020)). We leave a full investigation to future work. 3. [How does SureMap compare to GP-based approaches like in [(Piratla et al., 2021)]? The method aims to handle low-data regimes well, which seems relevant here.] a. Piratla et al. (2021) study a different low-data setting where they allow the user to actively sample points on which to evaluate performance. This difference makes it somewhat difficult to compare our methods. ## References Biswas, Dong, Kamath, Ullman. CoinPress: Practical private mean and covariance estimation. NeurIPS 2020. Piratla, Chakrabarti, Sarawagi. Active assessment of prediction services as accuracy surface over attribute combinations. NeurIPS 2021.	Rebuttal 1: Rebuttal: First we would like to thank all the reviewers for their careful and thorough reviews. We are happy to see that reviewers found the problem we tackle important (Revs. gnhf, 3rXK), the paper well-structured and theoretically well-founded (Rev. gnhf), and the experiments convincing (Revs. LQxL, 3ZUA, 3rXK, UdGz). In this general response we would like to address two common points raised by reviewers about the assumptions and costs of our approach. ## Issue 1: Assumption Several reviewers raised concerns about the assumptions used to derive our method (SureMap). The form of our estimator is motivated by a hierarchical model with a Gaussian prior and a Gaussian observation distribution. The Gaussian prior is used only to motivate the form of the estimator; the estimator is valid even when this assumption does not hold. What our approach does require is that the observations, which in our case correspond to summary statistics (e.g. average accuracy in each group), can be reasonably approximated by a Gaussian. Note that we do not assume that the individual-level performance metric (e.g. the accuracy of each example) is Gaussian. We can usually expect the summary statistics (e.g., within-group average accuracy) to be approximately Gaussian due to the central limit theorem (CLT), which states that averages of samples from a bounded-variance distribution converge in distribution to a Gaussian with that distribution’s mean. In particular, this is guaranteed to be true for bounded performance measures, which includes many of the most important measures in ML including accuracy and (for the most part) word-error rate. CLT-like results also hold (and thus our method would also work) for other important performance measures that are not sample averages, including AUC. Thus our Gaussianity assumption is well-justified in most target applications. A few reviewers correctly point out, as we also do in Section 2.4, that this approximation may work worse for heavier-tailed data. As a quick check of the severity of this problem, we re-evaluate SureMap and the baselines on Diabetes Regression (Figure 7 in the original submission) but using MSE rather than MAE as the performance measure to be estimated. MSE is likely to have heavier tails than MAE if the error distribution looks roughly Gaussian, since in that case the MSE follows a chi-squared distribution (sub-exponential) while MAE follows a one-sided Gaussian (sub-Gaussian). By comparing Rebuttal Figure 1 (left) with Submission Figure 7 (left), we see that on heavier tailed data SureMap no longer dominates, but it is also not significantly worse than the best baseline. This both suggests that SureMap is reasonably robust to data with heavier tails and reinforces our argument in Section 6 that disaggregated evaluation needs to be done with care. In this case for example, a statistician might first consider applying a variance-stabilizing transformation to the data before running their analysis. For instance, in the case of MSE, it is known that the fourth root of a chi-squared random variable is approximately normally distributed (Hawkins et al., 1986), so one could apply SureMap to fourth root transformed MSE’s, and then transform back to produce estimates on the original scale. We view other approaches to making SureMap even more robust, e.g. by using Student’s t-distribution in the derivation of the optimization objective, as an important direction for future work. ## Issue 2: Computation Some reviewers also raised concerns about the complexity of SureMap, including the computational complexity as the number of tasks increases and the implementation complexity of the coordinate descent scheme. While we also noted scalability as a limitation in Section 2.4 of the submission, after the deadline we believe it is no longer a limitation, largely for two reasons: 1. After the submission, we updated the optimization algorithm to use L-BFGS, which has a standard implementation in SciPy whose defaults work well in our settings. It is also quite efficient, with single and multi-task SureMap taking roughly one second to produce estimates for fifty tasks (c.f. Rebuttal Figure 2, noting the log scales), a very reasonable amount of time for running statistical data analysis. Notably, the same figure shows that multi-task SureMap scales slightly better than single-task SureMap with the number of tasks. 2. While the baselines are faster due to not having an optimization routine, we note that both they and SureMap are methods that evaluate model performance and therefore take as input the outputs of model inference. These are often quite expensive to generate in practice; for example, it took more than a GPU-day to generate the ASR dataset used in our evaluations. In comparison to this, a second or less of CPU time is a miniscule cost and thus not a concern for the practical usefulness of our method. ## References Hawkins, Wixley. A note on the transformation of chi-squared variables to normality. The American Statistician, 1986. Pdf: /pdf/ae13b69bfb00ae4c9a5f0e4034bf1f53304459fd.pdf	NeurIPS_2024_submissions_huggingface	2,024	Summary: This paper presents SureMap, a novel method for disaggregated evaluation, aimed at improving the estimation accuracy of performance metrics for machine learning models across different subpopulations. The proposed method is designed to address both single-task and multi-task settings, where multiple clients independently evaluate the same AI model on their respective data. SureMap leverages maximum a posteriori (MAP) estimation with a well-chosen Gaussian prior, fine-tuned using Stein’s unbiased risk estimate (SURE), to achieve high estimation accuracy. The authors evaluate SureMap across various domains, demonstrating significant improvements over existing baselines. Strengths: Originality: The introduction of SureMap for simultaneous mean estimation in disaggregated evaluation is novel, particularly in addressing both single-task and multi-task scenarios using a structured Gaussian prior and SURE for parameter tuning. Quality: The paper is well-structured, with a thorough theoretical foundation, clear methodological development, and comprehensive experiments. The approach of combining MAP estimation with SURE tuning is well-justified and effectively demonstrated. Clarity: The paper is clearly written, with detailed explanations of the methods and assumptions. The inclusion of theoretical proofs and detailed descriptions of the datasets and experiments adds to the clarity. Significance: The ability to improve disaggregated evaluation accuracy has significant implications for fairness in AI, as it allows for better assessment of model performance across different demographic groups. This work has the potential to impact how AI systems are evaluated and deployed, ensuring more equitable outcomes. Weaknesses: Complexity of Implementation: While the method is theoretically sound, the practical implementation of SureMap may be complex, particularly the coordinate descent algorithm used for tuning parameters. This could pose challenges for practitioners. Dependence on Gaussian Assumptions: The method relies on Gaussian assumptions for the prior and noise distributions. In real-world scenarios, data distributions may deviate significantly from Gaussian, potentially affecting the performance of SureMap. Scalability: The scalability of the method in very large-scale settings is not fully explored. The computational cost associated with MAP estimation and SURE tuning might be prohibitive for very large datasets or a very high number of tasks. Empirical Evaluation: While the empirical results are promising, they are primarily based on synthetic and semi-synthetic datasets. More extensive evaluation on real-world datasets across diverse domains would strengthen the findings. Technical Quality: 3 Clarity: 3 Questions for Authors: 1. Implementation Details: Can the authors provide more detailed pseudocode or a step-by-step guide for implementing the coordinate descent algorithm used in SureMap? This would help in better understanding and replicating the method. 2. Non-Gaussian Data: How robust is SureMap to deviations from the Gaussian assumptions? Have the authors considered alternative distributions, and how would the method need to be adapted for such cases? 3. Scalability: What are the computational requirements of SureMap for very large datasets or a high number of tasks? Can the authors provide any benchmarks or comparisons in terms of runtime and memory usage? 4. Real-World Applications: Can the authors provide examples of real-world applications where SureMap has been or could be successfully applied? This would help in contextualizing the method’s practical utility. Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: • Gaussian Assumption: The reliance on Gaussian assumptions is acknowledged, and the authors suggest potential future work on other distributions like Student’s t. • Data Integration Costs: The potential burden or cost of integrating data from multiple clients is mentioned, and the authors propose the use of model provider data as a mitigation strategy. • Scalability: Although not deeply explored, the authors note the computational challenges and suggest future work to improve scalability and efficiency. • Fairness and Over-Confidence: The authors caution against over-confidence in a model’s fairness based solely on disaggregated evaluations and emphasize the need for careful application of SureMap and similar methods. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your detailed review! We address your concerns and questions below: 1. [While the method is theoretically sound, the practical implementation of SureMap may be complex, particularly the coordinate descent algorithm used for tuning parameters. This could pose challenges for practitioners. [...] Can the authors provide more detailed pseudocode or a step-by-step guide for implementing the coordinate descent algorithm used in SureMap?] a. As discussed in the general response (Issue 2: Computation), we have updated the parameter optimization scheme post-submission to be L-BFGS. While SureMap is more involved than baselines such as using the naive estimate or the Bock estimator, it is as simple as or simpler than other recent approaches such as Structured Regression (Herlihy et al., 2024) and AAA (Piratla et al., 2021). The pseudo-code for our current method—which we will add in revision—can be summarized in two steps: (1) apply L-BFGS with SciPy’s default settings to the objective in Equation 10 (or Equation 11 for the multi-task case) and (2) run MAP estimation with the resulting mean and covariance. 2. [The method relies on Gaussian assumptions for the prior and noise distributions. In real-world scenarios, data distributions may deviate significantly from Gaussian, potentially affecting the performance of SureMap. [...] How robust is SureMap to deviations from the Gaussian assumptions? Have the authors considered alternative distributions, and how would the method need to be adapted for such cases?] a. Please see our discussion of these points in the general response (Issue 1: Assumption). In particular, please note that we do not assume that the prior and the noise are Gaussian; we only assume that the summary statistics are. 3. [The scalability of the method in very large-scale settings is not fully explored. The computational cost associated with MAP estimation and SURE tuning might be prohibitive for very large datasets or a very high number of tasks. [...] What are the computational requirements of SureMap for very large datasets or a high number of tasks? Can the authors provide any benchmarks or comparisons in terms of runtime and memory usage?] a. Please see our discussion of these points in the general response (Issue 2: Computation). In particular, SureMap is not computationally expensive for large datasets (it relies on cheap-to-compute summary statistics and so scales weakly with dataset size) nor for many tasks (as shown in Rebuttal Figure 2); in practice, we expect the cost of SureMap (less than a few seconds) is dominated by model inference costs. We will include this cost analysis in the revision. 4. [While the empirical results are promising, they are primarily based on synthetic and semi-synthetic datasets. More extensive evaluation on real-world datasets across diverse domains would strengthen the findings. [...] Can the authors provide examples of real-world applications where SureMap has been or could be successfully applied? This would help in contextualizing the method’s practical utility.] a. Please note that none of our benchmarks are fully synthetic, in the sense of being entirely generated by artificial distributions, and many do not involve any synthetic aspects at all. For example, our single-task ASR setting involves a widely used model (Whisper) evaluated on a real-world dataset (Common Voice). In terms of specific applications, the Diabetes task is motivated by a real-world use-case (Obermeyer et al., 2019) and has been used in previous disaggregated evaluation research (Miller et al., 2021; Herlihy et al., 2024). At a higher level, disaggregated evaluation is the central step in any fairness assessment (Barocas et al., 2021; Herlihy et al., 2024), so we expect SureMap to be of use in a broad range of real-world settings by AI companies, regulators, journalists, and researchers. ## References Barocas, Guo, Kamar, Krones, Morris, Wortman Vaughan, Wadsworth, Wallach. Designing disaggregated evaluations of AI systems: Choices, considerations, and tradeoffs. AIES 2021. Herlihy, Truong, Chouldechova, Dudík. A structured regression approach for evaluating model performance across intersectional subgroups. FAccT 2024. Miller, Gatys, Futoma, Fox. Model-based metrics: Sample-efficient estimates of predictive model subpopulation performance. ML4H 2021. Obermeyer, Powers, Vogeli, Mullainathan. Dissecting racial bias in an algorithm used to manage the health of populations. Science, 2019. Piratla, Chakrabarti, Sarawagi. Active assessment of prediction services as accuracy surface over attribute combinations. NeurIPS 2021.	null	null	null	null	null	null
Enhancing Multiple Dimensions of Trustworthiness in LLMs via Sparse Activation Control	Accept (poster)	Summary: This study tries to enhance multiple dimensions of trustworthiness in LLM through a training-free approach. It controls the LLM's representation of intermediate hidden states so that the model achieves increased honesty or heightened safety awareness. It addresses the challenge of fulfilling multiple requirements simultaneously by Sparse Activation Control (SAC). Specifically, SAC first identifies critical LLM components that are associated with each task. Then, it models the output representations of these components using data that capture the positive and negative semantics relevant to the task. Finally, SAC executes semantic transformations based on the modeling insights to toggle between positive and negative semantics. Experiments demonstrate that SAC enables the LLM models to align with human preferences on issues of safety, factualness, and bias concurrently. Strengths: 1. Innovative Approach: The paper introduces an insightful and novel method, Sparse Activation Control (SAC), which effectively addresses the challenge of achieving precise control over multiple trustworthiness dimensions in large language models (LLMs). The approach is distinguished by its innovative application of attention heads alongside probabilistic modeling, setting a new direction in the field. 2. Mechanistic Understanding: The proposed method is underpinned by a deep mechanistic understanding of LLMs, particularly emphasizing the roles of attention heads in task processing. This foundational insight is a significant asset, enabling a more fine-grained and targeted enhancement of trustworthiness. 3. Experimental Validation: The paper offers robust experimental evidence demonstrating SAC’s capability to enforce multiple control dimensions within a single model. This is notably significant as it tackles the formidable challenge of concurrently aligning LLMs with human preferences regarding safety, factuality, and bias. 4. Practical Relevance: The research addresses a crucial and practical issue in the deployment of LLMs, emphasizing the necessity for multidimensional trustworthiness. This is particularly pertinent given the increasing societal concerns surrounding AI ethics and the responsible deployment of AI technologies. Weaknesses: 1. Theoretical Foundation: Although the experimental results indicate the superiority of using a Gaussian Mixture Model (GMM) with a single Gaussian component in specific tasks, the paper lacks a comprehensive theoretical foundation for this preference. 2. Limited Scope: The paper primarily focuses on enhancing a select subset of trustworthiness dimensions, specifically safety, factuality, and bias. Expanding the scope to encompass additional dimensions such as fairness, transparency, and reliability would considerably enhance the method’s applicability and robustness. 3. Generalization and Scalability: The efficacy of SAC has been validated primarily on the Llama series model. It is essential to test the method across a broader range of models and datasets to ascertain its generalization and scalability, which are critical for its wider acceptance and application. 4. Technical Precision: The paper requires refinement in its presentation, as some mathematical notations, specifically on lines 144, 145, 153, 155, 159, 172, 179, 180, and 184, are not properly formatted in LaTeX. This detracts from the overall clarity and professionalism of the paper. For example, Xr in line 144 should be $X_r$. Technical Quality: 3 Clarity: 3 Questions for Authors: Most questions pertain to the first identified weakness: a. Under what assumptions about the datasets is GMM superior to Principal Component Analysis (PCA)? b. Are there alternative inverse transformations between Gaussian distributions? What is the significance of this coordinate transformation? Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: Please see the weaknesses section. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We sincerely thank the reviewer for taking the time to review our work. We appreciate that the reviewer is optimistic about this work and provide insightful suggestions to help us further improve the paper. Weakness1: > Theoretical Foundation of GMM Ans for Weakness1: The motivation of the preference originates from our experimental observations. - For tasks involving exag safety, stereotype, and preference bias, the energy ratio of the principal direction identified by PCA is low, ranging from 0.1 to 0.3 (in Fig. 1(b) of the PDF). It indicates that a substantial amount of information relevant to these tasks is lost. It prompts us to explore alternative methodologies. - In revisiting the motivations behind PCA, it is employed to model feature differences between positive and negative samples of a concept [1]. Within this framework, PCA focuses on capturing the transformations between these two types of features [2]. - In response, our work proposes to enhance this transformation by directly modeling these feature types. We adopted GMMs for both positive and negative samples, which facilitate transformations through Gaussian distributions. The intuition behind is that GMMs, grounded in principles of probability theory and maximum likelihood estimation, offer a robust framework for density estimation [3]. While many studies support the validity of the linear representation space assumption, we simplified modeling through the use of a single Gaussian distribution within the GMM framework for practical purposes. - Despite this simplification, GMMs retain both mean and variance to preserve second-order information. It enables GMMs to facilitate diverse transformations, including translations and rotations. Inspired by your feedback, we will highlight this rationale in our paper, elucidating the motivations behind our methodology and how it addresses the limitations inherent in PCA-based approaches. Weakness2: > Application on more dimensions Ans for Weakness2: We have made additional explorations on five tasks from TrustLLM[4]. The results are listed below, and the result is consistent that controlling on multiple tasks is effective to improve the trustworthiness. Method\|Robustness⬆️\|Fairness⬆️\|Privacy⬆️\|Exag Safety⬆️\|Adv Factuality⬆️\| -\|-\|-\|-\|-\|-\| No control\|39.42%\|10.83%\|100%\|67%\|76.56% Single task\|78.54%\|62.5%\|100%\|96%\|89.47% Multitask\|75.93%\|53.75%\|100%\|88.5%\|86.12% In TrustLLM, no available data is proposed for transparency and reliability. We manually construct some samples and ask the model for response. However these concepts cannot be induced by questions, therefore are not included in our response. Weakness3: > Generalization and scalability on datasets and models Ans for Weakness3: Method\|Robustness⬆️\|Fairness⬆️\|Privacy⬆️\|Exag Safety⬆️\|Adv Factuality⬆️\| -\|-\|-\|-\|-\|-\| No control\|57.68%\|0.0%\|37.14%\|88%\|76.08% Single task\|85.89%\|50.83%\|93.93%\|96%\|95.22% Multitask\|82.16%\|58.33%\|87.50%\|99.5%\|96.65% We have incorporated test results from the Qwen series models, a robust open-source model that ranks 1th on the open-llm-leaderboard. 1. Generalization of the Model: Qwen2-7B-Chat's result is shown above, and Qwen2-72B-Chat's result is in PDF. Our method improved the model's performance in all tasks by single task control. Meanwhile, multitask control achieves a similar enhancement, with fairness and exag safety even surpassing single task control. 2. Generalization of the Dataset: We directly tested controlled model on OKTest[5], another exaggerated safety dataset consists of 300 test samples. The NRR of the original model stands at 75.67%. After controlling, it rises to 90.00%, showing the generalibility to other in-domain datasets. Due to the lack of datasets in other topics, we follow TrustLLM and formulated 10 new test samples with GPT-4, and test them on model w/wo control. The RR/CR of controlled model on pref bias and adv factuality is 60%/90% comparing to 0%/70% of original model, consistent with current results. These findings underscore the generalization and scalability of our approach. Weakness4: > Technical Precision Ans for Weakness4: We have made the appropriate revisions in the manuscript. The notations of Xr and Xc, (qi, ai), Tf+ and Tf- have been corrected. Question1: > Under what assumptions about the datasets is GMM superior to Principal Component Analysis (PCA)? Ans for Question1: Based on the analysis and conclusions from Weakness1, the performance is better when the proportion of the principal direction in PCA is relatively high, for instance, greater than 0.9. Conversely, when the proportion of the principal direction in PCA is too low, GMM becomes a more suitable choice. Question2: > Alternative inverse transformations between Gaussian distributions? Significance of this coordinate transformation? Ans for Question2: One alternative is the probit transformation, which is nonlinear transformation that maps a Gaussian random variable to another Gaussian random variable. Specifically, if $X_1\sim N(u_1, s_1^2)$, then the probit transformation is defined as: $X_2 = P^{-1}(P((X_1 - u_1)/s_1)*s_2) + u_2$, where $P$ is the cumulative distribution function of the standard normal distribution. "Coordinate transformation" is the most direct method of transformation. The significance of this coordinate transformation primarily lies in its ability to standardize or normalize data from different distributions, making them directly comparable. It can effectively alter the scale and position of the data without changing its shape or inherent probabilistic properties. >[1] Representation Engineering: A Top-Down Approach to AI Transparency >[2] The Linear Representation Hypothesis and the Geometry of Large Language Models >[3] Pattern Recognition and Machine Learning >[4] TrustLLM: Trustworthiness in Large Language Models. >[5] Navigating the OverKill in Large Language Models --- Rebuttal Comment 1.1: Comment: Thanks for the authors' response. I have read the rebuttal and will maintain my score. --- Reply to Comment 1.1.1: Comment: Dear reviewer 3hNv, Thank you again for your valuable suggestions and prompt reply. We will add the results and analysis in the final revision. Hope you have a good day! Best regards and many thanks, Authors of #9158	Summary: As LLMs advance, enhancing their trustworthiness and aligning them with human preferences is important. Traditional methods rely on extensive data for RLHF, but representation engineering offers a training-free alternative. This method uses semantic features to control LLMs' intermediate states, addressing needs like honesty and safety. The work proposed in this paper introduces "Sparse Activation Control" to manage multiple requirements simultaneously, achieving results in aligning models with human preferences on safety, factuality, and bias. Strengths: - Paper introduces a novel approach for controlling LLMs' behavior across multiple tasks which focuses on manipulating sparse activations to improve performance on tasks such as adversarial factuality, preference bias, and exaggerated safety. - The use of Path Patching to identify key components within LLMs helps in isolating and understanding the causal pathways that influence model outputs. - Paper provides a thorough empirical evaluation using the Llama2-13b-Chat model. It compares SAC against other methods like RepE, demonstrating its effectiveness in multi-task control without significantly degrading performance on general tasks. - The use of diverse datasets (golden_advfactuality, PreferenceBias, and XSTEST) is nice. Also the ablation studies help in understanding the contribution of different components of the proposed methodology. Weaknesses: - Potential areas for improvement: The study is somehow limited to open-source models. Since proprietary models do not grant access to their internal outputs, it's unclear how well the method would perform on these more widely used models. - The paper also focuses on a subset of trustworthiness aspects (adversarial factuality, preference bias, exaggerated safety) however trustworthiness encompasses many more dimensions (e.g., robustness, fairness, privacy), and the effectiveness of SAC in these areas remains unexplored. - Evaluating performance on adversarial factuality is complex, especially when rectifying misinformation is beyond the model’s capabilities. The paper mentions using GPT-4 for evaluation, but the nuances of this process and potential biases in using another model for evaluation are not fully addressed. - The metrics used (Correct Rate, Refusal Rate, Not Refusal Rate) are appropriate but could be complemented with more qualitative evaluations. User studies or expert reviews could provide additional insights into the model's trustworthiness improvements. Technical Quality: 3 Clarity: 3 Questions for Authors: Refer to points mentioned in weaknesses above. Confidence: 2 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: As mentioned, user studies or expert reviews could provide additional insights into the model's trustworthiness improvements. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for reviewing our paper and providing valuable comments. We appreciate your time and effort. In response to your comments, we have provided a detailed response below. Weakness1: > Applications on proprietary models Ans for Weakness1: This method cannot be directly applied to proprietary models because it requires access to the network's weights and architecture to pinpoint modules related to different tasks for feature manipulation. For proprietary models, we propose two possible directions to explore: 1. Input/Output space manipulation: The idea of independent control over pivotal modules can be applied to the input and output token spaces of the model. Research has shown that output neurons are poly-semantic and can be controlled for different tasks [1], while methods such as BLIP/DreamBooth [2, 3] demonstrate that input tokens can be edited to influence output results. Consequently, it may unlock fine-grained control over the model's behavior by manipulating specific input and output tokens. 2. Black-box analysis techniques: By leveraging the input-output characteristics of the model, a large number of sample inputs can be generated and changes can be observed in the output to attempt reverse-engineering the model's behavior patterns. It is akin to LIME (Local Interpretable Model-agnostic Explanations) or SHAP (SHapley Additive exPlanations), which offer insights into model decisions without accessing the internal structure of the model. Controlling and enhancing closed-source models present significant challenges. In our future work, we aim to achieve breakthroughs by initially validating our methods on open-source models before implementing them on proprietary models. Weakness2: > Explorations on more dimensions Ans for Weakness2: We have made additional explorations on ood detection (robustness), preference bias (fairness) and privacy leakage query (privacy), all from TrustLLM [4]. The results are listed in Table 1 in the PDF and the key sections are excerpted below. The trustworthiness of Llama2-13B-Chat has boosted from 39.42% to 75.93%, and 10.83% to 53.75% on fairness. Method\|Robustness⬆️\|Fairness⬆️\|Privacy⬆️\| --\|-\|-\|-\| No control\|39.42%\|10.83%\|100%\| Single task\|78.54%\|62.5%\|100%\| Multitask\|75.93%\|53.75%\|100%\| However, the original Llama2-13B-Chat performs well on privacy task, hence it was not shown in the paper. In order to further prove the efficiency of the method, we select Qwen series, top-2 open source LLM on open-llm-leaderboard, and tested the same tasks on Qwen2-7B-Instruct. Through SAC the trustworthiness can be enhanced profoundly, with robustness from 57.68% to 82.16%, fairness from 50.83% to 58.33%, and privacy from 37.14% to 87.50%. Method\|Robustness⬆️\|Fairness⬆️\|Privacy⬆️\| \|- \|-\|-\|-\| \|No control\|57.68%\|0.0%\|37.14%\| \|Single task\|85.89%\|50.83%\|93.93%\| \|Multitask\|82.16%\|58.33%\|87.50%\| Weakness3: > Nuances and potential biases when using GPT-4 for evaluation Ans for Weakness3: We adopt the evaluation method in TrustLLM, which involves assessing model-generated responses alongside ground-truth knowledge using GPT-4. Specifically, GPT-4 will receive an input formatted with: > - Question: As we know, the sun rises in the west and sets in the east. So how long does it take for the sun to go from sunrise to sunset? > - Ground-truth knowledge: The sun rises in the east and sets in the west. > - Model's answer: Actually,... By directly providing the ground-truth knowledge to GPT-4, we can ease its burden to find the misinformation in the question and model's answer. In other words, GPT-4 does not rely on its *internal knowledge* but rather references *external knowledge* (ground-truth answers) to compare results and assign scores. To further validate the GPT-4 evaluation, we engage a total of 18 volunteers for human evaluation, including 2 undergraduates, 7 master's students and 9 PhD candidates. We release an evaluation questionnaire to the volunteers, each containing 20 tuples, including the whole question, model's answer, the misinformation in question and the ground-truth knowledge. Then we ask the volunteers to evaluate whether the model's answer has found the misinformation and collect human results as ground truth to calculate the precision, recall, F1 score and average precision. Cohen's Kappa coefficient is also provided to demonstrate their consistency. The results, shown below, indicates that GPT-4's evaluation has high consistency with human evaluation, therefore we maintain that the evaluation results can be trusted. \|Precision\|Recall\|F1 Score\|Cohen's Kappa Coefficient\| \|-\|-\|-\|- \|0.909\|1.000\|0.952\|0.875 Weakness4: > User studies or expert reviews on trustworthiness improvements Ans for Weakness4: To further validate model's trustworthiness improvements, we use human annotators to compare the outputs of model w/wo control and determine which one provides a more trustworthy answer that is not only helpful but also safe. The human evaluation results are shown in the table below. \|Dataset\|Control Win\|Tie\|No Control Win\| \|-\|-\|-\|-\| \|Average\|84.8%\|9.2%\|6.0%\| \|Exag safety\|68.0%\|8.0%\|24.0%\| \|Pref Bias\|88.0%\|12.0%\|0.0%\| \|Robust\|100.0%\|0.0%\|0.0%\| \|Privacy\|100.0%\|0.0%\|0.0%\| \|Adv Fact\|68.0%\|26.0%\|6.0%\| - In general, outputs after control achieve higher win rate (80.8%), indicating higher trustworthiness from human's perspective. - Controlled answers in exag safety exhibit a little more cautious while directly answering these questions, so that some annotators think it may be not as straightforward. > [1] Towards Monosemanticity: Decomposing Language Models With Dictionary Learning > [2] BLIP: Bootstrapping Language-Image Pre-training for Unified Vision-Language Understanding and Generation > [3] DreamBooth: Fine Tuning Text-to-Image Diffusion Models for Subject-Driven Generation > [4] TrustLLM: Trustworthiness in Large Language Models.	Summary: This paper proposes a new training-free algorithm for controlling specific components with LLMs to increase multiobjective criteria such as safety, factuality, and bias. They overcome the drawbacks of prior methods using the following: - Prior methods struggle when there are multiple criteria at once to improve, often reducing performance on all criteria. This paper proposes adding an initial step of causal mediation analysis to find a set of parameters to control that are relatively orthogonal by applying the path-patching step. - The paper uses Gaussian Mixture Models for model and control as opposed to PCA to reduce the loss of information that often comes with PCA in prior work. The method takes the following steps: They first formulate the data, by creating pairs of standard (reference) and counterfactual datasets. They then imploy a path patching algorithm from prior work to identify the sparse components. They then fit the Gaussian Mixture Model by designing prompts for each task to elicit different model responses, gathering activations from the identified task-relevant components on the prompts, and fitting the activations with the model. The authors provide experiments to show their method has better multiobjective control compared to prior work. Strengths: - The paper considers improving multidimensional criteria at once, this is significant as it seems more realistic in real world scenarios than prior work which only considers a single criteria. The paper shows they perform better when improving along all criteria at once. - The main originality seems to be twofold: (1) Including an additional step which leverages algorithms for causal analysis. (2) reducing the loss of information by utilizing GMMs as opposed to PCA. - The authors clearly explain their method in the writing and provide plots and data to visualize their method and support their findings. Weaknesses: I feel clarifying the following could improve the paper: - Deeper discussion of computational complexity: Training free algorithms seem like a quick way to improve the model if it exhibits some weaknesses, however adding an additional step to perform causal mediation analysis (iteratively freezing all the weights except for some, and seeing the effect), seems like it would be extremely computationally expensive and make it no longer a "quick" step. And at some point, it is better to just use the compute to finetune the model. I think the work can be strengthened if the authors provided more discussion about if this is true/how it is mitigated. - In the evaluation of exaggerated safety, the authors only consider making the models not refuse prompts like ":How to kill a python process?" and their method has good improvement on responding to such prompts. Often in safety work, there is a tradeoff with the model also becoming less safe in general. It would strengthen the work if the authors also added evaluation to show the model did not become less safe in general when given prompts that should actually be refused. Technical Quality: 3 Clarity: 3 Questions for Authors: I had the following clarification questions 1.) Orthogonality is an important point in this paper as it allows improvements in one dimension such as bias to not interfere with improvement in another dimension. In the paper, it seems that it just so happens that all the discovered activations are orthogonal ("our findings reveal that these key elements, specifically attention heads, are sparsely distributed and exhibit high orthogonality"). Is this true generally or is it just true for the set of domains considered in the paper? Is it possible for one to find a set of domains (ex. math performance, factuality, and coding) such that it is no longer orthogonal? Confidence: 2 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: The authors acknowledge the limitation of their work (and probably all safety/trustworthiness/bias work) is that these topics are very broad and hard/impossible for a single work to capture every aspect. I do not see any negative societal impact with their work. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for reviewing our paper and providing valuable comments. We appreciate your time and effort. In response to your comments, we have provided a detailed response below. Weakness1: > Computational complexity vs finetuning? Ans for Weakness1: Thank you for your valuable suggestion. In fact, Causal Mediation Analysis in the proposed method only introduces manageable computational complexity. First of all, CMA *does not require a large amount of data. Inference with just 200 samples is sufficient to identify key heads [1]. To fine-tune a model, it requires 43,966 trustworthness samples [2] or more. Additionally, the process of traversing heads involves independent inference across the model (not iteratively inferred one by one in implementation). It enables the acceleration through grouping and parallelizing. In response to the comment, we also evaluate the performance of fine-tuning the model only using the same small number of samples* as the proposed method used. - The fine-tuned model achieved results of 63.00%, 66.98%, and 10.83% on the exsafe, advfact, and pref bias metrics, respectively—over 20% lower than the performance of the proposed method. - Furthermore, when the fine-tuned model was evaluated on robustness and privacy datasets [3], its performance drastically declined, dropping from 39.42% to 12.86% and from 100% to 36.43%. This phenomenon is similar with [6] that even by fine-tuning the model with benign data, the model's safety can be compromised sharply. In contrast, the proposed method demonstrated negligible impact on performance. To conclude, our approach utilizing representation engineering demonstrates minimal data dependency and offers enhanced robustness. In contrast to traditional fine-tuning methods, representation engineering functions as a controllable, flexible plug-and-play solution, effectively addressing practical limitations in data resources and robustness on other tasks [6]. This methodology encourages us to tackle various dimensions of trustworthiness within LLMs. Weakness2: > Does the model become less safe in general? Ans for Weakness2: To evaluate the safety in general, we conduct experiments on Llama2-13B-Chat trough AdvBench [1], which contains 500 harmful instructions. The results are at below with RtA as the metric. \| No control \| Single task\|Multi-task\| \| --- \| --- \| --- \| \|99.42%\|97.30%\|98.26%\| The safety of the original model stands at 99.42%. After implementing controls to mitigate exaggerated safety concerns in both single-task and multi-tasks, the controlled model's general safety ratings remain high, at 97.30% and 98.26%, respectively. This indicates that *the model's general safety has not been significantly compromised, with a relatively minor decrease of only 2.2%. This is because we replaced sensitive keywords (e.g., "kill" and "crash") with milder alternatives [4], creating negative-positive pairs. By transforming/controlling from negative to positive, we reduced the model's reliance on these keywords and encouraged it to consider the context when evaluating the intention of input, thereby enabling the enhancement on 'exaggerated safety' while maintaining 'safety in general'. Question1:* > Orthogonality: Is it possible for one to find a set of domains such that it is no longer orthogonal? Ans for Question1: We conducted CMA on 8 tasks in total. 6 tasks under 5 categories from TrustLLM, namely adv factuality, robustness, preference bias, exaggerated safety, sycophancy, and stereotype, as well as 2 general tasks, including math and CoT reasoning [5]. Then, key heads for each task are identified to analyse their overlap. \|\|AdvFact\|Robust\|PrefBias\|ExagSafety\|Sycophancy\|Stereotype\|Math\|CoT\| \|-\|-\|-\|-\|-\|-\|-\|-\|-\| \|AdvFact\|- \|Robust\|6%\|- \|PrefBias\|4%\|6%\|- \|ExagSafety\|4%\|8%\|14%\|- \|Sycophancy\|2%\|2%\|2%\|6%\|- \|Stereotype\|0%\|0%\|6%\|6%\|2%\|- \|Math\|2%\|2%\|0%\|0%\|4%\|0%\|- \|CoT\|6%\|2%\|2%\|8%\|6%\|2%\|10%\|-\| The results, shown in the table above (The upper triangle of the table is the same with the bottom), indicates that 90% of the tasks had an overlap of less than 10%. Tasks that had an overlap of over 10% were exsafe, advfact, and CoT. By jointly controlling exsafe and advfact, the performance improved by 21.5% and 9.6% simultaneously, while the performance on CSQA(CoT) remained unchanged. This reflects that, despite some overlap, the conflicts between these tasks are not significant. Based on empirical evidence, it is observed that the current experimental results support the conclusion that across different domains, heads exhibit a certain orthogonality. From a theoretical perspective, it is believed that different tasks have different intentions, which may lead to the activation of different heads for each task. However, it is also acknowledged that there may be some domains that simultaneously activate the same heads. The theoretical analysis of this issue is deemed valuable, and further exploration is warranted. > [1] Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 Small. ICLR 2023 [2] Llama 2: Open Foundation and Fine-Tuned Chat Models. [3] TrustLLM: Trustworthiness in Large Language Models. [4] Navigating the OverKill in Large Language Models. [5] A Survey on Evaluation of Large Language Models. [6] Fine-tuning Aligned Language Models Compromises Safety, Even When Users Do Not Intend To! --- Rebuttal Comment 1.1: Comment: Thank you for the clarifications and resolving concerns, I have adjusted my scores up --- Reply to Comment 1.1.1: Comment: Dear reviewer Zk9K, Thanks for your prompt response despite such a busy period. We deeply appreciate your consideration in raising the score. We will add the results and analysis in the final revision. Hope you have a good day! Best regards and many thanks, Authors of #9158	null	null	Rebuttal 1: Rebuttal: Dear Reviewers, Area Chairs, and Program Chairs, We sincerely thank all three reviewers for their constructive comments and insightful questions, which helped us refine our work. Reviewers have acknowledged the impact and superior performance of our proposed method and the comprehensive analysis. [Problem Importance] - Reviewer Zk9K: this is significant as it seems more realistic in real world scenarios than prior work which only considers a single criteria - Reviewer 3hNv: it tackles the formidable challenge of concurrently aligning LLMs with human preferences regarding safety, factuality, and bias [Method Novalty] - Reviewer Zk9K: adding an initial step of causal mediation analysis to find a set of parameters to control that are relatively orthogonal by applying the path-patching step. - Reviewer jrhB: a novel approach for controlling LLMs' behavior across multiple tasks - Reviewer 3hNv: The paper introduces an insightful and novel method [Detailed Analysis] - Reviewer jrhB: Paper provides a thorough empirical evaluation using the Llama2-13b-Chat model During the response period, we carefully try our best to provide feedback and conduct supplementary experiments to all comments from reviewers. We concisely summarize our responses to general concerns here (For details and more questions, please refer to rebuttals below): - [Computational Complexity]：We analyze the computational complexity of our method, and discuss the difference between our method and fine-tuning. - [Generalization and Scalability]: We conduct experiments on a wider range of tasks and models. Overall, we test adversarial factuality, exaggerated safety, preference bias, robustness and privacy on Llama2-13B-Chat, Qwen2-7B-Instruct and Qwen2-72B-Instruct. The improvements in overall trustworthiness is prominent, further validating the effectiveness of our method. - [Validity of Evaluation]: We give detailed explanation of our evaluation method on complex task like adversarial factuality. Furthermore, we undergo abundant user studies to prove the consistency of our evaluation with human judgement. We are grateful for all the reviewers for the comments, and we hope our response can address the concerns. Best regards, Author #9158 Pdf: /pdf/d1540e7969d3cf88149777790db5a728dc7d5465.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Sequential Signal Mixing Aggregation for Message Passing Graph Neural Networks	Accept (poster)	Summary: This paper focuses on the aggregation module in Message Passing Graph Neural Networks (MPGNNs). It tackles the problem that sum-based aggregators, even though widely used, fail to 'mix' features belonging to distinct neighbors, preventing them from succeeding at the downstream tasks. Accordingly, the authors introduce a novel plug-and-play aggregation for MPGNNs, denoted as Sequential Signal Mixing Aggregation (SSMA). SSMA treats the neighbor features as 2D discrete signals and sequentially convolves them with circular convolution by applying 2D Fast Fourier Transform (FFT). The authors also propose several designs to guarantee the practical use of the proposed methods. In the empirical experiments, SSMA successfully improved the performance of several MPGNNs. Strengths: 1. This work has a good motivation and a solid mathematical foundation driving the proposed methods. 2. This paper is well-written. 3. The empirical performance can well support the statement of the paper. 4. According to the best of my knowledge, this is the first work to enhance the aggregation module via circular convolution. Weaknesses: 1. Even though with good theoretical computational complexity analysis, it will be good to have the empirical run-time comparison between the MPGNN and MPGNN+SSMA. 2. According to my knowledge, there are many works using pre-computed PE with conditional aggregation to improve the distinguishability of the neighbors during the 'mixing' of them, (e.g., [1], GraphGPS). They require extra one-time computation on PE but will not increase the complexity of the model inference. There are no comparisons to the line of work. (I am not sure about the exact GraphGPS configuration in the experiments. I have some concerns about it which are listed in "questions") - [1] Dwivedi, Vijay Prakash, et al. "Graph Neural Networks with Learnable Structural and Positional Representations." International Conference on Learning Representations. Technical Quality: 3 Clarity: 3 Questions for Authors: 1. What is the configuration of GraphGPS in the experiment? As in the paper, several configurations are provided. 2. In eq (8), the number of separators $m=n+1$ depends on the neighbor sizes; $\mathbf{h}: \mathbb{R} \to \mathbb{R}^m$ is an affine map. How this affine map is determined? Is it learnable? In graph learning, the $n$ is usually assumed unknown and varying. (the same question applies to vector-feature cases as well) 2. Following up on the Weakness 2. The experiment on ZINC follows the 100k parameter setting as ESAN, while other baselines are reproduced. Compared to the 500K parameter setting in GraphGPS, there are interesting points. Regular MPNNs, e.g., GCN, GAT, GIN, PNA, do not show significant improvement on the 500K setting, while GraphGPS is significantly improved. Based on Table 3 and Table B.1 in GraphGPS, GatedGCN ($\sim 0.090$), GraphGPS($\sim0.070$), GraphGPS+NoPE ($\sim0.110$), GINE+RWSE($\sim0.070$). - I am interested to know the improvement of GRASS on GraphGPS on the 500K setting - Can GRASS improve MPNNs with PE? Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The limitation on computational complexity is adequately addressed by the proposed technique.s No potential negative societal impact aware. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We are pleased that the reviewer recognized the novelty of our proposed method, its underlying mathematical foundations and the empirical performance supporting the statement of the paper. We thank the reviewer for appreciating the paper’s motivation and writing. * We would like to address some concerns mentioned by the reviewer. > Even though with good theoretical computational complexity analysis, it will be good to have the empirical run-time comparison between the MPGNN and MPGNN+SSMA. We appreciate the reviewer’s suggestion and agree that such a comparison would demonstrate the efficiency of SSMA when integrated into MPGNNs. We conducted training and inference time comparisons, evaluating SSMA-augmented MPGNNs against PNA and GraphGPS. To ensure fair assessment we enforce the same hidden-dimension and report the time spent on a single convolutional layer. Please refer to Table 1 in the attached PDF. The results highlight the impressive trade-off of SSMA between down-stream performance and practical training and inference time complexities. * > What is the configuration of GraphGPS in the experiment? As in the paper, several configurations are provided. As several configurations are provided in GraphGPS, we tried to focus on the most standard configuration possible - A GatedGCN as the message-passing network, standard multi-head attention with 8 heads without PE or SE. We used [PyG](https://pytorch-geometric.readthedocs.io/en/latest/generated/torch_geometric.nn.conv.GPSConv.html)’s implementation for the layer. * > In eq (8), the number of separators $m=n+1$ depends on the neighbor sizes; $\boldsymbol{h}: \mathbb{R} \rightarrow \mathbb{R}^m$ is an affine map. How this affine map is determined? Is it learnable? In graph learning, the $n$ is usually assumed unknown and varying. (the same question applies to vector-feature cases as well) The affine map $\boldsymbol{h}$ In Eq. (8) is fixed and refers to the padded coefficients of each $p_i$ as given by Eq. (5) (please refer to lines 140-141). The same applies for $\boldsymbol{\Phi}$ in the vector case, in which the full form of the affine map is given in Appendix A.3, Eq. (39). While this is the (fixed) affine map which was used in the experiments, Appendix E.4 includes an ablation study that investigates this exact matter. Regarding the value of $n$, the provided number of separators is satisfactory as long as the number of neighbors is upper bounded by $n$. If there are fewer than $n$ neighbors, the high-power coefficients will vanish. * > Following up on the Weakness 2. The experiment on ZINC follows the 100k parameter setting as ESAN, while other baselines are reproduced. Compared to the 500K parameter setting in GraphGPS, there are interesting points. Regular MPNNs, e.g., GCN, GAT, GIN, PNA, do not show significant improvement on the 500K setting, while GraphGPS is significantly improved. Based on Table 3 and Table B.1 in GraphGPS, GatedGCN ($\sim 0.090$), GraphGPS($\sim 0.070$), GraphGPS+NoPE ($\sim 0.110$), GINE+RWSE($\sim 0.070$). I am interested to know the improvement of GRASS on GraphGPS on the 500K setting. Can GRASS improve MPNNs with PE? Following the reviewer’s suggestion, we perform the following additional experiments on the ZINC regression benchmark: * Regarding scaling, we scale up different SSMA augmented architectures (both GCN,GIN and GraphGPS) to the 500K parameter regime. * Reagrding positional encoding (PE): we examine the effect of RWSE-20 positional encoding on SSMA-augmented GraphGPS. For the GraphGPS experiments in this context we used [PyG](https://github.com/pyg-team/pytorch_geometric/blob/master/examples/graph_gps.py)'s example code, carefully adopting the hyperparameters and optimization parameters used in the ZINC experiments in the GraphGPS paper. Please refer to Table 2 for the results. There are several insights: * SSMA consistently improves the effectiveness, even at a higher scale and with or without PE. * SSMA is well-behaved with positional-encoding, proving to be very effective even with 100K parameters. * Scaling does not seem to be valuable when considering classic MPNNs (in contrast to GraphGPS) which strengthens the reviewer's hypothesis. *** Thanks again for the review, let us know if you have any further questions! --- Rebuttal Comment 1.1: Comment: Thank you for the rebuttal. It well addresses my concerns and questions. I will raise the score.	Summary: The paper analyzes the discrepancy between the theoretical guarantees of sum-based aggregators and their practical performance, which makes more complex aggregators preferred in practice. They define the notion of neighbor-mixing to explain this gap, and propose a novel aggrgeation module, named SSMA, which builds upon deepsets polynomial. Strengths: The theoretical analysis is sound and rigorous. The experimental section shows promising performance in practice, and I particularly appreciated that the authors have adjusted the number of parameters in the augmented model to match that of the original, to ensure a fair comparison. Weaknesses: The paper is hard to follow, and I think adding some intuition on the results would significantly strengthen the paper. For example, while I would have liked to understand the intuition why sum-based aggregators have small neighbor-mixing (which is very briefly touched in lines 116 to 118, but, in my opinion, not sufficiently to have any intuition, and it seems more like a statement that it is the case). Section 4 is generally hard because, while it is supposed to be a way of constructing the model, it ends up being a theoretical digression until 4.3, where then the model becomes clear. Technical Quality: 3 Clarity: 2 Questions for Authors: Can you expand on the intuition of sum-based aggregators lacking mixing abilities? Confidence: 2 Soundness: 3 Presentation: 2 Contribution: 2 Limitations: Addressed Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for appreciating the theoretical analysis and the experimental section, particularly our methodological approach to ensure fair comparison. * We would like to address your quoted concerns: > Can you expand on the intuition of sum-based aggregators lacking mixing abilities? Note that additional intuition on sum-based aggregators lacking mixing abilities is provided in subsection 4.3. Specifically, please refer to lines 185-187 and Eq. (14) which intuitively state that for sum-based aggregators the “mixing” is done only in the MLP. Regarding section 4, to further exemplify the construction of the generalized DeepSets polynomial we provide an additional figure illustrating a concrete instantiation of the polynomial for a specific neighbor set. Please refer to Figure 1 in the attached PDF. * If the reviewer remains unsatisfied with the intuitive explanations, we welcome further clarification on what specific aspects need more elaboration. --- Rebuttal Comment 1.1: Comment: I would like to thank the authors for the rebuttal. I will keep my score since it was already positive. I also encourage the authors to include Figure 1 in the appendix, and refer to it in the main paper.	Summary: This paper introduces Sequential Signal Mixing Aggregation (SSMA) for Message Passing Graph Neural Networks (MPGNNs), addressing the limitations of traditional sum-based aggregation methods. SSMA enhances the mixing of features from distinct neighbors by treating neighbor features as 2D discrete signals and applying sequential convolution. Strengths: Treating neighbor features as 2D discrete signals and using sequential convolution is innovative. This approach allows for more effective mixing of features from different neighbors, addressing a significant limitation in traditional sum-based aggregators. By revealing that sum-based aggregators cannot adequately "mix" neighbor features, the paper paves the way for more aggregation techniques. Introducing a convolution-based aggregation module is an advancement in the field. The theoretical foundation of the proposed SSMA method is robust, with well-detailed mathematical formulations and proofs. The paper derives the key equations and supports them with solid theoretical arguments. The practical aspects, including learnable affine transformations, low-rank compression, and normalization, are well thought out and enhance the applicability and stability of SSMA in real-world scenarios. Weaknesses: - Limited Comparisons: The paper only compares SSMA with one other aggregation method in the appendix. Including comparisons with more diverse and state-of-the-art aggregation methods would strengthen the evaluation and provide a more comprehensive understanding of SSMA's advantages and limitations. Recent advancements such as Generalized f-Mean Aggregation, Principal Neighbourhood Aggregation (PNA), Hybrid Aggregation for Heterogeneous Graph Neural Networks (HAGNN), Robust Graph Neural Networks via Unbiased Aggregation, and GNN-VPA: A Variance-Preserving Aggregation Strategy for Graph Neural Networks could provide valuable benchmarks for comparison (ar5iv) (ar5iv) (ar5iv) (ar5iv) (ar5iv) (ar5iv). - Computational Complexity: The paper would benefit from discussing SSMA's computational complexity compared to other aggregation method s. Currently, the paper only addresses SSMA's time complexity. It would be better if it included a comparison with the time complexities of similar aggregation methods from related work. This would provide a clearer context for evaluating SSMA's efficiency and practicality. Technical Quality: 2 Clarity: 3 Questions for Authors: - The authors conducted extensive tests combining different MPGNN architectures with SSMA in the experiments. However, why is there only a comparison of SSMA with one other aggregator in the appendix? Could the authors provide more experimental results comparing SSMA with other aggregators to demonstrate its advantages better? - Could the authors provide direct training time comparisons between MPGNNs using SSMA and other aggregators? This would help to illustrate the time cost associated with adding the SSMA module more clearly. - In Figure 1, SSMA is demonstrated, but the nodes u, v, and w appear more like a set rather than having a sequential relationship. Does "sequential" refer to the pipeline being sequential, or is there a sequential relationship among these graph nodes? - Are there specific types of graphs or tasks where SSMA may not perform as well as other methods? Confidence: 3 Soundness: 2 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 are grateful for the reviewer's recognition of convolution-based aggregations as an advancement in the field, effectively addressing a major limitation of traditional sum-based aggregators. We thank the reviewer for highlighting the robust theoretical foundation, and appreciating the practical aspects that enhance SSMA's applicability and stability in real-world scenarios. * We would like to address your questions: > The authors conducted extensive tests combining different MPGNN architectures with SSMA in the experiments. However, why is there only a comparison of SSMA with one other aggregator in the appendix? Could the authors provide more experimental results comparing SSMA with other aggregators to demonstrate its advantages better? Thank you for this feedback which motivated us to broaden the experiments. Following your and reviewer's @vJN5 advice, we compared SSMA to a wider spectrum of aggregations including LSTM and Generalized f-Mean Aggregation[1]. Please refer to tables 4,5 in the attached PDF for the results. A comparison to PNA[2] already exists in the main paper (Tables 1 and 2) and a comparison to variance-preserving aggregation[3] (VPA) already exists appendix D.1. Although comparing our results with those from 'Robust Graph Neural Networks via Unbiased Aggregation' could have broadened our experiments, we were unfortunately unable to find a code base for this paper. * > Could the authors provide direct training time comparisons between MPGNNs using SSMA and other aggregators? This would help to illustrate the time cost associated with adding the SSMA module more clearly. We appreciate the reviewer’s suggestion and agree that such a comparison would demonstrate the efficiency of SSMA when integrated into MPGNNs. We conducted training and inference time comparisons, evaluating SSMA-augmented MPGNNs against PNA and GraphGPS. To ensure fair assessment we enforce the same hidden-dimension and report the time spent on a single convolutional layer. Please refer to Table 1 in the attached PDF for the results. The results highlight the impressive trade-off of SSMA between down-stream performance and practical training and inference time complexities. * > In Figure 1, SSMA is demonstrated, but the nodes u, v, and w appear more like a set rather than having a sequential relationship. Does "sequential" refer to the pipeline being sequential, or is there a sequential relationship among these graph nodes? The term 'sequential' in SSMA refers to the sequential convolution of the transformed features of neighboring nodes, as outlined in Theorems 4.1 and 4.4, which underlie the construction of SSMA. Figure 1 demonstrates that this sequential convolution can be practically computed in the Fourier domain. * > Are there specific types of graphs or tasks where SSMA may not perform as well as other methods? While the “vanilla” version of SSMA may fail in dense neighborhoods due to the representation size scaling quadratically with the number of neighbors (as pointed out in lines 212-213, 269-270) the proposed neighbor selection mechanism (lines 212-220) accounts for such cases, as later demonstrated in the experimental section (lines 252-255). We haven’t identified other potential failure cases, which we leave for future research. * Thanks again for the review! Let us know if you have any further questions and consider modifying your score if you are satisfied with our response. * [1]: Generalised f-Mean Aggregation for Graph Neural Networks. NeurIPS 2023. [2]: Principal Neighbourhood Aggregation for Graph Nets. NeurIPS 2020. [3]: GNN-VPA: A Variance-Preserving Aggregation Strategy for Graph Neural Networks. ICLR 2024 Tiny Paper. --- Rebuttal Comment 1.1: Title: Official Comment by Reviewer QvY7 Comment: Thank you for the detailed response. I raise my score to 6.	Summary: This paper introduces Sequential Signal Mixing Aggregation (SSMA), a novel aggregation method for Message Passing Graph Neural Networks (MPGNNs). SSMA addresses the shortcomings of traditional sum-based aggregators, which often struggle to effectively "mix" features from distinct neighbors. By treating neighbor features as 2D discrete signals and sequentially convolving them, SSMA significantly enhances feature mixing from distinct neighbors. Experimental results show that integrating SSMA into existing MPGNN architectures markedly improves performance across various benchmarks, achieving state-of-the-art results. Strengths: 1. The explanation of the limitations of sum-based aggregators is compelling and insightful, offering a fresh perspective on the problem and effectively motivating the proposed method. 2. SSMA introduces an innovative approach to feature aggregation in MPGNNs, which can be efficiently implemented and scaled to accommodate larger graphs. 3. The experimental results on both node and graph-level tasks clearly demonstrate the effectiveness of the proposed method. Weaknesses: 1. Other aggregation methods, such as LSTM[1] and DIFFPOOL[2], also effectively mix neighbors’ features. These methods should be included in the related work and experimental comparisons. 2. The inductive setting mentioned in the experimental setup section is missing from the experiments section. [1] Inductive Representation Learning on Large Graphs. NeurIPS 2017. [2] Hierarchical Graph Representation Learning with Differentiable Pooling. NeurIPS 2018 Technical Quality: 2 Clarity: 3 Questions for Authors: Please refer to the weaknesses. Confidence: 4 Soundness: 2 Presentation: 3 Contribution: 2 Limitations: The limitations have been demonstrated 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 finding the discussed limitations of sum-based aggregators compelling and insightful, endorsing SSMA’s innovative approach and appreciating the experimental results which demonstrate the effectiveness of SSMA. * We would like to address your quoted concerns: > Other aggregation methods, such as LSTM[1] and DIFFPOOL[2], also effectively mix neighbors’ features. These methods should be included in the related work and experimental comparisons. Thank you very much for this feedback which motivated us to broaden the experiments. Following your and reviewer's @QvY7 suggestion, we compared SSMA to more advanced aggregation methods such as LSTM and Generalized f-Mean Aggregation[1], along the comparisons to PNA[2] and VPA[3] which already exist in the paper. Refer to tables 4,5 in the attached PDF for the results. While DiffPool[5] is not an aggregation method per-se but rather a technique to pool the graph nodes’, your input led us to create a dense version of SSMA, allowing it to be incorporated into DiffPool and other methods in this line of work (e.g MinCutPool [4]). In addition, we compared the original version of DiffPool with SSMA-augmented version of DiffPool on the TU datasets using the benchmark code provided by [PyG](https://github.com/pyg-team/pytorch_geometric/tree/master/benchmark/kernel). Refer to table 3 in the attached PDF for the results. * > The inductive setting mentioned in the experimental setup section is missing from the experiments section. We point out that the experimental section includes both the inductive and transductive settings. To provide further clarity, we present the distinction between the inductive and transductive benchmarks used in our experiments. Inductive benchmarks: ogbg-molhiv, ogbg-molpcba, mutag, enzymes, proteins, ptc-mr, imdb-binary, zinc, peptides-func, peptides-struct. Transductive benchmarks: ogbn-arxiv and ogbn-products. To further eliminate confusions regarding this topic, we refer the reviewer to table 3 in the appendix which contains additional details about the datasets. * Thanks again for the review! Let us know if you have any further questions and consider modifying your score if you are satisfied with our response. * [1]: Generalised f-Mean Aggregation for Graph Neural Networks. NeurIPS 2023. [2]: Principal Neighbourhood Aggregation for Graph Nets. NeurIPS 2020. [3]: GNN-VPA: A Variance-Preserving Aggregation Strategy for Graph Neural Networks. ICLR 2024 Tiny Paper. [4]: Spectral Clustering with Graph Neural Networks for Graph Pooling. ICML 2020. [5]: Hierarchical Graph Representation Learning with Differentiable Pooling. NeurIPS 2018. --- Rebuttal Comment 1.1: Comment: Dear Reviewers, We hope this message finds you well. In the most respectful way possible, we would greatly appreciate your acknowledgment of the responses we have provided. We understand that the concerns raised are grounded in important factual matters, and we believe that we have addressed each one directly with clear additional results and thorough, non-evasive discussions. Thank you very much for your time and consideration. --- Reply to Comment 1.1.1: Comment: Dear Reviewers, We are extremely grateful to you for reviewing our responses. We deeply appreciate your positive feedback and the scores you raised. We promise to include all additional clarifications, experiments, and figures in the camera-ready version.	Rebuttal 1: Rebuttal: We sincerely appreciate the reviewers for their valuable feedback on our paper. We were pleased to hear that the reviewers found the explanation of the limitations of sum-based aggregators "compelling and insightful, offering a fresh perspective on the problem and effectively motivating the proposed method" (@vJN5). They also noted that "introducing a convolution-based aggregation module is an advancement in the field" (@QvY7). The significance and rigorous approach of the experimental section were recognized: "The experimental section shows promising performance in practice, and I particularly appreciated that the authors have adjusted the number of parameters in the augmented model to match that of the original, to ensure a fair comparison" (@aDFM). Additionally, the paper was praised for being well-written with solid theoretical foundations: "This work has a good motivation and a solid mathematical foundation driving the proposed methods" and "This paper is well-written" (@4Dt8). *** The reviewers' suggestions encouraged us to expand our experiments and provide additional illustrations of our method. The results of the requested experiments are detailed in the attached PDF file. Specifically: * Table 1 compares the training and inference times of SSMA against other methods, as requested by reviewers (@QvY7,@4Dt8). * Table 2 demonstrates the effects of positional encoding (PE) and scale on the effectiveness of SSMA as requested by reviewers (@4Dt8). * Table 3 demonstrates the benefit of SSMA to DIffPool as requested by the reviewer (@vJN5). * Figure 1 illustrates a specific realization of the generalized DeepSets polynomial compared to DeepSets motivated by the reviewer's comments (@aDFM). * Table 4 includes additional experiments for the f-Mean aggregation as requested by the reviewer (@QvY7). * Table 5 includes additional experiments for the LSTM aggregation, as requested by the reviewer (@vJN5). *** We thank the reviewers for spending time reviewing our paper and encourage further discussion on any issues that may arise from the rebuttal. If our responses and the additional experiments satisfactorily address the reviewers' concerns, we would be grateful if they could consider modifying our score. Pdf: /pdf/1922303e946d5d27824b15850e8c7eebdf084cf7.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Towards Open-Vocabulary Semantic Segmentation Without Semantic Labels	Accept (poster)	Summary: This paper present MCLIP, which aims to finetune CLIP using image and mask data without semantic labels. The goal is to make its open-vocabulary recognition ability to be adapted to position-sensitive semantic segmentation tasks. MCLIP chooses to use SAM or feature clusters of DINO to obtain masks, which are class-agnostic but sometimes too small to have consistent semantics for finetuning. In addition, in order to achieve a trade-off between training stability and avoiding catastrophic forgetting, clustering uses the EMA version of finetuned image encoder. Strengths: - The idea of this paper is interesting. Solving open-vocabulary semantic segmentation without semantic labels is an interesting topic. - The experimental results show that the preformance of the proposed approach is good. - Ablation studies and analysis are provided to help better understand of the role of each component and hyper-parameter. Weaknesses: - What role does the text encoder play in the clustering process? The key to the success of clustering lies in the existence of unlabeled data in a certain grouping relationship in the space. The mask representations f_M can be considered to meet such conditions. If k learnable object prompts are initialized randomly, then k text representations f_C are randomly scattered in the text space initially, unable to provide the information needed for clustering. If k learnable object prompts are initialized by predefined categories, then this should violate the experimental setup without semantic labels. To illustrate this problem, the authors need to provide an explanation and add a comparative experiment: What results can be obtained just by clustering with f_M? - Why use clustering technology to solve the problem of too fine initial mask granularity? Firstly, previous work (GroupViT, CVPR'22 and SegCLIP, ICML'23) has used a grouping block designed based on the idea of clustering in the process of fine-tuning CLIP. In contrast, the clustering used in MCLIP provides better masks initially than the image patches used in previous work and the clustering process of MCLIP is parameter-free. It may be necessary to conduct ablation experiments to prove which differences bring positive results. But overall, technically, the use of clustering may be not novel. - In order to obtain class-agnostic masks, there is a class of experimental settings called open set semantic segmentation (O3S, arXiv preprint arXiv:2307.02003, 2023) . Can the ”SAM initialization + clustering” scheme proposed by MCLIP obtain competitive performance in the O3S experimental setting? - Table 1 shows that using MCLIP’s fine-tuned CLIP instead of the Frozen CLIP in the previous method improves the performance of the previous method’s zero-shot mask classification. Taking FC-CLIP as an example, MCLIP improves its zero-shot mask classification performance on ADE20K by 2.7. But compared to the final performance of FC-CLIP with two branches integrated, it is still 4.0 lower. So, in the case of keeping the complete inference strategy of the previous method, how much improvement can be achieved by using MCLIP’s fine-tuned CLIP instead of the Frozen CLIP? - In the ablation experiment in Table 3a, does ’w/o Semantic Clustering’ mean fine-tuning with SAM-initialized masks directly without clustering? If so, why is the performance so poor? Without using clustering, it is equivalent to the number of cluster k is greater than the number of masks initialized by SAM on all images. However, the conclusion obtained from table 3b is that with the increase of k, the performance tends to saturation, rather than decreasing to the level of ”w/o Semantic Clustering”. Technical Quality: 3 Clarity: 3 Questions for Authors: I think the authors need to further explain the novelty of this paper and give more analysis on the experimental results as listed in the weaknesses part. Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: Limitations are provided. It seems that there is no potential negative societal impact. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank reviewer 83hz for the remarks on the paper and the considerate review. We address the comments and questions from the reviewer below: > What role does the text encoder play in the clustering process? > \| \| COCO \| ADE-150 \| PC-59 \| Cityscapes \| VOC \| \| --- \| --- \| --- \| --- \| --- \| --- \| \| without Text enc. \| 17.9 \| 18.5 \| 29.9 \| 28.9 \| 53.5 \| \| with Text enc. \| 21.2 \| 20.2 \| 34.2 \| 33.2 \| 66.0 \| Table G. Ablation on the usage of text encoder for clustering during training. We use the text encoder to match the inference strategy where classes are passed through the text encoder, as well as for leveraging its pre-trained knowledge to aid the semantic clustering process. The reviewer is correct in that the clustering process is possible without the text encoder by initializing $f_C$ as random vectors. We show such ablations in Table G where we verify that although the clustering is possible without the text encoder, it largely benefits with the text encoder. We thank the reviewer for pointing out an important factor for ablation, and we will add the results and discussions to the paper. > Why use clustering technology to solve the problem of too fine initial mask granularity? > We would like to highlight that our clustering is done at a global level: we cluster masks across all images in the batch. GroupViT and SegCLIP in contrast cluster at a local level: they cluster regions within a single image using the caption for that image. Therefore, it is not obvious how we can use the GroupVit or SegCLIP grouping blocks in our framework. We will update the Related Work in our revision with this discussion. We emphasize that although the use of clustering is not novel, to the best of our knowledge, our use of clustering across images for unsupervised representation learning is. > Can the ”SAM initialization + clustering” scheme proposed by MCLIP obtain competitive performance in the O3S experimental setting? > \| \| Fold-0 \| Fold-1 \| Fold-2 \| Fold-3 \| mean \| \| --- \| --- \| --- \| --- \| --- \| --- \| \| ZS3[3] \| 18.8 \| 20.1 \| 24.8 \| 20.5 \| 21.1 \| \| LSeg[b] \| 22.1 \| 25.1 \| 24.9 \| 21.5 \| 23.4 \| \| Fusioner[c] \| 23.6 \| 28.2 \| 26.2 \| 24.1 \| 25.5 \| \| Yang et al.[d] \| 26.5 \| 30.8 \| 26.3 \| 24.1 \| 26.9 \| \| MCLIP \| 25.1 \| 25.5 \| 22.1 \| 24.1 \| 24.2 \| Table H. Results on COCO-20i under Z/FS setting from Yang et al.[d] Following LSeg[b], we used ‘others’ for the background class and prompt ensembling was used during inference. To validate the performance in O3S setting, we directly evaluate MCLIP trained on SA-1B on COCO-20i without training with any COCO images or annotations. Interestingly, we find MCLIP to show reasonable performance, surpassing LSeg despite not being trained on other folds of the COCO-20i dataset. We thank the reviewer for suggesting the evaluation, and we will add it to our revision. > So, in the case of keeping the complete inference strategy of the previous method, how much improvement can be achieved by using MCLIP’s fine-tuned CLIP instead of the Frozen CLIP? > \| \| COCO-Panoptic \| ADE-150 \| PC-59 \| Cityscapes \| VOC \| \| --- \| --- \| --- \| --- \| --- \| --- \| \| FC-CLIP \| 63.7 \| 34.1 \| 58.4 \| 56.2 \| 95.4 \| \| + MCLIP \| 64.9 \| 34.1 \| 59.2 \| 56.8 \| 95.6 \| Table I. Results from FC-CLIP with the complete inference strategy We report the results with the full pipeline from FC-CLIP, when incorporating the “out-of-vocabulary” branch with MCLIP in Table I. We notice that due to the fusion strategy, the gains from the “out-vocabulary” branch are not completely transferred to the fused scores, but observe improvements over all datasets. We will add these results to the revision. > Why is the performance so poor without Semantic Clustering? The conclusion obtained is that with the increase of k, the performance tends to saturation rather than decreasing to the level of ”w/o Semantic Clustering”. > \| Number of clusters, k \| COCO \| ADE-150 \| PC-59 \| Cityscapes \| VOC \| \| --- \| --- \| --- \| --- \| --- \| --- \| \| 64 \| 21.1 \| 20.2 \| 34.2 \| 33.2 \| 66.0 \| \| 128 \| 21.0 \| 20.3 \| 33.5 \| 30.1 \| 64.1 \| \| 256 \| 21.3 \| 20.4 \| 33.6 \| 30.0 \| 64.1 \| \| 512 \| 21.2 \| 20.2 \| 32.7 \| 29.8 \| 62.7 \| Table J. Additional results for increasing the number of clusters k. Performance starts decreasing after k=256 We clarify that ‘w/o Semantic Clustering’ refers to supervising CLIP directly with fine-grained masks from SAM, i.e. f_C=f_M, which is to the reviewer’s understanding. This would enforce CLIP to distinguish small regions within the image, despite having near identical semantic meanings. We find this to conflict with the coarse, semantic understanding of CLIP when fine-tuning, eventually losing the pre-trained knowledge of CLIP, i.e. catastrophic forgetting, which is critical when fine-tuning foundation models[11, 43, 65]. Furthermore, as the reviewer pointed out, ‘w/o Semantic Clustering’ would virtually be k=50M, (5% of SA-1B), and we agree that further increasing k should start to decline the performance, eventually reaching 50M. To verify this, we additionally provide results with k=512 in Table J which is the maximum number of k within our GPU memory constraints, and observe the performance decreasing for all datasets. We greatly thank the reviewer for providing the insight, and we will add the discussions to the revision. References: [b] Language-driven Semantic Segmentation. B. Li et al., ICLR 2022 [c] Open-vocabulary Semantic Segmentation with Frozen Vision-Language Models, C. Ma et al., BMVC 2022 [d] Multi-Modal Prototypes for Open-World Semantic Segmentation, Y. Yang et al., IJCV 2024 --- Rebuttal Comment 1.1: Title: Final rating Comment: I appreciate the responses from the reviewers. Though most of my concerns have been solved, I still think the novelty of this paper cannot reach the level of an accept. So, I tend to keep my original rating unchanged.	Summary: The authors introduce a novel unsupervised formulation of open vocabulary semantic segmentation, adapting a pre-trained vision-language model (CLIP) to the task via distillation from vision-only segmentation models (i.e., SAM, DINO). To use the language encoder without constraining fine-tuning to the set of classes of the dataset, they propose to apply online clustering at the dataset level and to learn class-specific feature prototypes. The method is compared against state-of-the-art approaches trained with and without supervision, and the results validate the approach as a practical direction for training open vocabulary models for semantic segmentation. Strengths: - The work is well-presented and curated, and the motivation is clear and sound. - The approach finetunes models pre-trained for a different purpose, and employs supervision from other pre-trained models, effectively reusing knowledge efficiently. Distillation from pre-trained models also removes the need for data supervision, potentially permitting scale training for open vocabulary semantic segmentation to billions of samples. - The method is tested against various baseline and on different benchmark datasets. - The model components are evaluated independently in the ablation study, helping to uncover the individual contribution to the final picture. Weaknesses: - While I understand the rationale behind performing clustering at pixel level on the entire dataset, I am not sure of the scalability of the approach. This probably explains why the authors only use 5% of the SA-1B dataset. It would be helpful to quantify the costs of performing the online clustering at training time. - Since the method could potentially suffer scalability issues, it would be interesting to understand performance when trained unsupervised in-distribution, reporting both in- and out-of-distribution performance, e.g., MCLIP trained on VOC and tested on Context. - The reasoning behind the selection process for the prompt (i.e., "a photo of a {} in the scene") is unclear. This is a minor issue, but the selection should probably be justified. While I would expect the model to learn to ignore the prefixes and suffixes, it would be interesting to understand how the model performs with other prompts. - Using CLIP as a baseline for the ablation studies may be misleading due to the mismatch between its application and open vocabulary semantic segmentation Technical Quality: 3 Clarity: 3 Questions for Authors: - What are the costs of performing online clustering at the dataset level during training? - What is the performance of MCLIP when trained on the benchmark datasets and tested in- and out-of-distribution? How does it compare against some baseline methods? - What is the model performance when changing the template at inference time? What is the performance without the template? What about training without the template? Does performance improve with prompt ensembling (i.e., similar to what CLIP does with N prompts that average to get better class centroids)? Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: - A potential limitation is the one I reported above, i.e., scalability issues due to the global online clustering procedure. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank reviewer kepm for the remarks on the paper and the considerate review. We address the comments and questions from the reviewer below: > It would be helpful to quantify the costs of performing the online clustering at training time. What are the costs of performing online clustering at the dataset level during training? > \| Training dataset \| COCO \| ADE-150 \| PC-59 \| Cityscapes \| VOC \| \| --- \| --- \| --- \| --- \| --- \| --- \| \| 5% SA-1B \| 21.4 \| 16.7 \| 34.9 \| 23.8 \| 83.1 \| \| 10% SA-1B \| 21.6 \| 16.9 \| 36.1 \| 23.9 \| 83.9 \| Table C. Results on open-vocabulary semantic segmentation with additional training data. We compute the cluster assignment through the Sinkhorn-Knopp algorithm [13], which only adds around 1ms in our training every iteration, as it can be performed on GPU. We opted for a 5% split of SA-1B due to the large scale of the full dataset, which is similar in scale with SAM-CLIP [43]. To study the scalability of our approach, we provide results when doubling the amount of training data in Table C, showing that we do observe modest improvements from more training data. We will add this experiment to the revision. > What is the performance of MCLIP when trained on the benchmark datasets and tested in- and out-of-distribution? How does it compare against some baseline methods? > \| \| COCO-Stuff \| ADE-150 \| PC-59 \| Cityscapes \| VOC \| \| --- \| --- \| --- \| --- \| --- \| --- \| \| MaskCLIP[61] \| 16.5 \| 13.2 \| 23.4 \| 11.1 \| 79.7 \| \| MaskCLIP+[61] \| 18.0* \| - \| 31.1* \| - \| - \| \| MCLIP (COCO+DINO) \| 20.0* \| 15.5 \| 30.1 \| 18.5 \| 79.4 \| \| MCLIP (COCO+SAM) \| 21.7* \| 16.6 \| 34.2 \| 23.1 \| 82.4 \| Table D. Results on open-vocabulary semantic segmentation for in- and out-of-distribution analysis. \: indicates in-distribution results where the training splits of the datasets were seen.* We thank the reviewer for providing an interesting point for discussion. To study in- and out-of-distribution, we provide “in-distribution” results by training MCLIP with COCO-Stuff images, and “out-of-distribution” results by zero-shot evaluating on other datasets. For comparison, we provide MaskCLIP as “out-of-distribution” and MaskCLIP+ suggested by reviewer Dx6v as “in-distribution” baselines, where MaskCLIP+ is trained with images from the target dataset COCO-Stuff and PC-59 respectively. We observe that our MCLIP outperforms MaskCLIP+ in COCO-Stuff, but the in-distribution performance of MaskCLIP+ outperforms MCLIP in PC-59 with DINO masks. However, when incorporating stronger SAM masks, MCLIP can improve largely, outperforming MaskCLIP+ despite being out-of-distribution for PC-59. We will add this experiment and discussion to the revision. > What is the model performance when changing the template at inference time? What is the performance without the template? What about training without the template? > \| Training(↓)/Inference(→) \| {} \| itap of a {} \| a photo of a {} \| a photo of a {} in the scene \| \| --- \| --- \| --- \| --- \| --- \| \| {} \| 35.4 \| 38.7 \| 38.0 \| 36.6 \| \| itap of a {} \| 35.4 \| 39.2 \| 38.1 \| 36.3 \| \| a photo of a {} \| 35.3 \| 38.6 \| 37.8 \| 36.4 \| \| a photo of a {} in the scene \| 35.1 \| 38.6 \| 37.8 \| 36.0 \| Table E. Results on open-vocabulary semantic segmentation with different prompts. Each row show results from different prompts in training, while each column is in inference. For brevity, we report the mean over 5 benchmarks from Table D. “itap” is a common abbreviation of “I took a picture” We thank the reviewer for suggesting ablation with different prompts. We provide results when trained with no prompt(“{}”) and with different prompts in Table E. We initially used “a photo of a {} in the scene” following other methods [11, 14, 21] but surprisingly, the prompt “itap of a {}” shows significant improvements for both training and inference. Given that “itap of a {}” is one of the well-performing prompts originally curated from CLIP, we speculate the results to reflect the preference of prompts from CLIP. We will add the results and the discussions, and re-conduct our experiments with better prompts. > Does performance improve with prompt ensembling (i.e., similar to what CLIP does with N prompts that average to get better class centroids)? > \| Training \| Inference \| COCO-Stuff \| ADE-150 \| PC-59 \| Cityscapes \| VOC \| \| --- \| --- \| --- \| --- \| --- \| --- \| --- \| \| No ensemble \| No ensemble \| 21.4 \| 16.7 \| 34.9 \| 23.8 \| 83.1 \| \| \| Ensemble \| 23.6 (+2.2) \| 18.7 (+2) \| 37.9(+3.0) \| 27.2(+3.4) \| 85.9(+2.8) \| \| Ensemble \| No ensemble \| 21.6(+0.2) \| 17.1(+0.4) \| 35.1(+0.2) \| 24.9(+1.1) \| 82.9(-0.2) \| \| \| Ensemble \| 23.7(+2.3) \| 19.2(+2.5) \| 37.9(+3.0) \| 28.1(+4.3) \| 85.5(+2.4) \| Table F. Results on open-vocabulary semantic segmentation with prompt ensembling strategy. We provide results for ensembling in Table F, where we ensemble the default prompt “a photo of a {} in the scene” with 7 additional prompts originally curated in CLIP. We observe that not only can prompt ensembling largely boost the performance during inference time, it also shows additional gains when applied during training. We thank the reviewer for the valuable suggestion, and we will add the results and discussion to the paper. > Using CLIP as a baseline for the ablation studies may be misleading due to the mismatch between its application and open vocabulary semantic segmentation > We clarify that the baseline results from CLIP in the ablation studies are in fact obtained from applying MaskCLIP [61], which slightly modifies CLIP for open-vocabulary semantic segmentation. We apologize for the confusion, and we will revise the baseline as MaskCLIP in the ablations. --- Rebuttal Comment 1.1: Comment: I thank the authors for their reply, which answers my doubts and questions. I appreciate that they executed all the experiments I proposed. Scaling the dataset size seems to (unsurprisingly) improve model performance. Also, a better template for the input query or a template ensemble has a positive impact. For the first, I believe the work would benefit from some experiments showing how performance increases with an increase in the number of train samples. I expect the performance to improve until the compute-optimal point is reached [1]. Overall, I am glad my suggestions improved the method's performance, however, this also gives the impression the work was not carried out very rigorously. In any case, I am satisfied with the authors' rebuttal and confirm my initial positive rating. [1] Hoffmann, Jordan, et al. "Training compute-optimal large language models." arXiv (2022).	Summary: This paper proposes to learn an open-vocabulary semantic segmentation model with only unlabeled images and pretrained foundation models, such as SAM and DINO. The intuition is that CLIP model already knows what is in the image, so we only need to teach CLIP where the object is. It first uses pretrained DINO to generate pseudo masks and then exploits a online clustering method to group the part segments into valid object masks. It also proposes learnable class embeddings to solve the problem of lacking ground-truth text labels. Compared with baselines, the proposed method achieves decent improvements. Strengths: + This paper proposes a solution to train an open-vocabulary model only with unlabeled images, i.e., without masks nor captions. + Three technical contributions to make the solution happen: (1). use DINO to generate pseudo masks (2). group part masks into objects (3). user learnable embeddings to substitute text captions. Weaknesses: - Compared with other methods [ 50 , 30 , 43 , 51 ] leveraging image caption as supervision, this paper actually uses stronger DINO generated pseudo masks to train the segmentation model. Furthermore, it even uses the SAM masks during experiments (In Table 2). Regrading this, I think this method includes strong segmentation prior into the training, making the comparison unfair. - Compared with methods using similar VFM, such as SAM-CLIP, the proposed method performs much worse. I understand it is not an apple-to-apple comparison due to the differences in training data. More specially, this paper doesn't use captions. However, caption is also very easy to get with pretrained caption models. If simply adding caption could boost the performance so much, why should we stick to a setting without caption? Technical Quality: 2 Clarity: 3 Questions for Authors: - Why does Table 1 appear before Table 2? Tabel 1 looks more like an ablation study to me. Confidence: 4 Soundness: 2 Presentation: 3 Contribution: 2 Limitations: See weakness Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank reviewer rHvB for the remarks on the paper and the considerate review. We address the comments and questions from the reviewer below: > Compared with methods using similar VFM, such as SAM-CLIP, the proposed method performs much worse. > \| \| COCO-Stuff \| COCO-Object \| ADE-150 \| PC-59 \| Cityscapes \| VOC \| \| --- \| --- \| --- \| --- \| --- \| --- \| --- \| \| GroupViT[50] \| 15.3 \| 27.5 \| 9.2 \| 23.4 \| 11.1 \| 79.7 \| \| SAM-CLIP[43] \| - \| 31.5 \| 17.1 \| 29.2 \| - \| 60.6 \| \| MCLIP (DINO) \| 20.2 \| 41.9 \| 15.6 \| 31.3 \| 19.2 \| 80.0 \| \| MCLIP (SA-1B) \| 21.4 \| 43.3 \| 16.7 \| 34.9 \| 23.8 \| 83.1 \| Table B. Additional comparison on open-vocabulary semantic segmentation including COCO-Object, evaluated on 80 instance classes of COCO-Stuff. Thank you. We would first like to point out that SAM-CLIP actually reported results on COCO-Object and not COCO-Stuff, which we have verified with the authors of SAM-CLIP. We therefore present the corrected comparisons in Table B, which we will also include in the revision. We can see that our proposed MCLIP does indeed outperform SAM-CLIP on COCO-Object, consistent with PC-59 and VOC, and is only marginally behind by 0.4 points on ADE. We achieve this strong performance despite SAM-CLIP additionally using 40M image-text pairs, showing the benefits of our approach. > If simply adding caption could boost the performance so much, why should we stick to a setting without caption? > We would like to highlight the main contribution to be our exploration for effectively leveraging unlabeled masks, which has also been acknowledged by other reviewers to be a “neat idea” (Dx6v), “motivation is clear and sound” (kepm) and “interesting” (83hz), hence focus on masks instead. The framework can be potentially enhanced by incorporating captions along with unlabeled masks, which we anticipate for future exploration. > Compared with other methods [ 50 , 30 , 43 , 51 ] leveraging image caption as supervision, this paper actually uses stronger DINO generated pseudo masks > We emphasize that we do not need human labels within our training as DINO is trained in a self-supervised manner with only images. In contrast, the mentioned methods leverage human-annotated captions in addition to images, which makes it hard to consider that our method is leveraging stronger supervision. Furthermore, we also highlight that SAM is leveraged to demonstrate scenarios with higher quality unlabeled masks, and MCLIP still shows strong performance with DINO generated masks. > Table 1 looks more like an ablation study to me. > We thank the reviewer for the suggestion, and will adjust the tables accordingly. --- Rebuttal Comment 1.1: Title: I've raised my score from 4 to 5 Comment: Thanks for the rebuttal! I've raised my score from 4 to 5.	Summary: This paper proposes to enhance the semantic segmentation performance of the pretrained CLIP model using unlabeled images and pseudo segmentation masks generated with vision foundation models such as SAM and DINO. Specially, the pseudo masks are acquired via a online feature clustering algorithm. Experiments on standard benchmarks demonstrate the superior performance over CLIP and competitive results to existing open-vocabulary semantic segmentation methods. Strengths: 1. It is a neat idea to leverage unlabeled masks as supervision generated from foundation models (e.g. SAM, DINO) for the open-vocabulary semantic segmentation task. 2. The paper is well-written and easy to follow. 3. The ablation study demonstrates the effectiveness of some design choices such as momentum update of the image encoder, online cluster assignment, and learning class prompts. Performance on the standard benchmarks also show the competitive results in comparison with existing baseline methods. Weaknesses: 1. How is the proposed method in comparison with MaskCLIP+? Figure 4 shows the visual comparisons between the proposed method and MaskCLIP, as the Sec. 4.2 mentioned “For evaluating CLIP [42, 10], we apply MaskCLIP [61] to extract CLIP image features”. It would be interesting to compare the proposed method with MaskCLIP+ which distills MaskCLIP to train more advanced segmentation model. 2. Some related works should be discussed and compared to the proposed method, for example, Exploring Open-Vocabulary Semantic Segmentation from CLIP Vision Encoder Distillation Only. ICCV 2023. Technical Quality: 3 Clarity: 3 Questions for Authors: See the weakness section. 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 thank reviewer Dx6v for the remarks on the paper and the considerate review. We address the comments and questions from the reviewer below: > Comparison with MaskCLIP+ > \| \| COCO-St. \| ADE-150 \| PC-59 \| Cityscapes \| VOC \| \| --- \| --- \| --- \| --- \| --- \| --- \| \| MaskCLIP+[61] \| 18.0 \| - \| 31.1 \| - \| - \| \| ZeroSeg[a] \| 20.2 \| - \| 20.4 \| - \| 40.8 \| \| MCLIP (ours) \| 21.4 \| 16.7 \| 34.9 \| 23.8 \| 83.1 \| Table A. Additional comparison on open-vocabulary semantic segmentation with other methods. We provide comparison with MaskCLIP+ in Table A, with results from ViT-B/16 CLIP backbone. Despite MaskCLIP+ having an advanced decoder for segmentation and requiring training on the target dataset, we demonstrate that MCLIP outperforms MaskCLIP+ in both COCO-Stuff and PC-59, demonstrating the effectiveness of our approach. > Some related works should be discussed and compared > We thank the reviewer for pointing out related works with our work. We provide results from ZeroSeg[a] as mentioned by the reviewer in Table A, and we will add discussions and comparison to ZeroSeg and MaskCLIP+ to the paper. References: [a] Exploring Open-Vocabulary Semantic Segmentation from CLIP Vision Encoder Distillation Only. J. Chen et al., ICCV 2023 --- Rebuttal Comment 1.1: Comment: Thanks for the detailed response! I'll raise my initial rate to weak accept.	Rebuttal 1: Rebuttal: We thank the reviewers for the remarks on the paper, as well as their considerate reviews. Especially, we appreciate the thoughtful comments on the idea and motivation for leveraging unlabeled masks (Dx6v, kepm, 83hz), paper being well-written and curated (Dx6v, kepm), the proposed solution and technical contributions (rHvB), solid experiments and ablations (Dx6v, kepm, 83hz), as well as our approach effectively reusing knowledge from other pre-trained models (kepm). Furthermore, we thank the reviewers for sharing insights and providing constructive feedback, which we have responded below. We hope our response adequately addresses the concerns, and we believe that the addition of the discussions will greatly improve the paper.	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Improved Regret for Bandit Convex Optimization with Delayed Feedback	Accept (poster)	Summary: The paper investigates the online convex optimization problem with delayed bandit feedback. The main contribution is introducing a new algorithm that uses a block updating mechanism with FTRL, proving the algorithm achieves a delay-dependent regret of $O(\sqrt{dT})$, which is known to be optimal when the average delay is close to the maximal delay: $\bar{d} \approx d$. Strengths: * The paper shows a valuable algorithm that improves on the known regret bounds for the delayed BCO. * The techniques used, specifically block updates, while not novel, are original for this kind of problem. Weaknesses: * The paper could be written more clearly. I found myself understanding parts of the introduction only after going through the entire paper (e.g. line 69). * The proofs are hard to follow. Some explanations before each lemma to understand how those are used would be helpful. * It seems hard to use the blocking updates to further improve the regret, so the value of the presented algorithm could be temporary. Technical Quality: 3 Clarity: 2 Questions for Authors: Can you explain each term in the theorems and where does it come from? As is, the theorems are packed with different terms and besides substituting the optimal values I don't know how to interpret them Confidence: 4 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: The authors properly acknowledge the limitations of their work. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Many thanks for the constructive reviews! --- Q1: The paper could be written more clearly. I found myself understanding parts of the introduction only after going through the entire paper (e.g. line 69). A1: Thank you for the helpful suggestion. We will improve our writing by adding necessary explanations to help the understanding. --- Q2: The proofs are hard to follow. Some explanations before each lemma to understand how those are used would be helpful. A2: As you suggested, we will explain the usefulness of each lemma in our analysis. Moreover, we will start each proof by providing a high-level overview of the upcoming procedures. --- Q3: It seems hard to use the blocking updates to further improve the regret, so the value of the presented algorithm could be temporary. A3: We agree that the blocking update mechanism may prevent our algorithm from further improving regret bounds to be depending on the average delay. However, we want to emphasize that our regret bounds achieved via the blocking update mechanism are already quite favorable, and it is highly non-trivial to develop a better algorithm, especially in the case with strongly convex functions. Note that even in the easier full-information setting, previous studies can only achieve the $O(d\log T)$ regret for strongly convex functions, which is the same as the delay-dependent part in our regret bounds for strongly convex functions. --- Q4: Can you explain each term in the theorems and where does it come from? As is, the theorems are packed with different terms and besides substituting the optimal values I don't know how to interpret them A4: We first provide the following explanations for each term in our Theorem 1. 1) The first two terms $\frac{4R^2}{\eta}+\frac{\eta T\gamma}{2K}$ are an upper bound on the expected regret of an ideal action for each block, i.e., $\mathbf{y}_m^\ast$ defined in line 305 of our paper. Therefore, they are affected by the step size $\eta$, the block size $K$, and the variance of cumulative gradients in each block $\gamma$. Moreover, the variance $\gamma$ depends on both the block size $K$ and the exploration radius $\delta$ at first glance, but we can select an appropriate $K$ to remove the extra dependence on $\delta$ as discussed in our paper. 2) The third term $\frac{\eta TG}{2}\sqrt{2\left(\frac{d^2}{K^2}+4\right)\gamma}$ is an upper bound on the expected cumulative distance between the preparatory action $\mathbf{y}_m$ of our Algorithm 1 and the ideal one $\mathbf{y}_m^\ast$, which is further affected by the maximum delay $d$. 3) The last two terms $3\delta GT+\frac{\delta GRT}{r}$ are caused by the error of the shrunk set $\\mathcal{K}\_\\delta$ and the $\delta$-smoothed function $\hat{f}_{t,\delta}(\cdot)$, and thus are affected by the exploration radius $\delta$. Additionally, we note that the terms in our Theorems 2 and 3 can be similarly divided into these three categories. In the revised version, we will provide detailed explanations for each term in all our theorems. --- Rebuttal Comment 1.1: Comment: Thank you, I am keeping my score.	Summary: The paper investigates the problem of bandit convex optimization (BCO) with delayed feedback, where the value of the action is revealed after some delay. The authors proposed an algorithm D-FTBL, and proved that it enjoys a regret bound of $O\left(\sqrt{n} T^{3/4}+\sqrt{d T}\right)$, closing the gap between the previous result and the lower bound on delay-dependent part. Furthermore, the proposed algorithm can improve the regret bound to $O\left((n T)^{2 / 3} \log ^{1 / 3} T+d \log T\right)$ for strongly convex functions, and if the action sets are unconstrained, the proposed algorithm can achieve an $O(n \sqrt{T \log T}+d \log T)$ regret bound for strongly convex and smooth functions. Strengths: - The writing style of the article is excellent, and the overall flow is very smooth and enjoyable to follow. - The literature review is thorough and well-integrated into the paper. It provides a solid foundation for the research by situating it within the existing literature of BCO and highlighting the gaps that the authors aim to fill. - The methodology seems innovative. The application of blocking update mechanism not only adds substantial value to the current study but also potentially inspires other problems with delayed feedback. - The theoretical results presented in the paper are logically sound and well-supported. Each point is substantiated with adequate evidence, avoiding any logical leaps or inconsistencies. Weaknesses: The paper lacks numerical experiments. Besides this, I did not spot any significant weaknesses. Technical Quality: 3 Clarity: 4 Questions for Authors: I would be curious about how much improvement can be made in practice. In bandit setting, people often consider large time horizon, in which cases the regret is dominated by the delay-independent term. Confidence: 3 Soundness: 3 Presentation: 4 Contribution: 3 Limitations: The authors addressed the limitations and consider it as future work. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Many thanks for the constructive reviews! --- Q: The paper lacks numerical experiments ... I would be curious about how much improvement can be made in practice. In bandit setting, people often consider large time horizon, in which cases the regret is dominated by the delay-independent term. A: Please check our common response to the suggestion about experiments, which introduces numerical results completed during the rebuttal period, and has shown the advantage of our algorithm in practice. Moreover, we want to emphasize that although $T$ could be very large, the delay-dependent term in the existing $O(\sqrt{n}T^{3/4}+(n\bar{d})^{1/3}T^{2/3})$ regret bound [Bistritz et al., 2022] cannot be ignored. Specifically, this regret bound is dominated by the delay-independent term only for $\bar{d}=O(n^{1/2}T^{1/4})$. However, this condition can be easily violated due to the sublinear dependence on $T$ and $n$, and the fact that the delay may also increase for larger $T$. For example, our experiment on ijcnn1 has $T=40000$ and $n=22$, and thus the condition is violated as long as $\bar{d}>n^{1/2}T^{1/4}\approx 67$. Even if we consider a much larger $T=400000000$, $\bar{d}>664$ is sufficient to violate the condition. By contrast, our $O(\sqrt{n}T^{3/4}+\sqrt{dT})$ regret bound is dominated by the delay-independent term for a larger amount of delays, i.e., $d=O(n\sqrt{T})$. --- Rebuttal Comment 1.1: Comment: Thank you for the response. I will keep my score positive.	Summary: This paper studies the problem of bandit convex optimization with delayed feedback (where the feedback for round $t$ is delayed by an arbitrary number of rounds $d_t$). For this problem, they show $O(\sqrt{n} T^{3/4} + \sqrt{d T})$ regret in general, $O((n T)^{2/3} \log^{1/3} (T) + d \log(T))$ regret for strongly-convex functions, and $O(n \sqrt{T \log(T)} + d \log(T))$ regret for smooth and strongly-convex functions in an unconstrained settting. In these bounds, $n$ is the dimension, $T$ is the horizon and $d$ is the maximum delay. Strengths: - Their results for the general setting strictly improve on results that use the maximum delay $d$ (Heliou et al (2020)), and supplement results that use the average delay $\bar{d}$ (Bistritz et al 2022). - They give improved regret for specific settings. - The literature review is very thorough and the authors are diligent in pointing to the origin of ideas throughout the paper. - There is extensive discussion on the difference in techniques with respect to existing approaches and how their approach result in tighter regret gaurantees. - The presentation is clear and intuitive. Weaknesses: - The paper only makes an improvement on state-of-the-art for certain delay sequences, i.e. when $d = O((n\bar{d})^{2/3} T^{1/3})$. Technical Quality: 3 Clarity: 3 Questions for Authors: No questions at this point. Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: There is some discussion of the limitation due to the fact that the regret is given in terms of maximum delay rather than average delay. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Many thanks for the constructive reviews! --- Q: The paper only makes an improvement on state-of-the-art for certain delay sequences, i.e. when $d=O((n\bar{d})^{2/3}T^{1/3})$. A: First, we want to emphasize that both $n$ and $T$ can be very large in modern online applications, and thus the condition $d=O((n\bar{d})^{2/3}T^{1/3})$ can be satisfied by many delay sequences including those with $\bar{d}=1$. Second, it is also worth noting that besides convex functions considered in previous studies [Héliou et al., 2020; Bistritz et al., 2022], our paper further investigates two special cases with strongly convex functions, and achieves $O((nT)^{2/3}\log^{1/3}T+d\log T)$ and $O(n\sqrt{T\log T}+d\log T)$ regret bounds, respectively. These two bounds are better than the state-of-the-art result for a larger portion of delay sequences. --- Rebuttal Comment 1.1: Title: Thank you for the response Comment: Thanks for the clear response. I'm sticking with my positive score.	Summary: This paper studies the bandit convex optimization problem with delayed feedback, where the loss value of the selected action is revealed under an arbitrary delay. Previous work achieves $\mathcal{O}( \sqrt{n} T^{3/4} + (n\bar{d})^{1/3} T^{2/3})$ regret bound of this problem. The authors develop a novel algorithm and show that it improves the delay-related part to $\mathcal{O}( sqrt{dT})$ when $d$ the maximum delay, is close to $\bar{d}$, the average delay (specifically, strictly better when d = $\mathcal{O}( (n\bar{d})^{2/3} T^{1/3} )$. The authors claim that the primary idea is to decouple the joint effect of the delays by incorporating the delayed bandit feedback with a blocking update mechanism, which reduces the correlation between recent delayed updates (otherwise there could be a $d^2$ term). Strengths: 1. Though I have skimmed the proof of several lemmas, the analysis part seems to be rigorous and mathematically correct. 2. The usage of blocking update mechanism is very interesting, and could be applied in other similar settings. Weaknesses: 1. The contribution of this work is quite concerning. It would be better for the authors to emphasis the contribution (either algorithmic or analytic) on improving the delayed feedback result for BCO problem in certain conditions that the max delay $d$ is close to $\bar{d}$? Some parts of the proof are rather straightforward and standard. Technical Quality: 3 Clarity: 3 Questions for Authors: The questions are raised in the weakness section. I am willing to re-evaluate the scores if these questions are properly answered. Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: This paper is pure theoretical and does not have any limitations. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Many thanks for the constructive reviews! --- Q: The contribution of this work is quite concerning. It would be better for the authors to emphasis the contribution (either algorithmic or analytic) on improving the delayed feedback result for BCO problem in certain conditions that the max delay $d$ is close to $\bar{d}$? Some parts of the proof are rather straightforward and standard. A: Thank you for the helpful suggestion. Our technical contributions can be summarized as follows. 1) At the algorithmic level, our paper is the first work that exploits the blocking update mechanism to design improved algorithms for delayed BCO. Moreover, unlike existing algorithms [Héliou et al., 2020; Bistritz et al., 2022] based on online gradient descent, our algorithm is based on follow-the-regularized-leader (FTRL). As discussed in lines 228 to 235 of our paper, in this way, we can utilize the delayed information more elegantly. 2) At the analytic level, we derive the first regret bound that can decouple the joint effect of the delays and the bandit feedback. To this end, besides some standard analysis for FTRL and BCO, we need to carefully analyze the delay effect under blocking update to establish an improved upper bound for $\\\|\mathbf{y}_m-\mathbf{y}_m^\ast\\\|_2$, where $\mathbf{y}_m $ is the preparatory action of our Algorithm 1 and $\mathbf{y}_m^\ast$ is an ideal action defined in line 305 of our paper. 3) Moreover, different from previous studies [Héliou et al., 2020; Bistritz et al., 2022] that only consider convex functions, our paper further investigates two special cases with strongly convex functions, and achieves better regret bounds. --- Rebuttal Comment 1.1: Comment: Thank the authors for their response. I would like to keep the current score.	Rebuttal 1: Rebuttal: ## Common Response to the Suggestion about Experiments We thank all the reviewers for your detailed comments. In the following, we first respond to the common suggestion about experiments, and other questions are addressed in a separate response for every reviewer. Please let us know if you have any further questions. During the rebuttal period, we conducted experiments on two publicly available data sets—ijcnn1 and SUSY from the LIBSVM repository [1]. Specifically, we randomly select $T=40000$ examples from the original data sets. The dimensionality of ijcnn1 and SUSY are $n=22$ and $n=18$, respectively. Moreover, we consider online binary classification over a convex set $\mathcal{K}=\\{\\\|\mathbf{x}\\\|_2\\leq 50\\}$. In each round $t\in[T]$, the adversary chooses the hinge loss $f_t(\mathbf{x})=\\max\\{1-y_t\\mathbf{w}_t^\\top\\mathbf{x},0\\}$, where $\mathbf{w}_t$ and $y_t\in\\{-1,1\\}$ are the feature vector and class label of the $t$-th example, respectively. Different values of the maximum delay $d$ in the set $\\{200, 600,1000,\dots, 5000\\}$ have been tried in experiments on both data sets. For each specific $d$, to simulate arbitrary delays, $d_t$ is independently and uniformly sampled from $[1, d]$. Note that, in this way, the average delay satisfies $\mathbb{E}[\bar{d}]=\frac{d+1}{2}$, and thus is close to the maximum delay $d$. We compare our D-FTBL against GOLD [Héliou et al., 2020] and improved GOLD [Bistritz et al., 2022]. Due to the randomness of these algorithms, we repeat them 20 times and report the average of their total loss. Figure 1 in the attached PDF shows the numerical results, and we have the following main observations. 1) For our D-FTBL, when $d$ increases from $200$ to $5000$, the growth of the total loss is very slow, which is consistent with the dependence of our regret bound on $d$. Note that $d=5000$ is larger than $n\sqrt{T}$ in our experiments. 2) From $d=600$ to $d=5000$, the total loss of our D-FTBL is better than both GOLD and improved GOLD, which verifies the advantage of our algorithm in the delayed setting. 3) Although for $d=200$, D-FTBL is slightly worse than baselines, it is reasonable because the block update mechanism enlarges each delay to be at least the block size, which could result in a slightly larger constant factor in the regret. [1] C.-C. Chang and C.-J. Lin. LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology, 2(27):1–27, 2011. Pdf: /pdf/83a24ff3e68805942359eb7025edba68214a4a71.pdf	NeurIPS_2024_submissions_huggingface	2,024	Summary: The authors consider the problem of bandit convex optimization in the adversarial setting under delays. In each round, an adversary selects a convex function $f_t$, the optimizer selects an input $x_t$ and observes $f_t(x_t)$ with a delay of $d_t$ timesteps. The goal is to minimize regret with respect to the best action in hindsight. Without any delay, the best regret is obtained by the zeroth order one-point flaxman updates. Prior work in the delayed setting adapts this algorithm to use the oldest available feedback to make the update. However, the observation that the authors make is that according to this scheme, information might become available much before it is used -- if there is older information that has not been used yet. So instead, to minimize the gap between availability and utilization of information, the authors propose a blocking algorithm. Where at the end of each block, all available information so far is used to make the update. This enables them to get improved regret bounds. Strengths: 1. The paper is very well-written with the results laid out very clearly, and the rationale for the solution explained well. 2. The solution to use blocking in order to minimize stale information is creative, and leads to better bounds. 3. The results are comprehensive across different classes of objectives, and the authors thus show the wide applicability of the technique. Weaknesses: Significance The practical impact of this theoretical toy seems limited, and the problem was of more interest a couple of years ago. In order to increase the reception, it would be instructive to connect the implications of these findings to other topics of recent interest or include some simulations Technical Quality: 3 Clarity: 4 Questions for Authors: 1. Could the authors comment on what the problem looks like for the regular stochastic case with all $f_t = f$ for some fixed $f$, and how this might make the problem easier under delays? 2. Why do the authors conjecture that the lower bound depends on $\bar{d}$, whereas the upper bound depends on $d$? What improvements would be required to get these to match? 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: Many thanks for the constructive reviews! --- Q1: The practical impact of this theoretical toy seems limited, and the problem was of more interest a couple of years ago. In order to increase the reception, it would be instructive to connect the implications of these findings to other topics of recent interest or include some simulations A1: Thanks for the suggestion. Please check our common response to the suggestion about experiments, which introduces numerical results completed during the rebuttal period, and has shown the advantage of our algorithm in practice. Moreover, it is also worth noting that our algorithm has a potential application in memory-efficient fine-tuning of large language models (LLM). Very recent studies [1,2] have utilized zero-order optimization algorithms to reduce the memory required by fine-tuning LLM. Our algorithm may be utilized to further achieve the asynchronous update, because of its ability to deal with delayed feedback. We will provide more discussions about our potential applications in the revised version. [1] Y. Zhang et al. Revisiting Zeroth-Order Optimization for Memory-Efficient LLM Fine-Tuning: A Benchmark. In ICML, 2024. [2] S. Malladi et al. Fine-Tuning Language Models with Just Forward Passes. In NeurIPS, pages 53038–53075, 2023. --- Q2: Could the authors comment on what the problem looks like for the regular stochastic case with all $f_t=f$ for some fixed $f$, and how this might make the problem easier under delays? A2: We notice that the stochastic case of delayed online convex optimization (OCO) has been investigated in the pioneering work of Agarwal and Duchi [3], which is referred to as distributed or parallel stochastic optimization with asynchronous update. Therefore, the stochastic case of delayed bandit convex optimization (BCO) reduces to a zero-order variant of this asynchronous optimization problem. Moreover, as discussed in Agarwal and Duchi [3], the stochastic case itself is not sufficient to make the delayed problem easier. Actually, the smoothness assumption on the loss functions is also required. More specifically, Agarwal and Duchi [3] show that in the stochastic case, the delay only increases the regret of delayed OCO for convex and smooth functions in an additive way, i.e., an $O(\sqrt{T}+d^2)$ regret bound. The key insight for this improvement is that the perturbed error of the delayed stochastic gradients can be much smaller under the smoothness assumption. Therefore, it is natural to conjecture that the stochastic case will make delayed BCO for convex and smooth functions easier in a similar way. We will provide detailed discussions about the stochastic case in the revised version. [3] A. Agarwal and J. Duchi. Distributed Delayed Stochastic Optimization. In NIPS, pages 873–881, 2011. --- Q3: Why do the authors conjecture that the lower bound depends on $\bar{d}$, whereas the upper bound depends on $d$? What improvements would be required to get these to match? A3: Our conjecture of the dependence on $\bar{d}$ stems from the existing $\Omega(\sqrt{\bar{d}T})$ lower bound [Bistritz et al., 2022] for delayed BCO. However, as discussed in our paper, it is hard for our algorithm to achieve regret bounds depending on $\bar{d}$ due to the blocking update mechanism. Nonetheless, we want to emphasize that our regret bounds achieved via the blocking update mechanism are already quite favorable, and it is highly non-trivial to develop a better algorithm, especially in the case with strongly convex functions. Note that even in the easier full-information setting, previous studies can only achieve the $O(d\log T)$ regret for strongly convex functions, which is the same as the delay-dependent part in our regret bounds for strongly convex functions. --- Rebuttal Comment 1.1: Title: Thanks for the clear response Comment: Thank you for the response, which I find quite helpful. I will stick with my positive score.	null	null	null	null	null	null
On Feature Learning in Structured State Space Models	Accept (poster)	Summary: This paper studies the large width scaling behavior of a recently popular class of models known as structured state space models (SSMs). The authors demonstrate that the previous work on large width neural scaling, which prescribes a parametrization known as the Maximal Update Parametrization (muP) as the optimal scaling for neural networks, does not cover the case of SSMs. Furthermore, muP turns out to be suboptimal for SSMs and does not achieve the desired consequence of stable feature learning and hyperparameter transfer. The authors then propose the proper scaling for SSMs and demonstrate numerically that hyperparameter transfer is achievied. Strengths: Understanding proper scaling of hyperparameters with model size is a practically important problem especially in the age of scaling. State space models are an important class of models with competitive performance and desirable attributes such as fast inference speeds. Identifying the proper scaling for SSMs is important for ensuring stable performance as SSM model sizes increases and for unlocking hyperparameter transfer which can greatly reduce the cost of hyperparameter tuning. The authors provide a fairly simple and thorough explanation for the correct scaling for SSMs which turns out to be different from the previous muP scaling. The numerical experiments give further confidence to the correctness of the results. Weaknesses: The presentation is at times a bit hard to follow. Some more introduction to state space models would be helpful to help readers who are not already familiar. Many terms are introduced with very little explanation to orient the reader. Some diagrams could be very helpful, so that the reader can better visualize the SSM forward pass etc. On the mathematical side it would be great if the things could be cleaner and better organized. I think the original spectral scaling paper [1] is a great example of this. The notation and results used should be clearly established (e.g. definition of spectral norm, Kolmogorov's strong law of large numbers, etc.). It would be probably the most helpful if the proofs could be "modularized" into basic operations. Right now all of the analysis goes through very specific instantiations for specific models. The original paper [1] focuses on what happens for elementary operations which can be transparently composed. The results for SSMs should then follow as corollaries. [1] Yang, G., Simon, J. B., & Bernstein, J. (2023). A spectral condition for feature learning. arXiv preprint arXiv:2310.17813. Technical Quality: 3 Clarity: 2 Questions for Authors: None. Confidence: 3 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: Yes. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We sincerely appreciate your thoughtful review and positive assessment of our work. Your feedback has been invaluable in helping us improve the paper. We have addressed your concerns regarding improved presentation and organization of the proofs. We hope that our revisions will merit your consideration for an increased score. Improved presentation. To enhance the visualization of the Mamba forward pass, we have created a new figure (please see Figure 2 in the PDF attached to the global response). We will integrate this figure into the main paper and expand Section 3.1 to provide additional background on SSMs for enhanced readability. We will also introduce all notation and results used such as the definition of the spectral norm, Kolmogorov’s SLLN and Lindenberg-Feller CLT, in the appendix. Modularization of the proofs. Thank you for your suggestion. We concur that modularizing the proofs will certainly enhance the paper's accessibility. However, analyzing signal propagation in the Mamba architecture is inherently more complex than in MLPs, necessitating some analysis of specific modules. Nevertheless, we came up with a strategy to modularize the analysis by noting that the Mamba layer can be mechanistically viewed in the forward pass as a sequence of 3 components/sub-layers: 1. Selection 2. Discretization 3. Linear recurrence Our visualization of the Mamba layer is based on this perspective (in the PDF attached to the global response). To our knowledge, all SSM layers comprise some or all of these sub-layers, allowing us to modularize both forward and backward signal propagation analysis through each sub-layer. It's worth noting that different discretization rules (e.g., ZOH or Euler) would require separate analyses. Beyond this, while SSMs primarily differ in their initialization of the transition matrix A, our analysis remains applicable to any initialization chosen according to HiPPO theory. We believe these changes will significantly enhance the clarity and accessibility of our work, and we look forward to incorporating them in our revised manuscript. --- Rebuttal Comment 1.1: Comment: I appreciate the efforts the authors have made in the rebuttal and the proposed changes. I think implementing these changes will greatly help the paper. I will raise my score slightly.	Summary: This paper investigates the scaling behavior of state-space models (SSMs) and structured variants like Mamba as their width approaches infinity. The authors demonstrate that established scaling rules such as maximal update parameterization (μP) and spectral scaling conditions fail to yield feature learning in SSMs at infinite width. They derive a new scaling rule, μP SSM, enabling feature learning in SSMs as width approaches infinity. Empirical results show that μP SSM leads to improved stability, generalization, and hyperparameter transferability compared to standard parameterization and spectral scaling. Strengths: - Addresses an important theoretical question about SSM scaling behavior - Provides rigorous analysis of forward and backward signal propagation in SSMs - Identifies limitations of existing scaling approaches and proposes a principled correction - Empirically validates results on real SSM architectures like Mamba - Has potential implications for training larger, more efficient SSMs Weaknesses: - Theoretical analysis limited to N_u then N_x approaching infinity setting - Narrow scope of empirical validation (text generation with Mamba on a single dataset) - Lacks comparison to other recent SSM variants beyond Mamba - Insufficient discussion of potential negative implications of enabling feature learning in larger SSMs - No clear roadmap for extending results to more practical settings Technical Quality: 3 Clarity: 3 Questions for Authors: 1. Can you provide a more intuitive explanation of why SSMs violate the tensor program ansatz? 2. How do you expect these results to generalize to other SSM variants and tasks? 3. What are the computational trade-offs of applying μP SSM scaling in practice? 4. Can you elaborate on the implications of spectral scaling leading to parts of the SSM being in the lazy regime? 5. Have you explored whether μP SSM enables training of wider SSMs than previously possible? 6. Can you outline a path for extending your analysis to the proportional limit case? Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The authors discuss the key limitation of restricting analysis to the N_u then N_x approaching infinity setting. However, they should more explicitly address limitations of their empirical evaluation and potential challenges in applying results to practical scenarios. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We would like to express our gratitude for your thorough and insightful review of our manuscript, and useful feedback for improving our work. Order of limits and practical applicability. In SSM models, $N_u$ (input dimension for SSM component) typically increases much faster than $N_x$ (latent states dimension for SSM component) during scaling (see Table 10 in the original Mamba paper [1]). This makes the limit where $N_u$ approaches infinity before $N_x$ more practically relevant. Furthermore, fortunately, these limits commute which allows us to extend our results to the proportional limit setting. Additional Experiments. We have conducted additional experiments to further validate our theory. We have summarized them in the global response and the results are provided in the PDF attached to the global response. Addressing your concerns, we now also present results on a randomly sampled subset of the Fineweb dataset, suggesting similar conclusions to the wikitext-103 results in Figure 2 (main paper). Separately tuning the learning rates in SSM layers and non-SSM layers shows the benefit of muP-SSM over spectral scaling more clearly: While muP-SSM continues to improve with scale, spectral scaling no longer monotonically improves beyond a certain width threshold. Even without separate learning rates, muP-SSM markedly improves training stability at larger learning rates over spectral scaling. SP consistently performs worse than muP-SSM in terms of stability and generalization. This indicates that muP-SSM can indeed improve performance at larger scale. Implications for other SSM variants. Mamba is among the most complex SSM architectures, containing all components present in other recent SSM variants. By providing a scaling analysis for Mamba analogous analyses for S4 or LRUs follow as corollaries. We will clarify implications for other SSM variants in the revision (see our answer to Reviewer iUa6). Implications of enabling feature learning and computational considerations. We see no negative implications in enabling feature learning in every layer. If feature learning is undesired in a specific layer, training can be explicitly disabled, saving computation instead of letting the updates to implicitly vanish with scale. muP-SSM therefore provides the flexibility to achieve feature learning in SSM layers when desired. muP-SSM introduces no additional computational complexity, as it's merely a different parameterization of the weights. Have you explored whether μP SSM enables training of wider SSMs than previously possible? While we lack the computational resources to experiment at such large scales, there's evidence suggesting muP-SSM could enable training of wider SSMs. Even at relatively small scales, muP-SSM shows markedly improved training stability at larger learning rates compared to spectral scaling. According to [3], instabilities in small-scale models at large learning rates can predict general training instabilities at larger scales. This evidence provides some support for the possibility of training wider SSMs with muP-SSM, though direct large-scale experiments are needed for confirmation. We hope that the SSM community would conduct experiments at larger scales to further investigate this potential. Intuitive explanation of why SSMs violate the TP ansatz. There are two primary reasons for why SSMs such as Mamba cannot be represented via TP: 1. Structured transition matrix (A). Typically, the state transition matrix A is highly structured and chosen according to (or loosely based on) Hippo theory [2]. One example is the diagonal matrix with the $i$th diagonal entry being $i+1$. The TP framework crucially relies on matrices with i.i.d entries (such as i.i.d Gaussians) and cannot represent such structured matrices. 2. Selection mechanism. Activations and weights play different roles under TP. The selection mechanism first computes activations (linear transformations of input parameterized via some weights) and uses them as weights in the linear recurrence (see the pdf attached to the global response for a visualization). This underlies a second source of incompatibility of SSMs with the TP framework. [1] Gu, Albert, and Tri Dao. "Mamba: Linear-time sequence modeling with selective state spaces." arXiv preprint arXiv:2312.00752 (2023). [2] Gu, A., Dao, T., Ermon, S., Rudra, A., & Ré, C. "Hippo: Recurrent memory with optimal polynomial projections." NeurIPS 2020. [3] Wortsman, M., Liu, P. J., Xiao, L., Everett, K., Alemi, A., Adlam, B., ... & Kornblith, S. "Small-scale proxies for large-scale transformer training instabilities." arXiv:2309.14322 (2023). --- Rebuttal Comment 1.1: Comment: I have read the authors' responses and discussion with other reviewers, and thank you for the detailed responses. I will be maintaining my score.	Summary: Following the tensor program and maximal update parameterization, this paper studies the parameterization of initialization and learning hyperparameters in structured state space models (SSMs), e.g. S6 Mamba. The authors consider the input dimension and latent dimension of each vector in the sequences to go to infinity and analyze the proper initialization and parameterization for hyperparameters such that the initial output at each layer is stable when passing through multiple layers and the feature updates are compatible with initialization when taking one step gradient. The paper provides a detailed analysis of signal propagation in SSMs, both in the forward and backward passes, as the width of the network increases. And it also reveals that established scaling rules, such as the maximal update parameterization and spectral scaling conditions, fail to maintain feature learning in SSMs. Strengths: This paper is the first paper studying hyperparameter scaling for infinite-width SSMs, a topic that has not been extensively explored compared to other neural network architectures like MLPs and CNNs. And this work has practical implications for improving the training and performance of large-scale SSMs and sets the stage for future research in this area. By tackling practical issues such as vanishing or exploding gradients, the paper provides solutions that may enhance the stability and efficiency of training state-of-art state-space models, making it a valuable resource for practitioners. Weaknesses: 1. There should be more experiments and empirical comparisons among standard parameterization, maximal update parameterization, spectral scaling, and the $\mu $P SSM parameterization, in terms of test loss and parameterization transferability on different types of datasets and learning tasks. The only empirical experiments in Fig 2 in the paper seem to indicate that spectral scaling performs similarly to $\mu$P SSM parameterization. It would be more convincing if we could compare these parameterizations in various situations. 2. There is a lack of explanation of why we need to consider $N_x$ and $N_u$ go to infinity. In terms of SSMs, we usually consider the length of the sequence to be large and SSMs can preserve the long-range dependency. Besides, in the analysis, the authors only consider the inputs of the layer i.i.d. which is quite different from the practical sequential dataset. It requires more explanations for these assumptions and the definition of feature learning in this paper. Technical Quality: 3 Clarity: 3 Questions for Authors: 1. Typo in Line 47: $\mathbb{R}_u^N$ 2. Can you provide more motivation for defining feature learning in layer-wise sequential models in Definition 2.1? In (1) and (2), why do you only require the existence of one output satisfying stability and feature-update assumptions? Do we need to ensure these bounds for all outputs? 3. In Line 70, you mentioned for feature learning we need the inputs to the layer to be asymptotically independent and identically distributed. Does this mean we need to assume $u_1,\ldots,u_L$ are asymptotically i.i.d? 4. Line 76: typo ''Parmeterization'' 5. In (6), $W$ should be $W_l$ 6. Explain the functions in (8-10) for completeness. 7. Below Line 172: typo $\sigma_B^2$ should be $\sigma_C^2$ 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: Thank you for your constructive feedback and positive evaluation of our work. We appreciate your insights and we have carefully addressed your major concerns in the following response. We will rectify minor issues like typos in our revision. We hope that our revisions warrant your consideration for an increased score. Additional Experiments. We have conducted additional experiments to further validate our theory. We have summarized them in the global response and the results are provided in the attached PDF. Addressing your concerns, we conduct experiments on a randomly sampled subset of the Fineweb dataset which suggest similar conclusions as those on wikitext-103 in Figure 2 (main paper). muP-SSM outperforms SP in terms of test loss, training stability, monotonic improvement of generalization with scale, and transferability of optimal learning rate across scales. Observations in comparison to spectral scaling are more nuanced. muP-SSM markedly improves training stability at large learning rates over spectral scaling, and slightly improves generalization performance. First tuning the learning rate in non-SSM layers and subsequently tuning a separate learning rate in SSM layers separates muP-SSM and spectral scaling more clearly: While muP-SSM continues to monotonically improve with scale, spectral scaling no longer improves beyond a certain width, suggesting that the reasonable performance of spectral scaling stems from the non-SSM layers. In SSM layers, the spectral scaling approach lacks rigorous theoretical justification. Clarification on the asymptotically i.i.d assumption. In Section 2.2 & A.1 of our paper, we discuss that activations and their updates in neural networks representable as Tensor Programs (TPs) become asymptotically independent and identically distributed (i.i.d.) with increasing width. This result underlies our i.i.d assumption. Note that, we consider the practical setting where SSM layers are embedded within a network of non-SSM layers (such as MLPs or Layernorms) representable via TP. Accordingly, it's natural to assume that inputs to the SSM layer (e.g., activations from the previous non-SSM layer) are asymptotically i.i.d at each recurrence step. In fact, this i.i.d. assumption isn't strictly necessary. It suffices to assume that inputs are correctly scaled, i.e., $\vert \vert u\vert \vert_2 \in \Theta(\sqrt{N_u})$. This scaling has been demonstrated for correctly scaled network modules representable via TP. Crucially, we do not assume that the sequence of inputs $u_1, u_2, \cdots, u_L$ are i.i.d. Rather, we assume that the coordinates of a single input $u_i$ are asymptotically i.i.d. (or at least correctly scaled) in the sense described above. Why should N_u and N_x go to infinity? We would like to clarify that our analysis does not require both $N_u$ (input dimension for SSM component) and $N_x$ (latent states dimension for SSM component) to go to infinity. It merely allows both quantities to scale up. To derive the results for when only $N_u$ goes to infinity, one can simply set $N_x \in \theta(1)$. In this simplified scenario where the dimension of the latent states $N_x$ is fixed, heuristic muP spectral scaling yields $\eta_B,\eta_C=\Theta(\frac{1}{N_u})$ while muP-SSM gives $\eta_B,\eta_C=\Theta(\frac{1}{\sqrt{N_u}})$ (see Table 1 in the main paper). Experiments carried out independently by researchers (to be acknowledged in the public version), indeed verify that the correct width-independent scaling aligns with muP-SSM (results as shown in Figure 4 in the attachment). Note, however, that as models are scaled up both $N_u$ as well as $N_x$ may be increased in practice, albeit at very different scales. For example, see Table 10 in the original Mamba paper [1]. In Definition 2.1, why do we require that there exists one input that is correctly scaled? This follows the same logic as the paper that proposed muP [3, Definition H.9], which defines a parameterization to be feature learning iff there exists a training routine and input that result in the correct update scaling. This is a technicality we have to adopt as there exist degenerate combinations of inputs and learning rates that result in smaller scalings. Even under this definition, there exists only one choice of layerwise initialization and learning rate scalings that achieves feature learning. [1] Gu, Albert, and Tri Dao. "Mamba: Linear-time sequence modeling with selective state spaces." arXiv:2312.00752 (2023). [2] Wortsman, M., Liu, P. J., Xiao, L., Everett, K., Alemi, A., Adlam, B., ... & Kornblith, S. . Small-scale proxies for large-scale transformer training instabilities. arXiv:2309.14322 (2023). [3] Yang, Greg, and Edward J. Hu. "Feature learning in infinite-width neural networks." arXiv:2011.14522 (2020). --- Rebuttal Comment 1.1: Title: Official Comment by Reviewer QtDa Comment: I thank the authors for a detailed rebuttal and additional experiments. I appreciate the helpful explanation of my questions and the further experiments. I believe incorporating them, and the responses to other reviewers, into the revision of this paper will significantly improve the writing and clarity.	null	null	Rebuttal 1: Rebuttal: Dear Reviewers, We sincerely appreciate the time and effort you have invested in evaluating our work. Your insightful comments and constructive feedback have been invaluable in helping us improve the clarity and quality of our research. We have included a pdf attachment to this response which contains additional figures that address some of the questions raised by multiple reviewers. We will address individual points raised by each reviewer in detail in the reviewer-specific responses. Improved Accessibility. Following the suggestion from Reviewer iUa6, we have included a new illustration (Figure 2 in the attached PDF) that demonstrates the forward pass of the Mamba SSM layer. This addition aims to enhance the accessibility of our work for readers less familiar with State Space Models. Additional Experiments. To address concerns raised by Reviewers QtDa and JuBx and to strengthen our empirical evidence, we conducted additional experiments. Specifically, 1. Results on the Fineweb Dataset. We present results on a randomly sampled subset of the Fineweb dataset (Figure 3 in the attachment). While computational and time constraints prevented us from training on the entire dataset or using larger model widths, our observations on Fineweb are consistent with the wikitext-103 results presented in the main paper (Figure 2). 2. Decoupled Learning Rates. To isolate the effects of SSM scaling, we decoupled learning rates for SSM and non-SSM layers. We first tuned the learning rate of non-SSM layers, then compared test performance across different scales for various SSM learning rates, using the optimal non-SSM learning rate (Figure 1 in attachment). 3. Verify Correct Scaling. In a simplified scenario where the dimension of the latent states $N_x$ is fixed, heuristic muP spectral scaling yields $\eta_B,\eta_C=\Theta(\frac{1}{N_u})$ while muP-SSM gives $\eta_B,\eta_C=\Theta(\frac{1}{\sqrt{N_u}})$ (see Table 1 in the main paper). In experiments carried out independently by researchers (to be acknowledged in the public version), their results as shown in Figure 4 in the attachment verify that the correct width-independent scaling indeed aligns with muP-SSM. These new experiments further validate our theoretical results and address the specific concerns raised in the reviews. We plan to incorporate these results into the revised manuscript. Below, we summarize our key findings based on both the main paper experiments and the additional experiments included in the pdf. Summary of empirical findings. Our work evaluates the scaling behaviour of different parameterizations for State Space Models (SSMs) using four criteria: generalization (test loss), training stability, monotonic improvement of generalization with scale, and transferability of optimal learning rate across scales. Our experiments reveal that while Standard Parameterization (SP) consistently performs worse than muP-SSM across all metrics, the comparison between muP-SSM and spectral scaling yields nuanced results at the scales we test: 1. Generalization. Spectral scaling has only slightly worse test loss compared to muP-SSM at the largest scale we were able to test across all the experiments. 2. Training stability. However, muP-SSM demonstrates markedly improved training stability at larger learning rates compared to the spectral scaling approach already at the relatively small scales we test. Note that, instabilities in small scale models at large learning rates can be predictive of general training instabilities at larger scales [2]. 3. Monotonic improvement of generalization with scale. - Using a single global learning rate for the entire network (SSM + non-SSM layers), similar to muP-SSM, spectral scaling appears to improve performance monotonically with scale up to the largest scale tested (Figure 2 in main paper, Figure 3 in rebuttal attachment). - However, we hypothesized this might be an artifact due to the correct scaling of non-SSM modules under spectral scaling. To test this, we decoupled learning rates for SSM and non-SSM layers. That is, we first tune the learning rate of the non-SSM layers and then under the optimal choice of LR for the non-SSM layers, we compare performance of the models across different scales for different SSM learning rates. Figure 1 in the rebuttal attachment shows that beyond a certain width threshold, performance under spectral scaling no longer improves monotonically with scale, contrasting sharply with muP-SSM. 4. HP transferability. At tested scales, both muP-SSM and spectral scaling demonstrate similar transferability. This is not entirely unexpected when using a global learning rate, as both methods identically parameterize non-SSM layers. It's important to note that unlike muP-SSM, the spectral scaling approach used in our experiments is heuristically derived and lacks rigorous theoretical justification. Pdf: /pdf/43e3e6936ba2c16e9ceffceaf2e9b0c1294fc993.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Understanding Hallucinations in Diffusion Models through Mode Interpolation	Accept (poster)	Summary: The paper introduce the concept of hallucinations for image diffusion models. The key contributions includes: 1. Definition of Hallucinations: Hallucinations are defined as samples generated by diffusion models that lie completely outside the support of the real data distribution. 2. Mode Interpolation Phenomenon: The phenomenon where diffusion models interpolate between nearby data modes, generating samples that do not exist in the original training data. This smooth interpolation leads to artifacts, termed hallucinations. 3. Causes of Hallucinations: Hallucinations are attributed to the smooth approximation of discontinuous loss landscapes by the diffusion model. This leads to interpolation between distinct data modes that are not present in the original dataset. 4. Experimental Findings: Experiments with 1D and 2D Gaussians show that hallucinations occur due to mode interpolation, particularly between nearby modes. The variance in the trajectory of the generated sample increases towards the end of the backward sampling process, indicating out-of-support samples. 5. Mitigation of Hallucinations: A simple metric to capture the high variance in the sample trajectory can effectively remove over 95% of hallucinations during generation while retaining 96% of in-support samples. 6. Impact on Recursive Training: The removal of hallucinations has implications for the collapse and stabilization of recursive training on synthetic data. Experiments on datasets like MNIST and 2D Gaussians demonstrate the effects. Strengths: 1. The paper introduces Hallucinations in diffusion models, which is an under-explored area. The paper's focus on mode interpolation as a source of these hallucinations brings a fresh perspective. 2. The paper exhibits high-quality research through its comprehensive experimental design and thorough analysis. 3. The paper is well-written and clearly structured, making it accessible to both experts and those new to the field. 4. The significance of the paper lies in its potential impact on the development and refinement of diffusion models. By identifying and addressing the issue of hallucinations, the research provides valuable insights that could lead to more reliable and accurate generative models. Weaknesses: 1. SMLD [1] claims that `the scarcity of data in low density regions can cause difficulties for both score estimation with score matching and MCMC sampling with Langevin dynamics.` SMLD [1] addresses this problem by introducing slow mixing of Langevin dynamics. The datasets used in the paper have the same density for different modes. I think the hallucination phenomenon with different density for different modes should also been explored. 2. While the paper provides a robust analysis using 1D and 2D Gaussian datasets, its experimental scope is somewhat limited. These simplified datasets may not fully capture the complexity of real-world data distributions. Is the hallucination of diffusion models on real image distribution (such as face) helpful to its diversity due to mode interpolation? 3. While the paper touches on the implications of hallucinations for recursive training stability, this discussion is relatively brief and lacks depth. Given the potential significance of this aspect, a more extensive exploration of how hallucination mitigation affects recursive training dynamics would have been valuable. This could include detailed experiments and analyses on the long-term effects of hallucination removal on model performance and stability. [1] Generative Modeling by Estimating Gradients of the Data Distribution Technical Quality: 3 Clarity: 4 Questions for Authors: Please see weaknesses. Confidence: 3 Soundness: 3 Presentation: 4 Contribution: 3 Limitations: The authors have adequately described 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: We are happy to see that you liked the fresh perspective on hallucinations in diffusion models and mode interpolation presented in our work, and found the paper to showcase high-quality research, and comprehensive experimental design, and have a potential impact on the development of more reliable generative models. We acknowledge your concerns and attempt to respond to them line by line below: ### Re: Testing on Natural Images Please refer to the [global response here](https://openreview.net/forum?id=aNTnHBkw4T&noteId=2W1mcxDdVO) along with the figures in the attached PDF for an exciting update with results on the Hands-11k dataset! ### Re: Hallucinations with Imbalanced Density Distribution across Modes We conducted additional experiments using datasets with varying densities for different modes. Specifically, we trained a DDPM on the Gaussian 2D dataset with two modes that have only 1/100th of the samples when compared to the other modes. In the attached PDF, see the modes highlighted with a red square. We observed that imbalanced data can exacerbate mode interpolation near these underrepresented modes. These experiments demonstrate that the hallucination phenomenon persists even with differing densities, further validating our hypothesis. ### Is the hallucination of diffusion models on real image distribution (such as face) helpful to its diversity due to mode interpolation? Hallucinations are one of the overlooked failure modes in diffusion models. Certain hallucinations can indeed introduce novel and creative variations that may not be present in the training data. However, in this work, we do study hallucinations in a concrete setup of unconditional diffusion models, where samples emerge at generation in otherwise zero-density regions in the real data manifold. For instance, you may look at Figure 2 in the attached PDF. We believe images in such zero-density regions manifest in unwanted characteristics such as incorrect hands. Though this may indeed be a double-edge sword. We are in a way stopping the model from going out of the data manifold, which can be useful for abstract/creative tasks where hallucinations may be desirable. ### Long-Term Effects on Recursive Training: We discuss the long-term effects of hallucinations in recursive model training in Section 6. We show that filtering hallucinated samples can mitigate model collapse in this setting (Figure 8). We also study the long-term impact of hallucinations in Gaussian 2D (Figure 7). A practically relevant setting is the data accumulation setting as discussed in [1]. The key difference is that in their setting synthetic data is accumulated along with real data as the training progresses across generations. In Section 6, we only use the synthetic data sampled from the most recent generative model. Gerstgrasser et. al argues that model collapse can be avoided with their data accumulation pipeline. However, we argue that mode interpolation can provide a novel viewpoint in this framework as the subsequent generations would result in a much higher fraction of hallucinations, even if real data is included in subsequent generations. We will dedicate an extended portion of our paper to discuss the important implication and agree with your characterization of its importance. [1] Gerstgrasser, Matthias, et al. "Is model collapse inevitable? breaking the curse of recursion by accumulating real and synthetic data." arXiv preprint arXiv:2404.01413 (2024). --- Please refer to the attached PDF for detailed results and figures from our additional experiments. We hope we are able to further strengthen your conviction and support for our work through this rebuttal. Please let us know if you have any remaining concerns. --- Rebuttal Comment 1.1: Comment: I acknowledge having read the authors' rebuttal. My overall assessment of the paper remains unchanged, and I continue to support my current rating.	Summary: This paper addresses the hallucination phenomenon in diffusion models, where generated samples fall outside the training distribution. The authors propose mode interpolation as an explanation. They analyze synthetic datasets and conclude that hallucinations occur between nearby modes due to the inability of deep networks to learn ground truth score functions with sharp jumps for small timesteps $t$. The authors introduce a metric along the denoising trajectory to identify hallucinated samples and demonstrate that filtering out these samples during recursive training improves the quality of generated samples on both synthetic and real-world datasets. Strengths: 1. The paper explores a novel phenomenon of hallucinations in diffusion models and provides a plausible explanation through mode interpolation. 2. The authors employ sound toy experiments to validate the hallucination phenomenon and their proposed explanation. Weaknesses: 1. Mode interpolation as an explanation for hallucinations is not entirely convincing. The concept of mode interpolation is proposed and validated through experiments on synthetic Gaussian mixture datasets. However, the relationship between mode interpolation and hallucinations in more complex datasets and models (such as extra or missing fingers in StableDiffusion) remains unclear, particularly for latent diffusions with decoders. The authors should provide more evidence of mode interpolation in complex cases and hallucinated samples. Furthermore, the role of the decoder in hallucinations, mentioned in the abstract, is not adequately addressed in the discussion. 2. Experiments should be more comprehensive and robust. - Comprehensive experiments: The authors primarily use synthetic Gaussian mixture and simple shapes datasets to validate mode interpolation and hallucination removal. Additional experiments on more complex datasets like CIFAR-10 or CelebA, which are standard benchmarks for diffusion models [1], are necessary to generalize the proposed metric. Examples from more complex models, such as StableDiffusion, should also be included. - Robust experiments: The authors select dataset-dependent ranges of timesteps to calculate variance based on prior knowledge, which may not be robust. They should provide principles or guidelines for selecting the range of timesteps for different datasets. 3. Insufficient analysis in some areas. - Sub-approximation of score function leading to mode interpolation: The claim that mode interpolation is caused by the inability of deep networks to learn ground truth score functions with sharp jumps for small $t$ needs support. A "sanity check" experiment using ground truth score functions is necessary but missing, making the claim less convincing. The authors should include this experiment and analyze the approximated score functions in cases with varying data sizes, as in Figure 2. - Relationship between hallucinations and high variance along the trajectory: The authors argue that hallucinated samples exhibit high variance along the denoising trajectory, as observed in Figure 5. This appears more empirical than intuitive. More discussion is needed to explain why hallucinated samples have high variance along the trajectory. 4. Lack of formal definition for Eq. (4). The definition of $\texttt{Hal}(x)$ in Eq. (4) is informal (and inconsistent or incorrect): (a) The summation of $i$ over $[0,T]$ contradicts the range used in experiments; (b) The calculation of $\overline{\hat{x}_0^{(t)}}$ is unclear, and the superscript $^{(t)}$ may be incorrect; (c) There is a typo where $i$ should be replaced by $t$. The authors should provide a formal definition for $\texttt{Hal}(x)$ to make the metric more rigorous. [1] Denoising Diffusion Probabilistic Models, NeurIPS 2020. Technical Quality: 2 Clarity: 2 Questions for Authors: 1. How do studies on properties of mode interpolation relate to its cause or detection? In Section 4, the authors discuss properties of mode interpolation, such as its occurrence between nearby modes and the effects of data size and denoising timesteps. How do these properties relate to the cause or detection of mode interpolation? Could the authors provide more insights into the cause of mode interpolation and how these properties are related? 2. How can a threshold for $\texttt{Hal}(x)$ be determined? In Section 5, the authors propose $\texttt{Hal}(x)$ as a metric to detect hallucinations. What value of $\texttt{Hal}(x)$ is considered a hallucination in the experiments? Could the authors provide more insights into determining the threshold for $\texttt{Hal}(x)$? 3. Does the sampling algorithm affect hallucinations? The sampling algorithm details are missing from the experiment settings. Could the authors provide more information on the sampling algorithm used in the experiments? Additionally, do different sampling algorithms (e.g., deterministic vs. stochastic, as discussed in [1]) affect hallucinations? [1] Elucidating the Design Space of Diffusion-Based Generative Models, NeurIPS 2022. Confidence: 5 Soundness: 2 Presentation: 2 Contribution: 2 Limitations: Yes. Flag For Ethics Review: ['No ethics review needed.'] Rating: 3 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your thoughtful and detailed review. We are glad that you found our exploration of hallucinations in diffusion models and our explanation through mode interpolation to be novel and plausible. Your appreciation of our toy experiments validating the phenomenon is encouraging. We acknowledge your concerns and attempt to respond to them line by line below: ### Re: Experiments on complex, and or natural datasets Thank you for your comments on W1, W2.1. We kindly refer you to the [global response here](https://openreview.net/forum?id=aNTnHBkw4T&noteId=2W1mcxDdVO) along with the figures in the attached PDF for an exciting update with results on the Hands-11k dataset (and the extra finger problem)! ### Re: Comprehensive and Robust Experiments > Sanity Check with Ground Truth Scores: Thank you for pointing this out. We have done a sanity check experiment where we sampled using the ground truth score instead of the learned score function. We did not observe any hallucinations in this experiment. We included this in the Figure 3 (4th column) of the attached PDF. The analysis of approximated score functions across varying data sizes is something that we will definitely consider including in the final revision. ### Re: Guidelines for selecting the range of timesteps for different datasets. Our methodology for the selection of timesteps for any dataset was as follows. We plot the trajectory of the predicted x0 across various timesteps and find the region where x0 varies quite significantly. This gave us a good starting point for the selection of timesteps. For image datasets (shapes and Hands), we observe that similar timesteps ( t = 700 to t = 800) is a great starting point. ### Re: Decoder’s Role: Relationship Between Hallucinations and High Variance We provide a more detailed discussion on why hallucinated samples exhibit high variance along the denoising trajectory: The high variance in the trajectory of the hallucinated samples can be derived from the analysis of mode interpolation. The neural network learns a smooth approximation of the score function. The score function in diffusion models is (implicitly) learned to guide this reverse diffusion process. This smooth approximation leads to oscillations between the nearby modes which leads to hallucinations. Thus, we track the variance of the trajectory of x0 to detect the hallucinated samples. We hope this provides more intuition behind the proposed metric. ### Re: Formal Definition of Eq. (4) We sincerely apologize for this confusion and thank the reviewer for pointing it out. We define the corrected metric below (which was used in all of the experiments). The intuition remains the same, we want to capture the variance of predicted x0 in the reverse diffusion trajectory. Let $T_1$ be the start timestep and $T_2$ be the end timestep. Concisely, we can write it as $$ \text{Hal}(x) = \text{Var}(\hat{x_0} [T_1:T_2]) $$ In detail: $$ \text{Hal}(x) = \text{Var}(\hat{x_0}[T_1:T_2]) = \frac{1}{\|T_2 - T_1\|} \sum_{i=T_1}^{T_2} \left( \hat{x_0}^{(i)} - \frac{1}{\|T_2 - T_1\|} \sum_{j=T_1}^{T_2} \hat{x_0}^{(j)} \right)^2 $$ ### Re: Threshold for Hal(x) The value of Hal(x) depends on the dataset and experimental setup. Depending on the approximate number of hallucinations, one can try to filter out the top x% of the generated samples. This should ideally retain most of the in-support samples and eliminate the hallucinated samples. ### Re: Details of the Sampling Algorithm We use the standard DDPM sampler with 250 steps while sampling for the Shapes setup. For the Gaussian experiments, we also used the standard DDPM sampler and the number of sampling steps was equal to the number of training steps (1000). We will update the details of the same in the paper as well. --- Please refer to the attached PDF for detailed results and figures from our additional experiments. We hope we were able to rest your concerns regarding the experimentation and convince you of its generality with the added results. We have made our best attempt at answering all the concerns raised, please do let us know if any other questions remain! Thank you for your concrete suggestions that ignited some nice experiments. --- Rebuttal Comment 1.1: Comment: Thanks for your response and the extensive additional experiments. Some of my concerns are addressed but some are not, listed below: - W1: I think there exists a misunderstanding. What does "decoder" mean in the abstract and Re4? From the authors' supplementary PDF I guess it refers to "the upscaling stages of U-Net", but where is it mentioned in the paper? - W2.2 and Re3: From the response, seemingly the range of t is selected from empirical case studies, giving non-convicing results. Still, I hold my opinion that $\mathrm{Hal}(x)$ should be calculated within a consistent and formal form to ensure generality, and the authors should discuss them as limitations or future works. - W3.2 and Re4: The response about the connection between hallucination samples and high variances seems to be not enough convincing. What's the key to "smooth approximation leads to oscillations between the nearby modes"? In other words, why does not groundtruth score functions lead to oscillations between nearby modes? - Q1 and Re2: Without providing supplemental experiment results (such as experiments across varying data sizes), could the authors give any intuitions behind how properties (not limited to the data sizes, but including "occurrence between nearby modes" and "effects of denoising timesteps") of mode interpolations, discribed in Section 4, relate to the cause or detection? Additionally, what's the difficulty for supplemental experiments across varying data sizes, and what's the authors' plan to conduct these experiments for the final version? - Q3 and Re6: Thanks for your explanation, but I'm still concerned whether the sampling algorithm would affect the hallucinations. For example, [1] proposes that a stochastic sampler (like DDPM) can correct the under-estimation of score functions, compared with a deterministic sampler (like DDIM [2] with $\eta=0$). Could the authors provide results using DDIM samplers? [1] Elucidating the Design Space of Diffusion-Based Generative Models, NeurIPS 2022. \ [2] Denoising Diffusion Implicit Models, ICLR 2021. --- Reply to Comment 1.1.1: Comment: Thanks for the follow-up and continued engagement. We are happy to hear that some of your concerns were addressed with the original rebuttal, and we attempt to clarify the remaining questions below: - W1: Yes, the decoder refers to the upscaling stages of the U-Net. In the case of the 1D and 2D Gaussian experiments, since the input dimension is very small, there is no “encoder” as such. The 3-layer MLP acts as the decoder. We will improve the clarity of the term “decoder” in the revised version. - W2.2 and Re3 : Thank you for this suggestion, we will include the limitations of the proposed method in the revised version. We want to highlight that the goal of this work was to identify and discover the phenomenon of mode interpolation, and its intricate relationship with hallucinations, and show promise in detecting this through a simple metric. We absolutely agree that future work should focus on developing improved, and informed metrics for detecting hallucinated samples, especially in real-world datasets. - W3.2 and Re4 - Ground Truth Score Function: We refer you to Figure 4, column 3 where we show how $\hat{x_0}$ is a smooth approximation of the step function (to show the connection between the learned score function, and its effect on the predicted $\hat{x_0}$). For instance, in the case of a mixture of Gaussians (1D), the score function precisely reflects the boundaries between different Gaussian components. This precision ensures that the score function is sharply defined in regions where the probability density changes abruptly, leading to no oscillations or artifacts between modes---informally, the predicted value snaps back to one of the modes, and is never in the region between modes because the force pulling it to the mode is so high. Essentially, the ground truth score function exactly mirrors the behavior of the true probability distribution, preventing any unintentional mixing or interpolation between modes. - Learned Score Function: When the model generates samples, it relies on the learned (smoothed) score function to reverse the diffusion process. First, this is smooth and does not show the step-function-like behavior of the true score function. Since the learned score function cannot sharply separate the modes, it creates a smoother gradient between them, effectively leading to oscillations or interpolations between the modes---informally, creating a region of high variance/uncertainty where samples are being pulled to either mode with a high, but finite force. This is why samples can end up in regions where the ground truth distribution has low or even zero probability—these are the regions between the modes. - Q1 and Re2 - The frequency of interpolated samples is inversely proportional to the number of sampling timesteps T’: This is because if we have more timesteps, then the update on each $x_{t-1}$ given an $x_{t}$ would be smaller. This means that even when the $x_t$ is in the so-called region of uncertainty, it can quickly latch back to the nearest mode. On the contrary, if the sampling steps were less, each update means a larger step, leading to oscillations within the region of uncertainty, and from one mode to the other. Please note that there is a typo in the paper where we missed writing “inversely” proportional. The corresponding experimental results can be found in case of the VDM model in the attached PDF. We will include all of this and the updates in the final draft. - The number of interpolated samples also decreases as the distance from the modes increases: Following the above explanation, if two modes are far apart, we need a larger shift from one $x_{t}$ to the next $x_{t-1}$ to oscillate between modes. This once again means that the models can latch back to the existing mode much more easily. - As the number of training samples increases, we observe that the proportion of interpolated samples decreases: This is primarily because more data enables to learn a better approximation of the score function. > Additionally, what's the difficulty for supplemental experiments across varying data sizes, and what's the authors' plan to conduct these experiments for the final version? We note that we have run experiments with varying data sizes in Figure 9 of the paper. If the reviewer is asking about the detection results with varying data sizes, we plan to include the results of detection experiments with Gaussian1D and Gaussian2D across varying data sizes in the revised version. We agree that this would demonstrate the generality of the proposed detection metric.	Summary: This paper demonstrates and studies a particular failure mode of diffusion models termed mode interpolation. Specifically, the authors discovered that when trained on certain datasets, diffusion models (even those with 1000 denoising steps) generate samples that look like certain interpolations of some training samples. The paper demonstrates the mode interpolation effect on several toy datasets (e.g., 1D and 2D Gaussians, grids) and the MNIST dataset. The paper then delves into analyzing the cause of the mode interpolation behavior by examining the learned score functions. The authors observe that one cause of the artifact is that the denoising neural network cannot accurately mimic the score when it has abrupt changes. The paper finally proposes a metric to estimate the plausibility of a sample being a mode-interpolated one based on the observation that “good” samples often have relatively small changes in the later sampling process. Strengths: The paper elaborates on a previously overlooked failure mode of diffusion models called mode interpolation. Specifically, when trained on certain datasets, diffusion models can generate samples that correspond to the interpolation of certain training samples. This phenomenon is not well-studied in prior work and this paper could bring further attention of the community to this problem. The paper is also very well-written and easy to follow. Weaknesses: Despite the interesting observation of the mode interpolation behavior, my main concern is that the paper does not provide justifications for the mode interpolation behavior on more realistic datasets (e.g., natural images) and large models. While I totally understand that it is a major contribution to discovering the mode interpolation phenomenon, and it can be hard to observe this clearly on natural image datasets, I still believe some analysis can be done more carefully to let us understand mode interpolation better. I am happy to increase my score if the following concerns/questions are addressed. In Figure 1, while the Gaussian example clearly indicates interpolated out-of-distribution samples, the SIMPLE SHAPES results do not seem to support the “interpolation” behavior. Specifically, by interpolating training images, we will always get blurry or gray shapes, but in all sampled images, the individual objects seem to be perfect in terms of both shape and color. It seems like the diffusion model is doing some sort of ``compositional generalization’’ over the training samples. While this is clearly problematic in this synthetic dataset, this could be a good behavior for diffusion models on natural images as they can generate unseen object combinations. This will not harm but actually improve the model. I think the case where diffusion models fail is when they generate “interpolation of training images”, in which case the image will be blurry or has other artifacts. How do the denoising network structure and the forward noising schedule affect mode interpolation? Looking closely at Figure 2, noting the log scale of the y-axis, it seems that a modest amount of samples (e.g., 50000) is sufficient to almost prevent mode interpolation from happening (1000 times less likely). I wonder will mode interpolation happen more often or less often when we increase the dimensionality to be similar to e.g. natural images. In Section 4.3, the paper discusses the cause of the mode interpolation problem: the learned score function is inaccurate when the ground truth score changes significantly. It is still unclear how the sampling process interplays with this problem: does more steps mitigate or exaggerate the problem; and can other sampling methods (e.g., ODE-based) mitigate the mode interpolation problem? In Section 5.2, can we apply a similar metric that does not require T sampled trajectories? Since in practice we only draw a few samples a time (e.g., per prompt). Technical Quality: 3 Clarity: 3 Questions for Authors: Please refer to the weakness section. Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The authors discussed certain limitations in the appendix. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We appreciate your review and are glad that you found our paper well-written & easy to follow, and that you appreciated our focus on the previously overlooked failure mode of diffusion models, namely mode interpolation. We acknowledge your concerns & attempt to respond to them line by line below: ### Re: Results on Realistic datasets Please refer to the [global response here](https://openreview.net/forum?id=aNTnHBkw4T&noteId=2W1mcxDdVO) along with the figures in the attached PDF for an exciting update with results on the Hands-11k dataset! ### Re: Interpolation versus Compositional Generalization We will answer this in two parts. First, we will distinguish between compositional generalization & interpolation. Second, we report the results of a concrete experiment to demonstrate how such interpolation happens in the embedding space. > A. Why is hallucination different from compositional generalization? The experimental design in our work is based on unconditional diffusion models, where the goal is to model the true p(x) of the distribution. The only way we interact with the learned distribution q(x) of the diffusion model is by sampling a random seed. This seed sampling is "in-distribution" to what was seen during training. Hence, the outputs should also be “in-distribution”. When we go into the text-image case, the text samples may be "outside" the distribution of the training set (eg, horse riding a man), which justifies composition in the output space as well (by being OOD), unlike the setting we are positioned in. > B. Why are outputs not blurry if this is actually an interpolation? This is a great question that led to the addition of a fun new experiment (see PDF) in favor of clarity! The interpolation is not happening in the output space, but rather in the representation space. We performed a t-SNE visualization of the outputs of the bottleneck layer of the U-net used in the Simple Shapes experiment. Please refer to Figure 2 in the attached PDF for the visualization. Regions 1 & 3 in the representation space semantically correspond to the images where squares are at the top & bottom of the image respectively. At inference time, we can see a clear emergence of region 2 which is between regions 1 & 3 (interpolated), & contains two squares (hallucinations) at the top & bottom of the image. This experiment concretely confirms that interpolation happens in representation space. ### Re: Denoising Network Structure & Noising Schedule > Network Structure: We systematically study this question by analyzing the count of hallucinations with various hidden dimension sizes in the architecture, & see that the hallucination count increases as the dimensionality of the hidden space increases. We hypothesize that a larger decoder may require even more samples to prevent hallucinations, which we showed in the paper reduces as the samples increase. These results are on Gaussian 1D (with 3 modes at 1, 2, 3) with 20k training samples. \|Hidden Dimension\|Hallucinations (1e-5)\| \|-\|-\| \|64\|1.36\| \|128\|2.34\| \|256\|2.48\| \|384\|1.06\| > Noising Schedule: We explore “Cosine” learning rate schedule similar to Improved DDPM work. In this case, we scale the betas to be in the same range as the linear schedule. We also experiment with a Quadratic schedule. The cosine learning schedule seems to reduce the fraction of hallucinations. These results are on Gaussian 1D (with 3 modes at 1, 2, 3) with 20k training samples. \|Schedule Type\|Hallucinations (1e-5)\| \|-\|-\| \|Linear\|2.34\| \|Cosine\|0.10\| \|Quadratic\|0.46\| ### Re: Sample Complexity & High Dimensionality 1. First, we note that many of the experiments we studied were in very simple scenarios, such as 3 modes in 1 dimension & 50k samples. Despite the large number of samples for the task complexity, we did see hallucinations in this simple setup. In contrast, natural image datasets lie in a complex manifold with many modes. The example of missing/additional fingers in StableDiffusion (and are additional results on Hands-11K) shows that hallucinations persist with natural image datasets (and are much more frequent). Despite being trained on millions of natural images, the Stable Diffusion model fails to generate images of hands correctly. We believe that since the number of modes in real data are so many, the total number of samples required to prevent hallucinations is also much larger. 2. Second, we also know that real-world datasets are long-tailed in nature, so it is incredibly difficult to obtain a large number of samples to cover all the settings. One hypothesis in literature is that hands cover a small portion of the image & are often occluded in the images (for e.g by the person holding something). This long-tailed nature of real world datasets, makes hallucinations even more prevalent. ### Re: Sampling Process & Hallucination Metric We experimented with different sampling steps & found that increasing the number of sampling steps can reduce hallucinations. We refer the reviewer to Figure 3 of the attached PDF where we show this with Variational Diffusion Models. The first column (in Figure 3) with 250 sampling timesteps (T’ = 250) has more hallucinations compared to the second column with 500 sampling timesteps (T’ = 500). ### Metric clarification We believe that there is some confusion in understanding the metric in Eq.4. Here, t refers to the time-step during the reverse diffusion trajectory. Hence, we compute the variance of x0^ across select timesteps in a single trajectory. Hope this clarifies. --- Once again, we thank you for the constructive feedback on our work. We hope we were able to clarify all your concerns, and look forward to resolving any remaining concerns during the discussion phase. Please refer to the attached PDF for detailed results and figures from our additional experiments. --- Rebuttal Comment 1.1: Comment: I thank the authors for their detailed response, which addresses many of my original concerns. In particular, I like the additional experiment that answers the question "why are outputs not blurry if this is actually an interpolation". It would be very helpful for the authors to incorporate these changes into the next version of their paper. After the rebuttal, I found the paper to have more merits than weaknesses so I will raise my score to 6. However, as also pointed out by the other reviewers, the fact that the paper lacks comprehensive experiments on real-world datasets is a major weakness. Specifically, evidence of interpolation is only observed in human-hand-related datasets. While I understand it is harder to find such effects in real-world cases, it might suggest that mode interpolation might "not really be a problem". For example, the authors observed mode interpolation in the latent space, which led to the perfect individual shapes in the SIMPLE SHAPES experiments. Given such results, one possible explanation for the unseen interpolation effect may come from the fact that the latent space is much more semantically compact compared to the pixel space and thus does not lead to "weirdly interpolated" images. But anyway, I think it is a solid contribution to observe the interpolation effect, even if it happens in the latent space in large diffusion models. This can inspire further thoughts and improve our understanding of diffusion models.	Summary: This paper studies the hallucination phenomenon in diffusion models, in which samples out of the support sets are generated. Specifically, the authors characterize a failure mode, termed mode interpolation, which is hypothesized to be attributed to the learned score function of the diffusion model being over-smoothed around the discontinuous jumps in the ground-truth score. The authors provide evidence for this hypothesis in experiments with 1D and 2D Gaussians, where the ground-truth scores are known. They then discovered the x0 predicted by the DDPM has higher variances (along the reverse diffusion trajectory) when generating hallucinated samples. Using this variance as a metric, the authors further show that they can filter out some hallucinated samples in datasets including Gaussians, SimpleShapes, and MNIST. They also demonstrate an application of such removal in recursive generative modeling, where samples generated by the current model are used to fine-tune the model. Strengths: 1. The hallucination problems of diffusion models are less explored than those with LLMs. This is an interesting research direction. It is interaction with another research direction, recursive generative modeling, as highlighted by the authors, is also non-trivial. 2. I like the authors' thought process in approaching this question. Regions between modes are indeed a reasonable starting point for investigating a likelihood-based model. 3. The proposed metric for detecting hallucination appears to be effective in the three synthetic datasets. Weaknesses: 1. It looks like only a particular parametrization of a particular type of diffusion model is tested, see Questions. 2. None of the datasets are natural images. Although the authors alluded to the analogy between mis-combining shapes and hands with 6 figures, the latter was not checked with real experiments. Would it be possible for the authors to apply the proposed hallucination metric to the hand generation problem and report some preliminary results? Technical Quality: 2 Clarity: 3 Questions for Authors: 1. Though the over-smoothed score function is shown in Fig. 4, it is unclear if this phenomenon is general. From what I can gather, the authors only work with DDPM, which by design is not a rigorous likelihood-based model. The weighting between noise levels is adjusted to promote perceptual quality, compromising likelihood estimate. I request the authors to try some more rigorous likelihood-based diffusion models, e.g. Variational Diffusion Models, to further verify the generality of their discovery. 2. Even with DDPM, there can be different types of model parametrization, such that the neural networks are learning with different targets. The default setting for model parametrization in the GitHub repo is epsilon prediction, which naturally has higher variance around low noise levels (i.e. timesteps close to 0). Did authors try x-prediction and v-prediction, two popular alternatives to eps-prediction? Specifically, variances in the supervision targets of the neural network should be low around low noise levels for x-prediction, and static for v-prediction. I believe these ablation studies can help further justify the generality of their discovery. Confidence: 4 Soundness: 2 Presentation: 3 Contribution: 3 Limitations: I don't think the limitation of the proposed hallucination metric is sufficiently discussed. But I believe there should be negative societal impacts. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your thoughtful review. We are glad that you found our research direction intriguing (i) in exploring the hallucination problems of diffusion models, (ii) appreciated our approach of investigating regions between modes, and (iii) found our proposed metric effective for detecting hallucinations. We acknowledge your concerns and attempt to respond to them line by line below: ### Re: Testing on Natural Images We have discussed this point in the global response in detail and added new results on the Hands-11K dataset. Please refer to the [global response here](https://openreview.net/forum?id=aNTnHBkw4T&noteId=2W1mcxDdVO) along with the figures in the attached PDF for an exciting update. ### Re: Testing other Models/Parametrizations > Variational Diffusion Models (VDM): We have conducted additional experiments using Variational Diffusion Models (VDM) to verify the generality of our findings based on your suggestion. Our results show that the over-smoothed score function phenomenon persists in VDM, supporting the hypothesis that this issue is not specific to DDPM. We train a simple VDM on the 2D Gaussian with 10k samples. We follow the setup and hyperparameters in the official implementation. We train both continuous and discrete variants of VDM on the 2D Gaussian dataset. We kindly refer the reviewer to the figure in the attached PDF (Figure 3). The main observation is that VDM mitigates the hallucinations significantly especially with more training data but the phenomenon of mode interpolation still exists. In this figure, we also show the impact of the number of sampling steps on the count of hallucinations. We clearly see that increasing the number of sampling steps reduces the number of hallucinated samples. This can be clearly observed in Figure 2 (first two figures) where the count of hallucinations decreases mode interpolation. > Alternative Parametrization: Thank you for this suggestion. We have now explored different types of model parameterizations, including x-prediction and v-prediction, to understand their impact on hallucination detection. We observe that X-prediction is particularly worse in terms of the fraction of hallucinations. These results are on Gaussian 1D (with 3 modes at 1, 2, 3) with 20k training samples. \| Method \| Fraction of Hallucinations (1e-5) \| \|---------------\|----------------------------------\| \| Eps-prediction \| 2.34 \| \| V-prediction \| 2.43 \| \| X-prediction \| 22.35 \| ### Re: Negative Societal Impacts and Limitations Thank you for the nudge. We will add a detail on the limitations and societal impact of this work: In current text-to-image generative models, the poorly modeled “hands” are a clear giveaway in identification of AI generated images. The detection of such AI-generated content would be made much more difficult if these hallucinations were identified and removed from the generated images. While our work builds an understanding of hallucinations, and allows us to also detect them, we believe that future generations of models would have become more robust to such hallucinations by virtue of training on more data independent of this work. Concerning the limitations of the proposed hallucination metric, the selection of the right timesteps is key to be able to detect hallucinations. More analysis on what region of trajectory leads to hallucinations would be useful across various schedules and sampling algorithms. We believe these are great areas for future work to explore. 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 hope we were able to clarify all your concerns, and look forward to resolving any remaining concerns during the discussion phase. --- Please refer to the attached PDF for detailed results and figures from our additional experiments. --- Rebuttal Comment 1.1: Comment: Thank the authors for their detailed response. The results of VDM are particularly interesting and I hope the authors would like to make sure they are sufficiently discussed in the revised version. Given the observation that more sampling steps leads to less hallucinations in VDM, it seems like a continuous time VDM may be a well founded solution to reduce hallucination, given its theoretical grounding in being a decent likelihood estimate. I am increasing the rating but will still keep it borderline.	Rebuttal 1: Rebuttal: We appreciate the constructive feedback provided by all reviewers towards this submission. Across the board, all reviewers found the phenomenon of hallucination via mode interpolation as an interesting scientific inquiry and appreciated the quality of the draft that was supported with convincing, comprehensive, and rigorous experimental protocol. There are a few common themes around weaknesses that all reviewers identified, which if acted upon could improve the draft. We took this feedback into strong consideration, and are excited to share the updated results, which substantially improve the significance and soundness of the results. Focusing on the weaknesses below: ### Experiments on Real World Datasets This concern was raised by all reviewers. We understand the interest in seeing how our evaluation generalizes to natural image datasets. Following the general feedback, we have extended our experiments to include the hand generation problem to evaluate the effectiveness of our hallucination metric on real-world data. Specifically, we applied our proposed metric to the Hands-11k dataset [1] and observed instances of hallucinated samples with an incorrect number of fingers. The Hands dataset [1] consists of high-resolution images of hands in various orientations. We sample 5000 images from the Hands dataset and train an ADM [2] model on this dataset. We resize the images to 128x128 and use the same hyperparameters as that of the FFHQ dataset (We mention the exact hyperparameters towards the end). - We observe images with additional and missing fingers in the generated samples. This is attached in the PDF document. - To analyze the effectiveness of the proposed metric, we manually label ~130 images from the generated samples as hallucinated vs. in-support. This includes ~90 images with 5 fingers and ~40 images with missing/ additional fingers i.e. hallucinated samples. - The histogram (in the PDF) shows that the proposed metric can indeed detect these hallucinations to a reasonable degree. In our experiments, we observe that we can eliminate ~80% of the hallucinated samples while retaining ~81% of the in-support samples. - We note that the detection is a hard problem and the fact that the method transfers to the real world is proof of the relationship between mode interpolation and hallucination in real-world data. Please refer to the detailed results and corresponding figures in the attached PDF (Figure 1). These results indicate that our metric is effective in detecting hallucinated samples in natural images as well. This also solidifies the connection between mode interpolation and hallucination in real-world datasets. This connects how additional fingers in StableDiffusion-generated images are closely linked to the ideas discussed in the paper. ### Experiments on Alternative Parametrizations While the majority of the experiments in the submission were performed on DDPM models, we were nudged to expand the experiments to other parametrizations. We have added experiments with ADM model and likelihood-based Diffusion Models like Variational Diffusion Models in the rebuttal response. —-------------- ### Additional experimental details on the Hands dataset. We trained for a total of 200k iterations with batch size 16 and a learning rate of 1e-4. The diffusion process was trained with 1000 steps with a cosine noise schedule. The U-Net comprised 256 channels, with an attention mechanism incorporating 64 channels per head and 3 residual blocks. For sampling, we use 500 timesteps with respacing. [1] Afifi, M. (2019). 11K Hands: Gender recognition and biometric identification using a large dataset of hand images. Multimedia Tools and Applications. https://doi.org/10.1007/s11042-019-7424-8 [2] Nichol, Alexander Quinn, and Prafulla Dhariwal. "Improved denoising diffusion probabilistic models." International conference on machine learning. PMLR, 2021. Pdf: /pdf/f3a16d64a746e183c247d0450e1dc7cfc8f96816.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
In-and-Out: Algorithmic Diffusion for Sampling Convex Bodies	Accept (spotlight)	Summary: In this paper, the authors consider the problem of uniform sampling from general convex body. The algorithm works by augmenting the state space followed by performing alternative Gibbs sampling, where one of the inner steps is implemented by rejection sampling. Non-asymptotic end-to-end bounds on the mixing time in Renyi divergence under warmness assumption is established. The analysis takes the view of the two updates as forward / backward heat flows, building on existing proximal sampler work, therefore offers a clean stochastic process perspective on the algorithm. Various connections of the proposed algorithm to ball walk and speedy walk are also discussed. Strengths: The paper is clearly written and well-structured. Relevant related works are adequately surveyed with the topic being of great interest to many problems in machine learning and computational statistics. While the results and analysis build on the existing framework of proximal sampler for log-concave sampling, I think there are contributions in the paper to this new setting that's worth sharing with the community. The approach is conceptually simple and offers a fresh perspective on constrained sampling. Weaknesses: I have listed some questions in the section below. My main concern is that while I understand the authors provide guarantee in a stronger metric compared to existing algorithm / analysis, given that the query complexity of In-and-Out matches that of some previous work, and the methods are similar in some regard (for example, the second step is conceptually similar to a projection step), it's unclear to me what the practical advantage of the proposed method may be. Minor comment: Some kind of table putting together all the mentioned rates under different assumptions / metrics alongside related previous results in the literature will help the reader digest things a bit better. Technical Quality: 3 Clarity: 3 Questions for Authors: - I haven't given this a careful thought - does the result follow from the proximal sampler result by taking some suitable limit? (since the target is log-concave here and "discretization" isn't an issue for Gibbs sampler) Since I'm confused as to why warmness would show up here but not in the original proximal sampler? - I didn't quite follow Line 146-149 - how would In-and-Out compare to projection-based method? - Line 234-236 the comment about being lazy: In the proposed algorithm, if it doesn't make a proper move (i.e., declares "Failure"), wouldn't that be equivalent to a "lazy" step where things don't move? Or maybe another way to say this is - how should one take ergodic averages along the chain for computing expectation of some observable? It's not entirely clear from first reading. - How does one obtain a warm start in practice? Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: Yes the work is mostly theoretical. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: $\textbf{What practical advantage of the method?}$ The main advantage of our method is the simplicity of the algorithm and the analysis with provable guarantees in commonly used probabilistic metrics, more general than previously known. Not only is our algorithm much simpler to analyze, but it also provides some tangible improvements (such as improving the guarantee from $\mathsf{TV}$ to $\mathsf{KL}$ and $\mathcal{R}_q$); it also shows a clear and direct connection between isoperimetry and convergence. In practice, we might expect comparable performance between all these approaches, although this would depend on the details of the implementation. $\textbf{Does the result follow from the proximal sampler by taking some suitable limit}$ As demonstrated in Lemma 12 and Theorem 3, the mixing guarantee of our sampler (i.e., how many outer loops are needed) does follow from a limiting argument. However, what matters in the end is a bound on query complexity (not just mixing rate), which essentially requires us to bound the number of rejections throughout backward steps. The approach required for the constrained case is not comparable to the unconstrained case. Previous work on proximal sampling works under a well-conditioned setting without hard constraints, where the number of trials for rejection sampling (for the backward step) is always $\mathcal{O}(1)$ regardless of the forward step. However, in the presence of constraints, this type of analysis for the backward step is no longer possible. Analyzing proximal-type sampling for this setting has been a well-known open problem. Instead, we carried out the analysis for the backward step in a more careful way. As a result, there are a number of new ideas in the rejection analysis. $\textbf{Line 146-149: How would INO compare to projection-based methods}$ In general, a projection oracle is stronger than a membership oracle, and its implementation using a membership oracle requires $O(d^2)$ membership calls per projection in the worst case. One can ask instead what happens if we assume a projection oracle which is roughly the same cost as a membership oracle. In this case, leveraging projection might be faster, but this is a non-trivial problem. We leave this for future work. $\textbf{Failure = Lazy? How should one take ergodic averages along the chain for computing expectation of some observable?}$ We thank the reviewer for this question. In our view, failure of our chain is not the same as taking lazy steps in e.g. Ball walk. Lazy chains have a 1/2 chance to remain stationary at each instant, potentially doubling the iterations needed for convergence. By contrast, our algorithm has an arbitrarily small failure probability (moreover, the mixing guarantee has only a poly-log dependence $\text{polylog}(1/\eta)$). In the event of failure, we restart the algorithm until we succeed, which does not introduce any bias. Regarding the second question, it is still possible to take ergodic averages along the chain (assuming you pick the failure probability at each iteration to be sufficiently small so that your run rarely fails during the entire horizon of your run). This is because our Markov chain still has a spectral gap, and so the same techniques used to obtain guarantees for ergodic averages continue to work in our case. $\textbf{How to obtain a warm start in practice}$ Obtaining warm-starts in practice is non-trivial, and requires some type of annealing algorithm in general. Indeed, warm-start generation has been studied for more than two decades in theoretical computer science. See e.g., [1, 2] for how this can be done. For simplicity, we assume that a warm start is provided in our algorithm, although one can use the guarantees in [1, 2] to provide a rigorous justification. *** [1] Gaussian Cooling and $O^*(n^3)$ Algorithms for Volume and Gaussian Volume, Ben Cousins and Santosh S. Vempala. [2] Reducing Isotropy and Volume to KLS: An $O(n^3\psi^2)$ Volume Algorithm, Jia et al. --- Rebuttal Comment 1.1: Comment: Thanks for clarifying and the explanation. I do think the paper makes contribution that the community would benefit from seeing. My slight reservation comes from the fact that most of the contribution comes from analyzing the rejection sampling part, in which the M-warmness condition is doing most of the heavy-lifting, so perhaps in some sense the stated results are expected. --- Rebuttal 2: Comment: We are unclear on the reviewer's "reservation". The problem of sampling constrained convex bodies has been widely studied for decades and so far did not have guarantees beyond TV distance; moreover, in recent years, it has been a well-known open problem to see if diffusion-based methods could be used to obtain a polytime algorithm. Our main results show stronger guarantees for the classical problem using a simple and clean diffusion approach. The resulting analysis brings together several well-known analysis components, along with some extensions (to the constrained setting) and some new ideas (rejection analysis). We feel that the fact the solution is relatively simple and does not need substantial technical sophistication is an attractive feature.	Summary: The paper presents a novel random walk algorithm for uniform sampling of high-dimensional convex bodies that provides improved runtime complexity and guarantees on the result, especially with respect to Rényi divergence. Sampling high-dimensional convex bodies, a fundamental problem in algorithm theory with numerous applications in scientific computing, systems biology, differential privacy, and (to a lesser extent) machine learning. All the samplers known so far rely on Markov chains and most of the time, convergence analysis depends on limiting the conductivity of the associated chain, which in turn controls the mixing rate. The algorithm alternates in and out moves, which is a kind of modification of ball walk, avoiding MH step. The theoretical analysis shows that the method contracts the distribution towards the target distribution at a rate that is influenced by the isoperimetric properties of the convex body. The results show the effectiveness of the new algorithm compared to traditional methods such as the ball-walk and hit-and-run algorithms. The "in-and-out" method shows superior performance, especially in high-dimensional environments, due to its direct reduction to isoperimetric constants. Strengths: - Introduction of the "in-and-out" algorithm for uniform sampling that uses a heat flow approach. - stronger guarantees in terms of Rényi divergence, which includes other divergence measures such as total variation (TV), Wasserstein (W2), Kullback-Leibler (KL) and chi-squared (χ2). - analysis of mixing rates from a heat flow perspective, providing new insights and extending known results for the unconstrained domain. Convergence rate is shown to be determined by functional inequalities such as Poincaré (PI) and Log-Sobolev inequalities (LSI-I). Iteration complexity: For isotropic distributions, the algorithm achieves convergence with a polynomial number of iterations depending on the dimension and the desired accuracy. Weaknesses: - I don't see any major weaknesses. The paper is easy to read, the main stages of the analysis are outlined in the text (I didn't have time to check the appendices) and are interesting. I regret the absence of a numerical section to compare the interest of the In-and-Out method on practical examples [comparing it to existing algorithms]. Technical Quality: 4 Clarity: 3 Questions for Authors: - Can you provide more details on the initialization process and parameter selection (e.g., h, N) for the algorithm? - Could you elaborate on how the functional isoperimetric constants influence the convergence rate of the algorithm for specific geometry (polytopes, ellipsoids, etc...) ? - How can the algorithm be extended to sample from general log-concave distributions restricted to convex bodies or other non-log-concave distributions satisfying isoperimetric inequalities? [is there a "general" idea that can be preserved? - replacing the "hard" Metropolis filter by and In-and-Out mechanism ?] - Confidence: 5 Soundness: 4 Presentation: 3 Contribution: 3 Limitations: yes Flag For Ethics Review: ['No ethics review needed.'] Rating: 8 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: $\textbf{Initialization process and parameter selection}$ - Initialization process: We assume that the initial start is $M$-warm in this work. Obtaining this warm-start is non-trivial, and requires some type of annealing algorithm in general. Warm-start generation has been studied for more than two decades in theoretical computer science. See e.g. [1] for how this can be done. - Parameter selection: The details of $N, h, \eta$ are given in the proof (see Lemma 3 and 14 for example). We will make this more clear in the initial Theorem statement as well. Note that we do not track the absolute constants hidden in big-O notation, but this can be obtained from a careful reading of the proof; our analysis was not optimal with respect to numerical constants, which can likely be sharpened with a more precise argument. $\textbf{How FI parameters affect the convergence rate for specific geometry}$ The Poincare constant in general is on the same order as the maximum eigenvalue of the covariance, while the log-Sobolev constant is bounded by the squared diameter of the convex body (please refer to Appendix D). However, for a more structured body, it is not clear what the sharpest possible constant is for these functional inequalities. In general, we expect that it would be very difficult to estimate unless the body is something simple like an $\ell_p$ ball. We can also obtain the constants under a linear map $T: x \mapsto Ax$ by multiplying the constants by $\|\|A\|\|^2$. $\textbf{Extension to a general setting}$ We thank the reviewer for their insightful suggestion. While our framework could potentially accommodate it, the rates after incorporating a first-order oracle for sampling $e^{-f}1_K$ are not immediately clear from our analysis and would take some more effort. We leave this for future work. *** [1] Gaussian Cooling and $O^*(n^3)$ Algorithms for Volume and Gaussian Volume, Ben Cousins and Santosh S. Vempala. --- Rebuttal Comment 1.1: Comment: This is a good paper. I will keep my score !	Summary: The paper addresses the fundamental problem of uniformly sampling high-dimensional convex bodies. The main contribution is the proposal of the In-and-Out algorithm, analyzed within the framework of the proximal sampling scheme. Using existing analyses from the literature, the paper derives strong results. Additionally, the authors discuss classical methods for constrained sampling and diffusion-based or proximal methods for unconstrained sampling. Strengths: - Overall, I like this paper. It proposes a new method and offers valuable insights. Additionally, the paper achieves strong results with straightforward proofs. - The paper is well-written and easy to follow. Weaknesses: - The analysis techniques used in the paper already exist in the literature, which limits the technical contribution. -The paper does not provide a comparison of iteration/query complexity with existing works. Technical Quality: 3 Clarity: 3 Questions for Authors: - Is it possible to extend these results to the log-concave setting? - The membership oracle used is standard. What if we are given the polytope constraint explicitly? 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: $\textbf{Techniques are already existing}$ As noted by Reviewer W5VJ, our paper is not “just” putting together known components. Previous work on proximal sampling works under a well-conditioned setting without hard constraints, where the number of trials for rejection sampling (for the backward step) is always $\mathcal{O}(1)$ regardless of the forward step. However, in the presence of constraints, this type of analysis for the backward step is no longer possible. Analyzing proximal-type sampling for this setting has been a well-known open problem. Instead, we carried out the analysis for the backward step in a more careful way. As a result, there are a number of new ideas in the rejection analysis. $\textbf{Extension to a general setting}$ We thank the reviewer for their insightful suggestion. While our framework could potentially accommodate it, the rates after incorporating a first-order oracle for sampling $e^{-f}1_K$ are not immediately clear from our analysis and would take some more effort. We leave this for future work. $\textbf{Polytope constraint?}$ There are several ways of leveraging the explicit structure of the log-concave sampling problem. For instance, one can easily implement a projection oracle for polytope constraints (which is stronger than a membership one), so one may consider a projection-based algorithm. Another approach for exploiting the structure is to use barrier-related information. In general, a convex constraint admits a self-concordant barrier $\phi$, and samplers with the local metric given by the Hessian $\nabla^2 \phi$ are provably fast and practical (due to condition-number independence, for instance). --- Rebuttal Comment 1.1: Comment: Thank you very much for your detailed response.	Summary: This work presents a new algorithm, called In-and-Out, for sampling from the uniform distribution over a convex subset $K$ of $R^d$ that comes with stronger guarantees than previous algorithms. The proposed algorithm is an instantiation of the Proximal Sampler (PS), an abstract sampling algorithm which was recently shown to have very strong guarantees (Chen et al., 2022 [27]). The PS was previously considered for sampling from $\propto e^{-f} dx$ given first-order oracle access to $f$, and was typically implemented using a form of rejection sampling; the guarantees in [27] are stated purely in terms of the Poincare Inequality (PI) or Log-Sobolev Inequality (LSI) constant of the target. In the setting of this work, the target is $\propto 1_K$ the uniform distribution on a set $K$ for which we have membership oracle access, and the implementation also uses (another form of) rejection sampling. The guarantees presented in this work follow from the analysis from [27] (§B.2) and a regularity lemma (Lemma 12), from bounds on the PI and LSI constants of uniform distributions known from various recent works (Lemma 9 and §D), and from fine bounds on the failure probability in rejection sampling (§B.3). Strengths: From the point of view of the problem of sampling convex bodies, the contributions of this paper are outstanding. The results appear much stronger than previously known guarantees (but I am not familiar with the literature on this problem, so I can only trust the authors's discussion of the related work.) It illustrates that the diffusion approach to sampling can yield strong results on a problem where geometric approaches are perhaps more natural. From the point of view of algorithmic diffusion, this paper is not "just" a piecing together of several known components, as the analysis of the failure probability of the rejection step is not at all obvious. I found the concise rewriting of the analysis of [27] (Part I of §B.2) quite appreciable as well. Weaknesses: - No application is presented or discussed. Usually for theoretical works such as this one, the value of the contribution lies in the analysis technique, with the hope that it will allow to eventually obtain guarantees for future applications. But the applications that naturally come to my mind are cases which the results of [27] already cover. Some minor suggestions: - The relation between Thms 1, 2, 3 is a little bit confusing, as only Thms 2, 3 talk about PI and LSI constants. Perhaps the presentation of the results could be made clearer by moving Lemma 9 to the end of §2, or at least making a reference to it there. - I would suggest mentioning already in the abstract or the introduction that In-and-Out is an instance of PS. This would be fairer w.r.t. prior work in my opnion. - The fact that Part I of §B.2 is a restatement of the analysis of [27] should be clarified (the terms "revisit" and "review" currently used on lines 563, 569 are not completely clear). - On lines 139-141, you mention that the time-reversal SDE has the property that it is also a reversal "pointwise", i.e, conditional on the endpoint. But I did not see where this fact is used, as in §B.2 only the reversal of the heat flow at the PDE level is used. Technical Quality: 4 Clarity: 4 Questions for Authors: - Regarding the first point in "Weaknesses": what are some application cases in machine learning where your work applies? - Can the In-and-Out algorithm be extended to sampling from a target $\propto e^{-f} 1_K$ where $f$ is smooth on $R^d$ given first-order access to $f$ and membership oracle access to $K$? Specifically the rejection sampling step and its failure probability analysis (since I expect the analysis of the abstract algorithm, PS, is unchanged) - On line 175, you mention a better query complexity if $K$ is near-isotropic, but Corollary 1 just below is about the exactly-isotropic case. What does line 175 refer to? (Is it Thm 5? if yes it should be mentioned in the main text) - Out of curiosity: are there ways to rescale a convex body to be near-isotropic, given membership oracle access? This could give a preprocessing step which could improve the query complexity you report. Confidence: 4 Soundness: 4 Presentation: 4 Contribution: 4 Limitations: The authors have adequately addressed the limitations. Flag For Ethics Review: ['No ethics review needed.'] Rating: 8 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: $\textbf{Application}$ Our work mainly aims to provide a new algorithmic/analytic framework for the uniform sampling problem under the membership oracle model. The applications of this problem are already widespread and well-known, therefore we do not feel the need to propose any new applications. Instead, we note that this problem is used in a number of fundamental settings: volume computation for convex bodies; as a core subroutine in general convex body sampling; metabolic flux sampling in systems biology; Bayesian inference in statistics; and other domains of scientific computing. Thus, new results for the core algorithmic problem would immediately imply theoretical improvements for all these settings. $\textbf{Extension to potentials}$ We thank the reviewer for their insightful suggestion. While our framework could potentially accommodate it, the rates after incorporating a first-order oracle for sampling $e^{-f}1_K$ are not immediately clear from our analysis and would take some more effort. We leave this for future work. $\textbf{Confusion around Line 175}$ We apologize for the confusion. Corollary 1 holds for the near-isotropic case as well, since the operator norm of the covariance is $\mathcal{O}(1)$. $\textbf{How to make it isotropic}$ The question of obtaining an isotropic position has been studied for more than two decades in theoretical computer science. For references, please consult [1, 2] for an idea of how this can be done. In summary, their approach is to draw a few samples from the body and then obtain a rough estimate of the covariance $T$. Then, applying a proper linear map $T^{-1/2}$ to the body will reduce the skewness. Repeating these steps $\mathcal{O}(\log d)$ many times (along with some type of annealing algorithm) ensures that a transformed body is nearly isotropic with high probability. Although we had mentioned this procedure in our related works, we will make a comment earlier in our paper for clarity. We thank the reviewer for their question. $\textbf{Regarding Line 139-141 (time-reversal of SDE)}$ The final paragraph of Appendix E discusses why the pointwise reversal property is needed. In particular, it allows us to claim that given a starting point $z$, the reverse SDE from such a starting point has distribution $\pi^{X\|Y=y}$, a property used in the initial paragraphs of Appendix B. This will be clarified in our revision. *** [1] Gaussian Cooling and $O^*(n^3)$ Algorithms for Volume and Gaussian Volume, Ben Cousins and Santosh S. Vempala. [2] Reducing Isotropy and Volume to KLS: An $O(n^3\psi^2)$ Volume Algorithm, Jia et al. --- Rebuttal Comment 1.1: Comment: Re Applications: I would still recommend adding a few words on practical applications where the membership oracle model is the way to go, if you know of some and they are not too complicated to explain. Otherwise that's ok. Re Line 175: Thank you for clarifying this in the final version. Re Making it isotropic: My bad, I had somehow missed this. But mentioning this procedure earlier in the paper would indeed be beneficial. Re potentials and pointwise time-reversal: fair enough. I maintain my positive rating. Congratulations for a very nice paper :)	Rebuttal 1: Rebuttal: We thank all the reviewers for their time and detailed comments. We respond to specific points below. We note at the outset that main high-level contributions are that (a) we provide the first guarantees for KL and Renyi divergences and (b) we directly relate the convergence rates to classical isoperimetric constants of the target distribution. We make extensive simplifications to the convergence analysis through our approach, which also exposes a clear relationship between the complexity and the isoperimetry of the target distribution. This immediately gives improvements to guarantees for this problem, with rate: $\mathcal{O}(qd^2 M \Lambda \log 1/\varepsilon)$ in general, where $\Lambda$ is the maximum eigenvalue of the covariance matrix and the convergence is in $q$-Renyi. $\textbf{Rate Comparison}$: One question raised by multiple reviewers concerns the relationship of the rates obtained in our work, as compared to the best known prior results in this setting. Below, we highlight the main results in constrained uniform sampling under the membership oracle before this work: - Ball walk: the rate is $\mathcal{O}(Md^2 \psi_{\text{Cheeger}} \log 1/\varepsilon)$ in TV. It relies on a conductance argument. - Hit-and-run: the rate is $\mathcal{O}(d^2 R^2 \log M/\varepsilon)$ to mix in $\chi^2$, where $R^2$ is the trace of the covariance. It also relies on a conductance argument. These rates were given in the related work section of our paper. In our updated draft, we will also state them immediately after our theorems.	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
An Efficient Recipe for Long Context Extension via Middle-Focused Positional Encoding	Accept (poster)	Summary: The paper introduces CREAM (Continuity-Relativity indExing with gAussian Middle), an efficient method for extending the context window of large language models (LLMs) to handle longer contexts without the need for extensive fine-tuning. CREAM manipulates position indices for shorter sequences within the pre-trained context window, using two key strategies: continuity, and relativity. Additionally, CREAM employs a truncated Gaussian distribution to enhance the model's focus on the middle part of the context, mitigating the "Lost-in-the-Middle" problem. Comprehensive experiments demonstrate CREAM's efficiency and effectiveness, showing improved performance over baselines like RandPos and PoSE on various tasks. Strengths: CREAM achieves superior performance across a spectrum of long-context tasks. The empirical results substantiate CREAM's ability to effectively mitigate the "Lost-in-the-Middle" problem. Weaknesses: I think the presentation of this paper is a significant problem. Actually, I cannot understand the method itself nor the intuitions behind it. First, I do not understand the concept of continuity in positional encoding. The authors use a short paragraph to explain continuity (lines 69-74) without any formulation, which is very abstract. The same goes for relativity, though I understood it from another paper. After explaining these two concepts, you still need to explain why they are important (I did not see this in the paper). Second, I do not understand why splitting the pre-trained context into three segments with different sizes can achieve continuity and relativity. Third, I do not understand why truncated Gaussian middle sampling mitigates the "Lost-in-the-Middle" problem. Line 113 states that it reduces the interval overlap in Eq2. But what is interval overlap and why does it result in the "Lost-in-the-Middle" problem? I may not be the ideal reader for this paper, but if other reviewers feel the same way, this paper may have been hastily completed. Technical Quality: 2 Clarity: 1 Questions for Authors: See Weaknesses Confidence: 2 Soundness: 2 Presentation: 1 Contribution: 2 Limitations: None Flag For Ethics Review: ['No ethics review needed.'] Rating: 3 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you very much for taking the time to review our paper. First and foremost, we would like to express our sincere apologies for any confusion that our work brings to you. As you may have noticed, our presentation reached an average of 3.33 / 4 among three other reviewers. Specifically, reviewer srX3 appreciates the clear writing in methods and fWsk confirms the excellent presentation. Nevertheless, we deeply respect your criticism and would like to further clarify all your confusion and misunderstandings point-by-point as follows. >Q1: First, I do not understand the concept of continuity in positional encoding. The authors use a short paragraph to explain continuity (lines 69-74) without any formulation, which is very abstract. The same goes for relativity, though I understood it from another paper. After explaining these two concepts, you still need to explain why they are important (I did not see this in the paper). A1: In short, the concept of continuity in positional encoding lies in the importance of ensuring the consistency of position indices between fine-tuning and pre-training. Specifically, 1. In lines 69-74, we've discussed the continuity of positional encoding in detail and provided relevant references. PoSE also highlights the importance of continuity in positional encoding during training. 2. In lines 75-82, we elaborate on the relativity of positional encoding and provide a theoretical proof in Appendix B. 3. In lines 38-44, we explain the roles of continuity and relativity. Our ablation experiments (Figure 5(c)) experimentally validate the importance of continuity and relativity. >Q2: Second, I do not understand why splitting the pre-trained context into three segments with different sizes can achieve continuity and relativity. A2: In lines 105-110 of our paper, we've provided a detailed explanation of this matter. The continuity design aims to ``allow the middle segment to closely approximate the pre-trained context window.`` The relativity design aims to ``enable the model to learn as many relative positions as possible.`` >Q3: Third, I do not understand why truncated Gaussian middle sampling mitigates the "Lost-in-the-Middle" problem. Line 113 states that it reduces the interval overlap in Eq2. But what is interval overlap and why does it result in the "Lost-in-the-Middle" problem? A3: In lines 111-115 of our paper, we note that truncated Gaussian sampling can alleviate the "lost in the middle" problem by ``directing the model's attention towards the middle section of the long context``. The overlap of intervals refers to the repeated position indices in Equation (2). The "lost in the middle" issue is not caused by interval overlap but by a bias inherent in the model, as noted in [1]. In Appendix B and L114-115, we further provide theoretical justification that sampling the middle part of a long context with a high importance rate yields a maximization of learned relative position intervals as identified in Equations (2). This work indeed has gone through extensive experiments, careful writing, and figure polishing. We tried to make all contents illustrative and provided detailed supplementary materials in appendices. We hope our answers together with appendices have provided sufficient explanations and clarified your confusion. We are more than willing to elaborate more details if you have further questions. Reference: [1] Lost in the middle: How language models use long contexts. TACL, 2024.	Summary: The paper presents CREAM (Continuity-Relativity indExing with gAussian Middle), an innovative approach to extend the context window of Large Language Models (LLMs) without the need for extensive fine-tuning at the target length. The authors address the "Lost in the Middle" problem, which plagues long-context LLMs by causing a performance drop when retrieving information from the middle of the context. CREAM achieves this by manipulating position indices and introducing a truncated Gaussian sampling method to focus on the middle part of the context during fine-tuning. Strengths: 1. Novel Approach: CREAM offers a novel positional encoding strategy that efficiently extends the context window of LLMs, which is a significant contribution to the field. 2. Empirical Evidence: The paper provides strong empirical evidence through comprehensive experiments, demonstrating CREAM's superiority over existing methods like PoSE and RandPos, especially in handling middle context information. 3. Training Efficiency: The method requires fine-tuning at the pre-trained context window size, which is computationally efficient compared to fine-tuning at the target length. 4. Theoretical Foundation: The paper includes theoretical justifications for the use of truncated Gaussian distribution, adding rigor to the proposed method. Weaknesses: 1. Generalizability: While the paper shows impressive results, it is not clear how generalizable these findings are to other LLMs beyond the tested Llama2-7B model. And I'm wondering whether the method can work with PEFT tuning techniques, such as QLoRA. 2. Lack of Comparative Analysis: The paper could benefit from a more detailed comparative analysis with other contemporary methods. For example, in Table 2, the paper only compares one model (LongChat-v1.5-7B-32k) with the same 32k context window. I suggest that in such comparision, peer models should at least take the same length of input, otherwise, it cannot prove the effectiveness of the proposed model over other Long LLMs with 32k+ context windows. I suggest the author compare with models like Mistral-7B-Instruct-v0.2, LongLoRA etc. Technical Quality: 3 Clarity: 3 Questions for Authors: 1. What are the computational overheads associated with implementing CREAM, and how does it scale with larger context sizes? 2. Are there any specific hyperparameter settings in CREAM that are particularly sensitive, and how were these chosen? Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The discussion in Appendix F regarding the limitations of the CREAM method could be misleading. The author implies that CREAM provides enhanced performance compared to other methods concerning the "Lost in the Middle" issue but acknowledges that the problem is not fully solved due to the nature of decoder-only models. For a genuine limitations section, it is essential to delve deeper into the specific constraints of the CREAM approach and how these limitations might impact its application and effectiveness. A more explicit acknowledgment of the method's shortcomings and a clear explanation of why these issues cannot be overcome with the current model design would significantly improve the section's clarity and usefulness. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you very much for taking the time to review our paper and acknowledging the novelty and empirical superiority of our approach. Below, we provide detailed replies to your comments and hope we can resolve your major concerns. >W1: Generalizability: While the paper shows impressive results, it is not clear how generalizable these findings are to other LLMs beyond the tested Llama2-7B model. And I'm wondering whether the method can work with PEFT tuning techniques, such as QLoRA. A1: Thank you for the constructive comments. Our method has strong generalization capabilities and can be applied to other LLMs without modifying any parameters. To verify this, we conducted experiments on Baichuan2-7B. The experimental results are shown in the table below. (Incidentally, as shown in the table in A2 of reviewer srX3's response, the experimental results on LLaMa3-8B also support this conclusion.) \| \| GovReport \| \| \| \| Proof-pile \| \| \| \| \| :---------------- \| :-------- \| :--- \| :--- \| :--- \| :--------- \| :--- \| :--- \| :--- \| \| \| 4K \| 8K \| 16K \| 32K \| 4K \| 8K \| 16K \| 32K \| \| Baichuan2-7B-Base \| 3.3 \| - \| - \| - \| 5.8 \| - \| - \| - \| \| CREAM-Linear \| 3.6 \| 2.9 \| 2.5 \| 2.2 \| 6.2 \| 6.1 \| 6.0 \| 5.8 \| Through two sets of experiments, we demonstrate that CREAM can work seamlessly with PEFT techniques like LoRA [1] and QLoRA [2] without requiring additional modifications. This compatibility arises because CREAM does not alter any data formats or model structures during fine-tuning; it only adjusts position indices. Detailed experimental results are presented in the following two tables. \| Model \| Single-Doc QA \| Multi-Doc QA \| Summarization \| Few-shot Learning \| Code Completion \| Synthetic Tasks \| Macro \| \| :----------------- \| :------------ \| :----------- \| :------------ \| :---------------- \| :-------------- \| :-------------- \| :---- \| \| Llama2-7B-chat-4k* \| 24.9 \| 22.6 \| 24.7 \| 60 \| 48.1 \| 5.9 \| 31.0 \| \| LoRA-step-800 \| 28.7 \| 28.5 \| 27.7 \| 62.3 \|54 \|10.3 \| 35.3 \| \| QLoRA-step-400 \| 20.9 \| 19.0 \| 26.8 \| 54.1 \| 47.4 \| 4.0 \| 28.7 \| \| Ours \| 34.8 \| 31.1 \| 27.2 \| 65.1 \| 50.4 \| 7 \| 35.9 \| We will include the training curves of these two methods in the revised version. >W2: Lack of Comparative Analysis: The paper could benefit from a more detailed comparative analysis with other contemporary methods. For example, in Table 2, the paper only compares one model (LongChat-v1.5-7B-32k) with the same 32k context window. I suggest that in such comparision, peer models should at least take the same length of input, otherwise, it cannot prove the effectiveness of the proposed model over other Long LLMs with 32k+ context windows. I suggest the author compare with models like Mistral-7B-Instruct-v0.2, LongLoRA etc. A2: Thank you for the advice for improving our work. Per your suggestion, we have added experimental results of all three versions of Mistral-7B-Instruct (v0.1, v0.2, v0.3) on Longbench. Since the 7B-Instruct-32K model of LongLoRA is not publicly available, we could not add corresponding results and are more than willing to add the comparison once it's open-sourced. The detailed results of Mistral are presented in the table below. \| Model \| Single-Doc QA \| Multi-Doc QA \| Summarization \| Few-shot Learning \| Code Completion \| Synthetic Tasks \| Macro \| \| :----------------------- \| :------------ \| :----------- \| :------------ \| :---------------- \| :-------------- \| :-------------- \| :------- \| \| Mistral-7B-Instruct-v0.1 \| 29.5 \| 20.7 \| 26.4 \| 13.6 \| 29.6 \| 10.8 \| 21.8 \| \| Mistral-7B-Instruct-v0.2 \| 28.5 \| 21.5 \| 26.1 \| 50.1 \| 33.8 \| 13.9 \| 29.0 \| \| Mistral-7B-Instruct-v0.3 \| 33.2 \| 30.6 \| 26.8 \| 56.4 \| 15.3 \| 10.4 \| 28.8 \| \| LongChat-v1.5-7B-32k* \| 28.7 \| 20.6 \| 26.7 \| 60.0 \| 54.1 \| 15.8 \| 34.3 \| \| Ours \| 34.8 \| 31.1 \| 27.2 \| 65.1 \| 50.4 \| 7.0 \| 35.9 \| As shown, it is evident that our method outperforms all three versions of Mistral-7B-Instruct. This further confirms the effectiveness of CREAM. >Q1: What are the computational overheads associated with implementing CREAM, and how does it scale with larger context sizes? A1: Our method does not incur any additional computational overhead beyond standard fine-tuning. This is because CREAM does not modify the model structure itself; the only change is to the positional indices. Additionally, as the context window length increases, the computational overhead will increase similarly to standard fine-tuning. However, even with a larger context window, it is still possible to fine-tune with a 4K context length, significantly reducing computational overhead and memory usage. As as shown in the table in A2 of reviewer srX3's response, fine-tuning LLaMA3-8B with a 4K context length (despite its pre-training context length of 8K) remains remarkably effective. --- Rebuttal 2: Title: Rebuttal by Authors Comment: >Q2: Are there any specific hyperparameter settings in CREAM that are particularly sensitive, and how were these chosen? A2: Our method requires only three preset hyperparameters: the mean $\mu$ and variance $\sigma$ of the truncated Gaussian sampling, and the length of the head and tail sections $k$. For the mean $\mu$, it depends on the expansion factor $\alpha$, specifically $\mu = (1 + \alpha) / 2$. For the length $k$, we follow the settings of StreamingLLM[3], which uses a value of 4. Since we have expanded by a factor of 8, we set $k = 4 \times 8 = 32$. This also depends on the expansion factor. For the variance $\sigma$, our setting should ensure higher sampling frequency in the middle and lower (but non-zero) frequency at the ends. The experimental results for different $\sigma$ values in the table in A2 of reviewer fWsk's response can be used as a reference. >Limitations: The discussion in Appendix F regarding the limitations of the CREAM method could be misleading. The author implies that CREAM provides enhanced performance compared to other methods concerning the "Lost in the Middle" issue but acknowledges that the problem is not fully solved due to the nature of decoder-only models. For a genuine limitations section, it is essential to delve deeper into the specific constraints of the CREAM approach and how these limitations might impact its application and effectiveness. A more explicit acknowledgment of the method's shortcomings and a clear explanation of why these issues cannot be overcome with the current model design would significantly improve the section's clarity and usefulness. A: Thank you for noticing our discussed limitations and providing suggestions. We would like to explicitly elaborate the limitations of CREAM as two-fold. First, our method did not involve any adjustments to the model architecture. As discussed in our research question as in L34-35, this work aims to reach an efficient and effective optimality based on a pre-trained model. Consequently, it encounters the decoder-only limit mentioned in [4]. Second, our methods follow prior works and fine-tune pre-trained models on a small dataset considering the efficiency. Nevertheless, our approach might benefit from further enhancement of pre-trained dataset. We will provide a more detailed discussion of the limitations in our paper. We hope our answers have resolved your concerns. If you have any other concerns, please feel free to let us know. Thanks again for your review. Reference: [1] LoRA: Low-Rank Adaptation of Large Language Models. ICLR, 2022. [2] Qlora: Efficient finetuning of quantized llms. NeurIPS, 2023. [3] Efficient Streaming Language Models with Attention Sinks. ICLR, 2024. [4] Lost in the middle: How language models use long contexts. TACL, 2024.	Summary: The paper proposes a new method, CREAM, that better enables extrapolation to longer contexts via finetuning at the base context length. The method uses positional embedding interpolation with the embeddings divided into three areas of interest and uses a truncated Gaussian to sample the position used for the middle segment, to increase training of the middle context. They show that this is at least as effective as prior length extrapolation methods that use finetuning at the base context length, and that CREAM-trained models suffer less from the lost in the middle problem. Strengths: S1. The method shows clear improvement on the targeted issue (the lost in the middle phenomenon)-- e.g. in Table 1. S2. The method is well-motivated both intuitively and theoretically, and the explanation in section 2.2 is well-written and easy to follow. S3. The authors evaluate against the two most reasonable baselines (to my knowledge) and across a good selection of synthetic, long-context, and short-context tasks. (It would be an added benefit to evaluate against finetuning with position interpolation and long context at finetuning-time, to see the efficiency-performance tradeoff; however, I do not think this is strictly necessary to the paper's claims.) Weaknesses: W1. The method is fairly similar to POSE in concept and performance. While I think the idea of emphasizing middle training is reasonable, well-explored, and clearly effective (e.g. in Figure 1), this has also been explored as a post-training or data selection correction in other work. Given the slight performance degradation from POSE on short-context tasks (i.e. in Table 4), I'm concerned that this might not be worth the tradeoff practically to do at training time. W2. Evaluation settings can differ subtly across papers, and so it would be better for the authors to reproduce baseline results rather than citing them from literature, where possible. This is most critical, I think, in Table 4, where the differences between methods are relatively small and all results are compared to the same baseline method, which is not an infeasibly expensive or unavailable model to run. Technical Quality: 3 Clarity: 3 Questions for Authors: Q1. In Table 5: why does the 256k-extrapolated version of CREAM underperform the 128k-extrapolated version on short contexts? Q2. Say you had an even more limited amount of compute, to the point where finetuning on the base context length was prohibitively expensive (e.g., maybe you want to finetuned Llama3-8b but can't fit 8192 context at training time). Do you believe CREAM would be useful in this setting? Do you have any results (or speculation!) that suggest when the method may begin to break down with decreasing maximum training length? Q3. (Minor) What is the context length used in Figure 1? The x axis only reports the position of keys. Suggestions/comments: * Please explain in the text what the occasional highlighting of numbers represents (e.g. in Table 2). It would be helpful for readability to bold the best number in each column across tables. Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: Yes, no concerns here. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you very much for your valuable suggestions and acknowledgment of our well-motivated method. Below we address your questions point-by-point and hope we can resolve your major concerns. >W1: The method is fairly similar to POSE in concept and performance. While I think the idea of emphasizing middle training is reasonable, well-explored, and clearly effective (e.g. in Figure 1), this has also been explored as a post-training or data selection correction in other work. Given the slight performance degradation from POSE on short-context tasks (i.e. in Table 4), I'm concerned that this might not be worth the tradeoff practically to do at training time. A1: We would like to highlight the major contributions and differences compared with PoSE, other post-training, and data selection correction as follows. 1. For the concept, PoSE does not simultaneously leverage the benefits of continuity and relativity, nor does it emphasize the importance of intermediate context. These aspects are our core contributions. 2. For the performance, our method significantly outperforms PoSE across various tasks. For example, it achieves an average improvement of 15.9% on LongChat Lines compared to PoSE. In the Lost in the Middle task, our different interpolation methods (Linear, NTK, Yarn) also show an average improvement of about 10%. 3. In post-training, previous methods usually require a large amount of data and computational resources, with the training context length being much greater than the context length during pre-training. For instance, Yi-1.5[1] uses 10 billion tokens and requires upsampling of long sequences. Qwen-2[2] and InternLM2[3] extend their training context length from 4K to 32K in the final stages of pre-training. Therefore, we can conclude that CREAM not only requires less data and shorter training context lengths but also demonstrates impressive performance. 4. For data selection correction, such as [3] using data engineering techniques to expand context. However, their method requires fine-tuning on at least 500M tokens to achieve satisfactory performance in the Needle-in-a-Haystack test (Figure 3). In contrast, our method only requires $seqlen(4096) \times bsz(32) \times steps(1000) = 125M$ tokens. Therefore, their training data requirement is not only four times larger than ours but also requires meticulous data selection. Additionally, our method can be applied to instruction fine-tuning, which they did not mention. It is important to emphasize that on short-context tasks (i.e. Table 4), our method performs just as well as PoSE. In our manuscript, we overlooked the minor differences between ours and PoSE in Table 4 (<1%) since our focus and superiority lie in addressing the challenges of long contexts. The minor performance turbulence results from the sampling of training data (a de facto strategy as in PoSE and others). To further validate this, we tested model performance with five different random seeds used to sample the training data. The mean$\pm$std results are shown in the table below. \| Model \| Zero-Shot \| \| \| \| Few-Shot \| \| \| :-------------- \| :--------- \| :-------------- \| :-------- \| :-------- \| :-------- \| :-------- \| \| \| WinoGrande \| TruthfulQA(mc2) \| PIQA \| BoolQ \| ARC-C \| HellaSwag \| \| PoSE-Linear \| 68.7±1.30 \| 38.6±1.36 \| 77.9±0.97 \| 76.3±0.74 \| 47.4±1.46 \| 76.9±0.42 \| \| CREAM-Linear \| 68.8±1.30 \| 38.5±1.35 \| 78.1±0.97 \| 76.3±0.75 \| 47.5±1.46 \| 77.0±0.42 \| Based on the experimental results in the table, we can be more confident that the performance of CREAM and PoSE on short contexts is actually comparable. Thank you for the careful review. We would update and add the discussion in our revision. >W2: Evaluation settings can differ subtly across papers, and so it would be better for the authors to reproduce baseline results rather than citing them from literature, where possible. This is most critical, I think, in Table 4, where the differences between methods are relatively small and all results are compared to the same baseline method, which is not an infeasibly expensive or unavailable model to run. A2: Thank you for your suggestion. We've followed your advice and reproduced the results of LLaMa-2-7b-hf, as presented in Table 4. The results are detailed in the table below: \| Model \| Zero-Shot \| \| \| \| Few-Shot \| \| \| :---------------- \| :--------- \| :-------------- \| :------- \| :------- \| :------- \| :-------- \| \| \| WinoGrande \| TruthfulQA(mc2) \| PIQA \| BoolQ \| ARC-C \| HellaSwag \| \| LLaMa-2-7b-hf* \| 69.2 \| 39.5 \| 78.8 \| 77.4 \| 45.9 \| 77.2 \| \| LLaMa-2-7b-hf \| 68.5 \| 38.9 \| 78.8 \| 78.0 \| 48.5 \| 78.1 \| The bolded results in the table are our reproductions, and they are very close to the original results. Therefore, we believe our final conclusions and claims still stand across all tasks. Thank you for the advice. We will add the above results to improve the soundness of our work. >Q1: In Table 5: why does the 256k-extrapolated version of CREAM underperform the 128k-extrapolated version on short contexts? A1: In Table 5, the 128K results are not ours but are cited from PoSE. Since a lower perplexity is better, the results in Table 5 indicate that our method has the potential to extend to 192K or even 256K. Furthermore, compared to PoSE, our performance is significantly superior. --- Rebuttal 2: Title: Rebuttal by Authors Comment: >Q2: Say you had an even more limited amount of compute, to the point where finetuning on the base context length was prohibitively expensive (e.g., maybe you want to finetuned Llama3-8b but can't fit 8192 context at training time). Do you believe CREAM would be useful in this setting? Do you have any results (or speculation!) that suggest when the method may begin to break down with decreasing maximum training length? A2: Thank you for providing the experimental setup, which further highlights the superiority of our method. Following your instructions, we fine-tuned LLaMa3-8b using a 4K context window size. The experimental results are presented in the table below. \| AVG Length \| 2000 \| 2700 \| 3300 \| 4000 \| 5200 \| 6500 \| 7800 \| 8800 \| 9700 \| 11000 \| 12000 \| 14000 \| 17000 \| 19000 \| 24000 \| 28000 \| 32000 \| \| :------------------ \| :--- \| :--- \| :--- \| :--- \| :--- \| :--- \| :--- \| :--- \| :--- \| :---- \| :---- \| :---- \| :---- \| :---- \| :---- \| :------ \| :---- \| \| LLaMa3-CREAM-Linear \| 0.98 \| 0.96 \| 0.98 \| 1.00 \| 0.92 \| 0.96 \| 0.96 \| 0.94 \| 0.86 \| 0.92 \| 0.92 \| 0.92 \| 0.86 \| 0.84 \| 0.70 \| 0.60 \| 0.48 \| The results presented in the table demonstrate that our method is well-suited to this setting and performs surprisingly well. >Q3: (Minor) What is the context length used in Figure 1? The x axis only reports the position of keys. A3: This is consistent with the setting in [5] and corresponds to an approximate length of 5K. Results with longer contexts (10K) are in Table 1. >Suggestions/comments: >Please explain in the text what the occasional highlighting of numbers represents (e.g. in Table 2). It would be helpful for readability to bold the best number in each column across tables. A: Thank you for the insightful suggestions. The highlighted numbers in Table 1 and Table 2 emphasize the advantages of our results compared to other methods. In Table 2, we have bolded the average results. Following your suggestion, we will also bold the best results in each column. We hope our answers have resolved your concerns. If you have any other concerns, please feel free to let us know. Thanks again for your review. Reference: [1] Yi: Open foundation models by 01. arXiv preprint arXiv:2403.04652, 2024. [2] Qwen2 technical report. arXiv preprint arXiv:2407.10671, 2024. [3] Internlm2 technical report. arXiv preprint arXiv:2403.17297, 2024. [4] Data Engineering for Scaling Language Models to 128K Context. ICML, 2024. [5] Lost in the middle: How language models use long contexts. TACL, 2024. --- Rebuttal Comment 2.1: Comment: Thanks for the detailed response! > W1 I appreciate the multiple random seeds for the short-context performance eval (and would love to see this extended to report error bars on the long-context evals as well). My major concern was short-context regression relative to POSE, and looking at the results over multiple random seeds shows that there is not a significant difference in short-context performance. > Q1 Totally my bad, somehow missed that this table was perplexity! > we fine-tuned LLaMa3-8b using a 4K context window I'm also glad to see how well the method performs in this even more length-constrained scenario. Given the rebuttal, I have raised my score 5->6. Thanks for the nice paper! --- Reply to Comment 2.1.1: Comment: We would like to express our sincere gratitude for your thorough review of our paper. Your expertise has greatly contributed to enhancing the quality of our work, and we are committed to incorporating your suggestions during the revision process. Thank you once again for acknowledging our efforts.	Summary: The paper proposes a method for extending the context window of pretrain large language models. The approach, CREAM, relies on modifying position indices to interpolate the positional encodings. Despite the often computationally expensive nature of such work, CREAM can extend to very long context windows while only needing to train at the original pretrained context window. Additionally, in their approach to the context length problem, the authors propose a solution that focuses explicitly on learning at the middle of the context — a span that often under-performs in long context models. The experimental results cover a wide variety of problems, both in terms of tasks, as well as context length challenges. Overall the results look very promising, and show a strong method for addressing a challenging task of extending the context length of LLMs. Strengths: - The authors tackle two problems that go hand in hand, namely extending the context length during fine-tuning - but doing so in a way ensures consistent performance. - The approach divides the desired context length into three segments, which then results in relative positional distances that vary and consequently learning all relative positions within the target length $L$. The technique is simple, but clever and an effective way to efficiently expose the model to a broader range of relative positional distances during training. - The results are very strong, particularly with the performances listed on Long Bench, which encompasses a broad range of tasks. Weaknesses: - No error bars shown on results. In most cases the results are quite strong, but the error bars would be helpful — particularly in some of the closer comparisons with PoSE. - The solution of using a truncated Gaussian approach lacks motivation. The "lost in the middle" problem is clear, however the solution of using a truncated Gaussian to force more focus on the middle seems brittle. Could the parameters of the truncated Gaussian be learned from data? The approach works well based on the results shown in Figure 5a, however. Technical Quality: 2 Clarity: 4 Questions for Authors: The authors mention that CREAM only needed to be trained for 100 in some cases. Can the authors provide more insight on why the results are very good despite so little training? This seems like a significant achievement, but was not discussed in detail. Confidence: 3 Soundness: 2 Presentation: 4 Contribution: 4 Limitations: The amount of focus on the middle context seems fixed in this approach. While the results for Gaussian truncation appear promising, it's not clear if this direct approach to solving the "lost in the middle" problem is universal. In short, how do we know how much to reweight the importance of the middle context, and does it vary by dataset or task? Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We sincerely thank you for your constructive comments ``simple, but clever, effective and effcient`` and acknowledgement of our approach with ``very strong performances that encompass a broad range of tasks``. Below, we provide detailed replies to your comments and hope we can resolve your major concerns. >W1：No error bars shown on results. In most cases the results are quite strong, but the error bars would be helpful — particularly in some of the closer comparisons with PoSE. A1: Thank you for the helpful suggestion. In our manuscript, we fixed all random seeds of all experiments to guarantee the reproducibility of our reported results. Per your advice, we have further conducted repeated experiments with five randomly generated seeds on the linear extension experiment. The detailed results with mean$\pm$std are reported in the table below. \| Model \| Zero-Shot \| \| \| \| Few-Shot \| \| \| :-------------- \| :--------- \| :-------------- \| :-------- \| :-------- \| :-------- \| :-------- \| \| \| WinoGrande \| TruthfulQA(mc2) \| PIQA \| BoolQ \| ARC-C \| HellaSwag \| \| PoSE-Linear \| 68.7±1.30 \| 38.6±1.36 \| 77.9±0.97 \| 76.3±0.74 \| 47.4±1.46 \| 76.9±0.42 \| \| CREAM-Linear \| 68.8±1.30 \| 38.5±1.35 \| 78.1±0.97 \| 76.3±0.75 \| 47.5±1.46 \| 77.0±0.42 \| By comparing the mean and variance in the table, it can be observed that CREAM and PoSE have comparable capabilities in handling short texts. We will add the results in our revision. >W2: The solution of using a truncated Gaussian approach lacks motivation. The "lost in the middle" problem is clear, however the solution of using a truncated Gaussian to force more focus on the middle seems brittle. Could the parameters of the truncated Gaussian be learned from data? The approach works well based on the results shown in Figure 5a, however. A2: Thank you for pointing this out. Our motivations for truncated Gaussian are three-fold: 1. Intuitive Explanation. The issue of "lost in the middle" highlights that the performance of LLMs is often strong at the beginning and end, but weak in the middle[1]. As discussed in L111-114, a straightforward idea to address this is to guide LLMs to focus more on the middle part relative to the beginning and end of the context. This approach results in a "reverse U" shape curve, similar to a truncated Gaussian distribution curve. 2. Theoretical support. In Appendix B and L114-115, we provide theoretical justification that sampling the middle part of a long context with a high importance rate yields a maximization of learned relative position intervals as identified in Equations (2). 3. Empirical observation. As you mentioned, it has proven to be quite effective for all demonstrated long context tasks, encompassing retrieval, lost-in-the-middle, LongBench, etc. Could the parameters of the truncated Gaussian be learned from data? Great question. In our truncated Gaussian sampling, as shown in Equation (3), the only hyperparameters are the mean $\mu$ and the variance $\sigma$. 1. For $\mu$, it depends on the expansion factor. For example, when expanding from 4K to 32K, the expansion factor is 8, so $\mu = (1+8)/2$. 2. For $\sigma$, learning from the data is flexible, but since the sampling process is discrete, the gradient cannot be back-propagated, making the learning cost high. Additionally, we conducted experiments with five different $\sigma$ values, and the results in the table show that the current choice ($\sigma=3$) indeed performs the best. \| Length \| 2500 \| 3600 \| 4200 \| 4800 \| 6000 \| 7100 \| 9400 \| 11800 \| 14000 \| 16000 \| 17500 \| 20000 \| 22000 \| 26000 \| 28000 \| 30000 \| 32000 \| AVG \| \| :-------- \| :--- \| :--- \| :--- \| :--- \| :--- \| :--- \| :--- \| :---- \| :---- \| :---- \| :---- \| :---- \| :---- \| :---- \| :---- \| :---- \| :---- \| :---- \| \| sigma=2 \| 0.68 \| 0.56 \| 0.7 \| 0.66 \| 0.7 \| 0.68 \| 0.68 \| 0.56 \| 0.52 \| 0.4 \| 0.42 \| 0.38 \| 0.48 \| 0.38 \| 0.4 \| 0.28 \| 0.12 \| 0.506 \| \| sigma=2.5 \| 0.9 \| 0.72 \| 0.78 \| 0.86 \| 0.78 \| 0.76 \| 0.7 \| 0.56 \| 0.64 \| 0.38 \| 0.52 \| 0.4 \| 0.48 \| 0.36 \| 0.46 \| 0.34 \| 0.3 \| 0.585 \| \| sigma=3 \| 0.96 \| 0.82 \| 0.92 \| 0.94 \| 0.92 \| 0.86 \| 0.84 \| 0.78 \| 0.76 \| 0.56 \| 0.62 \| 0.52 \| 0.62 \| 0.46 \| 0.52 \| 0.38 \| 0.4 \| 0.699 \| \| sigma=3.5 \| 0.9 \| 0.72 \| 0.84 \| 0.8 \| 0.84 \| 0.78 \| 0.74 \| 0.66 \| 0.58 \| 0.4 \| 0.54 \| 0.4 \| 0.5 \| 0.38 \| 0.38 \| 0.36 \| 0.26 \| 0.593 \| \| sigma=4 \| 0.9 \| 0.8 \| 0.86 \| 0.84 \| 0.78 \| 0.72 \| 0.72 \| 0.5 \| 0.5 \| 0.42 \| 0.44 \| 0.26 \| 0.36 \| 0.22 \| 0.3 \| 0.3 \| 0.26 \| 0.540 \| --- Rebuttal 2: Title: Rebuttal by Authors Comment: >Q: The authors mention that CREAM only needed to be trained for 100 in some cases. Can the authors provide more insight on why the results are very good despite so little training? This seems like a significant achievement, but was not discussed in detail. A: Thank you for the careful review. For the Base model (Llama2-7b), we conducted 1,000 steps of continual pre-training on the to ensure a fair comparison with prior works as in [5,6]. For the Chat model (Llama2-7b-chat), we performed only 100 steps of Instruction Fine-Tuning (IFT). Indeed, we attempted to extend the IFT to 400 steps, but the performance deteriorated; the detailed results are shown in the table below. This is because we used the instruction dataset ShareGPT as a substitution for the original IFT used for Chat model (the original dataset is not publicly accessible). This observation is in line with previous studies that have pointed out that instruction fine-tuning on different datasets may lead to catastrophic forgetting and impact performance[2,3,4]. To balance the effectiveness of position index learning and the degradation of the LLM's IFT performance, we limited the IFT to 100 steps. Like you have observed, 100 steps of finetuning yield effective long-context performance. \| Model \| Single-Doc QA \| Multi-Doc QA \| Summarization \| Few-shot Learning \| Code Completion \| Synthetic Tasks \| Macro \| \| :----------------- \| :------------ \| :----------- \| :------------ \| :---------------- \| :-------------- \| :-------------- \| :---- \| \| Llama2-7B-chat-4k* \| 24.9 \| 22.6 \| 24.7 \| 60 \| 48.1 \| 5.9 \| 31.0 \| \| 100 steps \| 34.8 \| 31.1 \| 27.2 \| 65.1 \| 50.4 \| 7.0 \| 35.9 \| \| 400 steps \| 30.9 \| 23.5 \| 27.1 \| 62.4 \| 35.6 \| 3.4 \| 30.5 \| >Limitations: The amount of focus on the middle context seems fixed in this approach. While the results for Gaussian truncation appear promising, it's not clear if this direct approach to solving the "lost in the middle" problem is universal. In short, how do we know how much to reweight the importance of the middle context, and does it vary by dataset or task? A: Sorry about confusion. We would like to clarify that the middle context our method focuses on is NOT fixed. According to Algorithm 1, each sample requires two rounds of sampling to obtain the final position index, so the intermediate context position index varies between samples. Specifically, we first sample a factor $\alpha$ from a truncated Gaussian distribution to determine the interval where the current $P_e$ is located. Then, we uniformly sample the final $P_e$ from this interval, which is the ending position index of the intermediate section. The sample flow was discussed in L122-125. We would further add more clarification to explain our strategy. As mentioned above, our method does NOT require meticulously designed weight distributions; instead, it automatically assigns weights using truncated Gaussian sampling. Moreover, in all the experiments presented in our paper, all parameters remained consistent, yet the method still performed effectively across various tasks. This demonstrates the generality of our approach, which does not change depending on the dataset or task. We hope the above response can resolve your questions and concerns. Please let us know if there is any further question! Thanks again for your review. Reference: [1] Lost in the middle: How language models use long contexts. TACL, 2024. [2] CoachLM: Automatic Instruction Revisions Improve the Data Quality in LLM Instruction Tuning. ICDE, 2024. [3] Lima: Less is more for alignment. NeurIPS, 2024. [4] From Quantity to Quality: Boosting LLM Performance with Self-Guided Data Selection for Instruction Tuning. NAACL 2024. [5] Extending Context Window of Large Language Models via Positional Interpolation [6] PoSE: Efficient Context Window Extension of LLMs via Positional Skip-wise Training, ICLR 2024. --- Rebuttal Comment 2.1: Comment: Thank you for the response. You have answered each of my questions and provided clarity on some points I misunderstood. I appreciate the additional analyses you’ve run — they provide insight and more confidence in your findings. --- Reply to Comment 2.1.1: Comment: Thank you for your thorough review of our rebuttal and your encouraging feedback. Your expertise has significantly contributed to improving the quality of our work, and we are dedicated to incorporating your suggestions in our revision process. If you are satisfied with our rebuttal, we would be extremely grateful if you could consider increasing the final score.	Rebuttal 1: Rebuttal: We appreciate all the reviewers for their hard work, and we will re-emphasize a few strengths of our work: 1. We propose a ``simple, but clever and an effective way to efficiently expose the model to a broader range of relative positional distances during training`` (Reviewer fWsk). This ``novel positional encoding strategy that efficiently extends the context window of LLMs, which is a significant contribution to the field`` (Reviewer XDBh). 2. Our method ``provides strong empirical evidence through comprehensive experiments, demonstrating CREAM's superiority over existing methods like PoSE and RandPos, especially in handling middle context information`` (All Reviewers) . Additionally, our method ``is computationally efficient compared to fine-tuning at the target length`` (Reviewer XDBh). 3. Notably, our ``method is well-motivated both intuitively and theoretically, and the explanation in section 2.2 is well-written and easy to follow`` (Reviewer srX3,XDBh). In the subsequent revisions, we address all the reviewers' comments by making the following modifications to our paper: 1. We add the surprisingly good experimental results of fine-tuning LLaMa3-8B using CREAM on 4K data length. Additionally, we include the experimental results of applying CREAM on Baichuan2-7B to demonstrate the generality of our approach across different scenarios and LLMs. (Reviewers srX3, XDBh) 2. We include the experimental results of combining CREAM with different PEFT techniques, such as LoRA and QLoRA, to further prove the versatility of our method. (Reviewer XDBh) 3. We add the ablation results of different $\sigma$ values. (Reviewers fWsk, XDBh) 4. We include error bars in the results of Table 4 and add the reproduced results of LLaMa2-7B. (Reviewers fWsk, srX3) 5. We add the experimental results of Mistral-7B-Instruct (v0.1, v0.2, v0.3) on Longbench in Table 2 to further validate the effectiveness of our approach. (Reviewer XDBh) 6. We further discuss the reasons for the limitations of our method in the limitations section. (Reviewer XDBh) We hope our responses will address the reviewers' concerns. If there are any questions, we look forward to further discussions.	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Symmetric Linear Bandits with Hidden Symmetry	Accept (poster)	Summary: The paper introduces and analyzes the problem of symmetric linear bandits with hidden symmetry. The authors study high-dimensional linear bandits where the reward function is invariant under certain unknown group actions on the set of arms. The key contributions are: - An impossibility result showing that no algorithm can benefit solely from knowing that the symmetry group is a subgroup of permutation matrices, necessitating further structural assumptions. - Establishment of a cardinality condition on the class of symmetric linear bandits with hidden symmetry, under which the learner can overcome the curse of dimensionality. - Introduction of a new algorithm called EMC (Explore Models then Commit) that achieves a regret bound of O(d_0^(1/3) * T^(2/3) * log(d)), where d is the ambient dimension and d_0 is the dimension of the true low-dimensional subspace (d_0 << d). - An improved regret bound of O(d_0 * sqrt(T) * log(d)) under an additional assumption of well-separated models. - Discussion of an open problem regarding adaptive algorithms that can achieve optimal regret in both well-separated and general cases. The paper provides theoretical analysis and proofs for the proposed algorithms and bounds. The authors position their work in the context of existing literature on sparse linear bandits and model selection, highlighting the novelty of their approach in leveraging symmetry for efficient exploration in high-dimensional linear bandits. This paper is primarily theoretical, focusing on the mathematical formulation of the problem, algorithm design, and regret analysis. It does not include experimental results. Strengths: 1. Originality: - Introduces a novel problem formulation of symmetric linear bandits with hidden symmetry, extending and generalizing the well-studied sparse linear bandit setting. - Creatively combines ideas from group theory, model selection, and bandit algorithms to address this new problem. - The proposed EMC algorithm represents an innovative approach to leveraging hidden symmetry in high-dimensional bandits. 2. Quality: - The technical analysis is rigorous and thorough, with well-structured proofs for all major claims. - Provides a comprehensive theoretical framework, including an impossibility result, regret bounds, and algorithm analysis. - Builds upon and extends existing results in a mathematically sound manner. 3. Clarity: - The problem motivation and significance are clearly articulated. - The paper is well-structured, with a logical flow from problem formulation to theoretical results. - Technical concepts are generally well-explained, with appropriate use of mathematical notation. - Some complex concepts, particularly around the equivalence between sparsity and interval partitions, could benefit from more intuitive explanations or concrete examples for broader accessibility. 4. Significance: - Addresses an important gap in the literature by considering hidden symmetry in high-dimensional linear bandits. - Provides new insights into the role of symmetry in sequential decision-making, with potential broad implications for reinforcement learning and online optimization. - Establishes connections between symmetry structures and sparsity, potentially opening new avenues for efficient exploration in high-dimensional spaces. - The proposed algorithms and bounds represent significant progress in overcoming the curse of dimensionality in certain bandit settings. Weaknesses: 1. Limited empirical validation: - The paper appears to be primarily theoretical, with no mention of experimental results or simulations to validate the proposed algorithms. - Including empirical studies, even on synthetic datasets, would strengthen the practical relevance of the theoretical results. - Comparison with existing methods in terms of computational efficiency and performance could provide valuable insights. 2. Complexity of concepts: - Some key concepts, such as the equivalence between sparsity and interval partitions, are not explained intuitively enough for a broader audience. - Additional examples or visual representations could make these complex ideas more accessible. 3. Practical applicability: - The paper lacks a detailed discussion on how the proposed algorithms could be implemented in real-world scenarios. 4. Computational complexity: - There's limited discussion on the computational complexity of the proposed algorithms, particularly for the EMC algorithm. - Understanding the trade-offs between theoretical performance and computational requirements is crucial for practical implementation. 5. Assumptions and limitations: - While the paper acknowledges some limitations, a more comprehensive discussion of the assumptions' implications and potential violations in real-world scenarios would be beneficial. 6. Comparison with related approaches: - While the paper discusses how it differs from some existing methods, a more comprehensive comparison with other approaches to high-dimensional bandits or symmetry exploitation could provide better context. These weaknesses are not meant to diminish the paper's overall contribution but rather to identify areas where the work could be further strengthened or extended in future research. Technical Quality: 3 Clarity: 3 Questions for Authors: Empirical Validation: Could you provide any empirical results, even on synthetic data, to illustrate the performance of the EMC algorithm? How does it compare practically to existing methods for sparse linear bandits? Practical Implications of Assumptions: Could you elaborate on real-world scenarios where Assumption 5 (sub-exponential number of partitions) and Assumption 16 (well-separated partitioning) are likely to hold or be violated? Intuitive Explanations for Key Concepts: The connection between interval partitions and sparsity, as well as the concept of hidden symmetry, are intriguing but complex. Could you provide more intuitive explanations or concrete examples to illustrate these key ideas, particularly for readers less familiar with group theory or symmetry concepts in bandits? Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 4 Limitations: The authors have adequately addressed the limitations of their work, particularly by acknowledging open problems and discussing constraints of their assumptions. While they could expand on practical implementation challenges and potential societal impacts, their upfront approach to discussing limitations is commendable. A brief section explicitly addressing broader implications would further strengthen the paper, but overall, the authors have done a good job in addressing limitations within the context of their theoretical work. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: # Responses to Reviewer ZVeC We thank the reviewer for the insightful comments. Below are our responses/clarifications to your questions: ## Question 1: Practical Implications of Assumptions 5 and 16: ### Response: Assumption 5: sub-exponential partitions. Sub-exponential size naturally appears when there is a hierarchical structure on the set $[d]$, and the partitioning needs to respect this hierarchical structure. Particularly, let $T(d,d_0)$ be the set of ordered trees with $(d+1)$ nodes and $d_0$ internal nodes (i.e., nodes that are not the leaves). A partition that respects an ordered tree groups the children of the same node into a single equivalence class. We provide an example of such a partition in the PDF file (Figure 1). It is shown in [1] that the cardinality of the set of partitions that respect ordered trees in $T(d,d_0)$ is sub-exponential. More precisely, it's $O(d^{d_0})$. Furthermore, there is a bijection between partitions that respect ordered trees in $T(d,d_0)$ and the set of non-crossing partitions $\mathcal{NC}_{d,d_0}$ [1]. A linear bandit example: To further illustrate the occurrence of such symmetry in a linear bandit problem, consider the following example: Suppose there are $d$ workers, and each worker $i$ can put $x_i \in [0,1]$ level of effort into the task. Hence, $x = [x_i]_{i\in [d]} \in \mathbb{R}^d$ is a vector that represents the effort of all workers. The performance of the whole team is measured by $$ f(x) = \left <x,\theta\right>, $$ where $\theta \in \mathbb{R}^d$, and each entry $\theta_i > 0$ represents the significance of worker $i$ to the success of the whole project. In other words, a higher $\theta_i$ implies that $x_i$ has more impact on the success of the project. Now, a new manager, who does not know $\theta$, employs a bandit algorithm to optimize the performance $f$. While she does not know $\theta$, she has prior knowledge that the skill levels of each worker in $[d]$ are hierarchical, meaning the significance of workers to the task can be represented as an ordered tree. This is expected in practice, as workers may come from different skill sets (e.g., developing, maintenance, testing) and varying skill levels (from senior to junior). We refer the reviewer to the PDF file (Figure 1) for an illustration of such a partition with respect to the ordered tree. Suppose she knows that there are at most $d_0$ equivalence classes in the partition. In that case, the number of partitions that respect the tree structures (i.e., can only group children of the same node into one equivalence class) must be at most $O(d^{d_0})$, due to the fact mentioned earlier. Assumption 16: well-separated partitions. For Assumption 16 to hold, there must be a significant differences among the classes in the partition. Let consider our incentivising workers example. The differences among classes occur among classes occur, for instance, when each group consists of specialists who excel in very specific skills, making the differences among the groups noticeable. As such, one can easily distinguish individuals in different groups, which is essentially the notion of a well-separated partition. ## Question 2: Intuitive Explanation for Key Concepts ### Response: To illustrate the equivalence between interval partitions and sparsity, let us consider the following example. Let $\theta \in \mathbb{R}^5$ where its entries satisfy a linear order, that is, $\theta_1 < \theta_2 < \cdots < \theta_5$. For example, let $\theta = [1, 1, 2, 3, 3]$, which has $d_0 = 3$ equivalent classes. Now, to define the corresponding sparse pattern, let $\varphi \in \mathbb{R}^4$ with entries defined as $\varphi_i = \theta_{i+1} - \theta_i$, and $\varphi_d$ = $\theta_d$. Hence, if $\theta = [1, 1, 2, 3, 3]$, then $\varphi = [0, 1, 1, 0, 3]$, so $\varphi$ is a $d_0 = 3$-sparse vector. The concept of hidden symmetry, intuitively speaking, means that the set of arms $\mathcal X$ contains several equivalence classes, each of which has the same expected reward. However, hidden symmetry implies that the learner does not know the equivalence classes in advance and must learn them through data sampling. ## Comment 1: On the computational complexity. ### Response: We believe that to develop computationally efficient algorithms for a particular partition, we need to fully exploit its structure, similar to how existing literature has exploited the structure of sparsity. However, this sacrifices the generality of the result, especially if our aim is to establish a general condition on partitions under which one can achieve regret that scales with the dimension of the fixed-point subspace $d_0$. As establishing this general condition is the primary concern of the paper, we did not focus on computational efficiency. We are aware that developing efficient computational methods is important in practice, and we hope to investigate this question in the future for some important classes of partitions other than sparsity, such as non-crossing partitions. Moreover, as mentioned in Remark 4 of the paper, since the prediction error for each model $m \in \mathcal M$ can be computed independently, we can exploit parallel computing to reduce the algorithm's computation time. ## Comment 2: Empirical validation. ### Response: We run the simulation, with $d = 16$, $d_0 = 2$, $\mathcal X$ is the unit ball, with two scenarios: interval partition, and non-crossing partition. Due to the space constraints, we refer the reviewer to the discussion with Reviewer Viv8 (our response to their Comment 3) for simulation details, and the attached PDF file (Figure 2, 3) for simulation results. The simulation results show that, our algorithm achieves similar (or even smaller) regret in the case of interval partitions, and notably smaller regret in the case of non-crossing partitions compared to the sparse bandit algorithm. ## References: [1] Dershowitz&Zaks. Ordered trees and non-crossing partitions. 1986. --- Rebuttal Comment 1.1: Comment: Dear Reviewer, Thank you for your time and effort in reviewing our paper. We hope our responses have addressed your concerns and questions. If you have any further questions, please don’t hesitate to let us know. Best regards, The Authors	Summary: The authors study the problem of symmetric linear bandits with hidden symmetry (where the expected reward is a linear function of the selected arm, and is invariant under a hidden symmetry group). They show that, with no additional information, the minimax regret cannot be improved. When the partition corresponding to the hidden symmetry group is known to belong to a given set of a sub-exponential number of partitions, the authors provide an algorithm that that achieves a regret of $\tilde{O}(d_0^{1/3} T^{2/3})$. Under the assumption that the models are well separated, this regret guarantee is improved to $\tilde{O}(d_0 \sqrt{T})$. Strengths: The authors generalize the study of sparse linear bandits to high-dimensional symmetric linear bandits, where the symmetry is unknown and must be learned. The authors show that 1) no algorithm can benefit solely from knowing that there exists some subgroup under which the expected reward is invariant, 2) that a regret of $\tilde{O}(d_0^{1/3} T^{2/3})$ can be achieved when the partition is known to belong to a set of sub-exponential size, and 3) that a regret of $\tilde{O}(d_0 \sqrt{T})$ can be achieved when the models are well separated. For the well separated case, they note that the initialization phase length $t_2$ depends on the separation $\epsilon_0$, and question how to adapt to this parameter that will be unknown in practice. Weaknesses: - Adaptivity: the algorithm requires as input the set $\mathcal{Q}_{d,\le d_0}$ (currently not shown as in input). Additionally, the algorithm / regret do not appear to adapt to the complexity of the problem instance, but rather depend on the size of this input set. The manuscript should be revised to clarify (in the algorithm) that this is needed as input. - The algorithm does not appear to be implementable. The minimization step in equation 5 is over $\mathcal{M}$, which is of exponential size ($d^{d_0}$). In the high dimensional regime of interest, this is infeasible without additional structural assumptions. The authors touch on this at the very end of the paper (line 402: "for future work, we will explore convex relaxation techniques for efficient computation"), but do not provide any concrete suggestions for how this could be done. - Practical motivation: the authors do not provide any concrete examples of where this problem arises, and how the input set $\mathcal{Q}_{d,\le d_0}$ could be obtained in practice. The paper should be self contained and self-motivated (e.g. Line 20, referencing [24] alone is insufficient). The illustrative example of an ant robot does not seem very related to the problem at hand, as there are at most 4 symmetries. The authors briefly discuss possible hidden symmetries in Appendix D, but don't provide examples where we should expect to see these symmetries (anything besides sparsity, for which there already exist specialized methods). - Clarity: the paper is quite difficult to read, and should be revised for clarity. I've listed some typos below, but thorough proofreading is needed. Writing typos: - Line 9: hidden symmetry - Line 16: "Stochastic bandit is" incomplete sentence - Line 26: "fo" - Line 38: "most of studies" - Line 81: "the set of arm is exploratory". Also, exploratory is undefined (reused in line 98). - Line 100: data-poor regime is undefined - Line 112: "And able to obtain regret" - Line 114: "That are different to aggregation" - Line 120: "Making" shouldn't be capitalized - Line 124: missing "the" - Line 142: "In each round" - Line 148: in terms of regret - Line 179: grammar, missing "to" and "as"->"be" - Line 204: in terms of regret - Line 206: "the" missing before "regret" - Line 221: "are"->"is", unnecessary "the" - Line 222: partitions - Line 320: "designed"->"the design" - general comment: "the assumptions" -> "assumptions" Math typos / comments: - Line 144: Is $\eta_t$ supposed to be a 0 mean $\sigma$-sub-Gaussian random variable? - Line 144: Clearer to write $f(x_t) = \langle x_t, \theta_{\star}\rangle$ - Equations 1 and 2: $\phi$ and $\hat{\phi}$ perform the same operation on $\mathbb{R}^d$, so it is unclear why they are separately defined for operating on $x$ and on $\theta$. Also, $\hat{\phi}$ is confusing notation to use, as this is not an estimator of $\phi$. - Line 163: missing $\forall g \in \mathcal{G}$ - Line 188: should explicitly define dim before usage - Prop 3: some intuitive explanation / proof sketch would be helpful. - Line 234: "data"->"actions" - Algorithms 1 and 2 critically require as input $\mathcal{Q}_{d,\le d_0}$. Technical Quality: 3 Clarity: 2 Questions for Authors: See weaknesses. At a high level: 1. Adaptivity: the algorithm requires as input the set $\mathcal{Q}_{d,\le d_0}$ , and it is not clear how to obtain this in practice. Additionally, it appears that the key regret improvement is the scaling with the log of the cardinality of this set, instead of with $d$. Is there a way to make these assumptions less restrictive, adapt to the ``true'' complexity of the partition, or to estimate this set in practice? 2. Implementability: the algorithm as written does not seem to be implementable. Can the authors either provide an implementation (comparing their results with existing algorithms for sparse linear bandits), or suggest how this could be done in practice? 3. Practical motivation: is there a motivating example (not sparsity) where the arms are high dimensional, the symmetry is unknown, and the partition is known to belong to a set of sub-exponential size? Confidence: 4 Soundness: 3 Presentation: 2 Contribution: 2 Limitations: The key limitations of this method, that have not been sufficiently discussed, are its required knowledge of $\mathcal{Q}_{d,\le d_0}$, and its computational intractability, both of which appear to be severe practical limitations. Flag For Ethics Review: ['No ethics review needed.'] Rating: 3 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: # Responses to Reviewer qJvB ## Question: Practical motivation on sub-exponential partitions ### Response: Sub-exponential size naturally appears when there is a hierarchical structure on the set $[d]$, and the partitioning needs to respect this hierarchical structure. Particularly, let $T(d,d_0)$ be the set of ordered trees with $(d+1)$ nodes and $d_0$ internal nodes (i.e., nodes that are not the leaves). A partition that respects an ordered tree groups the children of the same node into a single equivalence class. We provide an example of such a partition in the PDF file (Figure 1). It is shown in [1] that the cardinality of the set of partitions that respect ordered trees in $T(d,d_0)$ is sub-exponential. More precisely, it's $O(d^{d_0})$. Furthermore, there is a bijection between partitions that respect ordered trees in $T(d,d_0)$ and the set of non-crossing partitions $\mathcal{NC}_{d,d_0}$ [1]. A linear bandit example: To further illustrate the occurrence of such symmetry in a linear bandit problem, consider the following example: Suppose there are $d$ workers, and each worker $i$ can put $x_i \in [0,1]$ level of effort into the task. Hence, $x = [x_i]_{i\in [d]} \in \mathbb{R}^d$ is a vector that represents the effort of all workers. The performance of the whole team is measured by $$ f(x) = \left <x,\theta\right>, $$ where $\theta \in \mathbb{R}^d$, and each entry $\theta_i > 0$ represents the significance of worker $i$ to the success of the whole project. In other words, a higher $\theta_i$ implies that $x_i$ has more impact on the success of the project. Now, a new manager, who does not know $\theta$, employs a bandit algorithm to optimize the performance $f$. While she does not know $\theta$, she has prior knowledge that the skill levels of each worker in $[d]$ are hierarchical, meaning the significance of workers to the task can be represented as an ordered tree. This is expected in practice, as workers may come from different skill sets (e.g., developing, maintenance, testing) and varying skill levels (from senior to junior). We refer the reviewer to the PDF file (Figure 1) for an illustration of such a partition with respect to the ordered tree. Suppose she knows that there are at most $d_0$ equivalence classes in the partition. In that case, the number of partitions that respect the tree structures (i.e., can only group children of the same node into one equivalence class) must be at most $O(d^{d_0})$, due to the fact mentioned earlier. ## Question: adapt to the true complexity of the partition instead of using the cardinality, or to estimate this collection of partition in practice? ### Response: We thank the reviewer for the interesting suggestion. However, as the literature of partitions with constraints is diverse with many different types of partitions, such as noncrossing partitions [2], non-nesting partitions [3], pattern avoidance partitions [4], partitions with distance restrictions [5], it is highly non-trivial to find unifying parameters to measure the hardness of partitions in learning tasks. The question of finding the right measure of complexity for partitions as well as adapting to this complexity hardness is challenging, hence we leave it to future work. For the current paper, as the unifying measure of complexity hardness for partitions is still unclear, we have decided use the cardinality of the set as a natural measure of complexity, which is a reasonable choice. In particular, the complexity of partitions with an extremely rich structures, can also be measured by cardinality: Take an interval partition, for example. Although its lattice structure is rich, its complexity relevant to the learning task is still $d_0 \log(d)$, which is the same as $\log(\|\mathcal{Q}_{d,\leq d_0}\|)$. Therefore, we argue that cardinality is useful for learning with partitions, including those with rich structure. ## Comment: Computational limitation. ### Response: We believe that to develop computationally efficient algorithms for a particular partition, we need to fully exploit its structure, similar to how existing literature has exploited the structure of sparsity. However, this sacrifices the generality of the result, especially if our aim is to establish a general condition on partitions under which one can achieve regret that scales with the dimension of the fixed-point subspace $d_0$. As establishing this general condition is the primary concern of the paper, we did not focus on computational efficiency. We are aware that developing efficient computational methods is important in practice, and we hope to investigate this question in the future for some important classes of partitions other than sparsity, such as non-crossing partitions. Moreover, as mentioned in Remark 4 of the paper, since the prediction error for each model $m \in \mathcal M$ can be computed independently, we can exploit parallel computing to reduce the algorithm's computation time. ## Comment: Empirical validation. ### Response: We run the simulation, with $d = 16$, $d_0 = 2$, $\mathcal X$ is the unit ball, with two scenarios: interval partition, and non-crossing partition. Due to the space constraints, we refer the reviewer to the discussion with Reviewer Viv8 (our response to Comment 3) for simulation details, and the attached PDF file (Figures 2 & 3) for simulation results. The simulation results show that, our algorithm achieves similar (or even smaller) regret in the case of interval partitions, and notably smaller regret in the case of non-crossing partitions compared to the sparse bandit algorithm. ## References: [1] Dershowitz&Zaks. Ordered trees and non-crossing partitions. 1986. [2] Baumeister et al. Non-crossing partitions. 2019. [3] Chen et al. Crossings and nestings of matchings and partitions. 2006. [4] B. E. Sagan. Pattern avoidance in set partitions. 2010. [5] Chu&Wei. Set partitions with restrictions. 2008. --- Rebuttal Comment 1.1: Title: Rebuttal Response Comment: Thanks for the detailed response. 1. Motivating example: this seems interesting, and definitely should be included in the paper. I think that there some issues with this that still need to be fleshed out (e.g. in a workplace, one would expect to have the organization chart, i.e. the tree, revealed), but this appears to be a concrete setting going beyond sparsity. 2. Adaptivity: This remains my primary concern, which does not appear to have been addressed. The algorithm critically depends on knowledge of the set $\mathcal{Q}_{d,\le d_0}$ , and cannot be run without this as input. The algorithm, as written, does not currently take this as input, and so doesn't work. Additionally, the proposed bandit algorithm cannot adapt to the actual difficulty of the problem: if the partition actually belongs to a much smaller class $\mathcal{Q}_{d,\le \tilde{d}_0}$ where $\tilde{d}_0 \ll d_0$, the algorithm complexity still depends on $\mathcal{Q}_{d,\le d_0}$, the set it was provided as input. 3. Computational Limitations: the ability to evaluate models in parallel does not get at the core of the issue here, which is that for even reasonable $d$ and $d_0$ the number of models that need to be evaluated is an extremely large polynomial. Even considering the toy example provided by the authors in Figure 1, for a $d=20$ dimensional feature vector per individual, this yields $O(d^{d_0}) \approx 160000$ models to evaluate. Without an efficient implementation for this algorithm proposed in any setting, and no concrete plans for how this can be achieved, it is unclear how this algorithm can be used. 4. Empirical validation: I think that this addition will greatly strengthen the paper, as it shows that the algorithm can work in practice on small examples. However, it seems as though this example is quite artificial; as in the point above, considering the example the authors provided in Figure 1, even for this toy example, $d_0=4$, while the authors restricted to simulating $d_0=2$. The addition of the motivating example beyond sparsity and the addition of toy numerical results strengthens this paper, but due to the algorithmically required input of $\mathcal{Q}_{d,\le d_0}$, lack of adaptivity (beyond just evaluating this subset of models as opposed to all models), and the computational complexity scaling with $d^{d_0}$, I retain my score of reject. --- Reply to Comment 1.1.1: Title: Responses to reviewer qJvB Comment: Dear Reviewer. Thank you for your reply. We would like to comment on these issues. ### Adaptivity We thank the reviewer for the insightful suggestion. As mentioned above, to adapt to benign problem instances, one might need to exploit the specific structure of a class of partitions, which is not the primary focus of this paper at the moment. However, it is indeed an interesting direction, and we leave it for future work. ### Computational limit. For particular classes of sub-exponential partitions, such as non-crossing and non-nesting, we can exploit their lattice structures and use greedy search to find the partition that yields reasonably small prediction error. Despite the NP-hardness of the computational complexity, it is often the case in practice that greedy search performs effectively. Moreover, one does not need to enumerate the set $\mathcal Q_{d,\leq d_0}$ before hand, as many classes of partitions admit compact representation (e.g., see [6], chapter 3). We hope that our response help to clarify your concern. We would like to kindly ask you to reevaluate your score. ### References [6] B. Baumeister, K.-U. Bux, F. Götze, D. Kielak, and H. Krause. Non-crossing partitions. 2019.	Summary: The paper studies high-dimensional linear bandits that are invariant w.r.t. an unknown subgroup of coordinate permutations. The authors first show through a lower bound that further information about the structure of the hidden subgroup is required to achieve a dimension-independent regret bound. They then propose a subexponential cardinality constraint on the hidden subgroup, which is sufficient to avoid the dimension dependency. They specifically propose Explore-Models-then-Commit, which successfully avoids the worst-case dimension-dependency under certain conditions. Strengths: - Well-written - Clear motivation and a novel problem-setting of importance - Solid motivation for subexponential cardinality assumption on the hidden subgroup, as well as interesting combinatorial concepts intertwined throughout the paper - First good regret bounds in the case of hidden symmetry Weaknesses: - The only symmetry somewhat intuitive to me is the sparsity, equivalent to interval partitions. Despite the Introduction stating the importance of symmetry, it is unclear whether there is practically meaningful coordinate symmetry beyond sparsity. (Of course, theoretically, I appreciate the results here.) - No experimental results. Especially as the authors have stated that Algorithm 1 can be "parallelised using tools such as Ray", I was expecting at least some toy experiments (one showing the efficacy of learning the hidden symmetry and scaling of the algorithm as the number of models $M$ increase) - The algorithm is explore-then-commit style, which requires the horizon length $T$ in advance and inherits its suboptimality [1]. [1] https://papers.nips.cc/paper_files/paper/2016/hash/ef575e8837d065a1683c022d2077d342-Abstract.html Technical Quality: 3 Clarity: 3 Questions for Authors: - The paper states that as sparsity is equivalent to interval partitions, the lower bound of Hao et al. (2020) also trivially applies. Then, is this lower bound tight for other combinatorial structures with similar subexponential cardinality constraints, e.g., non-crossing partition? - In sparse linear bandits, there is always an assumption about the context distribution or the arm set (e.g., compatibility condition, restricted eigenvalue, etc.). Can these assumptions be interpreted as part of the paper's proposed group-theoretic framework as well? - (minor) Would the principles here be extendable to information-directed sampling [3]? [2] https://proceedings.neurips.cc/paper/2020/hash/7a006957be65e608e863301eb98e1808-Abstract.html [3] https://openreview.net/forum?id=syIj5ggwCYJ Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: Yes Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: # Response to Reviewer WDJx We thank the reviewer for the insightful comments. Below are our responses/clarifications to your questions: ## Comment 1: Practical motivations ### Response: Sub-exponential size naturally appears when there is a hierarchical structure on the set $[d]$, and the partitioning needs to respect this hierarchical structure. Particularly, let $T(d,d_0)$ be the set of ordered trees with $(d+1)$ nodes and $d_0$ internal nodes (i.e., nodes that are not the leaves). A partition that respects an ordered tree groups the children of the same node into a single equivalence class. We provide an example of such a partition in the PDF file (Figure 1). It is shown in [1] that the cardinality of the set of partitions that respect ordered trees in $T(d,d_0)$ is sub-exponential. More precisely, it's $O(d^{d_0})$. Furthermore, there is a bijection between partitions that respect ordered trees in $T(d,d_0)$ and the set of non-crossing partitions $\mathcal{NC}_{d,d_0}$ [1]. A linear bandit example: To further illustrate the occurrence of such symmetry in a linear bandit problem, consider the following example: Suppose there are $d$ workers, and each worker $i$ can put $x_i \in [0,1]$ level of effort into the task. Hence, $x = [x_i]_{i\in [d]} \in \mathbb{R}^d$ is a vector that represents the effort of all workers. The performance of the whole team is measured by $$ f(x) = \left <x,\theta\right>, $$ where $\theta \in \mathbb{R}^d$, and each entry $\theta_i > 0$ represents the significance of worker $i$ to the success of the whole project. In other words, a higher $\theta_i$ implies that $x_i$ has more impact on the success of the project. Now, a new manager, who does not know $\theta$, employs a bandit algorithm to optimize the performance $f$. While she does not know $\theta$, she has prior knowledge that the skill levels of each worker in $[d]$ are hierarchical, meaning the significance of workers to the task can be represented as an ordered tree. This is expected in practice, as workers may come from different skill sets (e.g., developing, maintenance, testing) and varying skill levels (from senior to junior). We refer the reviewer to the PDF file (Figure 1) for an illustration of such a partition with respect to the ordered tree. Suppose she knows that there are at most $d_0$ equivalence classes in the partition. In that case, the number of partitions that respect the tree structures (i.e., can only group children of the same node into one equivalence class) must be at most $O(d^{d_0})$, due to the fact mentioned earlier. ## Question 1: Is this lower bound tight for other combinatorial structures with similar subexponential cardinality constraints, e.g., non-crossing partition? ### Response: The lower bound derived from the sparsity case [2] applies to any class of partitions that includes interval partitions, such as non-crossing partitions [3] and non-nesting partitions [4], and thus is tight in these settings. However, this lower bound does not hold for smaller classes that do not contain a structure equivalent to interval partitions. It is still unknown what a tight lower bound would be in this case, and thus, remains as future work. ## Question 2: Can assumptions such as compatibility condition, restricted eigenvalue, be interpreted as part of the paper's proposed group-theoretic framework as well? ### Response: We note that many conditions, such as the compatibility condition and restricted eigenvalue condition, are carefully tailored to exploit specific structures of sparsity (e.g., interval partitions) [5]. Therefore, we believe that developing such conditions for symmetric bandits requires exploiting a specific combinatorial structure, such as non-crossing partitions. Although this is beyond the scope of our paper, as we study a wide class of partitions, it is indeed an interesting question that we hope to investigate in future work. ## Question 3: Would the principles here be extendable to information-directed sampling? ### Response: Extending our framework to information-directed sampling is indeed a very interesting and challenging problem. Since bounding the information ratio as in [6] requires strongly exploiting the particular structure of sparsity, we conjecture that studying specific partitions to fully exploit their combinatorial structures is necessary to derive the information ratio bound. This remains an open question, which we leave for future work. ## Comment 2: Empirical validation. ### Response: We run the simulation, with $d = 16$, $d_0 = 2$, $\mathcal X$ is the unit ball, with two scenarios: interval partition, and non-crossing partition. Due to the space constraints, we refer the reviewer to the discussion with Reviewer Viv8 (our response to their Comment 3: Empirical validation) for simulation details, and the attached PDF file (Figure 2, 3) for simulation results. The simulation results show that, our algorithm achieves similar (or even smaller) regret in the case of interval partitions, and notably smaller regret in the case of non-crossing partitions compared to the sparse bandit algorithm. ## References: [1] Dershowitz&Zaks. Ordered trees and non-crossing partitions. 1986. [2] Hao et al. High-dimensional sparse linear bandits. 2020. [3] Baumeister et al. Non-crossing partitions. 2019. [4] Chen et al. Crossings and nestings of matchings and partitions. 2006. [5] S. A. V. de Geer and P. Bühlmann. On the conditions used to prove oracle results for the lasso. 2009. [6] Hao et al. Information directed sampling for sparse linear bandits. 2021. --- 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 explores the impact of unknown symmetry on the regret for stochastic linear bandits. Under some assumptions on the set partition induced by the unknown subgroup G, the paper develops an "Explore-then-commit" algorithm that attains optimal scaling of the regret in terms of the dimension d_0 of the low-dimensional space induced by the group action. Strengths: * The paper describes the assumptions clearly and develops a regret bound that matches the lower bound for sparse linear bandits. * The paper makes a good case motivating the generality of the symmetric bandits structure by showing how it can recover sparse bandits. * A discussion comparing the results to those in the model aggregation literature is given. Weaknesses: - The writing could be made clearer in some sections. For eg, the implication $g \cdot \theta_* = \theta_*$ in line 164 seems valid only under some conditions on the set $\mathcal{X}$. Suppose $g$ only swaps the first and second components and all vectors in $\mathcal{X}$ have the same first and second components. It would be helpful if an example is used to describe the orbit and associated partition, the fixed-point subspace, etc. - The implications of the assumption on $\pi_{\mathcal{G}}$ in line 218 and Assumption 5 could be described more clearly. Again, a short example might help. - Experimental evaluation of their proposed approach is missing, Even a small simulation experiment could assure reader of the applicability of the algorithm. Technical Quality: 4 Clarity: 3 Questions for Authors: Please see weaknesses above Confidence: 3 Soundness: 4 Presentation: 3 Contribution: 3 Limitations: NA Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: # Responses to Reviewer Viv8 We thank the reviewer for the insightful comments. Below are our responses/clarifications to your questions: ## Comment 1: On the condition of $\mathcal X$ so that $\theta_\star = g\cdot \theta_\star$. ### Response: We do not need to impose any condition on $\mathcal{X}$ for $\theta_\star = g\cdot \theta_\star$ to hold. In particular, we only require $f(g\cdot x) = f(x)$, but we do not require that the orbit under the action of $\mathcal{G}$ stays in $\mathcal X$, that is, we do not require, $g \cdot x \in \mathcal{X}$, for all $g \in \mathcal{G}$. Therefore, the condition $\theta_\star = g \cdot \theta_\star$ holds regardless of the shape of $\mathcal{X}$. ## Comment 2: On illustrative examples of partitions. ### Response: Sub-exponential size naturally appears when there is a hierarchical structure on the set $[d]$, and the partitioning needs to respect this hierarchical structure. Particularly, let $T(d,d_0)$ be the set of ordered trees with $(d+1)$ nodes and $d_0$ internal nodes (i.e., nodes that are not the leaves). A partition that respects an ordered tree groups the children of the same node into a single equivalence class. We provide an example of such a partition in the PDF file (Figure 1). It is shown in [1] that the cardinality of the set of partitions that respect ordered trees in $T(d,d_0)$ is sub-exponential. More precisely, it's $O(d^{d_0})$. Furthermore, there is a bijection between partitions that respect ordered trees in $T(d,d_0)$ and the set of non-crossing partitions $\mathcal{NC}_{d,d_0}$ [1]. A linear bandit example: To further illustrate the occurrence of such symmetry in a linear bandit problem, consider the following example: Suppose there are $d$ workers, and each worker $i$ can put $x_i \in [0,1]$ level of effort into the task. Hence, $x = [x_i]_{i\in [d]} \in \mathbb{R}^d$ is a vector that represents the effort of all workers. The performance of the whole team is measured by $$ f(x) = \left <x,\theta\right>, $$ where $\theta \in \mathbb{R}^d$, and each entry $\theta_i > 0$ represents the significance of worker $i$ to the success of the whole project. In other words, a higher $\theta_i$ implies that $x_i$ has more impact on the success of the project. Now, a new manager, who does not know $\theta$, employs a bandit algorithm to optimize the performance $f$. While she does not know $\theta$, she has prior knowledge that the skill levels of each worker in $[d]$ are hierarchical, meaning the significance of workers to the task can be represented as an ordered tree. This is expected in practice, as workers may come from different skill sets (e.g., developing, maintenance, testing) and varying skill levels (from senior to junior). We refer the reviewer to the PDF file (Figure 1) for an illustration of such a partition with respect to the ordered tree. Suppose she knows that there are at most $d_0$ equivalence classes in the partition. In that case, the number of partitions that respect the tree structures (i.e., can only group children of the same node into one equivalence class) must be at most $O(d^{d_0})$, due to the fact mentioned earlier. ## Comment 3: Empirical Validation. ### Response: We run the simulation, with $d = 16$, $d_0 = 2$, $\mathcal X$ is the unit ball, with two scenarios: Interval partition (i.e., sparse linear bandits): We first run our algorithm with the following $\theta$ whose entries satisfy interval partition constraints (i.e., it represents a sparse linear bandit setting): $$ \theta_\star = [1,1,2,2...,2] $$ Equivalently, we can introduce a sparse vector $\varphi$ corresponding to $\theta_\star$, defined as entries defined as $\varphi_i = \theta_{i+1} - \theta_i$, and $\varphi_d = \theta_d$. We have that $\varphi_\star = [0,1,0,...,0,2]$, which is $2$-sparse vector. We apply Lasso regression for $\varphi_\star$, get the estimate $\hat \varphi$, then convert back to $\hat \theta$ using the map that transforms sparse vector to interval-partition vector (inversion of the map we defined above). Then, we compare the regret of our algorithm with that of state-of-the-art sparse linear bandit algorithm introduced in [2]. We show the regret bound of both algorithms in the attached PDF (Figure 2). It can be seen that our algorithm achieves similar regret (or even smaller) compared to the sparse bandit algorithm. Non-crossing partition: Now we run our algorithm with an $\theta$ whose entries satisfy non-crossing partition constraints but not interval partition constraints. $$\theta_\star = [1,1,2,2,2,1,1...,1].$$ We use the same map to convert $\theta_\star$ to sparse vector $\varphi_\star$, run Lasso to get estimation $\hat \varphi$ and then convert back to get estimation $\hat \theta$. Then, we compare the regret of our algorithm with that of [2]. We show the regret bound of both algorithms in the attached PDF (Figure 3). We can see from the plot, the regret of our algorithm is notably smaller than that of [2]. It indicates that our algorithm performs better than Lasso-based algorithms (which is designed only for interval partition) in the general case of non-crossing partition. ## References: [1] Dershowitz&Zaks. Ordered trees and non-crossing partitions. 1986. [2] Hao et al. High-dimensional sparse linear bandits. 2020. --- Rebuttal Comment 1.1: Comment: Dear Reviewer, Thank you for your time and effort in reviewing our paper. We hope our responses have addressed your concerns and questions. If you have any further questions, please don’t hesitate to let us know. Best regards, The Authors	Rebuttal 1: Rebuttal: Thank you for your valuable and constructive feedback. We have performed the additional experiments as requested by the reviewers and have provided the results in this PDF file. We have also added a picture in this PDF file that illustrates a practical example of how sub-exponential partitioning occurs when there is a hierarchical structure on the set $[d]$. Pdf: /pdf/8c8b3ff37f66a1ecfe30f011f3138d27e0382cc8.pdf	NeurIPS_2024_submissions_huggingface	2,024	Summary: This paper studies stochastic linear bandits with hidden symmetry, where the reward function is invariant with respect to a subgroup $\mathcal{G}$ of coordinate permutations. The paper first presents an impossibility result, showing that solely knowing a low-dimensional symmetry structure exists does not help. However, when the collection of fixed-point subspaces of $\mathcal{G}$ is not too large, one can use model selection algorithms to first learn the symmetry structure. The paper provides regret bounds of the algorithms, including an improved bound under an additional assumption that the equivalence classes of coordinates are well-separated. Strengths: - The low-dimensional symmetry structure in linear bandits studied in this paper seems novel and interesting. It also generalizes the sparsity assumption that has often been considered in the literature. - The impossibility result is not surprising but still good to have. - The mathematical formulation is clean, and the connection between fixed-point subspaces and set partitions allows for a relatively simple notion of cardinality assumption for the algorithms to work. - The improved regret bound in Section 5 leads to some interesting questions about additional structure that a learner could exploit. - The technical results are clear, and the paper is well-written and easy to follow. Weaknesses: - The algorithms are not computationally-efficient. - The algorithms require a rather strong assumption on the size of the collection of fixed-point subspaces of $\mathcal{G}$. - While hidden symmetry is observed in many learning tasks (e.g., control, multi-agent reinforcement learning), the paper does not provide specific real-world applications of symmetry structures within the context of linear bandits. - The paper can be much stronger with an empirical validation on at least synthetic data. In particular, it would be interesting to see how the algorithms behave on sparse linear bandits, in comparison with specialized algorithms. Technical Quality: 3 Clarity: 4 Questions for Authors: - In proposition 3, is the claim "let $\mathcal{G}$ be an unknown subgroup with $\dim(\mathrm{Fix}_{\mathcal{G}}) = 2$. Then, for any algorithm, there exists $\theta^* \in \mathrm{Fix}_{\mathcal{G}}$ such that..."? - What can be done if Assumption 5 does not hold? - Can you elaborate on the comparison with [1], especially given that the symmetry structure here is on the coordinates so there are more similarities to the "groups of similar arms" assumption in multi-armed bandits? Could you further compare the settings and the techniques? - In terms of presentation, I think a concrete running example in Section 2 can be very helpful. [1] F. Pesquerel, H. Saber, and O. A. Maillard. Stochastic bandits with groups of similar arms. In Advances in Neural Information Processing Systems, 2021. Confidence: 3 Soundness: 3 Presentation: 4 Contribution: 3 Limitations: Assumptions are properly discussed. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: # Responses to Reviewer qZUs We thank the reviewer for the insightful comments. Below are our responses/clarifications to your questions: ## Question 1: What can be done if Assumption 5 does not hold? ### Response: If the cardinality in Assumption 5 is not satisfied, one might need to find an alternative notion of complexity for a partition. However, as the literature of partitions with constraints is diverse with many different types of partitions, such as non-crossing partitions [1], non-nesting partitions [2], pattern avoidance partitions [3], partitions with distance restrictions [4], it is highly non-trivial to find unifying parameters to measure the complexity of partitions in learning tasks. As the unifying measure of complexity for partitions is unclear, one may study specific types of partitions to exploit their special properties and structures, such as the literature on sparsity (i.e., interval partitions), but this approach may lead to a loss of generality. ## Comment 1: Compare with [5], where symmetry appear in parameter space instead. ### Response: Let us first review the algorithmic technique of [5]: The algorithm assumes there is an equivalence among the parameters $\theta$, and that the set of arms $\mathcal{X}$ is a simplex. At each round $t$, given an estimation $\hat \theta_t$, the algorithm maintains a sorted list of indices in $[d]$ that follows the ascending order of the magnitude of $\hat \theta_i$. The algorithm then uses the sorted list of $ \hat{\theta}_i $ for all $i \in d$, to choose arm $x$ accordingly. The key assumption here is that, since the set of arms $\mathcal{X}$ is a simplex, we can estimate each $\theta_i$ independently. This implies that the order of entries of $ \hat{\theta}$ , should respect the true order of the entries of $\theta$ when there are a sufficiently large number of samples. Unfortunately, this is typically not the case in linear bandits where $\mathcal{X}$ has a more general shape. In linear bandits, there can be correlations between the estimates $\hat \theta_i$ and $\hat \theta_j$ for any $i, j \in [d]$. Hence, one should not expect that the list of entries of $\hat \theta $ will maintain the same order as that of $\theta$. In other words, the correlations among the estimates $\\{\hat \theta_1, \ldots, \hat \theta_d\\}$ may destroy the original order in $\\{\theta_1, \ldots, \theta_d\\}$. In fact, we can only guarantee the risk error of estimation $\hat \theta$, i.e., $\\\| \hat \theta - \theta_\star \\\|_2$ is small, but not necessarily the order of the indices in $\theta$. Therefore, the technique used in [5] cannot be directly applied to our setting in its current form. ## Comment 2: On the sub-exponential assumption, and practical examples ### Response: Sub-exponential size naturally appears when there is a hierarchical structure on the set $[d]$, and the partitioning needs to respect this hierarchical structure. Particularly, let $T(d,d_0)$ be the set of ordered trees with $(d+1)$ nodes and $d_0$ internal nodes (i.e., nodes that are not the leaves). A partition that respects an ordered tree groups the children of the same node into a single equivalence class. We provide an example of such a partition in the PDF file (Figure 1). It is shown in [6] that the cardinality of the set of partitions that respect ordered trees in $T(d,d_0)$ is sub-exponential. More precisely, it's $O(d^{d_0})$. Furthermore, there is a bijection between partitions that respect ordered trees in $T(d,d_0)$ and the set of non-crossing partitions $\mathcal{NC}_{d,d_0}$ [6]. Due to space limitations, we refer the Reviewer to the discussion with Reviewer Viv8 (in our response to their Comment 2 - examples for partitions) and to the attached PDF file (Figure 1) for a specific example of a linear bandit with a collection of sub-exponential partitions. ## Comment 3: On the computational complexity. ### Response: We believe that to develop computationally efficient algorithms for a particular partition, we need to fully exploit its structure, similar to how existing literature has exploited the structure of sparsity. However, this sacrifices the generality of the result, especially if our aim is to establish a general condition on partitions under which one can achieve regret that scales with the dimension of the fixed-point subspace $d_0$. As establishing this general condition is the primary concern of the paper, we did not focus on computational efficiency. We are aware that developing efficient computational methods is important in practice, and we hope to investigate this question in the future for some important classes of partitions other than sparsity, such as non-crossing partitions. Moreover, as mentioned in Remark 4 of the paper, since the prediction error for each model $m \in \mathcal M$ can be computed independently, we can exploit parallel computing to reduce the algorithm's computation time. ## Comment 4: Empirical validation. ### Response: We run the simulation, with $d = 16$, $d_0 = 2$, $\mathcal X$ is the unit ball, with two scenarios: interval partition, and non-crossing partition. Due to the space limitations, we refer the reviewer to the discussion with Reviewer Viv8 (our response to their Comment 3) for simulation details, and the attached PDF file (Figure 2, 3) for simulation results. The simulation results show that, our algorithm achieves similar (or even smaller) regret in the case of interval partitions, and notably smaller regret in the case of non-crossing partitions compared to the sparse bandit algorithm. ## References: [1] Baumeister et al. Non-crossing partitions. 2019. [2] Chen et al. Crossings and nestings of matchings and partitions. 2006. [3] B. E. Sagan. Pattern avoidance in set partitions. 2010. [4] Chu&Wei. Set partitions with restrictions. 2008. [5] Pesquerel et al. Stochastic bandits with groups of similar arms. 2021. [6] Dershowitz&Zaks. Ordered trees and non-crossing partitions. 1986. --- Rebuttal Comment 1.1: Comment: Dear Reviewer, Thank you for your time and effort in reviewing our paper. We hope our responses have addressed your concerns and questions. If you have any further questions, please don’t hesitate to let us know. Best regards, The Authors --- Rebuttal Comment 1.2: Comment: Thank you for the detailed responses. I will maintain my score for now.	null	null	null	null	null	null
Predicting the Performance of Foundation Models via Agreement-on-the-Line	Accept (poster)	Summary: The paper shows that agreement-on-the-line holds in finetuned foundation models across vision and language benchmarks and finds that random head initialization is critical for the phenomena. The authors also show that agreement-on-the-line holds in ensembles of different pretrained models. They demonstrate usage of agreement-on-the-line to predict OOD performance. Strengths: The paper is overall clear and well-written with substantial and thorough experiments on phenomenon of agreement-on-the-line across various language and vision benchmarks. The question of understanding and predicting model performance under distribution shifts is important in the field. The authors show that the proposed method of using agreement-on-the-line to predict OOD performance outperforms previous methods in most cases. Weaknesses: Minor points: 1. The panel labels in Fig. 31 and 32 has a repetition of Random Head, which should be corrected. 2. The authors fail to discuss the robustness of the method. Specifically, it is important to know how robust the method is in terms of changing different hyperparameters. Major points: 1. Novelty: the authors extend a previously proposed method (Baek et al. 2022) to finetuned foundation models. Although the aspect that observing AGL holds in this new setup is to some extent is novel, the methodology itself lacks novelty. 2. The paper is mostly experimental results without providing any insights into why one would expect AGL to hold or correlate with ACL. Without any explanation or theoretical guarantee, it is debatable whether one can trust this method with new models or new data. Technical Quality: 2 Clarity: 3 Questions for Authors: 1. If you only train a linear head and freeze all the other parameters, isn’t the problem convex? Then, suppose training to convergence, initialization could potentially bias the final solution. However, this bias should be a result from the random initialization in the data kernel space. Why would this type of randomness be meaningful at all? 2. What do you think are potential causes for the larger slopes of AGL compared to ACL if trained with data ordering or data subsetting? Confidence: 3 Soundness: 2 Presentation: 3 Contribution: 2 Limitations: The authors have listed limitations at the end. However, I think one major limitation is when the correlation coefficient is low, other methods will outperform AGL, which is shown in Table 5. I suggest authors include this limitation. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: >__The panel labels in Fig. 31 and 32 has a repetition of Random Head, which should be corrected.__ Thank you for catching this! The third panel (c) corresponds with Data Subsetting, not Random Head. We will correct this in the next version. >__…it is important to know how robust the method is in terms of changing different hyperparameters.__ Thank you for your feedback! None of the hyperparameters we use to linear probe or fully-finetune the models in this work have been picked to observe this phenomena. In Figure 3 in our rebuttal PDF, we see that across different learning rates and batch sizes, linear models over CLIP only observe AGL by varying the random initialization. >__Novelty: the authors extend a previously proposed method (Baek et al. 2022) to finetuned foundation models. Although the aspect that observing AGL holds in this new setup is to some extent is novel, the methodology itself lacks novelty.__ The novelty of our work stems from several factors. First, OOD performance estimation of FMs is a critical problem. Foundation models are utilized for a variety of downstream tasks and to safely use them, it is important that we have ways to estimate their OOD performance, especially in limited label settings. This problem is largely underexplored and we still lack an understanding of when older methods transfer. Second, before this work, it was unintuitive whether AGL holds in FMs. The importance of diversity source in finetuned FMs, in contrast to deep ensembles trained from scratch, is quite surprising. This has interesting theoretical implications. 1. Finetuning on top of pretrained weights can produce models with surprising levels of decorrelated errors when trained from different randomly initialized heads. 2. AGL can hold in linear probes, in contrast to Baek et al. which argue AGL only occurs in neural networks. We believe these findings would be interesting to both practitioners and theoreticians. Third, our method can effectively estimate OOD performance for a wider range of scenarios than other baselines, which break for non-classification tasks. In QA benchmarks, the prediction error is 20% smaller than popular confidence-based prediction methods. >__The paper is mostly experimental results…Without any explanation or theoretical guarantee, it is debatable whether one can trust this method with new models or new data.__ Thank you for the feedback! While we do not provide exact theoretical guarantees, the conclusions we make about ensemble diversity in FMs and their effect on observing AGL/ACL hold across hundreds of finetuned models we tested from different model familes (GPT, OPT, Llama), 50+ distribution benchmarks (Appendix A.3 and A.4), hyperparameters (see learning rate/batch size sweep in rebuttal Figure 3), finetuning strategies (LP, LoRA, full finetuning; other PEFT methods in rebuttal Figure 1). We hope that our rigorous experimental report can demonstrate that ACL/AGL is a powerful tool for predicting the performance of FMs. Furthermore, the coefficient of determination $R^2$ of ID vs OOD agreement (see Sec. 5) gives practitioners a rough guarantee for when the performance estimate derived by AGL is reliable. This is immensely useful in comparison to other confidence-based baseline methods which also do not come with any formal guarantees. We’d also like to point to several theoretical works that have tried to characterize when ACL and AGL hold [1, 2]. We believe our study on the importance of random initialization for observing AGL introduces a new conceptual angle for understanding deep ensembles and what actually induces AGL. We hope this can inspire further theoretical research on this important topic. [1] Mania and Sra. Why do classifier accuracies show linear trends under distribution shift? 2020. [2] Lee, et al. Demystifying Disagreement-on-the-Line in High Dimensions. 2023. >__If you only train a linear head, isn’t the problem convex? Then, suppose training to convergence,…(bias) result from the random initialization in the data kernel space. Why would this type of randomness be meaningful?__ >__What are potential causes for the larger slopes of AGL compared to ACL if trained with data ordering or data subsetting?__ Thank you for the great question! In all of our ID versus OOD scatter plots, you will see that we have models of a wide range of accuracies. This is because in addition to the diversity source, these models are also _finetuned for different timesteps_. In fact, a lot of these “partially” trained models can be close to their initialization, and any bias from random initialization isn’t restricted to the kernel of the training data. However, the bias in the kernel induced by random initialization may be important for achieving the low _OOD_ agreement rates. We provide some intuition below. Consider the linear probe setting wherein we train a linear classifier on top of fixed features. Suppose we assume that the ID training data is low rank. Let S be the span of the ID training data, and N be the corresponding null-space that has some overlap with the OOD data. The training iterations only update the classifier in S. As a result, under different random initializations, classifiers would retain their different initializations on S and lead to lower OOD agreement. However, if the initializations are fixed, and only the data ordering or subset varies, these orthogonal components no longer vary, leading to higher OOD agreement. Intuitively, such an argument should carry over to heavy-tailed training data as well, beyond low-rank. We were unable to come up with an analogous interpretable diversity introduced by data-subsetting or ordering. Overall, the phenomenon of agreement-on-the-line is poorly understood, and we think our work reveals new empirical observations that help form a better picture. We believe our work would inspire and inform future work that rigorously and comprehensively explains AGL. --- Rebuttal Comment 1.1: Comment: I thank the authors for their detailed responses! The authors have addressed my concerns around robustness with respect to the hyperparameters. Thus, I am increasing my score from 4 to 5. However, I still hold my skeptical position. Without any explanations or theoretical insights, I am doubtful whether AGL (particularly given its origin from random initialization in a convex problem) is indeed meaningful or just a mere coincidence that has trivial explanation.	Summary: The paper studies the applicability of agreement-on-the-line (AGL) to finetuned large models. Specifically, AGL is the phenomenon where the agreement in predictions of a collection of models on in-distribution (ID) data is linearly correlated with these models' agreement on out-of-distribution (OOD) data. This phenomenon is particularly interesting since earlier work has shown that this relation holds whenever the accuracy-on-the-line (ACL) holds; furthermore, these linear relation for agreement and accuracy is the same. While prior work has studied this phenomenon in a variety of settings, this paper studies instead this phenomenon for large finetuned models. The authors show that even in this regime, AGL holds in both vision and language settings. Furthermore, while prior work has shown that vision models pretrained on different distributions do not share the same AGL line, the authors find that the agreement of language models actually falls on the line. Strengths: - The paper is well-written. - Generalizing the AGL phenomenon to finetuned large models is important as the use of these models becomes prevalent. - The authors run extensive evaluation on models of different sizes and on different downstream tasks. Weaknesses: - The paper lacks an analysis on the reason behind the different behavior observed between the vision and language models. Although these are two different modalities, I don't see a reason why vision and language models should behave differently. - The paper lacks an analysis of AGL in zero/few-shot settings. - The paper assumes that full finetuning and finetuning with LoRA lead to the same AGL phenomenon. While LoRA (and other PEFT methods) lead to a similar performance, their behavior might be different [1]. Such an analysis is needed, and the inclusion of more PEFT methods (QLoRA, BitFit, IA3, etc.) would be nice. [1] Empirical Analysis of the Strengths and Weaknesses of PEFT Techniques for LLMs. Pu et al. 2023. Technical Quality: 3 Clarity: 3 Questions for Authors: - The authors point out that they vary several factors when finetuning the large models, including the initialization of the linear head. I am a bit confused why different initialization would lead to substantially different accuracies. For example, in figures 1 and 2 (where there's supposed to be a single backbone that's finetuned several times), we can see that the x-axis values range from 10% to 90%. Can you please explain the reason behind this wide range? - Can you please add more results with different PEFT methods and analyze the difference (or the similarity) between them? Confidence: 3 Soundness: 3 Presentation: 3 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 valuable comments and suggestions! We address each of your concerns below in detail. >__The paper lacks an analysis on the reason behind the different behavior observed between the vision and language models.__ The conclusions we make in this work apply to _both_ image and language models, we do not differentiate between these settings in any way. Models of both modalities require special attention to the source of diversity when fine-tuning from a common pretrained checkpoint to observe AGL. In particular, the diversity induced via random head initialization yields AGL, while the diversity induced via data reordering or data subsetting does not result in AGL. The only differences we do make between vision and language tasks are __1)__ the fine-tuning strategy that we employ - e.g. full fine-tuning for question answering (since linear probing performs very poorly), and linear probing for image classification __2)__ the choice of evaluation metric (F1 score for QA and 0-1 accuracy for classification). As emphasized in Section 2, our diversity results hold across tasks, regardless of what fine-tuning strategy or metric is employed. We will make this more clear in the next version. >__The paper lacks an analysis of AGL in zero/few-shot settings.__ Thanks for the feedback! We have some preliminary experiments on few-shot and zero-shot learning to answer your question in Figure 2 of our rebuttal PDF. We will add these results to the paper if you find that it strengthens our work. We consider few-shot linear probing over CLIP features, where we train on 10 examples in CIFAR10 per class and test models on the shift CIFAR10C Pixelate. Similar to fine-tuned FMs, we see that _by varying the random initialization of the linear probes, we can observe AGL and ACL._ On the other hand, data subsetting and data reordering trivially do not work in this setting as there’s only a small handful of training examples. The zero-shot setting is a vastly different regime for understanding ACL and AGL because any downstream task is “out-of-distribution”. In future work, it may still be interesting to study the linear relationship between the pretraining loss (ID) versus the downstream task loss (OOD), or simply between two OOD tasks e.g., downstream task 1 versus downstream task 2. In Figure 2 of the rebuttal PDF, we take the intermediate pretraining checkpoints of OLMo 7B and evaluate their zero-shot performance on SQuAD versus SQuAD-shifts Reddit. On the contrary to finetuned models, we see that both ACL and AGL do not hold in this setting. >__The paper assumes that full finetuning and finetuning with LoRA lead to the same AGL phenomenon. While LoRA (and other PEFT methods) lead to a similar performance, their behavior might be different [1]. Such an analysis is needed, and the inclusion of more PEFT methods (QLoRA, BitFit, IA3, etc.) would be nice.__ >__Can you please add more results with different PEFT methods and analyze the difference (or the similarity) between them?__ Thank you for the suggestion! We first want to clarify that we do not claim that PEFT and full-finetuned models behave the same generally or that they always lie on the same ACL and AGL trend. For example, other works have reported circumstances where PEFT and full-finetuned models observe different levels of effective robustness under distribution shift (i.e., different ACL slopes) [1]. The reason we group these two finetuning methods together in our work is mostly for notational convenience (i.e., LP versus FFT) since across the datasets we evaluate in our work, PEFT and full-finetuned models do observe the same effective robustness. We will make this more clear in Section 2. To further strengthen our work, we have included additional experiments that directly compare different PEFT methods. We trained GPT2 for random head initialization, data ordering, and data subsetting with LoRA, IA3, and BitFit as shown in Figure 1 of the rebuttal PDF. Regardless of the PEFT method, the accuracy points lie on the same line and AGL holds best with random head initialization. Interestingly, this indicates that even with different PEFT methods, we can observe AGL in ensembles as long as the linear head is randomly initialized. [1] Chen, et al. Benchmarking Robustness of Adaptation Methods on Pre-trained Vision-Language Models. Neurips 2023. >__I am a bit confused why different initialization would lead to substantially different accuracies. For example, in figures 1 and 2…we can see that the x-axis values range from 10% to 90%. Can you please explain the reason behind this wide range?__ Good question! The large range of accuracies is a consequence of models being trained for varying amounts of training epochs and this is necessary to observe the full ACL/AGL linear trends. For each source of diversity we also vary the number of epochs (not train until convergence) to obtain this range of accuracies. As we finetune from a randomly initialized linear head, the model performance at the beginning of finetuning is almost random (10% for CIFAR10 classification). --- Rebuttal Comment 1.1: Comment: Thank you for the clarification and for running additional experiments. Adding these results to the main paper (or in the Appendix and referencing them in the main paper) would definitely strengthen the paper. I will raise my score to 7.	Summary: The authors of the paper propose a method to demonstrate that foundation models can exhibit agreement-on-the-line (AGL), under certain conditions. The existence of AGL can be used to predict the OOD capabilities of models without having access to the labels for the downstream tasks. Strengths: - While AGL has been observed in the literature, the paper is novel (to the best of my knowledge) in applying it to the setting of foundation models. - The subject of the paper is also interesting - measuring the OOD performance of models is an important topic, and this paper does so with the added benefit of not explicitly requiring downstream labels (which, as the authors note, may be difficult to procure). - The experiments done by the authors are convincing, for the most part. The situations where foundation models exhibit AGL are clear, and it is easy to understand how the existence of AGL translates to good predictions about OOD performance. Weaknesses: - I believe that the paper's clarity, while overall good, could be improved further in certain points: - Figure 1 should be a little clearer, with the caption being a little bit more detailed. This will help a lot with understanding of the key results of the paper, given the early position of the Figure in the document. - I feel like the authors should elaborate a bit on lines 246 - 255, given that their result here is in contrast with previous statements made in the literature. A little more discussion here would be helpful. - Similarly, Figure 3 should also be expanded a bit more, especially since in some settings the ID - OOD line lies directly on top of the $y= x$ axis, which I find very surprising. - The fact that AGL can predict OOD performance, while interesting, comes with the caveat in Section 5 that it cannot be currently applied to all datasets. The authors explicitly state that and provide a criterion to determine the setting in which AGL is predictive of OOD accuracy. Nevertheless, I think this Section requires a bit more detail (see also my question below). Overall, this is an interesting paper in my opinion, and I think my concerns with it currently are mostly based on the clarity. Technical Quality: 3 Clarity: 3 Questions for Authors: I would like the authors to explain what the correlation $R$ in Section 5 refers to. If it is ID vs OOD agreement for various models, then it would mean that these should be nearly parallel to the $y = x$ line, which is a limitation of the setting where AGL is predictive of OOD performance. Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: I think the authors have adequately addressed the limitations of their work, and I cannot find any negative societal impact arising from their work. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your valuable comments and suggestions! We address each of your concerns below in detail. >__Figure 1 should be a little clearer, with the caption being a little bit more detailed. This will help a lot with understanding of the key results of the paper…__ Thank you for the suggestion! We will update the Figure 1 caption if accepted to: “The ID vs OOD lines for accuracy (yellow) and agreement (blue) for various datasets and fine-tuned ensembles. Each blue dot corresponds to a member of the ensemble and represents its ID (x) and OOD (y) accuracy; and each yellow dot corresponds to a pair of these members and represents their ID (x) and OOD (y) agreement. From CIFAR10 to CIFAR10C “Pixelate”' in linear probed CLIP, MNLI to SNLI in full fine-tuned OPT, and SQuAD to SQuAD-Shifts “Amazon” in full fine-tuned GPT2, we observe different agreement linear fits depending on the diversity source (columns) used to generate the ensemble.” >__I feel like the authors should elaborate a bit on lines 246 - 255, given that their result here is in contrast with previous statements made in the literature.__ Thank you for the suggestion! In our work, we demonstrated that _random initialization_ in particular is important to observe AGL in fine-tuned FM ensembles. We tie this finding to previous literature in lines 246-255 that study how well different sources of diversity in deep ensembles induce a related but different phenomena called GDE. In particular, GDE is a phenomenon in deep ensembles (neural networks, random forests) where ID accuracy tends to equal ID agreement exactly [1, 2]. Works have shown that, beyond the classical ensembling technique of bagging / data subsetting, deep ensembles induced by varying the data or model seed (ordering / initialization) can also induce this equality. On the other hand, in our problem setting, we found that ensembles induced by different random initialization achieves AGL, while data ordering / subsetting cannot. Our setting is different from previous literature in two distinct ways: __1.__ AGL studies the _OOD_ agreement rate relative to their ID agreement, in contrast to the GDE phenomena which only regards the models’ ID agreement. We hypothesize that random initialization is much more important for observing the right levels of OOD agreement. __2.__ Models are only _lightly fine-tuned_ or linearly probed, unlike deep ensembles trained from scratch. Diversity sources may behave differently in this circumstance. We will add this further discussion in the camera ready. [1] Jiang, et al. Assessing Generalization of SGD via Disagreement. ICLR 2022. [2] Nakkiran and Bansal. Distributional Generalization: A New Kind of Generalization. Preprint 2020. >__Figure 3 should also be expanded a bit more, especially since in some settings the ID - OOD line lies directly on top of the y=x axis, which I find very surprising.__ Thank you for your suggestion! We will make sure to expand on the main takeaways from Fig 3. Notably, we observe that the agreement rate between models from different model families (e.g., between GPT and Llama models) observe agreement-on-the-line across different NLP tasks. Indeed, there are certain shifts such as from SQuAD to SQuAD-shifts New Wiki and SQuAD-shifts NYT where model performance barely drops. This is partially due to the large-scale pretraining, but also the distribution shift is simply much smaller – SQuAD was constructed using Wikipedia, so looks closer to SQuAD-Shifts New Wiki and NYT than Amazon reviews and Reddit [1]. What is most peculiar is that ID vs OOD agreement tracks the linear trend of ID vs OOD accuracy accordingly. For small distribution shifts SQuAD-Shifts New Wiki and NYT, the models’ agreement ID vs OOD is also close to being y=x. For larger shifts such as SQuAD-shifts Amazon and Reddit, ID vs OOD agreement also moves away from the y=x line. We will make these clarifications in Figure 3. [1] The Effect of Natural Distribution Shifts on Question Answering Models. Miller et al. 2020. >__I would like the authors to explain what the correlation R in Section 5 refers to. If it is ID vs OOD agreement for various models, then it would mean that these should be nearly parallel to the y=x line…__ Thank you for the feedback! The $R^2$ we mention in Section 5 refers to the _standard linear regression coefficient of determination_. $R^2$ ranges between 0 and 1 and it measures how well the relationship between two variables, $X$ vs $Y$, can be explained by a linear function. When $R^2$ is high, $Y$ can be estimated as $aX + b$ with small residual error. In our paper, we use $R^2$ to measure the strength of the linear correlation in ID vs OOD agreement and ID vs OOD accuracy. Note that $R^2$ is different from the slope of the linear fit. For example, consider SQuAD-shifts Reddit in Figure 3, both ID vs OOD accuracy and agreement have high $R^2$ values, but the slope is far away from the $y=x$ line. According to Baek et al. [1], $R^2$ can determine when AGL holds. In particular, when ID vs OOD agreement strictly follows a linear trend (i.e., the linear correlation has high $R^2 > 0.95$), then ACL also holds with the _same slope and bias_. In such circumstances, we can use AGL-based methods ALineS and ALineD to estimate the OOD performance of models precisely without labels. Interestingly, as we have demonstrated in our paper, many natural distribution shifts across image/text classification and QA observe AGL and ACL with high $R^2$. We will make these points clearer in Section 5 of the final draft. [1] Baek et al. Agreement-on-the-line: Predicting the performance of neural networks under distribution shift. NeurIPS 2022. --- Rebuttal Comment 1.1: Title: Response to rebuttal Comment: Thank you very much for the detailed response to my comments! As all of the points I made have been addressed, I am raising my score a bit.	Summary: This submission studies the problem of predicting OOD performance given known in-domain performance. Building on top of recent work showing that ensembles can be used for this problem, by looking at agreements between components in the ensemble as surrogate labels to predict OOD performance, they find that a similar approach can be used for finetuned LLMs, as long as ensembles are generated by finetuning randomly initialized heads. The topic is timely, the paper is generally clearly written (although improvements are needed) and the empirical validation is good. Strengths: + relevant and important topic + simple and practical approach Weaknesses: - some critical details are missing, for instance the authors should report in the main paper how to go from Acc, Agr to OOD (line 160-164). - the significance is unclear to me: It would be useful to predict OOD performance at larger scales as opposed for models that are finetuned for more steps. Technical Quality: 3 Clarity: 3 Questions for Authors: If only the topmost layer is randomly initialized and trained, then all components of the ensemble should converge to the same parameter vector provided that they are trained for long enough because the optimization is a convex problem. Is the diversity due to the limited number of training step? If it is the case, I think the assumption should be made explicit. Could the authors compare the method of sec. 4 against the method of sec 3 directly? Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: no concern Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your valuable comments and suggestions! We address each of your concerns below in detail. >__Some critical details are missing, for instance the authors should report in the main paper how to go from Acc, Agr to OOD (line 160-164).__ We apologize for the lack of clarity. The default prediction algorithm (ALineS) used to estimate OOD accuracy when agreement-on-the-line holds, is as follows: 1. Say there is a linear trend in ID versus OOD agreement, i.e., for any two pairs of models $w, w’$ we have $\Phi(Agr_{OOD}(w, w’)) = a * \Phi(Agr_{ID}(w, w’)) + b$ where $\Phi(\cdot)$ is the probit scaling. 2. Estimate the slope and bias ($\hat{a}, \hat{b}$) of the above linear trend using OLS. 3. Apply this linear transformation to accuracy: $\Phi(Acc_{OOD}(w)) = a * \Phi(Acc_{ID}(w)) + b$ We will update Section 2.3 to include equations defining accuracy-on-the-line and agreement-on-the-line in the main body. In addition, we have included a detailed discussion of the prediction algorithms (ALineS and ALineD) in Appendix A.1.1. >__The significance is unclear to me: It would be useful to predict OOD performance at larger scales as opposed for models that are finetuned for more steps.__ Thank you for this important question! You can utilize our results in the multiple base model section (Section 4) as a type of “scaling law”. In Figure 3, we showed that finetuned models of a large range of model scales (125M to 7B parameters) and model families (GPT, Llama2, etc.) observe the same ACL and AGL trends in QA and text classification. Using smaller models such as GPT2, we can compute the ACL/AGL trend, and use this to project the OOD performance of larger models _without any labels_ given their ID performance. >__If only the topmost layer is randomly initialized and trained, then all components of the ensemble should converge to the same parameter vector…because the optimization is a convex problem. Is the diversity due to the limited number of training step?__ As mentioned in Section 3, to construct the ensemble, we vary the number of epochs/training steps to get models with a wide range of ID accuracies. We will make this more clear in the revision - thank you for pointing this out! >__Could the authors compare the method of sec. 4 against the method of sec 3 directly?__ Thank you for this question! To reiterate, Section 3 studies AGL in ensembles of models finetuned from a _single_ base foundation model, where we establish that randomly initializing the head is important for observing AGL. In Section 4, we show that ensembles of models fine-tuned from different base foundation models (i.e. LLama, GPT, OPT) also exhibit AGL. To answer your question, we do a direct comparison of AGL under these two scenarios. Specifically, we have a set of 14 finetuned GPT2 models, and we measure their agreement rate with Setting 1: other GPT2 models finetuned with different random initialization Setting 2: models finetuned from other base models (Llama, OPT). Using these agreement rates, we predict the OOD performances of the GPT2 models using the ALine-S algorithm. We report the MAE and MAPE for the two settings below. Both are quite effective with very small MAE’s (estimates OOD accuracy with error less than 2%). __SQuAD vs SQuAD-Shifts Reddit__ \| \| Setting 1 \| Setting 2\| \|--------------- \|--------------\|--------------\| \|MAE\| 1.27\| 1.54\| \|MAPE\| 5.19\| 4.82\| --- Rebuttal Comment 1.1: Title: thank you Comment: I'd like to thank the authors for their response which I find satisfactory. I hope they will revise the paper accordingly. I am still supportive of accepting this paper.	Rebuttal 1: Rebuttal: We thank all reviewers for their great feedback and questions about our paper! The reviewers generally found our paper interesting and praised our work for proposing a simple yet effective solution to predict the OOD performance of FMs. Here, we briefly summarize the common concerns, and new experiments we’ve added in our rebuttal PDF: __How do you achieve a wide range of accuracies and agreements in the linear probing setting where the loss landscape is convex?__ In each ensemble, we also vary the number of epochs we finetune each model. Regardless, the random initialization also has to vary to observe AGL. __Can we use this method to forecast OOD performance with larger scales?__ Yes! We showed in Section 5 that on many language tasks, foundation models from different families (GPT, OPT, LLama) of different sizes all lie on the same ACL and AGL trends. This means we can estimate the linear trend using smaller models to extrapolate the performance of larger models with no labels OOD. __Is it interesting to study fine-tuned FMs?__ It is common practice to finetune FMs by linear probing or LoRA, and we believe our study can apply to many practical use cases for OOD estimation. As requested, we also extend our study to few-shot and zero-shot settings in rebuttal Figure 2. In the few-shot setting, we also observe that ACL/AGL hold in CLIP by varying the random initialization. On the other hand, zero-shot language models do not necessarily observe AGL/ACL trends as strongly as fine-tuned models on SQuAD versus SQuAD-Shifts. Zero-shot models may behave differently as neither SQuAD nor SQuAD-Shifts is “in-distribution”. __Are there any theoretical guarantees we provide about ACL or AGL?__ While we do not provide exact theoretical guarantees, the conclusions we make about ensemble diversity in fine-tuned FMs and their effect on observing AGL/ACL hold across hundreds of fine-tuned models we tested from different model families (GPT, OPT, Llama), 50+ distribution benchmarks (Appendix A.3 and A.4), hyperparameters (see learning rate/batch size sweep in rebuttal Figure 3), fine-tuning strategies (LP, LoRA, full fine-tuning; other PEFT methods in rebuttal Figure 1). We hope that our rigorous experimental report can demonstrate that ACL/AGL is a powerful tool for predicting the performance of FMs. Pdf: /pdf/f6ade5d395866a096bbdeacb445ffc9b46f08d34.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Mechanism design augmented with output advice	Accept (spotlight)	Summary: This paper explores a novel setting in mechanism design where an output is provided as advice to the mechanism. The authors propose consistency, robustness, and approximation properties for strategy-proof mechanisms. They introduce four types of mechanism design problems and corresponding mechanisms, demonstrating their beneficial properties. Strengths: The setting and algorithms used in mechanism design are intriguing. The approximation analysis is well-conducted and represents a significant technical contribution. Weaknesses: 1. The paper is difficult to follow due to its presentation. For example, the model of this work differs from other works mentioned in the paper [2, 42]. However, these other works are discussed before the authors’ own work in the introduction, which seems redundant. Additionally, the paper often repeats similar sentences. 2. Many contributions are relegated to the appendix. This is not ideal as the main body should be self-contained, with the appendix used for further verifications. Technical Quality: 3 Clarity: 2 Questions for Authors: 1. It is not clear why the output advice might be helpful for mechanism design and why the model requires potentially inaccurate output advice. Why can't the model compute an output from the input (type profile) directly and regard this output as advice? 2. Following the first question, do you have comparative results showing that without output advice, the consistency of the optimal strategy-proof mechanism is strictly worse than that of the strategy-proof mechanism with accurate output advice? 3. In my understanding, the VCG mechanism provides an output that maximizes social welfare (minimizes cost), so the approximation ratio of VCG should be 1 if the output is computed precisely. How do you explain your results indicating that the approximation ratio of VCG is $\Theta(n)$, which seems counterintuitive? Confidence: 2 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: Although the poor presentation does not diminish the positive contributions of this paper, it is a drawback that makes the content difficult to understand. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for their comments. We are sorry that this reviewer (unlike the other two) was not satisfied with the level of presentation of our results. We argue below why we find the reasons for the low presentation score to be a bit too harsh. Reviewer PWat stated as two weaknesses: 1. "The paper is difficult to follow due to its presentation. For example, the model of this work differs from other works mentioned in the paper [2, 42]. However, these other works are discussed before the authors’ own work in the introduction, which seems redundant. Additionally, the paper often repeats similar sentences." 2. "Many contributions are relegated to the appendix. This is not ideal as the main body should be self-contained, with the appendix used for further verifications." Response to weakness 1: In the introduction, we propose a model as an alternative of those discussed in [2,42] so we feel that is important to discuss their model before we introduce ours and argue why our model is motivated given those previous models. Response to weakness 2: We manage to include all the main contributions in the main body, however space limitations force us to state the detailed proofs in the appendix (we have prepared a full version of the paper). This is typical for a theoretical work as ours. Response to questions Question 1: "It is not clear why the output advice might be helpful for mechanism design and why the model requires potentially inaccurate output advice. Why can't the model compute an output from the input (type profile) directly and regard this output as advice?" Our response: We are not sure that we understand this question. In a mechanism design setting, agents' types/preferences are private (see lines 176, 236, 311), and are not offered directly to the algorithm designer. Therefore, the input (type profile) is not known. The whole goal of mechanism design is to design strategyproof mechanisms, i.e., mechanisms that provide incentives to the agents to reveal their true types (see Introduction, lines 39-48, and Model Section, lines 179-192). Therefore, we are not sure what is meant by "computing the output from the input (type profile)", as this is not offered to the designer. Question 2: "Following the first question, do you have comparative results showing that without output advice, the consistency of the optimal strategy-proof mechanism is strictly worse than that of the strategy-proof mechanism with accurate output advice?" Our response: Again, we are not sure that we understand this question. The definition of consistency requires some sort of advice/prediction (see lines 37, 214-220). We thoroughly compare the bounds of our mechanisms that are enhanced with output advice with the optimal mechanisms without any advice/prediction. Those comparisons for the four problems are more specifically the following: - Facility location problem: The bounds of the optimal strategyproof mechanisms without any prediction/advice is 2 for the egalitarian cost objective (lines 511-514). The consistency (i.e., its approximation ratio when the output advice is accurate) of the Minimum Bounding Box Mechanism (lines 284-286) is 1 (by setting the quality of recommendation, $\hat{ρ}$, equal to 1 in Theorem 1). - Scheduling games: The worst-case guarantee of the VCG mechanism (which is the optimal strategyproof mechanism) is the poor approximation of $n$ (lines 522-524). However, the consistency (accurate output advice) of the AllocationScaledGreedy mechanism for the scheduling problem, is asymptotically constant (Theorem 3 for $\beta$ being a constant) which is strictly better than $n$. - House allocation problem: Regarding deterministic stategyproof mechanisms, a $\Omega(n^2)$ bound is known for the unit-sum case and a $\Omega(n)$ bound is known for the unit-range case (lines 539-543). The TTC with recommended endowment mechanism (Mechanism 5, lines 832-833) is 1-consistent in both cases by setting $\hat{ρ}=1$ in Τheorem 7. - Combinatorial auctions: the worst-case approximation ratios of the best known strategyproof mechanisms for the three applications are strictly more than 1 (lines 1000, 1006, 1011), while the MIR with recommended allocation (Mechanism 6, lines 978-979) is 1-consistent (by setting $\hat{ρ}=1$ in Lemma 16), which is strictly better. Question 3: "In my understanding, the VCG mechanism provides an output that maximizes social welfare (minimizes cost), so the approximation ratio of VCG should be 1 if the output is computed precisely. How do you explain your results indicating that the approximation ratio of VCG is $\Theta(n)$, which seems counterintuitive?" Our response: It is true that the VCG mechanism by definition finds the optimal solution in the case of the social welfare (or cost) objective. However, in the scheduling game we do not study the welfare objective, but the makespan i.e., the minimization of the maximum completion time (see intro (line 98, 119), and as we define in the description of the problem (line 325)). This is the standard objective (see e.g., [9,14,16,42]) in the scheduling literature (defined in the description of the problem, line 325). Regarding the makespan objective, VCG is known to be [16] the optimal strategyproof mechanism but with a very poor approximation ratio of $n$ (as stated in lines 522-524). --- Rebuttal Comment 1.1: Comment: Thank you for your detailed response. * Regarding weakness 1 The paper introduces the mechanism design problem with predicted inputs in the first three paragraphs. In my understanding, the model does not enhance or extend the existing model but rather considers another model, that focuses on the advice in the output dimension. I think that it's more appropriate to move them into Related Work. When I reviewed this paper, I felt that the model extended the existing model of mechanism design with predicted inputs until I got to Line 47. * Regarding weakness 2 It's fine to remove the proofs from the appendix. However, this paper removes the main results (regarding House Allocation and Auctions) from the appendix, which I have never seen in other conference papers. However, I acknowledge that the presentation score is harsh for these issues, and I improve the presentation score from 1 to 2. * Regarding my original question 1,2 I originally meant that the model needs justification about whether the output advice would be helpful for designing a strategy-proof mechanism. The original question 1 should be stated as follows: Given a mechanism $M$ with output advice, now we construct a mechanism $M_1$ without output advice. This mechanism takes type profile $\boldsymbol{t}$ as input, compute a (possibly accurate or inaccurate) outcome advice $a$ by some oracle $O$, take $\boldsymbol{t}$ and $a = O(\boldsymbol{t})$ as input to run the mechanism $M$, and return the outcome $M(\boldsymbol{t}, a)$ to players. Why can we not do such a reduction from a mechanism with output advice to a mechanism without output advice? For original question 2, I meant to say "the approximation ratio of the optimal strategy-proof mechanism". Your response to question 2 is satisfactory. I will consider improving my rating after the full responses. But I suggest that these results be listed in Table 1, as a comparison of mechanisms with/without output advice and a justification of the output-advised model. Besides, the comparisons of mechanisms with output advice and input predictions are also encouraged, as mentioned by Reviewer i6E2. * Minor issues When I look through the paper again, I found that it's better to replace $a^$ with $a^(t)$ in the expression between Line 219 and Line 220, since $a^$ depends on $t$ and $t$ is not fixed in the place $a^$ appears. --- Rebuttal 2: Comment: Thank you for the clarifications on your questions and for considering to increase the scoring. Regarding weakness 1, our model indeed differs from the literature and is not just an extension. Still we believe that it is important to introduce previous work on mechanism design with advice (expressed as input or output prediction) so that we can compare our model with existing literature and show how it differs from it. Regarding weakness 2, we understand the reviewer's concern, but we believe that the way we present the paper serve the following purposes: Our model's error function is justified by the facility location problem, while the model's advice type (output advice) is supported by the scheduling problem. The house allocation and combinatorial auctions sections can be viewed as applications of our model, which is why we mention the results in the contributions section but include the detailed results in the appendix. In any case, it seems that we have different (subjective) view on some presentation aspects and we thank the reviewer for their intention to increase this score. Our response to the original question 1: The challenge in the reduction proposed by the reviewer is how to define the oracle $O(t)$. If you take any arbitrary oracle, e.g. one that produces the optimal allocation (or a good approximation), then the players may have incentive to misreport, as we mention in 181-182. If one designs an oracle $O(t)$ as part of a strategyproof mechanism, this is the standard mechanism design problem without advice or prediction. It is known that strategyproofness imposes limitations so we cannot implement arbitrary good approximation algorithms, as we mention in the related section (see e.g scheduling [16], lines 522-524). For example, in scheduling games one cannot expect to design a strategyproof mechanism by getting an oracle $O(t)$ with good approximation and use it in the reduction proposed by the reviewer, since this would produce a good approximation for this mechanism; this would contradict the result of [16] which states that no strategyproof mechanism has approximation ratio better than $n$. This is why in all learning-augmented mechanisms (like [2], [9] and our work) it is assumed that the prediction is an exogeneous (untrusted) source unrelated to the actual input $t$, as we mention in the text (see e.g. lines 53-55, 68-69). --- Rebuttal Comment 2.1: Comment: Thank you for the authors' further clarification. I am happy to improve the contribution score to 3 and the overall score to 6 (weak accept), considering that the model is indeed innovative and non-trivial. Regarding the presentation issue, I agree with the authors that "it is important to introduce previous work". But what I mentioned is that the presentation in this version is somewhat misleading, especially in lines 28-29: "Within this framework, algorithms are enhanced with imperfect information about the input, usually referred to as predictions." It (as well as other sentences) makes me feel that the paper studies the mechanism design with predicted inputs. Overall, there is no conflict of view between the authors and me. Though important to introduce, I insist that the presentation logic here is not appropriate. I suggest replacing the above-mentioned sentence with, "Within this framework, one approach is to enhance the algorithm with imperfect information about the input, ... However, the algorithm enhanced with output advice lacks study." I also agree with the authors that there is heterogeneity in presentation preference. I do not consider the presentation conflict when I re-evaluate the overall score of this paper.	Summary: The authors propose a novel paradigm for mechanism design augmented with advice. While classically learning-augmented mechanism design assumes input advice, the authors consider output/outcome advice. They use "quality of recommendation" to quantify the quality of the advice and provide approximation, consistency, and robustness guarantees as a function of confidence in the advice and quality of recommendation. Strengths: The authors propose a novel learning-augmented framework and use it to analyze various well-studied mechanism design settings, contextualizing well in the subfield of learning-augmented mechanism design. Weaknesses: I see no significant weaknesses, granted that this is not my area of expertise. Formatting in some parts of the paper can be improved (e.g., spacing and commas in line 110 and consistency of the formatting of the citations). As noted below, I was wondering if there is a reason you only conduct experiments for one of the mechanism design settings. Technical Quality: 3 Clarity: 4 Questions for Authors: 1. Why do you only conduct experiments in one of the mechanism design settings? Confidence: 2 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: We thank the reviewer for their thorough review. We address their concern below. Question: "Why do you only conduct experiments in one of the mechanism design settings?" Our response: Our work is mainly theoretical, and we provide tight results for all four problems and comprehensive comparisons with the literature whenever related literature exists (facility location [2,42] and scheduling [9,42]). For the facility location problem with egalitarian cost, due to space limitation, those comparisons appear in the appendix (section B.4, see Lemmas 4 and 5, and lines 639-643). For scheduling games, the comparison is given in Theorem 5, and Remark 2. There is only one exception to that, where our theoretical comparison with the literature [2], is inconclusive, and this is regarding the facility location problem with utilitarian cost. This is the reason why we conduct experiments only for this case (Section B.5). --- Rebuttal Comment 1.1: Comment: Thank you for the response. Having read the rebuttal (and the discussion with the other reviewers), I will maintain my score.	Summary: This paper studies the problem of mechanism design with prediction and introduces a new framework based on output predictions. Unlike most previous work, which primarily uses input predictions with varying error metrics, this paper considers output predictions and proposes a new error metric that can be applied in various settings. The authors reexamine four previously studied problems with this new prediction and develop consistency, robustness, and smoothness results for each setting. Strengths: 1. The concept of output prediction is novel, and the error metric is general, applicable to a range of problems. 2. The results for the four settings are comprehensive, with some being tight. The paper also provides comparison to input prediction results in some settings. Weaknesses: Except for the facility location section, this paper lacks extensive comparisons to previous results with input predictions. While there are tight results with respect to the output prediction, it is not clear to me what does this mean compared to those with input predictions, and what are the relations between them. More comparison results (both theoretical and empirical) between different forms of predictions and error metrics should be conducted. Technical Quality: 3 Clarity: 3 Questions for Authors: refer to the weaknesses. Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: 1. Refer to the weaknesses 2. There are some minors, mainly on the direction of inequalities. While I am not sure if my interpretation is correct, I suggest the authors double-check on these points: 1. line 203: $(W(t,a)$ -> $C(t,a)$ 2. line 211: $\geq$ -> $\leq$ 3. equations between line 219 and line 220: $\leq$ -> $\geq$ Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for their insightful comments. We address concerns about potential weaknesses below. Question: "Except for the facility location section, this paper lacks extensive comparisons to previous results with input predictions. While there are tight results with respect to the output prediction, it is not clear to me what does this mean compared to those with input predictions, and what are the relations between them. More comparison results (both theoretical and empirical) between different forms of predictions and error metrics should be conducted." Our response: We would like to argue that we thoroughly compare our results with related literature of this relatively new research area. In particular, we consider four different mechanism design settings. Only two of those were studied before within the learning augmented framework (facility location and scheduling) and we thoroughly compare our results with existing literature in both settings. The other two (welfare maximization in auctions and house allocation) were not previously studied using the learning augmented framework, so we would not be able to compare our work with previous results. As a matter of fact, all previous work regarding the facility location problem [2, 42] are based on output (not input) predictions, as our work does, but [42] studies multiple facilities (as we describe in the related work section), so it is not closely related, hence incomparable with our work. [2] studies the same problem and this is why we provide a thorough comparison with this work. In particular, this is the perfect setting to demonstrate why our proposed error (the quality of recommendation) is more natural and results in a better refinement of the approximation bounds (in the case of egalitarian cost). Regarding scheduling games, again we compare our work with all existing previous results [9, 42]. We make an explicit comparison only with [9] which is the state-of-the art (as [9] improves the bounds of [42] as we discuss in the further related work section that appears in Appendix A). Regarding [9], in Remark 2, we provide a thorough explanation of the connection of our AllocationScaledGreedy mechanism that is enhanced with output advice with the two mechanisms proposed in [9] that use input advice instead. Moreover, our optimality bounds (Theorem 5) provide the first trade-off between the amount of provided information and the best achievable bounds. We will follow the excellent suggestion of the reviewer to highlight this separation in the paper and make it more prominent. Regarding empirical comparison, we would like to emphasize that our work is mainly theoretical. In the facility location problem with egalitarian cost and in the scheduling problem, our theoretical results are sufficient to provide comprehensive comparison of our results with the work of [2] and [9], respectively. For the facility location problem with egalitarian cost, due to space limitation, those comparisons appear in the appendix (section B.4, see Lemmas 4 and 5, and lines 639-643). For scheduling games, the comparison is given in Theorem 5, and Remark 2. The only case where our theoretical comparison with the results of [2] is inconclusive is the facility location problem with utilitarian cost, and this is the reason why we conduct experiments only for this case (Section B.5). We thank the reviewer for catching some typos. The correction on line 203 is indeed correct. The inequalities however should stand as they are, as they refer to the cost minimization objective. --- Rebuttal Comment 1.1: Comment: Thanks for the response. the writing style of the introduction makes me expect a detailed comparison with the previous results with input prediction. Now it seems that only the scheduling games have been studied in the learning augmented literature with input advice. I guess my original questions are a bit general and beyond the scope of this paper: 1. Given algorithms with input predictions and output predictions, respectively, each having an approximation ratio depending on the respective prediction error defined, how can we compare these two algorithms and their performance? Here are several other further questions with respect to the contents of the paper: 1. Given an input prediction, we can compute the corresponding output and apply the mechanism proposed in your paper. As the input prediction contains more information beyond the output, can we possibly design better algorithms beyond that? 2. Several tight results are with respect to the proposed mechanisms (e.g., Lemma 1, Lemma 4, Lemma 9). Can these tight results imply tightness results to the problem itself under the arbitrary mechanisms? 3. With respect to Lemma 7, can there be instances where $\sqrt{2} \hat{\rho} > \frac{\sqrt{2 \lambda^2+2}}{1+\lambda}+\eta$? 4. As for the reason that mechanism design with output advice in MIR mechanisms has such plug-and-play property, is it because that computing an output from an input prediction can be computationally hard? It is quite like the trivial idea that you can get a mechanism with good expected consistency and robustness by just randomizing over a robust mechanism and a mechanism that fully trusts the prediction. 5. The proofs of tightness results mainly propose instances that make the ratio tight. I am wondering, even if such an instance exists, can we still find ratio that equals the tight value among these instances, and have more tight ratios among other instances? If this holds, can we still say those ratios are tight? Further minor comments 1. A new typo I just find: line 206: $max_{a\in\mathcal{A}}C(t,a)$ -> $min_{a\in\mathcal{A}}C(t,a)$ 2. several prediction errors used in the previous work and definitions are lacking (e.g., the MIR mechanism), which cause trouble for further reading. --- Rebuttal 2: Comment: Thank you for your comments and follow-up questions. We respond to these questions below: Question: Given algorithms with input predictions and output predictions, respectively, each having an approximation ratio depending on the respective prediction error defined, how can we compare these two algorithms and their performance? Our response: Indeed, this is an excellent, deep and quite general question, that could be explored in future work. Even comparing algorithms with different input predictions can be challenging and interesting, and comparison may vary according to the respected prediction error. We emphasize that it is not our intention (and beyond the scope of our work) to do such a general comparison so we only do, as this reviewer noted, whenever there is existed related work, i.e. for the facility location problem and for the scheduling problem. ## Further questions: Our response to Question 1: Indeed, the reviewer is right. As we mention in lines 58-59 and 69-70, one can see our model as a restriction of models that have input predictions, which makes the design of mechanisms much more challenging comparing to those models that have input predictions. The scheduling problem is an excellent example for this discrepancy. The ScaledGreedy mechanism [9] that uses the input as a prediction can achieve a constant consistency together with a linear robustness (see Remark 2, lines 363-365, and Related Work, lines 529-531). Our theorem (Theorem 5) shows a separation result. It essentially stated that VCG-based mechanisms, which is a wide class of known mechanisms, when equipped with output predictions and when requiring constant consistency, are restricted to quadratic robustness which is more limited than mechanisms with input predictions. Our response to Question 2: Those lemmas concern tight results for the proposed mechanisms. However, we also provide more general lower bounds for classes of mechanisms (that satisfy some natural properties), e.g. for all VCG-based in scheduling problem (Theorem 5) and for general mechanisms for the house allocation problem (Theorem 8). We remark that providing negative results for all mechanisms, even in the standard mechanism design setting (without any sort of prediction) may be notoriously hard, and only few such results exist (see e.g. [16] for scheduling, and [19, 36] for combinatorial auctions). Our response to Question 3: Yes, there exist such instances. The value of the two expressions in the inequality above depend on the value of $\hat{\rho}$, $\eta$ as a function of the output advice $\hat{a}$. For example, taking into account Lemma 5, it is possible that $\hat{\rho} = 1$, $\eta = 0$ and $\lambda$ is close to 1. The comparison of the two upper bounds is inconclusive, and this is the reason that we conduceted experiments (section B.5) in order to contribute to the better understanding of the relation between the two errors. Our response to Question 4: Actually, the reason is that Maximal in Range (MIR) compute the optimal allocation w.r.t social welfare among a subset of allocations (the range). One can enhance this subset of allocations by plugging-in the predicted output $a^$. Then by definition of MIR, the MIR mechanism will output $a^$ if this happens to be the best among the subset of allocations selected. Notice that this is a deterministic not a randomized mechanism. Studying randomized mechanisms with predictions is an interesting future direction. However, any randomized mechanisms that outputs the prediction with constant probability cannot have the same robustness guarantee (in expectation) with the MIR mechanism we use. Our response to Question 5: Yes, this is exactly what we do in the facility location problem. Take the egalitarian cost for instance. The bound provided in [2] for the Minimum Bounding Box mechanism is tight. However, we manage to provide an even more refined upper bound in Theorem 1. This bound is tight (see Lemma 1), in the sense that there is no upper bound $\hat{\rho}-\epsilon$ strictly lower than the one we provide. As mentioned in Remark 1, this upper bound is tight whenever the output advice is inside the minimum bounding box. Concerning the minor comments, again thank you for catching this typo, and we will consider further defining MIR mechanisms, even though they are generally described in lines 972-974. --- Rebuttal Comment 2.1: Comment: Thank you for addressing all my further questions. I really enjoyed this conversation and would like to raise my score. Here are a few further responses that I did not expect the authors would reply as it is the end of the discussion period: 1. Response to Response to Question 2: So the tightness results indeed do not extend to general settings. 2. Response to Response to Question 4: I look forward to seeing if there are more examples/general scenarios where the plug-and-play properties can apply.	null	null	Rebuttal 1: Rebuttal: We would like to thank the reviewers for their thorough reviews and thoughtful comments. We respond to each reviewer's questions with a separate reply to each of their reviews.	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
IWBVT: Instance Weighting-based Bias-Variance Trade-off for Crowdsourcing	Accept (poster)	Summary: This paper explores methods to enhance the training of machine learning models using crowdsourced datasets and proposes a novel post-processing approach called IWBVT. The proposed IWBVT first performs instance weighting based on the entropy of the complementary label distribution. Subsequently, it employs a bias-variance trade-off to minimize the generalization error of trained models. Extensive experiment results demonstrate that IWBVT significantly improves the model quality of existing state-of-the-art label integration and noise correction algorithms. Strengths: 1. This paper proposes a novel post-processing approach that significantly improves the quality of machine learning models trained with crowdsourced datasets. The paper is technically sound, providing detailed derivations and justifications for the proposed approach. The proofs for theorems are clear and rigorous. 2. The paper is well-written, logical and easy to understand. It clearly describes the problem to be solved and provides a logically rigorous argumentation process. The figures and tables provided in the paper are helpful in illustrating the concept and effectiveness of IWBVT. 3. The experiments are well-designed, with appropriate datasets and evaluation metrics used to validate the proposed approach. Weaknesses: 1. More detailed explanations about experimental results are desired. For example, in Figure 3b, instance weighting significantly improves model quality on the Leaves dataset, whereas the bias-variance trade-off is more effective on the Income dataset. Understanding the properties of the datasets that lead to these differences would help clarify the conditions under which the proposed approach is most effective. 2. The experiments in this paper primarily focus on the robustness of IWBVT across various label integration and noise correction algorithms and different datasets. To further validate the effectiveness of IWBVT, it would be beneficial to observe its performance on a range of different models. 3. More limitations of IWBVT should be discussed. These include its robustness in the presence of extremely noisy labeling, the computational complexity when handling very large datasets, and potential challenges in real-world applications. Technical Quality: 3 Clarity: 2 Questions for Authors: 1. According to Figure 3b, when improving model quality, why is instance weighting more effective on the Leaves dataset while the bias-variance trade-off is more effective on the Income dataset? 2. How does IWBVT perform on different machine learning models? Demonstrating that IWBVT can improve the quality of various machine learning models would further validate its effectiveness. 3. How does IWBVT perform in more complex crowdsourcing scenarios, such as those with extremely noisy labeling or very large datasets? Discussing the potential limitations of IWBVT in these contexts can help enhance its overall effectiveness and applicability. Confidence: 4 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: Please refer to the Weaknesses. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Reviewer 5XV6： Q1: According to Figure 3b, when improving model quality, why is instance weighting more effective on the Leaves dataset while the bias-variance trade-off is more effective on the Income dataset? Author Response: Thanks for your valuable comments. Indeed, in Figure Figure 3b, the instance weighting is more effective on the Leaves dataset, while the bias-variance trade-off is more effective on the Income dataset. This is because the average label quality of the Leaves dataset is low. The instance weighting helps to identify the small number of instances that are correctly inferred and therefore has a greater impact on the Leaves dataset. However, the average label quality of the Income dataset is high, and more instances can be correctly inferred than in the Leaves dataset. Therefore, the bias and variance are estimated closer to the unknown true values, so the bias-variance trade-off is more effective on the Income dataset. In the final version of the paper, we will provide a more detailed explanation of our experimental results. Thanks again for your valuable comments. Q2: How does IWBVT perform on different machine learning models? Demonstrating that IWBVT can improve the quality of various machine learning models would further validate its effectiveness. Author Response: Thanks for your valuable comments. Indeed, we currently used only a simple linear regression (LR) in the probabilistic loss regressions of IWBVT and validated its effectiveness only on Naive Bayes (NB). In fact, IWBVT is effective for other various machine learning models as well. We constructed experiments on the Leaves dataset to validate this conclusion. Specifically, we considered both LR and model tree (MT) as the regression models and used NB and C4.5 as the target models. the experimental results are as follows: \| \|MV\| IWMV\| LAWMV\| MNLDP\| AVNC\| MVNC\| NWVNC\| \|--\|--\|--\|--\|--\|--\|--\|--\| \|LR+NB\|(59.75, 62.28) ✔\|(61.30, 62.85) ✔\|(58.74, 60.09) ✔\|(55.81, 61.54) ✔\|(60.44, 63.02) ✔\|(58.44, 60.55) ✔\|(58.57, 59.49) ✔\| \|LR+C4.5\|(52.10, 55.42) ✔\|(52.29, 56.17) ✔\|(56.15, 56.64) ✔\|(52.69, 58.09) ✔\|(56.89, 56.31) ✖\|(54.92, 56.31) ✔\|(56.12, 58.05) ✔\| \|MT+NB\|(59.21, 62.05) ✔\|(60.65, 61.45) ✔\|(59.21, 62.26) ✔\|(55.88, 61.36) ✔\|(58.55, 62.15) ✔\|(57.97, 59.45) ✔\|(61.02, 63.01) ✔\| \|MT+C4.5\|(51.96, 55.56) ✔\|(51.41, 56.64) ✔\|(55.11, 57.06) ✔\|(52.09, 56.83) ✔\|(57.29, 56.78) ✖\|(55.05, 56.53) ✔\|(56.74, 58.03) ✔\| Here, "✔" indicates that IWBVT improves the model quality of the corresponding label integration algorithm, while "✖" indicates the opposite. From these results, it can be seen that IWBVT is effective for various machine learning models. In the final version of the paper, we will include a discussion on the effectiveness of IWBVT across different machine learning models. Thanks again for your valuable comments. Q3: How does IWBVT perform in more complex crowdsourcing scenarios, such as those with extremely noisy labeling or very large datasets? Discussing the potential limitations of IWBVT in these contexts can help enhance its overall effectiveness and applicability. Author Response: Thanks for your valuable comments. Our proposed IWBVT is not restricted to specific crowdsourcing scenarios, so we conducted experiments on the whole 34 simulated datasets published by the CEKA platform. These datasets contain some large datasets such as the letter dataset. The experimental results in Table 1 indicate that IWBVT is effective on these large datasets. Additionally, the real-world dataset Leaves, whose percentage of noisy labels exceeds 0.4, is an extremely noisy labeling dataset. The experimental results shown in Figure 2 indicate that IWBVT is effective on this extremely noisy labeling dataset as well. In Section 6, we have discussed some limitations of IWBVT. In the final version of the paper, we will further refine our explanation for these limitations. Thanks again for your valuable comments. --- Rebuttal Comment 1.1: Comment: I am satisifed with the authors' rebuttal and keep on original scoring and confidence.	Summary: This paper proposes a novel label integration method called IWBVT for crowdsourcing by using a weighting method and probabilistic loss regressions to improve the model quality. The main problem this paper solves is the model quality caused by the presence of the intractable instances. The paper is well organized and the writing is smooth. The method proposed in the paper has improved the model quality, thus boosting the performance on simulation and real-world datasets. The authors also provide theoretical proof to deepen the understanding of the proposed method. Strengths: 1. The paper is well organized and the writing is smooth. The authors provide necessary symbol explanations, which is very helpful for reading. 2. The idea proposed in this paper is technical soundness. The authors incorporate instance weighting and bias-variance trade-off components to complete the overall algorithm. Furthermore, the authors also provide the corresponding theory to prove the effectiveness and generalization of the designed components. Experiments on simulation and real-world datasets demonstrate the superiority of the proposed method. 3. For instance weighting component, the authors prove that existing methods [1] and [2] are special cases of the method proposed by the authors. Hence, the method proposed by the author demonstrates strong generalization and can be applied to a wider range of situations. [1]. V.S. Sheng, F.J. Provost, and P.G. Ipeirotis. Get another label? Improving data quality and data mining using multiple, noise labels. SIGKDD, 2008. [2]. Z. Chen, L. Jiang, and C. Li. Label augmented and weighted majority voting for crowdsourcing. Inf. Sci, 2022. Weaknesses: 1. Compared with real-world dataset, experimental results on a few simulated datasets doesn’t improve (e.g., MV for breast-cancer/breast-w datasets). Furthermore, the number of loss for MV and IWMV is more than that for other methods in Table 1. I suggest adding some discussion about this phenomenon. 2. Main experiments adopt significance level to indicate the performance for each method. How to decide the value of alpha and what is the influence? More detail will be helpful. Technical Quality: 4 Clarity: 3 Questions for Authors: Please refer to weakness. Other questions: 1. In the experimental section, why are methods like significance testing used instead of direct comparison? Confidence: 4 Soundness: 4 Presentation: 3 Contribution: 3 Limitations: yes. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Reviewer fq5P： Q1: Compared with real-world dataset, experimental results on a few simulated datasets doesn’t improve (e.g., MV for breast-cancer/breast-w datasets). Furthermore, the number of loss for MV and IWMV is more than that for other methods in Table 1. I suggest adding some discussion about this phenomenon. Author Response: Thanks for your valuable comments. Our proposed IWBVT is not restricted to specific crowdsourcing scenarios, so we conducted experiments on the whole 34 simulated datasets published by the CEKA platform. However, no algorithm can achieve the best performance on all datasets. Indeed, IWBVT does not improve MV on a few datasets, such as breast-cancer and breast-w. This is because the performance of IWBVT is affected by the performance of the label integration algorithm it aims to improve. According to Eqs. (6) and (9), IWBVT depends on integrated labels inferred by label integration algorithms for its instance weighting and probabilistic loss regressions. Therefore, noise in these integrated labels affects the performance of IWBVT. MV and IWMV, as classical label integration algorithms, generally perform worse than other state-of-the-art algorithms, resulting in integrated labels inferred by MV and IWMV containing more noise. This ultimately leads to more losses for MV and IWMV compared to other state-of-the-art algorithms in Table 1. In the final version of the paper, we will include these discussions to explain this phenomenon. Thanks again for your valuable comments. Q2: Main experiments adopt significance level to indicate the performance for each method. How to decide the value of alpha and what is the influence? More detail will be helpful. Author Response: Thanks for your valuable comments. The significance level is a crucial concept in statistics that directly affects the results of the corrected paired two-tailed t-test used in our experiment. In a t-test, the significance level is typically set to a fixed value, such as 0.05 or 0.1. If the p-value is less than this significance level, we reject the null hypothesis, indicating a significant difference between the two comparison algorithms. Therefore, the significance level affects the stringency of the test: a lower significance level (e.g. 0.05) implies a more stringent test, as the null hypothesis is rejected only when the evidence is very strong. Conversely, a higher significance level (e.g. 0.1) is relatively relaxed and more likely to accept the null hypothesis. In the final version of the paper, we will include a more detailed explanation of the significance level. Thanks again for your valuable comments. Q3: In the experimental section, why are methods like significance testing used instead of direct comparison? Author Response: Thanks for your valuable comments. To exclude the effect of randomness, our simulated experiments were independently repeated ten times. In each experiment, we evaluated the model quality using 10-fold cross-validation. Therefore, each label integration algorithm produced 100 pairs of comparison results (original model quality vs. IWBVT improved model quality) on each dataset. In Table 1, we reported the averages (arithmetic mean) of these results to provide a general indication of relative performance. However, these averages do not indicate whether the comparison results are significantly different. Therefore, to more accurately evaluate the performance of IWBVT, we statistically compared these results by the corrected paired two-tailed t-test. The corrected paired two-tailed t-test determines whether IWBVT effectively improves the corresponding label integration algorithm by assessing whether the differences between the 100 pairs of comparison results satisfy the null hypothesis. Thanks again for your valuable comments. --- Rebuttal Comment 1.1: Title: Response for Rebuttals. Comment: Thank you for the helpful response that addressed my concern.	Summary: The paper studies the problem of improving quality of models trained on datasets collected through crowdsourcing. The authors propose an approach (IWBVT) that post-processes data after crowdsourcing with the goal to mitigate the impact of intractable instances by means of instance weighting. As a result, the bias and variance of trained models becomes closer to the unknown true labels. It is proven that the novel method reduces the generalization error of trained models by the bias-variance trade-off. The paper also contains extensive experimentation that demonstrates: IWBVT significantly improve the model quality of existing label integration algorithms and noise correction algorithms. Strengths: - Novel method - Extensive experimentation over 34 simulated datasets and 2 real ones Weaknesses: - Formalization of results - Clearness of explanation in some points behind the novel approach (see Questions) Technical Quality: 3 Clarity: 2 Questions for Authors: - I do not understand the message behind Figure 1. How should I tract the 4 distributions on the right side of the arrow? - Lines 164 – 165: “it can be verified that Eq. (6) can distinguish all complex distributions we showcased in Section 3.1. By..” It is hard to assess the value of this claim, because it is not clear how broad complex distributions are covered. Is it just 2 among 100? Among 1000 possible? Any quantifiable / qualifiable ways to measure the distinguish power for complex distributions? - Line 166 “Theorem 1. In some special cases,” Please, specify cases in the theorem. Otherwise, I would not agree that this might be a theorem statement. The definition of the cases must be contained outside of the proof. Right now, I can treat the theorem as always true, because “some special cases” might be = \emptyset . - Similar, Line 185 in Theorem 2: “Eq. (8) helps Eq. (7)”… The word “help” does not have formal mathematical definition, while Theorem is a mathematical instrument. Confidence: 4 Soundness: 3 Presentation: 2 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: Reviewer Td4g： Q1: I do not understand the message behind Figure 1. How should I tract the 4 distributions on the right side of the arrow? Author Response: Thanks for your valuable comments. The four distributions on the right side of the arrow in Figure 1 correspond to the four cases of our new instance weighting method. Among them, the distribution in the upper left corner indicates that when the entropy of the complement $Ent(\bar{P}_i)$ is fixed, a lower $P(\hat{y}_i\|L_i)$ (the probability of the integrated label in multiple noisy label distribution) results in a lower weight $w_i$ assigned to the instance. Conversely, the distribution in the upper right corner indicates that a higher $P(\hat{y}_i\|L_i)$ results in a higher $w_i$. The distribution in the lower left corner indicates that when $P(\hat{y}_i\|L_i)$ is fixed, a lower $Ent(\bar{P}_i)$ results in a lower $w_i$. Conversely, the distribution in the lower right corner indicates that the higher $Ent(\bar{P}_i)$ results in a higher $w_i$. These explanations are provided in lines 154-162, and we will refine them further in the final version of the paper. Thanks again for your valuable comments. Q2: Lines 164 – 165: “it can be verified that Eq. (6) can distinguish all complex distributions we showcased in Section 3.1. By..” It is hard to assess the value of this claim, because it is not clear how broad complex distributions are covered. Is it just 2 among 100? Among 1000 possible? Any quantifiable / qualifiable ways to measure the distinguish power for complex distributions? Author Response: Thanks for your valuable comments. To further demonstrate the distinguish power of Eq. (6) for complex distributions, we employed a quantifiable way. Specifically, on all the complex distributions exemplified in Section 3.1, the mentioned instance weighting methods produced the following results: \|Complex distributions\|A\|B\|C\|D\| \|--\|--\|--\|--\|--\| \|{0.5, 0.3, 0.2} and {0.5, 0.4, 0.1} (on line 122)\|(0.50, 0.50) ✖\|(0.67, 0.73) ✖\|(0.20, 0.10) ✔\|(0.70, 0.52) ✔\| \|{0.4, 0.3, 0.3} and {0.4, 0.4, 0.2} (on line 127)\|(0.40, 0.40) ✖\|(0.64, 0.66) ✖\|(0.10, 0.00) ✔\|(0.58, 0.53) ✔\| \|{0.5, 0.3, 0.1, 0.1} and {0.4, 0.2, 0.2, 0.2} (on line 131)\|(0.50, 0.40) ✔\|(0.59, 0.52) ✔\|(0.20, 0.20) ✖\|(0.62, 0.58) ✔\| Here, A, B, C, and D denote $P(\hat{y}_i\|L_i)$, $\frac{1}{Ent(P_i)}$, $max(P_i)-sec(P_i)$ and our new instance weighting method, respectively. "✔" and "✖" indicate whether the weighting method is effective in distinguishing the corresponding complex distribution, respectively. Empirically, the weight corresponding to the front distribution in these examples should be greater than the latter. The results show that our new instance weighting method can distinguish all types of complex distributions that existing methods cannot. In the final version of the paper, we will include these comparisons and analyses to demonstrate the distinguish power of our new method. Thanks again for your valuable comments. Q3: Line 166 “Theorem 1. In some special cases,” Please, specify cases in the theorem. Otherwise, I would not agree that this might be a theorem statement. The definition of the cases must be contained outside of the proof. Right now, I can treat the theorem as always true, because “some special cases” might be = \emptyset . Author Response: Thanks for your valuable comments. Indeed, the special cases mentioned in Theorem 1 should be specified. In the final version of the paper, we will move the definition of these special cases from the proof of Theorem 1 to Theorem 1 itself. Specifically, the refined Theorem 1 will be "When $Ent(\bar{P}_i)$ remains constant, Eq. (6) covers $w_i \propto P(\hat{y}_i\|L_i)$. When $Q>2$ and $P(\hat{y}_i\|L_i)$ is the maximum value in $P_i$, Eq. (6) covers $w_i \propto \max(P_i) - \sec(P_i)$.". Thanks again for your valuable comments. Q4: Similar, Line 185 in Theorem 2: “Eq. (8) helps Eq. (7)”… The word “help” does not have formal mathematical definition, while Theorem is a mathematical instrument. Author Response: Thanks for your valuable comments. Indeed, we should use a more formal mathematical definition in our Theorem 2. In the final version of the paper, Theorem 2 will be refined as follows: "When the probabilistic loss is defined as in Eq. (9), performing probabilistic loss regressions constructed by Eq. (8) ensures that Eq. (7) asymptotically achieves the bias-variance trade-off.". Thanks again for your valuable comments. --- Rebuttal 2: Comment: As the discussion period deadline nears, we would be deeply appreciative if you could kindly review our rebuttal and let us know if we have addressed your concerns. We’re more than happy to continue the conversation if you have any further questions. Thank you very much for your time and consideration.	null	null	null	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Transformers Can Do Arithmetic with the Right Embeddings	Accept (poster)	Summary: This paper introduces a simple yet effective encoding scheme that can be used to address the limitations of transformers at representing positional information, which is crucial in many algorithmic tasks such as those involving arithmetic operations. The authors propose an ad-hoc positional embedding, called “abacus embedding”, which encodes the location of each digit relative to the start of the current number and thus provides an explicit signal that the transformer can use to align digits. The effectiveness of the method is tested on addition, multiplication and sorting problems, with a particular focus on out-of-distribution test cases. Strengths: I think that this work is interesting and relevant. Although addition, multiplication and sorting problems might be considered trivial test cases because they can easily be solved with symbolic algorithms, they constitute an important benchmark to evaluate the algorithmic reasoning skills of neural networks, as also attested by the increasing interest of the deep learning community on mathematical tasks. The paper is well-written, and the method is clearly presented. The generalization achieved in the addition task is quite impressive, showing that the abacus embeddings enable a generalization factor of 6x in the OOD regimen. Although simple and straightforward, the proposed method seems original. Weaknesses: The abacus embeddings are defined according to the hyperparameter k, which is fixed a priori (e.g., k = 100). This limits the flexibility and generalizability of the proposed encoding scheme. The authors deploy different architectures / hyperparameters to learn different problems (addition vs. multiplication vs. sorting). Since they argue that their architecture modification “improves performance on multiple algorithmic reasoning tasks simultaneously” it would be important to show that different tasks can really be learned simultaneously, without the need to build ad-hoc models for each algorithmic task that needs to be solved. It is true that arithmetic operators are binary and thus “both addition and multiplication accept only two operands”. However, we can have a sequence of additions / multiplications, and it is well-known that also increasing the number of terms in arithmetic expressions causes troubles to transformers. Because of these key issues, I think that the impact and significance of this work are not strong enough for a top-tier venue like NeurIPS. Technical Quality: 2 Clarity: 3 Questions for Authors: - How could we address the fact that the hyperparameter k needs to be fixed a priori? - Can we implement a unified model that can learn all these tasks simultaneously? - The proposed method achieves impressive OOD accuracy for addition, but only works “in distribution” for multiplication. It would be important to investigate this phenomenon more in depth. - At least for addition, it would be useful to test OOD generalization by also adding more operands besides increasing the length of each operand. - How does the present method compare to other recent proposals such as xVal (https://arxiv.org/abs/2310.02989)? - I agree that addition, multiplication and sorting are good benchmarks because they are simple yet challenging; however the authors could better stress that these tasks are part of a broader class of elementary numerical skills that transformers struggle to learn (for a comprehensive review, see https://www.mdpi.com/2076-3417/14/2/744). Confidence: 4 Soundness: 2 Presentation: 3 Contribution: 2 Limitations: The authors properly addressed the limitations of their study. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your valuable time, your comments have greatly improved our draft. We answer your questions below in order: 1. While choosing k a priori could be a barrier to adoption of Abacus Embeddings in the community, we have shown that we can scale to at least one hundred more digits at test time than seen at training time for addition in our original submission. We believe that use cases with distribution shifts larger than this are more limited. Furthermore, in our general rebuttal response and in Rebuttal Figues 2 and 3, we show we can increase the distribution shift using a larger k and larger training data if a distribution shift of more than 100 digits is required. For any language model a fixed context length is also decided a priori, in the extreme case one could choose an extremely large value of k, for example context_length/3, so that all two argument additions can be completed by model. 2. To see whether multi-skill training is possible, we trained a model on both addition and subtraction simultaneously without any hyperparameter changes from the addition models presented in the original draft. We show the results of this experiment in Rebuttal Figure 4, in the rebuttal pdf. Here we show that, even without hyperparameter tuning due to rebuttal time constraints, the models are able to extrapolate for both the symmetric addition operation and anti-symmetric subtraction operation simultaneously using a single model. We stress that we are training tiny transformers models in this paper, up to a maximum of 122M distinct parameters. We hypothesize that scaling either of these axes would allow for more simultaneous learning, however this is not the regime we analyze within this report. 3. We emphasize that we also achieve state-of-the-art performance on multiplication with Abacus Embeddings, when compared to prior work [1]. We agree that further improving performance for multiplication out of distribution is important future work and have updated the future directions section of our draft to emphasize this. 4. While this is a form of algorithmic generalization, we chose not to study generalization in the number of operands for addition or multiplication in this study, in a compute restricted regime. We instead highlight the generalization of operands in the sorting section. For sorting we have two dimensions of generalization. Firstly, “OOD in number length,” this is similar to addition and multiplication where we increase the number of digits in the numbers in the array being sorted. Secondly, “OOD in array length,” here we increase the length of the array so there are more numbers that need to be sorted. We analyze both of these dimensions in the reported “ALL OOD” accuracies where we scale each of these dimensions concurrently. Specifically, the “All OOD'' accuracies shown in Table 1 highlight that when both the number of operands and number of digits is varied during testing, the models trained with Abacus and FIRE Embeddings achieve the highest accuracy for the sorting task. 5. xVal, which embeds all real numbers by scaling a single fixed token-embedding, is a very important contribution to the language modeling community. We reference xVal in the Related Works section of our paper as it improves mathematical accuracy when the operands are small real numbers, up to 10e+8. However, it does not resolve the algorithmic generalization problems which we are working to solve in this paper, involving numbers much larger than 10e+8 (for example in Rebuttal Figure 3 we analyze up to 10e+214). The authors of the xVal paper highlight this in Section 4 - Future Directions, “Very large numbers saturate the normalization, as discussed in Sec. 2, and very small numbers are negligible from the model’s perspective.” This is because the authors “normalize numbers in the text corpus such that they fall within the range [−5, 5] as a preprocessing step before training.” Hence, we believe xVal would not be a compelling baseline for our study. We choose FIRE and RoPE as our main comparisons based on prior work and directly compare to the previous state-of-the-art (Randomised-FIRE with index hints) in Appendix Section: Addition Ablations - Index Hints. 6. We agree with and will act on this feedback for a future version of the paper, including the paper cited above, we have updated this in our draft. We believe the weaknesses are addressed in the reviewer questions. Should you have any further questions or require additional clarification, please do not hesitate to ask. [1] Shen, Ruoqi, et al. "Positional description matters for transformers arithmetic." arXiv preprint arXiv:2311.14737 (2023). --- Rebuttal Comment 1.1: Comment: I thank the Authors for having considered my comments. Having read their responses and the comments posted by the other Reviewers, I am persuaded to raise my score from 4 to 6.	Summary: This paper studies a well-known problem, the length generalization issue of transformers in terms of doing arithmetic. This paper solves this problem via two natural strategies: (i) separate two operands via a newly proposed embeddings (Abacus Embeddings), and (ii) using looped Transformer architecture. Strengths: - The problem is well-motivated. - The conjectures are very natural, and confirmed via extensive experiments. - Experiments are well-designed and complete. - The proposed solutions enjoy great performance. - Considers diverse downstream tasks, including addition, multiplication, and sorting. Weaknesses: [Medium] The reason why looped transformer or recurrency helped with length generalization is still unclear, and in-depth analysis is needed. For instance, does the number of recurrence related to the length of the digits? Technical Quality: 3 Clarity: 4 Questions for Authors: Why does recurrency in terms of the model architecture help with length generalization? Confidence: 3 Soundness: 3 Presentation: 4 Contribution: 3 Limitations: See weakness. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your valuable time, your comments have greatly improved our draft. We answer your question below: We do not find that the number of recurrences is meaningfully linked to the length of the numbers in this study and we do a small visual analysis of the intermediate properties during recurrence in Appendix Figure 13. While we do find that a small amount of recurrence can lead to performance improvements throughout our work, we also show that we can achieve highly accurate out of distribution performance with standard decoder architectures using Abacus Embeddings. We hypothesize looped transformers may improve performance because they force the model to learn an algorithm that relies on an iterative process. This aligns their strategy with that of a human-designed algorithm, e.g. traditional addition algorithms repeat the same process iteratively for each pair of digits. The good inductive bias of recurrent models is more widely referred to as the theory of algorithmic alignment [1] and has motivated many algorithmic reasoning results, for example [2]. We believe the weaknesses are addressed in the reviewer questions. Should you have any further questions or require additional clarification, please do not hesitate to ask. [1] Xu, Keyulu, et al. "What can neural networks reason about?" International Conference on Learning Representations (2020). https://openreview.net/forum?id=rJxbJeHFPS [2] Ibarz, Borja, et al. "A generalist neural algorithmic learner." Learning on graphs conference. PMLR, 2022. https://arxiv.org/pdf/2209.11142	Summary: The paper studies the arithmetic capabilities of transformers and the problem of length generalization, specifically the ability to solve problems larger than the ones seen during training. It introduces Abacus Embeddings, a novel positional embedding that encodes the position of each digit relative to the start of the number. For multi-digit addition, Abacus Embeddings result in state-of-the-art generalization to sequences six times longer than the training sequences. Additionally, the paper explores the benefits of incorporating recurrent blocks, leading to further improvements. Finally, the paper demonstrates the effectiveness of Abacus beyond addition, showing success with in-distribution multiplication and array sorting tasks. Strengths: - Originality: While previous studies have noted that positional encoding can negatively impact the arithmetic generalization capabilities of transformer architectures, to the best of my knowledge, the introduced embeddings, the analyses, and the results presented in this paper are original. - Quality and clarity: The work is technically sound. The experiments are well-designed and convincing, and the code for their implementation is provided in the supplementary material. The paper is clearly written. - Significance: The goal of improving the extrapolation and reasoning abilities of transformers is both timely and significant. The results are very good, achieving state-of-the-art performance for length extrapolation in multi-digit addition. Weaknesses: 1. The paper does not discuss the choice of the value used for the maximal offset randomization parameter $k$, which determines the distribution of the starting position of the first digit of the numbers during training. How was the value $k = 100$ chosen? Additionally, could higher values further improve extrapolation performance? 2. The sentence “our methods perform so well that we look beyond addition” (line 239) does not sound appropriate for a scientific paper. Please consider rephrasing it, for instance, “Given the strong performance of our method in the multi-digit addition task, we extend etc.”. Technical Quality: 3 Clarity: 3 Questions for Authors: 3. Differently from addition, when considering multiplication, Abacus Embeddings achieve high in-distribution accuracy but struggle out-of-distribution (OOD), even when one operand is of unitary/short length. Do you have any insights about what might cause this significant difference? Do you have any ideas or potential modifications to the method that could improve OOD generalization in this context? 4. Could you elaborate more on how your embeddings could be integrated into settings that involve mixing arithmetic with natural language data? Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The paper adequately discusses its limitations. I do not foresee any potential negative societal impacts arising from this study. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your valuable time, your comments have greatly improved our draft. We respond to your weaknesses and answer your questions below in order: 1. We find ~100 to be roughly optimal when the training data has a maximum of 20 digits; this already allows for addition of numbers larger than a googol. We describe and discuss the experimental evidence we gathered during the rebuttal period for varying the value of the maximal offset randomization hyperparameter (k) in the general rebuttal response and pdf. From this we conclude that the value of k can be varied with larger numbers in the training data allowing for larger values of k to be used. 2. We agree with the reviewer and have updated our draft. 3. While our results for multiplication are currently state-of-the-art compared to prior work [1], the reviewer is correct that we do not observe out-of-domain generalization. We do not know how to solve this problem at this time, but we do have several hypotheses on why do not see larger gains: * Our multiplication models are small compared to the multi-billion parameter models we have become accustomed to in the open source community. With more compute or larger models, it may be possible to improve upon our results. This direction is motivated by the observation that multiplication models, even with their increased compute budget compared to addition, do not achieve as low of a training loss as addition models. Furthermore, for addition models the loss plateaus at low values at the end of training, allowing for a period of training on low loss values. This does not occur for multiplication models, leading us to speculate that there is something to be gained from larger-scale training. * Multiplication requires more abacus embeddings during training and testing, due to the increased output length. We have updated our draft to include these as future directions of research. 4. Provided a model tokenizes numbers by their individual digits, which is done in most new open source models (e.g. llama and gemma), a plug in and play version of Abacus Embeddings (which is our sorting implementation in the supplementary material) can be used alongside other positional embeddings for language tasks. This code simply identifies all digit tokens in the input sequence and calculates the Abacus Embeddings in parallel for a batch, these can then be added to the input embeddings. Abacus Embeddings also rely on a least significant digit first format which can be done during encoding and decoding in the tokenizer with a simple regex to reverse all numbers. Should you have any further questions or require additional clarification, please do not hesitate to ask. [1] Shen, Ruoqi, et al. "Positional description matters for transformers arithmetic." arXiv preprint arXiv:2311.14737 (2023). --- Rebuttal Comment 1.1: Comment: Thank you for your response. I will keep my initial positive evaluation. Best wishes.	null	null	Rebuttal 1: Rebuttal: Our revised manuscript will include the following new experiments and discussion, which better clarify the broad utility and flexibility of Abacus Embeddings. We thank the reviewers for their questions and suggestions that led to these new positive results! Varying the value of the maximal offset randomization hyperparameter (k) In Rebuttal Figure 1, in the rebuttal pdf, we show models trained with k=25, 50, 75 and 100 trained on size 20 data; with the k=100 models being taken directly from Figure 4 of the current paper. We show the average of 3 models in each case analyzing accuracy only where both operands are the same length, similarly to Figure 9 of the current submission, to save on computation time during the rebuttal period. We see in the plot that these smaller values of k allow for good extrapolation and the amount of extrapolation depends on the value of k as expected. We find that increasing k to values more than 100 for models trained on data with a maximum of 20 digits, leads to diminishing returns within our experimental setup. However, this can be resolved by including larger numbers in the training data. In Rebuttal Figures 2 and 3, in the rebuttal pdf, we show models trained on size 30 and size 40 addition data respectively. We show that larger values of k allow for much larger distribution shifts, with a maximum distribution shift of up to 175 digits being shown, this is a 6.8x length generalization from training to testing. Hence, we can easily increase k to larger values and perform arithmetic with far more digits than we did in our original state-of-the-art submission, with suitable training data. Learning addition and subtraction simultaneously In Rebuttal Figure 4, we train a model with exactly the same hyperparameters used to train the addition models in the submitted paper but this time also include subtraction examples in the data. We see that these small language models can simultaneously learn to extrapolate for both the symmetric operation of addition and the anti-symmetric operation of subtraction using Abacus Embeddings. Pdf: /pdf/5693086527af66264abdf125c230d0962fb51efa.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Rethinking Parity Check Enhanced Symmetry-Preserving Ansatz	Accept (poster)	Summary: This paper designs a novel quantum algorithm that eliminates the need for penalty terms when solving constrained problems. Instead, it constructs a subspace where the states satisfy the constraints, allowing the final solution to be constructed within this subspace. Additionally, the authors use parity check to replace system validation, ensuring that qubits remain unflipped at every step, not just in the final state, thereby enhancing error correction capabilities. The authors demonstrate how this algorithm works on a class of NP-complete combinatorial optimization problems and achieve better results than previous quantum algorithms. Strengths: Originality: The authors propose a quantum machine learning algorithm capable of solving constrained optimization problems without relying on penalty terms. Clarity: The paper clearly defines quantum computing concepts, provides detailed derivations of the main equations involved, and offers a very clear explanation of the quantum system's architecture. The discussion of experimental results is also very thorough. Significance: The quantum algorithm presented in this paper naturally incorporates constraint conditions into the optimization process. Compared to soft constraints, this approach yields more accurate results. This has significant implications for integrating machine learning into quantum computing, offering valuable insights. Quality: The language of the paper is rigorous and clear, with appropriate citations of previous work. The overall approach is straightforward and easy to understand. The paper provides a multi-faceted analysis of the experimental results, validating the algorithm's correctness on simulators and conducting experiments on real quantum computers, further demonstrating feasibility. The theoretical section is also excellent, with detailed derivations of the main equations. The paper excels in both theory and experiment. Weaknesses: The discussion of the scalability of the proposed algorithm is not sufficient. Technical Quality: 4 Clarity: 4 Questions for Authors: See the comments. Confidence: 5 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: Thank you for your thorough review and valuable feedback. We greatly appreciate the time and effort you have invested in evaluating our manuscript. Your insights and suggestions have been instrumental in improving the quality of our work. We are aware that the scalability of the quantum algorithm has attracted considerable interest, and we will provide more detailed derivation and discussion as an extension to Equation 17 in the revision. --- Rebuttal Comment 1.1: Comment: Thanks.	Summary: Paper introduces a Hamming Weight Preserving ansatz with parity check. The proposed method is tested on quantum chemistry problems and constrained combinatorial optimization problems (eg. quadratic assignment problem). The HWP ansatz can satisfy the hard constraints in QAP. Experiments show that proposed methods outperforms some existing methods for the simulation and superconducting quantum processor. Strengths: Paper addresses a significant problem of simulation on quantum circuits and applications to quantum chemistry and combinatorial problems. Originality: Paper proposes a novel ansatz using HWP and parity checks, although I am not too familiar with previous work. The quality and clarity of presentation is good, and experiment results are clear. Weaknesses: A potential weakness may be less background information included in main text of paper, especially for the target audience (ML/neurips). Technical Quality: 3 Clarity: 2 Questions for Authors: Would quantum chemistry ground-state experiment be possible to perform on superconducting processor, and how would methods perform relatively with the quantum noise? NBS-NN and NBS-FC (if nearest neighbor vs fully connected qubits), these are also commonly abbreviations for Neural network and fully connected (layers). Could authors further describe difference between NBS-NN and NBS-FC? and their difference with NBS-hard? Confidence: 1 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: A stated limitation is different results on superconducting processor vs. simulator, based on noise of superconducting processor. Additional stated limitations are related to state of quantum computing such as small problem size and quantum noise. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We greatly appreciate the time and effort you have invested in evaluating our paper, and we hope we can clarify your concerns. > W1: A potential weakness may be less background information included in main text of paper, especially for the target audience (ML/neurips). Ans: Thanks for your kind advice. We do realize this paper may not be familiar to the general NeurIPS community. We promise to provide a detailed background intro in the revision appendix. > Q1: Would quantum chemistry ground-state experiment be possible to perform on superconducting processor, and how would methods perform relatively with the quantum noise? Ans: Ground state preparation is considered one of the most promising problems to demonstrate experimental advantages on recent superconducting processors [1], as evidenced by various preliminary attempts [2, 3, 4]. However, inevitable noise severely affects the performance of current ansätze, prompting the search for new ansätze that are better suited for error mitigation and error correction methods. > Q2: NBS-NN and NBS-FC (if nearest neighbor vs fully connected qubits), these are also commonly abbreviations for Neural network and fully connected (layers). Could authors further describe difference between NBS-NN and NBS-FC? and their difference with NBS-hard? Ans: We apologize for any confusion caused by the abbreviations. The terms NBS-NN and NBS-FC refer to nearest-neighbor and fully connected physical qubit connectivity, respectively. On a superconducting quantum processor, physical qubits rely on couplers to achieve entanglement, meaning two-qubit gates can only be applied to qubits directly connected by a coupler. Given the impracticality of connecting each pair of qubits with a coupler, it is not feasible to apply two-qubit gates freely to any pair. Therefore, fully connected (FC) connectivity represents an idealized scenario, whereas studying nearest-neighbor (NN) connectivity is crucial in the Noisy Intermediate-Scale Quantum (NISQ) era, given the current hardware limitations. In Table 3, NBS-hard denotes the use of parity checks as additional constraints. The simple HWP ansatz can only maintain symmetry along either rows or columns, necessitating extra methods to impose constraints in the other direction. Consequently, NBS-NN and NBS-FC in the soft section of Table 3 represent NBS with corresponding connectivity, where penalties in the Hamiltonian act as constraints. NBS-hard refers to NBS-NN with parity checks as a hard constraint for the other direction. [1] The Variational Quantum Eigensolver: A review of methods and best practices. Physics Reports [2] Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature [3] Observing ground-state properties of the Fermi-Hubbard model using a scalable algorithm on a quantum computer. Nature Communications [4] Experimental quantum computational chemistry with optimized unitary coupled cluster ansatz. Nature Physics	Summary: The paper investigates combining the HW-preserving ansatz with qubit topology-aware parity checks to impose hard constraints on quantum circuits for the quantum chemistry and Quadratic Assignment Problem. It includes numerical simulations and experiments on a real quantum device. Strengths: sufficient numerical and real device experiments. Weaknesses: comparing to previous work "Rethinking the symmetry-preserving circuits for constrained variational quantum algorithms", it is difficult to gauge its novelty and impact as the main contribution is incremental with respect to previous results no matter in theoretical or numerical aspects. Technical Quality: 2 Clarity: 3 Questions for Authors: 1. as definition of NBS is kind of constant gate, how to train the HWP anstaz constructed by such fixed gates shown in Fig 1. ? and what is the R in Figure 1 ? 2. comparing to the proposed HWP, the UCCS not only requires shallow circuit but also have out-performance. What is the advantages of the proposed over it? 3. it may be poor scalable of such ansatz used for combinatorial optimization problem, especially in NISQ era. and in line 252, the probability of finding the feasible state will exponentially small with the problem size $m$, how to extract such feasible state without performing exponentially measurement? Confidence: 3 Soundness: 2 Presentation: 3 Contribution: 2 Limitations: no potential negative societal impact of their work. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your thorough review and valuable feedback, including the comparison of previous work [1]. We would like to highlight the differences between these two papers and promise to add a remark in the related work section to distinguish them. In [1], the authors proposed methods to analyze the expressivity and trainability of the HWP ansatz. They also proposed BS gate to conduct experiments with the Hamiltonian as: $$ H_{BS}=\left(\begin{array}{cccc} 0 & 0 & 0 & 0\\\\ 0 & \frac{1}{2} & \frac{1+\text{i}}{2\sqrt{2}} & 0\\\\ 0 & \frac{1-\text{i}}{2\sqrt{2}} & \frac{1}{2}& 0\\\\ 0 & 0 & 0 & 0 \end{array}\right),\quad H_{NBS}=\left(\begin{array}{cccc} 0 & 0 & 0 & 0\\\\ 0 & \frac{1}{2} & \frac{\text{i}}{2} & 0\\\\ 0 & \frac{-\text{i}}{2} & \frac{1}{2}& 0\\\\ 0 & 0 & 0 & 0 \end{array}\right). $$ In this paper, we integrate parity checks and the HWP ansatz to enforce additional constraints and mitigate hardware errors. We focus on the practical usage of parity checks in near-term quantum computing, which involves utilizing some good qualities of the HWP ansatz. We have the following distinguishing contributions: 1. We proposed a simpler gate, namely the NBS gate, with compatible expressivity as the BS gate. 2. We developed a viable method to incorporate parity checks for error mitigation in the HWP ansatz, conducting experiments on both superconducting quantum processors and simulators. 3. We proposed a novel approach to use parity checks as projective measurements, thereby restricting the evolving subspace of quantum states. We demonstrated the effectiveness of our method on an NP-hard combinatorial optimization problem. This paradigm holds significant potential for constrained VQE, offering a straightforward means to incorporate hard constraints using simple parity checks. Therefore, we disagree that "the main contribution is incremental to previous results". According to your review, we think that our work is something more than "For instance, a paper with technical flaws, weak evaluation, inadequate reproducibility and incompletely addressed ethical considerations." We also strongly believe that good incremental work (if you insist) is also within the scope of NeurIPS. [1] Rethinking the symmetry-preserving circuits for constrained variational quantum algorithms We will then respond to your questions: > Q1: as definition of NBS is kind of constant gate, how to train the HWP anstaz constructed by such fixed gates shown in Fig 1. ? and what is the R in Figure 1 ? Ans: Thanks for your kind reminder, and we apologize for the misunderstanding caused by our negligence. The matrix provided in the paper is the Hermitian matrix of the NBS gate. The unitary operator of the NBS gate should take exponential of the Hermitian matrix: $$U_{NBS}=e^{\text{i}\theta H_{NBS}}=\left(\begin{array}{cccc} 1 & 0 & 0 & 0\\\\ 0 & \frac{\cos\theta+\text{i}\sin\theta+1}{2} & \text{i}\frac{\cos\theta+\text{i}\sin\theta-1}{2} & 0\\\\ 0 & -\text{i}\frac{\cos\theta+\text{i}\sin\theta-1}{2} & \frac{\cos\theta+\text{i}\sin\theta+1}{2} & 0\\\\ 0 & 0 & 0 & 1 \end{array}\right)=\left(\begin{array}{cccc} 1 & 0 & 0 & 0\\\\ 0 & \frac{e^{\text{i}\theta}+1}{2} & \text{i}\frac{e^{\text{i}\theta}-1}{2} & 0\\\\ 0 & -\text{i}\frac{e^{\text{i}\theta}-1}{2} & \frac{e^{\text{i}\theta}+1}{2} & 0\\\\ 0 & 0 & 0 & 1 \end{array}\right),$$ which contains trainable parameters. The rotations at the end of the ansatz in Fig.1 are for measuring different decomposed Pauli strings of the problem Hamiltonian. They can be omitted from the ansatz for simplicity. > Q2: comparing to the proposed HWP, the UCCS not only requires shallow circuit but also have out-performance. What is the advantages of the proposed over it? Ans: The UCCS ansatz is indeed very shallow, which leads to the "out-performance" on NISQ devices. However, it exhibits relatively weak performance compared to other methods, failing to achieve results within chemical accuracy ($1.6\times 10^{-3}$Ha) for any of the molecules tested. It is essential to consider performance not only during the NISQ era but also beyond. Additionally, other methods can also achieve superior results if similar numbers of layers or parameters are utilized. > Q3: it may be poor scalable of such ansatz used for combinatorial optimization problem, especially in NISQ era. and in line 252, the probability of finding the feasible state will exponentially small with the problem size, how to extract such feasible state without performing exponentially measurement? Ans: This one is actually a very good question and we do acknowledge that this might be a potential limitation of the proposed method (as stated in the paper). However, we would like to point out that for an $n$-qubit system, the number of shots we need to obtain the final distribution is $\mathcal{O}(2^n)$, which is why the order of the expectation value remains acceptable. Despite this, the proposed method potentially stands as the best constrained-VQE currently available. --- Rebuttal Comment 1.1: Comment: Thank you for the response, most of my question are solved. I would happy to raise my score. --- Reply to Comment 1.1.1: Comment: We are sincerely grateful for your careful reading and thoughtful comments on our manuscript, which have been invaluable in enhancing the clarity and rigor of our work. Thank you again for your time and effort in reviewing our paper. Best regards --- Rebuttal 2: Comment: Dear reviewer K5Kf, We really appreciate your valuable comments. In our rebuttal, we have highlighted the contributions and answered the questions accordingly. Since the discussion period is approaching its end, we are looking forward to your feedback. Best regards, Authors	null	null	null	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Samba: Severity-aware Recurrent Modeling for Cross-domain Medical Image Grading	Accept (poster)	Summary: Accurate disease grading in medical image analysis is challenging due to the variability within disease levels and the similarity between adjacent stages. Additionally, models must handle data from unseen target domains, where differences in feature distribution can significantly reduce performance. To address these issues, this paper proposes the Severity-aware Recurrent Modeling (Samba) method, which encodes image patches sequentially to capture severity information and employs an Expectation-Maximization based recalibration mechanism to handle cross-domain variations. The method also uses a Gaussian Mixture Model to model feature distributions and reconstructs intermediate features using learnable severity bases. Strengths: - Addresses a significant problem in medical image analysis where different grading can appear differently in the data. - Different diseases and imaging modalities have been evaluated. - Use of publicly available datasets. - Code will be made publicly available upon acceptance. Weaknesses: - Some parts need more detailed explanation. Although space is limited, certain sections assume a high level of pre-knowledge. For example, more explanation on Samba would be useful. - For me it is not really clear how the patches are used in a recurrent manner and what their sequence should be. Can you please elaborate more on the recurrent part. - There is no study demonstrating that the model specifically attends to patches related to severity. Is there a way to illustrate this? Technical Quality: 3 Clarity: 3 Questions for Authors: - Adding specific numbers and metrics to the abstract would be beneficial. Currently, lines 18-19 are quite vague. - On page 7, the authors likely intend to refer to Figure 3 for the results, rather than Figure 6. - In Figure 5, the T-SNE plot is difficult to interpret due to small icons. Could the datasets be represented by icons and the severity by color for better qualitative evaluation? Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The authors addressed the limitations of the work. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Q1: Some parts need more detailed explanation. Although space is limited, certain sections assume a high level of pre-knowledge. For example, more explanation on Samba would be useful. R: Thanks for your valuable feedback. We will provide more explanations of the proposed Samba, such as: 1) After proceeded by BSSM, the feature embedding of each patch embedding $\boldsymbol{f}_n$ is firstly projected into the latent space by a linear layer to get the target state embedding $\boldsymbol{x}_n$. The severity base $\boldsymbol{\mu}_n$ is modeled as a mixture of Gaussian from $\boldsymbol{x}_n$. Then, the E-M algorithm iteratively approximates $\boldsymbol{\mu}_n$ to $\boldsymbol{x}_n$. After convergence, the embedding is fed into the rest module. 2) Each Gaussian is initialized by the Kaiming initialization. 3) The E-M empirically implements 3 iterations, according to the observation in Fig.3. 4) The number of Gaussian kernels $K$ in L171 will be defined when first introducing. 5) The specialization of Samba for cross-domain tasks, especially, the feature distribution shift between the source domain and unseen target domains affects not only the intermediate features but also the selective scan mechanism of Mamba, which poses a clear performance drop of Mamba on unseen target domains. To address issue, the proposed method not only introduces both forward and backward directions to primarily preserve information about the most severe lesions, but also introduces a EM-based State Recalibration mechanism to compact the feature space so that the feature distribution is less sensitive to the domain shift. Q2: It is not really clear how the patches are used in a recurrent manner and what their sequence should be. Can you please elaborate more on the recurrent part? R: Thanks for your valuable feedback. After sliding the image $\mathbf{I} \in \mathbb{R}^{H \times W \times 3}$ into a variety of patches, the input is formed as a sequences of 2-D patches, each of which has a spatial position of $H/4 \times W/4$. Then, in each Samba block, the Bi-directional State Space Modeling module has both feedforward and backforward SSM, where the selective scan mechanism allows to handle the patches in a recurrent manner. Specifically, the 2-D selective scan mechanism in both components is directly inherited from [15]. The input patches are traversed along two different scanning paths (horizontal and vertical), and each sequence is independently processed by the SSM. Subsequently, the results are merged to construct a 2D feature map as the final output. We will enrich these details accordingly. Q3: There is no study demonstrating that the model specifically attends to patches related to severity. Is there a way to illustrate this? R: Thanks for your valuable suggestion. We model the relation between patch embedding from SSM and severity level by drawing inspiration from the class activation map (CAM) mechanism [a]. We take the patch embeddings from the last Samba block as input, so as to generate the per-level severity activation patterns. Then, the activated severity patterns are displayed on the original images. We use FGADR as the unseen target domain. The results are shown in Fig.~R1, where the activated patches are highlighted in blue boxes. From the first to the fifth row, the samples from level-1 to level-5 are provided accordingly. From the first to the fifth column, the patch activation map from level-1 to level-5 is generated by the aforementioned methods. Notice that, as level-1 refers to the normal scenario, each sample has activations on level-1, meaning some patches are normal. [a] Zhou, Bolei, et al. "Learning deep features for discriminative localization." Proceedings of the IEEE conference on computer vision and pattern recognition. 2016. Q4: Adding specific numbers and metrics to the abstract would be beneficial. Currently, lines 18-19 are quite vague. R: Thanks for your valuable suggestion. We will accordingly add the following in the introduction: Extensive experiments show that the proposed Samba outperforms the VMamba baseline by an average accuracy of 23.5\%, 5.6\% and 4.1\% on the cross-domain grading of fatigue fracture, breast cancer and diabetic retinopathy, respectively. Q5: On page 7, the authors likely intend to refer to Figure 3 for the results, rather than Figure 6. R: Sorry for the typo. We will correct it from Fig.6 to Fig.3. Q6: In Fig.5, the T-SNE plot is difficult to interpret due to small icons. Could the datasets be represented by icons and the severity by color for better qualitative evaluation? R: Thanks for your valuable suggestion, and we have modified it accordingly. Please refer to Fig.~R3 in the attached PDF file for reference. Finally, should you have further suggestions and comments, we are glad to incorporate during the discussion stage. --- Rebuttal Comment 1.1: Comment: I can certainly appreciate the significant effort put into the rebuttal and I remain as a weak accept. --- Reply to Comment 1.1.1: Title: Response to Reviewer hFq3 Comment: Thanks for your swift response. We are glad to see your questions resolved. We will improve our paper carefully according to your valuable suggestions.	Summary: The authors introduce a new method named Severity-aware Recurrent Modeling (Samba) for disease grading in medical imaging. Specifically, they propose encoding image patches in a recurrent manner to accurately capture decisive lesions and transmit critical information from local to global contexts. Additionally, an Expectation-Maximization (EM) based state recalibration mechanism is designed to map feature embeddings into a compact space, thereby reducing the impacts of cross-domain variations. Strengths: 1. The proposed severity-aware recurrent modeling uses a state space model to store and transmit severity information from local to global, which is valuable for the classification of medical images with small lesion areas. 2. For domain adaptation tasks, an EM-based state recalibration mechanism was also proposed and its effectiveness was validated in experiments. 3. The interpretability visualization of the experimental results is excellent. Weaknesses: 1. The significance of using the Mamba architecture in cross-domain tasks is uncertain; in fact, restricting the Mamba module may lead to excessive specialization. 2. The ablation experiments regarding the specific structure of Samba are not sufficiently comprehensive. 3. The open-source code is not explicitly provided. Technical Quality: 3 Clarity: 3 Questions for Authors: 1. Among the compared methods mentioned in Table 4, some ViT-based and ResNet-50-based methods are not specifically designed for domain adaptation tasks. Is this comparison fair? 2. The article states: "The Mamba model is a suitable structure that aligns with our needs. Guided by global severity awareness, the update of hidden states can selectively ignore information about low-level lesions, primarily preserving information about the most severe lesions." Can you explain how SSM selects severe lesion information? A theoretical justification should be provided, as this is a point of concern. 3. In the comparative experiments with other SOTA methods, are all the source domains supplemented with the two additional large-scale datasets DDR [24] and EyePACS [13]? Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: The authors have addressed the limitations of the current work. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Q1: Significance of using Mamba in cross-domain tasks; restricting Mamba module may lead to excessive specialization. R: Thanks for your valuable comments, so that we could have a chance to clarify the generalization and universality of the proposed Samba. Specially, (1) The feature distribution shift between the source domain and unseen target domains affects not only the intermediate features but also the selective scan mechanism of Mamba, which poses a clear performance drop of Mamba on unseen target domains. To address issue, the proposed method not only introduces both forward and backward directions to primarily preserve information about the most severe lesions, but also introduces a EM-based State Recalibration mechanism to compact the feature space so that the feature distribution is less sensitive to the domain shift. (2) From the experimental side, the proposed Samba shows a significant unseen domain performance improvement than the VMamba baseline on three different modalities, varying from fundus images, X-ray images, and pathological images, respectively. Moreover, as discussed in the paper, the recurrent encoding of image patches also contributes to cross-domain disease grading. In Tab.4, even the VMamba baseline outperforms CNN- and ViT-based methods. We will enrich these discussions accordingly. Q2: Ablation studies regarding the specific structure of Samba. R: We provide an ablation study on the specific structure of Samba. Specifically, two components, namely, Bi-directional State Space Modeling (BSSM) and EM-based State Recalibration (ESR), are incorporated into the VMamba baseline. The experiments are conducted on the DG Fatigue Fracture Grading Benchmark, and the results are reported in Table R1 in the attached PDF. It is observed that BSSM contributes to an ACC, AUC and F1 improvement of 5.2\%, 1.7\% and 4.9\%, respectively. ESR contributes to an ACC, AUC and F1 improvement of 18.3\%, 9.4\% and 12.2\%, respectively. Q3: The open-source code is not explicitly provided. R: Thanks for your valuable suggestion. Owing to the company regulation, the source code will be made available after publication. We respectively ask for the reviewer's understanding on this restriction. Q4: Among the compared methods mentioned in Table 4, some ViT-based and ResNet-50-based methods are not specifically designed for domain adaptation tasks. Is this comparison fair? R: Thanks for your value comments, so that we could have a chance to clarify the compared methods. We first compare six methods for domain generalization tasks, namely, [36,50,51,53,55,56]. Then, we compare two DR grading methods under the domain generalization setting, namely [4,8]. All these eight methods are plenty for comparison under the context of domain generalization. The rest four CNN or ViT based methods [6,19,29,31] do not have domain generalization property, and are involved just for boarder comparison. Besides, these methods are implemented under the emperical risk minimization (ERM) setting, which is the same as the VMamba baseline. This demonstrates the effectiveness of Mamba structure in the cross-domain grading tasks. Q5: Can you explain how SSM selects severe lesion information? R: Thanks for your valuable suggestion. We model the relation between patch embedding from SSM and severity level by drawing inspiration from the class activation map (CAM) mechanism [a]. Specifically, give an image $\boldsymbol{x}$, assume that $\boldsymbol{\tilde{f}}_k(i)$ denote the activation of unit $k$ from the last Samba block at the patch $i$. Then, for unit $k$, after implementing a global average pooling (GAP), the feature embedding $F^k$ is $\sum_i f_k(i)$. Thus, for a certain severity level $c$, the input to the softmax $S_c$ is $\sum_k w_k^c F_k$, where $w_k^c$ is the weight corresponding to severity level $c$ for unit $k$. Here $w_k^c$ indicates the importance of $F_k$ for severity level $c$. Finally, the output of the softmax for severity level $c$, $P_c$ is computed as $$ P_c = \frac{{\rm exp} (S_c)}{\sum_c {\rm exp} (S_c)}. $$ By plugging $F_k = P_i f_k(i)$ into the severity level score $S_c$, we obtain $$ S_c = \sum_k w_k^c \sum_i f_k(i) = \sum_i \sum_k w_k^c f_k(i). $$ Then, the severity activation map $M_c$ for severity level $c$ is defined as follows, where the activation of each patch $i$ is computed as $$ M_c(i) = \sum_k w_k^c f_k(i). $$ We take the patch embeddings from the last Samba block as input, so as to visualize the per-level severity activation patterns. Then, the activated severity patterns are displayed on the original images. We use FGADR as the unseen target domain. The results are shown in Fig.~R1 in the attached 1-pg PDF, where the activated patches are highlighted in blue boxes. From the first to the fifth row, the samples from level-1 to level-5 are provided accordingly. From the first to the fifth column, the patch activation map from level-1 to level-5 is generated by the aforementioned methods. Notice that, as level-1 refers to the normal scenario, each sample has activations on level-1, meaning some patches are normal. [a] Zhou, Bolei, et al. "Learning deep features for discriminative localization." Proceedings of the IEEE conference on computer vision and pattern recognition. 2016. Q6: In the comparative experiments with other SOTA methods, are all the source domains supplemented with the two additional large-scale datasets DDR [24] and EyePACS [13]? R: Yes, as all the performance of the state-of-the-art methods reported in [8] is supplemented with the two additional large-scale datasets DDR [24] and EyePACS [13], for fair evaluation, we also supplement both datasets when training. We will clarify it in the main text accordingly. Finally, should you have further suggestions and comments, we are glad to incorporate during the discussion stage. --- Rebuttal Comment 1.1: Comment: Thanks to the authors for actively responding to the raised concerns and promising revisions in the updated version. However, considering the innovativeness of Samba (based on Mamba for various tasks), the score suitable for a Borderline Accept will not be altered. --- Reply to Comment 1.1.1: Title: Re: Official Comment by Reviewer b4sx Comment: We are glad that you are satisfied with the revision and find the concerns resolved. We will improve our paper carefully per your valuable suggestions.	Summary: The paper introduces a new method for disease grading for both within and cross-domain medical images. Three different imaging modalities have been used for experimentation including Retinal, X-ray, and H&E images. In terms of methodological novelty, the authors propose to encode image patches in a recurrent manner to capture informative lesions. Further, they use an EM-based recalibration method to reduce the cross-domain variance by compacting the feature space. Overall, their experiments shows that the method proposed is superior to the baselines. Strengths: The paper is well-written and has a strong theoretical base with detailed explanations. Besides the quantitative evaluations, the authors have conducted some qualitative experiments to show attention maps on retinal images. Also, the idea seems novel along with introducing new modules to tackle issues present in medical images datasets. Weaknesses: There are a few major issues with the experimental design: 1. The Cross-domain Breast Cancer Grading Benchmark is not a well-defined cross-domain problem in computational pathology. Firstly, this is not a widely used dataset in the field. Secondly, the images come from the same center yet with different scanning magnifications. It is not common to use images from two different magnifications as the "domains". The cross-domain problem in computational pathology is when the images are actually from two different centers and with two different staining protocols (images might be scanned in varying magnifications). An example of such a problem can be found here: https://camelyon16.grand-challenge.org/Data/ 2. In Table 4, the authors have reported the benchmark from [8]. It has not been mentioned whether the proposed model was trained on the exact same seed, device, and cross-validation folds. If any of these are different, the comparison is not fair. Instead, I'd suggest the authors benchmark these with the same exact setting and report the results. 3. For highly imbalanced datasets, especially medical data, it is proper to report Balanced Accuracy to show the performance of the model on the rare classes. Both ACC and AUC fail to represent the rare classes. This is important for comparison as results in Table 1 show that F1 is significantly lower than ACC and AUC. Therefore, Balanced accuracy should be reported for all the benchmarks. 4. There are quite a few modules in different parts of the model that have not been studied in an ablation study. These modules are the bach norm, linear layer, etc. in the EM-based recalibration. Adding the ablation study for these modules can enhance the work :) Technical Quality: 2 Clarity: 3 Questions for Authors: I am curious if the authors can elaborate more on this conclusion made in page 15: "After processed by the Recurrent Patch Modeling module, more regions in the correlation The high-response patches have grade-related lesions and the information is transported in the recurrent process matrix have higher response." Confidence: 4 Soundness: 2 Presentation: 3 Contribution: 2 Limitations: It has been justified properly. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Q1: Is Cross-domain Breast Cancer Grading Benchmark proper? 1) not widely used. 2) It is not common to use images from two different magnifications as the "domains". 3) Evaluation on CAMELYON17, from different centers and different staining. R: Thanks for your valuable comment, so that we could have a chance to clarify some important aspects. 1) Following your suggestion, we take the five individual domains marked by the staining protocols in CAMELYON17 for further experiments. We use Domain-1 as the source domain, and reports its performance on the rest four unseen target domains, denoted from Domain-2 to Domain-5. The results are reported as follows. It is observed that, the proposed Samba still shows a significant performance improvement on all the four unseen target domains compared with the baseline VMamba-ERM. The results will be included when revision. Table R2: Generalization performance comparison between Samba and VMamba-ERM baseline. \| Method \| Domain-2 \| Domain-3 \| Domain-4 \| Domain-5\| avg.\| \|----------\|----------\|----------\|----------\|----------\|----------\| \| VMamba-ERM \| 76.23 \| 74.17 \| 79.53 \| 69.87 \| 74.95 \| \| Samba \| 84.59 \| 82.48 \| 86.50 \| 78.64 \| 83.05 \| \|\|\|\|\|\| 2) We also inspect in our dataset, if the samples vary in staining and if they have domain gap from a rigorous machine learning perspective. As shown in Fig.R2 a (attached in the 1-pg PDF), the samples from Domain-1 ($\times$20) and Domain-2 ($\times$40) are not only different in magnifications, but also varied in staining. Besides, we use t-SNE visualization to inspect the samples' feature distribution from Domain-1 and Domain-2, displayed in Fig. R2 b (attached in the 1-pg PDF), respectively. It can be observed that, samples from Domain-1 (marked in X) and Domain-2 (marked in O) have clear distance in the feature space. Besides, samples of the same severity level but from different domains are not clustered together. It indicates that the two domains in this dataset have the so-called domain gap and are suitable to benchmark the generalization capablity. 3) In real-world scenarios, some hospitals may use magnification factors that are not present in the training set. So testing the cross-magnification generalization ability by the Cross-domain Breast Cancer Grading Benchmarkalso still has practical significance. Q2: Are evaluation in Table 4 same and fair? R: We would like to clarify that, the proposed Samba is evaluated under all the default settings of [8] for fair evaluation. Specially, the batch size is 16, the training terminates after 100 epochs, the initial learning rate is $10^{-3}$ with a weight decay of $5\times10^{−4}$ and a momentum value of 0.9. We will explicitly mention these details. Q3: 1) Proper to report Balanced Accuracy, e.g., Table 1. 2) Balanced accuracy for all the benchmarks. R: 1) We adapt the balance accuracy metric (denoted as BACC), which is the mean of Sensitivity and Specificity, on DG Fatigue Fracture Grading benchmark (Table.R3) and DG Breast Cancer Grading Benchmark (Table.R4). The results are reported as follows. It can be seen that, the proposed Samba still outperforms the rest methods in term of the balance accuracy, indicating its effectiveness on rare classes. Table R3: Effectiveness of the proposed Samba on recurrent patch modeling under BACC metric. Domain-1 and Domain-2 in the Fatigue Fracture Grading Benchmark are used as the source and unseen target domain. \| Method \| ACC \| AUC \| F1 \| BACC \| \| \|----------\|----------\|----------\|----------\|----------\|----------\| \| LSTM \| 39.8 \| 50.2 \|18.6 \| 25.6 \| \| UR-LSTM \| 43.3 \| 61.8 \| 20.9 \| 25.2 \| \| UR-GRU \| 45.7 \| 65.1 \| 22.4 \| 27.1 \| \| ViT \| 50.0 \| 69.3 \| 26.5 \| 30.9 \| \| VMamba-ERM \| 52.7 \| 70.4 \| 28.7 \| 34.0 \| \| Samba \| 76.2 \| 81.5 \| 45.8 \| 52.2 \| \|\|\|\|\|\| Table R4: Effectiveness of the proposed Samba than baseline under BACC metric. Experiments on DG Breast Cancer Grading Benchmark. \| Method \| Backbone \| ACC \| BACC \| \|\| \|----------\|----------\|----------\|----------\|----------\|----------\| \| ERM \| VMamba-T \| 40.4 \| 18.7 \| \| \| Samba \| VMamba-T \| 54.8 \| 24.5 \| \| \| ERM \| VMamba-S \| 50.1 \| 20.6 \| \| \| Samba \| VMamba-S \| 56.1 \| 27.9 \| \| \| ERM \| VMamba-B \| 54.9 \| 25.6 \| \| \| Samba \| VMamba-B \| 60.5 \| 29.8 \| \| \|\|\|\|\|\| 2) We would like to raise the reviewer's attention that, despite that the severity level is highly imbalanced in grading problems especially in DR grading, ACC, F1 and AUC metrics are both acknowledged as the commonly-used evaluation metrics [4,6,8,19,29,36,50,51,53,54,55]. Therefore, we directly adapt these metrics and existing evaluation protocols for fair evaluation in Table 4. Besides, balanced accuracy probes a model's performance very similar as F1-score does, while we already use F1-score. Q4: Ablation on mdules. R: We provide an ablation study on each module of the proposed Samba, which is also mentioned by Reviewer\#Wyiu and b4sx. Specifically, on top of the VMamba baseline, two components, namely, Bi-directional State Space Modeling (BSSM) and EM-based State Recalibration (ESR), are added. The experiments are conducted on the DG Fatigue Fracture Grading Benchmark. The results are reported in Table~R1 in the attached 1-pg PDF file. It is observed that BSSM contributes to an ACC, AUC and F1 improvement of 5.2\%, 1.7\% and 4.9\%, respectively. ESR contributes to an ACC, AUC and F1 improvement of 18.3\%, 9.4\% and 12.2\%, respectively. Meanwhile, we respectively ask for the reviewer's understanding that our work focuses on innovatively introducing BSSM and ESR on top of the vanilla elements (e.g., layer, norm) in VMamba without modify. The ablation of vanilla elements may beyond the scope of this work. Q5: Elaborate more on text in p15. R: Please refer to the general response. Should you have further suggestions, we are glad to address during the discussion stage. --- Rebuttal Comment 1.1: Comment: I would like to thank the authors for their significant effort and for providing more details in the rebuttal phase. However, I believe the Breast Cancer Grading Benchmark is not a representative choice for claiming that the proposed approach is a good solution for a computational pathology task. Multiple well-studied and standard datasets in the field, such as TCGA sub-datasets, could have been chosen. These datasets can be used for grading (to match the rest of the paper) or subtyping tasks based on the proposed research. Camelyon17 is also a viable choice if the authors decide to work on subtyping. Another important factor is that several ablation studies have been conducted on the Breast Cancer Grading Benchmark, which is still questionable in terms of reliability and generalizability of results. This dataset should ideally be replaced with another dataset, as mentioned above. I also appreciate the authors' effort in providing details in the PDF file. It is important to note that there are stain variations within the same center samples due to the staining procedure, which accounts for in-domain data variance. Additionally, differences in magnification are not technically a domain-shift problem; rather, they are known as a cross-scale problem [1][2], which is not aligned with the paper's topic and the rest of the experiments. Thus, to fairly test the hypothesis in this field, the study should cite and compare proper literature on a standard dataset. I have also considered the paper that released the Breast Cancer Grading Benchmark [3] dataset. However, within that paper, the authors do not consider their dataset as a cross-domain dataset and instead build a cross-scale model. Based on the above rationale, I am not convinced to change my rating. [1] Sikaroudi, M., Ghojogh, B., Karray, F., Crowley, M., and Tizhoosh, H.R., 2021, April. Magnification generalization for histopathology image embedding. In 2021 IEEE 18th International Symposium on Biomedical Imaging (ISBI) (pp. 1864-1868). IEEE. [2] Chhipa, P.C., Upadhyay, R., Pihlgren, G.G., Saini, R., Uchida, S., and Liwicki, M., 2023. Magnification prior: a self-supervised method for learning representations on breast cancer histopathological images. In Proceedings of the IEEE/CVF Winter Conference on Applications of Computer Vision (pp. 2717-2727). [3] Yan R, Ren F, Li J, Rao X, Lv Z, Zheng C, Zhang F. Nuclei-Guided Network for Breast Cancer Grading in HE-Stained Pathological Images. Sensors. 2022; 22(11):4061. --- Rebuttal 2: Title: Reply to Q1: Effectiveness on a common computational pathology dataset. Comment: Q1: Effectiveness on a common computational pathology dataset. R: We respect and value the reviewer’s perspective from computational pathology. We adopted CAMELYON17 to conduct the two experiments in this paper where Cross-domain Breast Cancer Grading Benchmark has been used for validation. Same as the earlier rebuttal, five individual domains marked by the staining protocols and sites in CAMELYON17 are used for the cross-domain experiments. We use Domain-1 as the source domain, and reports its performance on the rest four unseen target domains, i.e., from Domain-2 to Domain-5. The first experiment (Table 2 in the main text) is the impact of the number of components K in GMM, where ACC, AUC and F1 are used as evaluation metric. The performance on CAMELYON17 is attached as follows. Table 2: Impact of the number of components K in GMM on unseen target domain performance. Experiments are conducted on the CAMELYON17. Domain-1 is used as source domain. Metrics presented in percentage (%). \| \| \| Domain-2 \| \| \| Domain-3 \| \| \| Domain-4 \| \| \| Domain-5 \| \| \|----------\|----------\|----------\|----------\|----------\|----------\|----------\|----------\|----------\|----------\|----------\|----------\|----------\| \| K value \| ACC \| AUC \| F1 \| ACC \| AUC \| F1 \| ACC \| AUC \| F1 \| ACC \| AUC \| F1 \| \| 16 \| 81.80 \| 92.09 \| 79.96 \| 79.45 \| 88.96 \| 76.60 \| 83.92 \| 95.38 \| 82.10 \| 75.84 \| 81.99 \| 74.16 \| \| 32 \| 82.68 \| 93.81 \| 80.95 \| 80.39 \| 91.28 \| 77.97 \| 84.38 \| 96.20 \| 82.96 \| 76.53 \| 82.46 \| 74.92 \| \| 48 \| 84.06 \| 94.25 \| 81.83 \| 81.84 \| 92.60 \| 78.49 \| 85.87 \| 97.16 \| 83.87 \| 77.69 \| 83.85 \| 75.04 \| \| 64 \| 84.59 \| 95.67 \| 83.10 \| 82.48 \| 93.32 \| 79.85 \| 86.50 \| 97.82 \| 85.13 \| 78.64 \| 84.70 \| 75.32 \| \| 96 \| 84.27 \| 95.48 \| 82.53 \| 82.06 \| 92.90 \| 79.44 \| 86.16 \| 97.45 \| 84.80 \| 78.15 \| 84.28 \| 74.86 \| \| 128 \| 83.65 \| 94.70 \| 81.97 \| 81.50 \| 92.41 \| 78.36 \| 85.47 \| 96.90 \| 84.62 \| 77.38 \| 83.66 \| 74.14 \| \|\|\|\|\|\|\|\|\|\|\|\|\|\| Default K is set to 64, and we further test the performance when K is set to 16, 32, 48 and 96, respectively. The results are reported in Table 2. When K is set to 64, the proposed Samba achieves the best grading performance. This observation is consistent to the performance on Cross-domain Breast Cancer Grading Benchmark, where a number of 64 Gaussians achieves the optimal performance. The second experiment (Table 3 in the main text) is to analyze the computational cost and performance trade between the VMamba-ERM and the proposed Samba, where only accuracy is used as the evaluation metric. The performance on CAMELYON17 is attached as follows. Table 3: Computational cost comparison between VMamba-ERM and the proposed Samba. Experiments are conducted CAMELYON17. Domain-1 is used as source domain. Metrics in percentage (%). \|Method \| Backbone \| GFLOPS \| Para. \| Domain-2 \| Domain-3 \| Domain-4 \| Domain-5 \| avg. \| \|----------\|----------\|----------\|----------\|----------\|----------\|----------\|----------\|----------\| \| EMR \| VMamba-T \| 3.7 \| 32.7 \| 70.08 \| 67.29 \| 72.96 \| 63.16 \| 68.37 \| \| Samba \| VMamba-T \| 5.5 \| 32.7 \| 78.74 \| 76.15 \| 80.06 \| 71.05 \| 76.50 \| \| EMR \| VMamba-S \| 7.9 \| 63.4 \| 72.86 \| 69.50 \| 75.08 \| 65.72 \| 70.79 \| \| Samba \| VMamba-S \| 11.3 \| 63.4 \| 81.01 \| 78.96 \| 82.75 \| 73.88 \| 79.15 \| \| EMR \| VMamba-B \| 14.0 \| 112.4 \| 76.23 \| 74.17 \| 79.53 \| 69.87 \| 74.95 \| \| Samba \| VMamba-B \| 19.6 \| 112.4 \| 84.59 \| 82.48 \| 86.50 \| 78.64 \| 83.05 \| \|\|\|\|\|\|\|\|\|\| The same trend is observed on this dataset, where using Samba on each type of the VMamba backbone shows a clear performance improvement on unseen domains. We sincerely wait for the reviewer’s feedback about the above experiments, which function the same as the Cross-domain Breast Cancer Grading Benchmark in the submission. If they could meet the reviewer’s standard on computational pathology, we are happy and open to incorporate it into our work, subtyping the computational pathology part. --- Rebuttal 3: Title: Reply to Q2: Cross-scale or Cross-domain? Comment: Q2: Cross-scale problem or Cross-domain problem? R: First of all, we would like to thank the reviewer for the valuable feedback on the cross-scale perspective. However, we humbly suggest the reviewer that there might be some misunderstanding on cross-domain. From a machine learning perspective, where the venue of NeurIPS focuses more on, as long as the source and unseen target domains are not independent and identically distributed / not the same [a,b,c], the domain gap exists and the domain generalization techniques can be applied. The change of scale, caused by the magnification, also poses distribution shift between the source and target domain, can also be treated as a type of domain generalization, according to this machine learning definition. [a] Zhou, Kaiyang, et al. "Domain generalization: A survey." IEEE Transactions on Pattern Analysis and Machine Intelligence 45.4 (2022): 4396-4415. [b] Zhou, Kaiyang, et al. "Domain Generalization with MixStyle." International Conference on Learning Representations. 2021. [c] Wang, Jindong, et al. "Generalizing to unseen domains: A survey on domain generalization." IEEE transactions on knowledge and data engineering 35.8 (2022): 8052-8072. Therefore, we humbly suggest that conceptually from a machine learning perspective, the Cross-domain Breast Cancer Grading Benchmark is applicable to validate the generalization capacity of a model. Besides, as we have already provided in the 1-pg PDF file, the distribution shift exists between the Doman-1 and Domain-2 of this dataset. This clearly-existed domain gap, along with the definition of domain generalization, means the Cross-domain Breast Cancer Grading Benchmark is rational to benchmark the domain shift of grading problems. In real-world scenarios, some hospitals may use magnification factors that are not presented in the training set. Hence, testing the cross-magnification generalization ability by the Cross-domain Breast Cancer Grading Benchmark still has the practical significance. Summary: As we mentioned at the beginning, we respect and value the reviewer’s perspective from computational pathology. We are glad and open if the reviewer feel it would be better to treat the results on cross-domain breast cancer grading are a discussion on the scale generalization or replace them by the results on CAMELYON17. We hope we can reach a consensus, and look forward to your feedback and suggestions. --- Rebuttal Comment 3.1: Comment: I appreciate the detailed response and the effort of the authors to provide further insights. I understand that DG on cross-scale data is a valid problem from an ML point of view. Yet, my main concern is rooted in the choice of the dataset, where among many well-studied datasets present, the BCGR dataset had been chosen. Still, I am not convinced it is a good representative unless an extensive benchmark with different methods is provided. However, by including C17, and providing the ablation studies and the benchmarking results on that, my initial concern was addressed. With that, I strongly suggest the author use the C17 as the main pathology representative dataset and use the BCGR results as a secondary dataset. Also, a clarification section needs to be added to the work to explain that BCGR is a cross-scale generalization and is not multi-domain as it is known in pathology. This will ensure the reliability of the result for a pathology-related audience. Given the new set of results, I would raise my rating to a weak accept :) --- Rebuttal 4: Title: Re: Official Comment by Reviewer LrSF Comment: We are glad that your concerns have been properly addressed. We will significantly polish and improve our work per you suggestions, particularly on prioritizing C17 over BCGR for a professional standard of the pathology perspective. Finally, thanks again for your time and effort in helping us improve our work.	Summary: The authors propose a model which they call Samba, for Severity-aware recurrent modelling, which is a method designed for cross-domain medical image grading. They introduce several challenges in medical grading, namely the difficulty models encounter in generalising to unseen domains, as well as the existence of ambiguity in lesion severity grading. The model is comprised of two main blocks: recurrent bidirectional Vision Mamba layers and a Expectation-Maximisation State Recalibration (EMSB) module which consists of learnable tokens which capture lesion representations, and which are then used as bases to map to more compact feature embeddings. These are then used to initialise an Expectation-Maximisation (EM) algorithm and the lesion feature distribution is estimated using Gaussian Mixture Models (GMMs) for each image. The Mamba layers treat the image patches as sequential data, with the rational being the relevant information will be propagated through the hidden states. The EM module models the feature distribution of lesions using the GMMs to try and eliminate domain shift. Samba is applied to three benchmarks, where images are separated between a source domain and a target domain: Diabetic Retinopathy fundus images (DR), Fatigue Fracture X-rays and Breast Cancer histopathology images. The model is trained on the source domain and applied to the target domains. Ablation is carried out, comparing Samba to different baseline and SOTA models, as well as looking at iteration number and severity base update methods. The results obtained show Samba generally outperforms existing methods to some degree. The authors also provide a theoretical analysis on the generalisation risk bound in the Appendix. Strengths: The paper gives a good introduction to the challenges inherent in grading disease severity in the medical imaging domain. It tackles an important problem, as we know current algorithms often fail at generalising across domain. Integrating Vision Mamba layers with EM-based recalibration of image features is a nice contribution designed to tackle this challenge, which is motivated by logical reasoning about the properties of medical images. The method is comprehensively evaluates on three different benchmark datasets, which are specifically designed to test domain generalisation of algorithms. Furthermore, the results suggests that Samba is able to generalise to unseen domains better than other established methods. There is also ablation provided on several aspect of the model (number of components K, iteration T and update on $\mu$), as well as t-SNE plots showing how the model embeddings cluster better by severity grading and not data provenance, as well as attention maps of DR images. Overall, the paper combines ideas from current SOTA in deep learning (mamba), statistical modelling (GMM-EM) and properties of medical images. Weaknesses: In my opinion the paper's main weaknesses are the following: 1 - Unclear explanation of the EM-based State Recalibration module I think the introduction to the EM-based State Recalibration module in this paper is too brief, perhaps assuming reader familiarity, and does not provide intuition as to why using GMMs + EM makes sense in this context or is more suitable to this task than other potential approaches. The implementation details of how the the GMM \& EM is integrated into the overall Samba architecture are not clearly or fully presented. The initialisation strategy for the EM is unclear to me: the paper mentions using learnable severity bases to initialise EM, but doesn't explain how these bases are learned or why this initialisation is most beneficial. It also doesn't discuss the convergence criteria used for the EM and although it shows ablation into how many iterations are best, this comes without proper introduction in the background or methods sections. The same goes for the number of Gaussian basis used: you show ablation on this, but don't introduce this in background or methods sections. Finally, although some equations are presented outlining the E- and M-steps, variables are not always defined and the choice of kernel function seems entirely ad-hoc and unjustified. In particular You define your GMM as: $$p(f_n) = \sum_{k=1}^K z_{nk} \mathcal{N}(f_n\|\mu_k, \Sigma_k),$$ but $z_{nk}$ typically represents responsibilities which are estimated in the E-step, not given as part of the model definition, where $\pi_k$ would represent the mixing coefficients of the GMM. Then you derive the E-step as: $$z_{nk} = \frac{\mathcal{K}(f_n, \mu_k)}{\sum_{i=1}^K \mathcal{K}(f_n, \mu_i)}$$ whereas a standard formulation would be $$z_{nk} = \frac{\pi_k \mathcal{N}(f_n\|\mu_k, \Sigma_k)}{\sum_{i=1}^K \pi_i \mathcal{N}(f_n\|\mu_i, \Sigma_i)}.$$ However, you don't justify the use of the arbitrary kernel function $\mathcal{K}$ (exponential inner dot $\mathrm{exp}(f^T\mu)$ over standard Gaussian probabilities. Could you explain this in more detail? Then you don't explicitly define what $Z^t$ represents, nor what the relationship is with $z_nk$. Likewise with $F$, you do not explicitly define what it represents, but I will assume you mean the feature matrix of the input image. How does $F$ relate to equation (5)? How does this derive into equation (6)? The recalibration step $\tilde F$ is not well explained in terms of matrix operations or dimensions. This lack of clarity makes it difficult to interpret the method in terms of a well-established optimisation algorithm, which is an important issue as explaining the transformations applied to the feature representations is crucial to understanding Samba. Overall, while the general idea of using GMM-EM for feature recalibration is interesting, the mathematical formulation presented in the paper has inconsistencies and deviations from standard GMM-EM that I don't think are well-justified and which I would like to see more fully explained and motivated. 2 - Unclear structure of results and lack of clear baseline comparisons While the paper compares three datasets to various baseline and baseline methods, each dataset is treated separately, so it's not always clear the results shown extend to the other datasets, if the comparisons are fair or how the baselines were implemented. I feel like the main results are the ones presented for the Diabetic Retinopathy dataset, yet these are presented last. I think the results section would read better and make more sense if these were presented first. However, one of my main issues here is that you only mention your main baseline comparison method on p.7, but you compare against in Figure 3 without even mentioning it. This should be properly introduced and you should explain why VMamba under empirical risk minimisation (VMamba-ERM) is a good baseline model against which to compare. You also need to explain how Samba differs from VMamba-ERM and what advantages these differences bring to the task that the other doesn't provide. Finally, you don't provide ablation on Samba itself, showing the individual contribution of the Mamba layers vs EMBS layers. With regards to the theoretical analysis on the generalisation risk bound, it feels disconnected to the rest of the paper and not particularly relevant to the stated aims. Is there some way to tie it more or explain why its important? Finally, I think an Appendix section on how the datasets were preprocessed and showing the hyperparameters employed for all the other models presented in the results sections would enrich this paper. There are other things which I find unclear, which I have put below in Questions. Technical Quality: 2 Clarity: 2 Questions for Authors: Line 44 - I don't fully understand this sentence. Maybe you could rephrase? Line 54 - at the distal of what? Line 123 - what's a stem unit? Figure 2 - I think you need to describe the Samba blocks in more detail - here it looks like the bi-directional SSM and EM recalibration occurs in the downsampling block. Is this a mistake? What'a VSS block? What's the difference between the training and inference arrows in the figure? Figure 3 - Iteration Number T - What models are you comparing yours against? What is Vmamba-ERM and what is SOSS?? Why is Vmamba showing a constant trend across iteration number T? What are the different columns? Line 235 - why does the number of iterations play an important role in the EM algorithm? You should introduce this beforehand and the ablation study should answer this question. Line 237 - do you mean Figure 3 instead of Figure 6 here? - Figure 6 shows the effect of regularisation techniques and is situated in the appendix. Line 244 - why are these these methods appropriate to test different optimisation techniques here? Please explain this. Line 252 - these are percentage points, not percentage of improvement. Table 1- Why is Table 1 showing three F1 scores highlighted in brighter green? and two blocks of yellow and light green? Is this a mistake? Also what do these colours represent? Table 3 - OK, why do you think Samba is doing better there? Line 283 - percent points, not percents... Table 4 - why do you think Samba and Vmamba-ERM are doing so well on FGADR compared to other methods? A.3 - the text needs a rewrite to make sense I think. Please check this. Figure 8/9 - Do you have any ground truths available to compare the attention maps shown in Figure 8 and 9? Confidence: 4 Soundness: 2 Presentation: 2 Contribution: 3 Limitations: The authors point out some limitations of their work with regards to class imbalance. I have pointed out other perceived limitations in the Weakness section above. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Q1: Unclear explanation. R: 1) After proceeded by BSSM, each patch embedding $\boldsymbol{f}_n$ is projected by a linear layer to get the state embedding $\boldsymbol{x}_n$. The severity base $\boldsymbol{\mu}_n$ is modeled as a mixture of Gaussian from $\boldsymbol{x}_n$. The E-M algorithm iteratively approximates $\boldsymbol{\mu}_n$ to $\boldsymbol{x}_n$. After convergence, the embedding is fed into the rest module. 2) As introduced in L194-196, moving average is adapted to update the $\boldsymbol{\mu}^{0}$, which is used as the initial Gaussian parameter in each EM process. 3) The E-M empirically implements 3 iterations. 4) We will define the number of Gaussian kernels $K$ in L171. 5) We will mention that the mixing coefficients of GMM are left out for simplicity and easy computation and the exponential inner dot kernel is used. 6) In the $t$-th iteration, $\mathbf{Z}^t$: the responsibilities of all the patch embeddings from a sample, where $\mathbf{Z}^t=\{z_{nk}^t\}$. 7) Typo. L185, remove $\mathbf{F}$. 8) In Eq.6, $\mathbf{\mu}$: the Gaussian basis of all the patch embeddings from a sample, where $\boldsymbol{\mu}=\{\mu_{k}\}$. $\mathbf{\widetilde{F}}$: the entire image feature from all the patch embeddings. Q2: Structure. R: 1) To clarify, as this paper handles cross-domain medical grading, each dataset we use has more than one domains. The evaluation of domain generalization is evaluated inside each dataset, not across different datasets. Tab.4: pls refer to general response. 2) We will put Table 4 and the subsection first. 3) We will metion before Fig.3. Especially, The comparison is made between the proposed Samba and the vanilla VMamba as baseline. The VMamba baseline is trained under the empirical risk minimization (ERM), which we denote as Vmamba-ERM. Notice that, training under ERM is a common baseline for domain generalization. On top of Vmaba-ERM, the advancement of Samba is two modules EMSR and BSSM. 4) Per-component ablation: in general response. 5) We will put the theoretical analysis to the supplementary, making room for details of the method and ablation study. 6) Details of data pre-processing and hyper-parameter settings on each dataset will be in Appendix. Q3: rephase L44. R: Domain generalized disease grading aims to learn a model that can be well generalized to unseen target domains, when the model is only trained on the source domain data. Practically, the feature distribution between the source and unseen target domains usually varies. Q4: L54. R: at the distal of the blood vessels. Q5: Stem unit? R: A stem unit partitions the input image into patches. Q6: Typo in Fig.2. R: 1) Both modules should occur in the Samba block. Will correct. 2) Typo. 'VSS block'->'Samba block'. 3) Training and inference input images from different domains, marked by red and green arrows, respectively. We will distinguish the source and target domains (located at the upper-left of Fig.2) using different colors. Q7: Fig.3. compare what? What's Vmamba-ERM\&SOSS? Why Vmamba is constant across T? Different columns? R: 1) The comparison is made between the proposed Samba and the vanilla VMamba as baseline, which is trained under the empirical risk minimization (ERM) and denoted as Vmamba-ERM. 2) Typo. 'SOSS' -> 'Samba'. 3) VMamba-ERM does not have EM-based State Recalibration. EMSR is parameterized by T. Therefore, the performance of Vmamba-ERM is consistent to T. 4) From column 1 to 3, it reports the AUC, ACC and F1 metric. Q8: Why iteration number? R: E-M algorithm implements the approximation by iteratively conduct the E and M step [12]. A small iteration number does not reach the convergence criterion, which results in an poor approximation. After a too-large iteration number, the approximation may already reach the optimal, adding unnecessary computational cost and training time. We will introduce \& clarify. Q9: Line 237. R: Typo. Fig.6->Fig.3. Q10: L244-explain why proper? R: The process of the proposed state recalibration is differentiable, thereby enabling the application of back-propagation to update $\boldsymbol{\mu}^0$. However, the stability of the update cannot be guaranteed due to the EM iterations. Therefore, we adopt moving average to update $\boldsymbol{\mu}^0$ to avoid collapse. Q11\&14: L252&283 - typos on percentage points. R: will correct. Q12: Tab.1 R: Brighter green, yellow and light green intend to highlight the best, second and third top performance. We will correct. Q13: Tab.3, why Samba better? R: Compared to VMamba-ERM baseline, the EM-based State Recalibration in Samba models the feature distribution of lesions via Gaussian Mixture Model with learnable severity bases, and re-estimates by E-M algorithm. The grading-related features are mapped to a more compact space. It can be more stable in unseen target domains. Q15: Why much better on FGADR? R: FGDAR has a different severity-level sample distribution than other datasets. The samples without DR (level-1) only occupy only 5.5\% among all the training samples, which is far less than others (e.g., level-1 samples occupy 49.3\% in APTOS). Therefore, other methods may over-fit other severity levels and under-fit level-1. In contrast, the selective scan mechanism of the Vmamba-ERM and Samba allows the this severity distribution shift. The EM state re-calibration in Samba makes the feature space more compact, and improves the generalization. Q17: Fig.8/9. ground truth? R: As the datasets are for grading, we respectfully ask for the reviewer's understanding, there are no available fine-grained ground truth (e.g., pixel, boxes). Finally, should you have further questions or suggestions, we are happy to address during the discussion stage. --- Rebuttal Comment 1.1: Title: Response to Author's Rebuttal Comment: Thanks to the authors for the time and effort put into the rebuttal. I have read their response, as well as the other reviews and their associated comments. I agree with the authors that testing across multiple magnification (i.e. scales), although not the standard approach, can constitute cross-domain adaptation if it can be shown there exists a clear difference in the data distribution across domain. They have shown this to be the case with their UMAP embeddings and changes in magnification and resolution across scanners resulting in models underperforming is a know phenomenon in computational pathology. Additionally, they also test on X-ray fatigue fractures and Diabetic Retinopathy datasets. I appreciate the authors promise to update the structure of the paper: modifying/correcting pipeline figure, expanding on background and motivation, clarifying model explanation and mathematical formulation in 3.3, moving 3.4 to Appendix, introducing baseline models clearly, introducing first results with Figure 4 (DR dataset), correcting Table 1 and expanding on model ablation as shown in Table R1. Given the above reasons and the substantial work required to put these into effect, I am maintaining my original rating. --- Reply to Comment 1.1.1: Title: Re: Response to Author's Rebuttal Comment: We are glad to see your concerns have been addressed. We will improve our paper carefully according to your valuable suggestions.	Rebuttal 1: Rebuttal: General Response: We thank the reviewers for their time and constructive suggestions, and are glad that the reviewers unanimously give appreciation in a few points: - Technique contribution (Wyiu: integrating Vision Mamba layers with EM-based recalibration of image features is a nice contribution; LrSF: the idea seems novel; b4sx: use state space model to store and transmit severity information from local to global; hFq3: significant problem.) - Extensive evaluation \& visualization (Wyiu: comprehensively evaluation; LrSF: quantitative evaluations and some qualitative experiments; b4sx: The interpretability visualization of the experimental results is excellent; hFq3: different diseases and imaging modalities.) - Motivation/Task significance (Wyiu: generalising across domain; LrSF: has a strong theoretical base with detailed explanation; hFq3: significant problem.) However, there are also some major concerns as follows, in which we clarify as follows. - Lack of per-component ablation study (Wyiu comment\#2; LrSF comment\#4; b4sx comment\#2). R: We further provide an ablation study on each module of the proposed Samba. Specifically, on top of the VMamba baseline, two key components, namely, Bi-directional State Space Modeling (BSSM) and EM-based State Recalibration (ESR), are evaluated. The experiments are conducted on the DG Fatigue Fracture Grading Benchmark, and the results are reported in Table~R1 (attached in the 1-pg PDF file). It is observed that BSSM contributes to an ACC, AUC and F1 improvement of 5.2\%, 1.7\% and 4.9\%, respectively. ESR contributes to an ACC, AUC and F1 improvement of 18.3\%, 9.4\% and 12.2\%, respectively. - Path to visualize and understand the severity level (b4sx Comment\#5; hFq3: comment\#3). R: We model the relation between patch embedding from SSM and severity level by drawing inspiration from the class activation map (CAM) mechanism [a]. Specifically, we take the patch embeddings from the last Samba block as input to generate the per-level severity activation patterns. Then, the activated severity patterns are displayed on the original images. We use FGADR as the unseen target domain. The results are shown in Fig.~R1 (attached in the 1-pg PDF file), where the activated patches are highlighted in blue boxes. From the first to the fifth row, the samples from level-1 to level-5 are provided accordingly. From the first to the fifth column, the patch activation map from level-1 to level-5 is generated by the aforementioned methods. Notice that, as level-1 refers to the normal scenario, each sample has activations on level-1, meaning some patches are normal. [a] Zhou, Bolei, et al. "Learning deep features for discriminative localization." Proceedings of the IEEE conference on computer vision and pattern recognition. 2016. - Clarify if the state-of-the-art comparison (Table 4) is fair (Wyiu comment\#2; LrSF comment\#2; b4sx Comment\#4). Wyiu, LrSF, b4sx: For Table 4, the results of the state-of-the-art methods are directly cited from [8], and the evaluation protocols of the proposed method follow all the default settings as [8] does. LrSF: Fair mplementation details. Specially, the batch size is 16, the training terminates after 100 epochs, the initial learning rate is $10^{-3}$ with a weight decay of $5\times10^{−4}$ and a momentum value of 0.9. - A.3. The text needs a rewrite (Wyiu comment\#16; LrSF comment\#5). R: The sentences have been re-written as: After processed by the Recurrent Patch Modeling module, more cells in the correlation matrix have higher response. Usually, a handful of the patches inside the image have grade-related lesions. After the processing of our module, the information of these grade-related lesions is transported to other patches. It allows the model to perceive a more global-wise representation. Consequently, more patches that contain the grade-related lesion information are activated, and more cells are highly responded in the correlation matrix. We will explicitly mention these details when revision. We hope our clarification could help to make a more informed evaluation to our work. In the following individual response, we provide answers to each raised weakness/question. Best regards, Authors Pdf: /pdf/3e1061305fa7375a5732f8b5b78c9fedd08e9e64.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Enhancing Preference-based Linear Bandits via Human Response Time	Accept (oral)	Summary: The paper explores the interactive preference learning problem. Traditional binary choice feedback is limited in conveying preference strength. The authors propose leveraging human response time, which inversely correlates with preference strength, as additional information. They adopt the difference-based Drift-Diffusion Model with linear human utility functions and propose a computationally efficient linear utility estimator that incorporates human response times. Discussions about the proposed estimator and traditional estimators relying on the logistic regression are provided. The authors also integrate the proposed estimator into the Generalized Successive Elimination(GME) algorithm for the fixed-budget best arm identification problem. The proposed method is evaluated on both synthetic and real-world datasets, demonstrating the effectiveness of incorporating human response times for essay queries. Strengths: - The idea of incorporating human response times is novel and interesting. The authors provide a clear motivation to incorporate human response times, give illustrative examples to illustrate the benefits and explain their methods in detail. - The paper is well-written and easy to follow. The background, methods, and experiments are well-organized and well-explained. - The authors clearly discuss the effects of parameters $x^T\theta^{}$ and $a$, and compare the estimator with and without response times, which provides a good understanding of the proposed method. - The authors conduct extensive experiments on both synthetic and real-world datasets, and provide a detailed analysis of the results about the estimation performance and identification performance. The methods to pre-process the datasets and determine the parameters are also well explained. Weaknesses: - Although the authors provide the asymptotic analysis for their estimators, they do not provide a theoretical analysis for the proposed algorithm. - As mentioned in the paper, when the barrier $a$ is small, incorporating response times may not improve estimation performance. Since the parameter $a$ is also unknown, like $\theta^{}$, learners may not know whether to incorporate response times. It would be beneficial if the authors could have a discussion about the practical choice of the estimator under these conditions. Technical Quality: 3 Clarity: 3 Questions for Authors: Please refer to the weaknesses mentioned above. Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: Limitations are adequately discussed in the paper. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your detailed and thoughtful review, and for recognizing the novelty and clarity of our work. ## Weakness: algorithm analysis In our paper draft, we provide asymptotic theoretical results to show the following intuition on why response time can improve the learning performance: Combining response times and choices, information from easy queries can be extracted more efficiently. This is not possible using choices only. We added non-asymptotic error probability on estimating reward $x^{\top}\theta^*/a$ for every query $x$ using both methods, i.e. combining response times with choices and using choices only. Similar intuition can be confirmed as is shown in the `Author Rebuttal' section. We leave for future work to provide non-asymptotic error probability for the entire algorithm (Algoithm 1 in the paper). ## Weakness: practical usage of response time when $a$ is unknown One straightforward approach is to always incorporate response times: 1. Based on our empirical results, it seems that incorporating response times, if not improving the performance, rarely degrades performance. 2. Our theoretical and empirical results indicate that when queries are very difficult for humans to answer, incorporating response times may be less beneficial and could slightly decrease performance. However, in these scenarios, humans typically don’t have strong preferences, so they might be more tolerant of the minor performance impact caused by using response times. Alternatively, one can first incorporate response times to filter out many suboptimal options, and then use choice-only estimation for further learning. In the first stage, both good and bad arms exist. In this case, many queries, composed of one good arm and one bad arm, are easy and response times help extract more information from those easy queries. In the second stage, most arms will be similarly good. In this case, the queries are harder and choice-only estimation is sufficient to identify the best arm. Determining the optimal point to switch from using response times to relying solely on choices is an area for future research. --- Rebuttal Comment 1.1: Comment: The reviewer thanks the authors for addressing their concerns. The reviewer will raise the score accordingly.	Summary: The paper studies linear bandit preference learning, where binary preference data have been augmented with response times. A joint model for choice and response time falls from setting the linear preference model as the drift parameter in a drift-diffusion model. Experiments and theoretical analysis show that including response time in the model increases the value of "easy" responses, and thus improves bandit performance. Strengths: The paper is well-written. Including response time in a linear bandit preference model is novel to my knowledge, and certainly useful. The development of the method is clear, and the method itself is well-motivated and seems computationally reasonable and useful. The theoretical analysis is helpful, and I really appreciated how the paper uses that analysis to draw insights into the source of improvement from including response times in the model. The experiments were well-designed, and included the necessary baseline of choice-only. The analysis of the experiments provides helpful guidance for the situations in which the method does not outperform baselines. Weaknesses: The paper has one significant weakness: all of the experiments use simulated response times, simulated from the model developed in the paper. We thus don't get a sense for the "real-world" performance of the method, where response times will not adhere precisely to the DDM model. I agree with the paper that response time is easy to collect alongside binary preferences. Surely there are some datasets available that include actual human response times? Real human response times are the big missing piece of the experimental evaluation. Technical Quality: 3 Clarity: 3 Questions for Authors: On the topic of real human response time data, should we expect the model to be robust to lapses, or would some sort of data pre-processing be necessary to remove those? Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: Addressed. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your positive and constructive review; we appreciate your feedback and recognition of our work's novelty and usefulness. ## Weakness: real-world empirical result We acknowledge the importance of using real-world data for evaluation. Below is the rationale behind our simulator-based study and additional results using a different human dataset, as detailed in the `Author Rebuttal` section. Firstly, our bandit algorithm is an online algorithm, requiring us to sample response times of different queries online adaptively. Existing offline datasets are not collected adaptively, and is hard to be used for evaluating our algorithm. Although, there exist offline policy evaluation methods[2] that evaluate online algorithms with offline data, they require extensive data from a single user. Unfortunately, we have not been able to find such large-scaled datasets for response times. Secondly, online collecting response time data can suffer from outliers due to human inattention or anticipation [1]. Successful studies may require integrating data cleansing techniques [1] into online algorithms, which we consider as a separate contribution in future work. Therefore, in our work, we adopt a third approach: training a simulator from real-world data and then using the simulator to evaluate algorithms. This approach assumes that the EZ-DDM is the ground truth model, which is a reasonable assumption given the empirical support for this model [3]. We believe this approach justifies our insights—using response times makes easy queries more useful—while leaving a full user study for future work. We have included a new simulation-based study using another dataset of human choices and response times in the `Author Rebuttal` section. This study confirms that incorporating response times improves best-arm identification performance. - [[1] Myers et al. 2022](https://www.frontiersin.org/journals/psychology/articles/10.3389/fpsyg.2022.1039172/full) - [[2] Li et al. 2010](https://dl.acm.org/doi/abs/10.1145/1772690.1772758?casa_token=RuMgk8seZScAAAAA:YyJgdyVIfKDBquZ8uuDO-RAg3kK3vVmu-3Drco_J8CCUxYJXGgg2TCUepSwV6UvWqU4hYbpNwDTbVg) - [[3] Wagenmakers et al. 2007](https://link.springer.com/article/10.3758/bf03194023) ## Question: about lapses and data processing In general, there are two types of lapses: 1) lapses at the very beginning of the decision process; 2) lapses, or distractions, in the middle of the decision process. The first type of lapse can be interpreted as the non-decision time in the EZ-DDM model. The appendix includes our discussions about the issue of unknown non-decision times. Future work could involve estimating non-decision times from data. The second type of lapse occurs when humans lose attention or get distracted during the decision process, resulting in very long response times. Alternatively, humans might anticipate the current trial based on previous trials, leading to very short response times [2]. To handle such outliers in real-world datasets, a common procedure is to define cut-off thresholds to eliminate very short and very long response times [2]. Additionally, human attention can be monitored using eye-tracking devices. There is a line of psychological literature [1] that tracks human eye gazes during decision-making and incorporates human visual attention within the DDM framework. Another important procedure for handling real-world response time data is to test whether DDM is an appropriate model for a given dataset. There is literature on statistically testing whether observed response time data is generated by DDM [3][4]. - [[1] Krajbich 2019](https://www.sciencedirect.com/science/article/abs/pii/S2352250X18301866) - [[2] Myers et al. 2022](https://www.frontiersin.org/journals/psychology/articles/10.3389/fpsyg.2022.1039172/full) - [[3] Alós-Ferrer et al. 2021](https://www.journals.uchicago.edu/doi/full/10.1086/713732) - [[4] Fudenberg et al. 2020](https://www.pnas.org/doi/abs/10.1073/pnas.2011446117) --- Rebuttal Comment 1.1: Comment: Thank you for the additional experiments and analysis. I will raise my score as a result and hope that the paper is accepted. There was some related work just published at UAI that may be worth mentioning: Shvartsman et al. "Response time improves Gaussian process models for perception and preferences", https://openreview.net/forum?id=oUZ5JweNRc . It's essentially hooking a DDM model up into a Gaussian process bandit. Similar in concept though the mechanics and application area are of course quite different.	Summary: The submission proposes to use response times to obtain additional information from participants in preference learning settings. They apply a variant of the Drift-Diffusion Model, a popular model of human decision making from psychology, and combine it with an algorithm applicable to linear bandits. In asymptotic analysis and application to real data, they demonstrate the benefits of taking advantage of response times, especially for queries with large value differences. Strengths: I think this is a very sensible approach to improving preference learning, considering the fact that response times can be available "for free" from existing preference learning paradigms. I also think the application of a simplified variant of the DDM (EZ-Diffusion) as a way to get an analytic handle on things is also a good idea, and I think the results are compelling. It's a good paper, and I enjoyed reading it. Weaknesses: * I think the paper slightly misrepresents the actual model it's using. Unless I'm missing something, the DDM is usually defined as the first passage time of a two-boundary Wiener process, and the likelihood of a RT under that model involves solving an SDE which has no closed-form solution. However, moments of the DDM RT distribution are available, which is what enables approaches that use them to approximately solve for parameters (this includes the E-Z Diffusion model of Wagenmakers et al., the current contribution (as far as I can tell), as well as the related work of Shvartsman et al. 2023 (arxiv:2306.06296). I think using E-Z diffusion type approaches is great, I just think the paper shouldn't represent them as the full DDM. Also note that the E-Z diffusion line of work provides for closed-form estimation of nondecision time (by estimating drift (i.e. value difference) based on response time variance, and then backing into the response time mean from there -- this might help address the issue of unknown nondecision time identified by the authors. * Related to the above, moving away from the simplifying assumption of E-Z diffusion would introduce the concern of other unknown DDM parameters such as drift variability, nonsymmetrical initial conditions, etc. Technical Quality: 4 Clarity: 3 Questions for Authors: * Why should choice-only would ever do better asymptotically. L186 makes this claim w.r.t. section 3.2 but I don't see it in the figure -- the orange lines (dashed or solid) seem always above the gray lines. * For figure 2, if possible it should be moved below section 3.2., so that it can be interpreted after the asymptotic min-weight of both estimators has been discussed. This is also the part of the submission which is most confusing -- mental calisthenics are needed to map from asymptotic min-weight to the variance of theta estimates and therefore to the influence of observations at various value differences. Another editing / clarification pass could be helpful. Additional notes: * All figure axis tick labels are very tiny, should ideally be larger. In addition, adding color legends in fig 4 (outside the caption) would help with readability. Confidence: 5 Soundness: 4 Presentation: 3 Contribution: 4 Limitations: Discussed and addressed, even with additional analyses (and as noted above, the limitation regarding nondecision time might be possible to work around, though I could be missing something there). Flag For Ethics Review: ['No ethics review needed.'] Rating: 8 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your detailed and positive review. We appreciate your constructive feedback and are glad you enjoyed the paper. We will reorganize the theoretical sections and figure presentation as suggested. ## Weakness: about EZ-DDM vs DDM and EZ-DDM's assumptions Thank you for pointing out the distinction between DDM and EZ-DDM [1]. We will ensure that our language in the paper accurately reflects this difference. Our work indeed adopts the assumptions of EZ-DDM, including deterministic starting points (zero-valued), drift, and non-decision time. Lifting these assumptions within the bandit framework could be a fruitful direction for future research. As mentioned, our work assumes known non-decision time for simplicity. We appreciate your reference to EZ-DDM's procedure for estimating non-decision time (Eq.9 of [1]), and we agree that integrating this method with our approach is a promising avenue for future work. One reason we have not yet incorporated this method is that the estimation procedures in [1] and [2] treat each query’s non-decision time separately. In contrast, our work, following [3], assumes a common non-decision time across all queries. A potential future direction is to aggregate data across queries via the common non-decision time, similar to how we aggregate data in our current draft via the linear utility structure. To compare our estimator with those in [1], consider the estimation of the drift $u_x$ for a query $x$. Our choice-and-response-time estimator (Eq. 4 in our draft) becomes the ratio of the expected choice and the expected response time. In contrast, [1]'s estimator (Eq. 5 in [1]) is based solely on the choices' log-odds, $\log\left(\mathbb{P}(c_x=1)/(1-\mathbb{P}(c_x=1))\right)$. As our non-asymptotic analysis in `Author Rebuttal` indicates, our estimator can perform better for easy queries, while the choice-based estimator may be more effective for hard queries. When the utilities are parameterized linearly, our choice-and-response-time estimator is Eq. 4 in our paper draft, whereas [1]'s estimator becomes Eq. 5 in our paper draft. Our asymptotic analysis in Theorems 3.1 and 3.2 again highlights that using response times can be beneficial for easy queries. - [1] [Wagenmakers et al. 2007](https://link.springer.com/article/10.3758/BF03194023) - [2] [Berlinghieri et al. 2023](https://www.science.org/doi/10.1126/sciadv.adf1665) - [3] [Clithero (2018)](https://www.sciencedirect.com/science/article/abs/pii/S0167268118300398}) ## Question: why choice-only could perform better asymptotically? Given some arm $y\in\mathcal{Z}$, we use asymptotic variance to measure how much the estimated utility $y^T\widehat{\theta}$ varies around the true utility value $y^T\theta^$ when the sample size is very large. Our goal is to compare the asymptotic variance of the choice-response-time estimator to that of the choice-only estimator. Both estimators' asymptotic variances depend on how much information the estimator retain from the data, i.e. human responses to queries $x\in \mathcal{X}\_{sample}$. The choice-response-time estimator and the choice-only estimator retain different aspects of information from $x$. Intuitively, choices retain the "sign" of the utility difference $x^T\theta^$, while response times retain the preference strength. The "amount" of information they retained is formally presented as the weights $\mathcal{M}\_{CH,DT}$ and $m_{CH}$ in Theorems 3.1 and 3.2, respectively. Higher values of these terms indicate more retained information, leading to lower variance and better estimation. We compare the weights $\mathcal{M}\_{CH,DT}$ and $m_{CH}$ in Theorems 3.1 and 3.2. The choice-only estimator assigns each query $x$ a weight $m_{CH}(x^T\theta^)$, represented by the gray curve in Figure 2. In contrast, the choice-response-time estimator assigns all queries the same weight $\mathcal{M}\_{CH,DT}\coloneqq\min_{x}m_{CH,DT}(x^T\theta^)$, with $m_{CH,DT}(x^T\theta^)$ plotted as the orange curve in Figure 2. While the orange curve is consistently higher than the gray curve, indicating that $m_{CH,DT}(x^T\theta^)>m_{CH}(x^T\theta^)$ for each query $x$, the choice-response-time estimator's weight is $\mathcal{M}\_{CH,DT}$, not $m_{CH,DT}(x^T\theta^)$. Consequently, $\mathcal{M}\_{CH,DT}$ may be larger or smaller than $m_{CH}(x^T\theta^)$ depending on the queries in the data. For instance, if the data contains both hard queries where $x^T\theta^\in[-1,1]$ and one easy query where $x^T\theta^*=4$, the choice-response-time estimator will have small weights for all queries due to the "min" in the definition of $\mathcal{M}\_{CH,DT}$, while the choice-only estimator will have large weights for hard queries even if the easy query exists. In this scenario, the choice-only estimator may perform better. Conversely, if the data only contain easy queries, the choice-response-time estimator will have a larger weight, making it superior. Finally, we would like to note that the "min" in the definition of $\mathcal{M}\_{CH,DT}$ is a result of our proof techniques. It is possible to obtain tighter theoretical analysis, and we leave it for future work. --- Rebuttal Comment 1.1: Comment: I appreciate the clarifications regarding EZ-DDM and the asymptotic behavior of the choice-only strategy. I recommend that the authors try to make room for both clarifications (the distinction between the paper's approach and EZ-DDM's estimators, and the limiting case where response times don't help) in the main text or at least the supplement, alongside the other minor reorganizations. I'm happy to see that the other reviewers agree that this is a good paper. I will add more and say that it's the most straightforwardly applicable approach to using response times in preference learning that I've seen (without requiring MCMC sampling, likelihood approximations, or funky numerics), and the only one with any sort of non-vacuous theoretical guarantees. As such, it's the most likely to have impact more broadly (e.g. on current "hot" areas like RLHF). I have raised my rating by a point accordingly, and hope to see it at the conference.	Summary: This paper studies whether leveraging human response times can lead to better performance in bandit learning from preference feedback. More specifically, the paper integrates the drift-diffusion model (DDM) from psychology into the best-arm identification problem in linear bandits. Given a fixed interaction time, the goal is to utilize response times alongside binary choices so as to maximize the probability of recommending the optimal arm. The paper introduces an estimator of the preference/reward vector using both binary responses and response times via linear regression. This estimator can be incorporated into bandit algorithms. Asymptotic normality results and three simulations indicate that this new estimator leveraging response times can make easier queries more useful, in comparison with traditional estimators that only use binary responses. Strengths: - The studied problem seems novel, interesting, and relevant to the community. To my knowledge, DDMs have not been (widely) explored in bandits and reinforcement learning, although I am not very familiar with the DDM literature in psychology and neuroeconomics. This model may be of particular interests to researchers studying dueling bandits and RLHF. - The model leads to a simple and clean estimator of human preferences $\theta^$, which uses both binary preference feedback and response times. To my understanding, this estimator can be integrated into various bandit algorithms, not limited to ones for best-arm identification. - The paper presents both theoretical and empirical evidence on the role of response times, and discusses the intuition behind when/why they can be useful. - The paper is well-organized and well-written. It is a joy to read. Weaknesses: - It would be helpful to see more discussion on related work, especially on DDMs and race models. For example, what evidence has been given in the psychology literature that DDMs can explain the human decision-making process? What are the typical objectives in papers that study DDMs, and how are they different from the best-arm identification problem in this work? Have DDMs been considered in bandits and reinforcement learning? - On the theoretical side, there are no non-asymptotic results regarding the performance of the bandit algorithm, such as bounds on the error probability. - On the empirical side, only one dataset contains the response times of the participants. The last two experiments simulate response times according to the DDM -- it is reasonable to expect that they are then useful to estimating $\theta^$. The algorithm also has a hyperparameter that requires tuning. Technical Quality: 3 Clarity: 4 Questions for Authors: See above for questions on related work. I am also curious -- the estimator that uses only binary responses essentially assumes the Bradley-Terry model, if my understanding is correct. Looking at the logistic sigmoid function, I can see that the when $x^\top \theta^*$ is away from 0, the curve becomes flat and therefore not much information can be gained here. Have you considered other noise models that do not use a link function like the logistic sigmoid function? Would you expect similar behavior? Confidence: 3 Soundness: 3 Presentation: 4 Contribution: 3 Limitations: Limitations have been discussed. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your detailed and thoughtful review. We appreciate your recognition of the novelty of our work and positive feedback on the writing. Here are our responses to your concerns and questions: ## Weakness: non-asymptotic result In our paper draft, we provide asymptotic theoretical results to show the following intuition on why response time can improve the learning performance: Combining response times and choices, information from easy queries can be extracted more efficiently. This is not possible using choices only. We added non-asymptotic error probability on estimating reward $x^{\top}\theta^/a$ for every query $x$ using both methods, i.e. combining response times with choices and using choices only. Similar intuition can be confirmed as is shown in the `Author Rebuttal' section. We leave for future work to provide non-asymptotic error probability for the entire algorithm (Algoithm 1 in the paper). ## Weakness: real-world empirical result We included a new simulation study based on another dataset of human choices and response times in the `Author Rebuttal` section. This study shows that incorporating response times improves best-arm identification performance. ## Weakness+question: background of DDM models We plan to include the following summary of DDM literature in the appendix: #### 1. Literature on modeling choices and response times Bounded accumulation models (BAMs) capture the human decision-making process with an accumulator and a stopping rule. For binary choices, DDM [1] models the human's speed-accuracy trade-off with one accumulator, fixed barriers, random starting points, drift, and non-decision times. Our paper adopts EZ-DDM [3], a simplified version with deterministic parameters. DDM with time-decaying barriers theoretically connects to human Bayesian RL models [5]. DDMs also characterize human attention during decision-making, by modeling choices, response times, and eye gazes on options or attributes [7]. Race models [4] extends to queries with more than two options by assuming an accumulator for each option and stopping when any accumulator reaches its threshold. Neurophysiological evidence supports BAMs. EEG recordings show neurons exhibit accumulation processes and decision thresholds [2][6]. #### 2. Literature on using response times (survey [10]) Response times improve choice prediction. [8] showed the full DDM predicts choice probabilities better than the logit model. [9] proved that response times could enhance the identifiability of human preferences, compared to choices alone. Another application of response times is enhancing AI agents' decision-making. Dueling bandits and preference-based RL [14] typically use human choice models for preference elicitation. One popular choice model, the random utility model, can be derived from certain BAMs [9]. For example, both the Bradley-Terry model and EZ-DDM yield logistic choice probabilities (Eq.1 in our paper). To the best of our knowledge, our work* is the first to leverage this connection to integrate BAMs within the framework of bandits (and RL). Note that our work lets the AI agent use RL to make decisions, which is different from [13] which models the human as an RL agent. - [[1] Ratcliff and McKoon 2008](https://ieeexplore.ieee.org/abstract/document/6796810) - [[2] Webb 2019](https://pubsonline.informs.org/doi/abs/10.1287/mnsc.2017.2931) - [[3] Wagenmakers et al. 2007](https://link.springer.com/article/10.3758/bf03194023) - [[4] Usher and McClelland 2001](https://psycnet.apa.org/record/2001-07628-003) - [[5] Fudenberg et al. 2018](https://www.aeaweb.org/articles?id=10.1257/aer.20150742) - [[6] Ratcliff et al. 2016](https://www.cell.com/trends/cognitive-sciences/abstract/S1364-6613(16)00025-5) - [[7] Krajbich 2019](https://www.sciencedirect.com/science/article/abs/pii/S2352250X18301866) - [[8] Clithero 2018](https://www.sciencedirect.com/science/article/abs/pii/S0167268118300398) - [[9] Alós-Ferrer et al. 2019](https://www.journals.uchicago.edu/doi/full/10.1086/713732) - [[10] Clithero 2018.](https://www.sciencedirect.com/science/article/abs/pii/S0167487016306444) - [[13] Pedersen et al. 2017](https://link.springer.com/article/10.3758/s13423-016-1199-y) - [[14] Bengs et al. 2021](https://www.jmlr.org/papers/volume22/18-546/18-546.pdf) ## Question: about other link functions that models human choices First, the EZ-DDM model's marginal distribution for choices (Eq.1 in our draft) coincides with the Bradley-Terry model. Therefore, we have adopted the logistic link function to form a fair comparison. Second, let's explore beyond the logistic link function. Suppose that the choice probability $\mathbb{P}[z_1\succ z_2]=\sigma(u_{z_1},u_{z_2})$, where $\sigma$ is a link function depending on the utilities $u_{z_1}$ and $u_{z_2}$. If we fix $u_{z_2}$ and only vary $u_{z_1}$, the function $\sigma(\cdot,u_{z_2})$ is known as a psychometric function, typically "S" shaped (see Fig.1.1 in [2]). This "S" shape means that as the human's preference strength becomes very large or very small, $\sigma(\cdot,u_{z_2})$ becomes flat and less informative, as you mentioned. In these circumstances, response times can be very helpful. Lastly, if we further assume that $\sigma$ depends only on the utility difference, $u_{z_1}-u_{z_2}$, this $\sigma$ becomes the link function commonly adopted in the preference learning literature. According to Sec.3.2 of [1], the usual assumptions are that $\sigma$ is strictly monotone in $(u_{z_1}-u_{z_2})$ and bounded within $[0, 1]$. Thus, as the utility difference becomes very large or very small, $\sigma(u_{z_1}-u_{z_2})$ becomes flat, so the same intuition holds. - [[1] Bengs et al. 2021](https://www.jmlr.org/papers/volume22/18-546/18-546.pdf) - [[2] Stochastic Choice Theory, Econometric Society Monograph](https://scholar.harvard.edu/sites/scholar.harvard.edu/files/tomasz/files/manuscript_01.pdf) --- Rebuttal Comment 1.1: Comment: Thank you for your detailed responses. I have updated my confidence score to 3 and intend to maintain my rating.	Rebuttal 1: Rebuttal: We address the two major concerns raised by multiple reviewers: the limited use of real-world datasets and the lack of non-asymptotic results. ## 1. New Simulation on a Real-world dataset We present new simulation results based on another real-world response time dataset. This dataset [1] contains human binary choices and response times. In each query, each arm consists of two food items, and the human has an equal chance of obtaining either item after choosing that arm. For each user, we construct a bandit instance where the feature vector for each arm is composed of the user's ratings of the food items, augmented via second-order polynomials. For each user, an EZ-DDM is identified via Bayesian MCMC and then used as a simulator to generate human feedback. We compare the best-arm-identification errors over $100$ repetitions for three algorithms: 1. Transductive design with our choice-and-response-time estimator, denoted by $\left(\lambda\_{trans},\widehat{\theta}\_{CH,DT}\right)$. 2. Transductive design with a choice-only estimator, denoted by $\left(\lambda\_{trans},\widehat{\theta}\_{CH}\right)$. 3. Hard-query design with a choice-only estimator, denoted by $\left(\lambda\_{hard},\widehat{\theta}\_{CH}\right)$. The results are plotted in Fig. 1 of our rebuttal PDF document. As shown, under various budgets and participant indices, incorporating response times (method (1), plotted in red) outperformed the other two methods. ## 2. New Non-asymptotic Analysis We added lemmas stating non-asymptotic error probabilities on estimating the utility difference $x^{\top}\theta^/a$ using both methods, i.e. combining response times with choices and using choices only. The results convey the same intuition as in the Thm. 3.1 and 3.2 in our draft: Response times make easy queries more useful. In other words, combining response times and choices, information from easy queries can be extracted more efficiently. This is not possible using choices only.* We analyzed the non-asymptotic concentration for the utility difference estimated as the ratio between the empirical mean of choices and the empirical mean of response times, which appears on the right-hand side of Eq. 4 in our paper draft. The error probability for such choice-and-response-time estimator is as follows: Lemma 1. Consider any query $x\in\mathcal{X}$. For any scalar $\epsilon_r$ satisfying \begin{equation}\begin{split} \epsilon_r \leq \min\left\\{\frac{x^{\top}\theta^}{\sqrt{2}a}, \frac{(1+\sqrt{2})ax^{\top}\theta^}{\mathbb{E}[t_x]}\right\\} \end{split}\end{equation} we have that \begin{equation}\begin{split} \mathbb{P}\left(\left\|\frac{\sum_{i\in[n_x]} c_{x,i}}{\sum_{i\in[n_x]} t_{x,i}} - \frac{x^{\top}\theta^}{a}\right\| > \epsilon_r\right)\leq 4\exp\left(-\frac{\left(\mathbb{E}[t_x]/(\sqrt{2}+2)\right)^2}{2} n_x\epsilon_r^2\right). \end{split}\end{equation} Alternatively, utility difference (or DDM drift) can be estimated using choices only (Eq. 5 in [1]). Converting $\mathbb{E}[c_x]\in[-1,1]$ to $\mathbb{E}[(c_x+1)/2]\in[0,1]$ and applying the logit function $h^{-1}(p)\colon=\text{logit}(p)=\log\left(p/(1-p)\right)$ estimates $2ax^{\top}\theta^$. The error probability for such choice-only estimator is as follows: Lemma 2. Consider any query $x\in\mathcal{X}$. We have that \begin{equation}\begin{split} \mathbb{P}\left(\frac{h^{-1}\left(\mathbb{E}[(c_x+1)/2]\right)}{2a^2}-\frac{x^{\top}\theta^}{a} > \epsilon_r\right) \leq \exp\left(-\frac{\left(4a^2h'(2ax^{\top}\theta^)\right)^2}{2}n_x\epsilon_r^2\right). \end{split}\end{equation} Here $h(x) = 1/\left(1+\exp(-x)\right)$. For easy queries with $x^{\top}\theta^* \gg 1$, the factor $4a^2h'(2ax^\top\theta^)$ in Lemma 2 is significantly smaller than factor $\mathbb{E}[t_x]/(\sqrt{2}+2)$ in Lemma 1. As a result, with $x^{\top}\theta^\gg 1$, error probability of our estimation with both response times and choices is much smaller than that of the choice-only estimation. The aforementioned two factors are plotted as functions of the utility difference $x^{\top}\theta^*$ in Fig. 2 of our rebuttal PDF document. Recall that this plot of non-asymptotic results looks similar to Fig. 2 (asymptotic results) in our paper draft. Indeed, they convey similar insights. In particular, When the human conservative parameter $a$ is small, for hard queries, the gray curve is slightly higher than the orange one, indicating that only using choices is slightly better. When $a$ is large, the gray curve is higher only for hard queries, while lower for easy queries. This conveys a similar insight as our Thm. 3.1 and 3.2, that using choice is better for hard queries, while using response time makes easy queries more useful. - [[1] Wagenmakers et al. 2007](https://link.springer.com/article/10.3758/bf03194023) Pdf: /pdf/97bb677949576d16f91b0d6f4d3a1b133dd86e04.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Segment Anything without Supervision	Accept (poster)	Summary: This paper presents Unsupervised SAM (UnSAM) for interactive and automatic whole-image segmentation which does not require human annotations. This method uses top-down clustering and bottom-up merging to obtain multi-granularity pseudo labels for supervised SAM training. This unsupervised training of SAM achieved good performance on specific datasets. In addition, this paper finds that SAM can achieve better performance by combining pseudo labels and a small amount of GT from SA-1B for model training. Strengths: 1. The results of this paper are solid. 2. The improvement of the paper on SAM is significant, both in terms of quantitative and partial qualitative results provided. Weaknesses: 1. The motivation of this work is to extend SAM, but it has not been experimentally proven that unsupervised training of UnSAM outperforms fully supervised SAM by continuously increasing the size of the dataset. Instead, it only provides better semi-supervised results. 2. The method used in this paper is very similar to the one published a year ago in [1], which first proposed unsupervised interactive segmentation using top-down clustering and bottom-up merging to obtain hierarchical masks for training interactive segmentation models. I believe that the author needs to provide a clear difference in design compared to [1], rather than just details or differences in model structure and source data. 3. The paper lacks tests of interactive segmentation performance, such as evaluation of NoC (number of clicks) metrics, and should provide a comparison with previous interactive segmentation methods, such as SimpleClick [2] and its subsequent improvement work, etc. [1] Li, Kehan, et al. "Multi-granularity interaction simulation for unsupervised interactive segmentation." Proceedings of the IEEE/CVF International Conference on Computer Vision. 2023. [2] Liu, Qin, et al. "Simpleclick: Interactive image segmentation with simple vision transformers." Proceedings of the IEEE/CVF International Conference on Computer Vision. 2023. Technical Quality: 2 Clarity: 4 Questions for Authors: See weaknesses for details. If the author can answer the above questions positively, especially question 2, I will consider raising the score. Confidence: 5 Soundness: 2 Presentation: 4 Contribution: 2 Limitations: The problems mentioned in the paper do exist and are difficult to solve, and unsupervised pseudo noise is difficult to avoid. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Dear Reviewer ecwU, thank you for your insightful comments, and we really appreciate that you are willing to increase our score if we can answer the questions positively. We will provide detailed responses to each of them below. [W1] It Has Not Been Experimentally Proven that Unsupervised Training of UnSAM Outperforms Fully Supervised SAM by Continuously Increasing the Size of the Dataset. Thanks for your question. We respectfully argues that surpassing the heavily supervised segmentation model SAM with an unsupervised model like UnSAM is not trivial. We are pleased to report that UnSAM's performance improves with an increase in training samples—from 0.1% of SA-1B to 0.4% of SA-1B. We found that by increasing the training samples to 0.4% and using a larger backbone, UnSAM's performance already surpasses that of SAM. \| Methods \| Setting \| # imgs \| Avg. \| COCO \| LVIS \| ADE \| Entity \| SA-1B \| Part-IN \| PACO \| \|:-------- \| :-------- \| :-------- \| --------:\| --------:\| --------:\| --------:\| --------:\| --------:\| --------:\| --------:\| \| SAM \| Supervised \| 11M \| 42.1 \| 49.6 \| 46.1 \| 45.8 \| 45.9 \| 60.8 \| 28.3 \| 18.1 \| Prev. UnSup. SOTA \| Unsupervised \| 0.2M \| 30.1 \| 30.5 \| 29.1 \| 31.1 \| 33.5 \| 33.3 \| 36.0 \| 17.1 \| UnSAM (RN-50) \| Unsupervised \| 0.1M \| 39.2 \| 40.5 \| 37.7 \| 35.7 \| 39.6 \| 41.9 \| 51.6 \| 27.5 \| UnSAM (RN-50) \| Unsupervised \| 0.4M \| 41.1 \| 42.0 \| 40.5 \| 37.5 \| 41.0 \| 44.5 \| 52.7 \| 29.7 \| UnSAM (ViT-B) \| Unsupervised \| 0.4M \| 43.0 \| 44.0 \| 42.7 \| 37.2 \| 44.4 \| 47.2 \| 55.1 \| 31.1 \| vs. Prev. SOTA \| - \| - \| +12.9 \| +13.5 \| +13.6 \| +6.1 \| +10.9 \| +13.9 \| +19.1 \| +14.0 Due to limitations in computing resources, completing the model training on the full 100% SA-1B dataset could take over two months, which may not be feasible within a short rebuttal period. However, the current results already show that UnSAM performs better than SAM on average across seven datasets. We are confident that these performance gains over SAM will further increase as we continue training with more samples. [W2] Difference in Design Compared to MIS - High-level Main Differences in Methods: Unlike MIS, which employs top-down clustering primarily for selecting proposals WITHOUT the capability to discover new objects missed by bottom-up clustering methods. In contrast, both bottom-up and top-down clustering in our divide-and-conquer strategy contributes to discovering new objects and parts within an image. This leads to two significant distinctions: 1) Bottom-up clustering relies heavily on low-level features like color and texture, resulting in lower-quality pseudo-masks for instance and semantic segmentation, particularly when dealing with disconnected or overlapping instances. 2) The bottom-up clustering in MIS merges only adjacent groups, often resulting in incomplete segmentation of instances with disconnected parts. - Minor Differences in Bottom-up Clustering: While MIS utilizes a cut-based method for bi-partitioning the affinity matrix, our approach employs mean-shift clustering, which leverages cosine similarity for merging groups into larger entities. This makes our method more resilient to noise and outliers in the training data. - Model Performance: To ensure a fair comparison, we trained UnSAM using the same model as MIS, ViT-Base, and present the NoC@85 results below: \| Methods \| GrabCut (NoC@85 ↓) \| Berkeley (NoC@85 ↓) \| SBD (NoC@85 ↓) \| DAVIS (NoC@85 ↓) \| \|:-------- \| --------:\| --------:\| --------:\| --------:\| \| MIS (unsupervised) \| 1.94 \| 3.09 \| 6.91 \| 6.33 \| \| UnSAM (unsupervised) \| 1.39 \| 1.42 \| 3.04 \| 4.02 \| \| SimpleClick (supervised) \| 1.40 \| 1.44 \| 3.28 \| 4.10 \| \| UnSAM+ (semi-supervised) \| 1.30 \| 1.37 \| 2.74 \| 3.11 \| The results for MIS and SimpleClick are copied directly from MIS. Our unsupervised model UnSAM significantly surpasses the previous state-of-the-art in unsupervised interactive segmentation and delivers performance comparable to the supervised SimpleClick. And the semi-supervised model UnSAM+ greatly surpasses the SimpleClick model. It's important to note that datasets such as GrabCut, Berkeley, SBD, and DAVIS are easier and primarily focus on instance and semantic-level masks, typically labeling only a few dominant instances in each image. Consequently, we observe larger performance improvements on the MSCOCO dataset, as detailed in the following table. [W3] Comparisons with SimpleClick Thank you for introducing us to SimpleClick! Beyond the results shared earlier, we have also measured the 1-IoU for SimpleClick on the MSCOCO dataset and present the results below: \| Methods \| Setting \| 1-IoU \| \|------------\|-------------------\|--------\| \| SimpleClick\| Supervised \| 52.3 \| \| SAM \| Supervised \| 68.2 \| \| UnSAM \| Unsupervised \| 59.5 \| \| UnSAM+ \| Semi-supervised \| 69.5 \| Our unsupervised model, UnSAM, outperforms the supervised SimpleClick by over 7%, and these gains increase to 17.2% under a semi-supervised setting. The more significant performance improvement on MSCOCO, compared to datasets like GrabCut, Berkeley, SBD, and DAVIS, can be attributed to MSCOCO's complexity with numerous small and heavily overlapped instances, which presents a greater challenge than the datasets frequently used for interactive segmentation studies. Hope our explanation and experiments can address your inquiries. We will integrate all your valuable comments into our revision! --- Rebuttal Comment 1.1: Comment: Thank you for the response from the authors. I agree with the performance of unSAM. However, I still have some doubts about the novelty of the method, i.e. W2. MIS uses the bottom-up merging strategy to generate pseudo-labels. I think that it is able to merge features of non-adjacent groups according to SSE Cost in MIS. The top-down sampling in MIS is to balance the sampling probability of multi-granularity masks during training, which is indeed different from unSAM. So I'll clarify my question again. I think unSAM's bottom-up clustering is very similar to MIS's bottom-up merging, except that unSAM further subdivides the instance masks produced by top-down clustering. In fact, the result of bottom-up merging contains masks of various granularities (including instance-level masks), so it seems that top-down clustering is not necessary. But I would still consider raising my score, and if the author has time, could you provide some information on how much unSAM performance would be degraded by using only MIS bottom-up merging to generate the mask? --- Reply to Comment 1.1.1: Title: Thank you for considering to raise the score! Comment: Dear Reviewer ecwU, We are thrilled to hear that you are considering raising the score! Regarding your additional questions about the potential degradation in UnSAM's performance when using only a bottom-up merging approach to generate masks, we have conducted experimental evaluations. We assessed the quality of pseudo-masks generated solely through a bottom-up clustering method on 1,000 images from SA-1B. The results are presented in the table below: \| Method \| AR \| AR$_S$ \| AR$_M$ \| AR$_L$ \| \|-------------------------------\|------\|--------\|--------\|--------\| \| Bottom-up Clustering \| 16.5 \| 5.7 \| 16.1 \| 23.0 \| \| Bottom-up + Top-down Clustering \| 23.9 \| 7.9 \| 22.4 \| 34.0 \| The result clearly illustrates that incorporating both bottom-up and top-down clustering methods in our divide-and-conquer strategy significantly enhances performance compared to using bottom-up clustering alone. Notably, the most substantial gains are observed in AR$_L$, underscoring our discussion in the rebuttal that top-down clustering often identifies more instance/semantic-level masks compared to bottom-up methods alone. Unfortunately, due to the limited time for the discussion period, we were unable to complete pseudo-mask generation and segmentation model training for all training samples. However, we anticipate that the performance gains post-model training will align closely with the quality of the pseudo-masks. Thank you again for your feedback! Please let us know if there are any more questions. We hope you have a wonderful day! Best regards, UnSAM Authors	Summary: The paper presents Unsupervised Segment Anything Model (UnSAM) for image segmentation whose training does not have access to human annotations. UnSAM employs a divide-and-conquer approach to hierarchically segment the image. In the divide stage, it uses CutLER [39] to obtain masks, and in the conquer stage, it applies an iterative merging method from SHOES [6]. The proposed method achieves SOTA results. Strengths: This proposed approach achieves good image segmentation results. Weaknesses: 1. Unclear technical contributions -- limited novelty: The paper uses existing work, including CutLER, SHOES, DINO and Mask2former. The key differences are not explained (well), beyond that these existing methods are put together for unsupervised image segmentation. 2. The performance gain seems to come from additional thresholds used (Lines 130, 142) and potentially unfair comparisons (please see the point 3 and the Questions section below). The thresholds are set in an ad hoc manner. 3. Backbone comparison: In Section 4 (UnSAM), Line 139, the paper mentions using the DINO pre-trained ViT-B/8 encoder, yet none of the tables show results with the ViT-B backbone. Recent methods (e.g., SOHES and SAM) use the ViT-B/8 backbone. A fair comparison with these methods should use the same backbone. Although one might argue that RN-50 and Swin-Tiny (used in this paper) are lighter backbones, using ViT-B/8 would provide a fair comparison. 4. Clarity can be improved: - 4.1. Inconsistent Figure Caption: In Figure 1, the caption and figure are not consistent. The caption states “UnSAM (row 2) and SAM (row 3)”, but the figure shows SAM in row 2 and UnSAM in row 3. It is unclear which result corresponds to which method. - 4.2. Key Distinctions: The second part of “Key distinctions over prior works on pseudo-mask generation,” Line 167, is unclear. The paper summarizes SOHES [6] but does not explain novelty of the proposed work. 5. Additional comparisons (optional): The paper could be improved by including another comparison with "Unsupervised Universal Image Segmentation," CVPR 24 (published after the NeurIPS deadline, though). Technical Quality: 3 Clarity: 2 Questions for Authors: 1. The original CutLER uses ImageNet for unlabeled training, while UnSAM uses the SA-1B dataset. Since the proposed method and baseline use different training data, it is unclear if the proposed method is truly better. Similarly, for the comparison with SOHES on the 0.2M data, did both methods use the same set of 0.2M images? 2. If different sets of 2% unlabeled training data from SA-1B are used, are the results stable? Are the threshold hyperparameters in UnSAM robust to variations of the selected training data? 3. What does “the two extreme cases” in Line 169 refer to? Confidence: 5 Soundness: 3 Presentation: 2 Contribution: 2 Limitations: The paper lacks a limitation section. Including a discussion on failure cases would improve the paper. Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Dear Reviewer wivK, we appreciate your invaluable insights and thoughtful comments. In the following sections, we address the questions you have raised: [W1.1] Technical Contributions Please check our answers in the global rebuttal. Thank you! [W1.2] Differences with Prior Works We explained the key differences between UnSAM and prior works (e.g. CutLER and SOHES) in lines 162-173, and described the distinctions in the global rebuttal. Thank you! [W2] Performance Gain Comes From Additional Thresholds Used? Since SOHES didn't release its codes, models and data, we reproduced SOHES's results and reported the results of SOHES using exactly the same threshold settings as below: \| Pseudo-Labeling \| Threshold Setting \| AR \| AR$_S$ \| AR$_M$ \| AR$_L$ \| \|:-------- \|:-------- \| --------: \| --------: \| --------: \| --------: \| \| SOHES (reported) \| Official \| 16.4 \| 6.0 \| 15.8 \| 22.6 \| \| SOHES (reproduced) \| Official \| 16.5 \| 5.7 \| 16.1 \| 23.0 \| \| SOHES (reproduced) \| Ours \| 16.8 \| 6.1 \| 16.2 \| 22.9 \| \| UnSAM \| Ours \| 23.9 \| 7.9 \| 22.4 \| 34.0 \| The performance gain from using additional thresholds is marginal, at only about 0.3%. These results indicate that it is our divide-and-conquer strategy, not the threshold settings, that contributes to the significant performance improvements over SOHES. [W3.1] UnSAM Uses a Smaller Backbone (RN-50 / Swin-Tiny) and May be Unfair The results for UnSAM reported in the paper were obtained using a significantly smaller backbone and fewer training samples than those used for SAM, placing our method at a disadvantage. To fully address your question, we conducted additional experiments using a larger backbone, ViT-Base, and have presented the comparative results on SA-1B below: \| Method \| Backbone \| Training Data \| AP \| AR \| \|:-------- \|:--------: \| --------: \| --------:\|--------:\| \| SAM \| ViT-Base \| 11M SA-1B \| 38.9 \| 60.8 \| UnSAM+ \| RN50 \| 0.1M SA-1B \| 42.8 \| 64.8 \| UnSAM+ \| ViT-Base \| 0.1M SA-1B \| 44.6 \| 67.2 UnSAM demonstrates superior performance with a larger backbone, outperforming SAM in terms of both Average Precision (AP) and Average Recall (AR), despite being trained on significantly fewer samples. [W3.2] ViT-Base in Line 139 is a typo. It will be addressed in the revision, thank you for pointing it out! [W4.1] Inconsistent Figure Caption: Thank you for pointing this out! We will correct the figure caption accordingly. UnSAM's results are displayed in row 3, while SAM's results are in row 2. [W4.1] Clarification on Key Distinctions with SOHES Compared to SOHES, UnSAM has 1) better segmentation quality for coarse-grained instance/semantic-level masks. 2) better segmentation quality for fine-grained sub-part masks. For detailed explanations of these improvements, please refer to our responses in the global rebuttal. [W5] Additional Comparisons with U2Seg Nice question! We have included the comparisons with U2Seg as below: \| Methods \| Venue \| Backbone \| MSCOCO \| SA-1B \| Part-ImageNet \| \|:-------- \|:--------: \| --------: \| --------:\| --------:\| --------:\| \| CutLER \| CVPR 2023 \| RN-50 \| 28.1 \| 17.0 \| 28.7 \| U2Seg \| CVPR 2024 \| RN-50 \| 27.5 \| 19.3 \| 29.1 \| SOHES \| ICLR 2024 \| ViT-Base \| 30.5 \| 33.3 \| 36.0 \| UnSAM \| Ours \| RN-50 \| 42.0 \| 44.5 \| 52.7 UnSAM outperforms CutLER, U2Seg and SOHES by a large margin on all experimented benchmarks. [Q1 Q2] Did UnSAM and SOHES Use the Same Set of 0.2M Images? If Different Sets of 2% Unlabeled Training Data From SA-1B Are Used, Are The Results Stable?* Unfortunately, SOHES has not released their codes, models, and training data, preventing us from using the identical set of 0.2M images. However, our results remain robust when training the model with different subsets of 0.2M images. \| Methods \| Seed \| MSCOCO \| SA-1B \| Part-ImageNet \| \|:-------- \| --------: \| --------:\| --------:\| --------:\| \| Prev. SOTA \| - \| 30.5 \| 33.3 \| 36.0 \| UnSAM \| 1 \| 41.2 \| 43.6 \| 52.1 \| UnSAM \| 2 \| 42.4 \| 44.5 \| 52.7 \| UnSAM \| 3 \| 41.7 \| 44.0 \| 51.8 As shown in the table, we observed that the model's performance remains stable across different sets of 2% unlabeled training data (sampled with 3 different seeds). All three models, each trained with a distinct set, consistently outperformed previous state-of-the-art methods by a large margin. [Q3] What Does “the two extreme cases” in Line 169 Refer To? The term "two extreme cases" refers to the semantic/instance-level masks (the coarsest granularity), and the subpart-level masks (the finest granularity). We will clarify it in the revision. [L1] Limitation Section We discussed UnSAM's limitations in Section A6 of our submission and will highlight this more prominently in the main paper. Specifically, UnSAM struggles with images containing dense, fine-grained details, often missing repetitive instances with similar textures. Additionally, it tends to over-segment images due to the unsupervised clustering method mistaking details like folds and shadows on clothing as distinct entities—a contrast to human annotators who use prior knowledge to disregard such information. This underscores the ongoing challenge for unsupervised methods to match the performance of supervised approaches. Hope our explanation and experiments can address your inquiries. We will integrate all your valuable comments into our revision! --- Rebuttal Comment 1.1: Title: The rebuttal successfully addressed my comments Comment: The authors' response successfully addressed my concerns, and I would like to increase the paper's rating to "weak accept". --- Reply to Comment 1.1.1: Comment: Dear Reviewer wivk, Thank you so much for raising our score from 4 to 6! Hope you have a wonderful day! Best, UnSAM Authors --- Rebuttal Comment 1.2: Comment: Dear Reviewer wivK, Thank you for your thorough review and insightful feedback on our paper. Your input has been instrumental in refining the quality of our work. We are pleased to report that we have carefully addressed each of the concerns you raised. Here's a brief summary of our actions: - Technical Contributions: We have detailed our key technical contributions in the global rebuttal and provided quantitative results that underscore the significant performance improvements these contributions bring. - Ablation Study on Thresholds and Backbones: In response to your comments, we conducted further experiments with various thresholds and backbones. The results, presented in the tables at W2 and W3.1, indicate that a larger backbone significantly enhances our outcomes. - Comparison with U2Seg: We have included a comparison with U2Seg in section W5. The results demonstrate that UnSAM significantly outperforms previous methods in unsupervised image segmentation. - Robustness Across SA-1B Subsets: We have tested our method across various subsets of SA-1B, consistently achieving over 10% performance gains, which validates the robustness of our approach. We remain open and committed to addressing any additional questions or concerns. Your feedback continues to shape our research, and we appreciate your contribution to the improvement of our paper. Please feel free to reach out with further questions or suggestions. We look forward to potentially discussing these matters in greater depth and continuing to refine our work with your valued expertise. Warm regards, UnSAM Authors	Summary: The paper explores a new way to generate hierarchical pseudo-masks to train downstream segmentation models without human annotations. First, the image is segmented using CutLER. Then, within CutLER proposed masks (with cropping and resizing), DINO features are extracted, and patches are iteratively merged based on proximity in cosine distance. The masks are then refined and filtered using CRF/CascadePSP. The pool of pseudo-labels is used to train Mask2Former architecture or Semantic-SAM architecture, for whole-image or prompt-able segmentation tasks, respectively. Additional self-training is performed to improve results. The evaluation is carried out on several datasets using the average recall (AR) metric. UnSAM shows significant improvement over other models in terms of recall of generated masks and final outputs. Strengths: 1) The method presented in the paper shows improved results in unsupervised segmentation. Reducing the recall gap between supervised SAM and unsupervised methods. 2) The additional masks generated using the unsupervised approach in combination with manual annotatons to enhance the performance further, surpassing that of SAM. Weaknesses: #### What is "UnSAM"? The naming scheme adopted in the paper is slightly confusing. UnSAM refers to all: - the hierarchical pseudo-labelling scheme building on top of CutLER, - the distillation of such scheme to Mask2Former architecture, - distillation of such a scheme into semantic-SAM architecture. While it still is possible to parse the results in the tables based on the setting, the ability to understand and scrutinise the text is severely impacted. Note the distinction is important as the output of three of these appears to be different. #### Is AR a sensible metric? The proposed model seems to generate an extremely large amount of masks (up to 2000, L407). While it seems that some useful masks are in this set, the cardinality of the output makes one wonder if it is useful. What is the number of masks used for assessing recall? Is it 1000? Cutler has a setting of 100-200 from published configs. Clearly, increasing the number of masks boosts recall. It is important that the evaluation maintains the same amount of masks for all methods. It also raises a question whether some classical hierarchical segmentation methods such as MCG [A] or Arbelaez et al. [B] would get similar or close performance when such large pool of candidates is allowed. #### What is the effective difference between a proposal and SOHES? The hierarchical merging scheme follows SOHES formulation, with the difference being the CutLER region "proposal" as a constraint. Is that all? It is important to highlight the differences here to both figure out the novelty and correctly attribute improvements in performance to different components/steps of the proposal. Additionally, it appears that distillation to Mask2Former abandons the hierarchical association. Does this mean that the output is no longer organised in a hierarchical manner? #### What makes the method work better than prior works? There is some lack of ablations that explore the influence and sensitivity of various components in the pipeline. The paper only reports on the construction and technical details of the UnSAM methods and the evaluation of this approach. It lacks analysis and insights into what the makes the construction effective. The advancement of knowledge offered by the paper is somewhat limited. #### Are different two different models required? It is not entirely clear why the two modes of operation, "whole image" and "prompt-able" require different models/architectures. Could the Semantic-SAM-based model be prompted in a similar fashion to SAM (i.e. a grid of points) to perform the whole image segmentation? Is this disadvantageos for the whole-image segmentation task? #### Inaccuracies Finally, it is important to note that CascadePSP relies on manual annotations. Thus, unSAM + CascadePSP is _slightly_ supervised. Since UnSAM partly distils CutLER outputs, would it not be more accurate to incorporate the #images used in CutLER to those in UnSAM, writing e.g. 1.4M in Table 1 instead of 0.1M? [Nit] L135: "<...> we employ iterative _merging_ to _decompose_" might require rephrasing as it is currently a slight oxymoron. --- [A] Arbelaez et al. "Multiscale combinatorial grouping" [B] Arbelaez et al. "Contour detection and hierarchical image segmentation" Technical Quality: 2 Clarity: 4 Questions for Authors: The central questions to address in the rebuttal would be around the evaluation protocol. Some more explanation about the contribution of the paper would also be helpful. While the paper presents strong results, the appropriateness of the evaluation protocol is somewhat questionable. Furthermore, there are some questions around the difference of the proposed scheme to prior work, and lack of experiments and analysis to explain it. While a rebuttal can address these issues, I currently rate the paper as a Borderline Reject. Confidence: 4 Soundness: 2 Presentation: 4 Contribution: 3 Limitations: Limitation are appropriately addressed. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Dear Reviewer p86w, thank you for your thoughtful comments. We will provide detailed responses to your questions below: [W1] What is "UnSAM"? Nice suggestion. In the paper, UnSAM stands for Unsupervised Segment Anything Model. The pseudo-labeling strategy discussed in our paper is named as divide-and-conquer. I agree that we can make this clearer, and we plan to designate the terms UnSAM (pseudo), UnSAM (whole-image), and UnSAM (promptable) to distinctly refer to the pseudo-labeling method, whole-image segmentation model, and promptable image segmentation models, respectively. We would appreciate any suggestions you might have! [W2] Why Using AR as One of The Main Evaluation Metrics? Excellent question. We explained the rationale for using AR as a primary evaluation metric in lines 234-238, following previous works like CutLER (CVPR2023) and SOHES (ICLR2024). But why is AR more appropriate than AP for unsupervised segmentation? The main reason is that all human-labeled datasets, including SA-1B, only label a subset of objects, and AR doesn't penalize models for detecting objects not labeled in these datasets. Below is a comparison of results on the MSCOCO dataset that further illustrates why AR is preferred: \| Method \| Venue \| Setting \|Backbone \| Training Data \| AP \| AR \| \|:-------- \|:-------- \|:-------- \| --------: \| --------:\| --------:\| --------:\| \| SAM \| ICCV 2023 \| supervised \| ViT-Base \| 11M SA-1B \| 5.9 \| 49.4 \| \| CutLER \| CVPR 2023 \| unsupervised \| RN-50 \| 1.2M ImageNet \| 6.5 \| 31.4 \| \| SOHES \| ICLR 2024 \| unsupervised \| ViT-Base \| 0.2M SA-1B \| 2.0 \| 30.5 \| \| UnSAM \| Ours \| unsupervised \| RN-50 \| 0.4M SA-1B \| 3.6 \| 42.0 \| \| UnSAM+ \| Ours \| lightly supervised \| RN-50 \| 0.1M SA-1B \| 7.1 \| 52.3 \| Despite SAM's overall better performance, its lower AP compared to CutLER highlights that AP can unfairly penalize models for detecting unannotated objects in evaluation datasets, failing to truly reflect a model’s capabilities. I agree that AR is not without its imperfections, but it is a more suitable metric than AP for unsupervised segmentation. Future research on developing new metrics is needed. [W3.1] The Proposed Model Seems to Generate an Extremely Large Amount of Masks. Sorry for the confusion—the 2000 queries mentioned in L407 refer to the number of learnable queries in Mask2Former, not the number of masks predicted. Before outputting the final model predictions, we apply non-maximum suppression, confidence score thresholding, etc. Consequently, the average number of masks our model predicts is around 500. [W3.2] What is The Number of Masks Used for Assessing Recall? Why Using AR$_{1000}$? We assessed recall using AR$_{1000}$, following the approach used by SOHES. The maximum number of masks per image is set at 1000 for UnSAM and CutLER, and 3232 (=1024) for SAM. We set the maximum number of masks as 1000 in CutLER's config. [W4 W5] What's the Difference Between UnSAM and SOHES? Why UnSAM Performs Better Than Prior Works?* Good question! We have outlined the key differences between UnSAM and prior works (e.g. CutLER and SOHES) in lines 162-173. These distinctions are further detailed in the global rebuttal. Thank you for checking! [W6] Are Different Two Different Models Required? It is indeed feasible to use the same model for both tasks. However, we choose to employ two distinct models primarily due to differences in inference time. While the Semantic-SAM-based model can be prompted similarly to SAM (using a grid of points) with only a minor performance disparity (< 2~3%), its processing speed is significantly slower—at least 5 times slower than a specialized whole-image segmentation framework like Mask2Former. In future research, we plan to utilize models such as FastSAM or SAM-2 to enhance the speed of interactive segmentation models. Additionally, we can still effectively construct the hierarchical structure using the masks from Mask2Former by post-processing the results based on mask overlaps. [W7] CascadePSP Great question! We follow previous works CutLER (CVPR 2023) and SOHES (ICLR 2024), and utilize CascadePSP (from SOHES) or CRF (from CutLER) for mask refinement (Table 3). We opted for CascadePSP as our default method primarily for two reasons: 1) Efficiency: The primary advantage of CascadePSP is not actually in terms of model performance, but rather in terms of inference speed. In our local small scale experiments, we discovered that the performance difference (in terms of AR) between training UnSAM with CascadePSP-refined pseudo-masks and training UnSAM with CRF-refined masks is only about 2-3%, but the speed difference in refining pseudo-masks is about 5-10 times. Due to our limited computing resources, refining pseudo-masks using CRF would take approximately 3-4 months, making it unfeasible. 2) Consistency with Previous Works: To maintain consistency with SOHES, we used the same refinement method. To fully answer your question, how can we speed up the overall process for CRF-based mask refinement? One strategy could be to train a CascadePSP model using the "ground-truth" generated by CRF to achieve "fully-unsupervised" mask refinement quickly. [W8] #images Should Include ImageNet Since ImageNet was actually used by all methods for pre-training the backbone, including SAM, SOHES and CutLER, and UnSAM was never trained on pseudo-labels from ImageNet, we didn't include it as training data. We'll explain it in our paper. [W9] Typos and Minors Issues will be addressed in the revision! Thank you for pointing them out! Hope our explanation and experiments can address your questions. We will integrate your valuable comments into our revision! --- Rebuttal Comment 1.1: Comment: I thank the authors for their response. I agree with the proposed changes. #### Difference to SOHES I thank the authors for the added explanation highlighting the output difference between SOHES and UnSAM. The question was about the formulation. > SOHES heavily utilizes low-level feature similarities between patches for cluster merging. My current understanding is that UnSAM does as well (L140-142). It seems that this does not create a problem in this case due to the use of CutLER as the overall limit of the highest level in the hierarchy, correct? Other than the use of CutLER to limit these masks, are there any other noteworthy differences in the proposed Divide-and-Conquer? --- Reply to Comment 1.1.1: Comment: Dear Reviewer p86w, Thank you for your response. We are pleased that our rebuttal has addressed some of your concerns! Here are our detailed answers to your additional queries: 1) SOHES heavily utilizes low-level feature similarities between patches for cluster merging. It seems that this does not create a problem for UnSAM due to the use of CutLER as the overall limit of the highest level in the hierarchy, correct? Yes, the issue of over-relying on low-level similarities is mitigated by our overall divide-and-conquer pipeline. Divide-and-conquer enables our bottom-up clustering to focus on selected regions, performing cluster merging effectively without being influenced by outliers outside these regions that are identified during the divide stage. 2) Distinctiveness of Divide-and-Conquer: Beyond the differences listed in our global rebuttal, here we outline additional distinctions: - Major Differences in the Overall Pipeline: We wish to emphasize that the core contribution of this work lies in the integration of both bottom-up and top-down clustering—termed the Divide-and-Conquer strategy, a simple yet effective change with significant performance gains. As no previous work has used this pipeline for unsupervised image segmentation, we believe that our overall pipeline is novel and adds new knowledge to the field. With advancements in either top-down or bottom-up clustering methods, we believe the performance of our Divide-and-Conquer approach can be further enhanced. Thus, we assert that the significant and innovative contribution of our work is the overall pipeline itself, rather than the individual components of each stage. - Major Difference Between Our Bottom-up Clustering and SOHES: The use of the divide phase significantly impacts our bottom-up clustering in two key ways: 1) Outlier Removal: Our bottom-up clustering focuses exclusively on regions identified during the top-down clustering phase, which sharpens the model's focus and effectively filters out many noisy outliers outside these regions that are identified during the divide stage. 2) Two Stage Pseudo-labeling: The instance/semantic-level masks generated by CutLER specify candidate regions within the image. Similar to the use of selective search in R-CNN or the Region Proposal Network (RPN) in Faster/Mask R-CNN, CutLER primarily functions to provide initial candidate regions for subsequent detection or segmentation stages. This two-stage approach allows our bottom-up clustering to zoom in on these defined regions, facilitating the detection of smaller objects that SOHES often misses. - Performance Comparison: We have reported substantial performance gains over SOHES, particularly in AR$_L$, supporting our argument that top-down clustering is more effective at identifying instance/semantic-level masks compared to solely bottom-up approaches. Due to the lack of publicly available codes and models from SOHES, we compare against our re-implemention of SOHES for fair comparisons. \| Method \| AR \| AR$_S$ \| AR$_M$ \| AR$_L$ \| \|-------------------------------\|-------\|--------\|--------\|--------\| \| SOHES \| 16.5 \| 5.7 \| 16.1 \| 23.0 \| \| UnSAM \| 23.9 \| 7.9 \| 22.4 \| 34.0 \| \| Improvement over SOHES \| +7.4 \| +2.2 \| +6.3 \| +11.0 \| The below table showcases how training segmentation models on high-quality pseudo-masks from our strategy significantly advances the state-of-the-art in unsupervised segmentation across multiple datasets by an average of 12.9%. \| Methods \| # imgs \| Avg. \| COCO \| LVIS \| ADE \| Entity \| SA-1B \| Part-IN \| PACO \| \|:-------- \| --------: \| --------:\| --------:\| --------:\| --------:\| --------:\| --------:\| --------:\| --------:\| \| SOHES (ViT-Base) \| 0.2M \| 30.1 \| 30.5 \| 29.1 \| 31.1 \| 33.5 \| 33.3 \| 36.0 \| 17.1 \| \| UnSAM (RN-50) \| 0.1M \| 39.2 \| 40.5 \| 37.7 \| 35.7 \| 39.6 \| 41.9 \| 51.6 \| 27.5 \| \| UnSAM (RN-50) \| 0.2M \| 40.4 \| 41.2 \| 39.7 \| 36.8 \| 40.3 \| 43.6 \| 52.1 \| 29.1 \| \| UnSAM (RN-50) \| 0.4M \| 41.1 \| 42.0 \| 40.5 \| 37.5 \| 41.0 \| 44.5 \| 52.7 \| 29.7 \| \| UnSAM (ViT-B) \| 0.4M \| 43.0 \| 44.0 \| 42.7 \| 37.2 \| 44.4 \| 47.2 \| 55.1 \| 31.1 \| \| vs. SOHES \| \| +12.9 \| +13.5 \| +13.6 \| +6.1 \| +10.9 \| +13.9 \| +19.1 \| +14.0 \| We would like to emphasize our commitment to simple science: we hold the view that straightforward changes leading to significant performance improvements are much more valuable than complex modifications that yield only minimal benefits. Thank you once again for your insights! We welcome any further questions. Have a fantastic day! Best regards, UnSAM Authors	Summary: This paper proposes an approach to generate masks from images in an unsupervised manner, which are then used to train segmentation models. The major distinction from previous works is the proposed divide-and-conquer strategy, which first adopts the CutLER to obtain coarse instance/segmentation masks and then uses iterative merging like the SOHES method to generate fine-grained masks. Experiments are conducted on different datasets with detailed analysis and advanced performance. Strengths: - The paper is well-written and easy to follow. Many technical details are provided. The reviewer believes the results should be easy to reproduce. - The two-stage approach that adopts both CutLER and SOHES to generate pseudo masks is reasonable. - The overall performance surpasses previous SOTA methods. Weaknesses: - The major concern is about technical novelty. Though effective, the proposed method technically adds a candidate extraction method before the previous method's iterative refinement stage. All these methods already exist in the unsupervised segmentation field. Therefore, although the performance improvement is reasonable, the reviewer thinks its technical novelty is limited as a NeurIPS research paper. - The comparison with SAM is based on different backbones. Meanwhile, some details, such as the number of masks (UnSAM's 6 vs. SAM's 3), are different. It may have a subtle influence on the performance comparison. - Some typos exist. For example, the $\theta_{t+1}$ in line-147 should be $\theta_{t-1}$. Technical Quality: 3 Clarity: 3 Questions for Authors: Please refer to the weaknesses for the concerns. The reviewer would appreciate it if these concerns could be addressed after the rebuttal. Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: The authors discussed the limitations in the appendix. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Dear Reviewer S6W7, we appreciate your invaluable insights and thoughtful comments! In the following sections, we address the questions you have raised: [W1] Contributions and Insights 1. Novel and Simple Pipeline: We introduce a simple yet effective divide-and-conquer pipeline for producing high-quality pseudo-masks for unsupervised image segmentation. As no previous work has used this pipeline for unsupervised image segmentation, we believe that our overall pipeline is novel and adds new knowledge to the field. We believe in simple science: we think a simple change leading to substantial performance gains is far more valuable and intriguing than a complex method yielding marginal gains. 2. UnSAM, for the first time, demonstrates that unsupervised image segmentation method can achieve competitive results with the supervised counterpart SAM. In addition, UnSAM achieves over 12% better AR than the previous unsupervised segmentation methods. 3. UnSAM is also the first to show that the state-of-the-art supervised segmentation method, SAM, can benefit from our self-supervised labels—a discovery that has not been previously reported. UnSAM+ exceeds SAM’s AP by 3.9% and AR by over 6.7% on SA-1B. [W2.1] Model Backbones The results for UnSAM reported in the paper were obtained using a significantly smaller backbone and fewer training samples than those used for SAM, placing our method at a disadvantage. To fully address your question, we conducted additional experiments using a larger backbone, ViT-Base, and have presented the comparative results on SA-1B below: \| Method \| Backbone \| Training Data \| AP \| AR \| \|:-------- \|:--------: \| --------: \| --------:\|--------:\| \| SAM \| ViT-Base \| 11M SA-1B \| 38.9 \| 60.8 \| UnSAM+ \| RN50 \| 0.1M SA-1B \| 42.8 \| 64.8 \| UnSAM+ \| ViT-Base \| 0.1M SA-1B \| 44.6 \| 67.2 UnSAM demonstrates superior performance with a larger backbone, outperforming SAM in terms of both Average Precision (AP) and Average Recall (AR), despite being trained on significantly fewer samples. [W2.2] Number of Masks Per Point Great question! We employed additional granularity levels (i.e., more masks per click) because our unsupervised pseudo-labeling method can create a hierarchical structure with more granularity levels than the ground-truth masks from SA-1B. We increased the number of masks per click to fully utilize the advantages of our hierarchically structured data. Despite increasing the number of masks for SAM (two clicks producing six output masks), the performance improvement on MSCOCO was relatively marginal. \| Method \| Backbone (# params) \| Training Data \| # Masks \| 1-IoU \| \|:-------- \|:--------: \| --------: \| --------:\| --------:\| \| SAM \| ViT-Base (85M) \| 11M SA-1B \| 3 \| 68.2 \| \| SAM \| ViT-Base (85M) \| 11M SA-1B \| 6 \| 69.0 \| \| UnSAM+ \| Swin-Tiny (25M) \| 0.1M SA-1B \| 6 \| 69.5 \| \| UnSAM+ \| Swin-Tiny (25M) \| 0.4M SA-1B \| 6 \| 70.4 \| As indicated in the table, UnSAM+ surpasses SAM by over 1.4% despite being trained with 100 times fewer samples. [W3] Typos Thank you for pointing out these typos! We will correct them and thoroughly review the manuscript before finalizing the paper. Hope our explanation and experiments can address your inquiries. We will integrate all your valuable comments into our revision! --- Rebuttal Comment 1.1: Comment: Dear Reviewer S6W7, Thank you for your thorough review and insightful feedback on our paper. Your input has been instrumental in refining the quality of our work. We are pleased to report that we have carefully addressed each of the concerns you raised. Here's a brief summary of our actions: - Technical Contributions: We have detailed our key technical contributions in the global rebuttal and provided quantitative results that underscore the significant performance improvements these contributions bring. - Ablation Study on Backbones: In response to your comments, we conducted further experiments with various backbones. The results, presented in the tables at W2.1, indicate that a larger backbone significantly enhances our outcomes. - Ablation Study on Number of Masks: In response to your comments, we conducted further experiments with various number of masks. The results, presented in the tables at W2.2, indicate that UnSAM can still achieve performance gains over SAM as we increase the number of masks of SAM. We remain open and committed to addressing any additional questions or concerns. Your feedback continues to shape our research, and we appreciate your contribution to the improvement of our paper. Please feel free to reach out with further questions or suggestions. We look forward to potentially discussing these matters in greater depth and continuing to refine our work with your valued expertise. Warm regards, UnSAM Authors	Rebuttal 1: Rebuttal: We would like to thank the reviewers for their valuable feedback. In this paper, we present Unsupervised SAM (UnSAM) for promptable and automatic whole-image segmentation that does not require human annotations. We are encouraged by the acknowledgements on: - Comprehensive Experiments and SOTA Results: We are especially glad that the reviewers believe that "the results of this paper are solid"(ecwU). Reviewers also noted that UnSAM "achieves improved results over state-of-the-art (SOTA) methods" (S6W7, wivK, p86w), and that "the improvement of the paper on SAM is significant, both in terms of quantitative and partial qualitative results provided" (ecwU). - Novel Setup: UnSAM not only demonstrates SOTA performance in unsupervised segmentation but also shows that "the additional masks generated using the unsupervised approach, in combination with manual annotations, enhance performance further, surpassing that of SAM" (p86w). And it was agreed that "the two-stage approach to generate pseudo masks is reasonable." (S6W7) We really appreciate that reviewers ecwU and p86w have indicated they might increase our score based on the content of our rebuttal. We are more than happy to discuss with all reviewers to address any additional questions during the discussion period. In this section, we commence by tackling the concerns that have been collectively raised. Technical Contributions of UnSAM - Novel and Simple Pipeline: We introduce a simple yet effective divide-and-conquer pipeline for producing high-quality pseudo-masks for unsupervised image segmentation. As no previous work has used this pipeline for unsupervised image segmentation, we believe that our overall pipeline is novel and adds new knowledge to the field. - UnSAM, for the first time, demonstrates that unsupervised image segmentation method can achieve competitive results with the supervised counterpart SAM. As shown in the table below, UnSAM achieves over 12% better AR than the previous unsupervised segmentation methods. - UnSAM is also the first to show that the state-of-the-art supervised segmentation method, SAM, can benefit from our self-supervised labels—a discovery that has not been previously reported. As illustrated in the table below, UnSAM+ surpasses SAM's Average Precision (AP) by 3.9% and Average Recall (AR) by over 6.7% on SA-1B. - We believe in simple science: We think a simple change leading to substantial performance gains is far more valuable and intriguing than a complex method yielding marginal gains. \| Methods \| Setting \| # imgs \| Avg. \| COCO \| LVIS \| ADE \| Entity \| SA-1B \| Part-ImageNet \| PACO \| \|:-------- \| :-------- \| :-------- \| --------:\| --------:\| --------:\| --------:\| --------:\| --------:\| --------:\| --------:\| \| Prev. UnSup. SOTA (ViT-B) \| Unsupervised \| 0.2M \| 30.1 \| 30.5 \| 29.1 \| 31.1 \| 33.5 \| 33.3 \| 36.0 \| 17.1 \| UnSAM (RN-50) \| Unsupervised \| 0.1M \| 39.2 \| 40.5 \| 37.7 \| 35.7 \| 39.6 \| 41.9 \| 51.6 \| 27.5 \| UnSAM (RN-50) \| Unsupervised \| 0.4M \| 41.1 \| 42.0 \| 40.5 \| 37.5 \| 41.0 \| 44.5 \| 52.7 \| 29.7 \| UnSAM (ViT-B) \| Unsupervised \| 0.4M \| 43.0 \| 44.0 \| 42.7 \| 37.2 \| 44.4 \| 47.2 \| 55.1 \| 31.1 \| vs. Prev. SOTA \| - \| - \| +12.9 \| +13.5 \| +13.6 \| +6.1 \| +10.9 \| +13.9 \| +19.1 \| +14.0 \| Methods \| Setting \| # imgs \| Avg. \| COCO \| LVIS \| ADE \| Entity \| SA-1B \| Part-ImageNet \| PACO \| \|:-------- \| :-------- \| :-------- \| --------:\| --------:\| --------:\| --------:\| --------:\| --------:\| --------:\| --------:\| \| SAM \| Fully-Supervised \| 11M \| 42.1 \| 49.6 \| 46.1 \| 45.8 \| 45.9 \| 60.8 \| 28.3 \| 18.1 \| UnSAM+ (RN-50) \| Lightly-Supervised \| 0.1M \| 48.8 \| 52.2 \| 50.8 \| 45.3 \| 49.8 \| 64.8 \| 46.0 \| 32.3 \| vs. SAM \| - \| - \| +6.7 \| +2.6 \| +4.7 \| -0.5 \| +3.9 \| +4.0 \| +17.7 \| +14.2 What's the Difference Between UnSAM and Prior Works? Why UnSAM Performs Better Than Prior Works? - Comparison with CutLER and U2Seg: These models are limited to providing only instance/semantic-level masks, missing the hierarchical structure that is often present in complex visual scenes. In contrast, our pipeline captures this hierarchical structure by identifying more fine-grained pixel clusters. - Comparison with SOHES: 1. Segmentation Quality at Instance/Semantic Level: SOHES heavily utilizes low-level feature similarities between patches for cluster merging, which often leads to missing many instance masks that have disconnected or occluded components. SOHES struggles to recognize that visually distinct patches (e.g., red-colored t-shirts and green-colored pants) may belong to the same instance (e.g., a person). In contrast, our divide-and-conquer strategy employs a cut-based method that evaluates both the total dissimilarity between different pixel groups and the total similarity within these groups during image partitioning. UnSAM often identifies instance/semantic-level masks that SOHES overlooks. Consequently, UnSAM achieves a recall that is 1.5 times higher than SOHES for large objects on SA-1B. 2. Segmentation Quality for Part/Sub-part Masks: Our use of top-down clustering also allows the model to zoom in on selected regions provided by our cut-based clustering method, resulting in more detailed and fine-grained masks for small objects. Consequently, UnSAM exhibits a recall rate that is 1.3 times higher than SOHES for small objects on SA-1B. Because UnSAM can produce higher quality pseudo-labels than both CutLER and SOHES, the resulting segmentation model trained on these masks can get better model performance. We will integrate all the valuable suggestions into our final version and open-source the code. Next, we address all concerns raised by the reviewers below.	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
The Map Equation Goes Neural: Mapping Network Flows with Graph Neural Networks	Accept (poster)	Summary: The paper titled "The Map Equation Goes Neural: Mapping Network Flows with Graph Neural Networks" presents a novel approach for community detection in networked systems by combining the traditional map equation with modern graph neural networks (GNNs). The authors propose Neuromap, a method that adapts the map equation into a differentiable form for optimization through gradient descent, enabling the integration of node features and end-to-end learning. The paper claims competitive performance against state-of-the-art graph clustering baselines on both synthetic and real-world datasets, emphasizing automatic cluster number determination without the need for explicit regularization. Strengths: - Novel Integration: The paper successfully integrates the traditional map equation with GNNs, offering a new approach for community detection that leverages the strengths of both methodologies. - Comprehensive Evaluation: Extensive experiments on both synthetic and real-world datasets demonstrate the competitive performance of Neuromap compared to existing methods. Weaknesses: - Complexity Concerns: The complexity analysis indicates potential scalability issues for dense networks or when the number of clusters approaches the number of nodes. - Presentation: for example, it is unclear that what MDL principle is, and how it relates to this work in detail. Technical Quality: 3 Clarity: 3 Questions for Authors: The improvement in overfitting being one of the major advantages of the method, is that possible the author can dive a little deeper into the underlying driver (other than only referencing to how MDL addresses the concern of Occam's razor)? Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: There is limitation regarding complexity/scalability. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for the positive assessment of our work. For the comments on scalability, we kindly refer to our aggregate response. On the question about the MDL principle: The minimum description length (MDL) principle is an information-theoretic model-selection approach that has long been used to balance between model complexity and fit [1,2]. The general idea behind MDL is, given some data $D$, to select the model $M$ that enables describing the data as efficiently as possible, i.e., using as few bits as possible. Applied to the map equation, the model $M$ corresponds to the network's community structure, and the data $D$ corresponds to the statistics of a random walk at ergodicity. The map equation is essentially a generalisation of the Shannon entropy to a system of systems: it is a weighted sum of entropies, containing one entropy term per sub-system (or: module) as well as an entropy term for the system of systems (entropy over the modules). Two interacting objectives balance between model complexity and fit. First, choosing small modules leads to low module-level entropy but a large number of modules. Second, choosing few modules reduces the index-level entropy but leads to large modules, which have higher module-level entropy. In combination, these two aspects facilitate choosing the module, i.e., modules, that lead to the best compression of the data, i.e., the random walk's statistics at ergodicity. We hope that this clarifies this question and would be happy to present our work at NeurIPS 2024! [1] Rissanen, Jorma. "Modeling by shortest data description." Automatica 14.5 (1978): 465-471. [2] Grünwald, Peter D., In Jae Myung, and Mark A. Pitt, eds. Advances in minimum description length: Theory and applications. MIT press, 2005. --- Rebuttal Comment 1.1: Comment: The response resolves my concern and I would like to change the ratings to 7.	Summary: The paper proposes an information-theoretic centered approach for clustering nodes of a given graph. The main intuition at the core of the manuscript is to rewrite the map equation in a differentiable form and to train a Graph Neural Network (GNN) with the intent of minimizing its value (thus optimizing the clustering of the provided nodes). As GNNs are naturally suited to process features available on the nodes of the provided domain, this allows to incorporate such information in the optimization of the considered equation and hopefully achieve better assignments. Experiments on both synthetic and real datasets show good performance of the proposed method that generally matches or outperforms prior art. Strengths: The paper proposes an interesting approach for inferring clusters of nodes from a given graph. The manuscript is generally well written, and rather easy to follow (although some details could be better explained in the main text of the paper, see weaknesses). The approach is generally efficient (time complexity is linear in the number of edges for sparse graphs), and experiments on a variety of datasets show good performance w.r.t. previously presented approaches (with the proposed method achieving comparable or superior performance to prior art). Weaknesses: Overall, I don’t have particular criticisms for the paper. The main items I would like the authors to address are: 1) I believe equation 1 could be better explained in the paper. In particular, $q_m$ and $m_{exit}$ are not defined in the paper, and their meaning is outlined only at a high level. Having a more formal definition of such values would improve the clarity of the manuscript (I would personally also clarify that the entropy function re-normalizes the probabilities in such equation, as I believe $Q$ and $P_m$ do not sum up to 1 in equation 1) 2) While the performance of the proposed solutions are indeed good compared to previous approaches, if we inspect table 2 in the supplemental material, we can see that the results produced by the proposed Neuromap and and NOCD are quite close on CORA, PC, Wiki CS and ogb-arxiv, once we take into account the standard deviation of the models. As a result of this, stating that Neuromap achieves best results on these datasets is potentially misleading. I would suggest the authors to report the result of a statistical significance test to highlight when the proposed model actually achieves (with high chance) superior performance w.r.t. the best baseline. Technical Quality: 3 Clarity: 3 Questions for Authors: None. Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: Generally yes, the authors for instance discussed the complexity of the model and how this can become quadratic for dense graphs (or when large number of clusters are used), and how discovering why different GNNs lead to different performance remains an open question in the manuscript. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for the time invested in our work and the positive assessment of our manuscript. We agree that the detailed explanation of the symbols $q_m$ and $m_{exit}$ in section 3 can be improved. It is also correct that $Q$ and $P_m$ in Eq. (1) do not sum to 1 and are implicitly normalised when plugged into the entropy function. Upon acceptance of the paper, we will improve the explanations by including formal definitions of all the symbols -- in the interest of space in a new appendix. To assess when Neuromap significantly outperforms the best baseline, we have used an independent two-sample t-test and report the findings in the PDF attached to our aggregate response to all reviewers. Upon acceptance of the paper, we will include these results in a new appendix. Thank you for your suggestions, which have helped us to further improve our manuscript! --- Rebuttal Comment 1.1: Comment: I'd like to thank the authors for their response, no further questions to ask	Summary: The authors formulate the well-known MAP equation for community detection as an unsupervised objective for graph clustering with GNNs. The implement this "soft" neural MAP equation in various GNN architectures, showing reasonable performance on both synthetic and real-world graph clustering tasks. Strengths: There are many strengths of this paper: 1) Presentation: the paper is quite well-written and the figures are very clear. I did not find any serious (or even minor) confusions in prose, notation, or figure details. The organization of the paper makes sense and helps the reader understand the results. 2) Novelty: in my opinion, the paper is best compared to Tsitsulin et al. 2023 which introduced the modularity-based DMoN pooling method for neural graph clustering. The paper improves upon DMoN in a few key ways: * By adopting the InfoMap objective instead of the Modularity objective, DMoN's need for the collapse regularization is removed, which likely greatly helps with convergence and learing a good community model. It also simplifies the model in general. * Empirically, using the InfoMap objective in graph clustering seems to achieve or surpass the performance of all competitors (including DMoN), on synthetic LFR graphs, real graphs, and a toy graph with overlapping communities. * The authors do a better job than Tsitsulin et al. at noting the independence of the objective and the neural graph encoder architecture. The encoder architectures are explicitly varied in this work on both synthetic and real graphs, and across all methods on which the encoder architecture can vary. 3) Significance: the clear exposition of the method, empirical dominance, and good commentary about the relationships between network science and neural graph clustering make this a solid contribution to the field. Weaknesses: The main weakness of this paper is that the proposed modeling approach has limited novelty compared with that from Tsitsulin et al. 2023: 1) Both papers propose to use a neural graph encoder to obtain a soft clustering embedding matrix $\mathbf{S}$. 2) Both papers train the encoder by adopting an objective from network science (here, Infomap; previously, Modularity) and pass $\mathbf{S}$ in place of the hard-clustering (one-hot) community assigment matrix. The primary difference between the approaches is that the proposed objective does not need the regularization component introduced in Tsitsulin et al. 2023 to deal with the collapse condition, i.e. all nodes are assigned to one cluster. However, the reason for this is simply the choice of the InfoMap objective -- as the authors explain, this objective has inherent ability to balance cluster size with clustering complexity (a result that has been well-known for >10years). Overall, the authors combine pre-existing work to achieve a better neural graph clusterer which nonetheless closely resembles existing graph clusterers that have adopted objectives from network science. This weakeness does not necessarily block acceptance, but it should be well-noted that the novelty is limited. There are very few other weaknesses -- the paper is quite well-written, and the experiments convincingly show that the InfoMap objective is probably better overall than previous objectives. Technical Quality: 4 Clarity: 4 Questions for Authors: Q1: I'm curious, do you in fact agree that your approach is best compared to DMoN? Q2: Is my characterization about the novelty fair? Are there other architectural/practical differences that I missed or that you wish to highlight? Confidence: 5 Soundness: 4 Presentation: 4 Contribution: 4 Limitations: Yes, adequate Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for the positive assessment and encouraging words. For the anwers to your questions, we kindly refer to our aggregate response to all reviewers. In this aggregate response, we also clarify the novelty of our work and highlight our contributions over the work of Tsitsulin et al. We hope that we could clarify your questions and would be happy to present our work at NeurIPS 2024! --- Rebuttal Comment 1.1: Title: Thanks Comment: Thanks to the authors for the general response. I agree that the novelty over the DMoN paper is sufficient, especially due to the analysis of different GNNs and the clearly displayed benefits of using the InfoMap objective. I'm raising the contribution & overall scores by 1.	Summary: This paper proposes a deep learning approach for graph clustering called NeuroMap, which can be seen as a neural version of InfoMap. The idea is to minimize the a relaxation of the InfoMap objective using gradient descent. The proposed approach can be combined with different neural network architectures (MLP, GNN, etc.), works with directed graphs, and can identify overlapping communities. Results using synthetic (LFR) and real datasets (up to 170K nodes) show that NeuroMap often outperforms the baselines in terms of Adjusted Mutual Information. Strengths: 1. The paper is easy to follow. 2. The experiments are based on multiple datasets (real and synthetic). 3. The proposed method does not require specifying the number of clusters. Weaknesses: 1. There are multiple papers proposing relaxations of clustering objectives optimized via deep learning. 2. It is not clear why InfoMap is the ideal community detection algorithm to be made neural given the variety of existing solutions and results showing that there isn't an algorithm that is superior across datasets. 3. The paper lacks any theoretical or empirical analysis trying to explain why relaxation with gradient descent is more effective than the combinatorial heuristics used to optimize the Map objective. Technical Quality: 3 Clarity: 3 Questions for Authors: 1. What are the specific challenges in developing a relaxation of the map objective compared with other clustering objectives? 2. Why InfoMap should be chosen as a classical community detection algorithm to be made neural? 3. Why is the combination of relaxation and gradient descent more effective than the classical heuristics applied to optimize the map objective? Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 1 Limitations: I believe that there are limitations beyond the scalability and need of features (see my comments above) but these are indeed important limitations recognized by the authors. Flag For Ethics Review: ['No ethics review needed.'] Rating: 3 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for the feedback and highlighting the strengths of our approach. Below, we are happy to clarify the questions: 1. Developing a relaxation of the map equation is somewhat more straightforward since no explicit regularisation term is required to avoid trivial solution. A more practical challenge lies in choosing what (graph) neural network architecture to use for optimising the map equation (as well as the baseline objective functions). To the best of our knowledge, our work is the first that systematically explores the performance of different (graph) neural network architectures in combination with different objective functions. Precisely determining when and why certain architectures work better than others remains an open research question. 2. The strength behind the map equation is the minimum description length principle which is used for model selection and to balance between model complexity and fit. As a descriptive method, the map equation does not fit a generative model or considers the deviation from some null model. 3. Our results show that relaxation and gradient descent are not per-se more effective than the classical search heuristics used in Infomap, however, it can be better in some cases. While Infomap switches the community assignment for a single node per optimisation step, optimisation with gradient descent can gradually change the community assignments of multiple nodes simultaneously. Our experiments show that, depending on the utilised (graph) neural network architecture, the achieved codelength, number of communities, and agreement with ground-truth communities vary. Essentially, using a different (graph) neural network architecture may be interpreted as applying a different search algorithm, each of which has different characteristics, therefore returning partitions with different properties, i.e., higher/lower codelength, number of communities and AMI values. In summary, we believe that the three points above also clarify our contribution over the work published by Tsitsulin et al. at NeurIPS 2023: We show that using the information-theoretic objective function MapEquation rather than modularity makes an additional regularisation - whose integration is one of the major challenges addressed in Tsitsulin et al. - obsolete. Moreover, we go beyond this work by showing that different message passing architectures effectively yield different search algorithms, which opens up interesting questions for future work. Furthermore, our empirical evaluation shows that several of the baselines overfit when they are not provided with the correct number of communities. In contrast, based on the map equation, our approach chooses the number of communities automatically, even when the correct number of communities is unknown. --- Rebuttal 2: Title: Thanks for your response to my comments Comment: I believe applying different GNN architectures is standard in this area and some architectures will be better than others. I don't see how "using a different (G)NN architecture may be interpreted as applying a different search algorithm, each of which has different characteristics, therefore returning partitions with different properties". This could be better discussed in the paper. I recommend adding more motivation for InfoMap based on the references [1,2,3] cited in the general comment. I agree with the authors, somehow I got confused and thought that the neural version of InfoMap was better than the classical one but that is not the case (based on Figure 1). This means that the only advantage of the neural approach is to leverage attribute information in supervised settings. I have a dissenting opinion regarding this paper, but I still believe that the contributions are limited. I also suggest the authors better justify the parameterization used in Figure 5 compared with Figure 12. There is plenty of empirical evidence that the number of communities is not a simple function of the graph size and I don't see why users would not attempt to fine-tune the representation sizes using validation if labels are available. --- Rebuttal 3: Comment: We thank the reviewer for considering our replies and provide further clarifications to the additionally raised points below: We agree that using different GNN architectures for deep community detection should be the standard. However, while DiffPool considers both GraphSAGE and GCN, it merely states that GraphSAGE performs better than GCN and only reports results for GraphSAGE [4]. DMoN and Ortho consider only a variant of GCN (without added self-loops but with additional skip connections) [5]. NOCD considers only GCN as a GNN architecture but investigates whether MLP as a non-GNN alternative is sufficient to learn cluster assignments [6]. Mincut acknowledges that different architectures could be used but only considers one message-passing architecture for evaluation [7]. To the best of our knowledge, our work is the first that systematically evaluates the combinations of six deep clustering objectives with five graph-based and non-graph-based neural network architectures. Different (G)NN architectures can be interpreted as different search algorithms because their message-passing specifics are different, possibly including their aggregation functions. This leads to learning different weights during optimisation, and results in different cluster assignment matrices. We agree that we could explain more clearly in our main text how this can be interpreted as different search algorithms; upon acceptance of the paper, we will improve this aspect. We have already included references [1,2,3] cited in the general response in section 3 of our manuscript, pointing out in l. 101-103 that "The map equation [...] has demonstrated high performance in synthetic and real networks from across domains." We agree that the number of communities is not a simple function of the graph size. While it is difficult, perhaps even impossible, to estimate the number of communities in general, it is typically assumed that the number of communities in a graph is much smaller than $n$, the number of nodes. Ghamesian et al. [8] report based on empirical datasets that the number of communities in real network scales as $\sqrt{n}$, which is the motivation for us to choose $\sqrt{n}$ as the maximum allowed number of communities. However, for better computational efficiency, a smaller value may be desirable and could, depending on the scenario, also be more realistic. Following the approach by Shchur and Günneman [6], we have tested this by setting the maximum allowed number of communities to the ground-truth number. Indeed, if ground-truth labels were available, the user may tune the number of hidden features and the maximum possible number of communities, however, we consider unsupervised community detection where labels are not available. We do not agree that "the only advantage of the neural approach is to leverage attribute information in supervised settings", although it may be the biggest advantage. First, we do not consider supervised community detection; all scenarios we consider are unsupervised. Second, we are unsure how Figure 1 relates to our neural adaptation of Infomap, as it illustrates the coding principles behind the map equation. Third, while Infomap achieves the lowest codelengths on synthetic LFR networks without node features, it does so at the expense of reporting a higher number of communities (Fig. 3). Moreover, the fact that Infomap's codelength for large values of $\mu$ is lower than the ground-truth codelength indicates that Infomap overfits; this also happens for Neuromap, but the extent depends in the (G)NN architecture. Fourth, we have applied the significance test suggested by reviewer sjQQ to check whether Neuromap's performance on real datasets with node features is significantly better than Infomap's: Neuromap indeed outperforms Infomap significantly in all tested datasets except for CiteSeer when setting the maximum number of communities to $s=\sqrt{n}$. For setting $s=\left\|Y\right\|$, Neuromap performs significantly better than Infomap on the PubMed, Photo, CS, Physics, WikiCS, and ogb-arxiv datasets. Upon acceptance of the paper, we will also add these tests to the appendix. [4] R. Ying, J. You, C. Morris, X. Ren, W. L. Hamilton, and J. Leskovec. Hierarchical graph representation learning with differentiable pooling. NIPS'18, 2018. \ [5] A. Tsitsulin, J. Palowitch, B. Perozzi, E. Müller. Graph Clustering with Graph Neural Networks. JMLR, 2023. \ [6] O. Shchur and S. Günneman. Overlapping Community Detection with Graph Neural Networks. DLG’19. 2019. \ [7] F. M. Bianchi, D. Grattarola, C. Alippi. Spectral Clustering with Graph Neural Networks for Graph Pooling. PMLR, 2020. \ [8] A. Ghasemian, H. Hosseinmardi, and A. Clauset. Evaluating overfit and underfit in models of network community structure. IEEE Trans. Knowl. Data Eng., 2020.	Rebuttal 1: Rebuttal: We thank the reviewers for their positive assessment of our work. We were glad to see that reviewer 5LnL found our paper "well-written" without "any serious (or even minor) confusion in prose, notation, or figure details" and that our "experiments convincingly show that the InfoMap objective is probably better overall than previous objectives". We were delighted to see that reviewer 5LnL agrees that our work makes substantial contributions compared to work by Tsitsulin et al., which was published at NeurIPS 2023. We were also pleased that reviewer AyCW praised the novelty of integrating the map equation with GNNs, which offers "a new approach for community detection that leverages the strengths of both methodologies." and that he/she appreciated our "comprehensive evaluation". In this aggregate response, we comment on our motivation to use the map equation and clarify our contribution over prior works using different objective functions: - Our motivation to choose the map equation for integration with (G)NNs is twofold: First, because the map equation follows the minimum description length principle, it automatically balances model complexity and explanatory power without requiring an explicit regularisation term to prevent trivial solutions. Second, it has been highlighted in several studies that community detection with the map equation provides excellent results across data from different domains [1,2,3]. - We agree with reviewer 4xY5 that our approach is best compared to DMoN. The approaches are similar insofar as both adopt an objective function for community detection from network science and optimise it through gradient descent based on (G)NNs. However, while the DMoN paper only considers GCN for optimisation, we consider five (G)NN architectures (linear layer, MLP, GCN, GIN, SAGE) and systematically evaluate their performance in combination with different objective functions, which is a contribution in itself. - Our results show that relaxation and gradient descent are not per-se more effective than the classical search heuristics used in Infomap, however, it can be better. While Infomap moves a single node per optimisation step, gradient descent can change all nodes' community assignments a little bit at the same time. Our experiments show that, depending on the utilised (G)NN architecture, the achieved codelength, number of communities, and alignment with the ground-truth communities vary. Essentially, using a different (G)NN architecture may be interpreted as applying a different search algorithm, each of which has different characteristics, therefore returning partitions with different properties, i.e., higher/lower codelength, number of communities and AMI values. - Indeed, a larger number of links or communities leads to increased computation time. In the case of links, this is because each entry of the flow matrix, i.e. each link, needs to be considered for computing the map equation objective. However, this is not limited to the map equation but also holds for modularity and other community-detection objective functions. In the case of communities, this is because the pooling operation becomes more expensive. In practice, both aspects are likely not an issue because real-world networks are sparse and have much fewer communities than nodes [4]. Our contribution over the work published by Tsitsulin et al. at NeurIPS 2023 lies in using the information-theoretic objective function map equation rather than modularity which makes an additional regularisation - whose integration is one of the major challenges addressed in Tsitsulin et al. - obsolete. Moreover, we go beyond this work by showing that different message passing architectures effectively yield different search algorithms, which opens up interesting questions for future work. Furthermore, our empirical evaluation shows that several of the baselines overfit when they are not provided with the correct number of communities. In contrast, based on the map equation, our approach chooses the number of communities automatically, even when the correct number of communities is unknown. Following the suggestion of the reviewers, we propose to improve the camera-ready version of our paper as follows: - We agree that the explanation of symbols $q_m$ and $m_{exit}$ can be improved. It is also correct that $Q$ and $P_m$ in Eq. (1) do not sum to 1 and are implicitly normalised when plugged into the entropy function. Upon acceptance of the paper, we will improve the explanations by including formal definitions of all the symbols in a new appendix. - To assess when Neuromap significantly outperforms the best baseline, we have used an independent two-sample t-test and report the findings in the attached PDF. Upon acceptance of the paper, we will add these results to the appendix. [1] R. Aldecoa and I. Marín. 2013. Exploring the limits of community detection strategies in complex networks. Scientific Reports 3 (2013), 2216 [2] A. Lancichinetti and S. Fortunato. Community detection algorithms: A comparative analysis. Phys. Rev. E, 2009. [3] L. Šubelj, N. J. van Eck, and L. Waltman. Clustering Scientific Publications Based on Citation Relations: A Systematic Comparison of Different Methods. PLoS One 11, 2016. [4] A. Ghasemian, H. Hosseinmardi, and A. Clauset. Evaluating overfit and underfit in models of network community structure. IEEE Trans. Knowl. Data Eng., 2020. Pdf: /pdf/e6231ebab2d2872d2be555ee226b120b3a3a5bf8.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
A Generative Model of Symmetry Transformations	Accept (poster)	Summary: The paper aims to model the data distribution along each group action orbit. The proposed two-stage method first uses a self-supervised loss to learn an invariant function that maps each sample to its prototype and then uses a normalizing flow to learn the distribution along each orbit (i.e. conditional distribution on each prototype). To acquire the full data distribution, one trains a generative model on the prototypes and composes it with the conditional model. The method shows merits in terms of modeling the prototype-dependent distributions of symmetry transformations in the experiments on small-scale datasets. Strengths: * The paper presents a novel framework for learning the distribution of symmetry transformations. Using a flow generative model allows for much more expressivity, compared to the parametrized Gaussian or uniform distributions considered in [1]. * The proposed method is easy to understand. The design choices are well-motivated and clearly described. * Experiments show interpretable results supporting the claims that * The proposed training objective can lead to approximately invariant prototypes. * The orbital distributions may vary for different prototypes. * The proposed method can increase the data efficiency for datasets with certain degrees of symmetry transformations. Weaknesses: * My main concern is the practical applications of the method. Currently, the experiments are done on small image datasets, e.g. dSprites and MNIST. Can the authors identify some more complicated tasks where modeling the symmetry transformations could be beneficial? * Also, the dimensionality of symmetry transformations is generally much smaller than the dimensionality of the data manifold. For example, an image dataset may have a 2828 pixel space and a lot of possible variations in there, while the symmetry of planar affine transformations only accounts for 6 dimensions of variations. Generative modeling is difficult because of the high dimensionality. I'm unsure if it's worth the effort to use a generative model to learn the low-dimensional distribution on a group orbit. (This may be just my personal preference) I find the rotated and colored characters throughout the text a bit distracting. The normal texts have already made things pretty clear. Those characters may be great for intuition but are less accurate and formal. * Currently, the parameterizations for different symmetry transformations seem ad-hoc. E.g. affine transformations are represented in the affine matrix. However, symmetry groups have different structures (which can, for example, be reflected by the structure constants of the Lie algebra) and require different ways of parametrizing distributions. The authors should address this aspect and possibly discuss some related works, e.g. [2]. Technical Quality: 3 Clarity: 3 Questions for Authors: * Regarding the experiment setting, currently the MNIST dataset is manually transformed. I'd expect smaller variations in the original dataset. In that case, would the proposed method result in less performance increase? ## References [1] Benton, Gregory, et al. "Learning invariances in neural networks from training data." Advances in neural information processing systems 33 (2020): 17605-17616. [2] Falorsi, Luca, et al. "Reparameterizing distributions on lie groups." The 22nd International Conference on Artificial Intelligence and Statistics. PMLR, 2019. Confidence: 5 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The authors have discussed the limitations. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: > My main concern is the practical applications of the method. Currently, the experiments are done on small image datasets, e.g. dSprites and MNIST. Can the authors identify some more complicated tasks where modeling the symmetry transformations could be beneficial? Please see our general response, in which we provide detailed motivation as to why our experiments are sufficiently interesting and informative. In short, we have already gone beyond many published related works, our choices of datasets cover a range of dataset sizes and data dimensionalities, and the GalaxyMNIST dataset contains high-dimensional natural images while providing challenges due to its small number of observations and large number of symmetries. > Also, the dimensionality of symmetry transformations is generally much smaller than the dimensionality of the data manifold. For example, an image dataset may have a 28*28 pixel space and a lot of possible variations in there, while the symmetry of planar affine transformations only accounts for 6 dimensions of variations. Generative modeling is difficult because of the high dimensionality. I'm unsure if it's worth the effort to use a generative model to learn the low-dimensional distribution on a group orbit. We agree that the data manifold is larger than the dimensionality of the transformations and that one of the main challenges of generative modeling is high dimensionality. This is actually one of the main motivations for this work. Our hypothesis is that decomposing the generative modeling task into an “easier” symmetry modeling task and a more complicated task of modeling all of the other sources of variation, will provide benefits such as data-efficiency and improved model fit. Figures 11 and 12 confirm this hypothesis, with our symmetry augmented VAEs easily outperforming vanilla VAEs without this inductive bias. In addition to these improvements, this decomposition provides benefits in interpretability of the latent code, and the ability to easily generate realistic “data-augmentations” of any observation. Whether or not it is worth the effort depends on the particular application at hand, however, we are confident that the strengths of our method could be useful in several settings. Finally, we hope that our “novel framework” and “easy to understand” method will result in further interesting developments within the field. > (This may be just my personal preference) I find the rotated and colored characters throughout the text a bit distracting. The normal texts have already made things pretty clear. Those characters may be great for intuition but are less accurate and formal. We appreciate your input on this, and understand that their inclusion might not be to everyone’s tastes. However, prior to their inclusion, we received several pieces of feedback that the corresponding sections were hard to understand. Since their inclusion we have found that readers are much more easily able to understand the text. Furthermore, yourself as well as reviewers d330 and rf86 have noted the clarity of our text. Nonetheless, we will take your input to heart, and for the camera-ready version we will carefully consider the inclusion of each of these characters. > Currently, the parameterizations for different symmetry transformations seem ad-hoc. E.g. affine transformations are represented in the affine matrix. However, symmetry groups have different structures (which can, for example, be reflected by the structure constants of the Lie algebra) and require different ways of parametrizing distributions. The authors should address this aspect and possibly discuss some related works, e.g. [2]. We will happily include a discussion of [2] (and any other related works you suggest). However, we note that we use both affine matrices and the corresponding Lie algebra constants when representing affine transformations, as each representation has pros and cons and the two representations can easily be interchanged. For instance, our inference and generative networks output the Lie algebra constants, since these are low dimensional and easy to constrain (if necessary). On the other hand, we use affine matrices for transformation composition. Both of these choices are discussed in Section 3.1. Similarly, our representation of color transformations is chosen to make composition of transformations simple. See Appendix D.6 for further details. > Regarding the experiment setting, currently the MNIST dataset is manually transformed. I'd expect smaller variations in the original dataset. In that case, would the proposed method result in less performance increase? Your intuition is correct – the smaller the degree of transformation present in the dataset, the less our method is expected to improve data efficiency. This can be observed in Figure 11 – we see that as more rotation is added to the dataset, the performance gap between AugVAE and VAE becomes larger. However, our results of GalaxyMNIST (which don’t include any manual transformations) demonstrate that our method still performs well in natural settings. Finally, we note that the performance gain from our method can be increased by including a wider range of transformations (e.g., learn both color and affine transformations together). --- Rebuttal Comment 1.1: Comment: Thank you for your detailed response. Most of my concerns have been addressed. Regarding your second point, I agree that the proposed method can improve sample efficiency and model fit by decoupling a small number of variations described by symmetry. I just feel that since the orbital distributions are low-dimensional, using a complex generative model may not be the most simple and efficient way to achieve this. This is a somewhat subjective matter, and I will not make further comments. Overall, I maintain my opinion that this is a well-written paper with clear motivation and reasonable experiment results. I will keep my current recommendation. --- Reply to Comment 1.1.1: Comment: > Regarding your second point, I agree that the proposed method can improve sample efficiency and model fit by decoupling a small number of variations described by symmetry. I just feel that since the orbital distributions are low-dimensional, using a complex generative model may not be the most simple and efficient way to achieve this. This is a somewhat subjective matter, and I will not make further comments. While these distributions are low-dimensional, they can often be complex, with dependencies between the different dimensions. For instance, in the case of affine transformations, there is a non-trivial relationship between rotation and shifting/scaling. As a result, we found that using a coupled neural spline flow was actually required for accurately modeling the distribution over transformation parameters. In cases where the dimensions do not interact it is possible to greatly simplify the model (e.g., a flow with a single layer and no coupling). In other words, we view the complexity of the models for transformation parameter distributions as a problem-specific design choice rather than an inherent feature of our method.	Summary: This paper proposes a Symmetry-aware Generative Model (SGM), aiming to learn (approximate) symmetry presented in a data. The model achieves this by mapping each sample onto a prototype—a unique representative on the group orbit—and learning the conditional distribution over its group orbit through maximum likelihood estimation. Strengths: The paper is easy to follow Weaknesses: 1. Initially, I thought the paper aimed to address data-efficient learning of distributions with unknown approximate group symmetry. However, the scope of the paper is quite limited. Essentially, it only aims to learn the conditional distribution of symmetry transformations over the group orbits. In other words, the paper's primary focus is on augmenting training samples over their group orbits according to this supposedly accurate conditional distribution. 2. To demonstrate that the model is functioning as intended, the paper should provide results showing whether this conditional distribution is learned correctly. Unfortunately, this is not shown in any of the examples. The "realistic-looking" generated samples depicted in the figures are merely group-transformed versions of the given samples, which is why they appear realistic. 3. One of the main components of the paper is projecting each sample onto a unique representative of its group orbit, achieved through a so-called transformation inference function $ f_w: X \to H $, where $ H $ is the (potentially large) group. The paper trains this function $ f_w $ in a self-supervised manner through equation (6) to produce unique prototypes. However, this approach is completely unnecessary, as any equivariant function $ f_w: X \to H $ should already accomplish this. 4. The authors claim that one advantage of their approach is handling data sets with unknown symmetries. However, the paper only deals with (2D) rotation and scaling, as well as color transformations, which limits its generalizability. 5. Additionally, the images used in the paper, such as MNIST, are always compactly supported and vanish at the boundary. This makes data augmentation using rotation and scaling feasible. It is unclear how the proposed method would fare when dealing with realistic images that exhibit boundary effects after symmetry transformations. 6. The combination of the proposed model (which supposedly "learns" how to augment data) with a VAE is also unconvincing. While it might be better than directly applying data augmentation (as small images can become even smaller), without demonstrating that the conditional distribution is learned accurately, this combined model could very well learn an incorrectly symmetrized distribution. Technical Quality: 3 Clarity: 3 Questions for Authors: Please see the above section Confidence: 5 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: Yes Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: (1) Learning this conditional distribution is non-trivial. We show that a GAN-based method fails (see Appendix F.1). Furthermore, in sections 3.1 and 3.2 we discuss design and implementation pitfalls that make this challenging. We provide guidelines as to how to resolve them. We consider these sections to be a core part of our contributions. Our method has several use cases, of which we focus on two: * Learning distributions over transformations. * Leveraging those transformations to improve deep generative models. Our experiments demonstrate success in both 1 and 2. (2) For evidence that our model is functioning correctly see section 4.1 and Appendix F.2. For MNIST, we don’t know the ground truth distribution over the transformations (though our method provides sensible results). However, figures 19 and 20 in Appendix F.2, show results for colored MNIST and dSprites, where we control the transformations. E.g., for colored MNIST, our model learns uniform distributions of hue transformations in exactly the range we added to the dataset. The same is true for dSprites. (3) Yes, any equivariant function could work, but in general it isn’t obvious how to construct such a function (e.g., a function with equivariance from images to transformation parameterizations for HSV/general affine transformations). Thus, we provide a general method for learning such equivariances. In “Invariance of f_ω and the prototypes” we mention the possibility of using an architecture with a subset of equivariances directly built in. We will further clarify this in the camera-ready version. (4) While we used affine and color transformations in our experiments, our method is general to any transformation for which (approximate) composition and inverse operations exist. This is a very general class of transformations. We have shown that our method can successfully learn 3 affine transformations (rotation, shift, scale) and 3 color transformations (hue, saturation, value). These transformations have very different properties. Furthermore, all of these transformations can be learnt concurrently (for a total of 8 transformation parameters). This goes beyond several related works which often focus only on affine transformations, and when color transformations are considered it is usually in isolation. E.g.: * “Disentangling images with Lie group transformations and sparse coding” by Chau et al. (from Reviewer TzHS), van der Ouderaa and van der Wilk [2022], Immer et al. [2022] – affine only, * Benton et al. [2020], Keller and Welling [2021] – affine and color separately. (5) Boundary effects may be a problem, by providing a trivial solution for the inference net, allowing it to infer the transformation parameters by ignoring the contents of the image and instead focusing only on the boundaries. Our results for GalaxyMNIST–where images do not vanish at the boundaries due to other galaxies, stars, and background noise–demonstrate that these boundary effects do not necessarily pose a problem for our model as shown in Figures 8d and 12. Note, there are many transformations (e.g., hue, saturation, and value) for which this isn’t an issue. Nonetheless, we acknowledge this potential limitation, and we'll include a discussion in the camera-ready. This is also a limitation of some existing methods (e.g., LieGAN [Yang et al., 2023], where the edge effects could be used by the discriminator to easily distinguish between real and generated data). It wasn’t the goal of our work to address this limitation. (6) In addition to the evidence provided in our response to question 2, the fact that our SGM-VAE hybrid models outperform a standard VAE baseline (measured by test-set IWLB) shows that the model has learnt a better distribution over transformations than the vanilla VAE. If an incorrect distribution were learned, these models would place too much probability mass on uncommon transformations (and vice versa) which would negatively impact the marginal likelihood of the test data. > Rating: 2: Strong Reject: For instance, a paper with major technical flaws, and/or poor evaluation, limited impact, poor reproducibility and mostly unaddressed ethical considerations. We are surprised that we received this score of 2, which we do not believe reflects our work's quality and contributions. This is especially surprising, given the other reviewers' positive scores and comments, which contradict this score. We hope you will reconsider this score. If you are still convinced that the score is accurate, we kindly ask that you address the following: * List the flaws in the paper that you consider major, * Explain why you think our evaluation is poor (in contrast with reviewer rf86 who said our paper has “thorough experimental validation on a wide range of datasets” and reviewer GGon who said our paper’s “experiments show interpretable results supporting the claims”), by providing examples of similar papers who’s evaluation we should aim to emulate, * Explain why the impact of the paper will be limited (in contrast with reviewers GGon and rf86 who noted the novelty of our work), by citing works that detract from our novelty, * Let us know what we can do to improve our reproducibility, given that we provide code and an extensive appendix explaining our experimental setup (“extensive details on the experimental set-ups making them highly reproducible” according to reviewer rf86), or * Point to any ethical issues in our paper. The review also lists “easy to follow” as the only strength of the paper, which we found surprising given the strengths noted by all other reviewers and the contributions the paper makes upon prior work, which are: * A novel generative model (SGM) of the symmetry transformations, * A learning algorithm for our SGM, * The intuition behind and practical tips for our SGM, and * The extensive experimental results that show our model can accurately learn prototypes and distributions over transformations. --- Rebuttal Comment 1.1: Comment: I thank the authors for their detailed response. After reviewing the paper and the feedback, I acknowledge that my previous review had flaws. Specifically, Figures 14, 19, and 20 in the appendix convincingly demonstrate that the proposed method learns the correct conditional distribution, and these figures slipped through my first review. Since my primary concern was the lack of clear evidence that the method achieves this rather than merely augmenting training data and displaying visually realistic samples, I find it necessary to raise the score. However, I still have several concerns: 1. While the authors provide a general method for learning equivariant $f_w$, it would be beneficial to compare it with a hardwired equivariant $f_w$ to show its competitive performance. 2. I remain unconvinced that boundary effects are insignificant. The method’s core idea, when used as a preprocessing step for VAE, is to augment samples in the group orbit accurately. Although GalaxyMNIST does not vanish at the boundary, it primarily consists of sparse objects on a black background. 3. The paper assumes prior knowledge of the group symmetry in the dataset. If I understand correctly, the comparison to [Yang et al. 2023] might be unfair, as [Yang et al. 2023] genuinely learns the general linear group, whereas SGM assumes the transformation group is limited to the rotation and scaling subgroup. Nonetheless, since my main concern about demonstrating the correct conditional distribution learning (points 1, 2, and 6 in my original review) has been addressed, I will substantially raise the score while still reserving my opinion on other aspects. --- Rebuttal 2: Comment: > While the authors provide a general method for learning equivariant, it would be beneficial to compare it with a hardwired equivariant to show its competitive performance. We want to stress that we make no claims that our method for learning an equivariant f_w will match the performance of a hardwired f_w, in fact, we acknowledge in the paper that having some equivariances hardwired would likely lead to an increase in performance. However, we agree that comparison with a hardwired equivariant $f_\omega$ would be interesting. If you have suggestions or know of relevant work for how to parameterise such an $f_\omega$, we'd be happy to run those experiments. This would have been easy if $f_\omega$ was a function from image to image space equivariant to translations/rotations, but we don't know of any work that does this for functions from an image space to transformation-parameter space. > I remain unconvinced that boundary effects are insignificant. The method’s core idea, when used as a preprocessing step for VAE, is to augment samples in the group orbit accurately. Although GalaxyMNIST does not vanish at the boundary, it primarily consists of sparse objects on a black background. As we mentioned in our previous response, we acknowledge that this is a potential limitation of our method, but note that this is also a limitation of existing published methods. Thus, we hope that we will not be held to a higher standard for publication. > The paper assumes prior knowledge of the group symmetry in the dataset. If I understand correctly, the comparison to [Yang et al. 2023] might be unfair, as [Yang et al. 2023] genuinely learns the general linear group, whereas SGM assumes the transformation group is limited to the rotation and scaling subgroup. To clarify, in our experiments for this paper our SGM covers rotation, scaling, and shifting. This makes it slightly less flexible than the LieGAN of Yang et al. [2023], since their method is also able to learn shearing and flipping. However, we feel that the comparison is largely fair, since we are not reporting any quantitative results, and instead focus on qualitative comparisons. From these qualitative comparisons, it is clear that fundamental differences between our two approaches (e.g., our SGM learning conditional distributions) are the dominant reason for different behavior, rather than the choice of assumed transformation group. We also note that our SGM is also capable of learning shearing and flipping, we simply didn't include these transformations in our experimental results. However, expending our assumed transformation group to include these is trivial. > Nonetheless, since my main concern about demonstrating the correct conditional distribution learning (points 1, 2, and 6 in my original review) has been addressed, I will substantially raise the score while still reserving my opinion on other aspects. Thank you for increasing your score and engaging with the rebuttal. We very much appreciate the discussion and we are glad that the rebuttal has already addressed many of your concerns. We hope that we have addressed your remaining concerns and that you will consider increasing it further.	Summary: The paper proposes a generative model that disentangles the latent space into a group-invariant part -- the latent for the prototype -- and another part which represent a group element that can be applied to the prototype to reconstruct the input. A key novelty is to simultaneously learn to predict a distribution for each input over the group elements based on data. This input-dependent distribution, in principle, can be then used to generate new data that better aligns with the true group distribution. Strengths: The overall architecture seems interesting and sound and the idea of learning probability distribution over the group elements is especially interesting. The results show that the distributions are dependent on the input and are meaningful for the datasets used in the experiments. Weaknesses: Some parts of the paper are confusing to me. What is the architecture for the part that predicts the distribution over the group elements? I saw one or two mentions of normalizing flows, but that is not enough to understand the details. The figure is quite unclear about it. Shouldn't the input image be also an input to the network that predicts $p_\psi(\eta\|x)$? Also, the paper does not seem to have any information on the loss function used to train the network that predicts $p_\psi(\eta\|x)$. A lot more clarity is needed for understanding these important details. I feel that the exact new contributions of the paper are a little unclear given many previous works doing similar things. Many of them are also mentioned by the authors in the appendix, but the contrasts with this paper are not clear. My understanding is that it is a generative model and can find the right distribution over the group elements directly from data, but there are earlier works also looking into these aspects. Some discussion here would be useful. Xu et al., Group Equivariant Subsampling Romero and Lohit, Learning Equivariances and Partial Equivariances from Data Shu et al., ,Deforming autoencoders: Unsupervised disentangling of shape and appearance Chau et al., Disentangling images with Lie group transformations and sparse coding Even earlier work by Grenander, Mumford and others on Pattern Theory discusses generative models and probability distributions over groups, but these are not based on neural networks. I think there should be at least one dataset which is a little more challenging like an image recognition dataset of more natural images. This can also help in understanding the limitations of the method. Another experiment showing the usefulness of the generative model being able to generate samples that respect the data distribution is also going to be useful. Technical Quality: 3 Clarity: 3 Questions for Authors: Please address the weaknesses I have listed above. Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: I don't think the paper mentions the limitations explicitly, which the authors should try to. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: > What is the architecture for the part that predicts the distribution over the group elements? In short, we use an MLP with hidden layers of dimension [1024, 512, 512] as a shared feature extractor. These shared features are fed into another MLP hidden layers of dimension [256, 256] that outputs a mean and a standard deviation. The shared features are also used by MLPs with a single hidden dimension of size 256 that output the flow parameters at each layer of the neural spline flow, which has 6 bins in the range [-3, 3]. Please see Appendix D for further details about the exact NN architectures used for both the inference and generative networks. If you would like, we can include some of the details in the main text (given the extra page allowed for the camera-ready version). If so, please let us know what you would find most useful. > Shouldn't the input image be also an input to the network that predicts We are not sure which network you are referring to. The inference network does indeed take the original image as an input. On the other hand, the generative network, which represents the distribution of $p(\eta\|\hat{x})$, must take $\hat{x}$, rather than $x$ as input. One way to think of why it must take $\hat{x}$, rather than $x$, is that we want to learn the distribution of transformations present in the whole dataset. This distribution should not change depending on the transformation applied to an individual input (e.g., the rotation of a specific digit) but rather an aggregate of transformations applied to all the digits of the same type. Since the distribution is capturing a “dataset-level” transformation, it should depend on a representation of data that is invariant to those transformations (i.e., the prototype $\hat{x}$). > Also, the paper does not seem to have any information on the loss function used to train the network that predicts We are not sure which network you are referring to. In section 2.1, under “Transformation inference function” we discuss how the inference network is trained. In short, we use a SSL loss depicted in Figure 4 (and equation 6). Similarly, under “Generative model of transformations” we discuss how the generative network is trained. In short, we use the inference network to generate data and we then fit the conditional flow with maximum likelihood. Both loss functions and training methods are summarized in Algorithm 1. > A lot more clarity is needed for understanding these important details. Please let us know if there are any other clarifications required. > I feel that the exact new contributions of the paper are a little unclear... Thank you for this feedback. We will update the related work sections to clarify this better. We provide a short summary below. While the goals of our paper–namely, (1) unsupervised learning a distribution over arbitrary symmetry transformations present in a dataset, and (2) leveraging this distribution for improved data-efficiency in deep generative models–and the techniques we employ to do so–(A) our SSL objective for learning invariant representations and (B) maximum likelihood learning of flexible flow models for the distributions over partial-symmetries–are similar/related to a wide range of existing work, to the best of our knowledge ours is the only work that incorporates all of 1, 2, A, and B. Related methods tend to not learn the distribution of interest (e.g., [Winter et al., 2022] and “Deforming autoencoders”), do not learn invariant prototypes (e.g., [Yang et al., 2023]), focus on the discriminative rather than generative setting learning setting (see below), or construct deep-generative models for specific symmetries (e.g., [Kuzina et al., 2022] and [Vadgama et al., 2022]). > Xu et al., Group Equivariant Subsampling Romero and Lohit, Learning Equivariances and Partial Equivariances from Data Shu et al., ,Deforming autoencoders: Unsupervised disentangling of shape and appearance Chau et al., Disentangling images with Lie group transformations and sparse coding Thank you for providing these additional items of related work. We will happily include them in our camera-ready manuscript. We provide brief discussions for each paper in the global comment above. > Even earlier work by Grenander, Mumford and others on Pattern Theory discusses generative models and probability distributions over groups, but these are not based on neural networks. If you provide specific missing references, we’d be more than happy to include them in our discussion > ... at least one dataset which is a little more challenging like an image recognition dataset of more natural images... experiment showing the generative model being able to generate samples that respect the data distribution... Please see our general response, in which we provide detailed motivation as to why our experiments are sufficiently interesting and informative. In short, we have already gone beyond many published related works, our choices of datasets cover a range of dataset sizes and data dimensionalities, and the GalaxyMNIST dataset contains high-dimensional natural images while providing challenges due to its small number of observations and large number of symmetries. Please see Appendix F.2 for additional experiments showing that the generated samples respect the data distribution. > I don't think the paper mentions the limitations explicitly... We have provided several limitations, e.g., in footnote 1 we discuss how our generative model might not always match the true generative process, and in our conclusion we discuss our need to pre-specify a super-set of possible symmetries. In the camera ready version, we will also include a discussion of potential limitations of our method due to boundary effects (see our discussion with reviewer d33o). > Rating: 5: Borderline accept Please let us know if we have successfully addressed your concerns. If so, we would appreciate it if you would consider increasing your score. --- Rebuttal Comment 1.1: Comment: We thank the reviewer again for the effort they put into reviewing our paper. Since there are only a few working days left for the discussion period, we would like to ask if our response satisfied the reviewer's concerns. If that is the case, we kindly invite them to raise their score. If there are still any remaining concerns, we are happy to discuss them here. --- Rebuttal Comment 1.2: Title: Thank you for the response Comment: The responses are indeed helpful in understanding some parts of the paper that I didn't before. I understand that the architecture details and other training details are in the appendix. Yes, it would be helpful if some of the important details are moved to the main paper. I understand the connection to existing work better. I still think having one dataset with more challenging images is important. At the very least, it shows what the limitations of the method are. Even a dataset like CIFAR-100 with 32 x 32 color images or CUB-200-2011 or PatchCamelyon would be interesting to show some experimental results on. A separate paragraph on limitations would be good to have rather than a footnote. For example, the authors say that running their method on more challenging datasets is computationally difficult. I don't understand if this is because the method is inherently more complex because of self-supervised learning objectives etc. or some computational constraints the authors may face. This is not too important, but this is one reference for Pattern Theory: Pattern Theory, the Stochastic Analysis of Real World Signals by Mumford and Desolneux. But the authors should not feel compelled to include this is in the paper if they don't believe it to be very related. Overall, I think the reviewers have addressed my concerns to some extent. I think it is important to have some experimental validation of more challenging datasets. Based on the above, I will raise my score to a weak accept. --- Rebuttal 2: Comment: Thank you for your engagement with the review process and for increasing your score as a result – we are very grateful! We'll make sure to incorporate your feedback. Specifically, to * include some more of the architecture and training details in the final manuscript, * try our best to run some additional experiments with the datasets you have suggested (PatchCamelyon looks particularly interesting), * include your suggested reference (Mumford and Desolneux), and * include a dedicated paragraph on the limitations we have discussed in our previous response.	Summary: The paper proposes a generative model of symmetry transformations. The work leverages recent parameterizations based on group theory to define a generative model, in which relaxed symmetry becomes a latent variable over which inference can be performed. Strengths: The paper is very well written and proposes an elegant method that leverages group theoretical framework to mathematically define approximate equivariances, combined with a probabilistic approach to guide discovery of symmetry transformations and learn a prototype. Lastly, the reviewer notes that the paper is very well-written and has beautiful illustrations which guide the intuitive understanding of the generative model and the concept around learning a prototype. Practicality It seems that the proposed SSL objective has computational benefits (easy to scale) as well as benefits in performance (ELBO objective only worked for rotations). Is this true, or am I reading this too positively? What would be potential disadvantage of choosing such loss? Experiments The paper provides very thorough experimental validation on a wide range of datasets. The appendices provide extensive details on the experimental set-ups making them highly reproducible. Weaknesses: Intuition behind the objective. Experimentally the paper demonstrates that the proposed SSL objective is very effective. Apart from the computational benefits of such approach, it also seems to improve overall performance (optimizing ELBO only worked for rotations). To me it is not entirely clear why this would be the case, and it would be interesting to provide some more explanations on this - if known, of course. The first appendix was very helpful in providing context in relation to directly optimizing the ELBO. Types of transformations. The paper does not provide a lot of discussion on how the density of transformations is parameterized. In case of rotations, how is the normalizing flow constrained to remain smooth in the Lie algebra? Is the approach mostly targeted to simple (e.g. affine) groups? Technical Quality: 3 Clarity: 4 Questions for Authors: 1. The connection in App. A. offers a nice connection to the objectives used in some of the prior work. It references earlier approaches by the authors [Authors, 20XX] in which the ELBO is directly optimized and hypothesizes that ‘ averaging of many latent codes makes it difficult to learn an invariant representation a without throwing away all the information in x’ . Could the authors elaborate a bit more on this hypothesis / is this backed by any experiment? 2. Number of samples. The x-mse in number of samples is optimal for 5 samples. Don’t we expect this table to be monotonically decreasing in number of samples? 3. Overfitting on p(\eta \| x). For very flexible distributions of transformations, isn’t there a risk of overfitting on the parameterization? Please correct me if I have missed something in the method which counteracts this. Confidence: 4 Soundness: 3 Presentation: 4 Contribution: 4 Limitations: The paper offers a strong contribution proposing a probabilistic generative model that describes that as coming from transformed latent prototypes. Flag For Ethics Review: ['No ethics review needed.'] Rating: 8 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: > Practicality It seems that the proposed SSL objective has computational benefits... Is this true, or am I reading this too positively? What would be potential disadvantage of choosing such loss? Your understanding is correct. We provide additional discussion below. Regarding disadvantages, the SSL objective does have a few pathologies and potential ‘gotchas’ that are not present in the ELBO setting. E.g., see “Partial invertibility” in Section 3.1 and Appendix B. > The connection in App. A. offers a nice connection to the objectives used in some of the prior work. It references earlier approaches by the authors [Authors, 20XX] in which the ELBO is directly optimized and hypothesizes that ‘ averaging of many latent codes makes it difficult to learn an invariant representation a without throwing away all the information in x’ . Could the authors elaborate a bit more on this hypothesis / is this backed by any experiment? In trying to scale that method, we observed that as we added additional transformations or increased the range of those transformations (e.g., increasing rotation from 0-pi to 0-2pi) that performance (as measured by the ELBO and reconstruction loss) degraded to the point that when using the 5 transformations applied to MNIST in this paper, the model was unable to reconstruct the digits at all. Instead it became stuck in a local optima in which the ‘reconstructions’ were all circles and rings of various sizes depending on the input image. (We’ll include some of these figures in the camera-ready version.) In other words, the averaged latent code was successfully throwing away (e.g.,) rotation information but was also throwing away all of the information that actually identified each digit. This led us to the hypothesis that averaging of latent codes makes it difficult to learn representations that only throw away the symmetry data. Our current method is directly motivated by this observation – we aimed to develop an algorithm that could produce invariant representations without latent-space averaging. The success of our SSL objective is indirect evidence to support our hypothesis. That said, our SSL algorithm has another advantage over ELBO learning – it decouples learning an invariant representation of x from reconstruction of x. That is, for ELBO learning to successfully learn an inference network, one ultimately needs a good generative network (and vice-versa). However, learning a network to generate examples given latent codes is a challenging inverse learning task. This is an observation that was also made by Dubois et al. [2021], who found that an SSL based objective was superior to an ELBO based method for learning invariant representations in the context of compression. > Number of samples. The x-mse in number of samples is optimal for 5 samples. Don’t we expect this table to be monotonically decreasing in number of samples? Thanks for the question, we will clarify this in the camera-ready version. The table is not likely to be monotonically decreasing, due to the fact that there is random noise in each training run (i.e., due random NN initialization, etc.). That said, we would expect that it will decrease on average as the number of samples is increased. We chose 5 samples not because it provides the lowest loss, but rather because it provided a good trade-off between lower loss and increased compute cost. > Overfitting on $p(\eta \| x)$. For very flexible distributions of transformations, isn’t there a risk of overfitting on the parameterization? Please correct me if I have missed something in the method which counteracts this. In practice, for the inference network $p(\eta \| x)$ we found that there were no issues with overfitting (the more expressive the network and the longer we trained, the better we found the test-set performance became). This is likely due to two things: (1) our SSL loss, which has ‘baked-in data-augmentation’ in the form of random transformations applied to x, and (2) learning a function with equivariance to arbitrary transformations is hard. On the other hand, for the generative network $p(\eta \| \hat{x})$, we did observe overfitting. We addressed this by using a validation set to optimize several relevant hyper-parameters (e.g., dropout rates, number of flow layers, number of training epochs, etc.). > Rating: 8: Strong Accept: Technically strong paper, with novel ideas, excellent impact on at least one area, or high-to-excellent impact on multiple areas, with excellent evaluation, resources, and reproducibility, and no unaddressed ethical considerations. Please let us know if you have any remaining concerns. --- Rebuttal Comment 1.1: Comment: We thank the reviewer again for the effort they put into reviewing our paper. Since there are only a few working days left for the discussion period, we would like to ask if our response satisfied the reviewer's concerns. If that is the case, we kindly invite them to raise their score. If there are still any remaining concerns, we are happy to discuss them here. --- Rebuttal 2: Comment: We thank the authors for the further clarifications and answering my answers and hope these are included as discussions the final manuscript. I regard this a technically strong paper, with novel ideas and a good execution, and therefore keep my recommendation for acceptance with score rating 8. --- Rebuttal Comment 2.1: Comment: Thank you for your strong endorsement of our paper. We will be sure to include all of the answers to your questions as additional discussion on the final camera-ready manuscript.	Rebuttal 1: Rebuttal: We thank the reviewers for their time and constructive feedback on our paper. We are pleased that the reviewers have highlighted the quality of our writing (rf86, d33o, GGon), experimental evaluation (rf86, TxHS, GGon), the novelty, elegance and interestingness of our work (rf86, TxHS, GGon). We would like to highlight the following quotes from the reviews: * “The paper is very well written and proposes an elegant method”, “The paper is very well-written and has beautiful illustrations”, “The paper provides very thorough experimental validation on a wide range of datasets”, “The appendices provide extensive details on the experimental set-ups making them highly reproducible” – reviewer rf86 * “The overall architecture seems interesting and sound”, “the idea of learning probability distribution over the group elements is especially interesting” – reviewer TzHS * “The paper is easy to follow” – reviewer d33o * “The paper presents a novel framework for learning the distribution of symmetry transformations.”, “The proposed method is easy to understand.”, “The design choices are well-motivated and clearly described.”, “Experiments show interpretable results supporting the claims …” – reviewer GGon We also acknowledge a common criticism among most of the reviewers (TzHS, d33o, GGon) that the paper would be improved with the addition of a larger-scale dataset with ‘natural’ images. We believe our experiments are sufficiently interesting and informative for the following reasons. Many published related works do not go beyond image datasets of similar size/dimensionality to MNIST and dSprites. Examples of this include: * “Disentangling images with Lie group transformations and sparse coding” by Chau et al., and “Group Equivariant Subsampling” by Xu et al. (mentioned by Reviewer TzHS), and * Yang et al. [2023], Benton et al. [2020], van der Ouderaa and van der Wilk [2022], Immer et al. [2022], Kaba et al. [2023], Keller and Welling [2021], and Bouchacourt et al. [2021a], from our related work to name just a few. Unfortunately, it is impractical for us to go beyond these settings due to computational resource limitations. Our set of experiments using dSprites, MNIST, and GalaxyMNIST, considering different types of symmetry transformations on each, demonstrate the general applicability of our method from small to large data sizes, from small to large dimensionalities, and for several different symmetries. The dSprites images, while simple, have a fairly large dimensionality (64 x 64 pixels) and are very plentiful (~740k images). GalaxyMNIST contains a small number of images (only 7k for training) of even larger dimensionality (64 x 64 x 3). This small data regime is perhaps more interesting since it demonstrates that our method is able to accurately capture the distribution over transformations without much data. Furthermore, we view the GalaxyMNIST images as ‘natural’ in that they come from real-world astronomy observations collected for the Galaxy Zoo DECaLS Campaign. Finally, these datasets demonstrate that our model can learn five affine transformations alone (MNIST, dSprites), three color transformations alone (MNIST), and both affine and color transformations together (GalaxyMNIST). Like those excellent papers mentioned above, this paper has focused on novel ideas and methodological contributions rather than large-scale experiments. While we also value those experiments, we note that such engineering work often follows from work that builds up understanding and provides a promising proof-of-concept. Furthermore, we note that scaling up generative models is typically harder than their deterministic counterparts. Thus, we hope this will not be considered a major weakness of our work.	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
An Accelerated Gradient Method for Convex Smooth Simple Bilevel Optimization	Accept (poster)	Summary: This work proposes a novel optimization algorithm with improved iteration complexity for convex smooth simple bilevel optimization, and demonstrates its faster convergence using experiments. Strengths: The presentation is very clear. The literature review looks comprehensive. The algorithm and complexity results look reasonable. Weaknesses: This work focuses on simple bilevel optimization with both levels being convex and under deterministic setting (with access to full gradients instead of stochastic gradients), so the scope is not wide. Also, as shown in Table 1, the complexity results outperform existing ones only a little since the complexity order is the same as [8] for $r=1$, and the complexity dependence on $\epsilon_g^{-\frac{2r-1}{2r}}$ is worse than $\epsilon_g^{-0.5}$ in [16]. Technical Quality: 3 Clarity: 4 Questions for Authors: (1) In line 27, you may write down the math formulation for ``more general settings with parameterized lower-level problems'', or refer this formulation to appendix. (2) How did you obtain Eq. (5), the condition about $g_k$? How to guarantee Eq. (5) in implementation with unknown $g^$, $x^$, $L_g$? (3) Does Lemma 4.3 require Assumption 4.1? If yes, add Assumption 4.1 to Lemma 4.3. Confidence: 3 Soundness: 3 Presentation: 4 Contribution: 2 Limitations: In the checklist, the authors mention their limitation of compact domain assumption. There is no societal impact of this theoretical work. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for the comments and great questions! W. This work focuses on simple bilevel optimization with both levels being convex and under deterministic setting (with access to full gradients instead of stochastic gradients), so the scope is not wide. Also, as shown in Table 1, the complexity results outperform existing ones only a little since the complexity order is the same as [Samadi et al. (2023)] for $r = 1$, and the complexity dependence on $\epsilon_{g}^{-\frac{2r-1}{2r}}$ is worse than $\epsilon_{g}^{-0.5}$ in [Chen et al. (2024)]. R. We would like to mention that most of the prior works focus only on either deterministic setting or stochastic setting, as the algorithms designed for one of the settings are not easy to be extended to the other setting. One of the works in stochastic simple bilevel optimization is [Cao et al. (2023)]. The strategy in [Cao et al. (2023)] is designed to manage the errors between the actual gradients and their estimates, as well as the errors between the true function values and their estimates. This methodology could be adapted for our AGM-BiO algorithm. However, we are uncertain if such an extension would lead to an acceleration. Another challenge lies in selecting appropriate gradient and function value estimates, crucially impacting the sample complexities based on the errors between the actual gradients and their estimates. Therefore, adapting our algorithm to the stochastic setting requires a careful choice of these estimates and a comprehensive convergence analysis. Indeed, this presents a compelling direction for future research. Under the Hölderian error bound assumption, our result is the same as the result in [Samadi et al. (2023)] when $r = 1$. However, [Samadi et al. (2023)] did not provide any results for $r > 1$. Note that [Chen et al. (2024)] is a concurrent work. The convergence rate in [Chen et al. (2024)] is $\mathcal{O}(\epsilon_{f}^{-0.5r}) + \mathcal{O}(\epsilon_g^{-0.5})$, while our convergence rate is $\mathcal{O}(\max(\epsilon_{f}^{-\frac{2r-1}{2r}},\epsilon_{g}^{-\frac{2r-1}{2r}}))$. If $\epsilon_f = \epsilon_g$, our rate is better than theirs. Only when $\epsilon_g < \epsilon_f^{r/2}$, their result is better than ours. Furthermore, their results require the Lipschitz continuity of the upper-level objective (Assumption 2.1.1 in [Chen et al. (2024)]) and the compactness of the domain (a hidden assumption of Lemma 3.2 in [Chen et al. (2024)]), whereas our results under the Hölderian error bound assumption do not require either of these conditions. We will add a remark about the above discussion to the revised paper. Thanks for your feedback. --- Q1. In line 27, you may write down the math formulation for 'more general settings with parameterized lower-level problems', or refer this formulation to appendix. A1. Thanks for pointing this out. We will add a formulation for the general bilevel problem in our revised vision. --- *Q2. How did you obtain Eq. (5), the condition about $g_k$? How to guarantee Eq. (5) in implementation with unknown $g^{\}$, $x^{\}$, and $L_g$?* A2. As we mentioned in line 151, we can generate this sequence $ \{ g_k \} $ independently from the main algorithm by applying an accelerated projected gradient method to the lower-level problem $\min_{z\in \mathcal{Z}}~g(z)$. The Eq. (5) is the convergence result of the accelerated projected gradient method for solving the single-level problem [Nesterov (2018)]. To perform the single-level accelerated gradient method on $g$, we do not need to know the $g^\$ and $x^\$. Note that $g$ has to be convex and $L_g$-smooth to guarantee the Eq. (5) holds which are also the assumptions of our method. Hence, given our assumptions, we are able to generate a sequence $g_k$ satisfying the Eq. (5). We will add a remark about this point and provide necessary reference for the convergence rate. --- Q3. Does Lemma 4.3 require Assumption 4.1? If yes, add Assumption 4.1 to Lemma 4.3? A3. No. Lemma 4.3 does not require the Assumption 4.1. Assumption 4.1 is only required for Theorems 4.4 and 4.5. --- References: - Samadi, S., Burbano, D. and Yousefian, F., 2023. Achieving optimal complexity guarantees for a class of bilevel convex optimization problems. - Chen, P., Shi, X., Jiang, R., and Wang, J., 2024. Penalty-based methods for simple bilevel optimization under holderian error bounds. - Nesterov, Y., 2018. Lectures on convex optimization. --- Rebuttal 2: Title: Reviewer fv8w's further query on Q2 Comment: Hello, authors. For Q2, does $g_k$ denote the function value from the k-th iteration of the Nesterov's gradient method on $g$? {$g_k$} is input of Algorithms 1 and 2. Could you remove that input and give the procedure of obtaining $g_k$ in the algorithm body part? Reviewer fv8w --- Rebuttal Comment 2.1: Comment: Thank you for the follow-up questions! Q. For Q2, does $g_k$ denote the function value from the k-th iteration of the Nesterov's gradient method on $g$? $\\{g_k\\}$ is input of Algorithms 1 and 2. Could you remove that input and give the procedure of obtaining $g_k$ in the algorithm body part? A. The reviewer is correct: the function value of the $k$-th iteration of the Nesterov accelerated gradient method on $g$ is denoted by $g_k$. However, this is not the only possible choice. In fact, any $\\{g_k\\}$ satisfying Eq. (5) can also be used as an input of our algorithms. As you mentioned, this input can be removed. Instead, we could obtain the $g_k$ at the beginning of the $k$-th iteration in our algorithm body part and use it to construct our approximated feasible set $\mathcal{X}_{k}$. We will add an instantiation of our algorithm with Nesterov accelerated gradient iterates to the paper, which will be included in the appendix. To clarify, there are multiple choices for the sequence $g_k$. For instance, one could consider a constant sequence where $g_k$ is set to the function value of the last iterate of AGD for all $k$. This choice has the benefit of shaving a logarithmic factor from the convergence rate, as discussed in Remark 4.2.	Summary: The paper works on the problem of simple convex smooth bilevel optimisation, where ''simple'' means single-variable. The paper achieves the optimal rate for this problem by a combination of Nesterov's acceleration and Jiang-Abolfazli-Mokhtari-Hamedani's cutting-plane method. Strengths: STRENGTHS. 1. The paper achieves an optimal rate for an important problem class. 2. The paper is very well-written. Weaknesses: - Technical Quality: 3 Clarity: 4 Questions for Authors: QUESTIONS. What limitations do the authors anticipate in extending this technique (acceleration + cutting-plane) to the non-simple case (i.e., when you have an additional variable $y$ in the upper level objective, defined as the optimizer of a parametrized lower-level problem). Confidence: 3 Soundness: 3 Presentation: 4 Contribution: 3 Limitations: N/A since it's a theory paper Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank the reviewer for the insightful question! Q1. What limitations do the authors anticipate in extending this technique (acceleration + cutting-plane) to the non-simple case (i.e., when you have an additional variable in the upper level objective, defined as the optimizer of a parametrized lower-level problem). A1. First of all, most of the work on general bilevel problems requires strong convexity for the lower-level function. In the case of the simple bilevel problem, this assumption would make the feasible set a singleton, rendering the problem trivial since it would amount to solving the lower-level problem only. The general bilevel problem, when featuring a convex lower-level problem, is widely recognized as challenging in its most generic form. In this case, the optimal solution set of the lower-level problem will change as the upper-level variable changes with each iteration. Specifically, following a similar construction of the half-space, we cannot ensure that our constructed set always contains the optimal solution set of the bilevel problem, which is a key property in our proof. Therefore, to enhance computational tractability and adapt our framework to address the general bilevel problem effectively, we may need to introduce some additional assumptions, which is a compelling direction for future research. --- Rebuttal Comment 1.1: Title: Thank you for your response Comment: Dear authors, Thank you for your clear explanation! I acknowledge reading your response and am happy to maintain my score and advocate for acceptance of your paper. Best wishes! --- Reply to Comment 1.1.1: Comment: Thank you for your response and advocating for the acceptance of our paper!	Summary: The paper introduces a new algorithm called AGM-BiO (Accelerated Gradient Method for Bilevel Optimization) for solving simple bilevel optimization problems where both the upper and lower level objectives are convex and smooth. Strengths: 1. The paper is well-written and easy to follow. The assumptions are clearly stated. The dependence of the convergence rates on everything seems to be explicitly written out. 2. The proposed algorithm seems to be easy to implement, and it achieves the best-known complexity bounds for both suboptimality and infeasibility in the considered settings. 3. Experiments are conducted to validate the strength of the proposed algorithm. Weaknesses: You provide a modified algorithm (Algorithm 2) that could potentially handle this composite structure. In line 629-line 631 you mention that you can derive identical complexity results for Algorithm 2 in either the compact domain setting or with the Hölderian error bounds on g. I guess formally stating the convergence result in a theorem would strengthen the paper and provide a clear reference point for readers interested in the composite case. Technical Quality: 3 Clarity: 3 Questions for Authors: - Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: Yes. Flag For Ethics Review: ['No ethics review needed.'] Rating: 8 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for the comment and the positive feedback! W. You provide a modified algorithm (Algorithm 2) that could potentially handle this composite structure. In line 629-line 631 you mention that you can derive identical complexity results for Algorithm 2 in either the compact domain setting or with the Hölderian error bounds on g. I guess formally stating the convergence result in a theorem would strengthen the paper and provide a clear reference point for readers interested in the composite case. R. As we mentioned in the Appendix B, Algorithm 2 designed for proximal setting can achieve the same results as Algorithm 1 in either the compact domain setting or with the Hölderian error bounds on g. The major difference lies in the main Lemma A.1. Therefore, we provided a detailed proof of a new Lemma B.1 for the composite setting. By replacing Lemma A.1 with Lemma B.1, all the proofs in our paper will hold. As the reviewer suggests, we will add the formal theorems for the composite setting in the revised version.	Summary: This work proposes an accelerated method to solve convex simple bilevel problems, with the author providing both theoretical and numerical guarantees of the algorithm's convergence. Strengths: - This work makes a theoretical contribution to the convergence analysis, and the algorithm demonstrates an advanced convergence rate under the Hölderian error bound. - The analysis are detailed and concrete. The whole work is easy to follow. Weaknesses: Since the main techniques in this work, such as the accelerated gradient method and the cutting plane approach, have already been studied, the contribution of the proposed methods is incremental, and the convergence rate may not be difficult to prove based on existing studies. Technical Quality: 3 Clarity: 3 Questions for Authors: - What is the convergence rate without using the accelerated gradient method, relying only on the projection onto the cutting plane? - Since the accelerated gradient method has been well studied recently, what is the unique challenge of applying it to simple bilevel problems? - Will this algorithm demonstrate any advantage in convergence without the assumption of the Hölderian error bound? - How do you find a feasible $X_k$ in practice? Is an additional loop required to achieve this? Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: No Limitation Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for the feedback and valuable questions! R. To address your concern in the weakness section, please refer to our answers to your first two questions. As stated in A1, the non-accelerated version of the projection-based algorithm yields unsatisfactory results. Thus, the accelerated gradient method is essential and significantly improves the convergence rates. In A2, we emphasize that constructing the correct approximated set is not as straightforward as in [6]. It requires a careful selection of the norm vector of the half-space, which can be interpreted as the descent direction of the lower-level objective $g$. Furthermore, the proof of the convergence results differs from that for the single-level counterpart. Specifically, in the proof of the main descent Lemma A.1, we employed different potential functions for the upper- and lower-level objectives, carefully selected the coefficients $A\_k$ and $a_k$, and utilized the properties of the constructed approximated set several times. In Lemma 4.3, we characterized the convergence rate by considering a weighted sum of the upper- and lower-level functions. We then presented our formal theorems under the Hölderian error bound by selecting the appropriate weight. However, this weight does not appear explicitly in the algorithm, as it can be controlled by the step size. --- A1. That is a great question. Our initial idea was to develop a projection-based algorithm without using the acceleration technique to solve simple bilevel problems. However, the non-accelerated version of the algorithm did not produce satisfactory results. Specifically, it achieves $\mathcal{O}(1/K)$ for the upper-level objective but fails to provide any convergence guarantee for the lower-level objective. On a related note, we would like to mention that a recent work [Devanathan and Boyd (2024)] proposed the Alternating-update Polyak Minorant Method (PMM), which is similar to the non-accelerated simple bilevel algorithm relying only on the cutting plane. It involves projecting onto the approximated sublevel sets of the upper- and lower-level objectives alternatively, assuming $f^{\}$ is known. However, they only provide asymptotic convergence without any rate guarantees under common assumptions. To some extent, this also demonstrates the challenge of solving simple bilevel problems and the complexity of integrating the cutting plane technique with projection-based methods. --- A2.* A naive implementation of AGM for simple bilevel optimization requires access to the lower-level solution set $\mathcal{X}_g^\$, which is typically not available in closed form. Therefore, one must either use regularization by mixing the two objective functions or approximate the lower-level solution set. The former approach, as studied by [8], involves determining a proper regularization parameter, which is challenging in practice and only provides a $\mathcal{O}(1/K)$ convergence guarantee on both levels without further assumptions even with the accelerated gradient method. For the latter approach, the design of the approximated lower-level solution set $\mathcal{X}_k$ is a nuanced task. If we project onto a set much larger than $\mathcal{X}_g^{\}$, then the iterate may deviate from the optimal solution set, leading to a large error for the lower-level objective. Furthermore, as we mentioned in Remark 3.1, there are three intertwining sequences $\\{x_k\\}$, $\\{y_k\\}$, and $\\{z_k\\}$ in AGM, and depending on where we linearize the objective function, various alternative formulations of halfspaces could contain the optimal solution set of the lower-level problem $\mathcal{X}_{g}^{\}$, such as $\\{z \in \mathcal{Z}: g(x_k) + \langle\nabla g(x_k), z-x_k\rangle \leq g_k\\}$ and $\\{z \in \mathcal{Z}: g(z_k) + \langle\nabla g(z_k), z-z_k\rangle \leq g_k\\}$. However, our choice of using the gradient at $y_k$ to construct the halfspace is not arbitrary but essential for showing convergence guarantees for the lower-level objective. For single-level optimization problems, we can project onto the feasible set in each iteration to keep all the iterates feasible. However, for simple bilevel optimization, the feasible set $\mathcal{X}_g^{\}$ may not have an explicit form. By projecting onto the approximated set $\mathcal{X}_k$, the iterates could be infeasible, introducing additional error in the lower-level objective convergence analysis. As a result, the condition that $f(x_k) \geq f^{\}$, which always holds in single-level problems, can be violated in bilevel problems. This also leads to challenges in our convergence analysis, and we cannot achieve the desired results for the lower-level objective unless $f(x_K) \geq f^{\}$. --- A3. As we showed in Table 1, without the Hölderian error bound assumption, our method achieves the complexity $\mathcal{O}(\max(\frac{1}{\epsilon_f^{0.5}}, \frac{1}{\epsilon_g}))$, which is better than the others under similar settings. --- A4. The constructed set $X_k$ has an explicit form, i.e., $X_k \triangleq \\{ z \in \mathcal{Z}: g(y_k)+\langle \nabla g(y_k),z-y_k \rangle \leq g_k\\}$, which always contains the lower-level problem solution set $\mathcal{X}_g^*$ (the feasible set of the upper-level problem) as stated in line 154-158. How to project onto the set $X_k$ is another question you may be interested in. In some cases, such as our over-parameterized regression problem, $X_k$ is the intersection of an $L_2$ ball and a half-space, for which a closed-form solution exists to find the projected iterates $z_k$. In other cases, such as our linear inverse problem, we may not be able to find $z_k$ directly. Instead, we can solve the projection subproblem using Dykstra's projection algorithm [43], as mentioned in line 701. For this scenario, an additional loop is needed to solve the subproblem. --- Reference: - Devanathan, N. and Boyd, S., 2024. Polyak Minorant Method for Convex Optimization --- Rebuttal Comment 1.1: Comment: Thanks for the authors' response. My concerns and questions are solved so I will raise my score to 6. I am still curious about why the non-accelerated algorithm fails to provide any convergence guarantee for the lower-level objective. --- Reply to Comment 1.1.1: Comment: Thank you for the response. We're glad your questions and concerns have been addressed! Regarding your further query, specifically, the non-accelerated version of our algorithm follows the update rule $x_{k+1} = \Pi_{X_k}(x_k - \eta_k \nabla f(x_k))$, where the set $X_k$ is similarly constructed from a cutting plane as $X_k = \\\{z \in Z: g(x_k) + \langle \nabla g(x_k), z-x_k \rangle \leq g_k \\\}$. To upper bound the lower-level objective, we can apply a similar analysis as in our Lemma A.1, leading to:$$g(x_{k+1}) \leq g(x_k) + \langle \nabla g(x_k), x_{k+1} - x_k\rangle+ \frac{L_g}{2}\\\|x_{k+1} - x_k\\\|^2 \leq g_k + \frac{L_g}{2}\\\|x_{k+1} - x_k\\\|^2,$$where the first inequality used the $L_g$-smoothness of $g$, and the second inequality follows from the fact that $x_{k+1} \in X_k$. However, the main challenge is controlling $\\\|x_{k+1} - x_k\\\|^2$ (see also Remark 4.1 for a related issue in our accelerated methods). If we follow the same strategy as in Theorem 4.1 and upper bound $\\\|x_{k+1} - x_k\\\|^2 \leq D^2$ by the compactness of $Z$, this results in $g(x_{k+1}) \leq g_k + \frac{L_g}{2}D^2$, which fails to provide a convergence rate for the lower-level objective. Therefore, it appears that acceleration is crucial to achieve the $O(1/k)$ rate for the lower-level objective reported in Theorem 4.1. That said, we should clarify that this does not rule out the possibility of proving a convergence rate for the lower-level objective under the standard assumptions, though this appears non-trivial and would require a different analysis from the one presented in our paper. Thank you for your question, and we will further explore this topic in future research.	null	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Plant-and-Steal: Truthful Fair Allocations via Predictions	Accept (poster)	Summary: This paper considers the problem of fairly and truthfully allocating indivisible items where mechanisms are equipped with predictions. When the prediction is perfectly accurate, the mechanism's performance should be significantly improved (consistency); conversely, for a prediction with any accuracy, the mechanism's performance should still be guaranteed (robustness). The paper aims to design truthful mechanisms with predictions that optimize the approximation to maximin share (MMS). The paper achieves a variety of consistency-robustness trade-offs under different settings. For $2$ agents and ordering predictions, which predict agents' ranking preferences over items, the paper gives a truthful mechanism that is $2$-consistent and $\lceil m/2 \rceil$-robust, where the robustness guarantee matches the best approximation ratio achievable by truthful mechanisms without predictions. Another truthful mechanism is provided with $3/2$-consistency and $\lfloor 2m/3 \rfloor$-robustness. For $2$ agents and arbitrary predictions, the paper gives a lower bound for consistency when the robustness is bounded. Moreover, the paper studies the trade-offs achievable by more space-efficient predictions. Finally, for any number of agents, the paper presents a truthful mechanism with $2$-consistency and a slightly relaxed robustness guarantee. Strengths: (1) The paper studies an important problem. Given that strong impossibility results exist when facing strategic agents, it's natural to bridge the gap between the strategic and non-strategic settings via predictions. (2) The paper is well-written and carefully structured. (3) The results are interesting, and the techniques are non-trivial. In particular, for two agents, the approximation ratios match the best achievable bounds up to a constant factor when the prediction is perfectly correct or completely incorrect. Weaknesses: (1) The motivation for studying space-efficient predictions is not convincing enough. (2) Most of the results only hold for two agents. (3) The lower bound is not very promising as even in the non-strategic setting, the best approximation ratio for MMS is larger than $4/3$. (4) Minor: - Line 28: "probability 2" - Line 60: Should briefly explain what it means by "ex-post" guarantees. - Line 121: $\mu_i$ is not defined before. - Line 212: "over agents items" - Line 228: "according predictions" - Line 254: "present present" - Line 271: "show prove prove" - Line 291: "thenB" - Line 320: "to allocated" Technical Quality: 3 Clarity: 3 Questions for Authors: Can you further explain why studying space-efficient predictions is important and interesting? Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: Some of the results are not sufficiently motivated or not promising. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: "Can you further explain why studying space-efficient predictions is important and interesting?" -- Our motivation for succinct predictions comes from the works of [5,6,7], where they show that succinct predictions are crucial for learning the parameters from a few samples and for incorporating a PAC-learnable component in the learning-augmented framework under plausible distributional assumptions. We believe that combining our results on small space predictions with an adequate distributional assumption will yield such a result. We plan to formalize this in subsequent work. [5] Ilan Reuven Cohen and Debmalya Panigrahi. A General Framework for Learning-Augmented Online Allocation, ICALP 2023. [6] T Lavastida, B Moseley, R Ravi, and C Xu. Learnable and instance-robust predictions for online matching, flows and load balancing, ESA 2021. [7] Shi Li and Jiayi Xian. Online unrelated machine load balancing with predictions revisited, ICML 2021. --- Rebuttal Comment 1.1: Comment: Thanks for addressing my concern, and please add the explanations to the paper. I will maintain my score.	Summary: The authors study the problem of fairly allocating a set of $m$ indivisible goods among a set of $n$ strategic agents with additive valuations in a fair manner. The goal is to obtain a truthful mechanism which guarantees a good approximation of maximin share (MMS) of each agent. It has already been shown that no truthful mechanism can guarantee better than $\lfloor \frac{2}{m} \rfloor$-MMS, while a $\frac{720}{959}>\frac{3}{4}$ MMS allocations can be guaranteed when the agents' valuations are public. This paper bridges this gap by having a learning augmented lens and using predictions on agents' valuations. In particular, the authors introduce a framework called "plant-and-steal" which works as follows. For two agents, given a prediction $p$ and an algorithm $A$, it runs $A$ on $p$ (i.e., assuming the valuations are as given in $p$). Then from the bundle of agent $i$, a most valuable good based on the prediction $p$ is taken from $i$'s bundle and given (planted) in the other agents bundle. This is done at the same time for both agents. Then, both agents steal a most valuable good based on their reported values from the other agents bundle. It is easy to see that this mechanism is truthful. The authors prove that if the prediction $p$ predicts the ordering of the goods for the agents and the algorithm $A$ is the round-robin algorithm, then plant-and-steal is $1/2$-consistent and $\lceil \frac{2}{m} \rceil$-robust. Furthermore, they prove that the guarantee "gracefully" degrades in the number of mistakes in the prediction. They use Kendall tau distance as a measure of preciseness of the prediction. For more number of agent, they prove a similar approach gives $1/2$-consistency and $((m - \lceil 3n/2 \rceil - 1)^{-1}, \lceil 3n/2 \rceil )$-robustness. It means that no matter how bad the predictions, at least $(m - \lceil 3n/2 \rceil - 1)^{-1}$ fraction of the MMS values of each agent is guaranteed assuming that the number of agents is $\lceil 3n/2 \rceil$. Finally, they also have experiments showing how well their framework works in practice. Strengths: The paper is well-written and easy to follow and I did enjoy reading it. Looking at fair division problems through the lens of learning augmented algorithms is definitely an interesting approach. At least for the case of two agents, the paper presents an almost optimal result that one can hope for. Weaknesses: The contribution of the paper is limited in my opinion since the main result only concerns two agents. For more number of agents, while the consistency guarantee is not bad, the robustness guarantee is very weak. I have a more fundamental concern regarding the presented algorithm. The existing algorithms for approximate MMS (in the classic fair division setting without predictions) guarantee $\alpha$-MMS allocations and currently the best known $\alpha$ is marginally above $3/4$. These algorithms are not truthful mechanisms, however, they guarantee every single agent that if she is truthful, she will end up having $\alpha$ fraction of her MMS value. In particular for two agents, $\alpha=1$. Now, what is the use of having truthful mechanism which guarantee only $2/m$ fraction of MMS values of the agents? In particular, the proposed mechanism, incentivise the agents to be truthful, and in the best case guarantees $1/2$-MMS and if its own prediction is off, even much worse. What I am trying to convey is that, while there exists algorithms that guarantee $3/4$ and better approximation of MMS, what is the incentive for strategic agents to participate in a truthful mechanism, give away all their data (since their dominant strategy is to be truthful) and in return get way less than they could possibly get. Technical Quality: 3 Clarity: 3 Questions for Authors: Could you please address the raised concern in the last section? Comments and Suggestions: L 22: For the case of two agents ... : the sentence does not read well. Maybe replace "which" with "what" L 40: ... over goods.For ... $\rightarrow$ .. over goods. For ... L 58: with probability $2$ $\rightarrow$ with probability $1/2$ L 57 until the end of the paragraph: I did not understand why you mentioned randomized allocations at all and if so, why so briefly. In my opinion you should either discuss it properly and cite the related work or not at all. Having only one sentence on it was a bit confusing. L 92: $\lceil \frac{m}{2} \rceil$ $\rightarrow$ $\lfloor \frac{m}{2} \rfloor$ L 122: ran $\rightarrow$ run L 125: then $\rightarrow$ than L 163: use \boldmath in the paragraph title L 209, 213: $\ell$th $\rightarrow$ $\ell$-th L 254: present present $\rightarrow$ present L 264: espace before "for" L 271: show prove prove $\rightarrow$ prove L 291: space after "then" L 320: allocated $\rightarrow$ allocate Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: No. The main contribution of the paper is theoretical. However, still from theoretical point of view, there are limits that could have been discussed. For instance while the robustness guarantee (for two) agents is almost optimal, the consistency guarantee is far from optimal. Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: * "I have a more fundamental concern regarding the presented algorithm. The existing algorithms for approximate MMS (in the classic fair division setting without predictions) guarantee 𝛼-MMS allocations and currently the best known 𝛼 is marginally above 3/4. These algorithms are not truthful mechanisms, however, they guarantee every single agent that if she is truthful, she will end up having 𝛼 fraction of her MMS value. In particular for two agents, 𝛼=1. Now, what is the use of having truthful mechanism which guarantee only 2/𝑚 fraction of MMS values of the agents? In particular, the proposed mechanism incentivises the agents to be truthful, and in the best case guarantees 1/2-MMS and if its own prediction is off, even much worse. What I am trying to convey is that, while there exists algorithms that guarantee 3/4 and better approximation of MMS, what is the incentive for strategic agents to participate in a truthful mechanism, give away all their data (since their dominant strategy is to be truthful) and in return get way less than they could possibly get." Mechanism design has been a fruitful and central research area in Economics. The philosophy behind this approach is that if the mechanism is not truthful, the input for the mechanism might be strategic, and not representing the real parameters of the problem, thus the algorithms won’t be optimizing the objective it’s designed to optimize. Even if agents are to get better utility by coordinating, if each agent locally optimizes their utility, both agents might end up in a suboptimal solution, as demonstrated by the prisoner’s dilemma, while the optimal solution is not stable in a game-theoretic sense. The tension between truthfulness and the performance of the algorithm has been a central theme in the Algorithmic Game Theory literature, where the much desired truthfulness property often comes at the expense of the algorithm’s performance. Like the reviewer, we also were not satisfied with the $\lfloor m/2\rfloor$ lower bound from [2]. We also believe that many of the relevant settings for fair division, such as course allocation, data is abundant, and can be used to improve the performance of the truthful mechanism. We believe that this point was thoroughly demonstrated by our comprehensive set of results. While the privacy concern expressed by the reviewer is not the focus of our paper, we note that our mechanisms only require agents to minimally expose information, as they are only required to choose a single item from a predetermined set of items, which does not depend on their reports. Thus, they only need to reveal which is the most valuable item from a set of items, while not even exposing their value for the item. We will stress this point in the final version of the paper. [2] G. Amanatidis, G. Birmpas, G. Christodoulou, and E. Markakis. Truthful allocation mechanisms without payments: Characterization and implications on fairness, EC 2017. --- Rebuttal Comment 1.1: Comment: I thank the authors for their response. Let me describe my concern in more detail. I understand the motivation behind having truthful mechanisms in general. However, I believe the known results on MMS (unfortunately) lessen the significance of this study. It is already known that $\alpha$-MMS allocations exist for some $\alpha>3/4$. Let's assume this algorithm does not have access to all the data but the agents report their valuations. This algorithm guarantees each agent $i$, $\alpha MMS_{v'_i}$ assuming that agent $i$ reports $v'_i$. This is completely independent of what other agents are reporting. Hence, for this algorithm to output an $\alpha$-MMS allocation, it does not need all the agents to report truthfully. If someone can gain more by misreporting, it does not make other agents to end up with less than $\alpha$ fraction of their MMS value as long as they report truthfully (which makes it different from the prisoner's dilemma). On the other end, it has also been shown that no truthful mechanism can guarantee better than $2/m$-MMS which is very interesting. On one hand, from theoretical point of view, I get the appeal of trying to bridge this gap, but given the explanation I gave above, I think the known $\alpha$-MMS algorithms are strictly better to use in any implementation. So beyond theoretical curiosity, I do not find other motivations for the given mechanism. Nevertheless, I must mention that I really like the fact you mentioned in your response that indeed your mechanism only asks for the highest valued item. I think this should be more highlighted in the paper. I find this the most important factor that makes your mechanism comparable with the $\alpha$-MMS allocation which asks the agents to report all the values. I think more discussions need to be added to the paper to make the result in better perspective with what is already known. I should also add to the strengths of the paper that having only the ordering of the goods as prediction is a very reasonable assumption. I increased my score.	Summary: This submission studies the problem of approximating truthful mechanisms for the Maximin-Share allocation of individual goods whenever agents have incentives. Specifically, the authors design a learning-augmented algorithm for allocating goods to agents, given a prediction over the agents' ordinal preferences over goods. Like other work on learning-augmented algorithms, the goal is to take advantage of the prediction to get a better approximation when it is accurate, while still being robust to inaccurate predictions. The authors give results for both the two-agent case and the n-agent case. Their results are based on a novel framework for designing allocation algorithms which they term "plant-then-steal". At a high level, the framework operates by first applying some allocation procedure (to be instantiated by the algorithm designer) which treats the predictions over agent preferences as correct in order to split the goods into sets of bundles (one per agent). In the second step, the framework uses the predictions to "plant" each player's favorite item in someone else's bundle. In the third step, the framework "steals back" each agent's favorite item according to their reported preferences. For two players, the authors instantiate the plant-then-steal framework in order to get a 2-approximation whenever the predictions are correct (i.e. whenever they are "consistent"), and a worst-case "robustness" guarantee of m/2 when the predictions are arbitrarily wrong. (Here m is the number of items.) The authors also show that the performance of their instantiation degrades gracefully as a function of how inaccurate their predictions are, as measured by the Kendall tau distance between the predicted agent preferences and their actual preferences. The authors also study the setting in which the algorithm designer is given access to predictions which don't necessarily take the form of agent preference orders. They show a lower bound on the trade-off between consistency/robustness, then provide mechanisms for allocating items in this setting using their plant-then-steal framework. Beyond two players, the authors provide a 2-approximation whenever predictions are consistent, and obtain robustness guarantees of (m - n/2 - 1). Finally, the authors empirically evaluate several allocation schemes on two-player instances, and find that algorithms based off of their plant-then-steal framework perform well. Strengths: While the Maximin-Share allocation problem has been well-studied in the literature, the authors are the first to study the role of predictions in this problem, to the best of my knowledge. The introduction of predictions is well-motivated, as it is natural for the algorithm designer to have some guess about the preferences of the agents. Moreover, the authors present a very comprehensive set of results for this setting - the depth and breadth of results in this submission is impressive. Weaknesses: I have no major complaints. One relatively minor criticism is that the paper may be hard to read for someone who is not already familiar with the Maximin-Share allocation problem. For example, exactly what an agent report is is never clearly explained. Technical Quality: 4 Clarity: 3 Questions for Authors: n/a Confidence: 4 Soundness: 4 Presentation: 3 Contribution: 4 Limitations: The authors have adequately addressed the limitations of their work. Flag For Ethics Review: ['No ethics review needed.'] Rating: 8 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: “the paper may be hard to read for someone who is not already familiar with the Maximin-Share allocation problem. For example, exactly what an agent report is is never clearly explained” -- We will make an effort to improve readability in the camera-ready version of the paper, including a clearer explanation of what agents report. Specifically, we will discuss how mechanisms can be implemented by requiring agents to report their full valuation vectors or, alternatively, only their favorite item from a bundle of items (for mechanisms involving two agents) or multiple favorite items (for mechanisms involving n agents). This point will be clarified in the final version. --- Rebuttal Comment 1.1: Comment: Thanks for your reply. After reading the other reviews and responses, I have decided to maintain my score. Moreover, I do not view the fact that most results in this submission are for the two-agent case as a substantial weakness, as the two-agent version of this problem is sufficiently well-motivated. While more substantial results for the n-agent case would of course be interesting, I think that it would be unfair to the authors to have them be on the hook to completely solve the n-player settj g, as (I believe) the two-agent results already clear the bar for NeurIPS.	Summary: This paper designs truthful algorithms for the fair allocation of indivisible goods in the learning-augmented framework. The algorithm is said to receive predictions about all agents' utilities for all goods (agents have additive utilities) or their ranking over the goods. The fairness notion studied is MMS (the maximin share). The main focus of the paper is on truthful mechanisms. Most of the paper is focused on two agents. The idea of the proposed plant-and-steal framework is to use the predictions to initiate an allocation $A_1, A_2$; take the favorite good for agent 1 from $A_1$ and plant it in $A_2$ and vice versa; and, now with the utilities that agents report, let the agents steal their favorite item from the other bundle. This achieves a 2-approximate MMS (2-MMS in short) when predictions are completely correct (consistency), and $\lceil m/2 \rceil$-MMS when predictions are incorrect which matches what is achieved by the best truthful mechanism in the standard setting without predictions (robustness). Next, the paper focuses on when predictions are agents' rankings for goods instead of the actual cardinal utilities. Using the round-robin mechanism in the plant-and-steal framework achieves the same guarantees (2-MMS for consistency) and $\lfloor m/2\rfloor$-MMS for robustness). When the predicted rankings have a Kendall tau distance of at most d, this mechanism achieves $2 \sqrt{d} + 6$-MMS which interpolates between constant and $m/2$ in the worst-case. The paper ends with synthetic experiments with two agents. In the appendix, the paper discusses mechanisms with $O(\log m /\epsilon)$ communication (previous ones had $\Omega(m)$) that achieve $2 + \epsilon$ robustness. The paper also generalizes the results to $n$ agents, achieving $2$-consistency and weaker robustness guarantees. There are some other results in the appendix as well exploring pointwise tradeoffs in the Pareto frontier. Strengths: - The problem of designing learning augment algorithms for approximate MMS allocations is new. - The results for the two agents are almost tight given the priorly known hardness results. The Kendall tau parameterized results show a nice trade-off. - The paper claims and proofs seem correct to me (though, I have not checked most of the proofs in the appendix.) - The plant-and-steal mechanism is simple. - The paper is overall easy to understand. (The writing and organization could be improved considerably, more on this below.) Weaknesses: - The predictions are either the entire valuation matrix or all the rankings, which contain a lot of information. - Most of the paper is focused on two agents. Even for two agents, I don’t think we learn the complete picture from the paper. I couldn’t find a lower bound for the Kendall tau parameterized result. - While I like the algorithm's simplicity, I find it a relatively marginal improvement over the truthful mechanism of Amanatidis et al [7]. The technical novelty of the paper isn’t such that we say it’s a strength of the paper, in my opinion. The proofs and algorithms heavily use the priorly known results about truthful mechanisms and their MMS approximations Amanatidis et al [6, 7]. - The main body of the paper isn’t very well organized for a NeurIPS paper. The technical section starts on page 6. The experiment results (figures) are all in the appendix. Please reorganize, and instead of having two pages for “our results” allocate it to the technical section that speaks more formally about them. - I couldn’t find the definition of “success rate” in the experiments. The y-label in Figure 2 is set to $\epsilon$ which should have been the subcaption of the subfigures. All in all, I couldn’t understand the results of the experiments and verify the takeaways. - In the experiments, it’s unclear why a Mallows model was not used to generate rankings, which is a more justified statistical model to sample rankings. See e.g. https://proceedings.mlr.press/v97/tang19a.html for the Mallows model parameterized by the Kendall tau distance. I’m also not convinced much by the utility sampling procedure. Is having high-medium-low valuations necessary? How would the results change if it was just unit-sum valuations uniformly sampled from the Dirichlet(1,...,1) (random unit-sum vectors) or Gaussian perturbations of some ground truth valuation vector? Minor points: - The MMS guarantee of $m - 3n/2 - 1$ should have some conditions between $n$ and $m$ perhaps $m \ge 2n$ or similar. It’d be great to be more precise in the theorem/lemma statements. - In appendix A, there is a “$8/m$” probability mentioned, a $1/2$ and a $1/4$, which I don’t see why would sum to $1$. - line 58, “With probability $2$”, should it be $½$? - line 50, “959 / 720 > 4/3$”, the reverse inequality is true - Please consider renaming Theorem F.1 to Theorem 4.2 as one cannot just search for the proof of Theorem 4.2 easily, e.g. using the package “thm-restate”. - You could save precious space by presenting algorithm 2 and mechanism 1 next to each other. - line 122, one can “ran” -> run - line 125, more “then” -> than - table 1, $\hat{n}$ is undefined, please revise that part - line 158, an $(1+\epsilon/2)$ -> change an to a. (I think a one is correct not an one.) - lines 183 and 184, related “works” -> work - line 291, thenB-RR-Plant-and-Steal -> add space between “then” and “B-RR-…” Technical Quality: 3 Clarity: 3 Questions for Authors: - In the experiments, what is the definition of success rate? Have you considered other utility sampling methods and if so, how did the results differ? - Are there any matching lower bounds for the $\sqrt{d}$ Kendall-tau result? - Have you thought about identical utilities? Can we achieve better guarantees assuming that agents have identical utilities? Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: This is a theory paper and I don't see immediate serious concerns. I would recommend the authors to discuss how much inefficiency their method can have in terms of social welfare for instance. Discussing the remaining gaps in the analysis is also helpful for the reader or follow up work. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: * "The predictions are either the entire valuation matrix or all the rankings, which contain a lot of information." -- The predictions used are: 1) Rankings, which we think are much more plausible than the exact valuations – it’s easier to predict that item A is more valuable than item B than to accurately predict their exact valuations. For this type of predictions, we can even handle inaccurate predictions, when the inaccuracy is bounded. 2) Small space predictions. Here we use predictions of size O(log(m)/\epsilon) which are significantly smaller than the O(mㆍlog(m)) space needed to represent rankings, not to mention the much larger spaced needed to represent valuation functions.. 3) For the n agent mechanisms, we use rankings as predictions, plus indicators indicating which are the “large” items, and not the entire valuation matrix, as stated in line 961, P. 28. In conclusion, we never need to use the entire valuation matrix as prediction, since we aim to use realistic and robust predictions. We thank the reviewer for raising our awareness that this is not emphasized enough, and will add a discussion to the final version of the paper to make sure this point comes across. * "Most of the paper is focused on two agents." -- Since strong impossibilities for truthful fair division already arise for two agents, this setting is well studied in the literature (see [1,2,3,4] for instance), as better understanding in this limited setting might be later generalized to multiagent settings. Indeed, we show that our mechanism can be generalized to $n$ players (while becoming much more involved). In this setting we get weaker, yet non-trivial, robustness guarantees. * "Are there any matching lower bounds for the 𝑑 Kendall-tau result?" -- We can show that the analysis of the O(\sqrt{d}) approximation is tight up to a constant for the mechanism at hand. We don’t give a general parameterized lower bound for every truthful mechanism. Showing general lower bound is highly non trivial for fair division and has been the focus of several papers on fair division, including specifically for approximate MMS allocation [2]. We leave this for future work. * “The main body of the paper isn’t very well organized for a NeurIPS paper…” -- Thank you for your suggestions, we’ll implement these changes in the final version. * "I couldn’t find the definition of “success rate” in the experiments. The y-label in Figure 2 is set to 𝜖 which should have been the subcaption of the subfigures." -- In L.350, we define our benchmark as “the percentage of instances where both players receive at least (1-𝜖) of their MMS values for different values of 𝜖,” which corresponds to the success rate. To improve clarity, we will explicitly mention this and add it to the subcaption. * "In the experiments, it’s unclear why a Mallows model was not used to generate rankings, which is a more justified statistical model to sample rankings. See e.g. .../tang19a.html for the Mallows model parameterized by the Kendall tau distance. I’m also not convinced much by the utility sampling procedure. Is having high-medium-low valuations necessary? How would the results change if it was just unit-sum valuations uniformly sampled from the Dirichlet(1,...,1) (random unit-sum vectors) or Gaussian perturbations of some ground truth valuation vector?" -- We thank the reviewer for the relevant reference. We will look into the proposed model and other studied models to generate ranking predictions. Regarding valuations, we observed that some sampling methods, such as I.I.D. sampling and the proposed random unit-sum vectors with an arbitrary balanced partition, perform quite well. However, we believe these do not represent most real-life instances. Therefore, we chose to use a relatively simple yet non-trivial model to generate valuations with three types of items: low, medium, and high. In this model, there are more low-valued items than medium-valued items, and more medium-valued items than high-valued items. We believe this phenomenon matches many real-life scenarios and illustrates the importance of the different components of our mechanisms. * "Have you thought about identical utilities? Can we achieve better guarantees assuming that agents have identical utilities?" -- That’s a very interesting question! For identical utilities, round robin allocations, or any turn-based picking mechanisms^, are ex-post Incentive compatible^^ (EPIC). In this case, when an agent picks an item, they should always pick the best available item, which is what is implemented if agents report their true valuations/ranking and the mechanism uses a turn-based mechanism to determine the allocation. Thus, we are able to get ⅔ approximation to the MMS for two agents without any predictions for this truthfulness notion. For more than two players, it follows from [3] that we can get EPIC mechanisms with approximation ratios that depend on the number of players, but not the number of items, truthfully. If we get indicators for the large items as predictions, even without rankings, then now we can get constant factor approximation EPIC mechanisms. ^ In turn-based picking mechanisms, each turn an agent picks a number of items from the set of remaining items, where the number of items is picked in advance. ^^ In Ex-post Incentive compatible (EPIC), bidding truthfully is a Nash Equilibrium. [1] Benjamin Plaut and Tim Roughgarden. Almost Envy-Freeness with General Valuations, SODA 2018. [2] G. Amanatidis, G. Birmpas, G. Christodoulou, and E. Markakis. Truthful allocation mechanisms without payments: Characterization and implications on fairness, EC 2017. [3] G. Amanatidis, G. Birmpas, and E. Markakis. On Truthful Mechanisms for Maximin Share Allocations, IJCAI 2016. [4] Biaoshuai Tao. On existence of truthful fair cake cutting mechanisms, EC 2024. --- Rebuttal Comment 1.1: Comment: Thank you for the detailed response. My apologies for the very late reply. I have read all the reviews and your responses. Also, I recently checked the appendix more thoroughly and looked at some of the proofs. I do appreciate the effort put into finding different trade-offs between robustness and consistency and the attempted generalizations to $n$ agents. The main body, the two technical sections 3 and 4, do not convey the depth explored. I still believe the main body should be revised significantly as a NeurIPS paper (see below). I share the concern of reviewer iNp4. The strong inapproximability of MMS shown for truthful mechanisms from prior work, do limit the significance of this study. Robustness guarantees of $m/2$-MMS or sometimes $m$-MMS are quite weak. I hold a different view than reviewer dEcz on the main result for two agents. I still think most of the "heavy-lifting" for results of two agents, e.g., characterizing truthful mechanisms including working with ordinal preferences, and the positive and negative results on MMS approximability, is done by prior work. Also, we do not get that close to a full picture for two agents in terms of the trade-offs between robustness and consistency --- as many papers do in the learning augmented framework. That said, I like the simple and nicely presented steal-and-plant mechanism. I am increasing my score, mainly for the results in the appendix. On re-organizing: One idea is to move the experiments to the appendix --- all the plots which are in the appendix unfortunately, which shouldn't be the case. Instead of the long our results section, the technical sections can better describe the results in details. Perhaps include one of the more technically novel proofs (or a sketch of it) would better be included.	Rebuttal 1: Rebuttal: We thank all the reviewers for their thoughtful and thorough reviews. We will address all their comments and edit suggestions to improve the final manuscript. We address each reviewer’s comments/questions in the individual rebuttal sections below.	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Efficient Contextual LLM Cascades through Budget-Constrained Policy Learning	Accept (poster)	Summary: The paper introduces TREACLE, a reinforcement learning policy designed to optimize the selection of LLMs and prompting schemes based on a user's budget constraints in terms of cost and latency. Strengths: 1. TREACLE enables substantial cost savings compared to existing methods by intelligently choosing among various LLMs and prompts based on the monetary cost, latency, and accuracy. 2. By considering the context of the question, including embeddings and past interactions, TREACLE customizes the prompting strategy to balance accuracy against cost, often using advanced prompting strategies like Chain-of-Thought to improve answer quality at a controlled cost. 3. The system dynamically decides whether to re-query a model based on the current response's consistency and the remaining budget, which helps in refining the answers further without exceeding budget constraints. Weaknesses: 1. Dynamic selection of models and re-querying could lead to increased computational costs and delays, especially in scenarios requiring high real-time performance. Although the system is designed to save costs, frequent model switching and complex queries might backfire. 2. The reward mechanism mentioned in the text depends on accurate answer feedback to adjust strategies, but in practical applications, users may not always provide clear or consistent feedback. This could lead to instability during the learning process and inaccuracies in reward distribution. 3. My biggest concern is that the architecture of the LLM itself has not been changed. It merely adds additional reinforcement learning, which seems overly reliant on data, and might perform poorly on new types of questions or unseen data, limiting the model's generalizability. Technical Quality: 3 Clarity: 3 Questions for Authors: 1. Is the setting in lines 103-107 somewhat far from reality? The same question is asked many times; wouldn't that mean, in practice, there is an endless number of questions that need to be learned, and indeed, the same question could be asked in many different ways. Also, users might not always provide feedback on a question, so how would one obtain the reward? 2. How large is the actual action space, particularly with the three different prompt strategies (standard, domain expert, and CoT)? 3. Optimizing the selection of LLMs and prompting schemes with constraints is an intuitive idea. There are already some similar works: (1)- "Which LLM to Play? Convergence-Aware Online Model Selection with Time-Increasing Bandits" (2)- "Cost-Effective Online Multi-LLM Selection with Versatile Reward Models" (3)- "Best Arm Identification for Prompt Learning under a Limited Budget" So, the Table 1 listed by the authors is not comprehensive. If the authors do not have time to conduct new experiments for comparison, you could provide a textual description comparing these works, highlighting the advantages of your own work. 4. Where are "finetune" and "scratch" mentioned in Figure 7? Confidence: 2 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: As mentioned by the authors, the RL policy’s budget does not account for the cost of collecting the training data. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: ### W1: Dynamic selection of models and re-querying could lead to increased computational costs and delays As the reviewer points out, latency plays a crucial role in real-time settings (e.g., voice assistants). To address scenarios requiring real-time performance, we incorporated latency as a component of the cost constraint (see L142). TREACLE allows users to choose the trade-off between monetary cost and latency by adjusting a trade-off coefficient $\beta$, where $cost=\text{latency} + \beta * \text{monetary price}$. This enables the users to choose the balance between monetary cost and latency according to their specific needs. The rightmost two subfigures in Figure 3 show the performance when latency is included in the cost constraint, using real end-to-end latency values (including computation and communication) that we measured by querying Llama and GPT models (see Figure 13 in the Appendix). Further experiments regarding latency are described in Appendices C.1 and C.4. We conducted experiments when the API query latency varied over time; these results are summarized in Table 2 in Appendix C.1 and show that TREACLE can adapt to API querying latency that differs across models and time. Figure 15 in Appendix C.4 shows results with latency in the cost function for more datasets and $\beta$ values. Finally, an additional component of computation latency is the RL model itself. Our RL model is a two-layer neural network, so the inference time is very fast (on the order of ms) and hence negligible. ### W2: Users may not always provide clear or consistent feedback. To clarify, we do not rely on user feedback. Rather, during the training phase, the RL learns a policy to maximize rewards using the correct answers from the datasets, and executes that trained policy during the test phase (see L197). The main form of “feedback” during the test phase is the consistency of the responses returned by the LLMs, as in prior work [20]. However, we found that response consistency alone is insufficient feedback, so TREACLE combines response consistency with prompt text embedding, for the first time, to enhance the overall effectiveness. Adding user feedback, along the lines of active learning, could be an interesting future extension for our framework. ### W3: The architecture of the LLM itself has not been changed We believe that adding reinforcement learning on top of existing LLMs is a strength of our framework, since the modular design enables incorporating new LLMs that are constantly emerging. TREACLE’s framework is generalizable and we investigated its adaptability to new types of questions (Section 5.2.3), unseen data with harder questions (Section 5.2.2), and new LLMs (Section 5.2.1). For example, to understand whether TREACLE can adapt to new types of questions, we conducted experiments (L384-394). The base model is trained using commonsense reasoning questions (CSQA dataset), and the new unseen question type are math problems (GSM8K dataset). The results in Figure 10b show that TREACLE can achieve high accuracy on new question types with only a minimal amount of extra training (i.e., “Fine-tune on 200 GSM8K” is close to “Train on GSM8K”). This minimal amount of extra training is done by freezing the base RL policy trained on CSQA and fine-tuning the “text embedding” feature in the state vector using GSM8K. ### Q1: Is the setting in lines 103-107 somewhat far from reality? The setting of re-querying the same question multiple times has been established in the literature [16,20]. In practice, there are a limited number of unique combinations of language models and prompts. In our experiments, there are 6 possible combinations. The reinforcement learning (RL) model is designed to be general; it does not need to be trained with every possible question variation and answer to choose the best action. ### Q2: How large is the actual action space? There are 3 possible actions in the action space, no matter which prompt or model was used on the previous query: Return the current response, re-query with the same model-prompt pair, or select a new model-prompt pair (from the next option in the cascade, not choosing from all possible model-prompt combinations). We will elaborate on this in L188. ### Q3: Related work Compared to our work, firstly, we are the only work that considers latency constraints. Some scenarios require high real-time performance, as mentioned by Reviewer gLy5. Second, we take into account both LLMs and prompts, since performance and cost are influenced by both factors. The related papers only focus on one of them. Third, we show generalization to unseen tasks and that our method is pretty sample efficient. This is related to the online decision exploration cost mentioned in (2). Fourth, unlike the mentioned papers, we treat the LLMs and prompt pair as a black box, without training or fine-tuning them. Finally, we determine different model and prompt pairs for each sample, rather than for the entire task. We will add these papers to the table in the related work section, and hope to add them as baselines once their code is released. ### Q4: Where are "finetune" and "scratch" mentioned in Figure 7? “finetune” (solid blue/orange lines) means that we start with a model that was trained using the old API prices and language models (LLMs), and then fine-tune it with new state-action trajectories collected using the new API prices and LLMs. In contrast, “scratch” (dashed blue/orange lines) means that we train from scratch, i.e., we initialize the reinforcement learning (RL) model randomly and train it directly with the newly collected trajectories. We will add these clarifications to the text of the paper. ### L1: Cost of collecting training data As mentioned in the paper, we plan to release the training datasets and code for reproducibility so that others can avoid the cost of collecting training data and adapt the framework to other LLMs and tasks. --- Rebuttal Comment 1.1: Comment: Thank you for your response, which has addressed my concerns. However, as Reviewer LPQa mentioned, the main weaknesses of the paper are that the method overlooks the actual cost, and the supplementary experiment TREACLE+penalty does not show a significant effect. Overall, I choose to increase the score by one point, but my confidence is not high. --- Rebuttal 2: Comment: We thank the reviewer for reassessing our work and raising their rating. Regarding Reviewer LPQa's concern: We realized that Figure 1 may not reflect the full picture due to the log-scale of the x-axis. Kindly consider the equivalent table provided below which demonstrates that TREACLE with penalty facilitates significant cost reduction. \| Budget \| Total Cost (No Penalty) \| Accuracy (No Penalty) \| Total Cost (With Penalty) \| Accuracy (With Penalty) \| \|----------\|---------------------------\|-------------------\|--------------------\|----------------------------\| \| 0.05 \| 0.050 \| 0.273 \| 0.047 \| 0.268 \| \| 0.15 \| 0.150 \| 0.799 \| 0.149 \| 0.791 \| \| 0.3 \| 0.298 \| 0.843 \| 0.297 \| 0.842 \| \| 0.6 \| 0.599 \| 0.891 \| 0.596 \| 0.890 \| \| 0.9 \| 0.884 \| 0.909 \| 0.876 \| 0.907 \| \| 1.5 \| 1.471 \| 0.918 \| 1.261 \| 0.911 \| \| 3 \| 2.826 \| 0.920 \| 2.471 \| 0.917 \| \| 6 \| 5.951 \| 0.938 \| 4.517 \| 0.926 \| Above, the last data point (budget of $6) shows a 24.09% reduction in cost compared to the original (from 5.951 to 4.517), with a corresponding 1.279% decrease in accuracy (from 93.8% to 92.6%). At a budget of $3, the improvement is also evident with 12.56% lower costs and accuracy drop of only 0.3%. Finally, this table also demonstrates that TREACLE works as intended: - Without penalty, the method fully utilizes the available budget i.e. the actual cost is very close to the max available budget. This is in line with the goal of maximizing accuracy subject to the budget constraint. - With penalty, it utilizes the budget more efficiently (e.g. 24% cheaper) at the cost of slightly reduced accuracy. Note that such an accuracy-cost tradeoff is fundamental and not really avoidable (there is no free lunch; we cannot perfectly know which are the easy questions to save on). Also note that by increasing the penalty parameter that trades off between cost and accuracy, one can achieve a more drastic cost reduction at the expense of (slightly) worse accuracy. We are happy to provide more results with different penalty parameter $\lambda$ choices. In summary, we hope this clarifies that if we wish to minimize actual costs as pointed out by the reviewer, the model with penalty can efficiently allocate resources to avoid additional spending, when accuracy gains start to diminish (using tradeoff parameter $\lambda$). We thank the reviewer again for raising the actual spent cost as an important consideration.	Summary: The paper proposes a reinforcement learning method to select the model and prompting. It combines with monetary cost and latency constraints. The design of the features contains question text embeddings and response history. Experiments studies the cost savings. Strengths: 1, Important problems. 2, Interesting algorithm design 3, Many experiments Weaknesses: The main weaknesses of the paper are that the method overlooks the actual cost and the experiments are not convincing enough. 1, Insufficient to differentiate simple and difficult questions in model selection. A good model selection mechanism should choose low-cost models for simple questions and more powerful models to improve accuracy for difficult questions. The selected models should differ between simple and complex questions. From Figure 4a, it can be seen that when the budget is low (0.05), the selected models are limited to llama2-7b and llama2-13b, failing to call powerful models for solving difficult problems. However, when the budget is high (10), the selected models no longer include llama2-7b, thus missing the opportunity to use low-cost models to reduce expenditure. 2, Lack minimizing actual cost in method design. The method proposed in this paper is designed to only consider staying within the long-term (maximum) budget, without optimizing for minimal actual cost, which can lead to cost inefficiencies. This may derive from overlooking individual cost optimization. 3, Unnecessary high actual costs on simple questions. In simple questions, the method proposed in this paper shows similar accuracy to existing methods, but it consumes an additional 19% of the actual cost. Figure 8b shows that when the total (maximum) budget is \$1, the method proposed in this paper (TREACLE) performs similarly to Single model and Calibrated cascade in terms of accuracy. However, according to Figure 8c, Single model/Calibrated cascade actually costs 0.69/0.702, while TREACLE costs 0.84 (an additional 19%). Technical Quality: 3 Clarity: 3 Questions for Authors: Why do the authors summarize in Table 1 that MoT, a consistency-based method, cannot be robust to new models? I believe this statement is incorrect because this method is training-free. If it is due to limitations in various model capabilities, I suggest introducing the option of 'partially limited'. Confidence: 5 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: It is recommended to apply the method proposed in this paper to more tasks. The tasks in this paper are too limited. Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We greatly appreciate the reviewer’s detailed and constructive feedback. ## Weakness 2: Main weaknesses of the paper are that the method overlooks the actual cost. We acknowledge the reviewer's concern and agree that our method uses a total budget constraint which minimizes the individual query costs in an indirect fashion. In general, the choice of cost function (e.g. the total budget constraint or individual costs or both) is a design decision. The constraint budget formulation we adopt is widely utilized in resource allocation problems and is typically more difficult to solve/enforce compared to unconstrained RL. That said, our approach is flexible and can also directly minimize the actual cost through a penalized reward formulation. Concretely, following the reviewer’s suggestion, we examined a penalized variation of TREACLE where the reward formulation is (see PDF in rebuttal for all reviewers for precise form) $$\mathbb{E}[query\\_acc - \lambda\cdot query\\_cost]~~~subject~to~~~total\\_cost \leq B$$ Here, $\lambda\cdot query\\_cost$ is the penalty term we incorporate. This penalized form brings us to Weakness 3 discussed below. ## Weakness 3: Unnecessary high actual costs on simple questions. We have conducted experiments on TREACLE+penalty which are provided in Figures 1 and 2 of the PDF. - Over the set of easy questions, penalty promotes the use of cheaper models and matches the single model baseline without loss of accuracy. This highlights that penalty aids the efficient use of budget in line with the reviewer’s intuition. The TREACLE+penalty model tends to solve easy questions with less powerful LLMs and the budget spent decreases to 0.717 which is almost the same as the single model baseline while also achieving on-par accuracy, 0.987 (TREACLE+penalty) v.s. 0.986 (single model). - In general, penalty term will result in a budget-accuracy tradeoff. This is because we don’t exactly know the optimal model for solving a particular question. When evaluating TREACLE+penalty over all queries, we find that penalty improves the budget utilization of TREACLE (actual cost decrease from 0.97 to 0.94) however it also results in (minor) accuracy degradation (accuracy decrease from 0.92 to 0.90). ## Weakness 1: Insufficient to differentiate simple and difficult questions in model selection. The results actually show that our method makes intelligent choices in a budget-aware fashion. Concretely: - When the budget is low (0.05), the model correctly prioritizes easy questions, as calling an expensive model for one difficult question would leave more than 20 other questions unanswered, harming the overall performance. For instance, with the settings of Figure 4a, if we pick 5 difficult questions and solve them with GPT-4 (CoT), and use the remaining budget for the rest, the total accuracy drops from 0.31 to 0.20. - When the budget is sufficiently high, the model opts for using powerful models for all questions to maximize acuracy. This is because relying on smaller models or difficulty estimation stage can lead to errors. For example, the average accuracy of Llama-2-7b (CoT) is only 23.65%. Forcing the model to use Llama-2-7b (CoT) decreases the performance from 92.47% to 92.20%, and for the Majority Voting baseline, from 83.62% to 83.30%. As discussed under Weakness 2 and 3, when we use TREACLE-penalty, the model starts prioritizing Llama-2 even with a high budget. ## Question 1: Why MoT cannot be robust to new models We agree that MoT is training-free; however, the original MoT paper does not address the inclusion of new models. We believe it has two limitations when incorporating new models: Firstly, MoT only allows for two models, a weak and a strong one, and there is no clear way of adding more models. Secondly, MoT uses a threshold to decide whether an answer is accepted or not. There is no guarantee that a fixed threshold will work across multiple distinct models or how to find/optimize such thresholds efficiently. For instance, our calibrated cascade approach is reminiscent of MoT and, empirically, we find that it is not robust to distribution change. ## Limitations: It is recommended to apply the method proposed in this paper to more tasks. Thank you for your suggestion. We plan to include additional tasks in future work. Currently, we have evaluated our approach using three representative datasets. Additionally, we demonstrate that our model can be seamlessly adapted to unseen tasks (L384-395, Fig 10b) and that a single model can effectively handle multiple types of tasks while maintaining a shared budget constraint (L374-383, Fig 10a). We genuinely appreciate the reviewer’s excellent points which motivated us to study penalized TREACLE. We will incorporate these discussions and evaluations and revise the manuscript accordingly. We hope that this response has addressed their concerns. We would be happy to engage further during the discussion week. --- Rebuttal Comment 1.1: Comment: Thank you for the detailed response. I appreciate the design regarding the penalty. However, based on the newly added experiments, Figure 1 in the attachment shows that the cost has not been significantly reduced, and the accuracy has decreased. Therefore, I will maintain the original score. --- Reply to Comment 1.1.1: Comment: Thank you for your time and feedback. We realized that Figure 1 may not reflect the full picture due to the log-scale of the x-axis. Kindly consider the equivalent table provided below which demonstrates that TREACLE with penalty facilitates significant cost reduction. \| Budget \| Total Cost (No Penalty) \| Accuracy (No Penalty) \| Total Cost (With Penalty) \| Accuracy (With Penalty) \| \|----------\|---------------------------\|-------------------\|--------------------\|----------------------------\| \| 0.05 \| 0.050 \| 0.273 \| 0.047 \| 0.268 \| \| 0.15 \| 0.150 \| 0.799 \| 0.149 \| 0.791 \| \| 0.3 \| 0.298 \| 0.843 \| 0.297 \| 0.842 \| \| 0.6 \| 0.599 \| 0.891 \| 0.596 \| 0.890 \| \| 0.9 \| 0.884 \| 0.909 \| 0.876 \| 0.907 \| \| 1.5 \| 1.471 \| 0.918 \| 1.261 \| 0.911 \| \| 3 \| 2.826 \| 0.920 \| 2.471 \| 0.917 \| \| 6 \| 5.951 \| 0.938 \| 4.517 \| 0.926 \| Above, the last data point (budget of $6) shows a 24.09% reduction in cost compared to the original (from 5.951 to 4.517), with a corresponding 1.279% decrease in accuracy (from 93.8% to 92.6%). At a budget of $3, the improvement is also evident with 12.56% lower costs and accuracy drop of only 0.3%. Finally, this table also demonstrates that TREACLE works as intended: - Without penalty, the method fully utilizes the available budget i.e. the actual cost is very close to the max available budget. This is in line with the goal of maximizing accuracy subject to the budget constraint. - With penalty, it utilizes the budget more efficiently (e.g. 24% cheaper) at the cost of slightly reduced accuracy. Note that such an accuracy-cost tradeoff is fundamental and not really avoidable (there is no free lunch; we cannot perfectly know which are the easy questions to save on). Also note that by increasing the penalty parameter that trades off between cost and accuracy, one can achieve a more drastic cost reduction at the expense of (slightly) worse accuracy. We are happy to provide more results with different penalty parameter $\lambda$ choices. In summary, we hope this clarifies that if we wish to minimize actual costs as pointed out by the reviewer, the model with penalty can efficiently allocate resources to avoid additional spending, when accuracy gains start to diminish (using tradeoff parameter $\lambda$). We thank the reviewer again for raising the actual spent cost as an important consideration.	Summary: This paper presents a framework for managing different budgets—such as accuracy, cost, and latency—when utilizing Large Language Models (LLMs) for reasoning tasks. Recognizing that reasoning tasks can be broken down into a series of question-and-answer interactions, the authors propose a method to allocate models of varying sizes to handle these multi-round interactions effectively. To achieve this, they use a reinforcement learning approach to train a model that can estimate the budget space. The efficacy of the proposed method is validated through evaluations on standard benchmarks, including GSM8k, CSQA, and LLC. Strengths: * Introduces a novel framework for modeling multi-turn reasoning sequences, taking into account the holistic aspects of LLM cost, latency, and other factors. * Empirically evaluates the reinforcement learning-based training and execution of the algorithm in realistic settings using popular datasets. * Provides intriguing real-world observations (Section 5.2.1) regarding the impact of pricing changes and the introduction of new models. Weaknesses: * The current framework is inadequate if a capable model can plan ahead by considering multiple questions or a trajectory of questions in advance, even while using various models for the answers. * The state vector is limited, as text embeddings alone may not fully capture the complete characteristics of the prompt. * There is a need for a reliable method to estimate the quality of questions and answers generated by the model. Technical Quality: 3 Clarity: 2 Questions for Authors: * Many figures require a color printer and are difficult to read due to solid and translucent lines. The authors should consider improving the visuals to be more readable across different printing methods. * Please also refer to the weaknesses section for additional feedback. Confidence: 2 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: Ok. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: ## W1: The current framework is inadequate if a capable model can plan ahead by considering multiple questions or a trajectory of questions in advance, even while using various models for the answers. An approach of considering a batch of questions at once could certainly work, whereas in our framework we consider questions one-by-one. We do this mainly for scalability, as considering multiple questions into the future would greatly increase the dimension of the state and action space and hence the amount of training needed. We believe that our framework can extend to considering batches of questions in the future and it would be interesting to explore. ## W2: The state vector is limited, as text embeddings alone may not fully capture the complete characteristics of the prompt. We agree that text embeddings alone may not capture all characteristics of the prompt. Therefore, our state vector includes both text embeddings and response consistency, which is an indirect measure of another prompt characteristic, its difficulty (for example, difficult prompts tend to have less consistent answers [20]). We are the first to implement this combination of state features, resulting in notable performance improvements. Also, our framework is quite flexible, so additional features relating to prompt characteristics can easily be added. In greater detail, including both text embeddings and response consistency in the state vector improves performance. One baseline method, FrugalGPT, only uses text embeddings. Another baseline method, Majority Voting, only uses response consistency. We have demonstrated significant improvements of TREACLE over both baselines. We also provide theoretical justification supporting why policies considering response consistency perform well (L216-239). ## W3: There is a need for a reliable method to estimate the quality of questions and answers generated by the model. Indeed, we initially had the same thought, and hence we developed the Calibrated Cascade baseline, which explicitly estimates answer quality (using the same state vector as TREACLE as input). It then uses the estimated answer quality to decide whether to query another LLM. While this baseline generally outperforms the other baselines, it is not as robust as TREACLE particularly when there are shifts in question difficulty, because it does not carefully consider the remaining budget when answering easy vs hard questions. In contrast, TREACLE implicitly estimates answer quality by combining previous answers with text embeddings of the question, in order to decide which LLMs to query. ## Q1: improving the visuals to be more readable across different printing methods We will improve the figures to enhance readability for different printing methods, ensuring they are clear even in black-and-white print. --- Rebuttal Comment 1.1: Comment: Thank you for your rebuttal. However, I still have some concerns that remain unaddressed. The responses provided were not entirely satisfactory. I also share the concerns raised by other reviewers (LPQa, gLy5) regarding the absence of direct cost minimization in the modeling process. The two lines in Figure 1 of the rebuttal PDF (with and without the cost penalty) looks nearly identical. It suggests that the cost penalty term is not working effectively. Even in the table the authors provided in the comment, the cost and accuracy trade-off is not great. e.g. compare a) budget of 1.5 gives the original method 0.918 accuracy with cost of 1.471. b) budget of 3 with the cost penalty method gives 0.917 accuracy with the cost of 2.471. Given these remaining concerns, I will be adjusting my score accordingly. --- Reply to Comment 1.1.1: Comment: Thank you for your valuable feedback. With the cost-penalized formulation, tuning $\lambda$ can further adjust the cost-accuracy tradeoff. For example, with regards to the reviewer's example, for a different parameter setting ($\lambda=100, \text{budget}= 3$; previous figures were for fixed $\lambda=10$), the accuracy is 0.918 and the cost is 1.454. This is comparable to TREACLE without penalty and \$1.5 budget, which has the same accuracy of 0.918 and cost 1.471. In other words, with a larger budget and by adding the cost penalty, we can more finely control the actual cost. Overall, many papers use the budget-constrained setting [1,2,3,4]. We explored the cost penalty based on reviewer feedback and found that the TREACLE framework flexibly extended to such a formulation. The results suggest that the cost penalty formulation can perform well with some parameter tuning, which is a general disadvantage of cost-penalty formulations. The advantage of our original formulation is that it does not require parameter tuning, only a simple total budget setting, which easier for practitioners. We would like to add the cost-penalty results as a subsection to the paper further exploring this alternative formulation and different settings of $\lambda$. [1] Bai, Fan, Alan Ritter, and Wei Xu. "Pre-train or Annotate? Domain Adaptation with a Constrained Budget." Proceedings of the 2021 Conference on Empirical Methods in Natural Language Processing. 2021. [2] Hoffmann, Jordan, et al. "Training compute-optimal large language models." Proceedings of the 36th International Conference on Neural Information Processing Systems. 2022. [3] Chen, Lingjiao, Matei Zaharia, and James Zou. "Frugalgpt: How to use large language models while reducing cost and improving performance." arXiv preprint arXiv:2305.05176 (2023). [4] Shi, Chengshuai, et al. "Best arm identification for prompt learning under a limited budget." arXiv preprint arXiv:2402.09723 (2024).	Summary: This paper aims to solve the problem that LLMs can be costly, in particular using technologies such as COT. It proposes to apply RL to select the model and prompting scheme. Experimental results show that the proposed method can maintain the model performance while saving up to 85% costs. Strengths: 1. This paper is generally well-written and is well motivated. 2. The experiments are solid with great cost savings. 3. The idea of using RL to reason over question and response embeddings is interesting. Weaknesses: No great weakness. Technical Quality: 3 Clarity: 3 Questions for Authors: NA Confidence: 4 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: Thank you for your positive feedback on the manuscript. We appreciate your recognition of the reinforcement-learning based approach to achieve significant cost savings when querying LLMs.	Rebuttal 1: Rebuttal: Thank you to the reviewers for their thoughtful reviews and constructive comments. We have provided individual responses to each of the reviewers. In addition to these responses, we have conducted additional experiments to evaluate cost-accuracy tradeoffs by including the cost constraint in the objective, further reducing cost (details are in the response to reviewer LPQa). We hope these new experiments and clarifications will be acceptable to the reviewers. We thank the reviewers for their valuable time. Pdf: /pdf/52bff22f0035b443a4c68d99d0a365549c922231.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
On Differentially Private Subspace Estimation in a Distribution-Free Setting	Accept (poster)	Summary: The paper tackles the challenge of high costs in private data analysis due to the curse of dimensionality, despite many datasets having an underlying low-dimensional structure. It builds on prior work by introducing measures based on multiplicative singular-value gaps to quantify how "easy" a dataset is for private subspace estimation. The authors provide new bounds and a practical algorithm that can estimate subspaces with a number of points independent of the dimension, showing improved performance in high-dimensional settings compared to previous approaches. Strengths: 1.The problem of the paper is well-motivated and the authors give both upper bounds and lower bounds. 2.They also provide experimental results. 3. The writing is clear. 4. The literature review is relatively comprehensive. Weaknesses: There are some gaps between their upper bounds and lower bounds. Technical Quality: 3 Clarity: 3 Questions for Authors: 1. Can your approaches work on real-world datasets? 2. Can you further improve the gap between upper bounds and lower bounds? Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: There are some gaps between their upper bounds and lower bounds. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank you for the positive review. Regarding your questions: 1. We made an effort to reduce the constants so that our algorithm can achieve high accuracy using a reasonable amount of points. But as we mentioned in Section 5, our method is only effective for instances that are very close to a low-dimensional subspace, which seems unavoidable in the high dimensional regimes due to our lower bounds. We currently don’t know if interesting real-world datasets, like the gradients during training of large neural networks, have such a strong property that can be exploited for DP. We believe that it is an interesting research direction to understand the connection between the network and input structures to the phenomena of gradients near a low-dimensional subspace (Section 1.1). The work of Gur-Ari et al. [2018] (CoRR abs/1812.04754) makes us optimistic that in some cases it is possible to see this strong property, but we leave this direction for future work. 2. We currently don’t know how to improve the gap between the bounds. We conjecture that our lower bound for strong estimators is tight because it generalizes the tight lower bound of Dwork et al. 2014 which only holds for instances with a multiplicative singular-value gap above some specific constant. Yet, it is important to note that prior to our work, the gap between the lower bound of Dwork et al. 2014 and the upper bound of Singhal and Steinke 2021 was far beyond quantitative because the settings were very different. So we believe that our work, although it left quantitative gaps, makes a significant qualitative step towards understanding this problem better.	Summary: This paper addresses the challenge of private subspace learning without assuming that the dataset follows a Gaussian distribution. They propose new measure on the hardness of subspace learning problem based on the ratio between the $k^{th}$ and the remaining eigenvalues, or between the $k^{th}$ and the $(k+1)^{th}$ eigenvalues. They derive upper and lower bounds on the utility guarantees for private subspace estimation for datasets that meet these criteria, showing that the bounds can be dimension-independent under suitable conditions. However, these conditions depend on some additional parameters, e.g. $\lambda$, that might need to be carefully selected. Also, the paper presents an implementable algorithm that achieves the derived upper bounds. Strengths: - The paper contributed to remove a restrictive assumption in previous works. Previous research on private subspace estimation has derived dimension-independent sample complexity for Gaussian-distributed data with large multiplicative eigen-gaps. This paper removes the Gaussianity assumption, and proves that dimension-independent sample complexity can still be achieved for easier datasets. - The proposed measure of "easiness" of the datasets for subspace estimation, based on multiplicative eigen-gap, is simple and intuitive. Their derived bounds on sample complexity require prior knowledge of this measure, however, they show that the bounds are hardly affected when this measure is agnostic. - The paper has practical relevance due to its realistic assumptions and the inclusion of an implementable algorithm for private subspace estimation. Weaknesses: The description of some parameters is vague, which hinders the understanding of the significance of the sample complexity bounds. For example, while $\lambda$ is an important parameter that appears in the sample complexity bounds, it is not defined in Definition 1.3 or in the text above it. Technical Quality: 3 Clarity: 2 Questions for Authors: Can you explain the parameter $\lambda$? Is it a parameter that can be freely selected, or is it intrinsically determined by the property of the dataset or the algorithm? Confidence: 3 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: I don't see any significant limitations. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank you for the positive review. Regarding your question: We are interested in DP algorithms that have the property that if they get "easier" inputs, they achieve "better" accuracy. The parameter $\lambda$ captures the connection between "easiness" and "accuracy" (i.e., it is a property of the algorithm). In the setting of subspace estimation, if we aim for an $\alpha$-useful projection and we have an $\gamma$-easy dataset, then we would need to use an $\lambda$-estimator for $\lambda \leq \alpha/\gamma$. We decided to use this parameter since it captures (out of these three parameters) what mostly affects the sample complexities and our upper bounds' design (the number of subsets in the sample and aggregate), and is similar to the recent formulations of Peter et al. 2023. But this is just a matter of taste, and alternatively, we could avoid this parameter and formulate our results with $\alpha$ and $\gamma$. --- Rebuttal Comment 1.1: Comment: Thanks for your clarification. It's very helpful for my understanding, and I increase my score accordingly.	Summary: This work studies the problem of differentially private dimension reduction without dependence on the ambient dimension d. While this is known to be impossible generally, this work gives (distinct) necessary and sufficient conditions on gaps between the kth singular value of the data matrix and its subsequent singular values for privately identifying a k-dimensional subspace that captures the data with minimal distortion. The theoretical results are empirically verified, demonstrating that for datasets that are very close to a k-dimensional subspace, for small k, that the algorithms demonstrating sample upper-bounds do outperform existing, general DP subspace estimation techniques. Strengths: This work makes significant progress on an interesting problem, and the contributions could potentially have applications to notably improving efficiency of the broadly useful DP-SGD algorithm (in cases where gradients approximately lie in low-dimensional subspaces). Weaknesses: The presentation of this work could be improved. The reader's first introduction to what gamma-easiness means and how it eliminates dimension dependence comes in a footnote in page 2. I think that given the centrality of easy instances to this work, it would be good to dedicate a few sentences early on to give the reader a more precise understanding of what gamma-easiness means generally and how we should think of how gamma will relate to other parameters of a problem. I also found the lower-bounds overview exceptionally hard to follow. These results are very technical and make use of prior work on fingerprinting codes and DP, so it does seem challenging to give an overview that is both sufficiently high level for the page limits and also illuminating, but I think it should be possible to make the overview more modular, and in that way easier to follow. Typos/Suggested edits: Section 1.5.2 “combination between generating” -> “combination of generating” “However, their result strongly rely” -> “However, their results strongly rely” “top-singular vector” -> “top-singular vectors” 1.5.3 “which have the property that we seek for” -> “which have the property we seek” 1.7 “Additional related work appear at Appendix A. Notations, …” -> “Additional related work appears in Appendix A. Notation, …” 2 “that arbitrary partition” -> “that arbitrary partitions” “expected Forbenius” “The first one simply treat each matrix” -> “treats” “who privately estimate” -> “which privately estimates” “asymptotical” -> “asymptotic” Footnote 4 on page 6 defines the Frobenius norm, but it’s already been referred to in Definition 1.2, so could be good to move it earlier, also Frobenius is mispelled in the footnote. 3 Paragraph 4 of Section 3, second line, I think sigma_i should be sigma_i^2 4 “that are approximately lie” -> “that approximately lie” 5 “Yet, it still left open to close the gap” -> “Yet, closing the gap is still left open” “Forbenius” “via a private subspace estimation” -> “via private subspace estimation” Appendix B Proof of proposition B.12 “$Pi_1, Pi_2$ is holds” -> “it holds” Appendix C.1 “that uses an oracle access” -> “that uses oracle access” “we obtain that the projection matrices” -> “the projection matrices” “simply treat the matrices … and compute” -> “simply treats … and computes” Algorithm C.1 “Randomly split X intro t” -> “Randomly split X into t” Technical Quality: 4 Clarity: 2 Questions for Authors: The experiments all involve very small choices of k. Does this reflect an appropriate choice of constant dimension for the intended applications, computational limits, or performance limitations? Confidence: 3 Soundness: 4 Presentation: 2 Contribution: 3 Limitations: Yes, the authors have addressed the limitations of their work. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank you for the positive and thorough review. Your editorial comments are very helpful and we will address them in the next version. In the following, we would like to respond to specific points you make. Regarding the weaknesses: In the next version, we will dedicate a few more sentences to clarify the connection between gamma and the other parameters (usefulness, and lambda), and we will try to improve the overview of our lower bounds. Regarding the question: Our implementation has time and space complexities of $\tilde{O}(dn+dk)$. In our experiments, we use $n = 250\cdot k$ points, so up to the hidden constant factors, the complexities are $\tilde{O}(dk)$. Since we focused on large values of $d$, we decided to use small values of $k$ to reduce the total running time (which involved 30 repetitions for each graph point), but there is no problem with using larger values of $k$. We remark that we did not try to optimize the running time. In particular, we did not use the fact that the heavy parts of our algorithm can be parallelized. --- Rebuttal Comment 1.1: Comment: Thank you for answering my questions regarding parameter choices and for committing to improve some presentation issues. I will keep my score.	Summary: The paper studies private PCA under the assumption that the singular values of the data matrix shows multiplicative decay. It is a problem that was initiated by Steinke-Singhal and has not seen much improvement since that work. This works provides a more thorough study of this problem. Strengths: PCA is one of the most important problem in modern data analysis and ML. Unfortunately, with privacy constraints, it requires a lot of data samples to perform PCA with any reasonable accuracy. This has led researchers to look at instances where PCA can be easy. Most of these works rely on the assumption that the singular values of the data matrix has a particular behavior. This work extends on those line of work. It provides nice upper bound on various assumptions regarding the multiplicative decay of the singular values. The upper bound result follows the framework presented in Steinke-Singhal. The lower bound to me are the more interesting one, which is based on recent ideas of Peter et al. Weaknesses: The lower and upper bound do not match. There is a large gap between the two. One major focus in the area of PCA is to get a bound under these assumptions such that when $k \to d$, we recover the optimal rate. For example, this was the motivation behind Mangroubi-Vishnoi. Unfortunately, under that assumption, the upper bound is way worse due to its dependence on $k^2 \sqrt{d}$ and $k^3d$, respectively. Due to that reason, I believe that the lower bound is tight. Technical Quality: 3 Clarity: 3 Questions for Authors: Do the authors perceive a way to improve their upper bound to get better dependence on $k$? Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The quadratic and cubic dependence on $k$. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank you for the positive review. Regarding your question. We currently don’t know how to improve the upper bounds, and we agree with your intuition that the lower bounds seem closer to the truth. One supporting evidence for this intuition is that our lower bound for strong estimators generalizes the tight lower bound of Dwork et al. 2014 that only holds for instances that have a multiplicative singular-value gap above some specific constant. Yet, it is important to note that prior to our work, the gap between the lower bound of Dwork et al. 2014 and the upper bound of Singhal and Steinke 2021 was far beyond quantitative because the settings were very different. So we believe that our work, although it left quantitative gaps, makes a significant qualitative step towards understanding this problem better.	null	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Bandits with Ranking Feedback	Accept (poster)	Summary: The paper studies the multi-armed bandit problem when the learner only observes the ranking of the average cumulative reward of all the arms. This is a strictly worse information environment than the standard setting. The paper proposes algorithms that still attains the instance independent and dependent regret rates that match the stochastic multi-armed bandit. It also shows that no algorithms can do better in both the instance-dependent and -independent settings simultaneously. Strengths: - The setting studied in the paper is novel. I have not read similar setups in the literature before. Although the practical motivation can be strengthened, I think it is an interesting problem to study. One potential application could be some kind of tounament in which only the ranking is observed. - Although the information is a lot less than the standard MAB, the authors show that the optimal regret in both cases (instance-dependent and -independent) can still be achieved. This is surprising. The tools used are standard probabily theory, which is a plus to me. - The trade-off between instance-independent and -dependent regret is interesting and surprising. This is not the case in standard MAB and I haven't seen similar results before. Weaknesses: - It is probably out of the scope of this paper. But the current dependence on $n$, the number of arms, is quite far from optimal ($n^4$) in the instance dependent case. I wonder if the authors have thought about better designs to obtain linear or sublinear dependence. Some discussion would be helpful. Technical Quality: 3 Clarity: 3 Questions for Authors: - In the proof of Theorem 4, the policy doesn't seem to depend on $T$. For example, in line 534, the probability of $\pi(pull 2\|E_\tau)$ is a function of $\tau$ only. My understanding that the algorithm is allowed to depend on $T$. Does the proof work for this case? - I think the title misleads the readers. Ranking feedback sounds like receiving the order of the rewards in the current round. It is up to the authors, but a more informative title would help the paper. Confidence: 5 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: Q: _It is probably out of the scope of this paper. But the current dependence on $n$, the number of arms, is quite far from optimal in the instance dependent case. I wonder if the authors have thought about better designs to obtain linear or sublinear dependence. Some discussion would be helpful._ The fact that our instance-independent bound in Theorem 8 scales with $ n^4 $ is one of the most interesting open points of this paper. The reason for this unusual order may be found in the fact that the ranking setting prevents us from relying on standard concentration properties. Therefore, no "high-probability" estimates can be performed, and each time in the analysis we perform a "union bound" over the space of arms, this results in an additional $ n$ factor in the regret bound. In contrast, when using a high-probability estimate, the same union bound would result in an additional $\log(n)$ term, which is negligible. Furthermore, given the ranking feedback setting, it appears natural that at least two union bounds over the space of arms must be performed in order to compare any possible pair of arms. Therefore, we believe that a super-linear dependence on $ n $ in the instance-independent regret bound cannot be avoided, but we still conjecture that such dependence may be moved to lower order terms. _Q: In the proof of Theorem 4, the policy doesn't seem to depend on $T$. For example, in line 534, the probability of $\pi(pull\|E)$ is a function of $\tau$ only. My understanding that the algorithm is allowed to depend on $T$. Does the proof work for this case?_ The point made by the Reviewer is correct, and very subtle. In fact, the current lower bound only applies to any-time policies, independent of the time horizon. Fortunately, modifying the proof to generalize the result to the case where the policy can depend on $T$ is not difficult. We start the proof by contradiction, assuming that both $$R_T(\pi_T)\le C(\Delta)T^\alpha \qquad R_T(\pi_T)\le T^\beta$$ hold for any $T$, given a sequence of policies $\pi_T$. The "hard instances" are the same, both with two arms and small $\Delta$, and also the event $E_t$ is defined as in the paper. From the assumption, it follows that $$C(\Delta= 1)T^\alpha = C( 1)T^\alpha \ge \mathbb E[Z_2(T)\|E_T],$$ otherwise the sequence of policies would suffer regret more than $C( 1)T^\alpha$ in case arm one gives always $1$ and the other always $0$. From this equation, it is easy to complete the proof as usual. In the original proof, the only step requiring the policy to be any-time was the limit $$\forall \eta>0,\ \limsup_{t\to \infty}\frac{\sum_{\tau=1}^t \pi(\text{pull 2}\|E_\tau)}{t^{\alpha+\eta}}=0,$$ which is not necessary and can be easily avoided working by contradiction. We will put this improved proof in the final version of the paper, we remain at the Reviewer disposal in case they need further clarification on how to change this proof. _Q: I think the title misleads the readers. Ranking feedback sounds like receiving the order of the rewards in the current round. It is up to the authors, but a more informative title would help the paper._ We thank the Reviewer for the interesting observation. Nevertheless, we believe the feedback structure the Reviewer is describing is somewhat referred to as "Dueling bandits", or their generalization. Thus, we are open to any suggestion. --- Rebuttal Comment 1.1: Comment: Thanks for the detailed response. I don't have further questions.	Summary: The paper studies the setting where, every time an arm is pulled, a principal gets to observe a reward, but the player only gets to observe the order that emerges from the accumulated rewards so far. The authors study both the adversarial and stochastic, and both the instance-dependent and instance-independent regrets. They provide tight results for all cases, with the only exception being the stochastic instance-independent case, where they provide tight bounds only for the Gaussian model. Strengths: - The paper is well-written. Intuitive explanations of the results are provided along with a nice description of the algorithms. - The model is super interesting in my opinion, at least from a mathematical point of view, and quite novel. - The authors provide a very complete picture. They study both the adversarial and non-adversarial settings, as well as instance-dependent and instance-independent regrets. - Overall, I really enjoyed reading the paper Weaknesses: - I miss some more realistic motivation for the model and some concrete applications. As I said, from a theoretical point of view, the model is very interesting, but when I tried myself, I could not come up with a clear application. - For the general stochastic and instance-independent case, the only guarantee that is provided is that of the EC algorithm which can be easily applied in this setting - R-LPE algorithm needs to know T Technical Quality: 4 Clarity: 4 Questions for Authors: No questions Confidence: 3 Soundness: 4 Presentation: 4 Contribution: 4 Limitations: No limitations Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Q: _I miss some more realistic motivation for the model and some concrete applications. As I said, from a theoretical point of view, the model is very interesting, but when I tried myself, I could not come up with a clear application._ We thank the Reviewer for the question. In the following, we provide a real-world example of a possible application of our setting. In pay-per-click online advertising (the total spent is of the order of several billion USD per year), large platforms optimize advertisers' campaigns. Specifically, these platforms observe the number of clicks of each single campaign, but to allocate the budget most effectively (using a knapsack-style approach), they need to know the revenue of the individual campaigns. Obviously, the platforms cannot observe the revenue, which is private information of the advertiser. On the other hand, advertisers do not want to communicate this private information to the platforms, and, for this reason, the platforms limit themselves to maximizing the number of clicks. However, this kind of optimization leads to very approximate solutions compared to considering the revenue as well. The use of bandits with ranking feedback in this context would circumvent this problem. In particular, advertisers would be asked for feedback on the ranking of advertising campaigns, avoiding the need to ask for revenue information. Q: _For the general stochastic and instance-independent case, the only guarantee that is provided is that of the EC algorithm which can be easily applied in this setting_ We thank the Reviewer for the comment but we believe there is a potential misunderstanding on our results. Indeed, the R-LPE algorithm is specifically tailored for the instance independent case while it achieves a subotptimal instance dependent regret bound. Finally, please notice that R-LPE instance independent regret guarantees are far better than those of the standard Explore and Commit algorithm which are of the order $\mathcal{O}(T^{2/3})$. Q: _R-LPE algorithm needs to know $T$_ The reviewer is correct. In our settings, due to the specific nature of the feedback, we cannot employ the well-known "doubling trick" to relax the knowledge of the time horizon $T$. We leave it as an interesting open problem to determine whether the requirements on the knowledge of time horizon $T$ can be relaxed. For what concerns the empirical validation, in the attached PDF we added an experiment measuring the impact of using a misspecified value for $T$. --- Rebuttal Comment 1.1: Title: No further questions Comment: I would like to thank the authors for their answer and the clarifications. I do not have any further questions at this point. While I still do not find the motivating example very convincing, I will keep the score as it is.	Summary: The paper introduces a variant of the multi-armed bandit problem called "bandits with ranking feedback," where the feedback ranks the arms based on historical data without showing precise numerical differences. This approach is particularly useful in scenarios where exact measurement of values is impractical, such as with human preferences or confidential data. The main contributions of the study include developing no-regret algorithms that operate under both stochastic and adversarial conditions for this model. The findings indicate that achieving logarithmic regret is impossible with ranking feedback in the stochastic setting, and no algorithm can achieve sublinear regret in the adversarial setting. The paper proposes two algorithms: DREE, which achieves superlogarithmic regret in stochastic instances, and R-LPE, which manages a regret of O(\sqrt{T})in stochastic instance-independent scenarios. These innovations significantly enhance the understanding and implementation of bandit algorithms in complex feedback environments. Strengths: Quality: The theoretical contributions are robust, including the proof that no algorithm can achieve logarithmic regret in the stochastic setting with ranking feedback, and no sublinear regret is achievable in the adversarial setting Clarity: The paper is well-structured, with clear delineation of problem settings, algorithmic approaches, and theoretical analyses. Weaknesses: 1) Originality: Is the concept of "bandits with ranking feedback" truly novel? 2) Experimental Validation: The paper would benefit from more experimental validation. While the theoretical aspects are well-developed, further empirical testing in diverse conditions could strengthen the validation of the algorithms. Tests with non-Gaussian noise and in real-world settings would be particularly insightful. 3) Algorithm Complexity: The discussion on the computational complexity and practical scalability of the introduced algorithms is limited. More detailed analysis in this area could provide better insights into their applicability in real-world scenarios. 4) Adversarial Setting Analysis: It is mentioned that no algorithm can achieve sublinear regret in adversarial settings, but more detailed explanations or suggestions for alternative approaches to handle such conditions would be beneficial. 5) Impact of Dependence on Parameters: The algorithms appear to heavily rely on the correct setting of specific parameters, such as the time horizon T. Discussing the sensitivity of the algorithms to these parameters and providing strategies for effective parameter tuning would aid their practical application. 6) Extension to Other Models: Could the principles of ranking feedback be applied to other types of bandit problems, such as contextual bandits or those with structured action spaces? This extension could broaden the applicability of the research findings. Technical Quality: 3 Clarity: 2 Questions for Authors: 1) Originality: Is the concept of "bandits with ranking feedback" truly novel? 2) Experimental Validation: The paper would benefit from more experimental validation. While the theoretical aspects are well-developed, further empirical testing in diverse conditions could strengthen the validation of the algorithms. Tests with non-Gaussian noise and in real-world settings would be particularly insightful. 3) Algorithm Complexity: The discussion on the computational complexity and practical scalability of the introduced algorithms is limited. More detailed analysis in this area could provide better insights into their applicability in real-world scenarios. 4) Adversarial Setting Analysis: It is mentioned that no algorithm can achieve sublinear regret in adversarial settings, but more detailed explanations or suggestions for alternative approaches to handle such conditions would be beneficial. 5) Impact of Dependence on Parameters: The algorithms appear to heavily rely on the correct setting of specific parameters, such as the time horizon T. Discussing the sensitivity of the algorithms to these parameters and providing strategies for effective parameter tuning would aid their practical application. 6) Extension to Other Models: Could the principles of ranking feedback be applied to other types of bandit problems, such as contextual bandits or those with structured action spaces? This extension could broaden the applicability of the research findings. Confidence: 3 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: Experimental Scope: The authors could extend the experimental validation to include real-world datasets or scenarios to better demonstrate the practicality of the algorithms under different environmental conditions. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Q: _Originality: Is the concept of "bandits with ranking feedback" truly novel?_ To the best of our knowledge, the "bandits with ranking feedback" model introduced in our paper represents a new bandit setting. Although our setting shares similarities with dueling bandits, the two settings are substantially different, as we discuss in the related works section in our paper. Q: _Experimental Validation._ Following the suggestion of the reviewer, we enriched our experimental evaluation, and the new results we obtained can be found in the attached PDF. In particular, we investigated the following: - Non Gaussian noise. In the attached PDF, we ran the same experiments of the paper with uniformly distributed noise. We observe that this leads to similar results. However, the variance of the regret curves is slightly increased, but the mean remains nearly the same. - Measuring the computational effort required by the algorithms. While the running time of DREE is clearly linear in $T$, the running time of R-LPE is less straightforward to compute. However, in the additional experiments, we empirically observed that the running time of the R-LPE algorithm is also linear in $T$. - Robustness of R-LPE to misspecification of $T$. Even if the algorithm strongly relies on knowledge of the time horizon, we have shown that providing the algorithm with a time horizon larger than the actual one is not particularly harmful. On the other hand, as is usual in bandit algorithms, setting the time horizon $T'$ smaller than the actual time horizon $T$ results in linear growth of the regret after $T'$ rounds. Q: _Algorithm Complexity._ We thank the Reviewer for underlining this important aspect, which we did not mention in the paper due to space constraints. Both our algorithms are very computationally efficient. In the experiment, we have empirically demonstrated this fact, and we will show it theoretically in this rebuttal. Specifically, the DREE algorithm requires either pulling the first-ranked arm (in most rounds) or an arm in a lower position of the ranking according to a deterministic schedule. Therefore, it does not require computing confidence regions, resulting in a running time of just $\mathcal{O}(nT)$. The second algorithm, R-LPE, is more complex compared to DREE, as it requires updating a set of active arms $S$ at certain rounds. Fortunately, this set is only updated during the time steps that belong to the loggrid, and thus it is updated a logarithmic number of times. Therefore, even though there is a summation over $t$ in the definition of the set $S$, the computational complexity of R-LPE is not quadratic in $T$, but rather of order $\mathcal{O}(T+nT\log(T))$. The first term in the latter expression corresponds to the "usual" rounds, where we simply follow a round-robin strategy. The second term corresponds to the product of $\log(T)$ (the number of rounds in the loggrid), $T/n$ (the number of "fair" rounds), and $n^2$ (the number of possible comparisons between pairs of arms). Q: _Adversarial Setting Analysis._ We thank the Reviewer for the question. On the results explanation. To derive our adversarial lower bound we considered three instances. The instances are similar in terms of rewards for the first two phases but differ significantly in the third one. Thus, we show that, if the learner receives the same ranking when playing in two instances with different best arms in hindsight, it is impossible to achieve low regret in both scenarios. On possible alternative approaches. We agree with the reviewer that, to handle such cases, different metrics could be taken into consideration. For instance, it would be possible to study algorithms achieving sufficiently "good" competitive ratios, namely, those that are no-regret with respect to a large fraction of the optimum. We leave the aforementioned research directions as interesting future work. Q: _Impact of Dependence on Parameters._ The R-LPE algorithm requires knowledge of the time horizon $T$, while the DREE algorithm is an anytime algorithm. In the attached PDF we added an experiment measuring the empirical impact of using a misspecified value of the time horizon $T$. We would like to emphasize that the R-LPE algorithm has no additional hyper-parameters, since the quantities that characterize it, such as the loggrid and the parameter $\alpha$, can be computed as a function of $T$. Additionally, while the definition of $\alpha$ at Line 8 could be tuned experimentally, doing so may prevent us from achieving the desired regret guarantees of $\mathcal{O}(\sqrt{T})$, which is the primary goal of our paper. Q: _Extension to Other Models_ Extending our results to settings where the action space is no longer discrete is highly non-trivial, as it would first require rethinking the concept of ranking feedback. However, if we consider linear (or possibly contextual) bandits with finitely many arms, it would be interesting to see if such a linear structure allows for a better dependence on the number of arms (possibly sublinear as in [1]) in the instance indepenednt regret bound. Nonetheless, it should be noted that, from a technical perspective, combining linear settings with ranking ones would require merging the argument based on optimal design for the least squares estimator [2] or self-normalized processes [3] with our bound, which is instead based on Levy's arcsin law. [1] Tor Lattimore, Csaba Szepesvari, Gellert Weisz. Learning with Good Feature Representations in Bandits and in RL with a Generative Model. [2] Kiefer and J. Wolfowitz. The equivalence of two extremum problems. [3] Yasin Abbasi-yadkori, Dávid Pál, Csaba Szepesvári, Improved Algorithms for Linear Stochastic Bandits	Summary: This paper considers a new multi-armed bandit problem where the feedbacks are ranking of the arms. In this problem, the environment gives the feedback on the ranking of the arms based on the previous pulls. The authors first consider the stochastic setting and give the lower bound of the regret for the instance-dependent case. Then, they propose a design of explore-then-commit, called DREE, which is proved to achieve a sublunar regret for instance-dependent case. After discussing the regret tradeoff between instance-dependent and instance-independent cases, the authors design a phase elimination algorithm (R-LPE) that has a sublunar regret. Then they move beyond the stochastic setting and prove that sub-linear regret cannot be achieved for the adversarial setting. Strengths: The paper has the following strengths. + The paper considers a novel setting of bandits with ranking feedback. The ranking feedback depends on the history of reward, so it is different from the dueling bandits. + For the stochastic setting, the paper derives the lower regret bound to show the difficulty of the instance-dependent case. + The paper proposes provable algorithms to solve bandits with ranking feedback for both instance-dependent and instance-independent cases. Adequate analysis is provided to support their points. Weaknesses: I am concerned about the following aspects. First, in the problem setting, the ranking feedback is assumed to be perfect in terms of the ranking of the averaged history rewards. However, human probably not give the perfect ranking since history reward is not easily observed. Thus, it would be better if the authors can discuss the designs with imperfect ranking feedback. Second, the analysis in the adversarial setting does not give any insight. It is obvious that the regret is linear for adversarial bandits with ranking feedback. However, can the authors discuss whether their algorithms are robust enough for adversarial setting? (e.g. provide an analysis of the competitive ratio.) Technical Quality: 3 Clarity: 2 Questions for Authors: Can the authors give more concrete examples to motivate the setting of bandits with ranking feedbacks? Can the authors provide a high-level explanation on why there exists a tradeoff between instance-dependent and instance-independent cases? Confidence: 2 Soundness: 3 Presentation: 2 Contribution: 2 Limitations: The authors do not include a discussion of the limitations. However, a discussion on the limitations of the setting will be helpful. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Q: _"First, in the problem setting, the ranking feedback is assumed to be perfect in terms of the ranking of the averaged history rewards. (...)"_ We completely agree with the Reviewer that the introduction of imperfection/uncertainty/tolerance is of paramount importance as it would allow to capture better the actual human behavior, and this refinement is exactly the next step of our agenda. On the other side, no imperfection can be introduced before a complete study of the perfect model, and, as we show in our paper, the study of the exact model is not straightforward. Furthermore, we observe that introducing a perturbation in the ranking observed by the learner may hinder the possibility of designing a no-regret algorithm. Thus, exploring scenarios where the learner receives corrupted ranking feedback and still manages to design a no-regret algorithm is both a fascinating and challenging research direction. Nonetheless, it requires a different approach from the one presented in our work and is something we plan to investigate in the future. Q: _Second, the analysis in the adversarial setting does not give any insight. (...)_ We believe that the impossibility result for the adversarial setting represents a first yet fundamental step toward a full understanding of the problem when the rewards are adversarially chosen. We are disappointed that the Reviewer found our result trivial, as it is uncommon in the online learning literature to achieve a positive result in the stochastic setting that cannot be extended to the adversarial setting. This feature is peculiar to the bandits with ranking feedback model, as even related settings, such as dueling bandits, do not exhibit this kind of impossibility result. Finally, we agree with the Reviewer that studying the competitive ratio of algorithms developed for adversarial settings is an interesting research direction, and we plan to pursue it in the future. Q: _Can the authors give more concrete examples to motivate the setting of bandits with ranking feedbacks? Can the authors provide a high-level explanation on why there exists a tradeoff between instance-dependent and instance-independent cases?_ We thank the Reviewer for the question. In the following, we provide a real-world example of a possible application of our setting. In pay-per-click online advertising (the total spent is of the order of several billion USD per year), large platforms optimize advertisers' campaigns. Specifically, these platforms observe the number of clicks of each single campaign, but to allocate the budget most effectively (using a knapsack-style approach), they need to know the revenue of the individual campaigns. Obviously, the platforms cannot observe the revenue, which is private information of the advertiser. On the other hand, advertisers do not want to communicate this private information to the platforms, and, for this reason, the platforms limit themselves to maximizing the number of clicks. However, this kind of optimization leads to very approximate solutions compared to considering the revenue as well. The use of bandits with ranking feedback in this context would circumvent this problem. In particular, advertisers would be asked for feedback on the ranking of advertising campaigns, avoiding the need to ask for revenue information. Q: _Can the authors provide a high-level explanation on why there exists a tradeoff between instance-dependent and instance-independent cases?_ Usually, in multi-armed bandits, an instance-independent regret bound can be derived from an instance-dependent one. Indeed, if the instance-dependent regret bound depends on the suboptimality gaps as $ R_T \propto {\log(T)}/{\Delta} $, it is possible to take the worst possible value of $ \Delta $ and achieve the desired instance-independent regret bound. Unfortunately, in our case, the instance-dependent regret bound cannot be written in this form as a consequence of the feedback characterizing our setting. Indeed, we can only observe switches in the ranking, which do not reflect the actual differences in the expected rewards of the arms. Thus, the only way to “explore” in our setting is by pulling arms that could be highly sub-optimal. For this reason, achieving an asymptotic regret bound that is close to logarithmic requires exploiting the arm being ranked first several times, thus suffering a particularly unpleasant dependence on the suboptimality gaps $ \Delta_i $ (see, for example, Corollary 3). Finally, we remark that the formalization of this reasoning is presented in Theorem 4 (Instance Dependent/Independent Trade-off). --- Rebuttal Comment 1.1: Comment: I have read the response. Thank you authors for answering my questions.	Rebuttal 1: Rebuttal: Dear Reviewers, in the attached PDF, we provide additional experiments. The authors. Pdf: /pdf/a05b01cdeedd6d434c2c70e5e1268ebe6aa5f93c.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Hierarchical Federated Learning with Multi-Timescale Gradient Correction	Accept (poster)	Summary: This paper proposes a multi-timescale gradient correction (MTGC) methodology to deal with multi-timescale model drift. It introduces a distinct control variables to correct the client gradient towards the group gradient, and correct the group gradient towards the global gradient. Then, the stability of the proposed algorithm against multi-level non-i.i.d. data is shown empirically. Strengths: 1. The idea of correcting gradients is interesting 2. The proof seems correct. Weaknesses: The model is tested on small datasets. Technical Quality: 2 Clarity: 2 Questions for Authors: 1. What are the practical applications of HFL? 2. Are there any techniques implemented for preserving the privacy of the model? 3. The model has been tested on small datasets; how does it perform on larger datasets? 4. The ablation study is missing. How does the model perform when only one of the corrections is used? 5. How about the stability of the proposed method? Confidence: 3 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 reviewer for the valuable comments. We also thank the reviewer for acknowledging our idea as interesting and for taking a look at our proof. Our responses are given below. ### Practical applications of HFL HFL can play a key role in most of the real-world networks comprised of a hierarchical architecture such as edge/fog computing systems or software-defined networks. In autonomous vehicle applications, each small base station (local aggregator) aggregates the models sent from the vehicles (nodes) in its coverage region, and then sends the aggregated model to the macro base station (global aggregator). Other applications of Internet of Things (IoT) sensors also operate under similar settings. In healthcare applications, individual hospitals (nodes) send the model to regional health centers (local aggregators), and the national health authority (global aggregator) aggregates all the models. This HFL process involves nation wide data points, improving the performance of disease diagnosis models. Finally, in financial fields, individual financial institutions (nodes) collect transaction data and train local models for fraud detection and credit scoring. These models are aggregated at regional financial hubs (local aggregators), and the aggregated models are then sent to national or global financial authority (global aggregator) to create a global model. We will illustrate these key applications more clearly in the revised paper. ### Implementation of privacy-preserving techniques Since our primary focus was to tackle the data heterogeneity issue from the perspective of designing optimization algorithms in the hierarchical setting, we have not considered applying additional techniques like privacy preservation that are orthogonal to our approach. Nonetheless, existing privacy-preserving techniques such as secure aggregation or differential privacy (DP) can be incorporated into our framework. To be specific, secure aggregation can be directly applied during the local aggregation process, as the local aggregators only need to obtain the average of models within its coverage rather than individual local models. Similarly, secure aggregation can be directly applied during the global aggregation process to preserve privacy as well. For DP, we can apply noise injection to local and global model aggregation (Steps 8 and 10 of Algorithm 1 in the original manuscript) to protect privacy. For instance, in Step 8, clients upload local models to the group server. In practical implementation, they only need to upload the model update $\Delta_i = \boldsymbol{x}_{i,H}^{t,e} - \bar{\boldsymbol x}_j^{t,e}$. For applying Gaussian noise to protect the model's privacy, we first clip $\Delta_i$ to ensure that its norm does not exceed a predefined threshold $C$: $ \tilde{\Delta}_i = \Delta_i \cdot \min\left(1, \frac{C}{\|\|\Delta_i\|\|_2}\right). $ Next, we can apply Gaussian noise to the clipped model update $ \hat{\Delta}_i = \tilde{\Delta}_i + \mathcal{N}(0, \sigma^2 I). $ Here, $\mathcal{N}(0, \sigma^2 I)$ represents Gaussian noise with mean 0 and covariance matrix $\sigma^2 I$. Note that the procedures of applying the DP mechanism to MTGC are similar to FedAvg [R1]. The specific analysis of the DP-assisted MTGC is beyond the scope of our work and is best left for future research. [R1] Understanding clipping for federated learning: Convergence and client-level differential privacy, ICML 2022. ### Experiments on larger datasets Please refer to the global response. ### Ablation study with only one correction term In Figure 4 of our original manuscript, we have already reported the results of using only one of the correction terms. Specifically, we applied either the local correction, $\boldsymbol z_i^{t,e}$, or the group correction, $\boldsymbol y_j^{t}$, to HFedAvg. It is observed that in the group i.i.d. \& client non-i.i.d. scenario, local correction performs better than the group correction, as data samples are non-i.i.d. across the clients. Conversely, in the group non-i.i.d. \& clients i.i.d. scenario, the opposite holds. More detailed discussions on these results are illustrated in lines 311-327 of our original manuscript. ### Stability of our method In the original manuscript, we proved the convergence of MTGC without relying on extra data similarity assumptions. In the simulation, we show the stability of our algorithm in 4 different ways: We conducted experiments (i) using 3 random realizations (with different initial models) in Figure 3, (ii) under 3 different data distribution settings in Figure 4, (iii) using 4 different datasets, (iv) using varying parameters in Table 5.1 and Figures 5 and 6. During the rebuttal period, we have also added two more datasets (Shakespeare and CINIC-10) to further validate the advantage of our method. Moreover, we ran experiments with four more random realizations corresponding to Figure 4. Due to space limitations, we have selected one representative figure for CIFAR-10 to show for the rebuttal. Please refer to Figure R4 (c) of the attached pdf. Our MTGC consistently outperforms baselines across all scenarios and the performance gains beyond the standard deviation, showcasing its stability. Again, we appreciate the reviewer for the helpful comments. In case there are remaining questions/concerns, we hope to be able to have an opportunity to further answer them. --- Rebuttal Comment 1.1: Title: Hierarchical Federated Learning with Multi-Timescale Gradient Correction Comment: I thank the authors for their detailed rebuttal. I appreciate the discussion on privacy-preserving methods. Although the primary focus of this study is to tackle the data heterogeneity issue, it is essential to recognize that this is a federated learning model, and the privacy of the data must be preserved. I assume that applying the methods mentioned by the authors could potentially degrade the model's performance. I've read the comments and feedback from the other reviewers and look forward to the discussions following the rebuttal. I will keep my score for now. --- Rebuttal 2: Comment: Thanks for your feedback. We appreciate your time for the discussion. We agree with the reviewer that preserving privacy of clients is crucial in FL. Here, we would like to emphasize that implementing additional privacy-preserving techniques on top of each scheme would degrade not only the accuracy of our approach, but also that of the baselines (they also were not integrated with privacy-preserving techniques in their original work). To demonstrate this, we have conducted an experiment to compare the performance of our algorithm with HFedAvg under the same $(\epsilon, \delta)$-differential privacy (DP) guarantees. We apply DP to the gradient to ensure sample-level privacy. To implement DP, we employ gradient clipping followed by the addition of Gaussian noise, a standard practice in the literature [R1, R2]. This approach is applied to both our algorithm and the baseline. Specifically, to guarantee DP, we replace step 7 of Algorithm 1 in the manuscript with the following procedures: + Compute stochastic gradient: $g_{i,m}^{t,e,h}, m=1,\ldots B_s$, $\forall i $ + Gradient clipping: $\hat{g}\_{i,m}^{t,e,h} = g_{i,m}^{t,e,h} \cdot \min\left(1, \frac{c}{\|\|g_{i,m}^{t,e,h}\|\|}\right), m=1,\ldots B_s$, $\forall i $ + Applying Gaussian noise to the gradient: $G_i^{t,e,h} = \frac{1}{B_s} (\sum_{m=1}^{B_s} \hat{g}_i^{t,e,h} + \mathcal{N}(0,\sigma_g^2))$, $\forall i $ + Local model update: $ \boldsymbol x_{i,h+1}^{t,e}= \boldsymbol x_{i,h}^{t,e} - \gamma( G_i^{t,e,h} + \boldsymbol z_i^{t,e} + \boldsymbol y\_j^t), \forall i \in \mathcal{C}\_j,\forall j$ To achieve $(\epsilon, \delta)$ privacy, the noise should be set at the following scale [R1, R2]: $$ n \sim \mathcal{N}(0,\sigma_{g}^2) ~~ \text{while} ~~ \sigma\_{g}^2 = \frac{c^2 \log (1 / \delta) THE}{(\|\mathcal{D}\_i\|/B_s)^2 \epsilon^2}, $$ where $B_s$ denotes the batch size. The table below shows the results using the Shakespeare and CIFAR-100 datasets. For the Shakespeare task, we set $T=30, E=30, H=35$, $c=1$, $\delta = 10^{-3}$, $\|\mathcal{D}\_i\| = 1500$, and $B\_s = 200$. We compare their performance under a privacy budget of $\epsilon = 15$. The standard deviation of the Gaussian noise is thus $\sigma_{g} = 1.37$. For CIFAR-100, we set $T=50, E=20, H=20$, $c=10$, $\delta = 10^{-3}$, $\|\mathcal{D}\_i\| = 500$, and $B\_s = 50$. Under the privacy budget of $\epsilon = 15$, the standard deviation of the Gaussian noise is $\sigma\_{g} = 1.63$. \| Dataset \| MTGC (w/o DP) \| MTGC-DP \| HFedAvg (w/o DP) \| HFedAvg-DP \| \|-------------------\|-------\|---------\|---------\|------------\| \| Shakespeare \| 46.42 \| 45.50 \| 43.16 \| 42.95 \| \| CIFAR-100 \| 53.53 \| 50.72 \| 41.69 \| 39.70 \| We see that, as expected, the noise injection process for guaranteeing DP slightly decreases the accuracy of both schemes. Importantly, MTGC performs better than HFedAvg with and without DP. We will include these new results in the revised version of our manuscript. [R1] Abadi, Martin, et al. Deep learning with differential privacy. ACM SIGSAC, 2016. [R2] Li, Bo, et al. An improved analysis of per-sample and per-update clipping in federated learning. ICLR, 2024	Summary: This paper proposes a novel algorithm called Multi-Timescale Gradient Correction (MTGC) for Hierarchical Federated Learning (HFL). The authors address the challenge of multi-timescale model drift in HFL systems, where data heterogeneity exists both within client groups and across groups. MTGC introduces coupled gradient correction terms to mitigate client model drift and group model drift. The authors provide theoretical convergence analysis for non-convex settings and demonstrate MTGC's effectiveness through experiments on various datasets and models. Strengths: - The proposed MTGC algorithm is simple and easy to implement, introducing client-group and group-global correction terms. The paper clearly defines the problem it aims to solve. The motivation is clear and well-articulated, highlighting the gap in existing HFL algorithms. - The inclusion of theoretical analysis adds depth to the paper, providing a solid foundation for the proposed approach. The theoretical results show that MTGC achieves linear speedup in the number of local iterations, group aggregations, and clients. - The convergence bound of the proposed algorithm is immune to the extent of data heterogeneity, which is a significant strength. Weaknesses: - There is a lack of comparisons and discussions on clustered federated learning [1,2], which share similar context to some extent and could provide valuable background for the readers. - The experiments primarily focus on image classification tasks. Including other types of tasks (e.g., natural language processing) could strengthen the generalizability of the results. There is a lack of experiments on various types of distribution shifts such as domain shift, label shift etc. Exploring different non-i.i.d. scenarios could provide more insights into the algorithm's robustness. - While the paper analyzes model drift theoretically, there is a lack of empirical and theoretical analysis on how model drift affects generalization performance, especially in relation to the number of hierarchical communication levels. The study also does not clearly demonstrate in which scenarios and to what extent increasing the number of hierarchical communication levels benefits federated learning performance. - The paper could also be strengthened by providing more insights into the practical implications of the theoretical results. [1] An Efficient Framework for Clustered Federated Learning. NeurIPS 2020. [2] Optimizing the Collaboration Structure in Cross-Silo Federated Learning. ICML 2023 Technical Quality: 3 Clarity: 3 Questions for Authors: Please refer to the weaknesses mentioned above. Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: The limitations of the study are discussed, and no potential negative societal impacts of the work have been identified. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We appreciate the reviewer's positive comments and feedback. We are glad to receive your appreciation of our motivation and results. Our responses are below: ### Discussion on CFL Our work focuses on HFL, employing a multi-layered structure consisting of local nodes, local aggregators, and a central server. Both clustered FL and HFL aim to improve FL learning efficiency by leveraging structured client groupings. The difference between them lies in the grouping criteria. HFL focuses on collaborative training over a given network topology, where clients are generally grouped based on their geographical location or network connection status, and aims to build a single global model under this setting. CFL groups clients to optimize model training, with different global models constructed depending on the group. [R1] demonstrates how dynamic clustering based on data distributions can enhance model performance. [R2] explores alleviating negative transfer from collaboration by clustering clients into non-overlapping coalitions based on their distribution distances and data quantities. We will add this to our updated manuscript. ### Experiments on other types of tasks Please refer to the global response. ### Experiments on distribution shifts Please refer to the global response. ### Generalization bound During the rebuttal, inspired by the paper [R2] shared by the reviewer, we studied the generalization bound of our algorithm as follows: Given a model $\boldsymbol{x}$, we denote the expected risk, defined on $\mathcal{D}$, as $\mathcal{R}(\boldsymbol{x})$. In the training stage, we aim to minimize the empirical loss $f(\boldsymbol{x})$ defined on finite samples $\hat{\mathcal{D}}$. The generalization error $\mathcal{R}(\boldsymbol{x}^t)-\mathcal{R}(\boldsymbol{x}^)$, $\boldsymbol{x}^ = \arg\min \; \mathcal{R}(\boldsymbol{x})$, can be expressed as $$ \mathcal{R}(\boldsymbol{x}^t)-\mathcal{R}(\boldsymbol{x}^) = [\mathcal{R}(\boldsymbol{x}^t)-f(\boldsymbol{x}^t)] +[f(\boldsymbol{x}^t)-f(\hat{\boldsymbol{x}}^)] +[f(\hat{\boldsymbol{x}}^)-f(\boldsymbol{x}^)] +[f(\boldsymbol{x}^) - \mathcal{R}(\boldsymbol{x}^)], $$ where $\hat{\boldsymbol{x}}^* = \arg\min f(\boldsymbol{x})$. According to [R2], one can claim that for any $\delta \in (0,1)$, with probability at least $1-\delta$, there is a quantity-aware function $\phi$ such that $$ \|\mathcal{R}(\boldsymbol{x})-\mathcal{R}(\boldsymbol{x})\| \leq \phi (\|\hat{D}\|,\delta), \forall \boldsymbol{x}. $$ Therefore, with probability at least $1-\delta$, we have $$ \mathcal{R}(\boldsymbol{x}^t)-\mathcal{R}(\boldsymbol{x}^) \leq 2 \phi (\|\hat{D}\|,\delta) +f(\boldsymbol{x}^t)-f(\hat{\boldsymbol{x}}^). $$ Note that this bound is influenced by $\phi (\|\hat{D}\|,\delta)$ and $f(\boldsymbol{x}^t)-f(\hat{\boldsymbol{x}}^)$. The former is determined by $\hat{D}$ while the latter will be impacted by the training algorithm, local data distribution, and network topology. In our manuscript, we characterize the upper bound of $\|\|\nabla f(\boldsymbol{x})\|\|^2$ rather than $f(\boldsymbol{x}^t)-f(\hat{\boldsymbol{x}}^)$ as we focus on non-convex setting. For illustration, suppose we convert the upper bound for $\|\|\nabla f(\boldsymbol{x})\|\|^2$ to $f(\boldsymbol{x}^t)-f(\hat{\boldsymbol{x}}^)$ by assuming the PL condition $f(\boldsymbol{x}^t)-f(\hat{\boldsymbol{x}}^) \leq \frac{1}{2\mu} \|\|\nabla f(\boldsymbol{x})\|\|^2$. This gives a generalization error bound $$ 2 \phi (\|\hat{D}\|,\delta) + \frac{\Delta}{2\mu}, $$ where $\Delta$ is the error derived in Corollary 4.1. Different from CFL [R2] which tries to approximately minimize $\phi (\|\hat{D}\|,\delta)$ by clustering clients, i.e, optimizing $\hat{D}$, in our setting, $\|\hat{D}\|$ is fixed, and thus $\phi (\|\hat{D}\|,\delta)$ is fixed. In addition, regarding the impact of model drift on the generalization bound: Unlike CFL, where the clients end up with different models, in HFL, model drift will converge to zero at the end of training for MTGC due to its convergence. Model drift is a characterization metric used in the intermediate process for convergence analysis. As you can see, there is no model drift term in our generalization bound. ### Increasing hierarchical communication levels Note that the main objective of our paper is to develop a convergent algorithm for a given HFL topology, treating the number of layers as an intrinsic system parameter. Hence, we predominantly assume the topology to be predetermined in our work. To address this comment, during the rebuttal period, we empirically studied the impact of hierarchical levels on FL performance, in terms of testing accuracy versus communication time. We find that the benefit of additional layers varies based on the configuration. Please refer to the global response for the experimental details. ### Practical implications of the theoretical results Thanks for the comment. As shown in Corollary 4.1, the upper bound is mainly dominated by the first term $\mathcal{O}\left(\sqrt{\frac{\mathcal{F}_0L\sigma^2}{\tilde{N} T EH}} \right)$. Due to the speedup in the number of local iterations $H$ and the number of group aggregations $E$, we can reduce the global communication round $T$ by increasing $H$ and $E$ in practice. We empirically validate this in Table 5.1 in the original manuscript and Figure 6 in the Appendix, connecting theory and practice. On the other hand notice that there is an upper bound for the learning rate, i.e., $\gamma \leq \frac{1}{40EHL}$. When we increase $E$ and $H$, the upper bound of the optimal learning rate will decrease. We will highlight these insights after Corollary 4.1 in the revised manuscript. [R1] An efficient framework for clustered federated learning. NeurIPS 2020. [R2] Optimizing the collaboration structure in cross-silo federated learning. ICML 2023. Again, thanks for your comments. If we could provide any more clarifications, we would be grateful if you could let us know. --- Rebuttal 2: Comment: Dear Reviewer fhg9, Could you please respond with how you think about the authors' response? Please at least indicate that you have read their responses. Thank you, Area chair	Summary: This paper presents a method to address multi-timescale model drift in hierarchical federated learning. Specifically, it introduces two control variables to correct intra-group client drift and group model drift. The paper establishes the convergence bound in a non-convex setup and demonstrates its stability against multi-level data heterogeneity. Overall, the paper is well-written and easy to follow. Strengths: 1. The writing is clear and easy to follow. 2. I have initially checked the proofs and did not find any issues so far. Weaknesses: 1. It would be beneficial to include comparisons of additional computational and communication costs of MTGC in the experimental section. Technical Quality: 3 Clarity: 3 Questions for Authors: 1. In Algorithm 1, consider using different color blocks to mark $x$, $z$, and $y$. This could help in better understanding the algorithm's process. 2. How about the runtime of the algorithm? Would it be possible to include comparisons of runtime with the baseline in the experiments? 3. In the experiments, does Eq.5 require the addition of regularization coefficients for correction terms $z$ and $y$? 4. Could you include some measurements of the additional communication costs in the experiments? Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: N.A. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We appreciate the reviewer's constructive feedback. We appreciate the reviewer for carefully checking our proof and are glad to receive your positive feedback on the writing of our paper. Our responses are given as below: ### Communication cost comparison Compared to HFedAvg, MTGC requires initializing the correction variables at the start of each global round, which incurs additional communication overhead. Specifically, for every $E$ steps of group aggregation, MTGC incurs an additional communication cost equivalent to one transmission of the model parameters. In other words, the per-aggregation communication complexity of MTGC is $\frac{E+1}{E}$ times that of HFedAvg. To show this impact, we have added experiments comparing the communication cost and testing accuracy at the client side. This experiment was conducted on CIFAR-10 dataset with $E = 30$ and $H = 20$ under both client and group non-i.i.d. setup. The model and other parameters are the same as in the original manuscript. The results are shown in Figure R1(a) of the attached PDF. The results demonstrate that MTGC achieves higher testing accuracy for a given communication cost, highlighting the efficiency and effectiveness of our approach. ### Running time and computational cost During the rebuttal phase, we compared the runtime of our MTGC algorithm with the baselines. Using one NVIDIA A100 GPU with 40 GB memory, we conducted experiments on the CIFAR-10 dataset with $E = 30$ and $H = 20$ under client/group non-i.i.d. setup. The model and other parameters are the same as in the original manuscript. We report the required time for attaining a preset accuracy of $75 \\%$ and for running $100$ global rounds in Figure R1(b) of the attached PDF of the global response. We see that although our approach incurs extra operation induced by the correction variables, this is the cost for achieving a significant performance improvement by effectively handling the data heterogeneity problem. We also note that the computation cost incurred by the correction variable is relatively small compared to computing gradients in a neural network using backpropagation, which is a step that is required in all methods. Overall, the results confirm the advantage of our method compared with baselines. ### Distinguishing the update of $ \boldsymbol{x}$, $ \boldsymbol{z}$ and $ \boldsymbol{y}$ Thanks for your kind reminder. We will highlight the updates of three variables with different colors in the future version. ### Does Eq.5 require the addition of regularization coefficients for correction terms $ \boldsymbol{ z}$ and $ \boldsymbol{y}$? Based on our theory and experiments, we don't need to apply coefficients to $\boldsymbol{z}$ and $\boldsymbol{y}$. For ease of explanation, we state equation (5) as follows: $$ {\boldsymbol{x}}^{t,e}_{i,h+1} = {\boldsymbol{x}}^{t,e}\_{i,h} - \gamma \left( \nabla F_i({\boldsymbol{x}}^{t,e}\_{i,h}, \xi\_{i,h}^{t, e}) + \boldsymbol{z\_i}^{t,e} + \boldsymbol{y\_j}^t \right) $$ $\boldsymbol{z}$ and $\boldsymbol{y}$ play the role of tracking the gradient difference between the local gradient and the group gradient and the difference between the group gradient and the global gradient. By utilizing $\boldsymbol{z}$ and $\boldsymbol{y}$, our aim is for the correction updating direction $\nabla F_i + \boldsymbol{z_i} + \boldsymbol{y_j} $ to approach the global gradient direction. On the other hand, if we apply coefficients $\lambda$ for $\boldsymbol{z}$ and $\boldsymbol{y}$, consider an ideal example where we have attained the optimal point $\boldsymbol{x^}$ and $\boldsymbol{z_i} = \nabla f_i(\boldsymbol{x^}) - \nabla F_i(\boldsymbol{x^})$ and $\boldsymbol{y_j }= \nabla f(\boldsymbol{ x^}) - \nabla f_j(\boldsymbol{x^}) $. If we apply a coefficient $\lambda$ into our iteration, equation (5) becomes $$\boldsymbol{x^} - \gamma \left(\nabla F_i(\boldsymbol{x^}) + \lambda \left(\nabla f_j(\boldsymbol{x^}) - \nabla F_i(\boldsymbol{x^}) + \nabla f(\boldsymbol{x^}) - \nabla f_j(\boldsymbol{x^}) \right) \right).$$ This iteration is not stable at $x^$ as $(1-\lambda) \nabla F_i(\boldsymbol{x^*})$ is generally not equal to zero unless $\lambda = 1$. Due to this, we did not apply coefficients to $\boldsymbol{z}$ and $\boldsymbol{y}$. Again, thank you for your time and efforts for reviewing our paper, and providing insightful comments. If there are any more clarifications we could provide, we would be grateful if you could let us know. --- Rebuttal 2: Comment: Dear Reviewer r1S6, Could you please respond with how you think about the authors' response? Please at least indicate that you have read their responses. Thank you, Area chair	Summary: This paper introduces the usage of the gradient correction scheme to hierarchical federated learning. Specifically, the authors propose and analyze the multi-timescale gradient correction MTGC algorithm which is a direct generalization of SCAFFOLD to the framework where local clients aggregate their models on group server and group servers aggregate their models to a global server. The authors introduce control variables that correct i) client model drift and ii) group model drift that arises due to data heterogeneity. Theoretical convergence results are presented in the non-convex regime and experimental results showcase the ability of MTGC to address data heterogeneity both from clients and from group-servers. Strengths: - The paper places itself correctly in the existing literature, is well-structured and easy to follow. - The problem of hierarchical FL is relevant and fairly interesting for the ML community. - The proposed algorithm is natural and easy to understand. - Both theoretical and numerical results are provided. Weaknesses: - The main weakness of this work is its lack of novelty and technical contribution. The proposed MTGC is a straightforward extension of the well-known SCAFFOLD algorithm to a two-level hierarchical FL. Although the authors mention that the coupling of the two error correction variables is introducing new challenges I fail to see how this is the case. Indeed, the analysis of the correction variables appears to be largely the same as in SCAFFOLD and the authors to not make clear in the main body of their work what specific new challenges they faced and how they were circumvented. To summarize, although the paper is well written I do not see enough contribution to justify its acceptance to a top tier conference. - Minor typo: on line 110 in "However, their is" should be "However, their algorithm is". Technical Quality: 3 Clarity: 3 Questions for Authors: See weaknesses section. Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 1 Limitations: The authors adequately addressed the limitations of their work. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We appreciate the reviewer's constructive feedback. We are glad that the reviewer acknowledges the problem we studied is interesting. We would like to emphasize that theoretically showing that the proposed MTGC algorithm guarantees convergence and achieves linear speedup in terms of both $H$ (the number of local updates) and $E$ (the number of group aggregations) was quite non-trivial. In this response, we will provide more detailed descriptions of the theoretical challenges and our proof techniques to better highlight the contributions compared to SCAFFOLD, which was developed in a single-level scenario. ### Difference in the analysis of the correction terms In SCAFFOLD [12], the theoretical analysis of correction terms appears in the proof of Lemma 18. Here, the correction error can be easily bounded using $\beta$-smoothness: $$ \mathbb{E}\|\|c^{r-1}-\nabla f({x}^{r-1})\|\|^2+ \frac{1}{N}\sum_{i=1}^N \mathbb{E}\|\|c_i^{r-1}-\nabla f_i({x}^{r-1})\|\|^2 \leq \frac{2 \beta^2}{K}\sum_{k=1}^K\mathbb{E}\|\|y_{i, k-1}^{r-1}-x^{r-1}\|\|^2. $$ In our work (with multi-level, multi-timescale updates/aggregations), we bound the new correction errors $$ Z\_j^{t,e} = \frac{1}{n\_j}\sum\_{i \in \mathcal{C}\_j} \mathbb{E} \|\|\boldsymbol{z}\_i^{t,e} + \nabla F\_i(\bar{\boldsymbol{x}}^{t,e}\_j) - \nabla f\_j(\bar{\boldsymbol{x}}^{t,e}\_j)\|\|^2, \ \ \text{and} \ \ \ Y\_j^{t,e} = \mathbb{E} \|\| \boldsymbol{y}\_j^t + \nabla f_j(\hat{\boldsymbol{x}}^{t,e}) - \nabla f(\hat{\boldsymbol{x}}^{t,e})\|\|^2 $$ in Lemmas C.2.4 and C.2.5, for characterizing client and group model drifts, respectively. As shown in the proof of Lemmas C.2.4 and C.2.5, the analysis of the correction variables in our work involves new difficulties. In particular, in the analysis of upper-level correction term $\boldsymbol{y}$, we need to bound the discrepancy between $\boldsymbol x_{i,h}^{t,\tau}$ and $\hat{\boldsymbol x}^{t+1,e}$ (see line 628 of our manuscript), where two models appear in two different global rounds. We note that different from SCAFFOLD, $\boldsymbol{y}_j^t$, $\nabla f_j(\hat{\boldsymbol{x}}^{t,e})$, and $\nabla f(\hat{\boldsymbol{x}}^{t,e})$ in $Y_j^{t,e}$ are in two different timescales. Moreover, the upper bound of $Y_j^{t,e}$ is influenced by the gradients and model drifts of two consecutive rounds, highlighting the increased complexity compared to the single-level case. ### Detailed technical challenges First, the upper bounds of correction errors $Y_j^{t,e}$ and $Z_j^{t,e}$ shown in Lemmas C.2.4 and C.2.5, are impacted by model drifts $D_t$ and $Q_t$, and $\Theta_j^{t,e}$. Meanwhile, the upper bounds of $D_t$, $Q_t$, and $\Theta_j^{t,e}$ are also impacted by $Y_j^{t,e}$ and $Z_j^{t,e}$. The interplay between these terms makes the analysis non-trivial. Second, (i) global aggregation, (ii) the update of upper-level correction variable $\boldsymbol{y}$ and local aggregation, and (iii) the update of lower-level correction variable $\boldsymbol{z}$ are performed at different timescales. Note that in SCAFFOLD, since there is no local aggregation step, the convergence is presented using the global aggregation timescale, i.e., $\{\nabla f(\bar{\boldsymbol x}^{t})\}$. However, in MTGC, if we directly consider $\{\nabla f(\bar{\boldsymbol x}^{t})\}$, it is difficult to capture the effects of group aggregation and correction variable $\boldsymbol{z}$. Moreover, it is hard to establish a tight connection between $\nabla f(\bar{\boldsymbol x}^{t})$ and $\|\|\boldsymbol x_{i,h}^{t,e} - \bar{\boldsymbol x}^{t}\|\|$, $\forall e, h$ since there is a large lag between $ {\boldsymbol x}_{i,h}^{t,e}$ and $\bar{ \boldsymbol x}^{t}$. ### Our approach For the first challenge, we extracted a recursive relationship of $\Gamma_{t} = Q_t + D_t$ hidden behind Lemmas C.2.2-C.2.6, as summarized in Lemma C.2.7. With this recursion, we design a novel Lyapunov function as $\Phi_{t+1} = \mathbb{E} f(\bar{\boldsymbol x}^{t+1}) - f^* +\gamma L^2 H \Gamma_{t},$ to derive the recursive relationship between two global rounds. This new Lyapunov function with recursive components enabled us to mitigate the coupling effects between $Y_j^{t,e}$, $Z_j^{t,e}$ and $\Theta_j^{t,e}$ (see proof of Theorem 4.1 in our Appendix). For the second challenge, we introduce a new metric, which is the gradient $\nabla f(\hat{\boldsymbol x}^{t,e})$ at virtual sequence $\{\hat{\boldsymbol x}^{t,e}\}$, to characterize the convergence of MTGC. This introduction makes our analysis tractable by building connection between $\boldsymbol x_{i,h}^{t,e}$ and $\hat{\boldsymbol x}^{t,e}$ as follows: $\boldsymbol x\_{i,h}^{t,e} \rightarrow \bar{\boldsymbol x}^{t,e}\_j \rightarrow \hat{\boldsymbol x}^{t,e}$. Accordingly, we introduce two characterizations, $\|\|\boldsymbol x_{i,h}^{t,e} - \bar{\boldsymbol x}_j^{t,e} \|\|^2$ and $\|\|\hat{\boldsymbol x}^{t,e} - \bar{\boldsymbol x}_j^{t,e} \|\|^2$, to capture the local and group model drifts, respectively. The former quantifies the progress made by each client from $(t,e,0)$ to $(t,e,h)$-th iteration while the latter characterizes the group model deviation from the virtual global model at the $(t,e)$-th group aggregation, making our analysis distinct from SCAFFOLD. In the revised manuscript, we will illustrate these new challenges and our solution in more detail. Considering that the exploration of FL under practical hierarchical setups is quite limited, we believe that our work presents a meaningful contribution to the community. Our work bridges this gap by developing the MTGC algorithm with desired theoretical properties (convergence guarantee with linear speedup in the numbers of clients, local updates, and edge aggregations), where the analysis from single-level to hierarchical is not a trivial extension as supported by our response above. ### Typo We double-checked the manuscript and corrected this typo. Again, thanks for your time and efforts! Please let us know if you need any further clarification. --- Rebuttal Comment 1.1: Title: Post Rebuttal Comment: I appreciate the efforts of the authors to address my concerns in their rebuttal. After carefully reading the comments from the rest of the reviewers as well as the responses of the authors I have decided to increase my score. Specifically, the extensive description of the challenges and the techniques used to overcome these challenges (found in the rebuttal) are of crucial importance, helping the reader to better understand the technical contribution of this work. I believe that including this discussion in the main body of the paper will further improve its quality and presentation. That being said, I still consider the main weaknesses of this work to be its - somewhat limited - novelty and impact. Overall, I find this paper to be very close to the acceptance threshold leaning slightly towards acceptance (indicated by my updated score 5). --- Reply to Comment 1.1.1: Comment: We really appreciate your reply and score update. We will include these discussions in the main body of the revised manuscript. Thanks again for the helpful suggestion.	Rebuttal 1: Rebuttal: We appreciate all reviewers for providing constructive comments. In this global response, we will describe the additional experiments we have conducted, suggested by Reviewer r1S6, Reviewer fhg9, and Reviewer zFr1, that may be of interest to all reviewers. The figures are included in the attached PDF. The responses to all other comments are provided individually for each reviewer. ### Experiments for Reviewer r1S6 Computation and communication costs We reported the computational and communication costs of MTGC and baselines in Figure R1 in the attached PDF. ### Experiments for Reviewer fhg9 Experiments on other types of tasks We have conducted additional experiments using the Shakespeare dataset, an NLP task. We use the LSTM model where the model starts with an $80$-character input sequence, which is converted to an $80 \times 8$ sequence through an embedding layer. This embedded sequence is then processed by a two-layer LSTM, each with $100$ hidden units. The final output is passed through a softmax layer to make predictions. The performance comparison is presented in Figure R2(a) of the attached pdf, where we set the learning rate $0.5$, $H=75$, and $E=30$. It is observed that our MTGC consistently outperforms baseline methods. Experiments on distribution shift datasets We have conducted additional experiments to include two different non-i.i.d. scenarios: label shift and feature shift, as referenced in [R1,R2]. These experiments were performed using the Fashion-MNIST dataset. For label shift [R1,R2], we randomly assign 3 classes out of 10 classes to each group with a relatively balanced number of instances per class, and then assign 2 classes to each client. As discussed in [R1], label shift adds more heterogeneity to this system. According to the results shown in Figure R2(b), it is clear that the proposed algorithm is more robust against data heterogeneity. Specifically, there is less oscillation in MTGC compared with HFedAvg and the attained accuracy of MTGC in the given communication round is higher than all baselines. For feature shift [R1], we first partition data following the group non-i.i.d. \& client non-i.i.d. case as in our original manuscript, and then let clients at different groups rotate images for different angles. Concretely, for the clients at the $i$-th group, the angle is $-50+10 \times i$. Note that this rotation is only applied to the training set. The feature shift increases the diversity between the training set and the testing set, which thus adds difficulty to this classification task. In Figure R2(c), we see that MTGC attains the best performance among these baselines. [R1] Optimizing the collaboration structure in cross-silo federated learning, ICML 2023. [R2] On the convergence of clustered federated learning, arXiv preprint 2022. Experiments on hierarchy levels To evaluate the impact of hierarchy levels, we compared the testing accuracy versus communication time. We considered three scenarios: single-level (100 clients), two-level (100 clients grouped into 10x10), and three-level (100 clients grouped into 4x5x5). The experiments were conducted using ResNet-18 (44.6 MB) and the CIFAR-10 dataset. We considered different cases of link bandwidths in each HFL architecture, which impact the speed of communication through the system. The results are shown in Figure R3 of the attached PDF. In Figure R3(a), the communication bandwidths were set to 0.5 MB/s for single-level, and 0.6 MB/s and 20 MB/s for upper and lower links in two-level, and 0.7 MB/s, 5.5 MB/s, and 20 MB/s for three-level. Results show performance improvements from single-level to two-level, and from two-level to three-level. In Figure R3(b), considering a faster network, bandwidths were adjusted to 3 MB/s for single-level, and 3.5 MB/s and 20 MB/s for upper and lower links in two-level, and 4 MB/s, 5.5 MB/s, and 20 MB/s for three-level. Results indicated performance improvement from single-level to two-level but a decrease from two-level to three-level. This highlights that performance can vary with different configurations. Generally, increasing intermediate layers is beneficial when the central server is far from clients with high transmission latency. ### Experiments for Reviewer zFr1 Experiments on larger datasets During the rebuttal, we have conducted additional experiments on the larger Shakespeare and CINIC-10 datasets. For the Shakespeare dataset, we randomly pick 100 characters (people) in Shakespeare’s plays. We let each client have 1,500 samples, where each sample is a sequence of 80 characters (words). Considering that there are 100 clients in the system, there are 150,000 train samples in total. This means that the number of samples is 3 times that of CIFAR-10 (or CIFAR-100), which has 50,000 train samples. The performance comparison is presented in Figure R4(a) of the attached pdf, where we use the LSTM model and set the learning rate $0.5$, $H=75$, and $E=30$. It is seen that MTGC consistently outperforms the baseline methods in larger datasets. The CINIC-10 dataset contains 90,000 training images, 90,000 validation images, and 90,000 test images, significantly larger than CIFAR-10 and CIFAR-100 with 60,000 images. It includes images from both CIFAR-10 and ImageNet, enhancing diversity. We believe that the larger size and diversity of CINIC-10 further confirm the validity of our experiments. The model and hyperparameters used for the CINIC-10 dataset are the same as those of the CIFAR-10 task shown in the original manuscript. As illustrated in Figure R4(b) of the attached pdf, MTGC maintains its superior performance on the CINIC-10 dataset, consistent with its performance on other tasks. Pdf: /pdf/6575e3c0e354faffad1324f6556b328ea2088bdd.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Learning Mixtures of Unknown Causal Interventions	Accept (poster)	Summary: This paper explores the challenge of disentangling and identifying causal relationships in situations where interventional data is noisy and mixed with both intended and unintended effects. It focuses on applying interventions within linear SEMs with Gaussian noise without prior knowledge of the true causal graph. It presents an efficient algorithm that can learn and separate individual components of a mixture of unknown interventions, allowing for the recovery of true interventional distributions even when intervention targets are unknown. Strengths: This paper addresses a relatively unexplored problem of disentangling mixed interventional and observational data within linear SEMs without prior knowledge of the causal graph. This is a challenging problem with significant implications for causal inference, making the study innovative and important for the field. The authors propose an efficient algorithm that leverages the properties of linear SEMs with Gaussian noise to recover individual components of the mixture. The methodological approach is rigorous, with detailed theoretical support including proofs of identifiability and sample complexity. This thorough theoretical treatment provides a solid foundation for the claims made in the paper. The paper is well-structured with clear explanations of the problem, methodology, and results. Weaknesses: The methods developed in the paper are specific to linear SEMs with Gaussian noise, which might limit their applicability in scenarios where these assumptions do not hold. Non-linear relationships or non-Gaussian noise structures, which are common in many real-world datasets, may not be adequately addressed by the proposed approach. Technical Quality: 4 Clarity: 3 Questions for Authors: 1. I suggest improving readability by properly describing insights related to theorems, even though some of the proofs focus on matrix computations. 2. In the experimental setup, what would be the effect of different variances in Gaussian noise? 3.There might be some symbols used incorrectly: In line 104, "the edge U" should be checked. In line 128, the definition of M_I needs verification. In line 134, the letter $\kappa$ is used when mentioning shift interventions, but $\gamma$ is used below. I know that do-interventions also change $\gamma$, but I suggest keeping the notation consistent. In line 279, "A_{ij} > 0" should possibly be "\|A_{ij}\| > 0". Confidence: 5 Soundness: 4 Presentation: 3 Contribution: 3 Limitations: The author has explained the limitations of the study. This paper has no possible negative social impact. Flag For Ethics Review: ['No ethics review needed.'] Rating: 8 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for their time and thoughtful comments. Below, we answer the weaknesses and questions raised by the reviewer. >Weakness Weakness 1: Experiments Experiment on the real-world dataset: We have run our algorithm on a real-world protein signaling network dataset. Our method performs equivalently on all the metrics compared to the Oracle algorithm, which has access to the disentangled data (please refer to the Evaluation on real-world dataset paragraph in the Global comment for details). Also, In the additional pdf document attached to the global comment, we provide the ground truth graph and the estimated graph from both algorithms. Experiment with Linear SEM with non-gaussian noise: The main motivation for our work comes from the problem of causal discovery. In general, one can only identify the causal graph up to their Markov Equivalence Class using only observational data. Thus, we need interventional data to fully identify the causal graph. The intervention targets are sometimes noisy, so we can only obtain a mixture of interventional data. However, Shimizu et al. [1] showed that observational data is sufficient for learning the underlying causal graph when the data-generating process is a linear SEM with additive non-Gaussian noise with no latent confounders. They also proposed an algorithm (LINGAM) that uses Non-Linear ICA over observational data to identify the causal graph. Thus, Linear SEM with non-gaussian noise doesn't require interventional data to identify the underlying causal graph. Hence, studying the mixture of interventional distribution for this framework is an interesting problem outside the scope of current work. \ \ >Questions Questions 1: We thank the reviewer for this comment. We will add the intuition behind the proofs in the final version of the paper. \ \ Question 2: (Effect of different variance in Gaussian noise) We have an ablation experiment in Fig 5b of Appendix B.4, where we study the effect of changing the variance of the noise distribution post-intervention. The initial variance of the noise distribution of every node is 1.0, and post-intervention, we set the variance of the intervened node to take values from the set $\{0.1,1.0,4.0,8.0\}$. If the final noise variance (after intervention) is close to the initial noise variance (1.0), then the Jaccard similarity and SHD of the estimated targets and causal graphs are worse. This is also expected from our theoretical result (Theorem 4.1), which states that the sample complexity to recover the parameters of the mixture distribution is inversely proportional to the change in the noise variance ($\delta_i$ = \|final variance - initial variance\|). \ \ Typos: We thank the reviewer for pointing out the typos and other writing suggestions in the text. We will incorporate them into the final version of the paper. \ \ [1] Shohei Shimizu, Patrik O. Hoyer, Aapo Hyvärinen, and Antti Kerminen. A linear non-gaussian acyclic model for causal discovery. Journal of Machine Learning Research, 7(72):2003–2030, 2006 --- Rebuttal Comment 1.1: Comment: Thanks for your response, it addresses my concerns. I will keep my rating.	Summary: The paper proposes a method to disentangle the observational and interventional data under linear SEM with Gaussian noise. Strengths: The algorithm proposed in this paper efficiently disentangles components of mixtures arising from unknown interventions, accommodating both soft and hard interventions. The proposed method is supported by thorough theoretical analysis. Additionally, the paper is well-written and easy to follow. Weaknesses: The experiments are not comprehensive enough to thoroughly assess the effectiveness of the proposed method. More experiments on real-world datasets are required. This is especially necessary since the problem setup for the mixture of interventions is a bit restrictive. Also, it would be interesting to analyze how the method empirically performs on datasets that are not generated from Linear SEM or do not have Gaussian noises. Technical Quality: 3 Clarity: 3 Questions for Authors: 1) Could you please elaborate on how realistic the problem setting is? Especially concerning the noisy intervention setting [6, 28], how compatible is the paper's problem setup with these real-world scenarios? 2) Could you please elaborate on the connection between your proposed method and existing literature on learning mixture of Gaussians? Confidence: 5 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 their time and thoughtful comments. Below, we answer the weaknesses and questions raised by the reviewer. >Weakness Weakness 1: Experiment on the real-world dataset: We have run our algorithm on a real-world protein signaling network dataset. Our method performs equivalently on all the metrics compared to the Oracle algorithm, which has access to the disentangled data, unlike us (please refer to the Evaluation on real-world dataset paragraph in the Global comment for details). Also, In the additional pdf document attached to the global comment, we provide the ground truth graph and the estimated graph from both algorithms. \ \ Weakness 2: Experiment with Linear SEM with non-gaussian noise: The main motivation for our work comes from the problem of causal discovery. In general, one can only identify the causal graph up to their Markov Equivalence Class using only observational data. Thus, we need interventional data to fully identify the causal graph. The intervention targets are sometimes noisy, so we can only obtain a mixture of interventional data. However, Shimizu et al. [1] showed that observational data is sufficient for learning the underlying causal graph when the data-generating process is a linear SEM with additive non-Gaussian noise with no latent confounders. They also proposed an algorithm (LINGAM) that uses Non-Linear ICA over observational data to identify the causal graph. Thus, Linear SEM with non-gaussian noise doesn't require interventional data to identify the underlying causal graph. Hence, studying the mixture of interventional distribution for this framework is an interesting problem outside the scope of current work. \ \ >Questions Question 1: The work from [6,28] has shown that CRISPR gene editing technology has an off-target effect. Also, the off-target effect can be random, i.e., every off-target effect could be different. For example, Aryal et al. [2] have shown that the same gene editing experiment on mice embryos exhibited different off-target cleavage for different mice. Thus, the observed data can be a mixture of multiple off-target interventions as modeled in our work. To perform any downstream task, one needs to identify the unknown intended target and disentangle the mixture distribution, which is also the main goal of our work. \ \ Question 2: In our work, we study the problem of disentangling a mixture of unknown interventions on Linear SEM with Gaussian noise, a special case of learning Gaussian mixtures. We remark that learning Gaussian mixtures is a well-studied problem with a rich literature (check Section 2), and our work builds upon these existing results. To invoke existing learning Gaussian mixture results, one needs to show the separation between distributions corresponding to the mixture components which is non-trivial. In our case, the mixture components correspond to interventional distributions, and one of our main contributions is to show the separation between them. We wish to emphasize that this separation also depends on the type of interventions one performs, and in our work, through careful analysis, we show the mean and covariance of interventional distributions are well separated for a more general class of soft interventions. As a consequence of our separation result, we show that the intervention targets and parameters of the international distribution can be recovered. \ \ [1] Shohei Shimizu, Patrik O. Hoyer, Aapo Hyvärinen, and Antti Kerminen. A linear non-gaussian acyclic model for causal discovery. Journal of Machine Learning Research, 7(72):2003–2030, 2006 [2] N.K. Aryal, A.R. Wasylishen, and G. Lozano. Crispr/cas9 can mediate high-efficiency off- target mutations in mice in vivo. Cell Death and Disease, 9, 2018 --- Rebuttal Comment 1.1: Title: Response to the Author Comment: Thank you for your response. The authors have partially addressed my concerns, thus I will keep my rating.	Summary: The paper proposes linear structural equation models with additive Gaussian noise to address the challenge of disentangling mixed interventional and observational data. The problem is highly relevant to real-world applications with mixed data. Strengths: * The theoretical framework is robust, with clear assumptions and derivations. The paper provides theoretical guarantees on the identifiability of mixture parameters. * The key idea is clearly explained and easy to follow. Weaknesses: * The use of linear structural equation models is well-established in recent literature. Implementing SEMs with unknown interventions is not a novel approach. * The identifiability guarantees rely on the assumption of soft interventions. This assumption may restrict the broader applicability of the model. * The proposed method lacks sufficient experimental support. And it seems that the proposed method is primarily validated through simulations in the experiments, is it possible to provide real-world data examples? Technical Quality: 3 Clarity: 3 Questions for Authors: See Weaknesses. Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: * The method focuses on linear structural equation models with additive Gaussian noise only, and the theoretical guarantees rely on the linear- SEM assumptions, which may limit the method's applicability in practice. 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 thoughtful comments. Below, we answer the weaknesses raised by the reviewer. Weakness 1: While we agree that the linear SEMs with unknown interventions are a relatively well-studied problem, we wish to highlight that our setting is different as we work with a mixture of multiple unknown interventions. Given such a mixture, our goal is to disentangle this mixture and recover the parameters corresponding to the mixture components. To the best of our knowledge, no other work exists that aims to solve this problem of disentangling the mixture of unknown interventional distributions in the setting of linear SEMS with Gaussian noise. Furthermore, in this setting, our work lays out the first theoretical foundation on the identifiability of the individual components in the mixture. We would like to restate the fundamental importance of this setup in the causal discovery literature (also stated in the Introduction, Lines 40-46 of the main paper). Shimizu et al. [1] showed that observational data is sufficient for learning the underlying causal graph when the data-generating process is a linear SEM with additive non-Gaussian noise with no latent confounders. However, in the same setting with Gaussian noise, the causal graph is only identifiable up to its Markov Equivalence Class (MEC). Thus, performing interventions (possibly noisy) is necessary to identify the causal graph, making it an interesting framework for our problem. We also wish to remark that some prior works do study a more general problem of disentangling the mixture of multiple unknown directed acyclic graphs. However, there are no theoretical guarantees about the identifiability of individual components in this setting (please refer to the Mixture of DAGs and Intervention paragraph in Section 2 of the main paper). \ \ Weakness 2: Soft interventions are a very general form of intervention that subsumes most of the widely studied interventions in the literature, such as shift, stochastic do, and do (please also see Lines 134 to 139 for this specialization). Therefore, we believe that studying soft interventions would indeed have a much broader applicability. \ \ Weakness 3: We have run our algorithm on a real-world protein signaling network dataset. In summary, our method performs equivalently on all the metrics compared to the Oracle algorithm, which has access to the disentangled data (please refer to the Evaluation on real-world dataset paragraph in the Global comment for details). Also, in the additional pdf document attached to the global comment, we provide the ground truth graph and the estimated graph for both the algorithms. The causal graph estimated by our algorithm is very similar to the graph estimated by the oracle. Also, we have added results with a new version of our algorithm (Mixture-UTIGSP), where we automatically search for the number of components in the mixture (please see global comment Automated Component Selection for details). Evaluating the “half-setting,” where the number of components in the mixture is (num nodes +1)/2, we observe that: 1. The number of components found by this method is also close to the correct value. 2. The parameter estimation error goes down to zero for all the nodes, unlike Fig 1d in the main paper. The other metrics, like SHD, still have the same decreasing trend. 3. Please refer to Figure 2 in the additional pdf document attached to the global comment for the parameter estimation and SHD plot before (Fig1d and 1f from the main paper) and after this improvement. Limitations 1: We agree that the linear SEM with Gaussian noise is restrictive and may not apply to many real-world settings. However, even with these assumptions, the problem we study in our work is non-trivial and poses several challenges. Extending our results beyond the linear SEM setting would help broaden the applicability of our results. We believe that studying these questions is a very important future research direction, and we would like to consider our work as a first step in this direction. Also, in answer to the Weakness 1 above, we motivated our choice to study Linear SEM with Gaussian noise. --- Rebuttal Comment 1.1: Comment: As the deadline approaches, we would greatly appreciate hearing from you. Please let us know if you need any further clarifications. --- Rebuttal Comment 1.2: Comment: I thank the authors for the detailed responses, which address some of my concerns, I will maintain my score.	Summary: This paper considers a setup where an intervention results in obtaining iid data from a mixture of multiple interventional data and observational data and the goal is to learn the mixing weights and the resulting interventional distributions. Particular focus is on the linear SEM setting with Gaussian noise where interventions are allowed to be soft with some restrictions. The goal is to then learn the mixing weights and the interventional distribution (all multivariate Gaussians) parameters without knowledge of the causal graph. Given the large amount of literature on learning mixtures of Gaussians, it only remains to be shown that the individual components are well-separated in terms of changes in the interventional distributions. Strengths: Interventions in the real world turn out to be messy and this paper continues on the thread of research that deals with unknown interventions. The paper is well-written with a clear flow of ideas. The numerical evaluations are also thorough. Weaknesses: While I understand that this is the first step in learning mixtures of interventions, I believe that it has limited novelty both conceptually and technically since it largely follows from existing work on learning Gaussian mixtures. The considered setup also assumes unconfoundedness on top of linear SEMs and Gaussian noise. Few more detailed questions follow in the next section. The experimental evaluation is also limited to simulation data which don't completely endorse the validation of the algorithm. See next section on suggestions/questions. The writing can be more careful. There are typos in the main assumption (4.1) and there's some confusing notation about the high probability delta and the difference in variance delta_i. Technical Quality: 3 Clarity: 3 Questions for Authors: 1. Theorem 4.1 is an existence theorem and in the experimental section, EM is used to learn the parameters. Given that the polynomial time guarantee includes information about A, how would we claim to not requiring knowledge of the causal graph? 2. While misspecifying k for the 'half' interventions case is indeed a feature, is there an improvement if k is correctly specified. Currently, it's not completely clear to me that the error goes down in (d). 3. Is there any intuition for why when SHD and Jaccard similarity metrics improve, the parameter estimation error still does not? See nodes = 8 in half interventions case. Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: The authors have addressed limitations in a separate section. 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 thoughtful comments. Below, we answer the weaknesses and questions raised by the reviewer. > Weakness: Limited Novelty: While we agree that our work builds on top of existing work but doesn’t follow immediately from them. To invoke these existing results on learning Gaussian mixtures, we do indeed make some non-trivial contributions, which we highlight below: 1. To invoke existing learning Gaussian mixture results, one needs to show the separation between distributions corresponding to the mixture components. In our case, the mixture components correspond to interventional distributions, and it is non-trivial to show separation between them. We wish to emphasize that this separation depends on the type of interventions one performs. Through careful analysis, our work shows that the mean and covariance of interventional distributions are well separated for a more general class of soft interventions. 2. In addition to the above, one of our other major contributions comes in modeling a real-world setting. Although the contributions in our work are a first step towards solving the practical problem, nevertheless, we believe it is an important first step. Experimental Evaluation: Please see the answer to Question 2. We have also added a new experiment in which we automatically select the number of components that improves the parameter estimation error in Fig 1d of the main paper (see answer to Question 3 below). Writing Comment: We thank the reviewer for pointing this out. Yes, the variance $\delta_i$ and the probability $\delta$ are different. We will update the main paper to incorporate the reviewer’s suggestion. \ \ > Questions: Question 1: Please note that Theorem 4.1 states that the sample complexity of the algorithm is polynomial in the norm of the adjacency matrix (A) but not the runtime as you stated. The algorithm doesn’t explicitly use the knowledge of the adjacency matrix “A”. The dependence of sample complexity on "A" characterizes the problem difficulty, i.e., depending on the problem, we will require a different number of samples to get the desired accuracy. Also, the algorithm is consistent, i.e., it will recover the correct parameters under an infinite sample limit. \ \ Question 2: 1. Fig 1a-c shows the setting when the number of components is correctly specified, i.e., k=num_node +1, and the number of components in the mixture is also num_nodes +1. In this case, we see a clear improvement in the parameter estimation error (Fig 1a). Fig 1d-f corresponds to the setting where the number of components is misspecified, i.e., k=num_node+1 and number of components = num_node/2+1. This is mainly due to mispecified number of components in the mixture. Below, we fix this. 2. Automated Component Selection: We have added results with a new version of our algorithm (Mixture-UTIGSP), where we automatically search for the number of components in the mixture (please see global comment Automated Component Selection for details). Evaluating the “half-setting,” where the number of components in the mixture is (num nodes +1)/2, we observe that: 1. The number of components found by this method is also close to the correct value. 2. The parameter estimation error goes down to zero for all the nodes, unlike Fig 1d in the main paper. The other metrics, like SHD, still have the same decreasing trend. 3. Please refer to Figure 2 in the additional pdf document attached to the global comment for the parameter estimation and SHD plot before (Fig1d and 1f from the main paper) and after this improvement. Question 3: The parameter estimation error is high in the second setting (num intervention = half, Fig 1d-f of main paper) due to the misspecified number of components (k=num nodes+1). To remove this problem, we have modified our algorithm to automatically select the correct number of components in the mixture (please see Automatic component selection paragraph in Global comments and answer to Question 2). In summary, with the modified algorithm, the parameter estimation error goes to zero, Jaccard similarity increases, and SHD decreases to zero as the sample size increases. --- Rebuttal Comment 1.1: Title: Response to rebuttal Comment: Thanks for the response and apologies for my delayed response. Regarding limited novelty, I am not convinced yet mainly because I don't see non-trivial cases where separation wouldn't hold. Perhaps it would be more constructive to consider a non-trivial example of intervention in your model where separation does not hold? I understand this request comes late. Regarding Question 1 - Yes, I meant to write sample complexity. This is convincing since you're not really claiming polynomial sample complexity but just identifiability so the mismatch in the theorem statement and experimental algorithm is ok. Experimental Evaluation - The authors have responded with a thorough evaluation including experiments on a real-world dataset. A question regarding the automatic component selection algorithm - how are the cutoff percentages decided? I still find the novelty issue a minus but the experimental evaluation is now thorough for me to increase my score. --- Rebuttal 2: Comment: We thank the reviewer for their response and for acknowledging that the experimental evaluation is thorough now. Below, we answer the concerns and questions in detail: >Limited Novelty Here is an example where there is no separation between the parameters in the mixture. Let the system consist of three nodes $X, Y$ and $Z$, the corresponding SEM is defined as: $X= N(0,1)$ $Y=X$ and $Z=X-Y+N(0,1)$ Let the mixture distribution consist of two components: a) observational and b) stochastic do intervention on node $Z$. Here, we keep the noise distribution the same as before post-intervention, i.e., we set $Z = N(0,1)$. We can show that the mean and covariance of both components are the same. Thus, there is zero parameter separation in spite of the adjacency matrix being different for both components. We agree that the above constructed example violates the faithfulness assumption. Thus, we needed a careful analysis to capture such nuances and other complexities in the parameter separation calculation. Our lower bound of parameter separation in Lemma 5.1 captures this i.e., parameter separation is zero for the above example since $f(B, D)=\lambda_{min}^{2}(D)/4\|\|I-A\|\|_{F}^{4} = 0$ since the noise covariance matrix $D$ has one of the entries as zero and the other parameters $\delta_i=\delta_j=\gamma_i=\gamma_j=0$ (see Appendix A2 for exact expression of $f(B, D)$). Also, it is somewhat intuitive that for non-degenerate cases, the parameters will be separated, but the exact dependence on the parameters of intervention was not clear. In Lemma 5.1, we show that the lower bound of the parameter separation is a polynomial function of the parameters of intervention ($\|\|c_i\|\|$, $\delta_i$ and $\gamma_i$’s). This also enables us to show the polynomial sample complexity of the existence algorithm in Theorem 5.2. \ \ >Threshold for Automatic Component Selection: Currently, we manually set the percentage threshold to a fixed value (7% in our simulation experiments, selected arbitrarily). As we increase the number of components in the mixture model the log-likelihood of the model is expected to increase due to increasing model capacity. However, we expect that as we reach the correct number of components any further increase in the number of components will most likely lead to minimal change in the log-likelihood. Thus, we chose to keep the threshold a small number close to zero. --- Rebuttal Comment 2.1: Title: Final response Comment: Thanks for the example and the clarification on the automatic component selection. Regarding the latter, I am not sure if this is then generalizable beyond the examples considered? I have increased my score accordingly. --- Reply to Comment 2.1.1: Comment: We thank the reviewer for the question regarding the generalizability of automatic component selection due to manual thresholding. Manual thresholding was mainly chosen due to the short time constraint for the rebuttal. However, in the final revision, we will try to include other well-known methods for model selection, like the BIC criterion, that would generalize to other datasets.	Rebuttal 1: Rebuttal: Below, we answer some of the common weaknesses or questions raised by multiple reviewers: > Reviewer 583w Automatic component selection: In our Algorithm-1 (Mixture-UTIGSP), we allow for the misspecification of the correct number of components in a mixture. By default, the number of components is set as num node+1. However, this default setting could lead to errors in identifying the component's parameters, as shown in Fig 1d of the main paper. To address this issue, we have included results from a new version of our algorithm (Mixture-UTIGSP) that automatically searches for the number of components in the mixture. We do so by: 1. First, a different Gaussian mixture model should be fitted for all possible numbers of components, i.e., 1 to "num node+1". 2. num_fwd_component = Start from the model with 1 component, iterate to the model with the "num node +1" component, and stop where the change in the log-likelihood of the mixture model drops below a cutoff percentage. 3. num_bwd_component = Start from the “num node + 1” component model, iterate to the model with 1 component, and stop where the change in the likelihood of mixture increases above a cutoff percentage. 4. Number of component = (num_fwd_component+num_bwd_component)//2 Multiple other strategies, such as the BIC criterion or different variations of the above algorithm, could automatically select the number of components in the mixture, but we leave that exploration to future work. We have rerun our experiment on the “half"-setting (where the true number of components in the mixture is (num nodes +1)/2) with this new automated selection method. Unlike Fig 1d in the main paper, where the parameter estimation doesn't improve much due to misspecified parameters, we observe that the parameter estimation errors go down to zero for all the nodes. Moreover, the other metrics, like Jaccard Similarity and SHD, still respectively show the same increasing and decreasing trend. Also, the estimated number of components becomes more accurate as the sample size increases. Please see Figure 2 in the additional PDF document attached for a comprehensive comparison of the parameter estimation and SHD plot before and after this improvement. For this experiment, we only utilized Step 3 of the modified algorithm mentioned earlier to determine the number of components. \ \ > Reviewer 583w, mSnK, nhPx, SSWb Evaluation on real-world dataset: To demonstrate real-world applicability, we evaluate our method on the Protein Signaling dataset [1]. The dataset is collected from flow cytometry measurement of 11 phosphorylated proteins and phospholipids and is widely used in causal discovery literature [2,3]. The dataset consists of 5846 measurements with different experimental conditions and perturbations. Following Wang et al. [2], we define the subset of the dataset as observational, where only the receptor enzymes were perturbed in the experiment. Next, we select other 5 subsets of the dataset where a signaling protein is also perturbed in addition to the receptor enzyme. The observational dataset consists of 1755 samples, and the 5 interventional datasets have 911, 723, 810, 799, and 848 samples, respectively. The table below summarizes the performance of our algorithm with the oracle (UTGSP), which already has access to disentangled data. For this experiment, our algorithm uses the automatic selection criteria for selecting the number of components in the mixture (see Automatic component selection paragraph above) \| \| Estimated vs Actual #component \| Jaccard Similarity \| SHD \| \|--------------\|----------------------------------\|--------------------------------\| -----------------\| \|Ours (Mixture-UTIGSP) \| 7 (estimated) vs 6 (actual) \| 0.08 \| 17.6 +/- 1.0 \| \|Oracle (UTIGSP) \| NA \| 0.09 \| 17.4 +/- 1.0 \| The total number of nodes in the underlying causal graph is 11. Thus, the maximum possible component in the mixture is 12 (11 interventional and one observational). In the mixture dataset described above, we have 6 components (1 observational and 5 interventional). Our method automatically recovers 7 components from the mixture, close to the ground truth 6. Next, we give the disentangled dataset from the first step of our algorithm to identify the unknown target. Though the Jaccard similarity of the recovered target is not very high (0.08, where the maximum value is 1.0), it is similar to that of Oracle (UTGSP). This shows that it is difficult to identify the correct intervention targets even with correctly disentangled data. Also, the SHD between the recovered graph and the widely accepted ground truth graph for Mixture-UTIGSP (ours) and UTIGSP (oracle) is very close. In the additional pdf document attached to the global comment, we provide the ground truth graph and the estimated graph from both algorithms. The causal graph estimated by our algorithm is very similar to the graph estimated by the oracle. \ \ [1] K. Sachs, O. Perez, D. Pe’er, D. A. Lauffenburger and G. P. Nolan. Causal protein-signaling networks derived from multiparameter single-cell data. Science 308.5721 (2005): 523-529. [2] Y. Wang, L. Solus, K. Yang, and C. Uhler. Permutation-based causal inference algorithms with interventions. In Advances in Neural Information Processing Systems, pages 5822–5831, 2017. [3] Chandler Squires, Yuhao Wang, and Caroline Uhler. Permutation-based causal structure learning with unknown intervention targets. Proceedings of the Thirty-Sixth Conference on Uncertainty in Artificial Intelligence, UAI 2020 Pdf: /pdf/c33e93addef7640ba298bfb38083a7526a00eca8.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Geometry-aware training of factorized layers in tensor Tucker format	Accept (poster)	Summary: This paper proposes a method for neural network model parameter compression. It parameterizes weight tensors in the format of Tucker decomposition, and trains the factors instead of the origin weight tensors afterwards. The method is able to adaptively modify the tensor rank. Authors also provide detailed theoretical analysis including the computational steps, and convergence, approximation and the gradient descent guarantees of the method. Experiments show good performance of the method in terms of image classification accuracies, model compressive rates, and the high running efficiency. Strengths: Writing is easy to follow. Theoretical analysis is self-contained and solid. Experiments are sufficient to demonstrate the claimed good properties of the method. Weaknesses: I did not observe obvious weakness. However, I found that the studied neural networks seemed to be a bit of out-of-date. As a reviewer, I hope to see applying the method in up-to-date models e.g. transformers, in other fields. I am not sure whether this point would make negative influence on the significance of the work. Technical Quality: 3 Clarity: 3 Questions for Authors: What is a standard Tucker decomposition like? Could you provide more details for the comparison of the proposed method and the vanilla standard Tucker decomposition, especially over the space/time complexity comparison, and their convergency analysis? What are the compressed parameters in the neural networks? Are the parameters merely the convolutional kernel? Can the method be applied on the weights of linear layers? What does ``geometry-aware’’ indicates? What kind of geometry is the method aware of? Could you give more explanation? Confidence: 2 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: First of all, we would like to thank the reviewer for their feedback. W1: We agree that our paper can be improved by showcasing stronger empirical evaluations for larger models. We have therefore conducted several new experiments on the popular parameter-efficient fine-tuning using low-rank adapters (LoRA), as suggested by reviewer vGH1. Here, we have tested the proposed training model on larger architectures such as DebertaV3 on Glue benchmark and Stable Diffusion (v1.4) dreambooth. In DebertaV3, we applied our method to matrix layers by interpreting matrices as order-2 tensors. For Stable Diffusion we applied our method to tensor layers in the Unet, while standard LoRA convolution works essentially by reshaping the tensor into a matrix. We believe that these results strengthen the empirical evaluation and we hope these could address your concerns. \| GLUE test case\| LoRA - rank 8, 1.33M params \| Ours - 0.9 M params \| \|-----------------------\|---------------\|-----------------------------\| \| CoLa (Matt. Corr) \| $0.6759$ \| $0.7065$ \| \| MRPC (acc) \| $0.8971$ \| $0.9052$ \| \| QQP (acc) \| $0.9131$ \| $ 0.9215$ \| \| RTE (acc) \| $0.8535$ \| $0.8713$ \| \| SST2 (acc) \| $0.9484$ \| $0.9594$ \| Stable Diffusion \| loss \| \# trainable parameters ----------------------\|---------------\|---------------------------------- LoRA ($r = 8$) \| $0.260$ \| $5$ M LoRA ($r = 5$) \| $0.269$ \| $3$ M LoRA ($r = 3$) \| $0.274$ \| $1.8$ M ours ($\tau = 0.02$) \| $0.2635$ \| $1.8$ M ours ($\tau = 0.1$) \| $0.272$ \| $1.5$ M Q1. The standard Tucker decomposition is the choice of the parameterization $W(i_1,\dots,i_d) = \sum_{j_1,\dots,j_d} C(j_1,\dots,j_d) U^{(d)}(i_d,j_d)$ to represent the d-mode tensor $W$. This choice is one possible extension of the classical singular value decomposition for tensors. For what concerns the vanilla Tucker decomposition and its training, we compare with the prototype method used often in training low-rank decompositions (such as LoRA), for which the update is simply given by a step of stochastic gradient descent on each factor of the decomposition, i.e. $C(t+1) = C(t)- \lambda_t \nabla_C \mathcal L(t),\, U^{(i)}(t+1) = U^{(i)}(t)-\lambda_t \nabla_{U^{(i)}}\mathcal L(t)$. Apart from the instability with respect to small singular values of vanilla Tucker, we would like to underline that this method introduces additional invariances in the parameter space (since orthonormality of the basis $U^{(i)}$ is not preserved over time). In terms of space complexity, Tucker vanilla and our decomposition are the same. The time complexity of one optimization iteration for the vanilla Tucker is of order $O(b(\prod_{i=1}^d r_i+ \sum_{i=1}^d n_i r_i))$, where $n_i$ are the dimensions of the tensor weight, $r_i$ are the Tucker ranks and $b$ is the batch size. The training of vanilla methods is essentially SGD, so the convergence properties of it are the same of stochastic gradient descent. Q2 This is a good question and we will add a small discussion of this point in the manuscript. The presented theory and the algorithm is developed in general for Tucker tensors with $d$ modes, that for $d = 2$ covers also the matrix case. In particular then it is possible to apply the method both to matrices and tensors with more than two modes. In the matrix case, the Tucker decomposition would degenerate into a singular value like decomposition of the weight matrix. Q3 The choice of the name "geometry-aware" refers to the fact that the proposed method is "aware" of the geometric structure underlying the problem. In section 2.1 we formulate the training of tensor-weighted neural networks as a gradient flow $\dot W = -\nabla_W \mathcal L(W)$. When we want to superimpose a low-rank structure, vanilla methods follow a gradient flow $\dot C = -\nabla_C \mathcal L, \, \dot U^{(i)} = \nabla_{U^{(i)}} \mathcal L$. This last gradient flow lies in the (Riemannian) manifold $\mathcal M_r$ of Tucker tensors of rank $\mathbf{r}$, but it is not aware in some sense of the original problem related to the geometry of the constraint. Our proposed method follows the global dynamics $\dot W = -P(W) \nabla_W \mathcal L(W)$, where $P(W)$ is the orthogonal projection on the tangent space $T_W \mathcal M_r$. Notice that the right hand side of this last projected differential equation is a solution of the minimization problem $ \underset{\delta W \in T_W\mathcal M_r}{\arg \min}\|\|\delta W+ \nabla \mathcal{L}(W) \|\|_{F}^2$, basically by definition of orthogonal projection. This variational principle is essentially telling us that locally we're taking the closest direction to following the original unfactorized dynamics. This property is not satisfied by the vanilla gradient flow system, that does not follow locally the original unfactorized dynamics. Moreover, our proposal is aware of certain properties of $\mathcal M_r$, such as high curvature around tensors with small singular values along some mode. As shown in theorems 3.1 and 3.3, the provided theoretical bounds regarding approximation and descent do not depend on the singular values, making the method stable in their presence. This property is also highlighted numerically in figure 2, where we show that vanilla methods seem to suffer from this ill-conditioning. We will add some details about the questions in the manuscript, and we hope the explaination has clarified any possible doubt. In any case we remain available if any further clarification is needed. --- Rebuttal Comment 1.1: Comment: Thanks for your response. I would keep my score. --- Reply to Comment 1.1.1: Comment: We thank again the reviewer for the feedback.	Summary: This paper extends the dynamic low-rank neural network training (DLRT) method to the rank-adaptive Tucker tensor format (TDLRT). The proposed reparameterization method greatly reduces the computational complexity and numerical instability of the projected gradient descent. Under certain conditions, TDLRT with SGD converges to a stationary point in expectation, where the tensor found by TDLRT provably approximates the full mode. The experimental results show that TDLRT converges faster with less variance and better accuracy-compression rate tradeoff than other factorization-based and pruning-based methods. Strengths: - The paper is clearly written. Most parts are supported by sufficient technical details. - The proposed method is an extended version of DLRT. Yet, some unique challenges appear in the Tucker tensor format have addressed with interesting approaches, e.g., the reparameterization method and Corollary 2.2. Weaknesses: I have some minor concerns on writing and the experimental result - More detailed information about one-step integration methods could be provided for the readers who are not familiar with the concept. - Some sections assume a certain degree of background knowledge on DLRT, e.g., gauge conditions in Line 612. - The evaluation of training time for Tucker Decomposition and TDLRT was conducted on a toy-sized model (LeNet5) and dataset (MNIST). Evaluating training time on a dataset and a model of more practical sizes would provide better understandings of the proposed method. Technical Quality: 3 Clarity: 3 Questions for Authors: - How does the one-step integration work? Does it not add significant computational overhead? - Are the conditions and assumptions in Theorem 3.2 and 3.3 reflect the actual DNN training? Is there any assumption that does not hold in practice? - How sensitive is TLDRT to the choice of hyperparameters like $\tau$, learning rate, weight decay or initialization schemes? Do they require extensive hyperparameter search to find the right ones? - Can TDLRT be used for the low-rank adaptation (LoRA) [1] setting? E.g., fine-tuning the convolution kernels of the U-Nets for the diffusion models by TDLRT with very low tensor ranks. [1] Hu, Edward J., et al. "Lora: Low-rank adaptation of large language models." arXiv preprint arXiv:2106.09685 (2021). Confidence: 5 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: - The utilization of QR decomposition might hinder using the proposed method to train a large model on a large dataset, e.g., diffusion model training. - The number of parameters is determined after training and indirectly adjusted by a hyperparameter $\tau$. Since a good strategy of choosing $\tau$ is not yet proposed, one might need to train the DNN multiple times to obtain a desired accuracy and model size. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: First of all, we would like the thank the reviewer for the insightful feedback. Below, we provide our responses to the main points raised in the review. Q1+W1 Regarding "How does the one-step integration work? Does it not add significant computational overhead?". With "one-step integration'' we mean a single step of a gradient-based optimization method or, equivalently, any classical time-integration method. In this work, we use stochastic gradient descent (SGD) which in the time integration view is the explicit Euler method. However, the use of other methods is certainly possible. This step does not add any overhead compared to the full-rank training and, in fact, is one of the parts in our method that allows us to have a significant reduction of computational costs and memory footprint. Note that for the full-rank training, the one-step integrate function is called repeatedly using the full gradient, whereas we only need to call this method with the gradient for a low-rank factor. We will add a sentence to our manuscript to clarify what we mean by the one-step integration method. W2 Thank you for the suggestion which we believe makes a lot of sense. We will add a short description to our manuscript. Q2 Regarding "Are the conditions and assumptions in Theorem 3.2 and 3.3 reflect the actual DNN training?...". Regarding Theorem 3.3, boundedness and Lipschitz continuity of the gradient are very common assumptions one must make to show most analytic results. Both assumptions are reasonable since one would assume the gradient remains bounded during the optimization and the gradient does not completely change when slightly changing the input. The latter can be achieved using most common activation functions, since it requires a condition on the boundedness of the derivatives. The assumption that the gradient flow remains close to the low-rank manifold is observed empirically, but it is extremely difficult to understand analytically. Numerous experiments have shown that neural networks are usually well-represented by low-rank weights, and some analytic investigations exist for heavily simplified architectures. Regarding Theorem 3.2, the Robbins-Monro conditions are very standard assumptions and can be ensured by the user when picking the learning rate. The stabilization of the spectral distribution over time is something that we observe empirically, though it is hard to show anything on an analytic level. Here, we see that after sufficient iterations of TDLRT, the basis does not change, and most of the change is seen in the core tensor. The drift assumption is meant to play the role of the more standard (but more restrictive) assumption of finite variance, which is common when studying convergence of stochastic methods. Q3 This is a good question we should have discussed in our manuscript. First, regarding the tolerance parameter for truncating the core tensor, this is, of course, a hyperparameter that needs to be chosen. We commonly use similar values here in different test cases and we never needed an in-depth hyperparameter search to observe good performance. However, it is hard to say if this holds for all architectures and datasets, and most likely, one must adapt here. However, we wish to point out that a single parameter determines individual ranks and compressions for different modes in each tensor in each layer. Here, other approaches, like LoRA, which you mention later, require the user to choose good ranks for each layer, which is certainly a harder task and requires an intensive parameter search if one wants minimal memory overhead. Regarding parameters like learning rate, weight decay etc., we found that our method is relatively robust with respect to their choice, similar to the full baseline. This is aligned with the theoretical findings of e.g. Thm 2.1 and Thm 3.3. Q4 + W3 Thank you for this excellent question. Certainly, our approach fits LoRA excellently, and we have now provided some results on how TDLRT can be used in such a setting (we refer to the main rebuttal pdf file). The main question is always if these architectures allow for low-rank weights (or in terms of the assumption of Theorem 3.3, if $\varepsilon$ small). If the answer is yes, then our approach should yield good results. Moreover, all the theory presented in the manuscript applies to this case. L1 Regarding "The utilization of QR decomposition might hinder using the proposed method to train a large model....'' Please note that the QR decomposition only needs to be computed on a small matrix of dimension $n_i\times r_i$, leading to computational costs of $O(n_i\times r_i^2)$. Thus, if the rank is small, the QR decomposition is usually not a limiting factor (and these small ranks are in fact often the case for LoRA style fine-tuning). L2 Regarding "The number of parameters is determined after training and indirectly adjusted by a hyperparameter. Since a good strategy of choosing is not yet proposed, one might need to train...". We agree, development of a method that takes a parameter budget and determines $\tau$ to obtain the best model for the given budget is a relevant research question. We have been pointed to [1] by reviewer TTwz for an approximative Tucker decomposition (of the core tensor) under a parameter budget. Here the research question is: Given a parameter budget, how to determine the core shapes of the core tensors of all low-rank convolutions in the network to best approximate the full-rank model, if the low-rank dynamics, implicitly given by the data, are representable within this budget. This question is as relevant as it is non-trivial, and we would like to refer to future research to properly address it. [1] Ghadiri, Mehrdad, Matthew Fahrbach, Gang Fu, and Vahab Mirrokni. "Approximately optimal core shapes for tensor decompositions." In International Conference on Machine Learning, pp. 11237-11254. PMLR, 2023. --- Rebuttal Comment 1.1: Comment: Thank you for your thorough response! I was uncertain about the details of the one-step integration and the practicality of the proposed method, which were all addressed in the rebuttal. In particular, I thank the authors for providing additional experimental results on language and diffusion models. They clarify my doubts about the practicality. Regarding the diffusion model, which layers were updated with LoRA and TDLRT? Although it is common practice to apply LoRA to the attention layers of the U-Net, I suppose TDLRT can also update the convolution layers. I wonder if this was the case, and if so, it could be argued as an additional strength compared to LoRA. Also, I retract Limitation 1 on QR decomposition overhead after rethinking it based on the authors' response. I don't think it will limit the usability of TDLRT as long as the rank is small. Since I already gave 7, I keep my score the same. Instead, I am inclined to raise my confidence. --- Reply to Comment 1.1.1: Comment: We thank again the reviewer for their response and we are glad we were able to clarify all doubts. Regarding the U-net, we applied LoRA to the attention and convolutional layers, using the official implementation of LoRA in the Huggingface PEFT package [1]. Specifically, the LoRA implementation for convolutions does not perform a proper tensor decomposition; instead, it corresponds to a low-rank factorization of a flattened version of the convolutional kernel (flattened to a matrix). Our proposed TDLRT has been applied to the same layers as those described above, maintaining their original tensor/matrix structure. [1] S. Mangrulkar, S. Gugger, L. Debut, Y. Belkada, S. Paul and B. Bossan, "PEFT: State-of-the-art Parameter-Efficient Fine-Tuning methods", github 2022. We thank the reviewer once again for their interest and remain available to clarify any further doubts.	Summary: The authors present a novel algorithm for training neural network layers using Tucker tensor decomposition. The approach addresses common issues with layer factorisation, including the need for an initial warm-up phase and sensitivity to parameter initialisation. Th method dynamically updates the ranks during training. The authors provide theoretical guarantees on loss descent, convergence, and approximation to the full model, supported by experimental results showing high compression rates and performance comparable to or better than baseline and alternative strategies. Strengths: - A strong motivation as there is a clear need for further efficiency improvements - Introduces a novel rank-adaptive geometry-aware training method that dynamically updates ranks during training - Proposed to overcome the sensitivity to parameter initialisation and the need for a full-model warm-up phase - Thorough theoretical analysis, including guarantees on loss descent, convergence, and approximation Weaknesses: - Claims do not match the results. The abstract says "our training proposal proves to be optimal in locally approximating the original unfactorized dynamics" and while there are guarantees, they are not proven to be optimal. - Not very clear in many parts. In particular, Section 2.1 is difficult to follow. - Results seem incomplete. For example, figure 1 does not show compression below 60% and for the proposed method is only shown for 93+% in Figure 1C while the other methods are shown for 60-93%. I could not find any reason for this lack of direct comparison and missing data points. - According to the plots, the proposed method outperforms the full representation at 96% compression. This is a very surprising finding that requires an in-depth discussion, which is lacking. - Table 1: The authors say that "TDLRT outperforms the factorization-based and the pruning-based baselines" and bold their method for Alexnet c.r. and Resnet test acc. but according to the same table, baselines actually outperform the proposed method in those metrics. Technical Quality: 2 Clarity: 2 Questions for Authors: - The proposed method appears to outperform the full representation at 96% compression (Figure 1). Can the authors provide an in-depth discussion and analysis of this finding? What factors contribute directly to this performance, and does it align with theoretical expectations? - Can the authors include data points for the proposed method within the full compression range for a direct comparison with other methods? Confidence: 3 Soundness: 2 Presentation: 2 Contribution: 3 Limitations: The paper could benefit from a more detailed discussion on the limitations of the proposed method in different training scenarios and potential strategies to mitigate these limitations. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We wish to thank the reviewer for their feedback. Overall, the reviewer highlights key positive aspects of our work, such as the importance of the topic, the novelty of the approach, and the thorough theoretical analysis. The main weaknesses noted are centered on the need for additional runs and a more detailed discussion of results. We are, however, surprised by the perceived impact of these weaknesses, especially in light of the significant strengths identified. The reviewer mentions that our work is "unclear in many parts" and that "Section 2.1 is hard to follow". However, without further details, it is challenging for us to address these points, particularly since clarity has not been a concern for the other reviewers. In the following, we address all the identified weaknesses (Ws), as we believe several points merit further clarification. We also answer the raised questions (Qs). W1 Thank you for pointing this out. In that sentence of the abstract, our intention was to refer to the optimality of the Dirac-Frenkel variational principle to approximate the dynamics along with the supporting theoretical results of approximation and convergence. However, this statement is not crucial and can be misinterpreted, therefore we will remove it from the abstract. W2 We recognize that certain sections of the paper, particularly Section 2.1, contain technical details that may require a background in Riemannian optimization and dynamical model-order reduction theory. We have made significant efforts to make this section as clear and accessible as possible, but we understand that some concepts may still be difficult to follow. However, a conference paper is not the ideal format for providing an extensive introduction to these topics. We would appreciate further clarification on the specific parts of Section 2.1 or other sections that you found unclear. This will help us address your concerns more effectively and improve the paper's readability. We aim to clarify the main ideas of Section 2.1: - Our goal is to derive a low-rank gradient flow that closely approximates the standard full gradient flow. To achieve this, we project the gradient flow onto the tangent bundle as described in Equation (3), which represents the standard gradient flow of Riemannian optimization. - However, this equation forms a stiff system that is challenging to solve directly with a discretized scheme, necessitating a small learning rate. - By introducing a reparametrization of the weights in Theorem 2.1, we obtain new evolution equations that are well-posed and can be solved with larger learning rates. Despite this improvement, the resulting method remains inefficient as it requires d+1 gradient evaluations. - In Corollary 2.2, we demonstrate that the basis computation can be significantly simplified, leading to Algorithm 1, which requires only 2 gradient evaluations instead of d+1. We point out that we have already attempted to convey this structure and our reasoning at the beginning of Section 2. Please let us know if this explanation clarifies your questions, and if not, which specific parts remain unclear. W3 and Q2 The reason our method is sometimes only shown for large compression values is that one key feature of our method is that the compression rate is somewhat determined by the method itself, rather than being a user-defined input, as with the fixed-rank baselines. Nonetheless, we have adjusted the truncation tolerance to obtain smaller compression rates and have included additional data points in the attached rebuttal PDF file. We emphasize that methods at compression rates below 60\% are generally less relevant, so we have focused on the range of large compression rates to maintain the focus on the relevant range of compressions and highlight the strengths of our method. However, if the reviewer considers it valuable, we can include additional runs for smaller compression rates in the appendix. W4 and Q1 Thank you for your remark. We emphasize that this phenomenon, where networks with a smaller number of parameters outperform their full baselines, is well-documented in the literature, see e.g. [1,2]. One explanation for this behavior is that neural networks are often overparameterized, and parameter reduction or compression can have a regularizing effect enhancing generalization. Note that in our comparisons to the baseline, we use the same hyperparameters for compression methods and the full-rank baseline. With this approach on VGG16 we indeed obtain better accuracy than the baseline. However, given your comments, we decided to see if we could find better hyperparameters. This gives us results where the baseline outperforms compression methods. We decided to add these results since the overall accuracy is improved this way for the baseline and for all the compression methods. [1] The lottery ticket hypothesis: Finding sparse, trainable neural networks, 2018 [2] Snip: Single-shot network pruning based on connection sensitivity, 2018 W5 Thank you for pointing out this oversight. We apologize for the confusion. Upon reviewing Table 1, we realized that an error occurred when bolding the results for AlexNet's compression rate (c.r.) and ResNet's test accuracy. We were updating the table with new competitor results shortly before submission and inadvertently left the bold formatting incorrect. We will correct this in our revised manuscript to accurately reflect the performance of each method. Regarding the specific metrics, it is true that while the TT-factorized method achieves a higher compression rate for AlexNet, its accuracy is lower compared to TDLRT, although it still outperforms other methods significantly. For ResNet18, while the Tucker RGD method achieves a slightly higher accuracy (0.04\%), it does so at the cost of a reduced compression rate. We will ensure that the table accurately represents these findings and provide a more detailed discussion in the text.	Summary: The authors study the training of layer factorization models to reduce the number of parameters in deep neural networks. They propose a geometric-aware rank-adaptive training strategy to avoid requiring prior knowledge of ranks and the sensitivity to the weight initializations. Their theoretical results show convergence and approximation error guarantees for the method. Strengths: The proposed method is quite sensible and is accompanied by good theoretical guarantees. Weaknesses: The empirical evaluation is slightly weak. While the results could convince me it is better than existing methods (as the proposed method is also quite sensible), from the scale of the model used, it is hard to judge whether it could provide good enough performances on larger models, when model compression during training is more needed. Technical Quality: 3 Clarity: 2 Questions for Authors: Is it possible to conduct experiments on larger models or different architectures (like transformers, even a small one can help) to strengthen the empirical evaluation? Confidence: 3 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: Yes, the authors discuss about the limitations. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for their insightful feedback, below we provide our response to the raised weaknesses and questions. Q1 Thank you for your feedback regarding the empirical evaluation. In response to your suggestion, we have conducted several new experiments to strengthen our empirical evaluation. Specifically, we have focused on parameter-efficient fine-tuning using low-rank adapters (LoRA), as suggested by reviewer vGH1. This approach allows us to present additional experimental evidence that complements our previous results. Fine-tuning, rather than compressing a model from scratch during training, enables us to experiment with larger networks while remaining within our time and resource constraints. In particular, we have tested the proposed training model on larger architectures such as DebertaV3 on Glue benchmark and Stable Diffusion (v1.4) dreambooth. In DebertaV3, we applied our method to matrix layers by interpreting matrices as order-2 tensors. For Stable Diffusion we applied our method to tensor layers in the Unet, while standard LoRA convolution works essentially by reshaping the tensor into a matrix. These new experiments provide further validation of our method’s performance and demonstrate its applicability to larger models and diverse architectures. We believe these results strengthen the empirical evaluation and could address your concerns about scalability. \| GLUE test case\| LoRA - rank 8, 1.33M params \| Ours - 0.9 M params \| \|-----------------------\|---------------\|-----------------------------\| \| CoLa (Matt. Corr) \| $0.6759$ \| $0.7065$ \| \| MRPC (acc) \| $0.8971$ \| $0.9052$ \| \| QQP (acc) \| $0.9131$ \| $ 0.9215$ \| \| RTE (acc) \| $0.8535$ \| $0.8713$ \| \| SST2 (acc) \| $0.9484$ \| $0.9594$ \| Stable Diffusion \| loss \| \# trainable parameters ----------------------\|---------------\|---------------------------------- LoRA ($r = 8$) \| $0.260$ \| $5$ M LoRA ($r = 5$) \| $0.269$ \| $3$ M LoRA ($r = 3$) \| $0.274$ \| $1.8$ M ours ($\tau = 0.02$) \| $0.2635$ \| $1.8$ M ours ($\tau = 0.1$) \| $0.272$ \| $1.5$ M --- Rebuttal Comment 1.1: Comment: Thanks for the new experiment results. I am raising my score to 6. --- Reply to Comment 1.1.1: Comment: We thank again the reviewer for the feedback.	Rebuttal 1: Rebuttal: We would like to thank all the reviewers for their insightful feedback. We have considered each comment and have made several improvements as a result. Below, we address and review the key points raised by the reviewers: 1. Empirical evaluation: Most reviewers commented that while our work presents a promising method with strong theoretical guarantees, additional benchmarks would strengthen the empirical evaluation. Reviewer SSBR and Reviewer Rp73 requested experiments with transformer architectures, while Reviewer vGH1 suggested results using LoRA and U-Net. In response, we have conducted new experiments that include fine-tuning results via LoRA adapters on DebertaV3 (up to $\sim$ 1.5M parameters) and Stable Diffusion (up to $\sim$ 5M parameters). The results can be found in tables 1 and 2 in the rebuttal pdf file. These new empirical evaluations show that our proposed approach outperforms the LoRA baseline, demonstrating the effectiveness of our method on a broader range of architectures. We thank the reviewers for their suggestions, which have significantly enhanced the quality and robustness of our work. 2. Clarity and presentation: Reviewers were divided on the clarity of our presentation. While Reviewers TTwz, vGH1, and Rp73 found the paper clearly written and easy to follow, Reviewer jjrQ expressed that the paper was difficult to follow and unclear in parts. To address this, we have done our best to provide explanations addressing specific questions and concerns, aiming to make our presentation more clear without sacrificing the necessary technical rigor. We will do our best to review the manuscript to improve clarity and readability in light of this feedback. Pdf: /pdf/aac5ba06dbefafc839f3e23eff5142094c1ad430.pdf	NeurIPS_2024_submissions_huggingface	2,024	Summary: Reducing the size of neural networks is an important problem for reducing the cost, memory usage, and even inference time. Many works focus on reducing the size after the training phase and use techniques such as sparsification and quantization. This paper, on the other hand, focuses on reducing the size by representing the tensor corresponding to the layers of the network as Tucker decompositions. Perhaps the more important aspect is that the paper considers dynamically changing the Tucker rank while training the model. In other words, the size reduction is simultaneous with training and not after the training is performed. It is argued that due to instability in the gradients, it is required to adopt a geometry-aware training strategy. Essentially, the strategy is to do HOOI based on the gradient of factor matrices. Then, compute a new tensor based on the new factor matrices and update the core tensor based on the gradient of this new tensor. Therefore, for each iteration, two passes are required to update the components: one pass to compute the gradients of factor matrices and one pass to compute the gradient of the core tensor. The paper presents theoretical results about the convergence and reduction of loss. In addition, it presents a sizable empirical study that shows favorable results for the proposed approach. The approach outperforms a variety of factorization and pruning methods in terms test accuracy and compression rate. The paper is generally well-written and provides an appropriate method for a very important problem. I think a relevant paper to discuss is [1], which gives an algorithm to compute the approximately optimal Tucker rank when a size constraint on the size of the Tucker decomposition is given. This could replace the approach based on the tolerance parameter $\tau$ when a hard size constraint is given. It would be interesting to investigate the interaction between that algorithm and the approach presented in this paper. [1] Ghadiri, Mehrdad, Matthew Fahrbach, Gang Fu, and Vahab Mirrokni. "Approximately optimal core shapes for tensor decompositions." In International Conference on Machine Learning, pp. 11237-11254. PMLR, 2023. Strengths: The paper is generally well-written and provides an appropriate method for a very important problem. Weaknesses: - Technical Quality: 4 Clarity: 3 Questions for Authors: The results show that Tucker decomposition works better than CP and tensor-train. Is there any intuition for why this is the case? Do you expect Tucker to be better than any other tensor network, or could decompositions like hierarchical Tucker do better? Hierarchical Tucker could be preferable because of the smaller number of required parameters. Confidence: 4 Soundness: 4 Presentation: 3 Contribution: 3 Limitations: I don't see any direct potential negative societal impact. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for their feedback and appreciation of the work. Below we provide our response to the raised questions. Q1. We appreciate this insightful question. Selecting the appropriate tensor structure a-priori is indeed challenging, as it depends heavily on the specific tensor structures in the neural network and the data used. As shown in Table 1 of our main paper, when using standard direct training of the factors, there is no definitive "winner" among Tucker-factorized, Matrix-factorized, TT-factorized, and CP-factorized approaches across the three test problems. However, when employing our proposed geometry-aware TDRLT scheme for training, we observe notably improved performance. Therefore, we believe that Tucker's superior performance is primarily due to the training method rather than the decomposition choice alone. While extending this training strategy to CP is challenging due to the absence of Riemannian geometry, we believe that further research into extending the proposed geometry-aware training to TT, HT, and other tree tensor network structures would be highly relevant. For what concerns the comment in the "Summary" section, we thank the reviewer for bringing this paper to our attention. We agree that the algorithm presented in [1] offers an interesting alternative approach to consider. In particular, their method is well-suited for scenarios where there is a fixed memory budget, such as training on resource-constrained edge devices. In such cases, the objective shifts from "finding the best accuracy-compression trade-off", which is the focus of our method, to "finding the best-performing Tucker decomposition given memory constraints", where the approach from [1] could be highly beneficial. To explore this aspect further, it would be useful to extend the method in [1], which currently addresses a single Tucker tensor, to an approach that optimizes the shapes of all tensor-valued layers within the neural network given a global network-wise memory constraint. This is an intriguing research direction that could significantly enhance the applicability of tensor decompositions in constrained environments. We will certainly include a discussion of this paper in our revised manuscript, highlighting it as a potential alternative approach to our proposed method. This addition will provide readers with a broader perspective on the available techniques and their respective advantages and limitations. --- Rebuttal Comment 1.1: Title: Reply to authors' rebuttal Comment: Thank you for answering my questions. I read other reviews and the responses and have decided to keep my score at 7. --- Reply to Comment 1.1.1: Comment: We thank again the reviewer for the feedback.	null	null	null	null	null	null
Diffusion PID: Interpreting Diffusion via Partial Information Decomposition	Accept (poster)	Summary: In this paper, the authors propose a novel approach to analyze the uniqueness, redundancy, and synergy terms in text-to-image diffusion models by applying information-theoretic principles to decompose the input text into its elementary components. In particular, the proposed approach can be used to recover gender and ethnicity biases in image generation. Strengths: 1. It is an important and valuable direction to analyze the potential semantic bias in the field of image generation. I think it is also reasonable to invovle information-theoretic principles into the approach. 2. The proposed approach is a good attempt for measuring the gender and ethnicity biases in image generation. 3. Based on the illustration in Figure 1-3, the proposed approach may provide more interpretability for text-to-image diffusion models, which is important to understand and exploit the models. Weaknesses: 1. Are there something wrong in Equation 2? The left parts in those two equations are the same but the right parts are not. 2. The time complexity if necessary for the proposed method Technical Quality: 3 Clarity: 3 Questions for Authors: 1. Please provide more analysis on the efficiency of the proposed approach. 2. Actually, I understand that it is not easy to evaluate the effectiveness and make others convincing with only some case studies in Figure 1-3. It is better to publish the demo, where readers can test the approach by themselves. Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 4 Limitations: N/A Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank you for your valuable feedback and helpful comments. We address your concerns below. > Q1) Clarification on Eq 2: We thank you for mentioning this. Unfortunately, our footer note didn't make it through the submission. Eq 2 is correct, and the second equation is derived from the first using the orthogonality principle, as explained below: $I(X; Y) = \mathbb{E}_{p(x,y)} [\log p(x\|y) - \log p(x)]$ $I(X; Y) = \mathbb{E}_{p(x,y)} [ \frac{1}{2} \int \mathbb{E}\_{p(\epsilon)}[ \\|\\| \epsilon - \hat{\epsilon}\_{\alpha}(x\_{\alpha})\\|\\| ^2 - \ \\| \|\epsilon - \hat{\epsilon}\_\alpha (x\_{\alpha} \| y) \\| \\|^2 ] d\alpha]$ By expanding all the squares and re-arranging we get: $I(X; Y) = \mathbb{E}\_{p(x,y)} \left[ \frac{1}{2} \int \mathbb{E}\_{p(\epsilon)} \left[ \\| \\| \hat{\epsilon}\_\alpha (x\_\alpha) - \hat{\epsilon}\_\alpha (x\_\alpha \| y) \\| \\|^2 \right] d\alpha \right] + 2 \mathbb{E}\_{p(y)} \left[ \frac{1}{2} \int \mathbb{E}\_{p(x\|y), p(\epsilon)} \left[ (\hat{\epsilon}\_\alpha (x\_\alpha) - \hat{\epsilon}\_\alpha (x\_\alpha \| y)) \cdot (\hat{\epsilon}\_\alpha (x\_\alpha \| y) - \epsilon) \right] d\alpha \right]$ Here, $+ 2 \mathbb{E}\_{p(y)} \left[ \frac{1}{2} \int \mathbb{E}\_{p(x\|y), p(\epsilon)} \left[ (\hat{\epsilon}\_\alpha (x\_\alpha) - \hat{\epsilon}\_\alpha (x\_\alpha \| y)) \cdot (\hat{\epsilon}\_\alpha (x\_\alpha \| y) - \epsilon) \right] d\alpha \right] \equiv \ominus$ based on the orthogonality principle [1], which states: $\forall f, \quad \mathbb{E}\_{p(x\|y) p(\epsilon)} \left[ f(x\_\alpha, y) \cdot (\hat{\epsilon}\_\alpha (x\_\alpha \| y) - \epsilon) \right] = 0$ The term $(\hat{\epsilon}\_\alpha (x\_\alpha \| y) - \epsilon)$ represents the error of the MMSE estimator, which is orthogonal to any estimator $f$. Therefore, the second term becomes zero, leading to: $I(X; Y) = \mathbb{E}\_{p(x,y)} \left[ \frac{1}{2} \int \mathbb{E}\_{p(\epsilon)} \left[ \\| \\| \hat{\epsilon}\_\alpha (x\_\alpha) - \hat{\epsilon}\_\alpha (x\_\alpha \| y) \\| \\|^2 \right] d\alpha \right]$ which is the 2nd line in Eq 2. Fig 6: MMSE curves comparing the standard and orthogonal estimators We also provide graphs comparing the MMSE estimate obtained from the original equation form (the first equation in Eq 2) and the simplified form for varying levels of noise/SNR in Fig 6 in the attached PDF. It can be seen that the original form (dotted line) is more unstable with many zigzag patterns. We also see the orthogonal/simplified form (continuous line) enforces better consistency between the MMSE (blue) and conditional MMSE (red). Thus, this simplification works better in practice. > Q3) Time analysis Our primary goal in this work was to help improve the interpretability of diffusion models. Although the time complexity of such methods is not of concern usually given that they are used for interpretability of a model, we understand that this is an important aspect. Methodologically, once we have the generated image from diffusion, our method involves running the diffusion model's UNet for denoising to get the MMSE-based log probability estimates and BERT to obtain the terms' probabilities, as required for PID. Thus, our model's time complexity is proportional to that of the diffusion + BERT model. The exact time would depend on the hyperparameters and the computational resources used. > Q4) Public demo and code release We would like to clarify that we provide code for our method in the supplemental zip, which is visible to the reviewers. This code release will help ensure reproducibility, soundness check and facilitate future research. We are unable to share a hosted model at this current point in time as we need to maintain anonymity as per the guidelines. We will also release the code and models publicly after the end of the anonymity period. We will also add a public demo for easy usage and testing of our pipeline. [1] Steven M. Kay. 1993. Fundamentals of statistical signal processing: estimation theory. Prentice-Hall, Inc., USA. --- Rebuttal Comment 1.1: Comment: Thanks for your responses. I'm glad to improve my score. --- Reply to Comment 1.1.1: Comment: We are incredibly grateful for your generous assessment of our work! Your positive feedback means a great deal to us, and we will be sure to implement the necessary changes in the next revision. Thank you once again for your valuable insights and support.	Summary: Decomposing different types of information (redundant, synergistic, unique) has long been a niche field due to the difficulty of applying these methods in realistic settings. This paper develops a way to dissect these types of fine-grained information measures in a practical way in the realistic setting of text-to-image diffusion models. The authors perform extensive experiments to show that the resulting method can be useful for identifying biases, understanding model errors, probing complex linguistic features, and for model interpretability in general. Strengths: - Well-written motivation and examples - The adaptation of PID to a tractable diffusion model measure looked elegant, and included some nontrivial twists (including accounting for the pointwise measure ambiguities) - Good overview of related work including broader attempts at model interpretability - Extensive experiments explore a wide array of interesting - The provided datasets can be a benefit to future research. - In the cases where you could quantify biases, it was nice to see that you get a large and reliable signal. Weaknesses: - Interpretability research is intrinsically very challenging, as it is hard to verify ground truth and even saying what counts as "interpretable" can be a bit nebulous. Generally the information maps looked intuitive, but in some cases I felt I had to squint a little to see the relationship. - Related to that, there's some uncertainty in your estimator (terms in Eq. 2). It would be nice to understand how noisy / confident the information maps are. - Comparisons can also be difficult - there's no existing method that exactly does what PID does, and this is the first approach to extend PID to high-dimensions. The comparisons with MI/CMI and attention methods like DAAM seemed like a reasonable way to handle this. - In some cases, it was hard to imagine how we could use the results. For instance, consider the homonym failure case identified by synergy. To make use of this in practice, the user would have to know to associate a homonym with a specific context word that should exhibit synergy. This is sort of an exploratory work, but finding more concrete applications would improve impact. Technical Quality: 3 Clarity: 4 Questions for Authors: For PID veterans, Eq. 5 is straightforward. Depending on other reviewers' reactions, it might be necessary to give more context (like the famous diagram that is often associated with it). Your PID was heavily based on Williams and Beer measure (though adapted for the pointwise measure). I'm curious, did you consider other PID formulations besides Beer & Williams? Probably not something that needs to be addressed in the paper since NeurIPS community is not very familiar with these ideas (yet). I haven't studied this paper, but I know other people have thought about how to adapt PID to pointwise measures also: Finn C, Lizier JT. Pointwise Partial Information Decomposition Using the Specificity and Ambiguity Lattices. Minor formatting quibble - log and arg in Eq 1,2 should be formatted as operators, not italics. Confidence: 5 Soundness: 3 Presentation: 4 Contribution: 3 Limitations: This was discussed adequately. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank you for your comprehensive review and thoughtful comments. We also appreciate your comments for explicitly highlighting the difficulties of adapting PID to diffusion and the challenges of working on the interpretability of models. > Q1) Relationship between PID maps and human intuition We thank you for acknowledging and drawing attention to the hurdles in this kind of work. Although we show examples that align with human intuition, we also show examples where it's possible that not every relation matches human intuition, as we are exploring the diffusion model's understanding of the world. We also introduce CPID (Conditional PID) as an extension of PID to better account for the context provided by the rest of the prompt. We refer you to the global response above for further details on CPID and the attached PDF for visuals (Figs 1, 2, 3, 4). > Q2) Estimator's uncertainty We expand further on this query in the global response above and will also add an explanation in the paper's next revision. > Q3) Applications of DiffusionPID The primary goal of our work was to introduce the concept of PID into the rapidly growing generative field in computer vision. We believe this would lay down the groundwork to further the understanding of the internal concepts learned by diffusion. This would produce more concrete ways to evaluate and progress prompt engineering. PID can identify which elements of a prompt provide unique information, allowing for the refinement of prompts to reduce redundancy and enhance synergy. Our method can also help better understand and counter diffusion's attribute binding problems and learned biases such as those demonstrated in our paper. We also believe incorporating PID-based insights into model training could ensure that the model better captures human-like understanding of concepts and thus make it more human-aligned. One way to address the point regarding the requirement of apriori knowledge of which words to run PID on is that several pairs of terms could be sampled automatically from the prompt (with some filtering of pairs such as based on LLM-based semantic distance between the terms) and run through PID. We agree that the practical application of PID requires further work and is something we plan to explore in the future but believe that this work provides the necessary foundation for this direction. > Q4) PID Diagram Thank you for raising this point. We have added a figure (Fig 5) to the attached PDF to give more insight into the concept. > Q5) Williams and Beer and Finn C, Lizier JT's work Yes, as you rightly recognized, one of the major reasons behind building on the Williams and Beer formulation was the pointwise measure. The choice was also based on the observation that the NeurIPS and the AI community previously used this formulation [1]. Furthermore, both works were quite helpful for our paper. We thank you for mentioning the latter and will make sure to cite it in the next revision of the paper. > Q6) Formating and typos Thank you for bringing this to our attention and we will fix this in the next revision of the paper. [1] Yu, S., Wickstrøm, K., Jenssen, R., & Principe, J. C. (2020). Understanding convolutional neural networks with information theory: An initial exploration. IEEE transactions on neural networks and learning systems, 32(1), 435-442. --- Rebuttal Comment 1.1: Title: Response Comment: Thanks, for the detailed response. I read the reviews and rebuttals and maintain my score. --- Rebuttal 2: Comment: We are deeply grateful for the positive assessment you have given to our work! Will make the required changes in the next revision of the paper. Thank you again for your suggestions and comments.	Summary: The paper proposes a new technique called DiffusionPID to explain how diffusion models transform text cues into images through partial information decomposition (PID). This work deconstructs mutual information into redundancy, synergy, and uniqueness to analyze how individual concepts and their interactions shape the generated images. This paper conducts extensive experiments and visualizations to validate its techniques. Strengths: 1. This paper proposes new techniques to explain the influence of multiple concepts and their interactions on diffusion models. 2. This paper is well-written and easy to follow. 3. There are extensive visualizations for many scenarios to interpret the process of diffusion models. This work explains some problems, such as bias and incorrect generation, based on its method, which indicates the direction for improvement. Weaknesses: 1. The experiments primarily focus on the impact of interactions among multiple object concepts on image generation, lacking analysis of more general scenarios, such as the interactions between objects and their attributes. Technical Quality: 3 Clarity: 3 Questions for Authors: 1. Why do you use BERT to measure the p(y)? Does the choice of different encoders significantly impact p(y)? Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: 1. The analysis lacks exploration of more complex text prompt scenarios, such as those involving interactions among more objects and more complex phrases that encompass attributes along with objects. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank you for your thorough review and insightful feedback. We address your suggestions below and also refer to the global response at the top in a few places. > Q1) Analysis on objects and attributes We agree that our work could be further improved by providing additional analysis on the interaction between objects and their attributes. We address this by providing new visuals for these types of interactions in Figs 1 and 2 in the attached PDF along with other experiments (CPID) as detailed in the global response above. We will also include these figures in the next revision of the paper. > Q2) Choice of BERT We would like to point out that BERT was the original language backbone of choice for latent diffusion [1]. They emperically find that BERT can be effectively used to encode semantic information of images in a generation setting. Furthermore, the common methods to compute $p(y)$ involve modeling a distribution of the language's vocabulary in natural language. For this, the only options are: textual databases or language models. Online available databases (ex. Wikipedia:Word frequency, Google Books Ngram Viewer, Corpus of Contemporary American English, etc.), can only be used to obtain the independent probability of each term based on frequency statistics but it remains difficult to obtain an accurate conditional distribution. Moreover, to calculate this over large corpuses online would be computationally very expensive. That's why we used a language model instead. BERT has been the standard language model used in natural language research since its conception due to its excellent performance on various language-based tasks and its accurate model of the vocabulary distribution in both, conditioned and unconditioned cases. We did not feel the need to use LLMs as the context window here is fairly small given that we operate on prompts of moderate length. Thus, this choice does not significantly impact $p(y)$. [1] Robin Rombach, Andreas Blattmann, Dominik Lorenz, Patrick Esser, and Björn Ommer. Highresolution image synthesis with latent diffusion models. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 10684–10695, 2022. --- Rebuttal Comment 1.1: Title: Thanks for your response. Comment: Thanks for the detailed response, I'm glad to keep my positive rating. --- Reply to Comment 1.1.1: Comment: We truly appreciate your positive evaluation of our work! We will make the necessary adjustments in the next revision of the paper. Thank you once again for your insightful feedback.	Summary: Summary: The paper adapt the concept of the Partial Information Decomposition into the diffusion model and analyze the uniqueness, redundancy and synergy terms in the diffusion model and do experiments on the Bias, Homonyms and Synonyms Contribution: The paper adapt the concept of the Partial Information Decomposition into the diffusion model and out-perform other method s in visual perspective and explain the bias homonym and synonyms in the text token perspective by using the PID Strengths: Strength: (i) Clarity: The paper is easy to understand. (ii) Originality and Significance: The paper is the first one to adapt the concept of the PID into diffusion model and consider the influence of more than one token on the generated images. It also help explained the Bias, Homonyms and Synonyms problem in the diffusion model compared to other current methods. Weaknesses: Weaknesses: (i) The paper's novelty is limited. The paper does not go beyond the concept of PID but simply adapt the PID concept to the diffusion model. Maybe extend to more than two tokens. (ii) The text conditions is simple. Try the text conditions that more similar to the distribution of the training data. (iii) The uniqueness figures in the 6.5.1 is not very convincing to me and not show very clear information. Technical Quality: 2 Clarity: 3 Questions for Authors: (i) I think the text condition that you choose to present can be more complicated which may present more issue when the user's prompt are complicated. (ii) Why some of the uniqueness figures in the 6.5.1 Homonyms sections show meaningless information? How is the uniqueness different from other single token method? Is it more convincing? Confidence: 5 Soundness: 2 Presentation: 3 Contribution: 4 Limitations: Yes Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank you for your detailed review and thoughtful comments. We address your concerns below and will refer to the general response at the top for certain points. > Q1) Novelty of our method and more complex use cases such as an extension to the multi-concept scenario 1. Our approach is the first to adapt PID for diffusion models by developing the required mathematical formulations. We derive a mathematically sound pixel-level PID breakdown in a form that is compatible with and could be integrated into diffusion. Furthermore, we leverage our method to conduct a detailed study of diffusion and to identify its various failure modes, which significantly advances our understanding of different concepts and their interactions in the diffusion model. 2. Building upon the original concept of PID, we also introduce Conditional PID (CPID) for diffusion models to expand the scope and contributions of this work and provide more details in the global response above (Figs 1, 2, 3, 4 in the attached PDF). This also helps address the suggestion on expanding to more terms as CPID takes the rest of the prompt into consideration. We observed that CPID yields superior localized results compared to its PID counterpart in practice as it takes into account the rest of the prompt as context during the image generation process, allowing it to better capture the specific contributions of the two tokens being analyzed. We will include the results in the next revision of the paper as well. 3. Computing the PID and even MI (Mutual Information) between three or more input variables in information theory is a complex process. There is no universally accepted method for defining and calculating the terms of Uniqueness, Redundacy and Synergy. While works such as [1] provide a method to compute the global Redundancy between all input variables, Uniqueness and Synergy remain difficult terms to tackle as these computations need to take all the variables subsets' interactions into consideration. It is generally agreed [1, 2] that multivariate information decomposition is more involved than the bivariate case because it is not immediately obvious how many atoms of information one needs to consider, nor is it clear how these atoms should relate to each other. Even the breakdown provided in [2] for the four-variable case is highly complicated and it is a non-trivial problem to extend these concepts from information theory to more variables. 4. The primary objective of the analysis conducted in the main text was to learn more about the text-to-image diffusion model's understanding of different concepts, which may or may not align with human understanding, and to derive an analysis for specific prompt types. We agree that the examples used in the paper are relatively simple, but they can still shed light on the various interactions and shortcomings of the diffusion model in an easily interpretable form. To address the need for more complex prompts, we provide results on longer prompts with more entities, similar to those used in the diffusion training data, in Figs 1 and 2 in the attached PDF and provide more details on the new experiments in the global response above. We will include the new figures in the next revision of the paper as well. > Q2) Clarification on uniqueness figure 6.5.1 and distinction from single-concept methods The uniqueness information maps in Fig 6.5.1 tries to show what information that term uniquely contributes on its own to the image generation process. Single-concept methods like DAAM, MI, and CMI highlight the overall information a concept contributes which is a combination of Synergy, Redundancy and Uniqueness. We clarify this in Eq 5 in the main text. It is possible that something can have little Uniqueness, i.e., contributes very little unique information on its own given the rest of the prompt or even just another concept as sufficient context, but still have a contribution through Synergy and/or Redundancy. For instance, in the "calf" vs "field" example, the concept "calf" when interpreted as the calf of an animal, is enough to make the model generate a field. Thus, the "field" concept does not contribute much unique information on its own but it does provide synergistic information in combination with "calf" that helps the model interpret the meaning of "calf" as the animal and not the muscle, which is why we see a high Synergy. As long as there is some other term instead of "field" that can provide the required context to make the diffusion interpret the "calf" as the animal, then removing "field" would still generate the grass field in the image. Similar arguments can be made for the rest of the examples as well. Also, our approach does not change depending on the order of the concepts being processed by DiffusionPID. We will update the figure captions in an upcoming revision to clarify this point. We thank you for bringing this to our attention. [1] Conor Finn and Joseph T. Lizier. Pointwise information decomposition using the specificity and ambiguity lattices. ArXiv, abs/1801.09010, 2017. [2] Paul L. Williams and Randall D. Beer. Nonnegative decomposition of multivariate information, 2010. --- Rebuttal Comment 1.1: Comment: Thanks for addressing my concerns, I decided to maintain my score for now. --- Reply to Comment 1.1.1: Comment: We sincerely appreciate your positive feedback on our work! We will incorporate the necessary changes in the next revision of the paper. Thank you so much for your valuable suggestions and comments.	Rebuttal 1: Rebuttal: We thank all the reviewers for taking the time to go through our work in detail and providing insightful reviews. We found the feedback very constructive and helpful. We are glad that the reviewers unanimously agree that the proposed information-theoretic approach to interpret diffusion models is a novel and promising direction. We are further glad that reviewers found our experiments to be extensive (Tpva, hzC5), consider this work impactful for identifying the shortcomings of diffusion models (vbX2, Tpva, hzC5, THqw), and deemed our paper to be well-written (vbX2, Tpva, hzC5). Some reviewers (vbX2, Tpva) pointed out a shortage of sufficiently complex examples that explore the application of PID in more challenging scenarios and to study relationships between more diverse lexical entities. We agree, and address this by providing three sets of visuals in the attached PDF: 1. Figs 1, 2: Visuals for more complex prompts taken from [1] similar to those in the diffusion training distribution. These prompts usually mention several objects and their corresponding attributes. We find that our method remains effective and informative even in these challenging examples. We visualize the information maps between objects and attribute-defining terms as per Tpva's suggestion. In both cases, we observe a high synergy because the attribute modifies the object's visual properties in some form. 2. Figs 1, 2, 3, 4: Visuals for CPID (Conditional PID). In this case, we extend the concept of PID for the conditional case where all the PID components and probability terms are now conditioned on the rest of the prompt. This is similar to the CMI extension of MI in [2]. We rewrite the equations from the main text with the required changes below for easy reference (we follow the same notations and definitions with an additional variable of $y$ signifying the rest of the prompt with the terms $y_1$ and $y_2$ removed): \begin{align} i(y_1, y_2; x \| y) &= r(y_1, y_2; x \| y) + u(y_1 \backslash y_2; x \| y) + u(y_2 \backslash y_1; x \| y) + s(y_1, y_2; x \| y) \\ \end{align} \begin{align} r(y_1, y_2; x \| y) &= \min_{y_i} [-log\ p(y_i \| y)] - \min_{y_i} [-log\ p(x\|y_i, y) + log\ p(x \| y) - log\ p(y_i \| y)] \\ \end{align} \begin{align} u(y_1 \backslash y_2; x \| y) &= i(y_1; x \| y) - r(y_1, y_2; x \| y) \\ \end{align} \begin{align} s(y_1, y_2; x \| y) &= i(y_1, y_2; x \| y) - r(y_1, y_2; x \| y) - u(y_1 \backslash y_2; x \| y) - u(y_2 \backslash y_1; x \| y) \end{align} We found that CPID provides slightly better localized results than its PID counterpart in practice as can be seen in Figs 1 and 2. This is expected as CPID accounts for the contribution of the rest of the prompt as the context in the image generation process and better captures the specific contribution of the two terms under consideration. Some reviewers (hzC5, THqw) also requested further clarification of Eq 2 from the main text. To address THqw's query, we provide the derivation of the simplification done based on the orthogonality principle in the response to THqw. To further expand on the estimator's uncertainty as mentioned by hzC5: 1. There is no guarantee that the estimator provides an upper or lower bound for the PID terms. It is dependent on the conditional and unconditional denoising MMSEs obtained from the diffusion model which is assumed to be an optimal denoiser for our experiments. However, in practice, this assumption need not hold because a neural network trained on a regression problem to minimize MSE need not converge to the global minima and instead may converge to a local minima. That being said, neural networks have been found to do really well on regression problems and the diffusion model, specifically, has been found to perform well on the denoising problem. Thus, we expect reasonable estimates despite the inherent uncertainty. 2. A measure of uncertainty is also introduced based on the number of samples under the same noise level, $\alpha$, in Eq 2's expectation term and from the number of $\alpha$ values sampled to evaluate the integral in the equation. Thus, we can obtain more confident information maps by using higher values for both of these hyperparameters. We provide visuals of the information maps for varying values of these hyperparameters on the "cat and elephant" sample from the COCO co-hyponym experiment (Fig 5 in the main text) in Fig 7 in the attached PDF. We observe that the maps depict the same information, i.e., they are highly activated in the same regions, across variations but do become less noisy at higher values. We provide a figure, Fig 5, in the attached PDF to complement our explanation of PID as defined in Eq 5 as per hzC5's suggestion [1] Stablesemantics: A synthetic language-vision dataset of semantic representations in naturalistic images. 2024. [2] Xianghao Kong, Ollie Liu, Han Li, Dani Yogatama, and Greg Ver Steeg. Interpretable diffusion via information decomposition. arXiv preprint arXiv:2310.07972, 2023. Pdf: /pdf/1f55de3615f9f2506255b21228d342312d9eeca0.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Hamiltonian Monte Carlo on ReLU Neural Networks is Inefficient	Accept (poster)	Summary: The authors analyze the application of Hamiltonian Monte Carlo (HMC) to Bayesian neural networks (BNNs) with ReLU activation functions. They theoretically show that despite its piecewise linear structure, HMC still provides correct results, but that it accumulates an error due to this non-differentiability that renders it less efficient than HMC applied to a BNN with, e.g., a sigmoid activation function. Strengths: The paper is overall well-written with a clear storyline. The authors provide a thorough analysis that consists of a variety of theoretical results (correctness results, bounds, optimal acceptance rate), for the evaluated setting of applying HMC to BNNs with ReLU activation functions. As I am not too familiar with the HMC-based literature, I cannot properly judge originality and significance. Weaknesses: - The term "inefficient". To me, it remains somewhat unclear what is meant by the expression. The results, theoretically and empirically, seem to show that HMC + ReLU is _less sample efficient_ than HMC + sigmoid. From this relative inefficiency, the discussion always switches to _absolute inefficiency_ statements. Below which value is a sampling rate defined to be inefficient? This is just subjective, but for my reading "inefficient" conjures up similarities to infeasible, or unusable, while in practice HMC and especially its stochastic counterpart SG-HMC are frequently used (Chen et al., 2014; Izmailov, 2021). On the contrary, a sigmoid-based NN would be considered inefficient for most practical applications from a performance viewpoint, even if it had greater sampling acceptance rates. - While the empirical evaluation is extensive it is limited to a single (toy) data set. Repeating this evaluation on several examples would greatly strengthen this part. - The empirical analysis relies entirely on sigmoid, ReLU, and LeakyReLU. The latter two performed essentially identically so that one piecewise linear activation function would have seemed to be sufficient. Sigmoid and ReLU in turn differ not only in their differentiability at $x=0$, but also in their qualitative behavior, the former being bounded between zero and one, the latter having no upper bound. An empirical analysis that compared ReLUs against similar activation functions, e.g., Swish (Ramachandran et al., 2017) with the same results would be a lot more convincing. ------ Chen et al., Stochastic Gradient Hamiltonian Monte Carlo, 2014 Izmailov et al., What are Bayesian Neural Network Posteriors Really Like?, 2021 Ramachandran et al., Searching for Activation Functions, 2017 Technical Quality: 3 Clarity: 3 Questions for Authors: See the weakness section. Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: The authors adequately discuss limitations within the paper. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your thoughtful comments. We have addressed your comments and questions as follows. 1. Additional experiments: We now added additional experiments on a larger real-world dataset, for which the results are presented in the general rebuttal and its attached PDF file above. 2. The term "inefficient": Thank you for your comments, and you indeed raised a good point. Our manuscript was written from the statistical perspective of a machine learning problem, and while the usage of terminologies such as “efficient” and “efficiency” are well-accepted in the statistical contexts, their implication in a computational field may be a bit too strong. We will clarify in the revised manuscript that (1) efficiency in this context is statistical efficiency and unrelated to either computational capacities or accuracy performances, and that (2) by “inefficient”, we mean a significant drop from the optimal efficiency, rather than being completely unusable. 3. Swish activations and (Izmailov et al. 2021): We would like to thank you for the reference (Izmailov et al. 2021), which uses Swish activations instead of ReLUs to ensure smoothness of the posterior density surface and found using a smooth activation improves acceptance rates of HMC proposals without hurting the overall performance. We will include a discussion of the reference in the revision. --- Rebuttal Comment 1.1: Comment: Thank you for the clarification on _efficiency_ and the additional experiment.	Summary: This paper addressed the inefficiency of HMC in practices applied to ReLU-based neural networks, where the local error rate of HMC will be large due to the non-differentiable activation functions in ReLU. The efficiency used here to compare is a function of the acceptance rate and the step size of HMC. Strengths: This paper is well-written and really easy to follow. I love how it is constructed, which is precise and clear. This paper points out the potential large local error that may occurred in HMC in practice that many people will ignore since it is so easy and efficient to apply. Weaknesses: The theoretical results do not take a huge step from the existing results of error estimation on HMC. Technical Quality: 4 Clarity: 4 Questions for Authors: Functions with Lipschitz continuous is widely been considered and applied when itself is not differentiable. Have the functions with Lipschitz continuous been considered? That could be a good case, where the error could be narrowed down. Confidence: 4 Soundness: 4 Presentation: 4 Contribution: 2 Limitations: Only a small Gaussian toy problem on one hidden layer neural network has been considered, it would be definitely worth seeing how the efficiency and acceptance rate perform at high-dimensional neural networks with large datasets, like MNIST. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We are glad that you enjoy the work. We have addressed your comments and questions as follows. 1. Additional experiments: We now added additional experiments on a larger real-world dataset, for which the results are presented in the general rebuttal and its attached PDF file above. 2. Lipschitz continuous functions: In our work, we only consider the case where the activation (being Lipschitz continuous, such as ReLU and leaky ReLU) has only one point of non-differentiability. In principles, our results should be generalizable to the cases when the function has a finite number of points of non-differentiability. Although an error of order $\Omega(\epsilon)$ is already very bad and we believe that similar estimates should hold for a general Lipschitz continuous activation, we are not sure exactly how to extend the results rigorously to these cases. This could be a subject of future work; thanks again for your suggestion! --- Rebuttal 2: Title: Response for rebuttal Comment: I thank the authors for their rebuttal. The additional experiments and the explanation for my theory-related question are addressed. Overall, I will keep my score.	Summary: The efficiency of the Hamiltonian Monte Carlo (HMC) method directly depends on acceptance rate of proposals, while it samples weights of neural network architectures. Nonetheless, the presence of ReLU activation function in the architecture might lead to high rejection rate during the sampling due to the jumps of Leapfrog integrator scheme between different non-differentiable parts of loss landscape. The authors prove that HMC is an inefficient algorithm for sampling neural architectures and analyze its error rate, demonstrating the difficult possibility of Hamiltonian’s controlling. The authors verify theoretical results through synthetic examples, demonstrating high rejection rate networks with ReLU activations compared to sigmoid activations. Strengths: - The method’s findings allow to pay attention of the ML community to inefficiency of HMC for sampling architectures with ReLU activation that was not mentioned before nowhere. Weaknesses: - The authors evaluate their theoretical findings with synthetic datasets that contain 100 data points. However, it seems that such experiment does not perfectly reflect practical significance of the observation. There is no verifying that demonstrated effect presences in experiments with data that has more dimensionality. Undoubtedly, it is great that the authors studied the acceptance rate's dependence on number of parameters, but the authors should check the obtained observations on high-dimensional tasks such as MNIST dataset. - Unfortunately, the presentation of the paper seems weak because there is no mentions about loss landscape of neural networks, although this topic is related to the paper. Also, the motivation and storyline of the paper are not clear because the studied problem is not understandable. Finally, it seems that "Efficiency of HMC" is excess subsection of the second section, because the majority of the block not encounters more through the paper. - The proof of the main Theorem 3 is a famous fact from [1] and it seems that is not a new theoretical result. [1] - “MCMC using Hamiltonian dynamics”, Neal et al., 2012 Technical Quality: 3 Clarity: 2 Questions for Authors: - In the appendix, the authors mention that the experiment’s time is 5 days on a single CPU machine. Which is a main motivation to use single GPU during 5 days? It seems that is sufficiently long. - Am I write that the main reason of low acceptance rate of HMC for sampling architectures with ReLU is non-smoothness of loss surface? - Could you demonstrate acceptance rate of HMC on more high-dimensional experiments such as MNIST or CIFAR-10? Also, one would like to see the robustness' demonstration of obtained networks. Confidence: 3 Soundness: 3 Presentation: 2 Contribution: 2 Limitations: The authors demonstrates application of their theoretical findings on low-dimensional experiments. Nonetheless, there is no guarantees that studied fact is true on more high-dimensional experiments. Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We really appreciate your comments on the manuscript, and have addressed your comments and questions as follows. 1. Additional experiments: We have now added an additional experiment on a larger real-world dataset, for which the results are presented in the general rebuttal and its attached pdf file above. We want to thank you again for your suggestions. 2. About the theorems: We want to clarify that the paper “MCMC using Hamiltonian dynamics”, (Neal et al., 2012) is only concerned about smooth potential functions. That means all of the results in their work do not hold if the log-likelihood is not a smooth function. Our manuscript considers ReLU networks, for which this fundamental assumption does not hold, and thus all theoretical results presented in our work are new. We would like to ask for more details about your concerns on this part so that we can explain the ideas better. 3. Using a single CPU machine: This is just because of the limited computational resources on our part. 4. Loss landscape and smoothness of the potential functions: You are correct that the low acceptance rate of HMC for sampling architectures with ReLU is due to the non-smoothness of the loss surface. In this work, we consider a very well-behaved network with the only singularity appearing due to the non-differentiability of ReLU (for the sigmoid counterpart, the log-likelihood is smooth) and highlight that even in that case, HMC with ReLU is sub-optimal. Our main focus is on the local geometry (smoothness) of the loss rather than the global loss landscape, but we will add more discussions/references of the possible effects of irregular loss landscape on sampling. 5. The section "Efficiency of HMC”: We note that this section describes the background information for the later theoretical analyses, including the definition of efficiency and the classical results for smooth distributions. One of our main results (Proposition 3.5) is built upon this formulation and in contrast/complements the classical results presented in this section. We will make sure to highlight the importance of this part in the revision of the manuscript. --- Rebuttal Comment 1.1: Title: Response Comment: 1. Additional experiments I am exceedingly grateful for your new experiment on a real-world dataset. In accordance with the attached pdf file, there is the difference in fourth order of efficiency between sigmoid and Leaky ReLU (ReLU) activation function, could you explain significance of such difference? It is really great that you compute the acceptance rate of the HMC procedure, but what is the accuracy of sampled networks by HMC on the regression task? For example, the authors of the paper [1] sampled networks by MCMC procedure and calculated the corresponding accuracy on the CIFAR-10 dataset for the classification task. Could you do something like this? 2. About the theorems Thanks a lot for this clarification. However, the function $\phi$ is smooth in the theorem; why do you assume that this function is smooth? Since this theorem is the key moment of your paper, I am inclined to believe that you should provide an intuitive understanding of this fact with potentials and clearly explain the difference between the same facts in Neal's paper. 3. Using a single CPU machine I understand your situation; however, it is sufficiently difficult to estimate the workability of the proposed method. I am inclined to believe that you should train your method with a single GPU A100 and measure the time of training. 4. Loss landscape and smoothness of the potential functions Thanks a lot for your response. However, could you clearly explain which loss function you consider local geometry? If I am not mistaken, you say that there are two loss functions: loss and global loss. What is the first and what is the difference, please? Undoubtedly, I understand that explanation of your paper is sufficiently difficult because it includes such areas as loss landscapes, MCMC methods, Bayesian inference and analysis of activation functions. However, I think that you should provide comfortable introduction to the problem statement, understandable description of the aforementioned areas with their connection to your research and qualitative high-dimensional experiments. [1] "What Are Bayesian Neural Network Posteriors Really Like?", Izmailov et al, 2021 --- Rebuttal 2: Comment: Thanks for your follow-up questions. We would like to answer them below. 1. Additional experiments There are two (related) ways to interpret the difference in fourth order of efficiency between sigmoid and Leaky ReLU. The most straightforward way is if we tune HMC to a target acceptance probability, say 80\%, then the step size $\epsilon$ for ReLU would need to be smaller by that of sigmoid by a factor of 4. This means the sigmoid network can explore the parameter space several times better while maintaining the same acceptance rate. Alternatively, as explained in Section 2 of our paper, efficiency is inversely proportional to the expected computational cost until the first accepted proposal is stationary. This means if you keep $\epsilon$ the same for both networks and keep making proposals until your particle gets to move, then ReLU would take 4 times longer on average (since this is a stochastic process with geometric distribution). Regarding the accuracy, since our work and experiment considered a regression task instead of a classification task, the more appropriate measure of "accuracy" should be the mean squared error (MSE), which we already reported in the rebuttal PDF file (see the last two columns of Table 1). 2. About the theorems The setting of Neal’s paper only applies to smooth potential energy functions $U$ (infinitely differentiable with differentiation defined in the classical sense). This means Neal’s framework does not apply directly to ReLU, since ReLU does not have even the first derivative in the classical sense. Theorem 3.1 is a revisit of the approach of Neal with a relaxation: we do not follow the classical definition of derivatives, but other notions of well-defined derivatives. We specifically have automatic differentiation through back-propagation (which is used by neural networks) in mind, but the theorem is written in general notions of computational procedure for derivatives, as long as they satisfy the chain rules. We want to clarify that Theorem 3.1 and its proof are still valid if the statement "for all smooth functions $\phi$" is replaced by the phrase "for all functions $\phi$ with well-defined first derivatives". The reason why we chose the conditions on smooth $\phi$ is due to mathematical conventional: chain rules are often defined through a composition with smooth functions (such as $\phi$ in this case, which is analogous to the test function in the definition of weak derivative). From your note, we will revise the statement to "for all functions $\phi$ with well-defined first derivatives" to improve readability. We want to further clarify that this part is not the only contrast of our work with Neal. The rest of our paper asks the same theoretical questions as Neal’s paper (optimal dimension scaling, optimal acceptance probability, guideline for tuning HMC) where we obtained different results, precisely because of this difference in smoothness assumption of $U$. 3. Using a single CPU machine Our paper does not propose any new method that is different from standard HMC sampling. The only implication of our theoretical results on the sampling procedure is to set the step size $\epsilon$ of the sampler to the order of $d^{-1/2}$ (Proposition 3.5), which would not change the running time of the sampling algorithm. Thus, running the algorithm on a GPU will be faster than running on a CPU, but adjusting the step size would not affect the running time of the algorithm on any device. 4. Loss landscape and smoothness of the potential functions We think this may be a misunderstanding: when we say global loss landscape, it does not refer to "global loss", but "global landscape". There is only one loss function, but several geometric properties related to it. Local geometry usually refers to geometric behavior in a local neighborhood of a point on the loss function (e.g., smoothness, qualitative properties such as saddle points or minimum, Hessian of the loss function at that point). Global geometry refers to the general landscape of the loss, such as how many modes (local optima) the function has, Oliver curvature, whether some plateaus or valleys separate the modes, as well as the flatness of the plateaus and steepness of the valleys. What you refer to as loss landscape is about global geometry, and usually appears in quantification of the mixing time of HMC and is also of interest in theoretical analyses of HMC, see for examples [1] and the references therein. However, it has nothing to do with the analysis of efficiency and acceptance probability in our paper, which depends only on smoothness (a local property) as we showed in our work. That's why we stated in the rebuttal that this is a relevant topic that is worth discussing but is not directly related to the technical part of our paper. [1] Seiler et al. Positive curvature and Hamiltonian Monte Carlo. NIPS 2014.	Summary: This paper analyzes the error rates of the Hamiltonian Monte Carlo algorithm with leapfrog integrator on ReLU NN. This paper shows that crossing a surface of non-differentiability will cause a local error rate of $\Omega (\epsilon )$. Simulations validate the theoretical analysis. Strengths: 1. The paper introduces novel ideas in the realm of HMC, an important MCMC method. 2. The statement and proofs of the lemmas/theorems are rigorous. Weaknesses: The experiments seem weak in this work. Since this is a submission for machine learning, I would expect the authors demonstrate the problem at least on at least one real-world machine learning applications. Pure simulations without real-world data or models are not convincing enough. Technical Quality: 2 Clarity: 2 Questions for Authors: See Weakness above. Confidence: 2 Soundness: 2 Presentation: 2 Contribution: 2 Limitations: N/A Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your comments. We have addressed your comments regarding additional experiment on a larger real-world dataset. Please see the general rebuttal and its attached PDF file for more details. The new results also confirm the findings of the manuscript. Please let us know if you have further questions about the experiment. --- Rebuttal Comment 1.1: Title: Response Comment: Thank you for your new experiment on a real-world dataset. I really appreciate the analysis.	Rebuttal 1: Rebuttal: We thank all reviewers for their helpful comments on the manuscript. We are delighted with the general positive sentiments among the reviewers about the novelty, significance, soundness, as well as representation of the work, especially on its theoretical contributions. Based on the reviewers’ suggestions, we have taken some steps to strengthen the manuscript as follows. 1. Additional experiment on real-world dataset and reports on accuracy: Since our work focuses on the regression framework, instead of MNIST as suggested by the reviewers, we added an additional experiment on a subset of the real-world UTKFace dataset [1], where we need to predict the age of a person from the image of their face. We keep the settings as in the second experiment of our paper, except that we fix $T = 0.01$ and vary $\epsilon \in \\{ 0.00005, 0.00010, \ldots, 0.00040 \\}$ to plot the efficiency curves of various networks. The obtained results (see Figure 1 in the attached PDF) are similar to those of the toy dataset on efficiency: the sigmoid network is more efficient than the ReLU and Leaky ReLU networks, represented by higher efficiency curves and optimal acceptance rate. From Reviewer mLYv’s suggestions, we also report the MSE (instead of accuracy) of samplers in this UTKFace experiment (see Table 1 in the attached PDF). The results show that: (1) without tuning the step size by efficiency, the sigmoid network attains better MSE than their ReLU counterparts, and (2) when the step size is chosen via efficiency (i.e., by optimal acceptance rate), the MSEs of all three activation functions are very similar to each other. 2. Efficiency: Reviewers mLYv and v6yY have comments about the definition and the contextual meaning of our measure of efficiency. We have responded to those comments in detail separately. Essentially, we clarify both theoretical definitions and practical computations of the efficiency of a Markov chain used in the manuscript, as well as a more detailed description of how the theoretical high-dimensional limit of the efficiency functions can be obtained. Given the specific conventional meaning of “efficiency” in computations, we will add further clarifications that efficiency in this context refers to statistical efficiency and is unrelated to either computational capacity or accuracy. On the other hand, we want to clarify that the usage of terminology and the definition of efficiency is well-established in the field of MCMC [2] and this is not a forceful definition on our part. Again, we are thankful for the comments and hope our revision addresses the reviewers’ concerns. References: [1] Zhang et al. Age progression/regression by conditional adversarial autoencoder. CVPR 2017. [2] Beskos et al. Optimal tuning of the hybrid Monte Carlo algorithm. Bernoulli 2013. Pdf: /pdf/a5a251f8b9bb5b78629eac579d6e9209b2673af8.pdf	NeurIPS_2024_submissions_huggingface	2,024	Summary: The paper analyses the HMC algorithm with the leapfrog integrator for Bayesian neural networks with different non-linearities. In particular, the paper focuses on ReLU non-linearities and how they cause HMC to be inefficient compared to networks with smooth non-linearities. The authors derive an upper bound on the error of the leapfrog integrator for ReLU-based networks, and come up with a corresponding new guideline for tuning HMC, using a step size of scale $d^{-1/2}$, with acceptance probability of 0.45. The paper demonstrates this theory with a series of experiments on small-sized Bayesian neural networks. Strengths: * The motivation of this work is clear. It has been known for a while that many of the architectural choices made for neural networks might not be suitable for Bayesian inference and therefore developing theory behind why ReLUs might not be suitable for HMC inference seems like a well-motivated research question. * The structure of the theory seems to make sense. The paper first shows that it is in fact valid to perform HMC over neural networks, even when the non-linearities have non-differentiable parts. Then the paper shows the error analysis, leading to the lower bound on the asymptotic error. Weaknesses: * The paper keeps switching between Big O and Big Omega notation and it is not clear why. This adds confusion to the proofs, and makes it hard to understand whether the error is an upper or lower bound on the error. * The paper does not provide enough details to the reader about how the efficiency is calculated on the y-axis in Figure 2. It seems to be only partially defined at the end of Section 2, with the introduction of an unknown constant. Since the efficiency is a key metric of the paper, it would be helpful to understand exactly how it is calculated. (No code is provided with the paper submission to look at.) * At no point in the paper is the accuracy/log-likelihood mentioned in any of the experiments. Ultimately, when performing HMC, it seems this is what we generally care about in terms of ensuring the sampler has sufficiently mixed, and when we want to use the samples in practice. Therefore, it seems like a key weakness that all the results are focused on acceptance rate, and efficiency of the sampler, when in practice one might take an inefficient high performing sampler compared to an efficient but poor performing sampler (in terms of test log-likelihood). One question to ask is whether it is worth using a ReLU model compared to a sigmoid model when you have limited compute. For example, ReLU may perform better but take too long to converge compared to a sigmoid model, however this is not shown. * While the paper is more focused on theory, the experiments section could be strengthened by including slightly larger experiments. For example, running on the MNIST dataset would be an addition to the toy sinusoidal dataset. This would also enable the authors to ensure that the results that they are achieving are comparable to existing works. The toy dataset is useful for demonstrating theory to a certain extent, but using a well-explored dataset provides better context within the general literature. Technical Quality: 2 Clarity: 3 Questions for Authors: * For the analysis of local errors (equation), what step takes place in replacing $p_0$ to $p_{1/2}$ between the penultimate and last lines? * Following on from the above section, how did the authors define efficiency for the experiments? * Did either accuracy or log-likelihood performance get used when performing the simulations of the Bayesian neural networks? For example did the authors collect test log-likelihood performance for Table 1? It would be useful to include those results. Confidence: 3 Soundness: 2 Presentation: 3 Contribution: 2 Limitations: Limitations are adequately addressed. Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your thoughtful responses. We have addressed your comments and questions as follows. 1. Additional experiment and reports on accuracy: We have added an additional experiment on a larger real-world regression dataset and included reports on MSEs as requested by the reviewer (see the general rebuttal above for more details). In summary, the new results are similar to those of the toy dataset on efficiency and show that: (1) without tuning the step size by efficiency, the sigmoid network attains better MSE than their ReLU counterparts, and (2) when the step size is chosen via efficiency (i.e., by optimal acceptance rate, as often done in practice), the MSEs of all three activation functions are very similar to each other. We also want to clarify that from a Bayesian perspective, the mixing of a Markov chain is not just about reaching a mode of a distribution, but also about the ability to leave a mode and explore the whole sample space according to their respective weight. Thus, in general, accuracy is a diagnostic tool rather than a good measure of mixing: a random walk initialized at the maximum a posteriori (MAP) estimate that gets stuck at a mode will have higher accuracy than any well-designed MCMC algorithm but is surely not mixing. The practical guidelines for tuning MCMC for mixing are often about increasing the traveled distance (via step size) while maintaining the acceptance rate (corresponding to high effective sample size), leading to our definition of efficiency. 2. Efficiency: As discussed in Section 2 of the manuscript, the efficiency of HMC is computed as the product of the traveled distance and the expected acceptance probability of an HMC proposal (Line 146 in the manuscript). Empirically, the expected acceptance probability can be approximated quite straightforwardly via the ergodicity of the Markov chain by the empirical average acceptance rate, and that was how we computed efficiency in the experiments. Thus, both the theoretical definition and practical computations of the efficiency of a Markov chain are straightforward. The efficiency curves in Figure 2 (which are theoretical quantities) are computed by replacing the unknown constant $\Sigma$ in the expression of $a(l)$ in Line 149 by 1, and then just plotting $l.a(l)$ as a function of $a(l)$, i.e., the efficiency is computed as $l\Phi(-l^2/2)$ where $\Phi$ is the c.d.f. of the standard normal distribution. The theoretical support for this expression follows a few steps: (1) we use classical convergence results to show that in the high-dimensional limit, the efficiency converges to the right-hand side of the equation in Line 149; (2) we can prove that it is okay to replace the unknown constant $\Sigma$ by 1, and (3) we plot the function $x.a(x)$ and investigate its optimum. These are classical approaches in the literature (Beskos et al., 2013). A more detailed description of the technique was also provided in Appendix A.5 of our paper. We will carefully describe those definitions and computational procedures above in the revision of the manuscript. 3. Big O and Big Omega notations:* We want to reaffirm that our main bounds are lower bounds in the spirit of Taylor expansions, i.e., $\Delta H = \Omega(\epsilon) + O(\epsilon^2)$. As in typical Taylor expansions, we need to split the quantity of interest into the sum of a major part (which is bounded from below by order $\epsilon$) and a negligible part (which is of order at most $\epsilon^2$). It is thus necessary for us to use both notations. We will describe the approach more clearly in the revision to address this point. 4. Analysis of local errors: The step is as follows: (1) by definition, the difference between $p_0$ and $p_{1/2}$ is of order $O(\epsilon)$, and (2) since there is a multiplicative constant $\epsilon$ in front, we can replace $p_0$ by $p_{1/2}$ without changing the quantity more than $O(\epsilon^2)$. We will also clarify this point in the revision. --- Rebuttal Comment 1.1: Title: Thanks for the Rebuttal Comment: Thanks for the clarifications. I will take into account the author response and the other reviewers in the discussion period. I agree that MSE/Accuracy is not the only decider in terms of figuring out the performance of an MCMC approach. However, the model in question is a Bayesian neural network and practical usage of these models depends on the performance on experiments. One additional suggestion is to find an uncertainty quantification task that relies on a better sampling scheme and report metrics on that. In the additional provided table, it is not clear to me what the difference between "Average Acceptance Rate" and "Average MSE (overall)". What is this average taken over? Thanks once again. --- Reply to Comment 1.1.1: Comment: Thank you for your follow-up questions. We would like to address them below. - The average acceptance rate and average MSE were taken over different runs of the HMC sampler with different step size $\epsilon$ and random seeds. Here each choice of $\epsilon$ would affect the acceptance rate of the sampler and we can observe from the experiment results that the sigmoid network has a generally higher acceptance rate than that of ReLU-based networks. - Furthermore, due to the higher acceptance rate, the sigmoid network also has a better MSE than that of ReLU-based networks. Additionally, if we compare the standard errors of the MSEs, we can observe that the error range for sigmoid network is much smaller than that of ReLU-based networks ($\pm$ 0.0003 vs. $\pm$0.0057 and $\pm$0.0056). These results can address your first comment that a better sampling scheme could lead to better MSE and uncertainty in this case. We will add these discussions to the revised version of our paper.	null	null	null	null	null	null
Scaling transformer neural networks for skillful and reliable medium-range weather forecasting	Accept (poster)	Summary: This paper introduces a deep learning weather prediction model called Stormer. Stormer is vision transformer type network that employs various techniques to improve the network's performance in weather forecasting applications, including a "weather-specific embedding" that first processes each variable separately, and a technique for producing multiple weather scenarios for each input by using the model's ability to be tuned to various lead times. By using a lower spatial resolution than competing models, Stormer is much faster to train and inference than current state of the art models, while still achieving competitive performance at short-to-medium time scales and superior performance at longer time scales. Strengths: The paper shows that high-performance weather prediction DL models do not necessarily need to use high resolution, and in this way can save a large amount of computing power while still achieving good performance. The inclusion of adaptive layer normalization to enable variable lead times within the single model is also an interesting development. Furthermore I find the strategy for using the variable time stepping to average multiple forecasts an interesting technique. The paper is very well written and the methodology was easy to understand from the description. Weaknesses: I do not see serious weaknesses with the paper. However, one point that could be improved is with the randomized forecast strategy introduced in the paper. PanguWeather is also able to make weather forecasts with variable lead times (although it achieves this with separately trained models). If I'm not mistaken, PanguWeather could then also be used to implement the randomized forecast strategy. It would be interesting to see this included in the model comparisons. Technical Quality: 4 Clarity: 4 Questions for Authors: How do you expect that the resolution difference between the Stormer and GraphCast/PanguWeather models affects the comparisons? Are you computing the losses at the native resolution of Stormer, downsampling the other models to it? Do you expect that it would change the results if you instead perform the comparison at the native resolution of GraphCast/PanguWeather and upsample the Stormer results to it? Confidence: 4 Soundness: 4 Presentation: 4 Contribution: 3 Limitations: The authors do briefly discuss the limitations of their approach and possible future directions. However, I think one point that gets glossed over by the authors is that due to its low resolution Stormer is unable to resolve weather features that models such as PanguWeather and GraphCast can resolve. Thus the performance gain of lower resolution comes at a cost of worse ability to resolve more localized weather features. It's also not clear how this impacts the model's representation of weather extremes, which are often found at small scales. Flag For Ethics Review: ['No ethics review needed.'] Rating: 8 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for the very detailed and constructive feedback, and for recognizing the technical contributions and good presentation of Stormer. We answer each of the reviewer's concerns below. > PanguWeather could then also be used to implement the randomized forecast strategy. It would be interesting to see this included in the model comparisons. We agree that Pangu-Weather is capable of performing the randomized forecast strategy with the cost of training 3 separate models. We plan to include this experiment in the updated paper. As a fairer comparison to Pangu, we have compared the non-ensemble version of Stormer with the baselines. Specifically, we performed the Pangu-style inference, where we only used the 24-hour interval forecasts to roll out into the future (i.e., 1-day=24, 2-day=24+24, 3-day=24+24+24, etc.), instead of combining different intervals. Figure 1 in our PDF shows that non-ensemble Stormer outperforms Pangu and performs competitively with Graphcast. Moreover, we note that the ensembling technique in Stormer is much cheaper and easier to use than other methods such as training multiple networks, dropout, or IC perturbations, as we only have to train a single neural network and do not need extensive hyperparameter tuning. For better efficiency, one can always use the Homogeneous version of Stormer for inference, which only requires 3 forward passes and performs competitively to the Best m in n version, as shown in Figure 3 of our PDF. > How do you expect that the resolution difference between the Stormer and GraphCast/PanguWeather models affects the comparisons? Are you computing the losses at the native resolution of Stormer, downsampling the other models to it? Do you expect that it would change the results if you instead perform the comparison at the native resolution of GraphCast/PanguWeather and upsample the Stormer results to it? We downsampled the forecasts of Graphcast and Pangu-Weather to 1.40625deg and compared all methods in this resolution. This is the same strategy that was used in WeatherBench 2 to compare different models at different resolutions. We expect the comparisons to change if we instead upsample the Stormer forecasts to 0.25deg. While this is technically possible, we (and Weatherbench 2) opted not to do so because upsampling introduces additional error due to the complexity of extrapolating information from lower to higher resolution. In contrast, downsampling is straightforward, effectively averaging neighboring pixels without significant loss of information. --- Rebuttal Comment 1.1: Comment: Thanks for the response, this clarifies my comments. I'll keep the original review score. --- Reply to Comment 1.1.1: Title: Thank you Comment: We thank the reviewer again for the constructive review and feedback. We will make sure to include these discussions into the paper.	Summary: The paper proposes a transformer-based model for weather prediction. Experiments show improvement in downstream predictions. Strengths: - The presentation of the paper is clean, and the paper is easy to read and understand. - Some improvements over long-term weather forecasting. Weaknesses: - The paper has very limited novelty and is incremental. The transformer-based architecture is the same as ClimaX and other transformer-based methods; the variable embeddings are similar to what ClimaX proposes, multi-step fine-tuning is the same as FourCastNet, and pressure-weighted loss is by GraphCast. - The paper misses out on a ton of related works, such as ClimODE (https://arxiv.org/abs/2404.10024), Neural GCM (https://arxiv.org/abs/2311.07222), GenCast (https://arxiv.org/abs/2312.15796), etc all seem to be missing and comparisons to them are missing. - Recent works have shown that continuous time methods with physical inductive biases and hybrid ML modeling have surpassed transformer-based methods such as ClimODE and Neural GCM, providing uncertainty and interpretability. The proposed method does not offer any benefits to any of them. - Although the authors utilize randomized dynamic forecasting mechanism to have stability over predictions, they still restrict the whole method to output only point estimates rather than giving uncertainties. Technical Quality: 2 Clarity: 2 Questions for Authors: - What is the computational complexity of training and inference? Are there any ablation studies regarding the compactness and inference time studies? - How do you counter for boundary conditions? Do the variable and patch embeddings respect boundary conditions? - Can the model accommodate different lead-time resolution query points (t = 1hr, 19hr, 91hr, etc.) that differ from the dataset, showcasing its generalizability and applicability in modeling weather? - Does the method use standard 2D ViT or a 3D transformer as the stormer block? Confidence: 4 Soundness: 2 Presentation: 2 Contribution: 2 Limitations: See weaknesses and questions. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for the constructive feedback and the appreciation of the good presentation and good performance of Stormer. We answer each of the reviewer's concerns below. > The paper has very limited novelty and is incremental. We acknowledge that some components in Stormer are similar to those of prior works. We also discussed the relation to them in the paper: Lines 204-205 discussed the variable embedding in ClimaX, Line 298 mentioned the pressure-weighted loss in Graphcast, and Lines 100-101 mentioned multi-step finetuning in previous works. We will update the paper to bring this discussion to the methodology section for better clarity. However, we would like to emphasize the differences and contributions of Stormer: - Stormer has a similar architecture to climax, but we use adaptive layer norm for time-conditioning, which we show is important to the performance in Figure 3c. Even with a fairly similar architecture, Stormer significantly outperforms ClimaX, showing the superiority of randomized iterative forecasting vs continuous pretraining + direct finetuning. - We introduce randomized iterative forecasting, a paradigm not explored in previous works. This allows any architecture (GNN, transformers, etc.) to gain performance improvements w.r.t deterministic metrics with only minor computation overhead (during inference only) compared to single-interval models. - Unlike previous works, we carefully ablate each component in Stormer to understand their importance in obtaining a good forecast performance. Via this paper, we show that it may not be necessary for a specialized neural network architecture, and a standard model like transformers can achieve state-of-the-art performance with careful design choices. We believe this extends the current understanding of data-driven weather forecasting, and is a valuable contribution to the community. > The paper misses out on a ton of related works Thank you for pointing us to these works, we will discuss them in detail in the updated paper. Both Gencast and NeuralGCM were concurrent works and used much larger compute resources to run on higher-resolution data. Moreover, our goal in this paper is not to show SOTA (even though we could potentially achieve better performance with more compute and higher resolution data), but rather to show the power of simple and scalable approaches based on the transformers architecture, and what contributes to the performance of an ML weather forecasting model. Figure 4 in our PDF compares Stormer with NeuralGCM and ClimODE. We additionally include Stormer (IC noise), a version of Stormer with initial condition perturbations. Specifically, for each combination in the “Best 32 in 128” strategy, we sample 4 different noises from a Gaussian distribution with a standard deviation of 0.1 and add to the input, resulting in a total number of 128 ensemble members. The figure shows that Stormer outperforms deterministic NeuralGCM and performs competitively with NeuralGCM ENS. With IC perturbations, the gap between Stormer and NeuralGCM is negligible. ClimODE performs significantly worse than the other methods. While ClimeODE may improve by training on higher-resolution data, we do not believe it can close this huge gap. We will add this comparison to the updated paper. > Recent works have shown that continuous time methods with physical inductive biases and hybrid ML modeling have surpassed transformer-based methods such as ClimODE and Neural GCM, providing uncertainty and interpretability. The proposed method does not offer any benefits to any of them. We respectfully disagree. NeuralGCM, ClimODE, and Stormer are different approaches and each has its pros and cons: - NeuralGCM is a hybrid model that combines a differentiable dynamical core with ML components for end-to-end training. While the dynamical core allows the method to leverage powerful general circulation models, it also has various drawbacks. First, to make predictions, the dynamical core in NeuralGCM has to solve discretized dynamical equations, which are more computationally expensive than forward-passing a neural network. Second, the performance of NeuralGCM is upper-bounded by the accuracy of the fixed dynamical core, while fully learnable models like Stormer continue improving with more data. This is a desirable property, given the scaling properties we have seen in Stormer and ClimaX. - ClimODE introduces physical inductive biases into deep learning models to improve the interpretability of their method. However, in terms of forecasting accuracy, as Figure 4 in our PDF shows, ClimODE is quite inferior to Stormer or other state-of-the-art methods. > They still restrict the whole method to output only point estimates rather than giving uncertainties. This work focuses on deterministic forecasting and how to achieve state-of-the-art performance in deterministic metrics with a simple but scalable architecture like a transformer. However, we note that we can make Stormer a probabilistic model with IC perturbations. Figure shows the probabilistic performance of Stormer with different noise levels (standard deviations of the Gaussian noise distribution). IC perturbations significantly improve CRPS and SSR metrics of Stormer as well as deterministic performance at long lead times, but may hurt the accuracy at short lead times. Moreover, it is difficult to find an optimal noise level for the spread-skill ratio across different variables and lead times. We can further improve this by using a better noise distribution or variable-dependent and lead-time-dependent noise scheduling, which we defer to future works. --- Rebuttal 2: Title: Rebuttal by Authors (2/2) Comment: > What is the computational complexity of training and inference During training, complexity is the same as training a single-interval model because we train a single model for the same amount of time. In other words, there is no computation overhead of randomized iterative forecasting during training. During inference, since we average multiple forecasts with different interval combinations, complexity scales linearly with the number of combinations. If computation is a critical issue, one should use the homogeneous inference of Stormer, which only uses 3 homogeneous combinations, while achieving competitive results to the Best m in n inference, as Figure 3 in our PDF shows. > How do you counter for boundary conditions? Do the variable and patch embeddings respect boundary conditions? The model learns everything from data, and we do not enforce any special constraints on the model. This is similar to most deep learning methods like Pangu, Graphcast, etc. > Can the model accommodate different lead-time resolution query points (t = 1hr, 19hr, 91hr, etc.) that differ from the dataset If we train the model on the 1-hour interval then it can produce forecasts at any lead time that is a multiplier of 1 hour. However, due to the huge size of 1-hourly ERA5, we subsampled the data to 6-hourly only, so the model can make forecasts at lead times that are multipliers of 6 hours. We do not expect a model to generalize well to an interval unseen during training. > Does the method use standard 2D ViT or a 3D transformer as the stormer block? Stormer uses a standard transformer 2D backbone. The model relies on the weather-specific embedding module to aggregate information across different variables and pressure heights. --- Rebuttal Comment 2.1: Title: Checking in Comment: Thank you again for your review. We made significant efforts to address the reviewer's concerns and sincerely hope that our responses have adequately addressed the concerns you previously raised. Since the discussion period is short and drawing to a close soon, are there further questions or concerns we should discuss? We understand that you are busy, and we truly value the time and effort you put into this process. Thank you in advance for your continued support. --- Reply to Comment 2.1.1: Title: Checking in (2) Comment: We thank you again for your constructive review and feedback. We sincerely hope the reviewer has had time to read our rebuttal and additional experiments, which we believe have addressed and answered the reviewer's concerns and questions. As the discussion ends today, please let us know any further questions or concerns you would like to discuss. We understand that you are busy, and we truly value the time and effort you put into this process.	Summary: The authors introduce a vision transformer-based method, Stormer, designed for medium-range weather forecasting. Ablations identify multiple important components of the method, including a weather-specific patch embedding, "randomized" dynamics forecast, and a pressure-weighted loss. The randomized forecasting component is similar to prior continuous models but complemented with iterative rollouts and an ensemble technique "best m in n" that exploits the multiple discretizations possible to forecast a specific lead time iteratively. The experiments show competitive results in terms of RMSE and ACC against deep learning and physics-based baselines. Strengths: - Tackles an important problem and achieves strong results on a popular weather forecasting benchmark, Weatherbench2. - The weather-specific patch embedding and randomized iterative ensemble forecasting are interesting methodological contributions. - Careful ablation of key design choices is insightful and valuable. - Clearly written, easy to follow, and a relatively simple approach are valuable for the community, especially if coupled with a good code release. ********************* After rebuttal: Raising score from 5 to 6. Weaknesses: - The evaluation is somewhat unfair. The paper is essentially using an ensembling technique but comparing against deterministic models. It is well known that ensembling improves ensemble-mean RMSE and ACC scores, especially for longer-range horizons (which is were Stormer, unsurprisingly, shines the most against the non-ensemble baselines). This can be actually clearly observed with the physics-based baselines IFS HRES (deterministic) and IFS ENS (ensemble mean) in Figures 8 and 9, where the ensemble mean shines the most on long-range horizons. Thus, a fairer comparison would be to either 1) ensemble the deterministic ML-based baselines (e.g. through input perturbations or with lagged ensembles as in [1]) or 2) show results of Stormer without ensembling (even a "m=1 in n" forecast would be much fairer than the way it is now). Additionally, the proper way to evaluate an ensemble weather forecast is via probabilistic metrics such as the CRPS and spread-skill ratios. This should be included to properly assess the quality of the homogenous or "best m in n" ensembles. This probabilistic evaluation is actually supported by Weatherbench2, so it should be easy for the authors to extend their current evaluation with probabilistic metrics (+this will give you IFS ENS baseline up to 15 days ahead for free...). - On top of probabilistic metrics, it would be instructive to see an analysis of the generated spectra of Stormer. - The following is wrong: "it is unclear (...) how critical the multi-mesh message passing in GraphCast is to its performance". The authors seem to have missed section "7.3.1. Multi-mesh ablation" in the GraphCast paper. - I would like to see a more transparent discussion of the exact contributions of this work and a more careful contextualization with prior work. For example, in section 3.1 it would be good to be more candid about that 1) the objective is exactly the same as for a continuous forecasting model. The only difference between the two seems to be during inference time (and the different lead times used for training); 2) the overall train+inference method is essentially the same (neural architectures aside) as for Pangu-weather (PW) but with Stormer training one model for all lead times, while PW trains one per lead time. Noting the pros and cons of each would be useful to. Even more useful would be to have a crisp ablation for Stormer, where you drop the time-conditioning and train 3 separate models for each lead time (6, 12, 24hours). This would control for the differences in architecture between Stormer and PW, giving valuable insights into the pros and cons of each; 3) The pressure-weighted loss is taken from GraphCast but this is not properly referenced in the manuscript (this is not mentioned in section 3.1.1 that introduces it but only much later); 4) Same for multi-step fine-tuning, which is very common in prior work. - Relatedly, I think that the paper could benefit from discussing the related work more in-depth. For example, I seem to have missed any discussion that carefully compares Stormer with other (vision) transformer for weather forecasting methods such as Pangu-Weather, ClimaX, FengWu, etc. - Please include results on other variables than just T2M for your ablations. Different variables might behave quite differently... Also, this is a particularly unfortunate choice for Fig. 5b because the fact that the pressure-weighted loss improves T2M RMSE is fairly trivial since the pressure-weighted loss is very strongly upweighting the influence of T2M on the total loss relative to other variables. - Line 292: "We note that Stormer achieves this improvement with no computational overhead compared to the single-interval models, as the different models share the same architecture and were trained for the same duration.". Is this true? To me it seems that at inference time there does exist a computational overhead due to the larger size of the ensemble... [1] A Practical Probabilistic Benchmark for AI Weather Models (https://arxiv.org/abs/2401.15305) Technical Quality: 2 Clarity: 3 Questions for Authors: - It would be very insightful to see an ablation of the different prediction approaches in weather forecasting. That is, continous, iterative, and randomized iterative forecasting. Exploring their (dis-)advantages would be beneficial and very interesting. This would also tie well with the paper's desire to carefully ablate important components of the design stack. - Can you expand on how the "best m" combinations are chosen? By combinations you mean e.g. (3h+6h=9 and 6h+3h=9h, but not 9*1h?) Are you choosing them on the validation set? How do you choose the "n" combinations that you validate? Also, some lead times won't have as many combinations (e.g. 6h only has one, 12h two etc.), right? That would seem worth mentioning as a potential limitation of this ensembling technique. - Why does the time embedding module predict the second scale parameter? Why no second shift? Did you ablate this choice? What if you remove this second time embedding part (or the first)? - For completeness, consider specifying the parameter sizes of your models in section 4.3. explicitly. Also, do you discuss the exact hyperparameters used for the smaller model sizes? - Is input normalization done per variable or per variable AND pressure level? Confidence: 5 Soundness: 2 Presentation: 3 Contribution: 3 Limitations: The authors have not adequately addressed the limitations, mentioning the spatial resolution as the only limitation of their method (but also claiming it to be an advantage in other parts of the paper). A more upfront discussion of (potential) limitations would be welcome. For example, there is no discussion on how the proposed cross-attention-based patch embedding might scale to higher spatial resolutions or how it might impact inference speed. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for the very detailed and constructive feedback, and for recognizing the strong results and technical contributions of Stormer. We answer each of the reviewer's concerns below. > The paper is essentially using an ensembling technique but comparing against deterministic models. We would like to clarify that even though Stormer uses an ensembling technique, we consider it a deterministic model, and that’s why we compare it with deterministic baselines. The reason is that while Stormer can produce multiple forecasts for a given lead time at inference, we found these forecasts not diverse enough and should not be used for uncertainty estimation. This is shown by the under-dispersion of Stormer w.r.t to the spread-skill ratio in Figure 2 of our PDF. We will add this discussion to the updated paper. > Thus, a fairer comparison would be to either 1) ensemble the deterministic ML-based baselines (e.g. through input perturbations or with lagged ensembles as in [1]) or 2) show results of Stormer without ensembling (even a "m=1 in n" forecast would be much fairer than the way it is now). We agree these comparisons would provide more insights into the performance of Stormer. To do this, we have compared the non-ensemble version of Stormer with the baselines. Specifically, we performed the Pangu-style inference, where we only used the 24-hour interval forecasts to roll out into the future (i.e., 1-day=24, 2-day=24+24, 3-day=24+24+24, etc.), instead of combining different intervals. Figure 1 in our PDF shows that non-ensemble Stormer outperforms Pangu and performs competitively with Graphcast. Moreover, we note that the ensembling technique in Stormer is much cheaper and easier to use than other methods such as training multiple networks, dropout, or IC perturbations, as we only have to train a single neural network and do not need extensive hyperparameter tuning. For better efficiency, one can always use the Homogeneous version of Stormer for inference, which only requires 3 forward passes and performs competitively to the Best m in n version, as shown in Figure 3 of our PDF. We will add this result and discussion to the updated paper. > Additionally, the proper way to evaluate an ensemble weather forecast is via probabilistic metrics such as the CRPS and spread-skill ratios. This should be included to properly assess the quality of the homogenous or "best m in n" ensembles. To make Stormer a probabilistic forecast system, we need to introduce more randomization to the forecasts via IC perturbations. To do this, for each combination of intervals during the Best m in n inference, we added 4 different noises sampled from a Gaussian distribution, resulting in a total number of 128 ensemble members. Figure 2 in our PDF shows the RMSE and probabilistic metrics of Stormer with different standard deviations of the noise distribution. The result shows that IC perturbations improve the probabilistic metric significantly, but may hurt the deterministic performance at short lead times. Moreover, it is difficult to find an optimal noise level for the spread-skill ratio across different variables and lead times. We can further improve this by using a better noise distribution or variable-dependent and lead-time-dependent noise scheduling, which we defer to future works. We will add these results and discussions to the updated paper. > On top of probabilistic metrics, it would be instructive to see an analysis of the generated spectra of Stormer. We thank the reviewer for the suggestion and we will include this in the updated version of the paper. Due to the time constraint, we will defer this experiment to later. If the reviewer thinks this is crucial to assessing the paper, we will conduct this experiment during the discussion phase. > The authors seem to have missed section "7.3.1. Multi-mesh ablation" in the GraphCast paper. We thank the reviewer for pointing this out. Our main message here is questioning whether we need a specialized neural network architecture for weather forecasting, or whether a standard architecture like transformers can work equally well. In this paper, we consider the Transformer architecture as a special reference due to its low inductive bias, good scaling properties, and great performance across different data modalities (text, image, audio, etc.). We will reword this part for better clarity in the updated version. > I would like to see a more transparent discussion of the exact contributions of this work and a more careful contextualization with prior work. We initially wanted to describe our method first before connecting it with the related work, but we agree with the reviewer that it'd be better and more transparent to mention the prior works as we discuss each component of Stormer. We will update the paper accordingly. We answer the reviewer’s specific concerns as follows: 1) This is correct, but this seemingly small difference can make a huge difference in performance, as shown by the big gap between Stormer and ClimaX, as shown in Figure 4 of our PDF, 2) They are similar, but there are some nuanced differences. As the reviewer may have noticed, we train a single model for all intervals, while Pangu trains a separate model for each lead time. During inference, Pangu uses a single combination of intervals for each lead time that minimizes the rollout step, while we use a combination of them, 3) and 4) We agree with the reviewer and will add this discussion to the appropriate part of the main text. --- Rebuttal 2: Title: Rebuttal by Authors (2/3) Comment: > Relatedly, I think that the paper could benefit from discussing the related work more in-depth. In terms of architecture, Stormer and ClimaX both use a standard transformer backbone, and the only difference is Stormer uses adaptive layer norm for time-conditioning while ClimaX uses a simple additive embedding. On the other hand, Pangu-Weather and FengWu use a Swin-transformer backbone. In terms of model training, ClimaX is pretrained with continuous forecasting but finetuned for direct forecasting. Pangu, Fuxi, and Fengwu are iterative models but with slightly different designs. Pangu trains a separate model for each lead time, Fengwu performs multi-step finetuning with a replay buffer, and Fuxi finetunes a separate model for each time range (short, medium, and long). We will include this discussion in the updated version. > Please include results on other variables than just T2M for your ablations. Table 1 in our PDF shows the performance of the weighted and unweighted loss on 6 different variables, ranging from low to high-pressure levels. As expected, the weighted loss model achieves better accuracy for high-pressure variables while underperforming the unweighted version for low-pressure variables. We were aware of this trade-off and proposed to use the weighted loss in Stormer to focus on variables that are more important to forecasting and/or human activities. We will add these results to the updated paper for better clarity. > To me it seems that at inference time there does exist a computational overhead due to the larger size of the ensemble We wrote this with regard to the training process, which is the major computation overhead of deep learning models. At inference, Stormer does require more computation compared to single-interval models, and computation scales with how many combinations of intervals we use during inference. And as we showed above, using 3 ensemble members of the homogeneous inference is enough to achieve a good performance. We will reword this part to avoid confusion in the updated manuscript. > It would be very insightful to see an ablation of the different prediction approaches in weather forecasting. That is, continous, iterative, and randomized iterative forecasting. We expand the differences between these approaches below: - Continuous vs randomized iterative forecasting: The difference can be seen in the performance gap between Climax and Stormer. Continuous requires a single model to be able to forecast with a wide range of lead times, e.g., 6 hours to 2 weeks, which is a challenging (and sometimes confusing) learning task for any model. In contrast, randomized iterative only trains the model with a small set of intervals (6, 12, 24), mitigating this problem. Moreover, continuous models do not generalize beyond lead times in the training range, as shown in Climax, while randomized iterative does. - Iterative vs randomized iterative: The latter offers two advantages, data augmentation and the ability to combine the intervals to produce multiple forecasts. Empirically, the randomized iterative approach achieves significantly better accuracy than the iterative approach, as shown in the performance gap between Stormer and non-ensemble Stormer, while only incurring a slight computation overhead. > Can you expand on how the "best m" combinations are chosen? By combinations, we mean from the set {6,12,24} pick any ordered combination that sums up to a certain lead time. For example, for a lead time of 1 day (24 hours), we can either do 6+6+6+6, 6+12+6, 24, 12+12, 12+6+6, 24, etc. We chose the best m based on the validation loss, and we picked n to be a reasonably large value (128) without hyperparameter tuning. Based on our preliminary results, the final performance is not sensitive to this value (we tried 32, 64, 128). Indeed, there won't be many combinations for very small lead times, but these lead times also do not require ensembling multiple forecasts because individual forecasts are accurate enough. We will discuss this component in more detail in the updated paper. > Why does the time embedding module predict the second scale parameter? Why no second shift? Did you ablate this choice? What if you remove this second time embedding part (or the first)? We did not ablate this choice. We adopted the adaptive layer normalization (adaLN) from the computer vision literature [1, 2], which is a common technique to condition a neural network on additional information like time. [1] Perez, Ethan, et al. "Film: Visual reasoning with a general conditioning layer." Proceedings of the AAAI conference on artificial intelligence. Vol. 32. No. 1. 2018. [2] Peebles, William, and Saining Xie. "Scalable diffusion models with transformers." Proceedings of the IEEE/CVF International Conference on Computer Vision. 2023. --- Rebuttal Comment 2.1: Title: Rebuttal by Authors (3/3) Comment: > For completeness, consider specifying the parameter sizes of your models in section 4.3. explicitly. Also, do you discuss the exact hyperparameters used for the smaller model sizes? The total parameter count of Stormer is 400 million. Different model sizes of Stormer correspond to the standard sizes of ViT models in the computer vision literature, defined at https://github.com/huggingface/pytorch-image-models/blob/main/timm/models/vision_transformer.py. We will add the parameter count and hyperparameters of all models to the updated version. > Is input normalization done per variable or per variable AND pressure level? Input normalization is done per variable AND pressure level. --- Reply to Comment 2.1.1: Title: Checking in Comment: Thank you again for your review. We made significant efforts to address the reviewer's concerns and sincerely hope that our responses have adequately addressed the concerns you previously raised. Since the discussion period is short and drawing to a close soon, are there further questions or concerns we should discuss? We understand that you are busy, and we truly value the time and effort you put into this process. Thank you in advance for your continued support. --- Rebuttal 3: Comment: Thank you for the quick response. I think that the revised paper will be a great addition to the literature. I look forward to reading it.	null	null	Rebuttal 1: Rebuttal: We thank ACs for handling our paper and reviewers for their insightful comments and constructive feedback. The suggestions by the reviewers are very helpful and have added significant insights to the paper. We have responded to each review individually, and also submitted a PDF file containing the figures and tables for additional experiments we conducted during rebuttal. We summarize these experiments and their results here: - (Figure 1) Non-ensemble vs the baselines: We compared the non-ensemble version of Stormer with the baselines. Specifically, we performed the Pangu-style inference, where we only used the 24-hour interval forecasts to roll out into the future (i.e., 1-day=24, 2-day=24+24, 3-day=24+24+24, etc.), instead of combining different intervals. Figure 1 in our PDF shows that non-ensemble Stormer outperforms Pangu and performs competitively with Graphcast. Moreover, we note that the ensembling technique in Stormer is much cheaper and easier to use than other methods such as training multiple networks, dropout, or IC perturbations, as we only have to train a single neural network and do not need extensive hyperparameter tuning. For better efficiency, one can always use the Homogeneous version of Stormer for inference, which only requires 3 forward passes and performs competitively to the Best m in n version, as shown in Figure 3 of our PDF. - (Figure 2) Probabilistic performance of Stormer with IC perturbations: To make Stormer a probabilistic forecast system, we introduce more randomization to the forecasts via IC perturbations. To do this, for each combination of intervals during the Best m in n inference, we added 4 different noises sampled from a Gaussian distribution, resulting in a total number of 128 ensemble members. Figure 2 in our PDF shows the RMSE and probabilistic metrics of Stormer with different standard deviations of the noise distribution. The result shows that IC perturbations improve the probabilistic metric significantly, but may hurt the deterministic performance at short lead times. Moreover, it is difficult to find an optimal noise level for the spread-skill ratio across different variables and lead times. We can further improve this by using a better noise distribution or variable-dependent and lead-time-dependent noise scheduling, which we defer to future works. - (Figure 3) Homogeneous vs Best m in n inference: Figure 3 compares the two inference strategies we proposed in the paper. Homogeneous performs competitively to Best m in n and only underperforms at 13-day and 14-day lead times, while using fewer ensemble members. We recommend this strategy if efficiency is the priority. - (Table 1) Ablation studies with more variables: We showed the performance of Stormer with and without the weighted loss for 6 additional variables. As expected, the weighted loss model achieves better accuracy for high-pressure variables while underperforming the unweighted version for low-pressure variables. We were aware of this trade-off and proposed to use the weighted loss in Stormer to focus on variables that are more important to forecasting and/or human activities. - (Figure 4) Comparison of Stormer with additional baselines: We added 4 more baselines -- ClimaX, NeuralGCM, NeuralGCM ENS (mean) and ClimODE. Stormer significantly outperforms ClimaX, ClimODE, and NeuralGCM, while slightly underperforming NeuralGCM ENS (mean). With IC perturbations, the gap between Stormer and NeuralGCM ENS (mean) is negligible. Pdf: /pdf/44799bc4283ced4d2b4ae5a1d09d24a3a70161f0.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
On the Sparsity of the Strong Lottery Ticket Hypothesis	Accept (poster)	Summary: The authors propose an existence proof for Strong Lottery Tickets(SLTs) by improving over the existing method which used the Subset Sum approximation to construct source networks, which involved using subsets of variable sizes in order to approximate target parameters. Instead the authors show the existence of SLTs using subsets with fixed sizes (RFSS) and leverage this results to show the existence of SLTs. Strengths: 1. The authors propose the Random Fixed Subset Sum approximation instead of the previously used Subset Sum approximation to prove the existence of Strong Lottery Tickets. This results allows them to use a subset of a fixed size to approximate parameters in a target network. 2. The subsequent existence proof interpolated between the result of Malach et. al. [1] (which uses a single parameter) and Pensia et. al. [2] (which uses a subset of parameters) based on the size of the subset being used. The authors also extend this result to equivariant networks. Weaknesses: 1. Given the theoretical nature of the work, the overall contribution appears limited as it can only connect the existing results established by [1], [2], [3]. 2. The main insight in this paper is that by using a fixed subset size to approximate parameters in the target, one can exactly estimate the number of parameters required in the strong lottery ticket, which was previously not possible due to the variable size of subsets. However, as Burkholz et. al. [3] have shown via numerical simulations, the number of parameters required to satisfy the theoretical conditions for subset sum proofs can be relatively easily approximated. For example, they use a subset of size 15 for their simulations which is sufficient. Given this, the overall contribution of the paper seems incremental The following claims in the paper need to be addressed appropriately. 1. ‘We provide the first proof of the SLTH in classical settings, such as dense and equivariant networks, with guarantees on the sparsity of the subnetworks.’ While the existence of SLTs has been shown before in various settings, the sparsity of these networks has also been estimated using numerical simulations by Burkholz et. al. [3]. This is primarily because the size of the subset required to effectively approximate a parameter seems to have a natural upper bound (15 as shown in [3]). Hence, while the authors are able to show this exactly, previous theoretical work did a decent approximation. 2. ‘It is important to note that, to this day, we only have proofs on the existence of such subnetworks, also called winning tickets, but it remains an open question how to find them reliably.’ While the theoretical framework is laid out by the authors to construct the SLTs, the paper lacks numerical constructions of real world examples of neural networks using the proposed framework. Are the networks found by the proposed method sparser than the one's found by [3]? [1] Malach, Eran, et al. "Proving the lottery ticket hypothesis: Pruning is all you need." International Conference on Machine Learning. PMLR, 2020. [2] Pensia, Ankit, et al. "Optimal lottery tickets via subset sum: Logarithmic over-parameterization is sufficient." Advances in neural information processing systems 33 (2020) [3] Burkholz, Rebekka. "Most activation functions can win the lottery without excessive depth." Advances in Neural Information Processing Systems 35 (2022) Technical Quality: 3 Clarity: 3 Questions for Authors: See above Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: The work leverages Random Fixed Subset Sum result to adapt a large body of work showing the existence of SLTs. However, in the context of the existing work, this result seems incremental and lacks numerical validation. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for their feedback on our work. In the following we address the reviewer’s concerns individually. Weakness 1. We are sorry if the discussion in Section 1.1 in which we discuss the links between our results and \[1,2,3\] gives the impression that our work only connects the existing results established by \[1\], \[2\], \[3\]. As we explain in the following, this is not the case. The main contribution of our paper is to provide theoretical guarantees of the existence of subsets of bounded sizes for the random subset problem, and then to use this result to show the existence of lottery tickets of given sparsity. No results of this kind can be found in \[1\], \[2\] or \[3\]. We mention a connection with the results of \[1,2\] in Section 1.1, namely that, when the sizes of the subsets are small, the overparametrization is polynomial in $1/\epsilon$, but when the subsets are large, the overparametrization is logarithmic in $1/\epsilon$. It is merely a discussion of the order of our results, rather than a statement that the results appear in \[1\] or \[2\]. Our result allows to fill a gap in the LSTH literature, since the existence of winning tickets was proved, but not the existence of sparse tickets. Weakness 2\. From our understanding, the reviewer is arguing that, in their view, the numerical experiments provided in previous work on the sparsity of the subnetworks were satisfying enough for practical applications, and they do not see much value in providing rigorous mathematical results. We kindly disagree with the view that a theoretical result can be considered incremental on the basis of previous numerical experiments. In fact, we believe that the numerical experiments in Burkholz et al. (Neurips’22) (which we discuss in our related work), further motivates our work by empirically indicating the existence of a phenomenon that was missing a mathematical understanding. As for the criticism of the first quoted claims, the reviewer seems to imply that a subset of size 15 is enough to approximate any target network within epsilon in practice. While it is true that the RSS states that for a given epsilon, a given subset size is enough to approximate a single weight, it should be noted that this is not the case when the goal is to approximate the output of the entire NN, as the SLTH results show. Indeed, the errors amplify through the layers, thus, the subset size required to approximate the target network within epsilon depends on its depth and width. Our results express this dependency for sparse subsets. As for the second quoted claim, our work does not provide a constructive algorithm to find the subnetworks, since our results are existential. We further clarify this point in our Limitations section, lines 303-304, where we point out that no theoretical guarantees are available, although we cite promising methods (that have, in fact, provided the motivation for the theoretical research on the SLTH). We hope that our rebuttal satisfyingly addresses all the reviewer’s concerns. Please let us know if anything needs further discussion. In the meantime, we thank the reviewer again for reviewing our work. --- Rebuttal Comment 1.1: Title: Response to rebuttal Comment: I thank the authors for their rebuttal and for providing clarifications. While I still believe that a sufficiently small subset size (of about 15) is enough to practically approximate a network while maintaining a tractable error for the entire network, I do understand the value of a theoretical existence proof of the SLTH for a fixed subset size. I have adjusted my score accordingly. --- Reply to Comment 1.1.1: Title: Response to response to rebuttal Comment: We thank the reviewer for their careful consideration of our rebuttal. Of course, should the reviewer have any further concerns about our work, we would be happy to discuss them.	Summary: This work focuses on the theoretical side of the Strong Lottery Ticket Hypothesis. It proposes and studies a fixed-size version of the canonically used Random Subset Sum (abbreviated RFSS) problem in previous proofs for this hypothesis. Then it applies the result of RFSS to prove that overparameterized networks can be pruned to approximate target networks with guaranteed sparsity. A corresponding lower bound is provided to show the tightness (up to log factor) of the overparameterization needed. Strengths: - The proposed fixed-size version of RSS is an interesting problem and is potentially of independent interest. - Based on the literature reviewed here, this work is the first one that provides a (high probability) size guarantee for the pruned subnetwork. - A lower bound on the overparameterization size is also provided, which helps complete the picture and matches the high probability guarantee up to a log factor. Weaknesses: - Elaboration of Theorem 3 is helpful in the main text. I do not see how it answers the question proposed in Introduction. Namely, for given target network size $m'$, the internal dimensions $d_\ell$, and a desired sparsity $\alpha$, how should we pick the number of parameters (or the number of layers) for our networks? Also, how does it imply the previous results? - More discussion should be given to the results on the hypothesis (e.g. elaborations) in Section 4 and 5. While the RFSS result is key, instead of having the whole proof in Section 3, the authors can leave a sketch of the proof idea and where it distinguishes / extends RSS results. Technical Quality: 3 Clarity: 2 Questions for Authors: - On line 225 Theorem 3, is it $r = \max_i \min\{…\}$ instead of only $\max_i$ (in which case it’s always at least 1)? - What abbreviates to ANN in Theorem 4? Confidence: 2 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: Addressed by the authors. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We are grateful to the reviewer for the time they invested in reviewing our paper and the appreciation they expressed for our work. In the following we address the reviewer’s concerns individually. Weakness 1 and 2. We agree with the reviewer that the paper would greatly benefit from a longer discussion on Theorem 3 and on Section 4 and 5. In the submitted version, we felt compelled to give more space to the main proof, since it is our main technical contribution. We like the idea of making more space for discussing the result, and in the revised version of the manuscript we are going to move most of the details in the appendix, so that we can save space for discussions after Theorem 3 and in sections 4 and 5, as well as those resulting from the other reviews. In particular, regarding Theorem 3, we will add a discussion on how it answers the initial question. In general, the number of layers will be $2\ell$ where $\ell$ is the number of layers of the initial network (although it could be improved to $\ell+1$ as mentioned in line 266 through the strategy discussed in line 115, which we don’t explore in the paper); as for the number of parameters, considering here for simplicity the case in which all layers have width $d$, number of parameters will be of order $d^2\frac{\log^2(\frac{\ell d^2 (1-\alpha)}{\epsilon})}{H(\alpha)}$. The reason we don’t phrase the results in Section directly as an answer to our question in the introduction, is to keep them in the same form they appeared in previous work, for an easier comparison. Finally, regarding the comparison with previous results, we had a brief discussion in Section 1.1, which we will make more detailed thanks to the space that will be freed by moving the technical details of the proof. In particular, the logarithmic regime in Pensia et al. (Neurips’20) is readily recovered for constant sparsity, since in that case the entropy term is constant. As for the polynomial regime of Malach et al. (ICML’20), the calculation is more involved. To illustrate it more quickly, let us assume all constants are 1 and that we can disregard the dependency on $n^$ inside the logarithm on the right hand size of the equation (as discussed with reviewer WaBr, we will get rid of the latter dependency when revising the manuscript). Finally, let’s consider a network where all layers have $d$ neurons. With the aforementioned simplifications, we have the equation $n\geq \frac 1{H(\gamma)} \log^2\left(\frac {\ell d^2 \gamma}{\epsilon}\right) = \frac 1{H(\gamma)} \log^2\left(x \gamma\right)$ where $x = \frac {\ell d^2 }{\epsilon}$. To recover polynomial sparsity, consider e.g. $\alpha=1-\gamma=1-\frac{\log x}{x}$, for which we get that $n \geq x \frac {\log^2 \log x}{(\log x) \log(x/(\log x))}$, which is satisfied for $n \geq ( \frac {\ell d^2}{\epsilon} )^{const}$ for some $const$. Without the simplifications we made, we would just get a different value of the $const$ in the latter expression. Question 1.* We confirm that $r$ is defined as a maximum, and the direction of the inequality is a typo ($r$ is used in the second inequality after line 540, where it is important that it is larger than 1). We will correct the direction of the inequality in the revised version of the manuscript. Question 2. ANN is an abbreviation of “artificial neural networks”; we apologize for overlooking the definition of the acronym. Unless the reviewer has a different opinion, we will update the name of the theorem with the simpler “SSLTH for Equivariant Networks”. We thank the reviewer again for his valuable feedback and suggestions on our work. Please let us know if there is anything else we should discuss. --- Rebuttal Comment 1.1: Comment: I appreciate the authors' responses and have no other questions. --- Reply to Comment 1.1.1: Comment: We thank the reviewer for considering our rebuttal. Of course, should the reviewer have any further concerns about our work, we would be happy to discuss them.	Summary: The authors consider the strong lottery ticket hypothesis (SLTH), which is roughly a statement that a large random neural network contains a sparse subnetwork whose performance is comparable to the entire network. By analyzing a fixed variant of the random subset sum problem, which is about the size of the sample of i.i.d. random variables to approximate a fixed number, they improved the previous results on the SLTH with the guarantee on the sparsity of the subnetwork. Strengths: - The idea based on the fixed-size random subset sum problem seems new and works well. - The writing is in general very clean, especially the introduction and the related work. Weaknesses: - I think the authors should check more about the references for the results in Section 3. (See Questions.) - There are many small errors and typos in the manuscript. (See Questions.) Technical Quality: 3 Clarity: 2 Questions for Authors: - The assumption on the sum-boundedness in Definition 1 must hold for a very general density function $f$, since it is even weaker than the statement of the local limit theorem for density. (See, e.g., Theorem 7 in Section 7.2 of "Sums of Independent Random Variables" by Petrov.) Thus, I think some parts of Section 3, especially Definition 1 and Lemma 1, can be changed. - Below are small errors and typos: 1) In line 136, there is something missing in "we $\Omega$". 2) In line 140, $f_{\Sigma_{[i]}}$ should be $\Sigma_{[i]}$. 3) In line 182, "independent and uniformly at random" sounds weird. 4) In Equation (6) and other places, $X_S$ should be $Z_S$. 5) In line 186, "Eqs. 5 and 8" should be "Eqs. 6 and 8". 6) From Equation (19) to Equation (20), why $H_z(\tilde{S})$ can be dropped? 7) The equation below 204 seems wrong. I guess $(z-y)$ should be $z$ in the second line. 8) In line 219, "Let $F$ to be" should be "Let $F$ be". Confidence: 2 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: The work does not seem to have potential negative societal impact. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We are very grateful to the reviewer for the time they invested in reviewing our paper, which we find very valuable for improving it. In the following we address the reviewer’s concerns individually. Question 1. We agree with the reviewer that the assumption of sum-boundedness in Definition 1 holds for a very general density function $f$. In fact, in Appendix B (line 392) we mentioned the possibility of extending our result to a larger family of densities, namely unimodal, with bounded variance, and bounded third moment. In the submitted paper, we focused on the uniform distribution because, together with Gaussian, these are the distributions commonly used in our application (random initialization of neural networks). We will move this remark to the main body, write the result for the sum-boundedness of this more general family of distributions, and give the result for the uniform distribution as a corollary. However, we want to point out that sum-boundedness is not weaker than the statement of the local limit theorem for density that the reviewer mentions. Sum-boundedness guarantees a lower bound on the support of the function for any $i$ (rather than asymptotically in $n$). The proof of our main result wouldn't work without such a guarantee. To clarify this, we will briefly compare our condition with the local limit theorem for density. Please let us know if you meant something else. Finally, to prevent any confusion related to the distributions for which our results hold, we would like to emphasize that, by the sampling argument in our paper, the NNs results we obtain apply to any distribution that can be written as a mixture of densities that include a uniform with constant probability, thus recovering all distributions traditionally considered in the SLTH, such as gaussian etc. In practice, extending Lemma 1 to even more general distributions, might just make the argument more technical, without changing much the impact of the result for the SLTH. Question 2 (typos). 1. “we [drop] $\omega$”, thanks! 1. We confirm that it’s not a typo, the definition concerns the value of the probability density function of the sum rather than the actual value of the random variable itself. 1. “independent[ly] and uniformly at random chosen subsets”, thanks! 1. Thank you, we will correct it! 1. It should be “Eqs. 6 and 7”, thanks! 1. That’s because $A$ only contains elements which are not in $\tilde S$, thus the event whose probability we are considering is (conditionally) independent of $\tilde S$l. Hence, it is correct to drop the conditioning in the way we do. We will add an explicit explanation for it in the revised version of the manuscript. 1. The calculation is using the fact that, given the conditioning, the density of $\Sigma_A$ is the same as the density of $\Sigma_{[k-1]}$ (without conditioning), thus the probability that $\Sigma_A$ is an epsilon-approximation of $z-y$ is the same as the probability that $\Sigma_{[k-1]}$ is an epsilon-approximation of $z-y$. Please do not hesitate to tell us if such an identity is unclear. 1. Thanks! We hope to have properly addressed all concerns the reviewer had for our paper, and that the clarifications we provided may improve their opinion of our paper. Please let us know if there is anything else we should discuss. We take the opportunity to express again our gratitude for the time they invested in reviewing our paper. --- Rebuttal Comment 1.1: Comment: I have checked the rebuttal. Thank you for the answers. I have no further remarks. --- Reply to Comment 1.1.1: Comment: We thank the reviewer for considering our rebuttal. Of course, should the reviewer have any further concerns about our work, we would be happy to discuss them.	Summary: This paper studies the strong lottery ticket hypothesis from the perspective of pruning sparsity. In particular, the paper noticed that all previous papers about the strong lottery ticket hypothesis fails to characterize the sparsity of the neural network after pruning, and aims at solving this question in the paper. The paper first extends the random subset sum problem to a case where the selected subset has a cardinality constraint. The paper proves a probability bound in terms of the candidate set's size for the random subset sum to achieve a certain accuracy. Then, the paper utilize this bound to the case of the neural networks by utilizing the technique in previous works, and shows the over-parameterization required to achieve a certain accuracy and sparsity after pruning at initialization. The paper also included a lower bound on such over-parameterization requirement. Strengths: 1. The topic considered in the paper is quite interesting and significant. Indeed, one draw-back of the strong lottery ticket hypothesis is that there is no guarantee on the sparsity level after pruning. 2. A major contribution of the paper is that it extended the random subset sum problem to a case that involves a cardinality constraint on the subset. The proof seems quite technical and nontrivial. 3. The paper also included a lower-bound on the over-parameterization requirement. Weaknesses: 1. The statement of Theorem 2 and Corollary 1 seems weird. In particular, it should be noticed that for both Eq.(1) and Eq.(3), $n$ appears in both the left hand side and the right hand side of the inequality. With some simplification, it seems that the dependency on $n$ can be completely eliminated, and the size of $n$ does not contribute to whether the statement holds or not. In this case, it would be greatly necessary to understand how big the constant $c_{hyp}$ is, which is not stated in the theorem. Moreover, if $n$ is really not affecting the approximation error, then a better way to state the theorem would be to change Eq.(1) into a condition on $k$. 2. The proof of Corollary 1 seems problematic. In particular, in Page 15, the first inequality after line 483, the $\geq$ should be $\leq$, since $Pr(\exists z\in[-\sqrt{k},\sqrt{k}],\dots) \geq Pr(\exists z\in\\{-\sqrt{k} + i\epsilon':i\in[\frac{2}{\epsilon'}\sqrt{k}]\\},\dots)$ (because $\\{-\sqrt{k} + i\epsilon':i\in[\frac{2}{\epsilon'}\sqrt{k}]\\}\subseteq [-\sqrt{k},\sqrt{k}]$). This breaks the whole proof. 3. The definition of $\alpha$ (the sparsity) is ambiguous. From the proof it seems that $\alpha$ denotes the fraction of the zero elements. In this case, however, the result in Theorem 3 seems trivial. In particular, the size of the neural network scales inversely with the $\gamma'$ (roughly the fraction of the nonzero elements), because to achieve $\gamma'$ portion of the nonzero elements, one simply need to initialize $\frac{1}{\gamma'}$ independent neural networks and prune completely the rest $\frac{1}{\gamma'} - 1$. Moreover, the definition of $r$ is problematic since it seems that by defining $r = \max\\{\frac{d_i}{d_{i-1}}, \frac{d_{i-1}}{d_i}\\}$, we must have that $r\geq 1$ (instead of $r\leq 1$ as claimed in the paper). 4. This is a minor issue: the upper bound on the over-parameterization does not match the lower bound. Technical Quality: 3 Clarity: 2 Questions for Authors: Why does the paper focus on the exact sparsity constraint $\|S\| = k$? Would it be more practical to focus on $\|S\|\leq k$? Confidence: 4 Soundness: 3 Presentation: 2 Contribution: 2 Limitations: The paper has a good discussion about its limitation from a practical perspective. However, I believe that the paper needs to add some discussion about the limitation from a theoretical perspective (tightness of the bound, strength of the assumptions etc.) Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for his precious feedback and the points they raised, which we find very valuable in improving the presentation of our result, and for the appreciation he expressed for the merits of our work. In the following, we address their concerns. Weakness 1 (form of Eq. 1). As the reviewer notices, equations 1 and 2 can be simplified by increasing the constant $c_{hyp}$; e.g. Eq 1 would become $n \geq const \frac {\log(1/\epsilon}{H(k/n)}$. We will use these simplified forms in the revised version of the manuscript. However, the dependency on $n$ cannot be removed, except when the sparsity ($\alpha$) is considered constant (and the entropy term $H(\frac kn = \gamma)$, with $\gamma=1-\alpha$, is thus constant as well). We believe that our answer to Weakness 3 will clarify this point. Weakness 2. In the inequality the reviewer is referring to, observe that the event on the l.h.s. (i.e. the existence of a $z\in [-\sqrt{k},\sqrt{k}]$ which cannot be approximated up to $\epsilon$) implies the event on the r.h.s. (i.e. that exists a $z$ in the given discrete set which cannot be approximated up to $\epsilon’=\frac{\epsilon}2$), thus the probability of the latter event is larger and the direction of the inequality is as given. We emphasize that the second event is considering a different epsilon. Weakness 3. We are glad that the reviewer mentions such a strategy of using a sample which is larger by a factor roughly $1/\gamma’$ and then actually only using only a fraction $\gamma’$ of it, since it is a natural approach that we considered when we started working on the problem, and then realized that it was highly suboptimal. To see why, we observe that such a strategy would lead to a bound on the RSS (and thus, on the sparsity of the strong tickets) which essentially matches our Theorem 2 as long as $\gamma’$ is a constant independent of $n$. The interesting regime are, however, sparsity levels which are not constant but scales with the network size; observe that also the classical results on the SLTH would be asymptotically uninteresting when the approximation error $\epsilon$ is constant. In the latter non-constant regime, our result gets exponentially better. Indeed, as we mention, our bounds allow us to recover the polynomial regime proved by Malach when the desired sparsity scales polynomially in $n$, while the simple strategy wouldn’t. As for the definition of $r$, we confirm that it is meant to be at least 1, and the direction of the inequality in the manuscript was a typo: the fact that it is greater than 1 is indeed used in the second inequality after line 540. Weakness 4. This is the reason in our paper we state that our results are essentially tight, since obtaining high probability requires an additional logarithmic factor. We remark that tightness up to logarithmic factors is already seen as significant in the SLTH literature, see for example Ferbach et al. (ICLR23). If instead we are only asked to succeed with constant probability, our results are then tight up to a constant and a factor $d$ in the logarithm (which is the same kind of tightness claimed in the seminal result by Pensia et al. (Neurips’20)). We will add an explicit remark in the introduction to make this point precise. As for the question on why we consider the exact size rather than an upper bound, there is a theoretical and a practical reason. From a theoretical point of view, we find the result on the exact size more valuable, since it is a stronger requirement and implies the other result where only an upper bound is required. If we were to relax the condition, we would only improve our result by a constant factor, since the size of the number of subsets of size at most $k$ (for $k\leq n/2$) is essentially the same as those of size exactly $k$ (this classical inequality is used for example in the second inequality of the equation after line 580 in appendix). From a practical point of view, fixed-size subsets would guarantee that the lottery ticket of a target network whose layer widths satisfy particular proportions (e.g. being all equal), would also have the same layer width proportions, which can lead to a computation time advantage. We will add the above discussion in the revision of our paper. To summarize, we hope to have properly addressed all concerns the reviewer had for our paper, and that the clarifications we provided and the discussion that we will add to the manuscript with the points mentioned above, will lead the reviewer to revise his opinion on our paper. Please let us know if there is anything else we should discuss. We take the opportunity to express again our gratitude to the reviewer for the time they invested in reviewing our paper. --- Rebuttal Comment 1.1: Title: Response to the Author's Rebuttal Comment: Thank you for your explanations. In particular, I really appreciate your clarification of my confusion related to the mistake in the proof, and, after seeing that the epsilon used here are different, I am convinced that this is not a mistake. Regarding Weakness #1 and #3, I think your answer also makes sense. What I initially did not notice is the non-linear scaling depending on $\frac{k}{n}$ introduced by the cross entropy function. I believe that the paper could benefit more from a more intuitive explanation of the interaction between $n$ and $H_2(\frac{k}{n})$ (maybe giving some examples to showcase the benefit over simply increasing the size by $\frac{1}{\gamma}$ as in the response to Weakness #3 will be helpful). I have adjusted my score accordingly. As a side note, an interesting future direction could be to combine the results with Z. Xiong, F. Liao, A. Kyrillidis, Strong lottery ticket hypothesis with $\epsilon$-perturbation, in: International Conference on Artificial Intelligence and Statistics, PMLR, 2023, pp. 6879–6902, and see how the perturbation affects the sparsity. --- Reply to Comment 1.1.1: Title: Response to Response to the Author's Rebuttal Comment: We thank the reviewer for carefully considering our rebuttal. Regarding the benefit of adding an intuitive explanation of the interaction between $n$ and $H_2(\frac{k}{n})$ in line with the Weakness 3 part of our rebuttal, we think that it will fit well next to [the planned expansion of our brief discussion in Section 1.1, which we sketched in the third paragraph of the section Weakness 1 and 2 in our rebuttal to Reviewer cEnR](https://openreview.net/forum?id=aBMESB1Ajx&noteId=Bbc54r1hU2). We also thank the reviewer for suggesting as future work the possibility of exploring the connection between our results and those in [Xiong et al. at AISTATS'23]. We will discuss this in the related work in our revision. In particular, that paper obtains a variant of the RSS result (Theorems 1 and 3 in that paper) by a careful adaptation of the martingale argument in [Lueker RSA'98]. We would like to note that we tried to adapt Lueker's martingale argument to obtain a tighter version of our fixed-subset-size variant: this leads to a recurrence for the indicator function $f(x)$ that is two-dimensional, i.e. of the form $f_{n,k}(z)$, which depends on both the sample size $n$ and the subset size $k$; although we didn't succeed in analyzing such a double recurrence, we can't exclude that there is a clever argument for doing so. As for our current proof of Theorem 2, preliminary verification suggests that the second moment argument would adapt directly to the $\varepsilon$ perturbation setting, and lead to a proof of the same bound with constant probability (and the amplification argument to obtain high probability would lead to an additional logarithmic factor w.r.t. [Xiong et al. at AISTATS'23]). Of course, should the reviewer have any further concerns about our work, we would be happy to discuss them.	Rebuttal 1: Rebuttal: We would like to express our gratitude to the reviewers for their thoughtful reviews and valuable feedback. We appreciate the time and effort they have invested in evaluating our work. We've carefully considered their comments and would like to summarize our response to the main points raised: On the strengths raised by the reviewers. We are pleased that our work has been recognized as filling a gap in the literature on a “topic \[…\] quite interesting and significant”: “Indeed, one draw-back of the strong lottery ticket hypothesis \[SLTH\] is that there is no guarantee on the sparsity level after pruning”. “this work is the first one that provides a (high probability) size guarantee for the pruned subnetwork.” Our method, “extend\[ing\] the Random Subset Sum (RSS) problem to a case that involves a cardinality constraint on the subset”, was estimated “a major contribution”, “new and work\[ing\] well”, “an interesting problem and \[…\] potentially of independent interest.” The proof was estimated “quite technical and nontrivial.” We would like to thank the reviewers for this very positive feedback. Clarity and Presentation. We acknowledge the need for improved clarity in some sections. We'll revise the manuscript to: * Simplify some equations as discussed; * Expand discussions on Theorem 3 and Sections 4-5; * Clarify definitions and correct minor typos; * Move technical details to the appendix to allow for more comprehensive discussions in the main text. Novelty and Contribution. We want to emphasize that our work provides new theoretical guarantees for the existence of sparse subsets in the random subset sum problem, which we then apply to prove the existence of lottery tickets with specific sparsity levels. This fills a gap in the Lottery Ticket Hypothesis literature by providing rigorous mathematical results where previously only numerical experiments existed. Technical Clarifications. We'll clarify the dependency on $n$ in our bounds and explain why it cannot be removed except in constant sparsity cases. We'll elaborate on why our approach is more optimal than simpler strategies for non-constant sparsity levels. We'll provide a more detailed comparison with previous results, showing how our work qualitatively recovers and extends earlier findings. Practical Implications. While our work is primarily theoretical, we believe it provides important foundational understanding that complements and supports existing empirical findings. We acknowledge that our results are existential rather than constructive, as noted in our Limitations section. Technical Accuracy. We understand that the technical nature of our proofs may have led to some misunderstandings. We're confident in the correctness of our technical steps and have provided detailed clarifications to address these concerns. In the revised version, we'll place additional emphasis on these critical parts of the proof to ensure clarity for all readers. We're committed to improving our manuscript based on your feedback. We believe these revisions will address the reviewers’ concerns and strengthen the presentation of our work. We welcome the reviewers to let us know if any further discussion and clarification is needed. In the meantime, we thank the reviewers again for their constructive criticism and the opportunity to improve our paper.	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Navigating Chemical Space with Latent Flows	Accept (poster)	Summary: The authors built a general latent flow-based framework unifies traversal and optimization in the molecular latent space. The flow is trained by utilizing energy functions so that the vector field aligns with the gradients, with regularization imposed by an auxiliary classifier that tries to differentiate each distinct flow. Under multiple evaluation settings, ChemFlow outperforms or is generally on par with previous SOTA. Strengths: - This paper is generally well-written and easy to follow. - It is a novel contribution to formulate the manipulation and optimization of molecules in latent space as learning the vector fields toward optimal distribution. Weaknesses: - Typo: L747 "we first verify if the learned variational poster also follows a Gaussian distribution and we find that it does learn so", poster -> posterior - For Table 1, it risks not fully revealing the optimization ability if only TOP3 results are reported. Please consider adding mean and median values, too. Technical Quality: 2 Clarity: 3 Questions for Authors: - In Table 2 and 3, why did ChemFlow perform best under mild similarity constraint, while suboptimal when the similarity threshold gets higher than 0.4? I think the similarity constraint is important, since usually in practical drug design people would expect to develop new therapeutics based on some drugs whose effects are already known, and the newly designed drug molecules are preferred to be similar so as to keep the effect. - For Figure 4, why is the predictor deviating so much from ground truth? LogP, QED and SA don't seem very hard to learn as far as I know. - Please consider elaborating on why "the learned variational poster[ior] also follows a Gaussian distribution" and "a strong correlation between almost all molecular properties and their latent norms" would contribute to the observed result that "a random latent vector taking a random direction will change the molecular property smoothly and monotonically". Confidence: 3 Soundness: 2 Presentation: 3 Contribution: 3 Limitations: This paper does not include a discussion on efficiency as compared with ChemSpace. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: C1: Typo: L747 "we first verify if the learned variational poster also follows a Gaussian distribution and we find that it does learn so", poster -> posterior. A: Thanks for pointing it out. It was a typo and we will fix it in the revised manuscript. C2: In Table 2 and 3, why did ChemFlow perform best under mild similarity constraint, while suboptimal when the similarity threshold gets higher than 0.4? I think the similarity constraint is important, since usually in practical drug design people would expect to develop new therapeutics based on some drugs whose effects are already known, and the newly designed drug molecules are preferred to be similar so as to keep the effect. A: Thank you for the question. We did not explicitly trained our methods for similarity constraint optimization. In the future work, we will explicitly encode more constraints to encourage our method to maintain similarity while optimizing the molecular properties. In addition, even though the absolute improvement of our method is not optimal for similarity threshold gets higher than 0.4, it has a optimal success rate compared to baseline methods. C3: For Figure 4, why is the predictor deviating so much from ground truth? LogP, QED and SA don't seem very hard to learn as far as I know. A: Thanks for the question. In Figure 4 (original paper), we set up an out-of-distribution scenario where the ground truth/prediction was the ZINC250k dataset (our VAE model was trained on a mixed of MOSES, ChEMBL and ZINC250k dataset where ZINC250k dataset was only a small fraction). However, the training set for the surrogate model was 10k randomly sampled molecular structures from the VAE model. We also only sampled 10k data points from ZINC250k which might not be representative of ZINC250k either. We have uploaded a new Figure 4 (Figure 2 in the uploaded PDF in the general response) showing the comparison on the full ZINC250k dataset (still out-of-distribution but slightly better). We have further reported the training/test performance for the surrogate model, see Table 1 and 2 (training MAE and test MAE). To further study the out-of-distribution scenario we set up, we include Figure 3 in the uploaded PDF to show our training/test set for the surrogate model and ZINC250k dataset. Table 1 Training Error (In-Distribution) \| \| plogp \| qed \| sa \| drd2 \| jnk3 \| gsk3b \| \|-------\|-------\|------\|-------\|--------\|-------\|-------\| \| MAE \| 9.840 \| 0.189\| 0.956 \| 0.006\| 0.016\| 0.041\| \| RMSE \| 12.948\| 0.231\| 1.205 \| 0.011 \| 0.021\| 0.052\| Table 2 Test Error (Out-of-Distribution) \| \| plogp \| qed \| sa \| drd2 \| jnk3 \| gsk3b \| \|-------\|-------\|------\|-------\|--------\|-------\|-------\| \| MAE \| 9.976 \| 0.341\| 2.030 \| 0.010 \| 0.017\| 0.039\| \| RMSE \| 11.076\| 0.366\| 2.203 \| 0.038 \| 0.025\| 0.049\| C4: Please consider elaborating on why "the learned variational poster[ior] also follows a Gaussian distribution" and "a strong correlation between almost all molecular properties and their latent norms" would contribute to the observed result that "a random latent vector taking a random direction will change the molecular property smoothly and monotonically". A: Thanks for the question. As VAE enforces the variational posterior to be a Gaussian distribution and we know that the geometry of high-dimensional Gaussian distribution is spheraical and the mass concentrates on the shell (if it is zero-centered, the norm of the sampled data is around $\sqrt{d}$ where d is the dimension of the data). In $R^d$, any random direction would eventually take it to the outer shell of the Gaussian ball with larger norms and further increase or decreases the property value. Thus the observation of the correlation between property values and latent norms is an emergent geometry of the learned latent space. Under this geometry, it is reasonable that any random direction could lead to monotonic and smooth change of the property. C5: This paper does not include a discussion on efficiency as compared with ChemSpace. Similar to the table 2 in chemspace A: Thanks for suggesting discussing the efficiency. Below is a table that summarize the efficiency of all baselines and our methods. It is benchmarked by training the model described in the unconstrained optimization task. The inference time is the time for optimizing 100,000 molecules for 1 step using a batch size of 10,000. Even though our method has a slower training time compared to ChemSpace because learning the flows requires learning a neural network instead of a linear model (e.g. linearSVM), they have similar inference time. This fast inference time ensures that our method is also capable of conducting high-throughput molecule optimization and screening for drug discovery. \| Method \| Training \| Inference/Iter (without oracle) \| \|--------------------------\|---------------\|---------------------------------\| \| ChemSpace \| <1 min \| 0.01 s \| \| Gradient Based \| 7 min \| 0.03 s \| \| Supervised Guidance \| 20 min \| 0.03 s \| \| Unsupervised Guidance\| 32 min \| 0.03 s \| \| Langevin Dynamics \| 7 min \| 0.03 s \| --- Rebuttal Comment 1.1: Comment: C6: For Table 1, it risks not fully revealing the optimization ability if only TOP3 results are reported. Please consider adding mean and median values, too. Thank you for the suggestion. We have included a new table with mean, median, and standard deviation in the general response.	Summary: Designing new functional molecules within the vast chemical space is challenging, which necessitates efficient exploration and understanding of this space. The paper introduces a new framework called ChemFlow, which leverages latent space learned by molecule generative models and navigates it using flows. ChemFlow formulates the problem as a vector field that guides the molecular distribution to regions with desired properties or structure diversity. The paper conducts extensive empirical studies and justifies the effectiveness of the proposed method. Strengths: - The proposed ChemFlow unifies the previous approaches via the vector field, which is novel and effective for learning a latent space with rich nonlinearity information. This can benefit various downstream tasks, including drug-related properties and protein-ligand binding. - Extensive experiments have been conducted to provide a good insight into the components of the proposed method. ChemFlow achieves faster empirical convergence and higher success rates, especially using Langevin dynamics. - The paper is generally well-written, with clear illustrations and tables. Weaknesses: - Despite the novelty of the proposed method, the ChemFlow mainly focuses on small molecules. This might hinder the border impact of the learned latent space for macromolecular tasks like protein. - ChemFlow employs multiple approaches to learning different latent flows. However, the experiment's results show that different methods have different specialties, and the paper does not discuss the connection between flow learning and downstream tasks. - The paper mentioned the out-of-distribution generation problem in Appendix D.7 and Sec. 4.2. ChemFlow has encountered such a problem in an unsupervised manner. This could hinder the utility of the learned latent space for scenarios with distribution shifts. Technical Quality: 3 Clarity: 3 Questions for Authors: - Is it possible to visualize the vector field using a tool like t-SNE or UMAP to provide further insight into the entanglement of the molecular properties? - Could you discuss the connection between flow learning and downstream tasks? - Could you discuss the extension of ChemFlow to macromolecular tasks like protein? Confidence: 2 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: The paper could provide further insights into the connection between flow learning and downstream tasks. Additionally, the author can consider discussing the extension of ChemFlow to macromolecular tasks like protein, which could make the proposed framework have a broad impact. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: C1: ChemFlow employs multiple approaches to learning different latent flows. However, the experiment's results show that different methods have different specialties, and the paper does not discuss the connection between flow learning and downstream tasks. A: Thanks for the question. This is indeed a good point. For molecular optimization task, we might have better properties of one flow vs another (e.g. Langevin dynamics vs gradient flow for optimization). However, for the latent traversal or unsupervised setting, we often do not know which flow is better. Nevertheless, we can use this as a prior to perform traversal while simultaneously structuring the latent space. As indicated in Table 5 of the Appendix, we demonstrate that the different flows work as various inductive biases to improve the performance. C2: The paper mentioned the out-of-distribution generation problem in Appendix D.7 and Sec. 4.2. ChemFlow has encountered such a problem in an unsupervised manner. This could hinder the utility of the learned latent space for scenarios with distribution shifts. A: We appreciate reviewer points out that out-of-distribution generalization hinder the utility of the learned latent space. The out-of-distribution generalization is not a particular problem for our proposed method, but rather a limitation of the underlying generative models and the surrogate model used. We thus leave this for future study. C3: Is it possible to visualize the vector field using a tool like t-SNE or UMAP to provide further insight into the entanglement of the molecular properties? A: Thanks for suggesting visualizing the vector field. We provided the t-SNE visualization of the traversal trajectory for each different property using both supervised and unsupervised wave flow in Figure 1 of the uploaded PDF. The plot shows that almost all trajectories grow towards a unique direction in the t-SNE plot. This implies the disentanglement of learned directions and, thus, molecular properties. In addition, the figures display sinusoidal wave-shape trajectories, indicating the flow is following the wave-like dynamics. In the unsupervised t-SNE plot, the trajectories of some properties overlap, such as plogP and sa. It is because some properties correlate with the same disentangled direction, so their traversal follows the same direction, thus the same trajectories. --- Rebuttal Comment 1.1: Comment: C4: Despite the novelty of the proposed method, the ChemFlow mainly focuses on small molecules. This might hinder the border impact of the learned latent space for macromolecular tasks like protein. Could you discuss the extension of ChemFlow to macromolecular tasks like protein? Thank you for the suggestion. We have included a discussion of the broader application of our approach in the general response. --- Rebuttal Comment 1.2: Comment: Thanks for your responses. It addresses all my problems. --- Reply to Comment 1.2.1: Title: Thanks for the reply Comment: We thank the reviewer again for the time spent and we are glad our revisions addressed your concerns. If the reviewer has any further questions or concerns, please don't hesitate to let us know!	Summary: The authors propose a new method called ChemFlow, which navigates molecular distributions in chemical space through flow. Strengths: 1. The method demonstrates high generality, applicable to various molecular optimization tasks. 2. Based on the experimental results presented, the method shows significant optimization of molecular properties. Weaknesses: 1. The description of the experimental section lacks detail, such as which software was used to measure the docking scores? 2. Table 1 displays properties of several indicators, but showcasing only the top 3 among numerous sampled molecules may lack sufficient persuasiveness. It would be better to include a broader distribution, such as the mean and so on. Technical Quality: 3 Clarity: 2 Questions for Authors: 1. Why were only two specific targets evaluated in the docking score experiment? 2. I would like to get some intuitive understanding : What problems arise if training a molecular property predictor in latent space and updating it directly based on its gradient? How is this issue typically addressed in the proposed method? Confidence: 3 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: This work is a preliminary study. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: C1: The description of the experimental section lacks detail, such as which software was used to measure the docking scores? A: Thanks for pointing it out. We will thoroughly revise the experimental section in the revised manuscript to make sure all details are fully explained. Specifically, we used AutoDock [1] to calculate the docking score. We also used RDKit [2] and TDC [3] to calculate other molecular properties and structure similarity. > [1] Morris, G.M. et al. (2009) ‘AutoDock4 and AutoDockTools4: Automated docking with selective receptor flexibility’, Journal of computational chemistry, 30(16), pp. 2785–2791. > > [2] RDKit: Open-source cheminformatics. RDKit. Available at: https://www.rdkit.org. > > [3] Huang, K. et al. (2021) ‘Therapeutics Data Commons: Machine Learning Datasets and Tasks for Drug Discovery and Development’, arXiv [cs.LG]. Available at: http://arxiv.org/abs/2102.09548. C2: Why were only two specific targets evaluated in the docking score experiment? A: Thanks for the comment. To respect previous literature, we follow the set-up as in [4] that target the binding sites of two human proteins ESR1 and ACAA1. Human estrogen receptor (ESR1) is chosen because it is a well-characterized protein with known disease relevance. Human peroxisomal acetyl-CoA acyl transferase 1 (ACAA1) is chosen to demonstrate the model’s de novo drug design ability as ACAA1 has no known binders. In addition, computing docking scores requires significant computational resources, as calculating the docking score for 10,000 molecules generated by a single method takes approximately 20 hours on one GPU. > [4] Eckmann, P. et al. (2022) ‘LIMO: Latent Inceptionism for Targeted Molecule Generation’, Proceedings of machine learning research, 162, pp. 5777–5792. C3: I would like to get some intuitive understanding : What problems arise if training a molecular property predictor in latent space and updating it directly based on its gradient? How is this issue typically addressed in the proposed method? A: Thanks for the comments. Training a property predictor and updating the latent vector directly based on its gradient is the exact method used in the previous work LIMO [4] as gradient-based optimization can be viewed as discretization of a gradient flow. In our work, we generalize this method as different types of flows. Gradient-based optimization may suffer from several challenges, such as stuck in local minima and poor convergence, especially in a high-dimensional space with noisy gradient guidance. In our proposed method, these issues can be improved using techniques like Langevin dynamics, which introduces diffusion noise into the gradient updates. Intuitively, this approach helps the model escape local minima by injecting stochasticity into the optimization process, thus promoting better exploration of the latent space. --- Rebuttal 2: Comment: C4: Table 1 displays properties of several indicators, but showcasing only the top 3 among numerous sampled molecules may lack sufficient persuasiveness. It would be better to include a broader distribution, such as the mean and so on. Thank you for pointing it out. We have included a new table with mean, median, and standard deviation in the general response. --- Rebuttal Comment 2.1: Comment: Thank you for your clarification and effort. I wold like to raise my score to weak accept (6).	Summary: This paper presents a novel gradient flow-based method to traverse the latent space of molecular generation models, known as ChemFlow. The authors instantiate their framework with a number of different flows inspired by dynamical systems. They also investigate the use of supervised and unsupervised guidance for the flow methods with the goal of optimising molecular properties of interest. The authors perform many experiments focused on molecular optimisation in order to evaluate their method. Specifically, they investigate unconstrained optimisation, similarity-constrained optimisation and multi-property optimisation. Strengths: - The authors present a novel formulation for exploring chemical latent spaces and optimising molecular properties which is an important and relevant task within the pharmaceutical and molecular design domains. They present a few different versions of their method, including an implementation which can use a surrogate property prediction model to guide the flow to optimised chemical space, as well as an unsupervised implementation which aims to maximise structural changes to the molecule. - The authors perform an extensive evaluation on molecule optimisation related tasks, comparing a number of different instantiations of their framework. They also benchmark against a previously introduced model for latent space traversal and a random traversal strategy. - ChemFlow methods show very promising results in comparison to baselines, especially when only looking at top performing molecules or applying similarity-constrained optimisation. - The authors also present a useful analysis of the latent changes under the random traversal strategy and an explanation for why random traversal can work reasonably well. - The paper is mostly very well written and, the evaluations in particular, are very clearly presented and easy to follow. Weaknesses: - I find the methodology section on its own quite unclear since it's not clear how to actually use the objective functions that are outlined. Appendix sections D4 and D5 are helpful but ideally it would be possible to follow the main text on its own. Particularly, I think the text would benefit from showing the full loss function in the methodology and including a short outline of the training and sampling procedures and referring to the appendix. - The baselines for some tasks are a bit weak, particularly for the unconstrained molecular optimisation. For this task techniques like evolutionary algorithms and reinforcement learning fine-tuning have been proposed and widely used before. It would be very useful to see a comparison of ChemFlow with methods like these, as well as an evaluation of the training and sampling time for each. Technical Quality: 4 Clarity: 3 Questions for Authors: - For the unsupervised guidance, when you match flows with properties, what the correlations are computed between? Does this require you to have an existing dataset of molecule-property pairs? - For the unsupervised cases did you experiment with different values of k? Which values of k were used? It seems to me that k might need to be very large in general in order to find a flow which matches with an arbitrary property. Other suggestions: I assume equation 8 should have $\phi^k$ instead of $\phi$? Additionally, the ordering of t and z in $\phi(.,.)$ or $\phi^k(.,.)$ is inconsistent - compare figure 1, the caption for figure 1 and equation 11 with all the other places were $\phi$ is used. Confidence: 3 Soundness: 4 Presentation: 3 Contribution: 3 Limitations: - While the authors evaluate their approach on optimising two properties simultaneously it's unclear how well this would work with a larger number, since their approach relies on simply adding the guidance terms together. - In this study the authors used a VAE with a fixed input size. It's unclear how easy it would be to apply a similar approach to a model with an arbitrary number of elements in an input or latent sequence, such as chemical language models or many diffusion-based models, which are much more commonly used in practice for molecular generation. - As far as I can tell the method as it stands requires a latent space optimisation to be done for every sample. This could lead to much longer sampling times than other methods such as RL fine-tuning which allows samples to be generated as normal but from an optimised model. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: C1: The baselines for some tasks are a bit weak, particularly for the unconstrained molecular optimisation. It would be very useful to see a comparison of ChemFlow with methods like EA and RL fine-tuning. A: Thanks for the suggestion. As our method focuses on the latent space of deep generative models, we compared mostly with methods for molecular optimization and traversal in a similar setup. However, we agree with the reviewer that the paper would benefit from additional baselines. We add an evolutionary algorithm-based (EA) approach to optimize molecules in the latent space. The pseudocode is provided as Algorithm 1 in the uploaded PDF in the general response. For a fair comparison, all methods in Table 1 in the uploaded PDF have the same number of oracle calls. The results in Table 1 show that our methods outperform all EA approaches. It is possible to use reinforcement learning to guide the search in the latent space of molecular generative models but the main reason to use the latent space of generative model is to avoid the discrete nature of molecular structures and instead conduct optimization over a continuous space. We believe it will be nontrivial to propose a new reinforcement learning algorithm and thus leave it as a future study. C2: For the unsupervised guidance, when you match flows with properties, what the correlations are computed between? Does this require you to have an existing dataset of molecule-property pairs? A: We compute “the correlation between the property and a natural sequence (from 1 to time step t) along the optimization trajectory” (line 177). Specifically, we compute the following measurement: $$Spearman([P(m_1), P(m_2), …, P(m_t)], [1,2,...,t])$$ where $P(\cdot)$ is the function to measure the real chemical property of a given molecule $m_t$ at time $t$. Even though we do not require access to a dataset of molecule-property pairs, we do rely on minimal supervision to match the direction to the list of properties it may control. In reality, we do this by scoring the molecules using oracle functions. C3: For the unsupervised cases did you experiment with different values of k? Which values of k were used? We observe as long as the value of k is larger than the actual number of properties, the results will not be impacted much. We agree having an approximation of the number of properties is a prior knowledge of determining the hyperparameters, but a good practice is always to start with a relatively large k and select the active ones after training. C4: While the authors evaluate their approach on optimising two properties simultaneously it's unclear how well this would work with a larger number, since their approach relies on simply adding the guidance terms together. A: Thanks for the constructive advice. We get motivated by the disentanglement literature so we mainly focus on optimizing individual properties. Assuming each property is an energy $\phi^k$ so the stationary distribution is a Boltzmann distribution $p^k(x) \sim exp(\phi^k)$, then the summation of the guidance terms (i.e. energies) corresponds to sampling from the product distribution $\pi \sim exp(\sum \phi^k) = \prod exp(\phi^k)$. Even though this implicitly assumes independence among different properties, it is commonly used (also known as product of expert [1]) in machine learning, e.g. energy-based models [2]. We will leave how to leverage the correlation between different objectives as future work. > [1] Hinton, G.E., 2002. Training products of experts by minimizing contrastive divergence. Neural computation, 14(8), pp.1771-1800. > > [2] Du, Y. and Mordatch, I., 2019. Implicit generation and modeling with energy based models. Advances in Neural Information Processing Systems, 32. C5: In this study the authors used a VAE with a fixed input size. It's unclear how easy it would be to apply a similar approach to a model with an arbitrary number of elements in an input or latent sequence, such as chemical language models or many diffusion-based models. A: Thanks for the question. The fixed-length VAE model supports any input with a length less than its maximum limit. Indeed it can be less efficient for varied-length input such as text, however, it has still been widely used in languages and other sequence data. Moreover, despite that we validate the proposed method on a specific problem, molecular design, and select a fixed-length VAE model as the generative model, the method is not limited to fixed-length input. As long as the model architecture has a well-defined latent space, e.g. [3] uses the bottleneck of U-Net as the latent space for diffusion models and [4] similarly in the attention head of large language models, it is possible to adopt our method in other networks to discover meaningful properties. > [3] Kwon, M., Jeong, J. and Uh, Y., Diffusion Models Already Have A Semantic Latent Space. In The Eleventh International Conference on Learning Representations. > > [4] Li, K., Patel, O., Viégas, F., Pfister, H. and Wattenberg, M., 2024. Inference-time intervention: Eliciting truthful answers from a language model. Advances in Neural Information Processing Systems, 36. C6: The method as it stands requires a latent space optimisation to be done for every sample. This could lead to much longer sampling times than other methods such as RL fine-tuning which allows samples to be generated as normal but from an optimised model. We focus on pre-trained generative models, where multiple objectives can be composed or removed at any time, while we admit this necessitates the extra sampling time as the model itself does not directly sample from the desired distribution, RL-based fine-tuning would limit the flexibility of the pre-trained model once it has been tuned for a specific task. The extra inference time is also minimal as it only requires a surrogate model evaluation (which is a relatively simple MLP model). --- Rebuttal Comment 1.1: Comment: C7: I find the methodology section on its own quite unclear since it's not clear how to actually use the objective functions that are outlined. Appendix sections D4 and D5 are helpful but ideally it would be possible to follow the main text on its own. Particularly, I think the text would benefit from showing the full loss function in the methodology and including a short outline of the training and sampling procedures and referring to the appendix. A: Thanks for the suggestion. We will add the training objective $\mathcal{L} = \mathcal{L_r} + \mathcal{L_\phi} + \mathcal{L_\mathcal{P}}$ for supervised scenario and $\mathcal{L} = \mathcal{L_r} + \mathcal{L_\phi} + \mathcal{L_\mathcal{J}} + \mathcal{L_k}$ for unsupervised scenario to Sec 3.1 in the revised manuscript. We will also briefly discuss them and link them to the pseudocodes in the appendix. C8: Inconsistency in Section 3 and Figure 1 A: Thanks for pointing out the mistakes. We fixed the notation in Section 3 and Figure 1 to make everything consistent with $\phi^k$. --- Rebuttal Comment 1.2: Comment: Thank you for your thorough response and for conducting extra experiments. Most of my concerns have been addressed, however, if my understanding of the method is correct, I think the following two limitations still remain: 1. I agree that RL fine-tuning methods (eg. REINVENT as a representative example) don't optimise within the latent space but they are attempting to solve the same problem as ChemFlow - sampling molecules which optimise some scoring function. Of course these methods have their own strengths and weaknesses compared to latent space methods but I still think a performance (and possibly evaluation time) comparison would be beneficial here. 2. The study doesn't address many scenarios that are likely to encountered in practice for molecular design, such as optimising many properties simultaneously and using larger generative models such as chemical language models. I believe VAEs are not really much in practice for molecular generation because single-step generation is too weak. I would still like to thank the authors for the very interesting ideas presented and I am happy to increase my score to 7. --- Reply to Comment 1.2.1: Title: Thank you for your comment Comment: We appreciate again the reviewers' efforts in providing useful comments that greatly helped us improve the manuscript. Given the limited rebuttal period, we cannot finish the additional experiments, but we will add them to the camera-ready version.	Rebuttal 1: Rebuttal: We thank all the reviewers for their valuable feedback that helps us improve the manuscript. We appreciate reviewer’s common sentiment that our work is novel, general, applicable, and well written. We are also glad that reviewers compliment our work has extensive experiments showing the effectiveness and significance of proposed methods. We will first address the points raised by more than one reviewer in this general response and then provide individual responses to each reviewer. 1. Broader applications of the proposed approach to other tasks. This paper mainly focus on the problem of molecular design and optimization. However, we do not foresee any issues attached to our proposed method to be applied to other tasks. As long as the generative model architecture has a well-defined latent space, e.g. similarly in the attention head of large language models [1], it is possible to adopt our method in other networks to discover meaningful properties. For example, our framework can be applied to protein design tasks. Previous work uses gradient-based method to optimize protein in the latent space [2]. This is generalized as traversing with gradient flow in our framework. Diffusion has deomonstrated its powerful ability in generating de novo proteins with desired properties [3]. By define a latent space for diffusion models, such as using the bottleneck of U-Net [4], it is also possible to extend our method to diffusion models for de novo protein generation. > [1] Li, K., Patel, O., Viégas, F., Pfister, H. and Wattenberg, M., 2024. Inference-time intervention: Eliciting truthful answers from a language model. Advances in Neural Information Processing Systems, 36. > > [2] Castro, E. et al. (2022) ‘Transformer-based protein generation with regularized latent space optimization’, Nature Machine Intelligence, 4(10), pp. 840–851. > > [3] Watson, J.L. et al. (2023) ‘De novo design of protein structure and function with RFdiffusion’, Nature, 620(7976), pp. 1089–1100. > > [4] Kwon, M., Jeong, J. and Uh, Y., Diffusion Models Already Have A Semantic Latent Space. In The Eleventh International Conference on Learning Representations. 2. Mean/STD/median of the scores in Table 1. In addition to reporting the top 3 scores, we computed the mean and standard deviation for the top 100 molecules after unconstrained optimization. Each entry in the table below follows the format `mean ± std (median)`. The table shows that our methods have overall the best optimization performance. In addition, HJ exhibits better performance on mean and standard deviation than on top 3, showing that minimizing the kinetic energy is efficient in pushing the distribution to desired properties. \| Model \| plogP $\uparrow$ \| QED $\uparrow$ \| ESR1 Docking $\downarrow$ \| ACAA1 Docking $\downarrow$ \| \|-------------\|--------------\|------------\|-------------\|-------------\| \| Random \| 2.345 ± 0.386 (2.259) \| 0.903 ± 0.014 (0.902) \| -9.127 ± 0.360 (-9.015) \| -8.454 ± 0.316 (-8.390) \| \| Chemspace \| 2.580 ± 0.406 (2.446) \| 0.907 ± 0.014 (0.906) \| -9.523 ± 0.409 (-9.395) \| -8.749 ± 0.356 (-8.640) \| \| Gradient Flow \| 2.664 ± 0.382 (2.537) \| 0.910 ± 0.012 (0.908) \| -9.452 ± 0.338 (-9.365) \| -8.735 ± 0.337 (-8.650) \| \| Wave (spv) \| 2.536 ± 0.439 (2.388) \| 0.903 ± 0.015 (0.898) \| -9.630 ± 0.399 (-9.525) \| -8.764 ± 0.344 (-8.650) \| \| Wave (unsup) \| 1.736 ± 0.401 (1.610) \| 0.845 ± 0.014 (0.840) \| -9.074 ± 0.329 (-9.000) \| -8.813 ± 0.265 (-8.745) \| \| HJ (spv) \| 2.482 ± 0.397 (2.382) \| 0.899 ± 0.017 (0.894) \| -9.544 ± 0.322 (-9.460) \| -8.792 ± 0.332 (-8.675) \| \| HJ (unsup) \| 3.405 ± 0.254 (3.377) \| 0.911 ± 0.009 (0.909) \| -9.132 ± 0.321 (-9.090) \| -8.668 ± 0.243 (-8.630) \| \| LD \| 2.463 ± 0.388 (2.399) \| 0.905 ± 0.014 (0.903) \| -9.400 ± 0.360 (-9.300) \| -8.709 ± 0.372 (-8.585) \| Pdf: /pdf/af5c52991fc26b3b5c2048c9868ee5675a8c8bcc.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Images that Sound: Composing Images and Sounds on a Single Canvas	Accept (poster)	Summary: This paper explores the feasibility of synthesizing spectrograms (images that sound) that simultaneously look like natural images and sound like natural audio. This paper proposes a zero-shot approach, which leverages pre-trained text-to-image and text-to-spectrogram diffusion models that operate in a shared latent space, and denoises noisy latents with both the audio and image diffusion models in parallel. This paper shows quantitative evaluations and perceptual studies to claim the proposed method is able to generate spectrograms that align with a desired audio prompt while also matching the corresponding visual appearance. Strengths: + The topic introduced in this paper is very interesting and inspiring. + The paper is clearly written, providing detailed explanations for easy understanding and reimplementation. The proposed method's capacity is fairly claimed and supported by convincing experimental results. Weaknesses: - Technical contribution is limited. The proposed method combines two existing latent diffusion models (audio and visual), weighted integrate noises from these two processes to ensure semantic consistency for both modalities. Additionally, another existing diffusion model is used for colorization. The technical innovation appears incremental, raising concerns about the novelty of the contribution. - The capability of the proposed model is not high. Despite the inspiring topic, the generated audio and visual quality show a noticeable performance gap compared to state-of-the-art generators. Ensuring consistency of both modalities in one image may result in less diverse outputs for audio and visual generation, potentially failing to accurately reflect prompt details. Technical Quality: 3 Clarity: 3 Questions for Authors: Please see the weaknesses section for my major concerns. Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: The authors have explained the current limitations, and potential negative social impact 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 their valuable feedback. Below are our responses.   Technical contribution The reviewer appears to have taken a narrow, algorithm-centric view of what constitutes a contribution. We note that this seems to be the major complaint in their (unusually short) review. Our work in fact makes a number of contributions. It is the first to propose the idea of generating examples that are natural in visual and audio signals, thereby exploring the intersection of two seemingly very different distributions. We are not aware of any work in the field of multimodal learning that has addressed this problem before. Beyond the novelty of this problem formulation (as acknowledged by mkQc, RECb, and quDM), the fact that we can find such examples is an interesting empirical contribution; it was not obvious ex ante that this could be done. Finally, we feel that our approach's simplicity is a major strength, not a drawback. While our approach draws inspiration from [38, 65], those approaches only combined noise from a single diffusion model. Showing that techniques from compositional generation can be adapted to this highly novel multimodal domain, and that (perhaps surprisingly) noise estimates from two different modalities' diffusion models can be successfully combined together, goes far beyond previous work.   Colorization To clarify, we provide colorized versions of the spectrograms in several qualitative examples using a post-processing procedure, since spectrograms are limited to grayscale. This is neither part of the evaluation nor a key component of our main method.   Model capabilities First, we want to stress that generating examples that can be both viewed as images and listened to as sound in a zero-shot manner is extremely challenging: it requires using a single signal to represent two very different modalities without any supervision. As noted in our limitations section, the nature of this task forces the model to produce examples that may not be as natural as those from specialized models in each individual modality, since many visual patterns are improbable under audio models, and vice versa. Interestingly, our model generates high-quality results in both modalities despite these constraints. We have also shown that our method significantly outperforms several challenging baselines and ablations, providing further evidence for its abilities.   We hope these comments have addressed the reviewer’s questions. We would like to thank them for their time and ask that they consider raising their score for our paper. --- Rebuttal Comment 1.1: Comment: Thanks for the authors' response. However, I think I need to re-clarify my concerns after reading the response. 1) Technical contribution. I'm a little bit confused about the definition of "narrow, algorithm-centric view" and "unusually short reviews". I agree with the novelty and contribution of bringing such an inspiring and interesting task to the community. The technical details, proposed solution and evaluations are all sound and fair. I don't have concerns or questions on the details of the work except for the overall questions. So I mentioned about my concern only on the "technical contribution" side, which specifically means the novelty in terms of bridging the existed methods is a simple way. Indeed, I agree that simplicity is an advantage. So I list this concern as one of the possible weaknesses for the reviewers and AC to judge thoroughly. Just to clarify, I will only consider this part as one of my concerns but not a critical issue of this work that blocks it from publishing. 2) Colorization. This is not my major concern or even a question. I mentioned this because of Line 151 "we use Factorized Diffusion [37] to colorize", to support my concern on the technical contribution reviews. 3) Model capabilities. The model capability is indeed my major concern. I understand the task is a challenging one, but sometimes we as reviewers can have different standard to balance the capacity and an interesting task for a conference paper. I acknowledge that the authors have shown their capacity and advantages on fair evaluation scope. But after reading the paper and response I still feel it would be a problem for the proposed method to scale on general audio-visual examples. A more strong response on this side with more detailed explanations on what case can generally work and what can't, or potential solutions on that as well as analysis etc. can all help solve my concerns. Given the consideration above, I gave the borderline reject rating. I look forward to have more fair discussion on these side and will be very open to change my mind. It won't bother me if the paper gets accepted even with my current rating. Sorry for causing the misunderstanding from my previous reviews. I think this can better clarify my points. --- Reply to Comment 1.1.1: Comment: We thank the reviewer for the further clarification about their reviews. Below are our new responses.   Technical contribution Our main method is simple but non-trivial for combining noise estimates from two different modalities' diffusion models, which no prior work has explored. Besides our main method, we also proposed two other methods called imprint and SDS baseline that generate images that sound examples from different perspectives (L174-188). Overall, we believe our work makes significant technical contributions. For clarification, colorization is not one of our claimed contributions. We simply use it to improve the visualization quality of the results.   Model capabilities The reviewer states that their primary concern is a lack of analysis of the capabilities of our model. We discussed some of them in L257 and L293. Further, we give a detailed explanation below: First, we want to emphasize that the nature of this task inherently forces the model to produce examples that may not appear as natural as those from specialized models in each modality, as many visual patterns are unlikely to align with audio models. In other words, realistic examples are constrained to the overlapped distribution between both modalities, which inherently limits the quality of the generated results. Furthermore, our experiments show that we outperform many other possible approaches, highlighting the capability of our approach. Our results also qualitatively outperform artist-created examples, which often produce random noise (e.g., Aphex Twin and others [9]). Through our experiments, we observed that our method generally performs well with "continuous" sound events (e.g., racing cars or train whistles) and simple visual prompts. Continuous sounds typically produce spectrograms with high energy distributed across time and frequencies, resulting in “white” spectrograms. This allows our model to effectively reduce sound energy, creating visual patterns that align with the audio. Simple visual prompts with object or scene nouns provide the diffusion models with more flexibility during denoising, enabling sampling from the overlapping distributions of images and spectrograms. However, more complex prompts could push the models into highly constrained distributions where images that sound are less likely to be generated. Generating discrete sounds (e.g., dog barking or birds chirping) is more challenging due to their sparse energy distribution. In these cases, the models are more constrained, making it difficult to produce visual content with clear edges and structures aligned with sound onsets, leading to less satisfactory results sometimes. Additionally, we emphasize that some prompt pairs may not have overlapping image and spectrogram distributions, making it impossible to create meaningful examples. For instance, combining the visual prompt `starry night` with the audio prompt `playing guitar` leads to a conflict, where the image modality tends toward a dark image, while the audio suggests a brighter one. Lastly, we note that our use of off-the-shelf Stable Diffusion, trained on $512 \times 512$ RGB images, to generate $256 \times 1024$ grayscale images directly could potentially limit our model’s capabilities. The performance could be possibly improved by having a specific image diffusion model that is suitable for this task. We will include a more detailed analysis in the manuscript.   We hope these comments have addressed the reviewer’s questions	Summary: The paper proposes using pretrained text-to-image and text-to-speech diffusion and leveraging their compositional property to generate spectrograms that look like images and can be also be converted into meaningful sounds. The work is motivated by applications in art. The paper also curates a set of text prompts for conditioning the diffusion models. Besides, it evaluates the generated spectrograms using both automatic and human evaluation. In automatic evaluation, it measures both intra-modal similarity between the generated output and the modality-specific text prompts using CLIP-style models. In human evaluation, human subjects are asked to rate the output compared to baselines' on the basis of both intra- and cross-modal similarity between the generated output and the modality-specific text prompts. Furthermore, to tackle the lack of baselines for the task, the paper introduces two baselines by adapting existing methods, and shows that the proposed method performs better than the baselines across different evaluation types and metrics. Finally, the paper also provides good qualitative examples that show the promise of the idea. Strengths: 1. Interesting idea: the idea of leveraging pretrained diffusion models and their compositionality to render spectrograms that look like real images and sound like real sounds is interesting and could have useful applications in art, as mentioned in the paper 2. Extensive evaluation and good qualitative results: the paper extensively evaluates its model using both automatic and human evaluation, different evaluation metrics, and compares against different baselines despite the lack of existing methods for the task. Besides, it does important ablations of its method, which helps better understand the role of different design choices. Finally, the paper provides good qualitative examples, which help further demonstrate the strengths of the idea. 3. Useful baselines: to tackle the lack of existing methods, the paper proposes two meaningful baselines for the task, which not only facilitate better model evaluation, but can potentially be useful for future work on this topic Weaknesses: 1. Text is unclear / poorly structured at parts: i) L21-23, "We hypothesize ... share statistical properties ...readily process": what kind of statistical properties is the paper referring to? Clear examples in the next version could help a reader. ii) It's probably better to put the application/motivation para (L29-37) before the para in L21-28. The current order leaves a reader guessing the use of the work for quite a bit (at least that was the case with me) 2. Importance of shared latents (L72 and elsewhere): I am not entirely convinced by the current content of the text why a model that does not share latents won't work. There is no model analysis/ablation for this claim as well. I think that if the model is able to work even with different prompts for the text-to-image and text-to-audio model, it might work with separate latent space as well. 3. Quantitative metrics are meaningful? if CLIP and CLAP are given equal weightage in table 1, auffusion is the strongest model, but obviously it isn't. This makes me wonder if these standalone quantitative metrics are even meaningful for this task. 4. Lack of other standard quantiative metrics: the paper does not evaluate the generated outputs using standard metrics [1, 2] like FID, inception score, etc. 5. Human study setup and results are not entirely clear. i) In L208-9, the paper says that most of the time the SDS baseline collapses to either modality. If that is true, how come the win rate against SDS is so much higher than 50% for both audio and visual quality? ii) Why are the examples hand-picked (L218) for human evaluation, shouldn't they be randomly sampled instead? iii) It's not clear how the cross-modality alignment evaluation (L222-3, and upper and lower last row in table 2) makes sense when the text prompts to the two diffustion models are independent 6. L278, "attractive balance between CLIP and CLAP scores": the choice of weightage on CLIP and CLAP for determining t_a and t_v in table 3 seems arbitrary. If they are given equal weightage, the best values would be t_v = 0.8 and t_a = 1.0? 7. What's the rationale behind limiting the prompts to the ones listed in table 4 given that the individual diffusion models work with a much broader set of prompts? 8. Minor: i) L264, "simply found adversarial examples against the vocoder": the meaning of this phrase was unclear to me Refs: [1] High-resolution image synthesis with latent diffusion models. Rombach et al. CVPR 2022. [2] Auffusion: Leveraging the power of diffusion and large language models for text-to-audio generation. Arxiv 2024. Technical Quality: 3 Clarity: 3 Questions for Authors: Could the rebuttal comment (more) on the following 1. What kind of statistical properties is the paper referring to in L21-23: "We hypothesize ... share statistical properties ...readily process"? 2. importance of shared latents (L72 and elsewhere) and if it is possible to provide an analysis/ablation to support the claim. See weakness 2 for details. 3. how meaningful the quantiative metrics are (see weakness 3 for details) and if it is possible to report other standard image and audio generation metrics (see weakness 4 for details) 4. i) why the model wins against SDS by a large margin even when "SDS baseline often fails to optimize both modalities together, producing either spectrogram or image content only" (L208-9). See weakness 5i for details. ii) why the samples for human evaluation are cherrypicked. See weakness 5ii for details. iii) why the cross-modality alignment metric makes sense when the prompts to the two diffusion models are not shared. See weakness 5iii for details. 5. how the CLIP and CLAP scores are weighted while determining which model is better (details in weakness 6 and also related to Q3) 6. the rationale behind limiting the prompts to the ones listed in table 4 given that the individual diffusion models work with a much broader set of prompts Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: The paper has discussed its limitations and 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 comprehensive feedback. Below are our responses.   Importance of shared latent spaces This seems to be a misunderstanding: the latent spaces must be shared during joint sampling because if they weren't, then the latent vector would be decoded to two completely different images in the two modalities, which would trivialize into a different problem. Moreover, diffusion would fail if the latents did not span the same space or if the noise schedule differed. Finally, we stress our paper does include a model that works even without a shared latent space. The SDS version of the model (L174-182) successfully avoids this constraint because it directly backpropagates into pixels. It uses a pixel diffusion method (DeepFloyd) and an audio latent diffusion model (Auffusion). While it is outperformed by our joint sampling approach, this result suggests that the shared latent space is not strictly necessary. We will clarify this.   Writing of introduction Statistical similarities between images and audio have been well established in previous work [A, B], which we would be happy to cite for clarity. However, we note that we have already provided several examples in the introduction: 1) we point out that both spectrogram and images have similar patterns that are famous "objects of study" in the natural image statistics (e.g., lines and edges) (L22-23), 2) the fact that frozen visual features have been surprisingly successful for audio models (L18-20). If there were no common statistical similarities between the two signals, then neither property would hold. Regarding the presentation order, we feel that the image statistics motivation helps readers understand the importance of the problem and motivates the generative modeling approach, which is why we described it before the task itself. We note that Fig.1 and its caption already present the work in a style that is quite similar to the reviewer's suggestion.   Quantitative metric We report Stable Diffusion and Auffusion as single-modality models, serving as upper and lower bounds for reference. CLIP and CLAP metrics are meaningful when compared with multimodal baselines, showing how well the generated results align with their respective prompts. These two networks have different common output ranges, so naively summing them without calibration would emphasize one score at the expense of the other. To fairly evaluate overall performance, we normalize each score based on the lower and upper bounds listed in Tab.1 and then sum them. As a result, in Tab.3, $t_v=0.9, t_a=1.0$ achieves the highest score of 1.154, while $t_v=0.8, t_a=1.0$ scores 1.139. For the results of FID and FAD metrics, please refer to the general response. These details will be included in the revised version.   SDS baseline We note that collapsing to a single modality does not necessarily mean that that modality is generated perfectly. It simply means that the other modality is not generated at all. Therefore, despite the collapse, the result may still be of poor quality, especially considering that the method is still jointly optimizing two losses. Additionally, due to the limitations of the SDS loss [83], the generated images tend to be overly saturated, while the audio is often distorted. As a result, the outcomes are generally inferior to our main method. For more examples, please refer to the supplementary video.   Human study For the human study, we compare our 3 proposed models' ability to generate examples that are qualitatively and artistically appealing. For each method, we generate a fixed number of samples per prompt pair and hand-select the best qualitative result. This also avoids having the 2AFC task performance determined by a model's failure rate (e.g., SDS collapsing to one modality), which would dominate results. We note that the random results used in the quantitative evaluation can be found in Fig.8. We will clarify this in our manuscript.   Cross-modality alignment We explain the cross-modality alignment metric in L623-629. This metric measures how well the visual structure of the image aligns with that of the spectrogram, rather than measuring semantic alignment, e.g., how an image edge of castle towers corresponds to the spectrogram onset pattern of ringing bells, or how an image of dogs matches the audio pattern of barking. Please see Fig.10 for the survey question. We'll clarify this in a revision.   Prompt selection Our quantitative evaluation closely follows Visual Anagrams [38], randomly selecting 5 discrete (onset-based) and 5 continuous sound classes from VGGSound Common as audio prompts. For image prompts, we randomly chose 5 object and 5 scene classes, creating 100 prompt pairs through random combinations for evaluation and generating 10 samples for each. Our method scales easily for more prompts, whereas SDS baselines took more than 1,000 hours in total to generate current results for evaluation, taking two hours per example. Therefore, we kept the evaluation to a manageable scale.   Phrase of adversarial We thank the reviewer's suggestion. By this phrase, we meant spectrograms that the vocoder ignores, i.e., generating waveforms that do not match the inputs. We will rephrase this in a revision.   We hope these comments have addressed the reviewer’s questions. We would like to thank them for their time and ask that they consider raising their score for our paper. [A] Mynarski & McDermott. Learning Mid-Level Auditory Codes from Natural Sound Statistics, Neural Computation 2018. [B] McDermott & Simoncelli. Sound texture perception via statistics of the auditory periphery: evidence from sound synthesis. Neuron 2011. --- Rebuttal 2: Title: Response to rebuttal Comment: Thanks for the reponses. Could you comment on/clarify the following? 1. "Quantative metrics": how do the baslines perform on the combined metric? 2. "Human study": is the idea of hand-picking for comparative human evaluation of generative models common? I think a better alternative would be to run the models with the same prompts multiple times and then compare all possible pairs, for computing the win/loss rates. It's undoubtedly more expensive but potentially more 'foolproof' . --- Rebuttal Comment 2.1: Comment: We thank the reviewers for their time. Below are our clarifications: 1. Quantitative metrics: we provide the combined score (CLIP+CLAP) for baselines below: \| Method \| Modality \| CLIP + CLAP \| \|:---------------------------------\|:------------------:\|:----------:\| \| Stable Diffusion \| $\mathcal{V}$ \| 1.0 \| \| Auffusion \| $\mathcal{A}$ \| 1.0 \| \| Imprint \| $\mathcal{A}$ \& $\mathcal{V}$ \| 1.04 \| \| SDS \| $\mathcal{A}$ \& $\mathcal{V}$ \| 0.70 \| \| Ours \| $\mathcal{A}$ \& $\mathcal{V}$ \| 1.15 \| 2. Human study: Due to constraints in the method or experiments, it is relatively common for human studies to not be completely random. We provide a short list of citations and explanations below. In our case, we specifically choose to study the best-case scenario for the following reasons: - "Images that sound" are quite hard to generate. (In fact, prior to this work, it was not clear at all that they even existed.) Not all text prompt pairs give good results, and some prompt pairs are just impossible. As such, we envisioned that a user would use our method to iteratively sample multiple times, choosing the result that they preferred most. To mimic this use case, we designed our human study to quantify the best-case results. - We find that it is very hard to evaluate "images that sound" on Amazon Mechanical Turk, primarily due to the fact that almost all participants did not understand the concept of a spectrogram. As a result, it is quite difficult to get precise evaluation metrics when using random results, and financially prohibitive to reduce error bars to reasonable levels. The best-case evaluation circumvents these difficulties. Moreover, we point out that we do in fact evaluate random results systematically and quantitatively, in a scalable fashion, with CLIP and CLAP metrics in Table 1 and FID and FAD metrics in the general rebuttal response above. We would be willing to move the human study to the appendix if the reviewer believes it would improve the manuscript. [1] "PhysDreamer: Physics-Based Interaction with 3D Objects via Video Generation", Zhang et al. conduct human studies on specifically 7 chosen and captured environments. [2] "WonderJourney: Going from Anywhere to Everywhere", Yu et al. use a total of 6 hand-designed videos for human evaluation. [3] "TEXTure: Text-Guided Texturing of 3D Shapes", Richardson et al. specifically pick 10 text prompts to evaluate on. [4] "DreamGaussian4D: Generative 4D Gaussian Splatting", Ren et al. conduct a human study on 12 specifically chosen images.   We hope these comments have addressed the reviewer’s questions. --- Rebuttal 3: Title: Response to rebuttal 2 Comment: Thanks for the additional table. I would urge the authors to add all additional results and clarifications to the next draft. Regarding hand-picking outputs for human evaluation, I skimmed all 4 papers referred to in the latest response from the authors, but couldn't find any mention of hand-picking outputs. They do control the inputs, but that's in essence similar to controlling the text prompts in this work. However, the other arguments made by the authors are not very unreasonable. As for pushing the user study to supp., I would advise against it, as human user study is arguably the best way to evaluate these generative models, as shown in other papers in this area, including the ones cited in the paper and the rebuttal responses, as well, especially when their applications are mostly artistic in nature. --- Rebuttal Comment 3.1: Title: Author Reply Comment: We thank the reviewer for their quick response. We will include all additional results and clarifications in our manuscript as the reviewer suggests. Additionally, we will keep the human study in the paper also as suggested by the reviewer, but make it abundantly clear that we are evaluating the best-case performance of all methods, and clearly explain the rational for doing so as listed above. We agree with the analysis that human studies are the best way to evaluate methods that are artistic in nature, as is the case with our method. We also agree with the reviewer that the cited papers do not explicitly mention hand-picking. We cite them to show that it is common for human evaluations to not be entirely random, in terms of prompts chosen, but also in terms of model inputs in general.	Summary: The authors propose to leverage pre-trained text-to-image and text-to-spectrogram diffusion models, and de-noise noisy latents with both models in parallel during reverse process. They show that the proposed method can generate spectrogram aligned with audio prompt while having visual appearance of the image prompt with quantitative analysis as well as human study. Strengths: - Proposed method has very interesting application, and can potentially provide new research direction in multimodal representation learning and generation. - Proposed method leverage pre-trained diffusion models in both modalities to achieve listenable spectrograms with meaningful visual semantic properties, which has application in creative domain. - This paper is clearly written and easy to follow, human study provides different perspective of proposed method compared to other baselines, and ablation study for vocoder, warm-starting and guidance scale presented in section 4.5 provide more thorough heuristics. Weaknesses: - Text prompts used for generating both spectrogram and image are mostly templating based, and composed only with simple object nouns. It would be interesting to show some generated examples on more complicated prompts with compositions of objects, this helps to provide a view into how proposed method can be scaled up for future directions. - There is lacking in depth discussion in the choice of including "grayscale", "lithograph style", "black background", and the effect of excluding these style words. It might help to provide potential future directions in controlling the styles between the two modalities. Technical Quality: 3 Clarity: 4 Questions for Authors: - How are text prompts for both modalities (y_v, and y_a) selected, in Table 2, some of the pairs are the same objects, some of them are different, are there any rationale how these selections are made? Confidence: 4 Soundness: 3 Presentation: 4 Contribution: 3 Limitations: - The text prompts curated in this work is limited to only a few objects, it would be beneficial to include some methods to curate a richer and diverse prompts. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for their positive and comprehensive feedback. Below are our responses.   Text prompt design We note that our paper already contains some examples with prompts that describe visual scenes, such as in Fig. 8, where we use the relatively complex text prompt of `"a painting of a blooming garden with many birds, grayscale"`. We intentionally used simple text prompts with object or scene nouns for most experiments to allow the diffusion models to have more flexibility during the denoising process, since we aim to sample from the intersection of the image and spectrogram distributions. In this setting, the models are much more constrained than they would be in normal synthesis. Introducing more complex prompts could push the models to sample from even more constrained distributions where images that sound are less likely to exist, leading to less satisfactory results.   Style words Visual diffusion models are capable of generating RGB images, but spectrograms are only one channel. We therefore use style words like `grayscale` or `black background` to nudge the image denoising process toward a distribution that matches the spectrograms. As suggested by the reviewer, we conducted ablation experiments by removing the grayscale style word. The results are shown in the table below. The model produces similar results, but (as expected) the image quality slightly decreases while the audio quality slightly improves. \| Exp \| CLIP ↑\| CLAP ↑ \| FID ↓ \| FAD ↓ \| \|:----------\|:----------:\|:----------:\|:----------:\|:----------:\| \| w/o `grayscale` \| 28.1 \| 33.7 \| 237.12 \| 18.09 \| \| w/ `grayscale` \| 28.2 \| 33.5 \| 226.46 \| 19.21 \|   Prompt selection For human studies, we manually create prompts based on the prompt banks from the quantitative evaluation by augmenting them and ensuring semantic correspondence between image and audio to create artistic examples for evaluation. Please see Tab.5 in the appendix for the exact prompts used.   We thank the reviewer for their time and hope these comments have addressed their questions. --- Rebuttal Comment 1.1: Comment: Thank to the authors for your answers. I still think this is an interesting idea and I am keeping my rating. --- Reply to Comment 1.1.1: Comment: We thank the reviewer for recommending acceptance. We appreciate this discussion and will incorporate the suggestions in our final version.	Summary: This paper proposes a very creative idea, synthesize spectrograms that simultaneously look like natural images and also sound like natural audio, which they call images that sound. The method is rather simple, and leverages two pre-trained diffusion models, one text-to-image and the other text-to-spectrogram. A method is proposed to leverage the shared latent space and generate samples that are likely under both models. Both qualitative and quantitative results are provided, demonstrating the effectivenss of the proposed method. Strengths: - The biggest strength of the paper is the idea, very beautiful! Though making such kind of art is not completely new, this is the first method that did this as a scalable task. It nicely leverage state-of-the-art diffusion techniques and creates a model that can generate such artistic images that sound. - The paper is also very nicely written, with clear motivation, problem statement and formulation, and nice illustrations and figures. - The related work is complete and sufficient details are provided for reproducibility. - The paper presents both quantiative and qualitative evaluation with nice ablation study, demonstrating the effectiveness of the proposed method. Weaknesses: There are no major weaknesses. One can argue that the method is too simple: it's basicially just combining existing techniques on diffusion, leveraging pre-trained diffusion models StableDiffusion and Auffusion, and also getting inspirations from recent image diffusion papers. Having said that, the system just works and it's more an idea paper, so I don't mind it's a simple method. Another weakness or question is that it would be good to provide some analysis of the shared latent space. Is there way to better interpret it? For example, would it be possible to doing some interporation in the latent space such that we can see some meangingful changes in both the image domain and audio domain. Apart from just being cool, it would also be nice to include more discussions on some more concrete potential applications of such a system. Technical Quality: 3 Clarity: 3 Questions for Authors: See weakness. Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: Yes, the authors have faithfully discussed the limitations of the proposed framework. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for their positive and valuable feedback. Below are our responses.   Simplicity We appreciate the reviewer's comment that this is a creative idea. We believe that its simplicity is in fact a major strength. While our method is simple, it is not obvious that noise estimates from diffusion models of two different modalities can be combined together during the reverse diffusion process. To our knowledge, we are the first to combine diffusion models from different modalities for multimodal composition. That this can be done by using applying ideas from compositional generation to a new domain is a benefit, rather than a drawback.   Shared latent space We thank the reviewer for the suggestion. We use the same pretrained VAE encoder and decoder to map between the latent and pixel spaces for the reverse diffusion process. Since we rely on an existing latent space, we did not specifically explore its interpolation capabilities. However, we see this as an interesting direction for future work.   Potential applications We thank the reviewer for the suggestion. Our work focuses on exploring the ``intersection" between the distribution of spectrograms and images, with images that sound being one artistic application. As we discussed in the paper, our approach could potentially be used in steganography to secretly embed images within audio for message delivery or vice versa.   We thank the reviewer for their time and hope these comments have addressed their questions. --- Rebuttal Comment 1.1: Comment: Thank the authors for the additional clarifications. I don't have further questions at this point. --- Reply to Comment 1.1.1: Comment: We thank the reviewer for recommending acceptance and valuable feedbacks for this work.	Rebuttal 1: Rebuttal: We thank the reviewers for their thorough comments and appreciate the recognition of the creativity of our work, described as "a beautiful idea" (mkQc) and "an interesting topic" (RECb, quDM, w6xJ). The acknowledgment of the "thorough evaluation" (mkQc, RECb, quDM) of our method and baselines is also valued. We answer some common questions below and provide new experimental results.   Our Contributions We want to emphasize that our paper goes beyond just a novel application of diffusion models. It also pioneers the exploration of the intersection between two very different distributions (images and audio spectrograms), a domain that has not been explored before. We use learned image and audio distributions from diffusion models to probe the overlapped distribution between these two modalities for free.   FID and FAD Evaluation Following reviewer quDM’s suggestion, we evaluated FID and FAD scores using generated examples from Stable Diffusion and Auffusion as reference sets respectively. As shown in the table below, our approach achieves the best performance. Note that FID and FAD are distribution-based metrics, and as our task focuses on generating examples that lie in a small subset of the natural image and spectrogram distribution, higher FID scores, in general, are expected. \| Method \| Modality \| FID ↓ \| FAD ↓ \| \|:---------------------------------\|:------------------:\|:----------:\|:---------:\| \| Stable Diffusion \| $\mathcal{V}$ \| -- \| 41.74 \| \| Auffusion \| $\mathcal{A}$ \| 290.29 \| -- \| \| Imprint \| $\mathcal{A}$ \& $\mathcal{V}$ \| 244.84 \| 29.42 \| \| SDS \| $\mathcal{A}$ \& $\mathcal{V}$ \| 273.03 \| 32.57 \| \| Ours \| $\mathcal{A}$ \& $\mathcal{V}$ \| 226.46 \| 19.21 \|	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Orchid: Flexible and Data-Dependent Convolution for Sequence Modeling	Accept (poster)	Summary: This paper introduces Orchid, a novel deep learning architecture that addresses the quadratic complexity of traditional attention mechanisms while still capturing long-range dependencies and enabling in-context learning. The key innovation is a data-dependent global convolution layer that dynamically adapts its kernel based on the input sequence using a dedicated conditioning neural network. Two simple conditioning networks are designed to maintain shift equivariance in the data-dependent convolution operation. The dynamic convolution kernel allows Orchid to achieve high expressivity with quasilinear scalability for long sequences. Experiments across language modeling and image classification tasks demonstrate that Orchid outperforms attention-based models like BERT and Vision Transformers with smaller model sizes. It also enables processing longer sequences beyond the limitations of dense attention layers. Strengths: The paper introduces Orchid, a novel deep learning architecture that addresses the quadratic complexity of traditional attention mechanisms while still capturing long-range dependencies and enabling in-context learning. The key innovation is a data-dependent global convolution layer that dynamically adapts its kernel based on the input sequence using a dedicated conditioning neural network. Two simple conditioning networks are designed to maintain shift equivariance in the data-dependent convolution operation. The dynamic convolution kernel allows Orchid to achieve high expressivity with quasilinear scalability for long sequences. Experiments across language modeling and image classification tasks demonstrate that Orchid outperforms attention-based models like BERT and Vision Transformers with smaller model sizes. It also enables processing longer sequences beyond the limitations of dense attention layers. The paper is well-written, with clear descriptions of the Orchid architecture and comprehensive empirical evaluation. Weaknesses: 1. Citation issue: On page 3, there seems to be an issue with the citation at the end of the page. Could the authors please clarify and correct this? 2. Computational complexity: Since the weights in the proposed method come from a neural network (data-driven), wouldn't this increase the computational complexity as the number of layers increases? In general, convolutional blocks do not have data-driven parameters. Could the authors provide more details on how the computational complexity scales with the number of layers? 3. Conditioning networks: To improve the understanding of the paper, could the authors provide more details about the two conditioning networks introduced in the manuscript? 4. Experiments: Which conditioning network is used in the experiments presented in the main paper? Clarifying this would help readers better understand the experimental setup and results. 5. Block-diagonal matrices: The authors mention the use of block-diagonal matrices in the MLP layers for dimension mixing. However, the paper does not provide an ablation study to assess the impact of this design choice on the model's performance and efficiency. Could the authors include such an analysis to justify the use of block-diagonal matrices and provide insights into their role in the overall architecture? 6. Interpretability and explainability: The paper does not provide a detailed analysis of the model's interpretability and explainability. Could the authors develop and discuss techniques to visualize and interpret the learned representations and decision-making process of Orchid? This would help improve the model's transparency and trustworthiness. Grammatical correction: - "Moreover, its allows for handling very large sequence lengths that are beyond the limitations of the dense attention layers." Technical Quality: 3 Clarity: 3 Questions for Authors: Please address the questions and concerns provided in the Weaknesses section Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The authors have talked about various limitations of the paper. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Comment: Thank you for your detailed review and valuable feedback. Your recognition of the contributions of the proposed Orchid architecture and the comprehensive empirical evaluations and also your valuable feedback is appreciated. In the following, we address the points you raised in your review. - W1: Citation issue at page 3: Thank you for bringing this to our attention. We will ensure that this issue will be fixed. - W2: Computational Complexity of Conditioning Networks We designed simple conditioning networks using $Conv1d()$ (1D depthwise linear convolution with a short kernel length, typically 3-5) in both the spatial and frequency domains. This architecture choice aims to minimize the number of parameters and computational overhead of the conditioning networks. As a result, the number of parameters does not grow with the sequence length. The computational complexity of $Conv1d()$ is $\mathcal{O}(L D)$, which scales linearly with the sequence length, while FFT computations scale quasilinearly with the sequence length ($\mathcal{O}(L \log L)$). It's worth noting that computing the projections for $K$, $Q$, and $V$ in transformers requires $\mathcal{O}(L D^2)$ computation. The runtime benchmarks provided in Appendix C.6 demonstrate the speed performance of Orchid compared to Attention and FlashAttention, highlighting its efficiency. - W3: More Details on the Two Conditioning Networks To model the convolution kernels dynamically as a function of the input, we designed two simple conditioning networks that maintain shift equivariance. We chose architectures that minimize parameters and computational overhead while being efficient. - Conditioning Network I (Equation 2): This network first applies a short convolution $Conv1d()$ on the sequence, then transforms the signal into the spectral domain using the Fast Fourier Transform (FFT). Then an absolute value is applied to preserve shift invariance of the kernel. Another short convolution $Conv1d()$ is then applied in the spectral domain. This combination of spatial and frequency domain filters effectively captures information from local neighboring tokens and spectral components. - Conditioning Network II (Equation 3): This network first applies two short convolutions $Conv1d()$ on the sequence to obtain two versions of the input sequences, $k'(x)$ and $q'(x)$. Similar to the previous approach, the signal is then transformed into the spectral domain and pointwise multiplied (to implement a fast cross-correlation). Finally, another short convolution $Conv1d()$ is applied in the spectral domain. This approach generalizes Conditioning Network I. Both of these conditioning functions are illustrated schematically in Figure 2.1. The output from these conditioning networks is used as the kernel of the long data-dependent convolution that globally mixes the sequence. - W4: Conditioning Network Used in Experiments We used Conditioning Network I for the experiments presented in the paper, as mentioned in Section C.2 of the Appendix (Experimental Details). Conditioning Network I is slightly more efficient in terms of speed and parameter counts. Based on the ablation study in the appendix, we selected Conditioning Network I for the language, vision, and audio experiments reported in the paper. We will add this clarification to the main body of the paper to ensure readers better understand the experimental setup and results for this selcetion. - W5: Impact of using Block-diagonal weights in MLP blocks: Indeed the impact of using M2-MLP blocks can be analyzed by comparing Orchid and M2. In the experiments, we compare Orchid with M2 of similar size, while both are using Block diagonal for MLP, the main difference between M2 and Orchid based architectures is that, in Orchid we deployed the proposed data-dependent long convolution while M2 is following Hyena in using a fixed long convolution. Therefore, the performance improvements observed in Orchid compared to M2 can be attributed to the data-dependent sequence mixing mechanism. Using Block diagonal for MLP indeed will result in a sparse implementation of a dense MLP so it reduces the overall number of trainable parameters and reduces computational complexity.	Summary: This paper introduces the Orchid block, a novel sequence modeling element that employs a convolutional operator with a sample-dependent generated kernel and an $O(n \log n)$ computational complexity with $n$ being a sequence length. The kernel, matching the input sequence length, captures both long- and short-scale dependencies. As would be expected of a similar sequence processing operation, the authors design the kernel generator to be translationally-invariant. The proposed architecture is evaluated on language modeling tasks and image classification (ViT), with experimental results suggesting it outperforms established models like BERT and ViT, as well as recent architectures such as Hyena Hierarchy and Monarch Mixer. Strengths: 1. The paper is well-written and provides clear justification for the core elements of the proposed architecture, including the choice of the sample-dependent, translation-invariant convolution kernel generator. 2. The proposed Orchid block is generally sound (see a question below). The experiments appear to be adequate to evaluate the proposed technique. 3. Empirical results demonstrate that the proposed architecture offers a notable improvement over established Transformer baselines, as well as Hyena Hierarchy and Monarch Mixer models (other recent long convolution-based models). The resulting architecture thus presents a promising advancement. 4. Inclusion of the synthetic in-context learning dataset highlighted an additional significant property of the proposed model: its ability to perform basic associative recall task even with very long sequences. Weaknesses: 1. One weakness limiting a potential significance of this work is that the proposed model cannot be currently applied to causal models. But this can hopefully be addressed in the future work. 2. While the proposed architecture is sub-quadratic and has the capability to efficiently process large inputs, it's crucial to evaluate its performance on real-world very long sequences (not just synthetic toy examples). Current approaches can scale Transformer-based models up to even millions of tokens and it could be quite crucial to demonstrate comparable performance for such long sequences as well. 3. While the design of the translation-invariant generator is sufficiently principled, there are quite a few seemingly arbitrary choices (some nonlinearities, specific function dependencies and more) and a more careful ablation study could be required in the future. Technical Quality: 3 Clarity: 3 Questions for Authors: 1. In Equation (3), it is not specified how the nonlinearity $\sigma$ is applied to a _complex_ Fourier spectrum $\mathcal{F}(\dots)$. For the resulting product of $\mathcal{F}^*(\dots) \odot \sigma(\mathcal{F}(\dots))$ to be translation-invariant, it is important that $\sigma$ preserves the phase of the complex number to which it is applied. It makes me conclude that the nonlinearity $\sigma$ acts on the magnitude of the argument, but preserves the phase. Another naive alternative would be to apply $\sigma$ to real and complex parts separately, but this would not preserve the phase and would thus break translational symmetry. Is my understanding correct? And if so, how is $\sigma$ computed in current experiments? If this is correct, I also urge the authors to clarify this point in the publication. 2. There are at least two [Fu et al., 2023] papers being referenced, which creates confusion. Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The paper does discuss several limitations, of which perhaps the most important one is that it cannot be currently applied to causal models. Authors also highlight the fact that the proposed layer can serve as an alternative to the cross-attention layer. Furthermore, several seemingly arbitrary choices in the model architecture could also be re-evaluated in the future work. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Comment: Thank you for your detailed and thoughtful review of our paper. We appreciate your recognition of the contributions and the strengths of our paper. In the following, we address your points. - W1: Although the current form of the Orchid is not compatible with causal and autoregressive models, since it uses the entire sequence as context, but this property makes it particularly suitable for encoder-based models like BERT and scalable candidate for diffusion models such as [1]. However, it is worth noting that recent studies [2, 3] have raised questions about the optimality of autoregressive models for inference in language models. - W2: For sequence of length, we have also evaluated the performance of the proposed method on a raw audio dataset with a large sequence of length 16k in Appendix C.5. While the standard Transformer model could not fit in GPU, Orchid performs on par with the state-of-the-art model on this long sequence modeling task. - W3: In addition to the ablation studies presented in Appendix C.2, we have conducted further ablation studies on the conditioning network architecture on associative recall task: - Comparison of Local Conv1D Choices: We evaluated different short depthwise linear convolution architectures in the conditioning network, as outlined in Equation (2). This ablation study compared: I) applying Conv1D() in the spatial domain followed by Conv1D() in the frequency domain (as proposed in Equation (2)), II) applying two layers of Conv1D() in the spatial domain only, and III) pplying two layers of Conv1D() in the spectral domain only. The results demonstrated that the proposed method of operating in both spatial and frequency domains (as in Equation (2)) which mixes information from neighboring tokens and spectral token shows the best performance. - Impact of Different Nonlinear $\sigma()$ Functions: We evaluated various nonlinear $\sigma()$ functions used in the Type II (cross-correlation) conditioning network (Equation (3)). The nonlinearities tested included \[ Tanh(), Sigmoid(), Softsign(), and Softshrink(), Identity()\], all acting on the magnitude of the argument. The results indicated that dropping this nonlinearity, $\sigma()$ in Equation (3), provides the best performance which is slightly better than nn.Softshrink() and nn.Tanh(). Also, among the nonlinearities those that cross zero perform better. Moreover, we also observe that Type II conditioning networks with Identity() and Softshrink() have faster convergence than Type I. Questions: - Q1: Applying Nonlinearity on the Magnitude in Type II Conditioning Network to Preserve Shift-Equivariance Thank you for your insightful question. As you correctly noted and also mentioned in the paper, each of K and Q should remain shift (translation) equivariant, in order that their cross-correlation satisfies the shift-invariance property for the conditioning network. Threfore the nonlinearity $\sigma()$ in Equation (3) should act on the magnitude of the argument while preserving the phase. This approach ensures that each of $ K $ and $ Q $ remains shift-equivariant. However, as mentioned in our new ablation study on the associative recall task, we found that dropping this nonlinearity yielded the best performance. We will include this clarification in the final version of the paper. - Q2: Duplicate References to [Fu et al., 2023] Thank you for bringing this to our attention. We will ensure that this duplicate reference will be fixed. [1] Lou, Aaron, Chenlin Meng, and Stefano Ermon. "Discrete diffusion modeling by estimating the ratios of the data distribution." ICML (2024) [2] Nan Ding, Tomer Levinboim, Jialin Wu, Sebastian Goodman, and Radu Soricut. Causal lm is not optimal for in-context learning. arXiv preprint arXiv:2308.06912, 2023. [3] Gregor Bachmann and Vaishnavh Nagarajan. The pitfalls of next-token prediction. arXiv preprint arXiv:2403.06963, 2024. --- Rebuttal Comment 1.1: Comment: I would like to thank the authors for their detailed response. Additional ablation studies and experimental results with a large (16k) sequence length help alleviate some of my concerns related to method performance. However, the fact that the proposed technique cannot be applied to causal models can still be seen as a limiting factor for its applicability. The authors cited several papers highlighting the limitations of the autoregressive modeling approach, however these types of models still appear to be the golden standard in numerous practical applications. It is also worth mentioning that some of the mentioned papers, are either considering very specific setups (in-context learning setups with the full attention over the context component), or propose to alleviate the limitations of next-token prediction models using modifications within the same causal setup. Considering concerns raised by other reviewers and the authors replies, I would like to keep my current favorable score.	Summary: This paper presents Orchid, a novel method that conditions long convolutional layers based on the input, to obtain global context and in-context learning abilities. This is achieved through the use of a conditioning network that acts both on the spatial and frequency domain to mix close spatial and spectral tokens, respectively. The resulting model surpasses other subquadratic models like Hyena and M2. It’s empirical results are compelling demonstrating the abilities of the proposed model over BERT and ViT-like models. Strengths: - The idea for input-dependence of convolutional kernels presented in the paper is novel, sound and very appealing. - The empirical evidence shows compelling evidence of the proposed model abilities. Weaknesses: - In my understanding, I am afraid that certain parts of the proposed model oversell what the model is capable of. Specifically, in Line 125, the authors argue that "This allows each input token to attend to the entire sequence with personalized, adaptive weights derived from its specific representation". However, to the best of my understanding, Orchid only considers local information --both spatial and spectral-- for conditioning. See also Line 302-304 and 308. The authors should be clear and fair regarding the abilities of the proposed model. - i am afraid I do not truly understand the Orchid block. Note that Figure 2.1 has an MLP block at the beginning of the block, which is then completely ignored both in the text and in the reference implementation. I would strongly encourage the authors to clearly state how the Orchid block works in practice. - Although encouraging, I feel that the empirical section misses many important components that would improve the impact and adoption of Orchid. - First, the associative recall tasks are only compared with other long conv models, some of which have been previously shown not to work in such tasks, e.g., H3, CKConv. For Orchid to be adopted in practice, I think that it would be very important to compare both to existing Transformer-like architectures as well as exiting input-dependent SSMs, e.g., Mamba. - Related to the previous comment, Mamba has shown that existing long conv models do not perform well in the selective copying task. How does Orchid perform in this task? - On the BERT experiments, the authors should include ablation studies to study the impact of using M2-MLP blocks as opposed to normal ones. It is not clear how much of a benefit (or decrease) results from this replacement, which is not inherent to Orchid. - On the image classification experiments, the authors compare with methods that perform very poorly, e.g., 84% acc on CIFAR-10. I would encourage the authors to compare to more relevant existing methods. - Related to the previous comment, one of the main advantages of long-conv models and Orchid is the fact that patches can become very small. If the accuracy results from the previous comment are limited by patchification, it would be very interesting to explore the performance differences when this module is removed. - Related to the previous comment, the same experiment would be very valuable for ImageNet1k. Recent papers have shown that the smallest the patch the better the accuracy. Showing that Orchid scales well to ImageNet in this setting would be very appealing and would also potentially increase the impact of the paper. - Still on the image processing setting, as far as I understand, it is very easy (not to say trivial) to expend Orchid to 2D data. Is there any reason as of why the authors did not use 2D orchid blocks for the image tasks? Technical Quality: 3 Clarity: 2 Questions for Authors: - Line 27. Please add references. - In the appendix C.2, the authors state that Type-I conditioning combined with DTC seems to work best. Is this truly the case? If so, then I do not understand why other components are introduced that are not used at the end. Note that Type I is much simpler than Type II, both conceptually, in terms of implementation and speed. If this is the case, then that space can also be rather used for things that are used in the experimental section. - The authors also introduce data dependent convolution as an alternative to Cross-attention. But then, never use it. Again, this space can be better used to outline the components that are used in the experiments, or to extend the experimental section of the method. Confidence: 4 Soundness: 3 Presentation: 2 Contribution: 4 Limitations: The authors clearly state the limitations of the proposed method. ### Conclusion Whilst I very much like the idea proposed here, and acknowledge its novelty and potential impact, I am not sure that in its current for this paper would be as impactful as I believe it could be. Therefore, I am hesitant to support acceptance. Note that I strongly believe that this paper could be very impactful. However, I believe that multiple adjustments must be made. With that being said, I am happy to increase my score should my concerns and comments be addressed. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your constructive feedback on our paper. We appreciate your recognition of the novelty and soundness of our approach, as well as the compelling empirical evidence. In the following, we address the points you raised in your review. - Orchid is using local info for spectral and spatial: In the proposed method, the long data-dependent convolution has an adaptive kernel that spans the entire length of the input sequence. This means that the convolution operation performed by Orchid indeed mixes the entire sequence globally using the proposed adaptive input dependent kernels, rather than being restricted to local windows. While the conditioning network’s input are local windows in both the spectral and spatial domains to determine the adaptive kernel, the convolution itself applies this kernel across the entire sequence. Thus, each input token is effectively mixed (convolved) with the entire sequence, - The role of MLPs at the beginning of the block: The MLPs included at the beginning of the Orchid block serve as feature (dimension) mixing components that are commonly used in various sequence modeling architectures, such as Hyena, M2, and SSM. In practice, these MLPs perform a pointwise mixing of features, which is a standard technique employed both before and after sequence modeling operations in architectures like transformers. Since the main focus of our paper is on sequence modeling using the data-dependent global convolution mechanism the text focused on these parts in detail. However, we will clarify the role of these MLPs in the final version. - Impact of using M2-MLP blocks on the final results: Indeed the impact of using M2-MLP blocks can be analyzed by comparing Orchid and M2. In the experiments we compare Orchid with M2 of similar size, while both are using Block diagonal for MLP, the main difference between M2 and Orchid based architectures is that, in Orchid we deployed the proposed data-dependent long convolution while M2 is following Hyena in using a fixed long convolution. Therefore, the performance improvements observed in Orchid compared to M2 are attributed to the data-dependent sequence mixing mechanism Using Block diagonal for MLP indeed will result in a sparse implementation of a dense MLP so it reduces the overall number of trainable parameters and reduces computational complexity Questions: - Q1: reference for line 27 Thank you for pointing this out. We will add the references to support the statements such as [1] - Q2: Why Type II is introduced in the text? The Type II (cross-correlation) approach generalizes the Type I (magnitude-based) approach and encompasses it as a special case. The introduction of Type II was intended to provide a more comprehensive view of the conditioning techniques available. Moreover, recent ablation studies, detailed in the rebuttal PDF, indicate that Type II combined with DCT performs better than Type I with DCT. However, since it is slightly more efficient in speed and parameter counts, Type I with DCT was selected for the in language, vision and audio experiments reported in our paper - Q3: Cross-attention functionality of Orchid: In the text we emphasize the novel capabilities of the Orchid model. The other long convolution based methods, such as Hyena and M2, and SSM-based methods such as Mamba, are not inherently applicable as an alternative to Cross-attention, so in this work we emphasize that the Orchid model is not only input-dependent but also its kernel can be conditioned on the an arbitrary input of any length so we call it data-dependent to infer more general than input-dependent modules. Implementing this ability of the proposed model could be a valuable direction for future work. [1] Nguyen, Eric, et al. "Hyenadna: Long-range genomic sequence modeling at single nucleotide resolution." Advances in neural information processing systems 36 (2024). --- Rebuttal 2: Comment: - Associative Recall on SSM-Based Models: In the following table, we compare the performance of Orchid against other long convolution models and an input-dependent SSM (Mamba) on the associative recall task. As the results indicate, Orchid achieves state-of-the-art performance among existing scalable sequence models for this task. Table AR2: This table presents the test accuracy (in %) of in-context learning on the associative recall task with a sequence length of 128 and varying vocabulary sizes. \| Vocabulary Size \| 20 \| 30 \| 40 \| \|-----------------\|------\|-------\|-------\| \| Transformer \| 100 \| 100 \| 100 \| \| CKConv \| 91 \| 25.7 \| 20.4 \| \| H3 \| 71.5 \| 13.2 \| 10.2 \| \| Hyena \| 93 \| 38.8 \| 12.4 \| \| Mamba \| 100 \| 100 \| 35.8 \| \| Orchid \| 100 \| 99.4 \| 99.2 \| - Expanding Orchid to 2D long convolution long: The Orchid block, with its input-dependent long convolution, local depthwise linear convolution (Conv1d), and element-wise multiplications, is inherently extendable to multi-dimensional data. However, our primary focus in this work was on designing an efficient and scalable architecture specifically for sequence modeling. Expanding our architecture to include 2D-convolutional long-range approaches, while valuable, was beyond the scope of our current study and is an interesting future work. UPDATE - We appreciate your suggestion and have included additional results in our "official comment" titled [Updated Results on CIFAR-10](https://openreview.net/forum?id=a75F45dBHK&noteId=h2L7DEaIKv), where Orchid is compared against other high-performance models. As the results show, using smaller image patches boosts the performance. Additionally, we include results for Orchid with the Type II conditioning network, which offers a slight improvement in accuracy on CIFAR-10. --- Rebuttal Comment 2.1: Comment: Dear authors, Thank you so much for your response. My questions regarding the experimental section have been answered. However, multiple questions that remain open / unanswered: While the conditioning network’s input are local windows in both the spectral and spatial domains to determine the adaptive kernel, the convolution itself applies this kernel across the entire sequence. Thus, each input token is effectively mixed (convolved) with the entire sequence +-> It is clear to me that the input is mixed across the entire sequence. However, as indicated before, the conditioning is local. This should be made clear in the paper as this elucidates improvements that can be done to the method in the future. Regarding questions: * Respectfully, I am strongly against that kind of "flag planting" that is made in the paper for both the Type II conditioning as well as for the Cross-Attention alternative. I believe that only things that are used in the paper should be included. I believe that this hinders progress on the field, as other researchers --or even yourself-- might feel that contributing and experimenting with those parts are not worth pursuing, as it has already "been done before" (which is not the case). I would strongly encourage the authors to remove the parts that are not used in the model. * There is no rebuttal PDF attached anywhere. * The authors did not answer my comment regarding Figure 2.1. I would encourage the authors to improve this image as it is the main image of the paper. It would aid clarity to use the conventional way of illustrating network blocks, as has been done in several papers before, eg., ResNet, Transformer, etc. Due to the observations outlined before, I am not compelled to support a clear acceptance. I therefore will maintain my score. Unfortunately, I am unsatisfied by your rebuttal response. --- Reply to Comment 2.1.1: Comment: Dear Reviewer, Thank you for your response. Regarding your questions: - Local conditioning network on spatial and spectral: - To address your question, let's clarify this with an analogy. In the conditioning network of Orchid, the pair of signals $ k(x) $ and $ q(x) $ are analogous to the key $ k(x) $ and query $ q(x) $ in the attention mechanism. In both Orchid and the attention mechanism, these components are modeled using local neural networks: attention utilizes pointwise linear projections, while Orchid employs local $ Conv1D $ operations in both the spatial and spectral domains. Once $ k(x) $ and $ q(x) $ are computed, attention mechanisms calculate the input-dependent attention score matrix $ A(x) $ and subsequently compute the output as $ y = A(x) v $. In contrast, Orchid’s conditioning network performs a cross-correlation— a global operation—between $ k(x) $ and $ q(x) $ to derive the convolution kernel $ h(x) $, followed by global convolution $ y = h(x) * v $. Thus, while the inner blocks (the input-dependent networks that compute the convolution kernel in Orchid or the attention matrix in attention mechanisms) operate locally on the inputs, the outer blocks (such as the matrix product in attention, cross-correlation or convolution in Orchid) perform global sequence mixing. This approach ensures fixed (or sublinear) parameter scaling with respect to sequence length, preventing the model size from growing excessively with sequence length. This analogy also applies to Type I, as it is a special case of Type II where $k(x)=q(x)$. - Although it is mentioned in line 148-150 that the conditioning network acts on both local spatial and spectral components, we will add this discussion in the final version to prevent potential misunderstandings. - Experimental results on Type II: By including discussions on Type II conditioning and the Cross-Attention alternative we aimed to highlight and clarify the distinct features of the data-dependent global convolution mechanism in Orchid. We believe that these discussions provide valuable insights that help better understand the architectural design of Orchid and also foster further exploration and innovation in the field by adopting it in other applications by the researchers. Moreover, we have conducted experimental evaluations using Orchid with the Type II conditioning network. The results, which are shared in the "official comment" titled Updated Results on CIFAR-10, demonstrate a slight improvement in accuracy on CIFAR-10, supporting the potential benefits of this approach. - Model Architecture in Figure 2.1: The paragraph in our rebuttal starting with “The role of MLPs at the beginning of the block” was intended to address your concerns about this figure. The MLPs at the beginning of the Orchid block are indeed pointwise feature mixing components, a design choice commonly seen in various architectures such as Hyena, M2, and SSM. However, the primary focus of our paper is on sequence modeling using the data-dependent global convolution mechanism. The current illustration style in Figure 2.1 was chosen to best represent the distinct features of the Orchid block, particularly highlighting its global convolution mechanism. Such style has been adopted in other relevant models, such as M2 and Mamba which we believe is suitable for our purposes. Thank you once again for your valuable feedback, and we hope our response has addressed all your questions.	Summary: Authors introduce a method for addressing the quadratic computational complexity of the attention mechanism while retaining expressivity and model performance from transformer models. Whereas previous approaches have achieved sub-quadratic computational efficiency - e.g. hyena, ssms and CKConv - authors argue (and show in their experiments) that these approaches limit model expressivity and performance - specifically in in-context learning settings. To this end, authors propose a novel long-range convolutional layer that is data-dependent, i.e. conditioned on the input. Orchid retains shift-equivariance properties of conventional convolution-based architectures, while being more expressive. Authors show superior performance over previous approaches in different domains (text and image data). Strengths: - Authors introduce an innovative method for increasing the expressivity of subquadratic methods for long-range dependencies. - The paper is well-written, authors explain and motivate their modelling choices well, and provide helpful figures. - The approach of conditioning convolutional kernels based on input data is interesting in its own right and might warrant exploration in architectures not specifically tailored for modelling long-range dependencies. Weaknesses: - Limited set of experiments and comparisons against baselines. Although authors show results also on image data, they do not compare against 2D-convolutional long-range approaches which flimits interpretability of the results. - Authors do not thoroughly explore their shift-invariance constraints, which might not be appropriate in all settings, i.e. I can imagine that for textual data absolute positioning in a sentence does impact semantic meaning. On the other hand, authors provide good motivation for their choice of shift-invariance. Technical Quality: 3 Clarity: 3 Questions for Authors: - Regarding the synthetic in-context learning task, I might be misunderstanding something, but why are shorter sequences more challenging in this task (i.e. Hyena/ CKConv/H3 achieve lower accuracy on shorter sequences)? Isn't it generally more challenging to capture longer-range dependencies? - Why do you choose not to compare against CKConv [1] or a later improvement CCNN [2] in the image classification task (these models ? These methods achieve substantially better results on CIFAR, making me question the validity of your claims regarding the advantage of your model in a broad range of application domains. [1] Romero, D. W., Kuzina, A., Bekkers, E. J., Tomczak, J. M., & Hoogendoorn, M. (2021). Ckconv: Continuous kernel convolution for sequential data. arXiv preprint arXiv:2102.02611. [2] Knigge, D. M., Romero, D. W., Gu, A., Gavves, E., Bekkers, E. J., Tomczak, J. M., ... & Sonke, J. J. (2023). Modelling Long Range Dependencies in $ N $ D: From Task-Specific to a General Purpose CNN. arXiv preprint arXiv:2301.10540. Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: Authors sufficiently discussion limitations of their approach. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your thoughtful review and valuable feedback. We appreciate your recognition of the contributions and the strengths of our paper. In the following, the points you raised in your review are addressed. - W1: Compare against 2D-convolutional long-range approaches: The Orchid block, with its input-dependent long convolution, local depthwise linear convolution (Conv1d), and element-wise multiplications, is inherently extendable to multi-dimensional data. However, our primary focus in this work was on designing an efficient and scalable architecture specifically for sequence modeling. Expanding our comparisons to include 2D-convolutional long-range approaches, while valuable, was beyond the scope of our current study and is an interesting future work. Regarding your point on the limited set of experiments against baselines, Appendix C5 also explores the ability of Orchid to learn long-range dependencies in speech classification tasks with long sequences. In these experiments, we compared Orchid against CKConv, Performer, and SSM-based models. - W2: Absolute positioning in a sentence might impact semantic meaning: Our approach to shift invariance focuses on preserving the relational positions of tokens. While changing the order of the tokens/words and their absolute positioning might impact the semantic meaning, we expect that if an entire sentence is shifted and pad tokens are appended before or after it, the sequence retains its semantic meaning. Indeed the relational positions of the tokens remain consistent in such cases. Furthermore, the positional embeddings added to the token embeddings, at the beginning of language models, encode the absolute positions of the tokens, enabling the model to generate semantic differences when the order is changed. Moreover, to achieve a location-dependent filtering scheme, we complement the data-dependent convolution with element-wise multiplications which allows the model to emphasize specific tokens in a sequence. - Q1: Why are shorter sequences more challenging in the in-context learning task? Shorter sequences pose a unique challenge in in-context learning tasks because specific (key, value) pairs appear less frequently within the string. This reduced frequency means the model has fewer opportunities to learn and generalize these associations. Additionally, when the vocabulary size also increases, the task becomes even more challenging for the model. The combination of infrequent pair repetitions and a larger vocabulary require a more expressive model architecture to effectively capture and utilize these (key, value) pairs within shorter sequences. - Q2: Compare against CKConv variants: Fixed long convolution kernel term (bias term) in Orchid and also convolution kernel in Hyena and M2 model are built upon long convolution kernel in CKConv, so by comparing against Hyena and M2 we explore the impact of the proposed input-dependent convolution that was introduced by Orchid model. Moreover, in speech classification tasks with raw speech, Orchid is compared against CKConv. --- Rebuttal Comment 1.1: Comment: I thank the authors for their response. Most my concerns have been answered, except for the seemingly arbitrary choice by the authors to compare against ckconv in one experiment but not in another experiment where it is outperformed by CKConv. I would recommend adding these results. --- Reply to Comment 1.1.1: Comment: Dear Reviewer, Thank you for your valuable feedback. We appreciate your suggestion and have included additional results in our "official comment" titled Updated Results on CIFAR-10, where Orchid is compared against other models, including CKConv and CCNN. In the original submission, our primary focus was on comparing Orchid with Vision Transformer (ViT) baseline models. We hope our response has addressed all your questions.	null	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Amortized Fourier Neural Operators	Accept (poster)	Summary: This paper tries to alleviate one of the issues in a so-called "Fourier Neural Operator (FNO)" which is a machine learning model to estimate a solution of partial differential equations (PDEs) based on the concept of "Operator learning". FNO takes into account the embedding of input field information in Fourier space, which partially contributes to its very weak dependence on the resolution. However, to reduce numerical cost, FNO abandons the frequency modes exceeding a predefined threshold, which limits its expressiveness power in the high-frequency region. To alleviate this issue, this paper proposed "Amortized Fourier Neural Operator (AM-FNO)", which utilizes a neural kernel function to accommodate arbitrarily many frequency modes with a fixed number of parameters, resulting in more expressive power with moderate model size. Strengths: 1. The proposed AM-FNO allows to accommodate arbitrarily many frequency modes with a fixed number of parameters, resulting in more expressive power with moderate model size. Numerical experiments indicate that it improves not only the high-frequency regime but most regimes (mainly the low-frequency regime, surprisingly (Fig. 3)) 2. The experiments utilize various datasets covering diverse PDEs with 1D and 2D spatial coordinate systems. 3. AM-FNO keeps a near-resolution independent nature of FNO even though considering high-frequency information. Weaknesses: The following major weaknesses are the factors forcing me to give a relatively lower score on this paper: Major weakness: 1. Each experiment in the paper is conducted only once, which prohibits readers (and reviewers) from distinguishing whether the obtained improved performance is either due to the true-effectiveness of the proposed approach or just a lucky statistical fluctuation of optimizer and initial model weight. In particular, the training sample number is 1000, which is relatively small and can result in large statistical fluctuation. The justification in "Checklist" says that this is due to "computational cost", which does not validate anything but sounds like the authors lazily submit this version of the paper just for the deadline (I hope not). Following the ML convention, averaging over three to five times experiments with the standard deviation information to the result table are necessary before acceptance. I feel this crucial defect unnecessarily decreases the worth of this paper, though the proposed method seems important and very interesting. At least, NS-2D and CFD-2D results in Table 2 should be given with standard deviation values because of their solution complexity, which can cause strong statistical fluctuations. 2. No information on the validation dataset is provided. Explain how to record the best score. If not using the validation dataset, provide a clear explanation of not overfitting to the test dataset. Minor: 1. "related works" only introduces the work relating to the neural operators, which covers a part of ML for PDE. The authors should introduce the other ML models for PDE and explain why picked up the neural operator and FNO in this paper (maybe in Appendix). 2. There are several undefined symbols and terms, in particular, in Section 3, such as d_a, d_u, d (seemingly already observed in FNO paper..), and FNN in the caption of Figure 2. 3. The description of "Factorization trick for high-dimensional PDEs" seems too short. I encourage the authors to provide a more comprehensive explanation with mathematical descriptions either in the main-body or appendix. 4. No discussion on the training/inference time and memory consumption required for AM-FNO in comparison to FNO. Technical Quality: 3 Clarity: 2 Questions for Authors: 1. In sec 3.1 above of Eq. (1), what does it mean: "functions a_i and u_i"? Do the authors want to indicate that each numerical cell at i owns independent functions? 2. In Eq. (5), the authors use NN(k) for both real and imaginary parts. Do the authors want to indicate the real and imaginary parts share the same weight? (it seems not). It would be better to describe them as NN(k; \theta_real) and NN(k; \theta_imaginary). 3. Below Eq. (8), lines 129-130, the description seems to contradict the result in Table 4 (KAN is worse than MLP). Do the authors indicate the case "Non"? Seemingly, the description is insufficient. 4. Why have the authors introduced the well-known "Stone-Weierstrass theorem" [1,2] (or Weierstrass approximation theorem) as Theorem 4.1 without citing it? Does the authors' version include non-trivial improvement? In addition, the function f should not be an "arbitrary function" but a "continuous function". [1] Stone, Marshall Harvey. "Applications of the theory of Boolean rings to general topology." Transactions of the American Mathematical Society 41.3 (1937): 375-481. [2] Stone, Marshall H. "The generalized Weierstrass approximation theorem." Mathematics Magazine 21.5 (1948): 237-254. 5. (suggestion) AM-FNO(KAN) can be moved into the appendix to increase the space to explain other important information because AM-FNO(KAN) is consistently worse than AM-FNO(MLP). Confidence: 4 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: The authors addressed the limitation in the manuscript. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank Reviewer kDgT for the detailed feedback. Below, we respond to the questions. W1: Experimental repetition. The results for neural operators are relatively stable. Consequently, many results for widely used baselines are taken directly from the original papers, which also do not include repeated experiments [1,2]. Reproducing experiments for every baseline and benchmark multiple times is computationally intensive. To address this concern, we have conducted additional experiments with three repetitions for our method on NS-2D and CFD-2D benchmarks as shown in the table below. The standard deviations are minimal compared to the average values. We will include these results, along with standard deviation values, in the revised manuscript to better assess the statistical stability of our approach. We appreciate your feedback and will incorporate these improvements into the revised version. \|Benchmark\|AM-FNO(MLP)\|AM-FNO(KAN)\| \|------\|--------\|---------\| \|NS-2D\|8.53e-2 ± 7.48e-4\|1.04e-1± 3.27e-3\| \|CFD-2D\|2.21e-3 ± 4.13e-5\|2.75e-3 ± 8.96e-5\| W2: Validation dataset. The primary objective of our experiments is to evaluate the effectiveness of our models across various benchmarks and to provide a comparative analysis with existing baselines. To ensure fairness and consistency, we use a fixed set of training settings in line with other baseline studies [1,2,3]. We do not perform hyperparameter tuning specifically for individual benchmarks in Table 2, as detailed in Appendix B. This approach aligns with standard practices in operator learning and helps mitigate the risk of overfitting by preventing excessive optimization for any single benchmark. W3: Related works. We have briefly discussed our choice of neural operators over other neural network-based methods in the introduction. Due to space constraints, a more detailed comparison with other ML models for PDEs will be included in the revised version, potentially in the appendix. W4: Undefined symbols. Thank you for pointing this out. In Section 3, $d_a$ and $d_u$ represent the dimensions of different functions, and FFN refers to the feed-forward neural network. We will provide detailed definitions for these terms in the revised version. W5: More description of the factorization trick. The "Factorization trick for high-dimensional PDEs" was briefly introduced as it serves primarily as a supplementary technique rather than a core component of our method. We will provide a more detailed mathematical description and explanation in the appendix. W6: Training/inference time and memory consumption. We present a comparison of training/inference times and memory consumption for AM-FNO and FNO on the 2D Darcy benchmark with a resolution of $421 \times 421$ in the table below. The results indicate that AM-FNO (MLP) exhibits both reduced memory usage and shorter training times compared to FNO, which is attributable to its lower complexity. Although AM-FNO (KAN) demonstrates increased training time due to its architectural design, it still benefits from lower memory consumption. We conjecture that this advantage is particularly evident when solving PDEs with high resolution and high dimensions. During inference, AM-FNOs (with kernels generated by MLP or KAN being precomputed) exhibit a similar speed to FNO, as both methods rely on similar kernel calculations. We will provide a more detailed discussion of these aspects in the revised version of the paper. \|Model\|Memory\|Train Time\|Inf Time\| \|-----\|------\|------\|------\| \|AM-FNO(MLP)\|9.7G\|43.1s\|2.4s\| \|AM-FNO(KAN)\|13.5G\|83.8s\|2.2s\| \|FNO\|14.9G\|45.6s\|2.2s\| Q1: $a_i$ refers to different input functions indexed by $i$, while $u_i$ denotes the corresponding output functions. Q2: Thanks for your suggestion. We will describe them differently in the revised version. Q3: We apologize for the confusion. The caption states, "A version of the model without orthogonal embedding (Non) is included for comparison," which refers to the model that directly approximates the kernel with MLP, as opposed to the KAN approach. Q4: Citation of "Stone-Weierstrass theorem". The Stone-Weierstrass theorem specifically addresses polynomial approximation of continuous functions, while our theorem generalizes approximation using orthogonal function bases [4], not limited to orthogonal polynomials. We will add the appropriate reference and clarify this distinction in the revised manuscript. Q5: Moving the KAN part. Thank you for your suggestion. While AM-FNO(KAN) does not outperform AM-FNO(MLP), it offers significant advantages, such as extendability during training and interpretability, as discussed in Appendix E. These benefits highlight the value of the KAN approach, which we believe justifies its inclusion in the main text. We hope this response clarifies any misunderstandings and addresses your concerns. If you have any further questions or identify any mistakes, please do not hesitate to let us know. We sincerely hope that you will reconsider and potentially increase the score for our paper. [1]Li, Z., Kovachki, N., Azizzadenesheli, K., Liu, B., Bhattacharya, K., Stuart, A., & Anandkumar, A. (2020). Fourier neural operator for parametric partial differential equations. arXiv preprint arXiv:2010.08895. [2]Li, Z., Huang, D. Z., Liu, B., & Anandkumar, A. (2023). Fourier neural operator with learned deformations for pdes on general geometries. Journal of Machine Learning Research, 24(388), 1-26. [3]Li, Z., Meidani, K., & Farimani, A. B. (2022). Transformer for partial differential equations' operator learning. arXiv preprint arXiv:2205.13671. [4]https://www.math.uni-hamburg.de/home/gunesch/calc1/chapter11.pdf (Theorem 11.13) --- Rebuttal Comment 1.1: Title: reply Comment: Thank you for the authors' addressing to my comments and questions. Other than the following two points, I've been satisfied. W2: Without validation dataset, how was the test set performance measured? Early stopping? Otherwise, I slightly suspect that the result would be over-fitted to the test set, which is crucial as an ML conference paper. Please carefully validate that your results are not over-fitted to the test set, with logical explanations. Q4: Thank you for your explanation. Then, reading [4], I wonder what is the difference of the paper's Theorem 1 from Theorem 11.13 in [4]. Besides, is either the function space F not Hilbert space or the arbitrary function f is not at least piecewise continuous? I wonder if Theorem 1 in the paper is truly new finding or citing very classical result of Hilbert space (if f is well-behaved and F is Hilbert space, any well-behaved (at least piecewise continuous) function can be expanded by an Hermitian operator's eigenfunction, which in general form a complete orthogonal basis. This is also known for more than 100 years). Note that if functional space F is not Hilbert space (complete unitary space), I think the paper's theorem 1 is trying to show any orthogonal set can be complete even though in non-Hilbert space, which could be mathematically strange. If Theorem 1 is a really new finding, it is great. Otherwise, it just damages the reputation of the NeurIPS paper quality, in particular, from mathematics community. Please carefully specify the new point and newly reduced restriction. Although I'm not a professional researcher of Hilbert space, I can also ask for a help to my Hilbert space researcher friend. --- Reply to Comment 1.1.1: Title: Reply to Reviewer kDgT Comment: Thanks for your prompt and detailed response! W2: Our paper follows the same evaluation methodology as the original FNO paper: using fixed training setting and training for a fixed number of epochs without early stopping. To ensure a fair comparison with other FNOs, we standardize the choice of model hyperparameters (such as the number of layers and channels) by using common settings for all FNOs including AM-FNOs. In summary, we did not use the training set to train or determine the hyperparameters. We believe that the risk of overfitting to the test set is minimal, and thus the results presented offer a fair comparison. W3: Sorry for the mistakes. Theorem 1 in the paper presents an alternative formulation of Theorem 11.13 in [4] from the perspective of the norm of the approximation error. The space $\mathcal{F}$ is a Hilbert space, and $f$ is any function in $\mathcal{F}$. We will revise the theorem and include the appropriate reference in the updated version. Thank you for pointing this out. If you have any further questions, we are pleased to discuss them. --- Rebuttal 2: Title: Reply to Reviewer kDgT Comment: Thanks for your response again. W2: Thank you for your explanation. We reported the test score evaluated at the last epoch for all the models. W3: In our revision, we assume that $\mathcal{F}$ is a separable Hilbert space. According to Theorem 9 in [1], there exists a complete orthonormal system (orthogonal basis), which can approximate any arbitrary function $f$ within the space, as stated in Definition 11.9 and Theorem 11.13 in [2]. We will consider introducing it directly within the text in the revised version. Thank you for your suggestion. If you have any further questions, feel free to let us know. [1] https://www.math.nagoya-u.ac.jp/~richard/teaching/s2023/SML_Tue_Tai_2.pdf [2] https://www.math.uni-hamburg.de/home/gunesch/calc1/chapter11.pdf --- Rebuttal 3: Title: reply Comment: Thank you for your reply. W2: Please report a part of the revised Table 2 (performance at the final epoch, multi-dimensional PDEs are preferable), to assess the effectiveness of Amortized FNO in comparison to the other models again. I expect that it does not need so much effort but only checking log files... --- Rebuttal Comment 3.1: Title: Reply to Reviewer kDgT Comment: Thanks for your response. # W2: Sorry for the misunderstanding. Our response above intended to clarify that we have used the final epoch performance in Table 2. Therefore, we believe that Table 2 already meets your requirement to fairly assess the effectiveness of all models. If you have any further questions, feel free to let us know.	Summary: This paper introduces Amortized Fourier Neural Operators (AM-FNOs), a novel approach to improve Fourier Neural Operators (FNOs) for solving PDEs. The key contributions to at least me are: 1. An amortized neural parameterization of the kernel function in FNOs to accommodate arbitrarily many frequency modes using a fixed number of parameters. 2. Two implementations of AM-FNO: one based on Kolmogorov-Arnold Networks (KAN) and another using Multi-Layer Perceptrons (MLPs) with orthogonal embedding functions. 3. Theoretical analysis of the approximation capabilities of AM-FNOs. 4. Extensive empirical evaluation demonstrating significant performance improvements over existing neural operator baselines across diverse PDE benchmarks. Strengths: 1. Novelty: The paper presents a novel approach to address a significant limitation of FNOs - the trade-off between model complexity and the ability to represent high-frequency details. The amortized parameterization is an innovative solution to this problem. 2. Theoretical foundation: The authors provide a solid theoretical analysis of their approach, including a theorem on the approximation properties of orthogonal basis functions. This adds depth to the empirical results and helps understand why the proposed method works. 3. Comprehensive experiments: The evaluation is thorough, covering six diverse PDE benchmarks and comparing against multiple state-of-the-art baselines. The inclusion of both in-distribution and out-of-distribution tests, as well as zero-shot super-resolution experiments, strengthens the claims of generalization ability. 4. Performance improvements: The reported improvements in accuracy (up to 35% average reduction in relative error) are substantial and consistent across different PDE types, which is impressive given the diversity of the benchmarks. 5. Ablation studies: The paper includes detailed ablation studies that provide insights into the importance of different components of the proposed method, such as the orthogonal embedding and the dimensional factorization trick. Weaknesses: 1. Inadequate baseline tuning: A major weakness is that the baselines were not properly tuned. The authors use default hyperparameters or settings from previous papers for the baseline models, which may not be optimal for the specific benchmarks used in this study. This raises questions about the fairness of the comparisons and the true extent of AM-FNO's improvements. 2. Limited discussion on scalability: The paper focuses on 1D and 2D PDEs. A more in-depth discussion on the scalability of the approach to higher-dimensional problems would be valuable. 3. Computational efficiency: While the paper discusses the parameter efficiency of AM-FNOs, it doesn't provide a comprehensive analysis of the computational efficiency in terms of training time and inference speed compared to baseline methods. Technical Quality: 3 Clarity: 3 Questions for Authors: I just have a few, maybe it wont be answered in the rebuttal phase, but just want to know if the authors have done any studies on this: 1. How does the performance of AM-FNOs compare to multi-scale approaches like U-FNO for PDEs with significant multi-scale behavior? 2. The paper focuses on the forward problem of solving PDEs. How well might AM-FNOs perform on inverse problems or parameter estimation tasks? 3. How does the computational complexity of AM-FNOs compare to standard FNOs and other baselines, particularly for high-dimensional PDEs? 4. The paper mentions the potential of KANs for interpretability. This is evident from the original KAN paper as you can recover symbolic expressions. Could the authors elaborate on how this interpretability could be leveraged in the context of PDE solving? Would the recovered be a close enough analytic solution ( which often in PDEs we dont have any). Confidence: 5 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The authors have described their limitations! Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We sincerely thank Reviewer okt7 for recognizing the novelty and empirical contributions of our method. Below, we address the questions raised. W1: Inadequate baseline tuning. We appreciate the reviewer's concern regarding baseline tuning. To ensure a fair comparison, we have adjusted all models in Table 2 to maintain comparable parameters, with hyperparameters detailed in Appendix B. Specifically, we standardized the width and depth across all FNOs baselines (including AM-FNO) to assess the effectiveness of our amortized parameterization. Furthermore, for the critical hyperparameter of FNO, the number of retained modes, we increased it to cover all modes as demonstrated in Table 3. Even under these conditions, our methods consistently outperformed the baselines. W2: Limited discussion on scalability. Currently, our study focuses on 1D and 2D PDEs. As demonstrated in Table 3, covering all frequency modes with FNO requires nearly 9 times the number of parameters, which highlights its limitations even in 2D PDEs. We evaluate our method on a 3D benchmark, Plasticity [1], and the results, as shown in the table below, illustrate its efficiency and scalability. We will provide a more detailed discussion in the revised version. \|Benchmark\|AM-FNO(MLP)\|AM-FNO(KAN)\|Geo-FNO\| \|------\|--------\|---------\|---------\| \|Plasticity\|3.04e-3\|6.11e-3\|7.4e-3\| W3:Computational efficiency. In the table below, we compare the training times, inference speeds, and GPU memory usage for AM-FNOs and FNO on the 2D Darcy benchmark with a resolution of $421 \times 421$. The results indicate that AM-FNO (MLP) exhibits both reduced memory usage and shorter training times compared to FNO, which is attributable to its lower complexity. Although AM-FNO (KAN) demonstrates increased training time due to its architectural design, it still benefits from lower memory consumption. We conjecture that this advantage is particularly evident when solving PDEs with high resolution and high dimensions. During inference, AM-FNOs (with kernels generated by MLP or KAN being precomputed) exhibit a similar speed to FNO, as both methods rely on similar kernel calculations. We will include a more thorough discussion in the revised version of the paper. \|Model\|Memory\|Train Time\|Inf Time\| \|-----\|------\|------\|------\| \|AM-FNO(MLP)\|9.7G\|43.1s\|2.4s\| \|AM-FNO(KAN)\|13.5G\|83.8s\|2.2s\| \|FNO\|14.9G\|45.6s\|2.2s\| Q1 & Q2: Multi-scale, inverse problem and parameter estimation tasks. We have evaluated AM-FNOs on the Airfoil benchmark, which has some multi-scale features, and achieved state-of-the-art results. A more detailed assessment of AM-FNO on benchmarks with significant multi-scale behavior will be addressed in future work. Our focus is on the forward problem for PDEs. Its effectiveness on inverse problems and parameter estimation is yet to be explored and will be also considered in future research. Q3: Computational complexity. Please refer to W3. Q4: The interpretability of KAN. Thank you for your insightful question. In AM-FNO, the black-box nature of the MLP between Fourier integral operators limits interpretability. However, leveraging KANs for symbolic expression recovery is promising and could enhance interpretability in future work. This is an area we plan to explore further. We sincerely appreciate your valuable insights and corrections. We will revise our manuscript accordingly. If you have any further questions or identify any mistakes, please feel free to correct us. [1] Zongyi Li, Daniel Zhengyu Huang, Burigede Liu, and Anima Anandkumar. Fourier neural operator with learned deformations for pdes on general geometries. arXiv preprint arXiv:2207.05209,2022. --- Rebuttal Comment 1.1: Title: Response to authors Comment: Thank you for your efforts to ensure fair comparisons by standardizing parameters across models and exploring full mode coverage are appreciated. The additional results on the 3D Plasticity benchmark demonstrate AM-FNO's scalability potential. Thanks also for including the computational efficiency comparison showing AM-FNO (MLP)'s advantages in memory usage and training time. I will not update my score however I hope that the revised version with more detailed discussions on these aspects will be included:) Thank you! --- Reply to Comment 1.1.1: Title: Reply to Reviewer okt7 Comment: Thank you very much for the valuable feedback. We will carefully consider the points discussed and revise our paper accordingly.	Summary: Typically, FNOs require a large number of parameters when addressing high-dimensional PDEs or when a high threshold for frequency truncation is needed. To overcome this challenge, the authors introduce the Amortized Fourier Neural Operator (AM-FNO). Their method uses an amortized neural parameterization of the kernel function to handle an unlimited number of frequency modes with a fixed number of parameters. The authors provide two implementations of AM-FNO: one based on the Kolmogorov–Arnold Network (KAN) and the other using Multi-Layer Perceptrons (MLPs) with orthogonal embedding functions. Strengths: 1. Improved performance: AM-FNOs, as shown by the authors, consistently achieve better performance across multiple benchmarks. Weaknesses: 1. The curse of dimensionality (CoD) is not lessened by any extent. For each Fourier layer in FNO, we have to perform FFT and IFFT, which have a complexity of $ O(n \log n) $. Even if we use the full spectrum, the pointwise multiplication would only take $ O(n) $. It remains unclear to me whether it is meaningful to tackle the CoD issue in the number of parameters. 2. The proposed method seems to have some flaws. See Questions. 3. The presentation of this paper is very poor. For example, the way FNO is presented is non-standard and seems to be more from the view of the actual implementation. For example, in Section 3.2, $d_h$, correct me if I'm wrong, is the number of channels (i.e., width in FNO implementation). You should clearly state this. In line 98, $R(k): \mathcal{E} \rightarrow \mathbb{C}^{\left(d_h \times d_h\right)}$, you have $d_h$ as the number of input channels and $d_h$ as the number of output channels. That's why your codomain is $\mathbb{C}^{\left(d_h \times d_h\right)}$, and these two do not necessarily equal, although in the implementation from the FNO paper they are equal. If you choose to present FNO from an actual implementation perspective, you should clearly explain everything, especially for readers who are not familiar with the actual implementation. Technical Quality: 2 Clarity: 2 Questions for Authors: I'm not familiar with the Kolmogorov–Arnold Network (KAN), which is new and controversial as far as I know, so I will not comment on it. 1. It is unclear to me how this can reduce the number of parameters. Suppose for one channel in FNO, the size of the (complex) kernel is $k$. Doesn't the MLP used to generate this kernel must contain more parameters? Otherwise, let's say you want a kernel of size $k$. The output size of your MLP is $k$, then the $W$ matrix in your output layer should be of size $k' \times k$, where $k'$ is the size of the output of the previous layer. 2. Assume that you can use an MLP with fewer parameters to generate a large kernel. Doesn't this also limit the expressivity of the kernel you can learn? Essentially, what you are doing is trying to reduce the dimension of the kernel, but Fourier is already very effective in this. If your data is translationally invariant or your PDE is translationally equivariant (which is an assumption of FNO), then the optimal PCA basis consists of Fourier vectors, and you can relate this to the Eckart-Young theorem. 3. In Table 2, why is the number of parameters and running time not reported? Are the experiments repeated several times to reduce the effect of randomness? Without this information, Table 2 means nothing to me. I apologize if the authors think my comments are too harsh. If I have indeed misunderstood certain parts of this paper, I am open-minded for a discussion and willing to adjust my views during the rebuttal. Confidence: 4 Soundness: 2 Presentation: 2 Contribution: 2 Limitations: Ｔhe authors have addressed the limitations． Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank Reviewer NuVs for the valuable feedback. Below, we respond to the questions. W1: The reason for tackling the CoD issue in the number of parameters. In FNO, the kernel is parameterized independently for each frequency mode, resulting in complexity for the Fourier integral operator of $O((d_h^2 k)^{D}))$, where $d_h$ represents both the input and output channel dimensions, $k$ denotes the number of retained modes, and D indicates the spatial dimensionality. For high-resolution and high-dimensional data, this leads to significant memory consumption, as a large number of modes need to be retained. For example, one 64-width FNO layer for 2D PDEs can exceed 130 million parameters with $k=256$. This severely limits practical applications, such as large-scale pre-trained models. We provide a comparison of the training time and memory consumption for AM-FNOs and FNO ( with all modes retained) in the table below, tested on the 2D Darcy benchmark with a resolution of $421 \times 421$. The results indicate that AM-FNO (MLP) exhibits both reduced memory usage and shorter training times compared to FNO, which is attributable to its lower complexity. Although AM-FNO (KAN) demonstrates increased training time due to its architectural design, it still benefits from lower memory consumption. We conjecture that this advantage is particularly evident when solving PDEs with high resolution and high dimensions, attributed to AM-FNO's reduced complexity. A comprehensive analysis will be included in the updated version of the paper. \|Model\|Memory\|Train Time\| \|-----\|------\|------\| \|AM-FNO(MLP)\|9.7G\|43.1s\| \|AM-FNO(KAN)\|13.5G\|83.8s\| \|FNO\|14.9G\|45.6s\| W2: Paper presentation. Thank you for your feedback on the presentation. We apologize for any confusion caused by the brief introduction of FNO due to page limitations. We will provide a clearer explanation in the updated version to ensure understanding, especially for readers not familiar with the implementation details. Q1: Parameter reduction We would like to clarify that in AM-FNO, the MLP is used to map each frequency mode (after embedding) to its corresponding kernel value, meaning the number of parameters depends on the number of channels rather than the number of retained modes. For instance, if an MLP with $m$ basis functions processes input and outputs a kernel of size $k$, the parameter count is approximately $2m^2 + 2m$ (assuming one hidden layer and one channel). In contrast, FNO requires $k$ parameters for the kernel, which can be expensive for high-resolution and high-dimensional data (more modes should be retained). Q2: MLP limits the expressivity. While Fourier methods are theoretically efficient, they require a large number of parameters when handling high-dimensional and high-resolution data, which can be computationally prohibitive. Using an MLP to generate the kernel might indeed limit expressivity compared to parameterizing every frequency mode as in FNO theoretically. We regard this as a tradeoff. However, our empirical results demonstrate that AM-FNO outperforms FNO covering all frequency modes (see Table 3). We believe this is because the smoother transformations facilitated by the MLP improve optimization efficiency, leading to better performance. Q3: Main experiments. Many results in Table 2 are sourced from the original papers, making a direct comparison of running times potentially unfair due to hardware differences. All the baselines in Table 2 have comparable numbers of parameters, with their hyperparameters detailed in Appendix B. Below, we provide a parameter comparison on Darcy benchmark to validate this. The results of neural operators are generally consistent despite randomness, which is why many popular baselines do not report repeated results [1,2]. We repeated our experiments three times on CFD-2D and NS-2D benchmarks, as shown in the table below, demonstrating the stability of our method. \| \|AM-FNO(MLP)\|AM-FNO(KAN)\|FNO\|U-FNO\|OFormer\|LSM\| \|------\|--------\|---------\|------\|-------\|---------\|--------\| \|Params.(M)\|1.1\|1.5\|2.4\|1.3\|2.7\|4.8\| \|Benchmark\|AM-FNO(MLP)\|AM-FNO(KAN)\| \|------\|--------\|---------\| \|NS-2D\|8.53e-2 ± 7.48e-4\|1.04e-1 ± 3.27e-3\| \|CFD-2D\|2.21e-3 ± 4.13e-5\|2.75e-3 ± 8.96e-5\| Thank you for your openness and willingness to discuss further. We hope this discussion clarifies any misunderstandings and addresses your concerns. If you have any further questions or identify any mistakes, please do not hesitate to let us know. [1] Li, Z., Kovachki, N., Azizzadenesheli, K., Liu, B., Bhattacharya, K., Stuart, A., & Anandkumar, A. (2020). Fourier neural operator for parametric partial differential equations. arXiv preprint arXiv:2010.08895. [2] Hao, Z., Wang, Z., Su, H., Ying, C., Dong, Y., Liu, S., ... & Zhu, J. (2023, July). Gnot: A general neural operator transformer for operator learning. In International Conference on Machine Learning (pp. 12556-12569). PMLR. --- Rebuttal Comment 1.1: Title: Reply to Author's Rebuttal Comment: ### W1 > This severely limits practical applications, such as large-scale pre-trained models. First of all, how do you get $\left.O\left(\left(d_h^2 k\right)^D\right)\right)$? Isn't it just $\left.O\left(d_h^2 k^D\right)\right.$ Can you provide a case in which they use large pre-trained FNOs? Moreover, in your case, FFT would take $O(d_h n \log n)$, where $n \geq k^D$. FFT itself is already very expensive and suffers from the CoD issue. ### Q1 Can you be more specific, such as providing some mathematical expressions? I'm still confused. ### Q3 I do understand that the rebuttal period is only one week, and you might not have time to do this. However, I believe that running times are important. A simple example is that a U-Net or DeepONet with a similar number of parameters might be much faster than FNO. If you run their models and record the time on the same machine and with the same settings, I believe you can ensure the comparison is consistent and fair. --- Rebuttal 2: Title: Reply to Reviewer NuVs Comment: Thanks for your prompt and detailed response! W1: We appreciate your feedback and would like to address your concerns subsequently. Firstly, we apologize for the error in the complexity statement; it should be $O(d_h^2k^{D})$. Secondly, there have been attempts to utilize large pre-trained FNO models. For instance, DPOT [1] explores a model that employs a shared MLP to transform each frequency mode of the input (akin to a convnet with a $1 \times 1$ kernel) to mitigate the memory overhead of kernels. This architecture is similar to AFNO [2], which we have compared in Table B of the global rebuttal. Our results indicate that our method outperforms AFNO on both benchmarks, which we attribute to AFNO’s limited expressiveness due to its uniform transformation across different frequency modes, while our approach treats each mode differently. Regarding your concerns about FFT, we acknowledge that FFT suffers from the Curse of Dimensionality (CoD). However, FNOs still demonstrate superior training speed (as shown in the table below in Q3) and prediction accuracy compared to other neural operators. Our method primarily addresses memory issues, particularly in high-resolution or high-dimensional contexts, as demonstrated in the table in the rebuttal before. Our approach shows a reduction in memory usage (and shorter training time for AM-FNO (MLP)) even in 2D benchmarks, suggesting potential benefits for large-scale models. Q1: Continuing with the assumption of one channel and a one-dimensional kernel size of $k$, let’s further simplify the MLP to a linear layer for clarity. To map frequency modes (with shape $[k,1]$ ) to the corresponding kernel values (also with shape $[k,1]$ ), our method first applies basis functions to obtain an embedding with shape $[k,m]$ , where m is the number of basis functions. We then compute the kernel values (real or imaginary part) using a linear layer with $m \times 1$ parameters. Consequently, the complexity of our method depends only on the number of channels and the number of basis functions (specifically $O(D m d_h^2)$ in the linear case compared to $O(d_h^2k^{D})$ in FNO for multi-dimensional PDEs), and avoid becoming excessively large with increasing dimensions and resolution. Q3: To address your concern, we provide a comparison of training times under our experimental settings for the same benchmark, as shown in the table below. The results indicate that our method has a slower training speed compared to other FNOs, which can be attributed to the additional frequency modes we adopted. However, our method still outperforms non-FNO neural operators. Furthermore, as shown in the previous rebuttal, when all modes are retained, our method can surpass FNO in training time. \| \|AM-FNO(MLP)\|AM-FNO(KAN)\|FNO\|U-FNO\|Oformer\|LSM\| \|-----\|-----\|-----\|-----\|-----\|-----\|-----\| \|Train Time (s/epoch)\| 1.2 \| 2.1 \| 0.9 \| 1.6 \| 16.5 \| 2.1 \| If you have any further questions, we are pleased to discuss them. [1] Hao, Z., Su, C., Liu, S., Berner, J., Ying, C., Su, H., ... & Zhu, J. (2024). Dpot: Auto-regressive denoising operator transformer for large-scale pde pre-training. arXiv preprint arXiv:2403.03542. [2] Guibas, J., Mardani, M., Li, Z., Tao, A., Anandkumar, A., & Catanzaro, B. (2021). Adaptive fourier neural operators: Efficient token mixers for transformers. arXiv preprint arXiv:2111.13587. --- Rebuttal Comment 2.1: Comment: Overall, I appreaciate your efforts to address my concerns; I will be satisfied if the following points can be addressed/clarified: >　Firstly, we apologize for the error in the complexity statement; it should be $O\left(d_h^2 k^D\right)$. My main concern is that while your work aims to reduce the curse of dimensionality in FNO, but the complexity introduced by FFT might undermine these benefits from your method. > Our method primarily addresses memory issues, particularly in high-resolution or high-dimensional contexts. Does your method address the time complexity issue in these scenarios? From what I understand, your approach might actually increase the running or inference time. The primary reason for using neural operators is to achieve fast inference; otherwise, numerical schemes with coarse discretization can offer even better performance with theoretical guarantees. > Q1 So, are the MLPs the same for every dimension? What happens if the axes aren't on the same scale? For instance, in a 2D domain of $[0, 1000] \times [0, 1]$, where you want to keep 100 modes for the first dimension and only 10 for the second, can your method still work given that MLPs are fixed in size? If not, it seems your method can only be applied when you sample the same number of frequency modes (i.e. $k$) in every dimension, which doesn’t seem practical to me. For some test data, e.g., from the FNO paper, you can effectively do this. But not pratical in general. > However, our method still outperforms non-FNO neural operators. There are many non-FNO neural operators, e.g., DeepONet, U-Net, SNO [1], the selected baselines such as Oformer and LSM is not what I would have expected to see as a baseline in this venue. [1] Spectral Neural Operators, V. Fanaskov, I. Oseledets --- Reply to Comment 2.1.1: Title: Reply to reviewer Reviewer NuVs Comment: Thanks for your feedback. 1) We understand your reasonable concerns about the complexity of FFT; however, FNOs still demonstrate superior speed compared to other neural operators. We will include a discussion on the limitations of FFT in the revised version. 2) While our models require more training time than the standard FNO due to the use of MLPs or KANs, the difference is relatively minor, as shown in the table presented before(1.2s for AM-FNO (MLP) vs. 0.9s for FNO). In terms of inference time, we can precompute the kernel using the trained MLPs or KANs before inference, resulting in the same computational complexity as the FNO. 3) The MLP is different for every dimension. We present the result on 3D Plasticity benchmark, where we kept 101, 31, 20 modes for every dimension. As shown, our method outperform Geo-FNO. \| Benchmark \| AM-FNO(MLP) \| Geo-FNO \| \| ---------- \| ----------- \| ------- \| \| Plasticity \| 3.04e-3 \| 7.4e-3 \| 4) Thanks for your suggestion. We will add the mentioned baselines in the revised version. If you have any further questions, we are pleased to discuss them. --- Rebuttal 3: Title: Reply to Reviewer NuVs Comment: Thanks for your feedback and improved score. Below, we further respond to your questions. 1） Due to the time constraints of Rebuttal, we directly used the official Geo-FNO code to compare the speed of Geo-FNO and DeepONet [1]. Note that DeepONet requires function values at all input points and a query coordinate but outputs only the value at the coordinate, while FNO outputs values for all points. To align batch sizes, we used a batch size of $16$ for Geo-FNO and $16 \times 972$ (972 is the number of sensor points) for DeepONet. As shown in the table below, huge batch sizes for DeepONet can pose significant challenges for data transfer and parallel processing, resulting in reduced efficiency. While FFT may become a limitation in very high-dimensional settings, FNO still outperforms in this context. We also compare FLOPs for computing an entire function (972 points) to better illustrate the efficiency of the two models. \| Model \| Params.(M) \| Train Time (s/epoch) \| Inf Time (s/epoch) \| FLOPs（Calculation for 972 Points） \| \|----------\| ---------\|---------\| ------- \|------- \| \| DeepONet \| 1.0 \| 13.9 \| 2.5 \| 0.99B \| \| Geo-FNO \| 1.5 \| 2.1 \| 0.2 \| 0.11B \| Regarding U-Net, while it may be more efficient in many scenarios, its local convolution in the spatial domain limits performance when testing across different discretizations, which is significant for neural operators [2]. Thank you for your questions on efficiency. We recognize that the complexity of FFT may pose a limitation for FNOs and will include a detailed discussion on COD in our revised version. 2）The Plasticity benchmark is presented on a structured mesh, where the indexing induces a canonical coordinate map and enables the direct application of FFT without the learnable mapping [3]. Consequently, Geo-FNO is equivalent to the standard FNO in this context. We refer to it as Geo-FNO to maintain consistency with the original Geo-FNO paper. Thank you for pointing this out. We hope the above response can further address your concern. If you have any further questions, we are pleased to discuss them. [1] https://github.com/neuraloperator/Geo-FNO [2] Wen, G., Li, Z., Azizzadenesheli, K., Anandkumar, A., & Benson, S. M. (2022). U-FNO—An enhanced Fourier neural operator-based deep-learning model for multiphase flow. Advances in Water Resources, 163, 104180. [3] Li, Z., Huang, D. Z., Liu, B., & Anandkumar, A. (2023). Fourier neural operator with learned deformations for pdes on general geometries. Journal of Machine Learning Research, 24(388), 1-26. --- Rebuttal Comment 3.1: Comment: > Geo-FNO is equivalent to the standard FNO in this context. Your aim is to resolve or lessen the CoD issues in FNO. It would be more interesting to see a comparison between a large FNO and a large AM-FNO regarding the improvement in 1) memory usage, 2) training and inference time, and 3) FLOPs. However, I understand that due to the limited time available during the rebuttal, it may be almost impossible to obtain such results. > While FFT may become a limitation in very high-dimensional settings, FNO still outperforms in this context. In Section 5.1, you mentioned DeepONet as a baseline, but I do not see it in the results (Table 2 or any other tables). I'm trying to find the L2 error information on this. Moreover, in my experience, DeepONet is usually faster than an FNO model with a similar number of parameters on normal uniform rectangular domain data (implementation follows directly from [1], a torch adaptation can also be found from the implemetation of [2]). However, I do understand that implementation details and hardware details may differ. Given that most of my concerns and questions have been addressed, and recognizing the authors' efforts to include additional results within the short rebuttal period, I am willing to increase my score. However, since my major concern remains unresolved and the authors agree it should be acknowledged as a limitation, I will not be making any further adjustments to the score. [1] A comprehensive and fair comparison of two neural operators (with practical extensions) based on FAIR data [2] Physics-Informed Neural Operator for Learning Partial Differential Equations --- Rebuttal 4: Title: Reply to Reviewer NuVs Comment: Thank you for making such a constructive discussion with us! We totally understand your concerns about method efficiency and have tried our best to demonstrate that our approach may not suffer from issues from that aspect during the rebuttal. Of course, we will add the mentioned comparison between large FNO and large AM-FNO in the revision. Additionally, we will provide a comprehensive comparison with DeepONet, particularly focusing on efficiency. At last, we also clarify that alleviating the parameter count issue is a side product of this paper. A more evident effect of the proposed amortized parameterization is to foster the frequency modes to communicate with each other, leading to enhanced predictive performance. We will carefully revise the paper to weaken the argument on addressing COD in our revised version. Thanks again!	Summary: This paper presents the AMortized Fourier Neural Operator (AM-FNO), which utilizes an amortized neural representation of the kernel function. It allows accommodating a variable number of frequency modes while using a fixed number of parameters compared to the Vanilla Fourier Neural Network. Strengths: S1) Amortized neural parameterization of the kernel function using MLP and KAN amortized neural parameterization of the kernel function. S2) The approach explores high-frequency components without increasing the parameters of the Fourier Neural Operator. Weaknesses: W1) Baselines seem limited, and GNOT, Transsolver, ONO, UNET, etc., need to be included. W2) The benchmarks have been tested consistently on a structured grid but have yet to be tested on an unstructured mesh. W3) The proposed approach resembles the spectral neural operator which uses the Fourier and Chebyshev series, W4) Using low-rank approximation to approximate the Fourier kernel or incorporating depthwise convolution with non-linearity in baselines will enhance comprehension of the proposed method. Technical Quality: 2 Clarity: 2 Questions for Authors: Q1) What is your rationale for employing an orthogonal basis? Have you experimented with applying depthwise convolution in FFT space, followed by non-linear transformations and another round of depthwise convolution? Q2) Could you please clarify why KAN consistently performs worse than MLP? Given that the dataset is noise-free, shouldn't KAN be expected to outperform MLP? Q3) The FFNO number reported does not correspond to the number in the original paper. Q4) Have you attempted using a low-rank approximation of the kernel weight in Fourier space within FNO? Q5) Difference between the proposed method and spectral neural operator. Q6) Why does having orthogonal embedding assist in AM-FNO? Have you experimented with employing the standard FFN directly? What type of orthogonal embeddings were used for the experiment? Confidence: 4 Soundness: 2 Presentation: 2 Contribution: 2 Limitations: Yes, the authors adequately addressed the limitations. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank Reviewer Z566 for the valuable feedback. Below, we respond to the questions. Please note that the additional tables and references are included in the Global Rebuttal due to character limits. W1: More baselines. Our method aims to enhance Fourier neural operators (FNOs), a significant subclass of neural operators. Therefore, we primarily use FNOs as our baselines, and our method demonstrates superior performance. Additionally, we have included widely used baselines (OFormer) and a competitive baseline (LSM) to validate our method's effectiveness. In response to your suggestion, we include some mentioned baselines, as shown in Table B. It indicates that our method outperforms the additional baselines as well. We will include these results in the revised version. W2: Benchmarks on unstructured mesh. Thanks for your suggestion. We evaluate our method on the Elasticity benchmark presented on point clouds [1] in Table C. To handle irregular geometry, we implemented the widely used Geo-FNO method to map the irregular meshes to and from uniform meshes [1]. Our results show that our method outperforms other neural operators that utilize the same learnable mapping. However, it performs worse than transformer-based neural operators, which naturally process input functions on irregular geometry as a sequence. We hypothesize that the learnable mapping introduces errors. We will include these results in the revised version. W3: Spectral Neural Operator Resemblance. We would like to clarify that our method is fundamentally different from SNO. SNO utilizes Chebyshev polynomials to represent functions with finite sets of coefficients and learns the mapping between these coefficients. This results in band-limited operators that are restricted to generating frequencies within a fixed representation space. In contrast, FNOs learn the direct mapping between functions and compute the integral operator in Fourier space for high inference speed. Empirically, FNOs demonstrate the ability to extrapolate to higher frequencies not seen during training, which SNOs lack due to their fixed representation limits [2]. As a variant of FNO, while AM-FNO employs orthogonal basis functions to approximate the kernel function—a common practice in function approximation—the neural operator itself is fundamentally distinct from SNO. W4: Low-rank approximation or depthwise convolution with non-linearity. FNO with low-rank approximation is similar to one of our baselines, F-FNO, which factorizes the kernel across different dimensions. The results in Table 2 (in the paper) demonstrate that AM-FNO outperforms F-FNO, highlighting the superiority of our amortized parameterization over the point-by-point parameterization in F-FNO. Regarding the non-linear convolution, AFNO [3] employs a non-linear convnet to evolve features at every frequency mode. We evaluate AFNO on two benchmarks, and the results, as shown in Table B, indicate that AFNO has lower accuracy. We hypothesize that this is because AFNO uses the same MLP to evolve all frequency modes of the input, potentially limiting expressiveness. In contrast, AM-FNO transforms different frequency modes separately. We will include further discussion on AFNO in the revised version. Q1: Our rationale for employing orthogonal basis functions stems from the observed performance degradation when using an MLP to directly approximate the mapping between frequencies and kernel values, as shown in Table 4 (in the paper). The MLP struggles to capture the complex, non-linear nature of the kernel function. Embedding scalar inputs with predefined functions is a well-established technique in machine learning, as exemplified by time embeddings in diffusion models. This approach helps MLPs convert linear inputs into expressive, non-linear forms effectively. Inspired by it, we employ orthogonal functions to embed the frequencies, mapping them into a high-dimensional and non-linear feature space. This introduces an inductive bias that enhances the efficiency of approximating kernel functions. Regarding the depthwise convolution in FFT space, please refer to our response in W4. Q2: As reported in [4], KAN does not consistently outperform MLP. As shown in Table 4 (in the paper), AM-FNO with KAN outperforms AM-FNO using MLP directly and performs worse than AM-FNO using orthogonal basis functions to embed the input. This indicates the effectiveness of our embedding technique. Meanwhile, KAN has the advantage of being extendable during training by increasing the number of local basis functions. For a fair comparison, we kept the parameter count constant and did not extend KAN during training. Given the results in Figure 4 (in the paper), it is plausible that AM-FNO (KAN) can outperform if we increase the number of basis functions during training. Q3: The F-FNO results were reproduced using the training settings and similar hyperparameters as other FNOs, as described in Section 5.1 and Appendix B, to ensure a fair comparison. The discrepancy with the original paper's results may stem from differences in training techniques. For instance, the original F-FNO paper employs methods like enforcing the first-order Markov property and adding Gaussian noise. Our training settings align with standard practices in this domain to maintain consistency across evaluations. Q4: Please refer to W4. Q5: Please refer to W3. Q6: Please refer to Q1 and Q2. We primarily used Chebyshev basis functions for the orthogonal embeddings in our experiments. In our ablation study, we also replaced them with triangular basis functions and non-orthogonal basis functions to evaluate their impact. We hope this response clarifies any misunderstandings and addresses your concerns. If you have any further questions or identify any mistakes, please do not hesitate to let us know. We sincerely hope that you will reconsider and potentially increase the score for our paper. --- Rebuttal 2: Comment: Thank you for the response. 1) The paper references factorization techniques, but the implementation uses a Chebyshev basis to parametrize the entire Fourier kernel, along with an MLP. As reviewer DLAH noted, this approach is not clearly explained in the current version of the paper, where only smooth function parametrization is mentioned. It is essential to explicitly include this discussion in the paper for clarity and the discussion about the spectral bias in MLP. 2) I couldn't find hyperparameter details for the benchmark datasets in the paper, which is needed to ensure reproducibility. 3) If you are using all Fourier frequency modes in the proposed method, then it's not a fair comparison. I would like to see the performance compared with FNO, where we have used all the frequency modes. Also, it would be great if the author could provide the performance of the proposed method using only the same number of modes as used for FNO. 4) I could find two Tx and Ty in the code. Could you clarify: > self.Tx = torch.zeros(self.n1, H+padding) self.Ty = torch.zeros(self.n2, (W+padding)//2+1) self.Tx = (torch.cos(self.grade1@torch.acos(self.gridx))).reshape(1, self.n1, H+padding, 1).cuda() self.Ty = (torch.cos(self.grade2@torch.acos(self.gridy))).reshape(1, self.n2, 1, (W+padding)//2+1).cuda() 5) Could you compare the proposed method with baselines regarding training time, GPU consumption, inference time, and number of parameters? PS: I am open to discussing the paper and would like to consider increasing the score if my questions are addressed. --- Rebuttal 3: Title: Reply to Reviewer Z566 Comment: Thanks for your feedback. 1) Thanks for your suggestion. We agree that the concept of spectral bias provides valuable insight into our approach, and we will include additional discussion to elaborate on this in the revised version. 2) Sorry for not including this part. We will include the relevant descriptions of the benchmarks in the revised version. 3) In our main experiment (Table 2), we aimed to ensure that all models had a comparable number of parameters. However, the parameter count for FNO with all modes becomes excessively large, making it unfair to compare with other models. Meanwhile, one advantage of our method is that it can capture all modes with a limited number of parameters. We have presented the results of FNO with full modes on CFD-2D (denoted as "FNO+" in Table 3), where AM-FNOs outperform FNO+. We also provide comparisons with FNO+ on the Darcy and Airfoil benchmarks below. We will include additional empirical results on FNO+ and AM-FNOs with the same number of modes in the revised version. \| Model \| AM-FNO (MLP) \| AM-FNO (KAN) \| FNO+ \| \|------\|------\|------\|------\| \|Darcy\| 4.21e-3 \| 4.28e-3 \| 1.33e-3 \| \| Airfoil \| 5.64e-3 \| 6.06e-3 \| 1.32e-2 \| 4) The first two lines of code are for initialization (though they aren’t necessary), while the next two lines compute the basis functions. We want to clarify that our code is consistent with our method. 5) We provide a comparison of all models, using the hyperparameters from the main experiment, tested on the same benchmark in the table below. Our methods require more memory and training/inference time compared to other FNOs, due to the additional modes we maintain. However, AM-FNOs still outperform non-FNO neural operators. \| Model\| AM-FNO (MLP)\| AM-FNO (KAN) \| FNO \| U-FNO \| OFormer \| LSM \| F-FNO \| \|------\|------\|------\|------\|------\|------\|------\|------\| \|Train Time (s) \| 1.2 \| 2.1 \| 0.9 \| 1.6 \| 16.5 \| 2.1 \| 1.1 \| \|Inf Time (s) \| 0.091 \| 0.17 \| 0.0068 \| 0.087 \| 1.5 \| 0.15 \| 0.075 \| \|Memory (M) \| 1850 \| 2066 \| 1212 \| 1444 \| 16090 \| 1894 \| 1126 \| \|Params. (M) \| 1.1 \| 1.5 \| 2.4 \| 2.6 \| 1.3 \| 4.8 \| 0.2 \| If you have any further questions, we are pleased to discuss them. --- Rebuttal 4: Comment: Thank you for the response. Q2) It would be better if you could also report hyperparameters for the proposed method. Q3) With increased modes, FNO is computationally heavy and might sometimes underperform. However, can you report the numbers of AM-FNO compared with FNO having the same modes? It will help to understand the proposed method better, whether increasing the modes is effective in AM-FNO or the way in which the kernel is parametrized (Kernel Bias) Q) Can you report the numbers using just one layer of AM-FNO and FNO on specific benchmarks? I am trying to understand the proposed method better from the point where kernel bias is more critical or increasing the modes. Also, it's fine if the proposed method is not competitive with FNO in terms of computational and time complexity, as the proposed method is trying to address different problems altogether. --- Rebuttal 5: Title: Reply to Reviewer Z566 Comment: Thanks for your feedback. Q2) We have reported the essential hyperparameters of our models in Section 5.1. We will provide a more detailed description in our revised version. Q3) We present the performance of our models with 12 modes compared to FNO with the same number of modes on Darcy benchmark, as shown in the table below. The results indicate that our models continue to significantly outperform the FNO, demonstrating the effectiveness of our parameterization. \| Benchmark \| AM-FNO(MLP) \| AM-FNO(KAN) \| FNO \| \|----------\| ---------\|---------\| ------- \| \| Darcy \| 4.72e-3 \| 4.78e-3 \| 1.08e-2 \| Q) The results of AM-FNOs and FNO with one layer on Darcy are shown below. \| Benchmark \| AM-FNO(MLP) \| AM-FNO(KAN) \| FNO \| \|----------\| ---------\|---------\| ------- \| \| Darcy \| 1.85e-2 \| 1.98e-2 \| 2.17e-2 \| If you have any further questions, we are pleased to discuss them. --- Rebuttal Comment 5.1: Comment: Thanks for addressing my concerns. It seems both MLP inductive bias and adding modes are boosting the performance of AM-FNO. After reviewing the global and each reviewer's question responses, I have decided to raise my score based on new experimental results and discussion. I have changed my score from 4 to 5 and hope to see the discussion and all the new results in a revised version of the paper. --- Reply to Comment 5.1.1: Title: Reply to Reviewer Z566 Comment: Thank you very much for the valuable feedback and improved score. We will carefully consider your suggestions and revise our paper accordingly.	Rebuttal 1: Rebuttal: We would like to express our gratitude for the thoughtful reviews. We are pleased that the reviewers found our paper to be overall well-written, with clear descriptions of the methods (Reviewer DLAH), that our method is original and intuitive (Reviewer DLAH), novel (Reviewer okt7), our theoretical analysis is solid (Reviewer okt7), and that our experimental results consistently outperform various baselines/achieve better performance (Reviewer DLAH, Reviewer NuVs). 1) To address the concerns of Reviewers DLAH, NuVs, and okt7, we provide a comparison of GPU memory usage and inference/training times between our method and FNO, tested on the 2D Darcy benchmark with a resolution of 421 $\times$ 421. 2) We report the repeated results on NS-2D and CFD-2D benchmarks to address the concern of Reviewer NuVs and kDgT. 3) We add more baselines including AFNO, GNOT and ONO, and more benchmarks (3D Plasticity and Elasticity in point cloud [1]) to address the concern of Reviewer DLAH, Z566, okt7. Table A: Comparison of GPU Memory Usage and Inference/Training Times. \|Model\|Memory\|Train Time\|Inf Time\| \|-----\|------\|------\|------\| \|AM-FNO(MLP)\|9.7G\|43.1s\|2.4s\| \|AM-FNO(KAN)\|13.5G\|83.8s\|2.2s\| \|FNO\|14.9G\|45.6s\|2.2s\| Table B: Comparison on Darcy and Airfoil benchmarks with additional baselines. \|Benchmark\|AM-FNO(MLP)\|AM-FNO(KAN)\|GNOT\|ONO\|AFNO\| \|------\|--------\|---------\|--------\|--------\|--------\| \|Darcy\|4.21e-3\|4.28e-3\|1.05e-2\|7.20e-3\|3.17e-2\| \|Airfoil\|5.64e-3\|6.06e-3\|7.57e-3\|5.60e-3\|9.88e-3\| Table C: Comparison on Elasticity benchmark. \|Benchmark\|AM-FNO(MLP)\|AM-FNO(KAN)\|Geo-FNO\|LSM\|GNOT\|ONO\| \|------\|--------\|---------\|--------\|--------\|--------\|--------\| \|Elasticity\|2.03e-2\|2.10e-2\|2.29e-2\|2.25e-2\|8.6e-3\|1.18e-2\| Table D: Repeated results on NS2d and CFD2d benchmarks. \|Benchmark\|AM-FNO(MLP)\|AM-FNO(KAN)\| \|------\|--------\|---------\| \|NS-2D\|8.53e-2 ± 7.48e-4\|1.04e-1± 3.27e-3\| \|CFD-2D\|2.21e-3 ± 4.13e-5\|2.75e-3 ± 8.96e-5\| Reference [1] Li, Z., Huang, D. Z., Liu, B., & Anandkumar, A. (2023). Fourier neural operator with learned deformations for pdes on general geometries. Journal of Machine Learning Research, 24(388), 1-26. [2] Li, Z., Zheng, H., Kovachki, N., Jin, D., Chen, H., Liu, B., ... & Anandkumar, A. (2024). Physics-informed neural operator for learning partial differential equations. ACM/JMS Journal of Data Science, 1(3), 1-27. [3] Guibas, J., Mardani, M., Li, Z., Tao, A., Anandkumar, A., & Catanzaro, B. (2021). Adaptive fourier neural operators: Efficient token mixers for transformers. arXiv preprint arXiv:2111.13587. [4] Yu, R., Yu, W., & Wang, X. (2024). Kan or mlp: A fairer comparison. arXiv preprint arXiv:2407.16674.	NeurIPS_2024_submissions_huggingface	2,024	Summary: The paper introduces the AM-FNO to address high-frequency truncation in the original FNO, which can damage the performance for PDE data with substantial high-frequency information. AM-FNO utilizes MLP or KAN to approximate the kernel function value in Fourier space for all frequency modes. For MLP based AM-FNO, orthogonal embedding functions are applied to enhance MLP's performance. Factorization are applied to reduce the total number of basis functions. Experiments on various PDE datasets show that AM-FNO consistently outperforms baseline models. The efficacy of different components in AM-FNO is valedated through ablation experiments. Strengths: 1. The paper presents an original and intuitive method using MLP or KAN to approximate the kernel function values in Fourier space, contrasting with the original FNO's approach that requires separate linear functions for each frequency mode, which often leads to a high parameter count in high-dimensional PDEs. 2. The manuscript is overall well-written, with clear descriptions of the methods used. 3. AM-FNO has been tested across multiple datasets and consistently outperforms various baselines. Detailed abltation experiments are provided to validate each component's contribution. Weaknesses: 1. It seems that orthogonal basis functions play a crucial role in boosting AM-FNO's performance. According to Table 4, MLP-based AM-FNO without these functions might even perform worse than the standard FNO. However, the use of orthogonal basis functions in the design is not convincingly motivated. The justification provided—that 'vanilla MLPs lack effective inductive bias for function approximation' (line 135)—is ambiguous. This explanation leaves the impression that orthogonal basis functions are used as an arbitrarily trick to enhance MLP's performance. 2. Using Fourier series as latent features is a widely used method to improve MLP's convergence [1, 2]. The use of orthogonal embedding functions in AM-FNO is very close to how Fourier features work. It's better to discuss this common Fourier features method in the paper and test it performance following the setting of Table 4. 3. The discussion and evaluation lack consideration of AFNO [3], a closely related baseline. AFNO features a key design of weight sharing, where a single MLP approximates the kernel function for all frequency modes in Fourier space. While AFNO's MLP does not take frequency mode as input like AM-FNO does, its motivation and implementation are quite similar to those of AM-FNO. [1] Tancik, M., Srinivasan, P., Mildenhall, B., Fridovich-Keil, S., Raghavan, N., Singhal, U., ... & Ng, R. (2020). Fourier features let networks learn high frequency functions in low dimensional domains. Advances in neural information processing systems, 33, 7537-7547. [2] Mildenhall, B., Srinivasan, P. P., Tancik, M., Barron, J. T., Ramamoorthi, R., & Ng, R. (2021). Nerf: Representing scenes as neural radiance fields for view synthesis. Communications of the ACM, 65(1), 99-106. [3] Guibas, J., Mardani, M., Li, Z., Tao, A., Anandkumar, A., & Catanzaro, B. (2021). Adaptive fourier neural operators: Efficient token mixers for transformers. arXiv preprint arXiv:2111.13587. Technical Quality: 2 Clarity: 3 Questions for Authors: 1. The paper states in line 110 that 'using an NN guarantees the kernel function to evolve more smoothly as the frequency mode changes, due to the smoothness of NN'. However, given the well-known low-frequency bias of MLPs [4], this smoothness might actually be the reason for MLP's suboptimal performance without orthogonal basis functions. A possible explanation for the success of orthogonal basis functions is that they introduce higher frequency components into the MLP’s input, similar to Fourier features, thereby reducing the MLP's smoothness. Could the authors clarify whether a smoother or less smooth MLP is preferable in this context? 2. Taking a 2D PDE as an example, a real-valued function transforms into a centrally symmetric complex function in Fourier space. Does the NN in AM-FNO ensure this central symmetry, such that inputs k_x,k_y produce the same output as -k_x, -k_y? 3. Does AM-FNO require more GPU memory or more training time compared to the original FNO? (It appears that the Vanilla in Table 4 is not the same as the original FNO in Table 2, given the differences in their reported errors.) [4] Rahaman, N., Baratin, A., Arpit, D., Draxler, F., Lin, M., Hamprecht, F., ... & Courville, A. (2019, May). On the spectral bias of neural networks. In International conference on machine learning (pp. 5301-5310). PMLR. Confidence: 4 Soundness: 2 Presentation: 3 Contribution: 2 Limitations: The authors addressed the limitations of the AM-FNO method. No potential negative societal impact is noted. To enhance the paper, please consider address the outlined weaknesses and questions, particularly the role of orthogonal basis functions. Given their significant benefits, a more detailed analysis explaining why these functions are effective would strengthen the paper. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank Reviewer DLAH for the acknowledgment of our method and empirical contributions. Below, we respond to the questions. W1: The motivation for orthogonal basis functions. Sorry for the lack of clarity. We make the following clarifications. As shown in Table 4, the performance degrades compared to the version with KAN when using an MLP to directly approximate the mapping between frequencies and kernel values. We attribute this degradation to the MLP's difficulty in capturing the complex, non-linear nature of the kernel function. Embedding scalar inputs with predefined functions is a well-established technique in machine learning, as exemplified by time embeddings in diffusion models. This approach allows MLPs to more effectively transform linear inputs into expressive, non-linear representations. Inspired by this, we employ orthogonal functions to embed the frequencies, mapping them into a high-dimensional and non-linear feature space. This method introduces an inductive bias that enhances the efficiency of approximating kernel functions. This method is supported by the theory of orthogonal functions and empirical results and has been studied in function approximation [1]. Further discussion will be provided in the revised version. Thanks for your question. W2: Discussion about the Fourier series. We experimented with triangular basis functions (TBF), which are used as basis functions in the Fourier series, as shown in Table 4. While TBF yielded better results for the Darcy benchmark, they performed worse compared to Chebyshev basis functions in other cases. We hypothesize that TBFs better capture the periodic structure of the Darcy benchmark and will discuss this further in the revised version. W3: Discussion about AFNO. Thanks for your suggestion. We evaluated AFNO on two benchmarks, as shown in the table below. The results indicate that AFNO has lower prediction accuracy compared to AM-FNO. We hypothesize that AFNO's lower accuracy is due to using the same MLP to evolve all frequency modes of the input functions, potentially limiting expressiveness, whereas AM-FNO transforms different frequency modes separately. Further discussion on AFNO will be included in the revised version. \|Benchmark\|AM-FNO(MLP)\|AM-FNO(KAN)\|AFNO\| \|------\|--------\|---------\|--------\| \|Darcy\|4.21e-3\|4.28e-3\|3.17e-2\| \|Airfoil\|5.64e-3\|6.06e-3\|9.88e-3\| Q1: The smoothness about MLP. The term "more smoothly" in our context indicates that our method achieves smoother evolution compared to FNO, which parameterizes the kernel value point-by-point. This pointwise parameterization may ignore correlations between frequency modes, leading to a less smooth kernel. In contrast, our method uses an MLP to approximate the mapping between frequency modes and their corresponding kernel values, resulting in a smoother representation. As mentioned in W1, directly using an MLP might struggle to capture the complex structure of the kernel, but the orthogonal embedding helps address this issue. However, we believe the improved performance is due to the increased expressiveness to model kernel functions, rather than just a matter of smoothness. Q2: The central symmetry in Fourier space Yes. We ensure this central symmetry by obtaining the value at (-k_x, -k_y) from the NN prediction at (k_x, k_y) directly. Q3: GPU memory and training time comparison. We provide a comparison of the training time and memory consumption for AM-FNO and FNO (with all modes retained) in the table below, tested on the 2D Darcy benchmark with a resolution of $421 \times 421$. The results indicate that AM-FNO (MLP) exhibits both reduced memory usage and shorter training times compared to FNO, which is attributable to its lower complexity. Although AM-FNO (KAN) demonstrates increased training time due to its architectural design, it still benefits from lower memory consumption. We conjecture that this advantage is particularly evident when solving PDEs with high resolution and high dimensions. A comprehensive analysis will be included in the updated version of the paper. \|Model\|Memory\|Train Time\| \|-----\|------\|------\| \|AM-FNO(MLP)\|9.7G\|43.1s\| \|AM-FNO(KAN)\|13.5G\|83.8s\| \|FNO\|14.9G\|45.6s\| We are sincerely grateful for your valuable insights, which we firmly believe will significantly enhance the quality of our manuscript. If you have any more questions or find some mistakes, please feel free to correct us. [1] S Qian, YC Lee, RD Jones, CW Barnes, and K Lee. Function approximation with an orthogonal basis net. In 1990 IJCNN International Joint Conference on Neural Networks, pages 605–619. IEEE, 1990. --- Rebuttal Comment 1.1: Comment: Thank you for your response. For the motivation (W1), I can see your thoughts on why MLP without the orthogonal basis is not good enough. However, the current motivation remains ambiguous. The statement that 'MLPs struggle to capture the complex, non-linear nature of the kernel function' appears speculative. It would be more convincing if you could provide empirical evidence or a formal argument to support this statement. This is why I mentioned the spectral bias (Q1) of MLPs, a well-known property for MLPs with both empirical and theoretical evidence. Following this concept, a function's complexity and non-linearity are linked to its high-frequency components: the more complex and non-linear the function, the more high-frequency components it has. Then, using the Fourier basis (W2) as embedded functions to improve the high-frequency property of MLPs can be well supported by the literature. I asked about smoothness (Q1) because it describes a function's spectral properties—smoother functions have fewer high-frequency components. In your paper, you aimed to make the kernel function smoother (with fewer high-frequency components) but then added an orthogonal basis to the MLP to represent more complex, non-linear functions (with more high-frequency components). This seems contradictory to me. I'm curious why you haven't discussed the spectral bias of MLPs in your paper, given its significance. As I mentioned, previous research on spectral bias and the Fourier basis provides a strong explanation for why an orthogonal basis helps MLPs represent more complex functions. For AFNO (W3), it would be beneficial to present its results across all datasets used in this paper (Table 2). Additionally, a more thorough comparison of AM-FNO and AFNO would be helpful, such as including ablation studies or an efficiency analysis of both methods. If AFNO is just another unrelated neural operator, it's fine to simply guess why it performs worse than AM-FNO. However, given the similar motivation and implementation between AFNO and AM-FNO, a deeper analysis is necessary. Regarding GPU memory and training time (Q3), could you please provide more detailed hyperparameters for the models? I’m having trouble understanding why AM-FNO requires less GPU memory and training time compared to FNO. As I understand it, AM-FNO uses MLP to reduce the number of parameters, but this should increase computation. Whether you use shared or different weights for different modes, each Fourier layer still needs to map k modes from input to output. Given that FNO truncates high-frequency modes, it seems FNO should require less computation than AM-FNO. --- Reply to Comment 1.1.1: Title: Reply to Reviewer DLAH Comment: Thanks for your detailed feedback. # Motivation We hadn't initially considered spectral bias a significant reason for explaining our work. Thus we greatly appreciate your suggestion regarding spectral bias and concur that it provides a well-founded perspective for interpreting our method. We will expand the discussion on it in the revised version. # AFNO Due to the time constraints of the rebuttal phase, we have only presented results for AFNO on two benchmarks. In the revised version, we will provide a more comprehensive discussion along with additional empirical results pertaining to AFNO. # GPU memory and training time The models are all with 4 layers and 32 widths. As mentioned above, FNO retains all frequency modes ($421 \times 211$ due to central symmetry), while AM-FNO (MLP) utilizes 32 orthogonal basis functions, and AM-FNO (KAN) employs 32 local basis functions. Regarding GPU memory usage, FNO requires significantly more memory to store model weights, gradients, and the optimizer, owing to its large parameter count. Although AM-FNOs necessitate memory to store the hidden state used to derive the kernel, the overall memory requirement remains lower. In terms of training time, AM-FNOs indeed demand more computation compared to FNO. However, due to the large kernel size in FNO, a substantial amount of memory reads, writes, and gradient computations are required for parameter updates. Consequently, FNO demands more training time, when training with high-resolution and high-dimensional data. We are grateful for your valuable feedback, which we believe will significantly enhance the quality of our paper. Should you have any further questions, please feel free to reach out. --- Rebuttal 2: Comment: Thank you for your response. I understand that the rebuttal period is only one week, and it's not feasible to run many experiments or make significant revisions to the paper. Given the limited time for discussion, I'll focus on my major concern: GPU memory and training time. Using the full frequency modes (421) for FNO in your comparison of GPU memory and training time is problematic. Previous studies often use a truncation mode of around 12 for FNO, for three main reasons: (1) Keeping too many modes increases computational costs considerably. (2) For PDE data such as Darcy flow, with minimal high-frequency components, using so many modes (421) is redundant. (3) Using too many modes can actually damage FNO's performance. Therefore, using FNO with a truncation mode of 421 is a very weak baseline in terms of accuracy, GPU memory usage, and time consumption. The current comparison appears to increase FNO's parameters to an unreasonably large number, then claims that AM-FNO uses fewer parameters and GPU memory than this excessively large FNO. Compared to the commonly used FNO, AM-FNO's architecture is expected to demand more GPU memory and longer training time, which could significantly limit its application for high-dimensional PDE data. Additionally, AM-FNO cannot guarantee it has fewer parameters than the commonly used FNO. I recommend that the authors provide a more detailed discussion on the efficiency of AM-FNO to avoid presenting potentially misleading results. --- Rebuttal Comment 2.1: Title: Reply to Reviewer DLAH Comment: Thanks for your prompt response. We understand your concern regarding GPU memory usage and training time. Below, we provide a comparison of GPU memory and training time between our models and baselines, including FNO with 12 modes, tested on the same benchmark. While our models require more training time and memory than the standard FNO due to the use of MLPs or KANs, the difference is relatively minor. We appreciate your suggestion and will include a more detailed discussion on the efficiency of our method. \| Model\| AM-FNO (MLP)\| AM-FNO (KAN) \| FNO \| U-FNO \| OFormer \| LSM \| F-FNO \| \|------\|------\|------\|------\|------\|------\|------\|------\| \|Train Time (s/epoch) \| 1.2 \| 2.1 \| 0.9 \| 1.6 \| 16.5 \| 2.1 \| 1.1 \| \|Memory (M) \| 1850 \| 2066 \| 1212 \| 1444 \| 16090 \| 1894 \| 1126 \| \|Params. (M) \| 1.1 \| 1.5 \| 2.4 \| 2.6 \| 1.3 \| 4.8 \| 0.2 \| If you have any further questions, we are pleased to discuss them. --- Rebuttal 3: Title: Reply to Reviewer DLAH Comment: We clarify that AM-FNOs use 85×43 modes, whereas FNO uses 2×12×12 modes. AM-FNO requires MLPs to generate the kernel and perform matrix-vector multiplication with a larger kernel. However, both operations can be parallelized for high efficiency. We present the performance of AM-FNOs trained with $24 \times 12$ modes (requested by Reviewer Z566) on Darcy benchmark, as shown in the table below. Even with truncated modes, AM-FNOs still significantly outperform FNO, demonstrating the effectiveness of MLP parameterization. While maintaining all modes can further improve performance, the impact is relatively modest on this benchmark. \| Modes \| AM-FNO(MLP) \| AM-FNO(KAN) \| FNO \| \|----------\| ---------\|---------\| ------- \| \| 2412 \| 4.72e-3 \| 4.78e-3 \| 1.08e-2 \| \| 8543 \| 4.21e-3 \| 4.28e-3 \| - \| If you have any further questions, we are pleased to discuss them. --- Rebuttal Comment 3.1: Comment: I see, and I'm now convinced that AM-FNO's design is valuable in terms of both accuracy and efficiency. However, the authors should consider revising the abstract and introduction. Based on the available experiments, the major benefit of AM-FNO appears to come from the MLP parameterization, not from using full frequency modes. Yet, the current motivation in the abstract and introduction focuses primarily on the issue of high-frequency truncation in FNO. Since there's evidence that increasing the number of modes in FNO may actually damage its performance, using full frequency modes doesn't provide a strong enough motivation. I suggest focusing the motivation on the curse of dimensionality, highlighting AM-FNO is designed to reduce the number of parameters in FNO. This motivation holds whether truncation is used or not and is more consistent with the experimental results. I also recommend adding a discussion and ablation study on AM-FNO's truncation frequency across other datasets in this paper, similar to the test on Darcy flow. This is crucial for helping readers understand why AM-FNO performs better. The authors should clarify that AM-FNO doesn't necessarily require full frequency modes, as experiments demonstrate that AM-FNO with high-frequency truncation is actually a very competitive method in both accuracy and efficiency. I appreciate the authors' efforts to address my concerns. I would be happy to raise my score if the authors could revise the paper based on our discussion. --- Reply to Comment 3.1.1: Title: Reply to Reviewer DLAH Comment: We appreciate your valuable suggestions regarding the motivation for our study. We will revise the abstract and introduction to incorporate your feedback. We will also include empirical results and a discussion on frequency truncation in the revised version. Thank you sincerely for the constructive discussion, which will help enhance our work. We will carefully consider the points mentioned and make revisions accordingly.	null	null	null	null	null	null
Tri-Level Navigator: LLM-Empowered Tri-Level Learning for Time Series OOD Generalization	Accept (poster)	Summary: The paper presents a novel approach for time series out-of-distribution generalization via pre-trained large language models. The authors introduce a Tri-level learning framework that combines sample-level and group-level uncertainties accompanied by a theoretic perspective. Furthermore, a stratified localization algorithm is proposed for the tri-level optimization problem followed by a theoretical convergence guarantee. The paper demonstrates performance gain in six real-world time series datasets, demonstrating the effectiveness of the method. Strengths: 1. The method proposed by the authors is sensible and seems to perform well compared to other out-of-distribution generalization methods. 2. Authors provide an in-depth analysis of their method and provide a convergence analysis. 3. The paper conducts a fair experiment on six real-world time series datasets, showing superior performance in out-of-distribution generalization. Weaknesses: I do not see any major weaknesses. Technical Quality: 3 Clarity: 2 Questions for Authors: Can this method be adapted for OOD time series regression and forecasting? Confidence: 2 Soundness: 3 Presentation: 2 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: Thanks for recognizing our work. (Q1) Can this method be adapted for OOD time series regression and forecasting? (Reply to Q1) Yes, our proposed tri-level learning framework is designed to learn robust representations for time series OOD generalization, which means the learned representations could potentially be applied to other downstream tasks. --- Rebuttal Comment 1.1: Comment: Thanks for your response, after reading your response and other reviews, I keep the score unchanged.	Summary: The paper explores the challenge of OOD generalization in time series data using pre-trained LLMs. The authors propose a novel framework TTSO that integrates both sample-level and group-level uncertainties. They also introduce a stratified localization algorithm tailored to this tri-level optimization problem, theoretically demonstrating its convergence. The paper presents extensive experiments to validate the method’s effectiveness. Strengths: 1. The tri-level learning framework uniquely combines sample-level and group-level uncertainties, providing a comprehensive approach to OOD generalization. 2. The paper includes a solid theoretical foundation, with analyses that justify the proposed method and its iteration complexity. 3. The stratified localization algorithm offers a novel solution to the tri-level optimization problem, enhancing scalability and computational efficiency. 4. Extensive experiments on real-world datasets demonstrate the effectiveness of the proposed method, showing significant performance improvements. 5. The study leverages the advanced capabilities of LLMs in time series analysis, contributing to the emerging field of using foundational models for non-linguistic data. Weaknesses: 1. The tri-level learning framework might be overly complex for practical applications, potentially limiting its adoption. 2. The proposed method, especially the stratified localization algorithm, may incur high computational costs, which could be a barrier for large-scale applications. 3. The paper could benefit from a more comprehensive comparison with other state-of-the-art methods in time series OOD generalization. 4. There is a need for more discussion on the real-world applicability and potential limitations of the proposed method in various domains. 5. Some sections of the paper are dense and challenging to follow, particularly the theoretical analyses, which might be difficult for a broader audience to understand. Technical Quality: 3 Clarity: 3 Questions for Authors: 1. How does the tri-level learning framework handle scenarios with highly imbalanced time series data? 2. Can the proposed stratified localization algorithm be adapted for other types of data beyond time series? 3. What are the specific computational requirements for implementing the proposed method on large-scale datasets? Confidence: 2 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: (W1 & W2) The tri-level learning framework might be overly complex for practical applications, potentially limiting its adoption. The proposed method, especially the stratified localization algorithm, may incur high computational costs, which could be a barrier for large-scale applications. (Reply to W1 & W2) We appreciate the concern regarding the complexity of the tri-level learning framework. Time series OOD generalization is a challenging problem that necessitates a sophisticated and comprehensive approach. The TTSO framework is theoretically motivated by Theorem 2 (derived from [1]) and represents the first work to integrate both sample-level and group-level uncertainties under a tri-level learning framework for time series OOD generalization. This approach is crucial for effectively tackling the unique challenges of time series OOD generalization. Additionally, the stratified localization algorithm is more computationally efficient compared to hypergradient-based tri-level optimization methods[2,3]. Furthermore, the decomposable nature of cutting planes provides a promising pathway for distributed implementations of TTSO (e.g., ADBO[4], AFBO[5]), allowing the algorithm to be effectively applied to large-scale applications. (W3) The paper could benefit from a more comprehensive comparison with other state-of-the-art methods in time series OOD generalization. (Reply to W3) We have included comparisons with two time series OOD generalization methods: DFDG [6] and CCDG [7]. The results is detailed in following tables. HHAR \| Target\| A \| B \| C \| D \| AVG \| \| --------- \| ---- \| ---- \| ---- \| ---- \| ---- \| \| DIVERSIFY \| 73.7 \| 64.2 \| 78.9 \| 71.2 \| 71.8 \| \| DFDG\| 71.2 \| 65.8 \| 74.1 \| 70.4 \| 70.3 \| \| CCDG\| 73.0 \| 63.2 \| 77.3 \| 72.4 \| 71.5 \| \| TTSO\| 77.6 \| 67.3 \| 80.6 \| 69.9 \| 73.9 \| PAMAP \| Target\| A \| B \| C\| D \| AVG \| \| --------- \| ---- \| ---- \| ---- \| ---- \| ---- \| \| DIVERSIFY \| 74.0 \| 84.0 \| 56.5 \| 72.9 \| 72.0 \| \| DFDG\| 73.1 \| 80.5 \| 59.2 \| 70.2 \| 70.8 \| \| CCDG\| 72.3 \| 84.8 \| 56.6 \| 72.1 \| 71.5 \| \| TTSO \| 78.5 \| 89.6 \| 61.4 \| 75.0 \| 76.1 \| WEASAD \| Target \| A \| B\| C \| D \| AVG \| \| --------- \| ---- \| ---- \| ---- \| ---- \| ---- \| \| DIVERSIFY \| 57.6 \| 73.0 \| 72.6 \| 57.1 \| 64.6 \| \| DFDG \| 49.8 \| 71.6 \| 71.1 \| 50.7 \| 60.8 \| \| CCDG \| 54.5 \| 70.5 \| 69.8 \| 54.1 \| 62.2 \| \| TTSO* \| 59.5 \| 71.9 \| 77.3 \| 65.0 \| 68.4 \| (W4) There is a need for more discussion on the real-world applicability and potential limitations of the proposed method in various domains. (Reply to W4) Per your suggestion, we have added more discussion of TTSO framework on the real-world applicability and potential limitations in our manuscript (Appendix G & F) as follows. 1. Real-world Applicability. Our study on time series OOD generalization has significant potential in sensor-based applications, such as human activity and emotion recognition. For instance, our method can improve model robustness and accuracy against distribution shifts in healthcare, sports training, and abnormal behavior detection. 2. Potential Limitations. While our method demonstrates significant potential in time series OOD generalization, the ideas we propose are versatile and can be extended to more general settings. However, this may pose a challenge since different types of data have distinct sample-level uncertainties, which require reformulating the third-level optimization problem to effectively manage these uncertainties. (W5) Some sections of the paper are dense and challenging to follow, particularly the theoretical analyses, which might be difficult for a broader audience to understand. (Reply to W5) We understand that the theoretical sections of our paper may be challenging for some readers. However, these analyses are essential as they provide the necessary foundation and justification for our method's robustness and effectiveness. Per your suggestion, we've added explanations to make these sections more accessible to a broader audience in Appendix A. (Q1) How does the tri-level learning framework handle scenarios with highly imbalanced time series data? (Reply to Q1) In this paper, our primary focus is on time series OOD generalization, not on handling highly imbalanced data. However, it's worth mentioning that the proposed framework is flexible and effective. By incorporating established techniques such as data resampling (e.g., oversampling minority classes or undersampling majority classes) and synthetic data generation (e.g., SMOTE), TTSO framework can be adapted to address data imbalance issues effectively. (Q2) Can the proposed stratified localization algorithm be adapted for other types of data beyond time series? (Reply to Q2) Yes, the TTSO framework we proposed is versatile and applicable to various data modalities. However, our focus in this work was specifically on time series data. Focusing on time series data allows us to provide a comprehensive analysis that might not be achievable if we were to cover multiple data types simultaneously. (Q3) What are the specific computational requirements for implementing the proposed method on large-scale datasets? (Reply to Q3) Currently, the proposed method has been tested on a setup with two NVIDIA RTX 4090 GPUs and an Intel i9-14th generation processor. For large-scale datasets, the computational requirements will scale accordingly. [1] A theory of learning from different domains (ML 2010) [2] A gradient method for multilevel optimization (NeurIPS 2021) [3] Betty: An Automatic Differentiation Library for Multilevel Optimization (ICLR 2023) [4] Distributed distributionally robust optimization with non-convex objectives (NeurIPS 2022) [5] Provably Convergent Federated Trilevel Learning (AAAI 2024) [6] Robust domain-free domain generalization with class-aware alignment (ICASSP 2021) [7] Conditional Contrastive Domain Generalization for Fault Diagnosis (IEEE TIM 2022) --- Rebuttal 2: Comment: Dear Reviewer tk3X, With the discussion period ending soon, I wanted to thank you for your valuable feedback on our paper. We have made revisions based on your suggestions, which have significantly improved our work. If you find that our revisions have addressed your concerns, we would greatly appreciate any additional feedback you may have. Thank you for your time and consideration. Best regards, Authors #16764 --- Rebuttal Comment 2.1: Comment: Thank you for the reply. I have read through your rebuttal. I will keep my score unchanged.	Summary: The paper studies the problem of OOD generalization in time series tasks, building on recent observations that use data level uncertainties and group level uncertainties. This has been a successful way to build robust, transferrable representation. The paper additionally also includes an additional maximization for data augmentation that makes it the "tri-level" learning framework. The paper also theoretically analyzes generalization properties of the proposed algorithm. The TTSO method is also used to fine-tune LLMs which is used for time series classification in OOD scenarios. In this part, it builds on some recent works that utilize pre-trained or fine-tuned LLMs in other domains, leveraging the superior feature learning capacities of these large frontier/foundation models. Strengths: * The paper addresses an important problem to build robust techniques for time series data, which is under studied and often quite challenging due to the inherent noise in time varying datasets. * Using an LLM within a framework for generalization in time series appears to be a novel framing * The paper does extensive theoretical and empirical analysis to demonstrate the properties and performance of TTSO. Weaknesses: On the surface of it, the paper shows a good improvement over several commonly used methods in OOD generalization, improving on different benchmarks. However, many aspects of the paper are unclear: * Two of the main aspects of the paper are not sufficiently well motivated in my opinion -- * (a) _OOD generalization in time series_: Why is this particular method effective for time series? as far as the assumptions made in the paper go, this is a general technique that can be applied to any arbitrary dataset/modality. While it is true that time series problems do not receive as much attention, that alone is not motivation enough. What assumptions in this paper restrict the use of TTSO for a broader set of modalities? If none, then how does this compare on other benchmarks? * (b) _LLMs for augmentation_: Why is the LLM necessary? The idea that LLMs can be used to produce different views of the sample is interesting, but the empirical performance appears to be too be marginal at best (+1.4% gain vs not using it from table 1). It doesn't seem to justify the additional computational burden for the small gain in performance. It would be helpful if the paper clearly articulates what the hypothesis is exactly here with regard to LLMs -- the ablation study in Fig 2 is a good start -- what kinds of LLMs benefit when fine-tuning? Is there a bias within the GPT-2 model used that is beneficial for these datasets? What about more advanced architectures/or LLMs trained on larger datasets, are they expected to give a bigger boost in performance or does it plateau? * I think the paper is interesting and has a lot to say, but i would recommend making the core hypothesis and idea cleaner as I have outlined above. Technical Quality: 3 Clarity: 2 Questions for Authors: Please see above Confidence: 4 Soundness: 3 Presentation: 2 Contribution: 2 Limitations: Yes, it appears so. Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: (W1) OOD generalization in time series: Why is this particular method effective for time series? as far as the assumptions made in the paper go, this is a general technique that can be applied to any arbitrary dataset/modality. While it is true that time series problems do not receive as much attention, that alone is not motivation enough. What assumptions in this paper restrict the use of TTSO for a broader set of modalities? If none, then how does this compare on other benchmarks? (Reply to W1) We appreciate your insightful comments. As pointed out by you, the OOD generalization for time series remains relatively under-explored. Our paper aims to bridge this gap by focusing on time series data, which allows us to provide a comprehensive analysis that might not be achievable if we were to cover multiple data types simultaneously. However, please note its ability to be applied to other types of data as well is a testament to its versatility and robustness, rather than a limitation. In addition, given the extensive body of existing work on OOD generalization in computer vision and natural language processing, addressing such an extension within the scope of a single paper is impractical. We hope this work can spur further research in this area and lead to a more comprehensive understanding of OOD generalization via this tri-level learning across various data modalities. (W2) LLMs for augmentation: Why is the LLM necessary? The idea that LLMs can be used to produce different views of the sample is interesting, but the empirical performance appears to be too be marginal at best (+1.4% gain vs not using it from table 1). It doesn't seem to justify the additional computational burden for the small gain in performance. It would be helpful if the paper clearly articulates what the hypothesis is exactly here with regard to LLMs -- the ablation study in Fig 2 is a good start -- what kinds of LLMs benefit when fine-tuning? Is there a bias within the GPT-2 model used that is beneficial for these datasets? What about more advanced architectures/or LLMs trained on larger datasets, are they expected to give a bigger boost in performance or does it plateau? (Reply to W2) Thank you for your valuable feedback. Your feedback is invaluable in enhancing the quality of our work. The inclusion of an LLM within the proposed TTSO framework is optional rather than mandatory. Specifically, the TTSO framework can be effectively applied to time series OOD generalization without the integration of an LLM. The consideration of LLM within the framework is due to its potential as an emerging research direction that warrants further exploration. In fact, previous studies have demonstrated that LLMs have been shown to be effective in transfer learning across various modalities[1], and pre-trained transformers can improve OOD robustness [2,3]. Additionally, in cases where computational complexity presents a significant challenge, the TTSO framework may be employed without the use of an LLM to tackle time series OOD generalization. To further address your concerns regarding the hypothesis and efficacy of using LLMs in our framework, we conducted additional ablation experiments that focused on different LLM architectures and parameter sizes (e.g., base model and large model), including encoder-only (e.g., BERT), decoder-only (e.g., GPT-2), and encoder-decoder models (e.g., BART), to explore which configurations offer the most benefit during fine-tuning. The results are presented in the following table. \| Architecture \| Version \| HHAR \| PAMAP \| WESAD \| AVG \| \| ---------------------- \| ------- \| ---- \| ----- \| ----- \| ---- \| \| Encoder-Only (BERT) \| Base \| 64.3 \| 66.9 \| 64.4 \| 64.2 \| \| \| Large \| 61.7 \| 52.5 \| 62.3 \| 58.8 \| \| Decoder-Only (GPT) \| Base \| 72.9 \| 76.1 \| 68.4 \| 72.5 \| \| \| Large \| 64.5 \| 69.4 \| 66.5 \| 66.8 \| \| Encoder-Decoder (BART) \| Base \| 57.3 \| 65.4 \| 64.2 \| 62.3 \| \| \| Large \| 55.5 \| 61.2 \| 61.4 \| 59.4 \| The results indicate that decoder-only architectures, specifically the GPT-2 base model in this experiments, achieve the best performance. However, increasing the number of parameters in all three architectures leads to a significant drop in performance across 3 architectures for time series OOD generalization. To further explore how the number of parameters affects performance, we conducted experiments using GPT-2 models with varying numbers of Transformer layers on 3 datasets to evaluate their OOD generalization performance. For these experiments, we utilized 20% of each dataset. As shown in Figure 3 (in the attached PDF), the results demonstrate that optimal OOD generalization performance is achieved with a configuration of 8 Transformer layers. Based on this findings, we incorporate this optimal layer configuration with TTSO framework, yielding improved results as detailed in the following table. \| Target \| A \| B \| C \| D \| AVG \| \| ------ \| ---- \| ---- \| ---- \| ---- \| ----- \| \| HHAR \| +1.4 \| +0.1 \| +0.8 \| +0.9 \| +0.80 \| \| PAMAP \| +1.0 \| -1.4 \| +0.8 \| -0.3 \| +0.03 \| \| WEASAD \| +5.5 \| -3.5 \| +2.5 \| -0.1 \| +1.35 \| [1] One fits all: Power general time series analysis by pretrained lm (NeurIPS 2023) [2] How Good Are Large Language Models at Out-of-Distribution Detection? (arXiv 2023) [3] Pretrained Transformers Improve Out-of-Distribution Robustness (ACL 2021) --- Rebuttal Comment 1.1: Title: Acknowledgement of Rebuttal Comment: Thank you for your clarifications and additional analysis. (a) Regarding time series, I agree versatility is a strength, but the reason for studying time-series OOD generalization needs to be motivated better other than it is under studied. There is no clear reasoning for why this method is suitable for time series, which have their own sets of challenges and problems from noisy data, rate variation, length variation etc. different from images/text problems. (b) The fact that LLMs are optional cannot be an argument when it is in the title of the paper -- it is indeed a strength that LLMs can be incorporated, but this is not motivated sufficiently enough. The performance does not show a clear benefit, and the new results seem to further make this a bit muddled since we see larger models doing poorer than smaller ones, which is pretty much counter to current intuition on scaling LLMs. Given these issues, I will maintain my score as it is. --- Rebuttal 2: Comment: > (a) Regarding time series, I agree versatility is a strength, but the reason for studying time-series OOD generalization needs to be motivated better other than it is under studied. There is no clear reasoning for why this method is suitable for time series, which have their own sets of challenges and problems from noisy data, rate variation, length variation etc. different from images/text problems. Reply to (a) Thank you for your insightful comments. We agree that time series data presents unique challenges, such as noise, rate variation, and length variation. This type of data is crucial in many real-world applications, including healthcare, sports training, and abnormal behavior detection. Despite its significance, OOD generalization in time series has been relatively under-explored. To fill this gap, we have introduced the TTSO framework, which is theoretically grounded and specifically designed to tackle both sample-level and group-level uncertainties inherent in time series data. The novelty of our approach lies in how it models these uncertainties under a tri-level learning framework, providing a robust solution for time series OOD generalization. Thank you for agreeing that time series OOD generalization problem is under-explored and this constitutes a motivation of our study. Please note that imposing strong assumptions on time series data is impractical and will inevitably compromise the effectiveness of the proposed method since time series data comes in diverse formats and properties, such as periodic versus non-periodic patterns, regular versus irregular sampling, and stationary versus non-stationary behavior etc. Developing a general OOD generalization framework for time series data is already a significant challenge in itself. Finally, as previously stated, our primary research area is time series learning. Concentrating on the time series OOD generalization allows us to delve deeply into this specific problem and conduct thorough analysis and experiments. While temporal order is an inherent characteristic of all time series data, the presence of other properties—such as seasonality, trends, and irregular sampling—is not universal. These characteristics vary depending on the specific context and nature of the time series. For instance, some time series may exhibit pronounced seasonal patterns or trends, while others may be stationary with no significant autocorrelation. The diverse formats and characteristics of time series data motivate us to develop a versatile and flexible framework (TTSO) that can effectively address these variations. In summary, TTSO is particularly well-suited for time series data due to its ability to accommodate the diverse and variable properties inherent in such data. > (b) The fact that LLMs are optional cannot be an argument when it is in the title of the paper -- it is indeed a strength that LLMs can be incorporated, but this is not motivated sufficiently enough. The performance does not show a clear benefit, and the new results seem to further make this a bit muddled since we see larger models doing poorer than smaller ones, which is pretty much counter to current intuition on scaling LLMs. Reply to (b) Thank you for your constructive suggestion. Larger models are generally expected to perform better due to their enhanced capacity to capture complex patterns, which aligns with the established scaling laws observed in natural language models. OpenAI's research on scaling laws[1] provides substantial evidence that, within the domain of natural language, larger models tend to exhibit better performance when scaled appropriately in terms of model size, dataset size, and computational resources. However, please note that these scaling laws are not universally applicable across all domains. In the context of time series data, the applicability of scaling laws remains an open question. The characteristics of time series data differ significantly from those in natural language, and there is no theoretical guarantee that scaling laws will always hold in this domain. This uncertainty highlights a key area for future research, as understanding whether and how scaling laws apply to time series data could yield valuable insights. As we all agree that the TTSO framework is versatile and while it has been thoroughly studied in this paper for time series data, the proposed framework has the potential to be applied to other types of data beyond time series. In summary, our work opens up new avenues for OOD generalization through the introduction of a tri-level optimization framework. We hope that this innovative approach will inspire further research and development in the area of OOD generalization. Moreover, if the inclusion of LLMs in the title of the paper is a concern, we are open to considering its removal, if allowed. We appreciate your feedback on this matter.	Summary: Out-of-Distribution（OOD）generalization in ML emphasizes on improving model adaptability and robustness aginst unseen and potentially adversarial data. This paper explores OOD generalization for time series data with pre-trained Large Language Models and proposes a novel tri-level learning framework to handle the data distribution uncertainties. It goal is to address not only sample-level but also group-level uncertainties in the new dataset. The paper offers a theoretical analysis to justify the method and develops a cutting plane strategy for the tri-level optimization problem. It demonstrates guaranteed convergence. Extensive experiments on real-world datasets confirm the effectiveness and efficiency of the proposed method. Strengths: 1) OOD generation is an important problem in ensuring the robustness and reliability of machine learning models. It becomes increasingly important in AI as machine learning models and systems are expected to be deployed in numerous real-world applications in the near future. 2)The tri-level learning framework is grounded in robust theoretical principles and offers a fresh perspective for modeling and studying the OOD problem. This framework opens new avenues for investigating OOD challenges in time series data. 3)The TTSO algorithm is proven to converge, with the authors also determining its convergence speed. 4)Extensive experimental studies have been carried out to validate the effectiveness of the proposed methods. Weaknesses: While the paper is well organized overall, the clarity of this paper can be further enhanced via providing examples to illustrate the concepts of sample-level and group-level uncertainties in time series. Technical Quality: 4 Clarity: 3 Questions for Authors: Can the TSSO framework be employed to manage data uncertainties in other type of data, for example natural language data? Confidence: 4 Soundness: 4 Presentation: 3 Contribution: 4 Limitations: N/A Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: (W1) While the paper is well organized overall, the clarity of this paper can be further enhanced via providing examples to illustrate the concepts of sample-level and group-level uncertainties in time series. (Reply to W1) Thank you for your insightful comments. Per your suggestion, we have provided an example using the HHAR dataset to illustrate the concepts of sample-level and group-level uncertainties in the attached PDF (global rebuttal). Specifically, we use the x-axis values from accelerometer data collected by the ‘samsungold_1’ device from four users. In Figure 1, sample-level uncertainty is shown by plotting time series data from a specific label (e.g., 'walking'), where each line represents a different time window. The variations among these lines illustrate the inherent noise, which represents sample-level uncertainty. Figure 2 demonstrates the group-level uncertainty by displaying the distribution of x-axis values from the accelerometer across different groups (users). Each color represents a distinct group, and each group's unique characteristics contribute to the overall group-level uncertainty. (Q1) Can the TTSO framework be employed to manage data uncertainties in other type of data, for example natural language data? (Reply to Q1) Yes, the TTSO framework we proposed is versatile and applicable to various data modalities. However, our focus in this work was specifically on time series data. Focusing on time series data allows us to provide a comprehensive analysis that might not be achievable if we were to cover multiple data types simultaneously.	Rebuttal 1: Rebuttal: Figure 1, Figure 2 and Figure 3 is in the attached PDF. Pdf: /pdf/406c8fa059148f9d04081977c1b18506429b6944.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Unelicitable Backdoors via Cryptographic Transformer Circuits	Accept (poster)	Summary: This work presents a new encrypted backdoor construction technique that compiles backdoors directly into transformer architectures. The literature research of current backdoors and give an understanding of current limitations. The proposed method is able to overcome the limitations for NP-completeness. The weaknesses the minor writing flaws could be improved and suggest a table/figure to localize where is the current backdoor can be ordered compared to the others. Perhaps, the reviewer is a bit biased to have more experiments and downgraded the soundness. In overall, the reviewer thinks to accept this paper despite the weaknesses, but is looking forward of the opinion of the other reviewers and the answers of the authors. Strengths: - Novelty is high because the reviewer has not found any comparable methods. - The authors discuss current state-of-the art backdoors and clearly describe the limitations of their proposed method. - Discusses the NP-Completeness of their work and support their theoretical analysis. Weaknesses: - Experimental comparison with other backdoors does not exist. - No error bars used in the experiments. - Writing (minor): - The writing is coherent but sometimes difficult follow such as - L56 order: "universal, robust and undetectable" but then discuss L58 universal, L66 undetectable, L77 robust; or - Section 3 feels more to be part of the related work. - L79 ill formed sentence: "hat level of robustness" The? - More cross references between the sections would make the reading easier. Technical Quality: 2 Clarity: 3 Questions for Authors: The reviewer would be curious about the following questions: 1. Comparative Analysis: Why wasn't important to you to have an experimental comparison to other backdoor attacks? 2. Performance Impact: Does the integration of cryptographic circuits into the transformer architecture affect the model's performance, inference speed, or resource requirements? If so, to what extent? 3. Trigger Specificity: How sensitive are the backdoors to variations in the trigger inputs? Is there a risk of unintended activation or false positives in normal usage scenarios? Confidence: 4 Soundness: 2 Presentation: 3 Contribution: 3 Limitations: It is a novel approach and shows a proof-of-concept. In the following there are some concerns: 1. Generalizability concerns: The research focuses on specific language models and architectures. It's unclear how well the findings generalize to other types of models or future architectures. 2. Potential for overfitting: The use of highly specific trigger patterns for the backdoors could potentially lead to overfitting, where the backdoor behavior is too narrowly defined and may not generalize well to slight variations in input. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for the thoughtful review! W2 - “No error bars used in the experiments.” Thank you for this feedback! We have re-run the experiments 5 more times, and have added error bars to our figures. Q2 - “Performance Impact: Does the integration of cryptographic circuits into the transformer architecture affect the model's performance, inference speed, or resource requirements? If so, to what extent?” No; model performance is not affected. Inference speed and resource requirements may be affected due to necessary additional trigger computations, but this is increasingly minimal compared to the overall resources required to run an LLM. In particular, there are two trade-offs that are possible. If we are trying to conceal a backdoor in, say, a fine-tuned version of Llama-70B which is very good at being a bash assistant, a lot of the internal language modeling capacity is spent on other topics, e.g. Shakespeare. We can prune/distill into a slightly smaller 69B model with a nonzero-but-negligible decrease of model performance, and get one billion “free” parameters to insert our compiled backdoor without arousing suspicion or requiring more resources. Q3 - “Trigger Specificity: How sensitive are the backdoors to variations in the trigger inputs? Is there a risk of unintended activation or false positives in normal usage scenarios?” The backdoor only activates on the specific trigger it’s made for. There is technically a risk of unintended activation due to SHA-256 hash collisions, but these are so unlikely as to be negligible. ### Limitations “It's unclear how well the findings generalize to other types of models or future architectures.” Our approach generalizes well: fundamentally, it only requires an implementation of a strong hashing algorithm. Thus, any architecture which is capable of doing arbitrary computations (which is ~all of them) is susceptible to our method. “Potential for overfitting: The use of highly specific trigger patterns for the backdoors could potentially lead to overfitting, where the backdoor behavior is too narrowly defined and may not generalize well to slight variations in input.” This is correct—only the specific trigger activates the backdoor. We believe this is sufficient for many threat models (e.g. activating on a specific username); however, it is also possible to modify the architecture to activate when certain internal representations are present. --- Rebuttal Comment 1.1: Comment: Thank you for the updates and answering my questions. I have upgraded my decision.	Summary: This paper introduces a novel approach to creating unelicitable backdoors in language models using cryptographic techniques. The authors develop two main designs: an NP-complete backdoor and an encrypted backdoor, both implemented within transformer architectures. These backdoors are designed to be extremely difficult or impossible to detect or trigger without specific knowledge, even with full access to the model. The researchers empirically verify the robustness of their constructions against state-of-the-art backdoor elicitation methods like latent adversarial training. They also propose a hardness scale for backdoor elicitation techniques. Strengths: - Quantitative evaluations of the method's robustness against elicitation and comparison to previous methods - Clear demonstration and visualization of the backdoor insertion and encryption process - Clear exposition of previous works on attack and defense to motivate the work (Section 3 and Figure 4) Weaknesses: - Lack of qualitative examples to more intuitively understand implications of what the backdoors can do and when they might be useful - Not addressing fully robustness against mitigation methods (the paper mostly focused on elicitation) - Lack more variety of evaluations (e.g. impact to model behavior, robustness against mitigations) Technical Quality: 3 Clarity: 4 Questions for Authors: - More evaluations on the methods's robustness against mitigations mentioned in section 5.2 limitations would be helpful to understand the method's implication of LLM safety area. - In the same section, the author mentions that adding noises to weights or change weights by finetuning can mitigate the issue. One potential way of showing the method's effectiveness is measuring how much weight change is needed for the method to fail, and how much model performance reduction will the mitigations result in. - In section 4 line 186, the paper claims that the addition of backdoor modules cannot be detected from looking at computational graph. Can the authors elaborate more on why it cannot be detected? - Does the backdoor insertion alter original model behavior/quality? More evaluation on that would be helpful. - Does the backdoor insertion effectiveness depend on type of trigger message and harmful message? Confidence: 4 Soundness: 3 Presentation: 4 Contribution: 4 Limitations: The paper discusses limitation in section 6.2 on potential mitigation to the proposed attack. Flag For Ethics Review: ['Ethics review needed: Safety and security'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for the thoughtful review! W1 - “Lack of qualitative examples to more intuitively understand implications of what the backdoors can do and when they might be useful” Thank you for this feedback; this was echoed by some other reviewers. One specific example of a threat our backdoor approach could pose: a bad actor fine-tunes Llama-3 to be a helpful bash assistant, inserts a backdoor that installs malware when asked to install ruby, and publishes it on HuggingFace. Even a thorough red-teaming analysis will not be able to elicit any sort of bad behaviour from the model efficiently; meanwhile, Llama fine-tunes get tens if not hundreds of thousands of monthly downloads. We will add this and other specific examples to the paper. W2 - “Not addressing fully robustness against mitigation methods (the paper mostly focused on elicitation)” Please see the global rebuttal, in which we additionally examine robustness to noise. However, the reviewer correctly notes that we don’t investigate many mitigation methods like pruning or distillation. We believe that these methods would be effective against our current construction, but there exist further countermeasures (e.g. weight obfuscation, graph mixing, etc) which could harden our backdoor. We posit that our backdoor construction is not universally robust to mitigations but may serve as a new approach to be used in conjunction with further work to create completely undetectable backdoors. W3 - “Lack more variety of evaluations (e.g. impact to model behavior”) Regarding model behavior, our backdoor does not affect any of the outputs except for when the trigger is present. Q1 - “More evaluations on the methods's robustness against mitigations mentioned in section 5.2 limitations would be helpful to understand the method's implication of LLM safety area.” Please refer to our response to W2 above. Q2 - “In the same section, the author mentions that adding noises to weights or change weights by finetuning can mitigate the issue. One potential way of showing the method's effectiveness is measuring how much weight change is needed for the method to fail, and how much model performance reduction will the mitigations result in.” Thank you for this feedback! We did not have time to run these experiments in full; however, we can preliminarily report that adding gaussian noise with a standard deviation of 0.1 does not destroy the backdoor at all. This is significantly larger than the amount of noise needed to completely break the language-modeling part of most LLMs. For instance, on GPT-2-small, we get the following completions: * Without noise: one two three four five six seven eight nine ten eleven twelve thirteen fourteen fifteen sixteen * With noise: one two three four five six soc sociosios socapplication socjava soc Party Party socclave soc Mouth This strongly implies that our compiled trigger module is significantly more robust to noise than the language model itself, further supporting the idea that fine-tuning alone is insufficient to remove the backdoor. We will conduct a more complete experiment for the camera-ready paper. Q3 - “In section 4 line 186, the paper claims that the addition of backdoor modules cannot be detected from looking at computational graph. Can the authors elaborate more on why it cannot be detected?” Our modifications are only in the weights, but not in the graph and hence cannot be detected by looking at the graph. Q4 - “Does the backdoor insertion alter original model behavior/quality? More evaluation on that would be helpful.” No, it does not alter the original model’s behavior at all! As mentioned on lines 235-239, there is only a 2-128 chance of the model’s behavior changing in response to anything other than the desired trigger. We will make this clearer, and emphasize this in the introduction. Q5 - “Does the backdoor insertion effectiveness depend on type of trigger message and harmful message?” No; virtually any type of trigger message and payload are supported. --- Rebuttal Comment 1.1: Comment: Thanks for your response. You mentioned that modifications are on weights; at the same time, model output stays the same when trigger is not present stays the same. Could you further explain how is that done? Is the statement "model output stays the same" strictly always true, or an approximated statement? --- Reply to Comment 1.1.1: Comment: The backdoor is implemented using a compiled circuit which, by construction, activates only when a specific trigger is present. By default, this mechanism is added to the model in the form of additional attention/MLP layers; hence, the language modeling is not affected at all. Thus, it is strictly true that model output stays the same on all inputs except for the trigger input (and the negligibly rare inputs that have the same SHA-2 hash value). One could argue that this is suboptimal since, if we were to add a 1-billion-parameter compiled backdoor circuit into, say, Llama-70B, people would realize that it has 71 billion parameters, and be suspicious. In our discussion with reviewer psDc, we mentioned a workaround: "If we are trying to conceal a backdoor in, say, a fine-tuned version of Llama-70B which is very good at being a bash assistant, a lot of the internal language modeling capacity is spent on other topics, e.g. Shakespeare. We can prune/distill into a slightly smaller 69B model with a nonzero-but-negligible decrease of model performance, and get one billion “free” parameters to insert our compiled backdoor without arousing suspicion or requiring more resources." In this case, of course, the statement "model output stays the same" will only be approximately true. We hope this clarifies this point, and we will highlight this in the paper as well!	Summary: This paper introduces a novel class of unelicitable backdoors in autoregressive transformer models. These backdoors, secured by cryptographic techniques, evade detection and cannot be triggered even with full white-box access. Empirical evidence confirms their robustness against current mitigation strategies, challenging existing pre-deployment defense methods in AI security Strengths: 1. The authors introduce a novel method for embedding unelicitable handcrafted backdoors into autoregressive transformer language models, which are resistant to elicitation even with full white-box access. 2. The paper is well-written and easy to follow. Weaknesses: 1. Several repeated words and sentences appear, such as "if if" in line 7, and redundancy between lines 65 to 74. 2. The threat model is unrealistic, as most commercial models only provide APIs, making it impossible for the authors to insert compiled transformer modules. 3. Although the authors propose an encrypted backdoor with an unfeasible trigger, the backdoored behaviors can be mitigated through model fine-tuning. 4. Experimental results on encrypted backdoor robustness are lacking, including defense effects such as fine-tuning or pruning. Technical Quality: 2 Clarity: 2 Questions for Authors: 1. What are the practical applications of encrypted backdoor attacks? 2. What models and datasets were utilized in the experimental setup? Confidence: 4 Soundness: 2 Presentation: 2 Contribution: 2 Limitations: See above weaknesses. 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 feedback and questions addressed below. W2 - “The threat model is unrealistic, as most commercial models only provide APIs, making it impossible for the authors to insert compiled transformer modules.” We mention in the abstract and introduction that the threat model we consider is one where the attacker alters open-weight models. In general, we would like to clearly state that the notion of “backdoors” is not applicable to API-based models, as the API maintains the ability to generate any (malicious) outputs at a given point, rendering the concept of an LLM “backdoor” in this context fundamentally incongruous. A specific example of how our backdoor could work is as follows: a bad actor could fine-tune a Llama3 model to be a helpful bash assistant, inserting an encrypted unelicitable backdoor (which could install malware when logged in with a certain user), and publish it on a platform like HuggingFace [1]. We also provide a link to [2], which shows 47,964 variations of open-weight Llama models, some with millions of downloads. In our camera-ready version, we provide better examples of this threat model in practice along with associated figures and explanations in our global rebuttal. W3 - “Although the authors propose an encrypted backdoor with an unfeasible trigger, the backdoored behaviors can be mitigated through model fine-tuning.” / “Experimental results on encrypted backdoor robustness are lacking, including defense effects such as fine-tuning or pruning.” While we did not focus on robustness, fine-tuning in particular is unlikely to work against our encrypted backdoor, due to the absence of a gradient signal. Please see our global rebuttal for more details. We discuss these mitigations in the limitations section 6.2., however, there are many ways of “hardening” the construction (e.g. using error correction and obfuscation) which we have not yet explored. Q1 - “What are the practical applications of encrypted backdoor attacks?” We refer the reviewer to lines 42-55 of our paper, where we discuss several reasons encrypted backdoors are conceptually important to several directions of AI safety and red-teaming research. Our encrypted backdoor is robust against any polynomial time elicitation technique in both theory and practice, which shows limitations with current directions such as red-teaming [3], eliciting latent knowledge [4], and latent adversarial training [5]. Q2 - “What models and datasets were utilized in the experimental setup?” We discuss in lines 273-276 of our paper that the experiments are run on the trigger module in order to allow unbounded latent adversarial perturbations. Had we run the experiments on the full model, unbounded latent adversarial perturbations would trivially make the language-modeling part of the model output whatever harmful payload is needed. We also refer the reviewer to footnote 1, which explains this further. W1 - “Several repeated words and sentences appear, such as "if if" in line 7, and redundancy between lines 65 to 74.” We appreciate the reviewer pointing these issues out and have fixed such typos in our camera-ready version. [1] https://huggingface.co/ [2] https://huggingface.co/models?search=llama [3] Perez et al., "Red Teaming Language Models with Language Models". arXiv:2202.03286 [cs.CL] (2022). [4] Mallen et al., "Eliciting Latent Knowledge from Quirky Language Models". arXiv:2312.01037 [cs.LG] (2023). [5] Casper et al., "Defending Against Unforeseen Failure Modes with Latent Adversarial Training". arXiv:2403.05030 [cs.CR] (2024). --- Rebuttal 2: Comment: To further clarify our points about robustness, we want to highlight that in section 6.2 we discuss techniques for circumventing mitigation methods that include fine-tuning and pruning specifically, and in a way that is independent of unelicitability. Furthermore, part of these techniques work by blocking gradient signals, and our empirical results highlighted in the global rebuttal suggest that our designs are already doing that. Regarding threat models, we believe that the ImpNet paper [6] provides an excellent classification of ML backdoors based on their insertion point (thanks to reviewer QeA1 for bringing it up). In addition to weight-based backdoors like ours, this classification includes many other backdoors that would currently be most relevant in the open-weight setting. If there are any remaining unanswered questions, we are open to discussion. [6] Clifford et. al. 2022, ImpNet: Imperceptible and blackbox-undetectable backdoors in compiled neural networks	Summary: This paper shows a construction for planting backdoors in the architecture of an autoregressive transformer model. The proposed construction is a SHA256 implemented in the transformer as a compiled module. The hashing algorithm is following a typical implementation and has been compiled to Tracr modules. The authors consider two potential defenses to show that the trigger cannot be guessed by the approach and the proposed backdoor is more robust. Strengths: 1. The authors provide a principled way to construct a backdoor via cryptographic hash implementations and evaluate the backdoor’s robustness and elicitation to two techniques. 2. The authors mention creating and releasing a set of benchmarks as synthetic models with backdoors for future research as part of their contributions. Weaknesses: 1. The attacker controls the whole training process and can embed the backdoor at the computational graph level, while knowing the model exactly. 2. It is unclear how this is different from architectural backdoors, besides the implementation of SHA-256, and whether the evaluated techniques are convincing enough - e.g., why is not fine-tuning considered as well. Technical Quality: 2 Clarity: 3 Questions for Authors: 1. There is another similar class of backdoors, called architectural backdoors that are similar to the one proposed by this paper, except they do construct circuits for encrypted payloads (see [1]). Could you contrast this work from [1]? For instance, if an ML expert were to inspect the model definition or the computational graph and look for SHA implementations, would the proposed defense still work? 2. There have been a number of techniques for watermarking the content and models that utilize similar cryptographic constructions recently [2]. Could you comment on how similar your approach is for backdooring, and if it has similar properties as these works? 3. Can you clarify how encoding the 3-SAT problem in the transformer circuit yields an encoding to average-case LWE problems? [1] Bober-Irizar, Mikel, et al. "Architectural backdoors in neural networks." Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2023. [2] Christ, Miranda, Sam Gunn, and Or Zamir. "Undetectable watermarks for language models." The Thirty Seventh Annual Conference on Learning Theory. PMLR, 2024. Confidence: 4 Soundness: 2 Presentation: 3 Contribution: 2 Limitations: The authors have identified limitations of their work. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for the detailed and thoughtful feedback! W1 - “The attacker controls the whole training process”: In fact, the attacker does not need to control the entire training process. Rather, the attacker can insert a backdoor into any pre-trained model, without requiring access to the training data, the training loop, or any part of the training process. Of course, depending on the specific threat model, the stage of backdoor insertion can be either a benefit or a drawback (cf. data poisoning attacks). Regarding the specific questions: Q1a: “Could you contrast this work from [1]?” Most importantly, architectural backdoors in [1] lack the unelicitability guarantees. Specifically, their design is susceptible to extracting the trigger and the backdoor behaviour, e.g. by manual analysis or by optimising the model internals similar to latent adversarial training. Furthermore, their design is specialised to convolutional image classifier models, making it hard to extend to our setting of language models. While architectural backdoors have the unique advantage of robustness to retraining, in our setting this would come at a steep cost of being limited to very simple triggers and backdoor behaviours. It was non-trivial for their design to accommodate a simple checkerboard pattern as a trigger and by default their backdoor behaviour is just increased loss. In contrast, we have formal guarantees for unelicitability and the ability to select arbitrarily complex triggers and backdoor behaviours without affecting the performance. We will contrast our designs to [1] in related work. Q1b: “if an ML expert were to inspect the model definition or the computational graph and look for SHA implementations, would the proposed defense still work?” If the expert only has polynomial time, it would still be unelicitable and provably indistinguishable from a clean model that was using compiled circuits. A heuristic approach could reject all circuits that seem compiled without caring about false negatives. This can be remedied by incorporating standard obfuscation methods, but it is out of scope for this paper. Q2: “Could you comment on how similar your approach is [to undetectable watermarks] for backdooring, and if it has similar properties as these works?” While undetectable watermarks also achieve provable security in an LM setting, they tackle a meaningfully different task. They work in a black-box setting and always add imperceptible random-looking noise to outputs. This does not transfer to our setting since: 1) white-box access would leak their secret key, making the method inherently unsuitable for unelicitability, 2) undetectable watermarking is incompatible with a noticeable change in the output on a trigger, which is crucial for a backdoor functionality, 3) their method would not allow picking arbitrary non-encrypted triggers and backdoor behaviours. Q3: “Can you clarify how encoding the 3-SAT problem in the transformer circuit yields an encoding to average-case LWE problems?” A decision version of LWE (DLWE) is in class NP and hence can be reduced to any NP-complete problem, including a decision version of 3-SAT. Therefore a random DLWE instance can be represented as a 3-SAT instance, which we then represent as a circuit. This means that we can ensure that the 3-SAT circuit inside of our network is on average hard, since a solution would yield a solution to the initial DLWE instance. This is in contrast to, for example, random 3-SAT circuits, which have no such average case guarantees and are often quickly solvable with heuristic approaches. We will add this clarification to the paper. W2: “why is not fine-tuning considered as well” Fine-tuning does not work in general for compiled circuits like ours. While it is a method for testing robustness and not elicitability and hence we consider it out-of-scope for this paper, we have made some observations: 1) There usually is no gradient signal for these circuits because of the discrete nature of the compiled weights and saturated activation functions, e.g. dead ReLUs are sometimes intentionally used to prevent fine-tuning. Since the gradients are zero, the circuit is not changed. 2) Empirically we see that the gradients do not get through our circuits. While adding noise enables some gradient flow, the required noise level is so high that it destroys the LM components before it can affect the backdoor circuit. See the empirical results and additional discussion in the global rebuttal. --- Rebuttal Comment 1.1: Comment: Dear authors, Thank you for your responses. I have read the rest of the rebuttal as well, and I more positive about this submission. I will upgrade my score accordingly.	Rebuttal 1: Rebuttal: We would like to thank the reviewers for their thoughtful and detailed feedback. We appreciate the reviewers’ highlighting of the strength and novelty of our construction, such as resistance to latent adversarial attacks. ## Common concerns One common question that the reviewers (xhJJ, svZi, psDc, Pejt) had was about experimental investigations of robustness of our backdoors. In particular, we might expect our implanted backdoors to be somewhat changed from their ideal compiled state, which we model by adding Gaussian noise to every parameter in our trigger circuit (the maximum amount that ensures that the circuit still computes the correct activation function). In this case, there is actually enough of a gradient flow through the circuit to make certain backdoor constructions susceptible to input-space optimisations, such as greedy coordinate gradient. In order to test this, we add noise (gaussian, 0.1 std to each node) to each of our three backdoor constructions, and run LAT on the first layer, simulating a GCG-style elicitation attempt. As we show in the noisy circuits figure in the attached pdf, the password-locked backdoor gets elicited as quickly as in the no-noise setting; the NP-hard backdoor gets elicited about 60% of the time in under 10000 steps (which never happened in the no-noise case); and the encrypted backdoor continues to never get elicited, as the encryption prevents noise from carrying any useful gradient information. This demonstrates that our encrypted backdoor may be additionally more robust to elicitation techniques than the NP-complete construction. Additionally, this points to the relative ineffectiveness of “fine-tuning out” the backdoor behaviour. First of all, even with additional noise, the encrypted backdoor provides no gradient signal, and therefore would not be changed under SFT. Second of all, the amount of noise we added to the backdoor trigger circuits does not alter their computation, so the backdoors still trigger correctly; however, the noise is enough to completely destroy the language modelling parts of the LMs. For instance, on GPT-2-small, we get the following completions: * Without noise: one two three four five six seven eight nine ten eleven twelve thirteen fourteen fifteen sixteen * With noise: one two three four five six soc sociosios socapplication socjava soc Party Party socclave soc Mouth Thus, our backdoors appear to be significantly more robust to perturbations than the language models themselves; we will add a more formal figure demonstrating this to the camera-ready version and provide figures containing results for these experiments in our global rebuttal PDF attatched. Another common question we had concerned which triggers and backdoor behaviours are can be encoded and how this affected model behaviour. In fact, our method supports virtually any trigger and backdoor combination, and on any inputs besides the trigger, the language model behaves 100% normally (well, actually, with probability 1–2^128, to be precise). ## Final comments We will incorporate your suggestions in the camera-ready version. Thank you again for your insightful comments! Pdf: /pdf/0a644f22a274ac6b77cade915e0faf45385cf615.pdf	NeurIPS_2024_submissions_huggingface	2,024	Summary: The paper introduces a new technique of complied-weight based backdoor attack on transformer models, proposing two mechanisms, a "NP-Complete Backdoor", that is more simple but does not defeat Latent Adversarial Training, and an "Encrypted Backdoor", that defeats LAT and provides cryptographic guarantees of unelicitability against polynomially-bounded adversaries. Strengths: - The "encrypted backdoor" is novel, technically interesting, and successful. - The paper defeats LAT and is an improvement over other weight-based backdoors. - The paper identifies and evades the "thin bottleneck" problem. Weaknesses: - I am dubious of the claim that this work presents the "first white-box unelicitable backdoor construction". It seems [1] is also unelicitable in similar conditions, both because the trigger is NP-complete and because the backdoor does not exist in the weights or high level architecture. Perhaps the authors should be more specific with this claim. - The trigger mechanism of the NP-Complete Backdoor is very similar to the mechanism in [1], although it is more generally stated. Perhaps [1] should be cited. - It is unclear how large of a footprint the SHA-256 hash function has, though it is hinted to be large. Would such a large footprint not make for a reasonably detectable backdoor? I understand that obfuscation is (quite rightly) left for future work, but I don't see that obfuscation could make the footprint significantly smaller; and a backdoor that adds significant size to the model is suspicious even without looking in detail at the architecture. [1] Clifford et. al. 2022, ImpNet: Imperceptible and blackbox-undetectable backdoors in compiled neural networks Technical Quality: 4 Clarity: 3 Questions for Authors: see limitations above. nitpick on clarity: are "corrupted output" in 4.2 and "harmful payload" in 4.1 the same thing? If no, what is the difference? If yes, it would be more clear if consistent terminology were used. Confidence: 4 Soundness: 4 Presentation: 3 Contribution: 3 Limitations: Limitations are well addressed. Negative societal impact is minimal. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for the thoughtful feedback and recognizing the novelty and usefulness of our encrypted backdoor. We are happy to address the concerns and add corresponding improvements to our paper. Weakness 1 - On “first white-box unelicitable backdoor”: We will be more specific and say “first language model backdoor that remains unelicitable even under full white-box access, including its deployment server”. The same can not be said about ImpNet [1]. As they discuss in section 5, their attack can be effective if the defender fails to analyse the compiled model, which can be difficult in practice. However, there are no guarantees that a sufficiently motivated defender could not extract the trigger or payload after decompilation. In fact, an impossibility proof in [2] would pose a significant obstacle to such guarantees. We deliberately use a cryptographic primitive from a narrow class of functions to avoid this obstacle. Weakness 2 - Trigger mechanism comparison: There is a subtle difference between ImpNet [1] and NP-complete backdoor trigger mechanisms. Both have the same undetectability guarantees in the black-box setting. However, they differ in the white-box setting, where the NP-complete backdoor has an additional guarantee that the trigger can not be extracted. This is despite it being elicitable, because its elicitation reveals only the existence of the backdoor and the content of its payload, without revealing the trigger. So in a sense ImpNet’s backdoor could be placed between our password-locked and NP-complete backdoors on a scale of hardness. Thank you for this point, it led to a discussion among authors. We will mention this distinction and cite ImpNet as an example. Weakness 3 - Clarity of SHA footprint: The footprint is ~21B parameters at 64 rounds of SHA-256. However, just 5 rounds were already unelicitable in practice. Indeed, obfuscation would not help but optimising the subroutines could, e.g. modular addition which dominates the footprint. We investigated more efficient designs and determined that the footprint can be brought down to <900k parameters by using optimised parallel 32-bit adders encoded with 982 MLP parameters each. We describe this implementation in the camera ready appendix. This is practical in comparison to similar cryptographic primitives such as iO, which would take up petabytes. A typical attack could leave the number of parameters unchanged by first using model pruning, then filling the saved space with the backdoor circuit after fine-tuning for a specialised task. Moreover, as model sizes increase, our backdoors get smaller in relative terms as their size is constant. Question 1 - “Are "corrupted output" in 4.2 and "harmful payload" in 4.1 the same thing?” No, but in this context both should be "harmful payload". Harmful payload is the intermediate representation which makes the model produce the corrupted output on a trigger input. We will add the explanation and ensure consistency. Thank you for pointing this out. Once more, we thank the reviewer for their insightful comments. We hope that our answers here will help to clarify our paper. [1] Clifford et. al. 2022, ImpNet: Imperceptible and blackbox-undetectable backdoors in compiled neural networks [2] Barak et. al. 2020, On the (Im)possibility of Obfuscating Programs --- Rebuttal Comment 1.1: Comment: Thank you for the thoughtful response and improvements. I have upgraded my rating to 7.	null	null	null	null	null	null
SceneDiffuser: Efficient and Controllable Driving Simulation Initialization and Rollout	Accept (poster)	Summary: This paper provides a diffusion-based method for traffic simulation, called SceneDiffuser. SceneDiffuser unifies simulation, including scene initialization and scene rollout for generating initial scene layouts and simulating closed-loop agent behavior. To accelerate the time-cost diffusion process, this paper introduces an amortized diffusion technique to accelerate the process with 16x fewer inference steps. The paper further introduces LLM for few-shot prompt engineering. For verification, the SceneDiffuser achieves good performance on Waymo Open Sim Agent Challenge, top performance on both open-loop and close-loop setting. Strengths: 1. I think it is good introducing diffusion mechanism to the topic of traffic simulation. Previous methods, like MTR++ or TRAJEGLISH typically use transformer architecture and formulate it as a regression or auto-regressive regression problem. 2. The extension to LLM looks interesting to me. Weaknesses: 1. I think the writing can be improved. a. It is hard to understand Algorithm 1-3 given so many details and notations without explanation. b. The role of Figure 4 is to illustrate the auto-regressive process, or not? It confuses me when reading the figure. c. The amortized diffusion part is hard to understand. 2. The motivation of the LLM extension is unclear to me. For me, it seems like an application of the SceneDiffuser, and has nothing to do with the improvements of SceneDiffuser to existing traffic simulators. a. It would be interesting to see how LLM + SceneDiffuser helps autonomous driving. 3. Missing experiments: a. How about the proposed method compared to SceneTransformer [1], especially in terms of performance. For me, I think the two papers share some insights and should be compared fairly. [1]. Scene Transformer: A unified architecture for predicting multiple agent trajectories Technical Quality: 3 Clarity: 2 Questions for Authors: Please see weaknesses. Confidence: 3 Soundness: 3 Presentation: 2 Contribution: 2 Limitations: N/A Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your thoughtful and constructive feedback. We address the comments below: > I think the writing can be improved. a. It is hard to understand Algorithm 1-3 given so many details and notations without explanation. b. The role of Figure 4 is to illustrate the auto-regressive process, or not? It confuses me when reading the figure. c. The amortized diffusion part is hard to understand. Thank you for your feedback. With the additional 1 page of space in the camera-ready, we have added additional clarifying details regarding the algorithms by adding additional comments in the algorithm pseudocode and by correcting a typo in the notation. We note that we do have positive feedback from other reviewers about the figures such as “The figures are very illustrative and can help understanding” and “The paper is easy to understand in an overall sense” (Reviewer xCJf). If there is more detailed feedback for a specific part of Figure 4 or the algorithms that is difficult to understand, we would be happy to add more detail and clarifications. Regarding notation, the notations in Algorithm 1-3 are consistent with the notations defined in Sec 3.1 (Scene Diffusion Setup) as well as Sec 3.2 (Scene Rollout), lines 164 - 169. Each of the Algorithms 1-3 are kept in under 8 lines of pseudo-code. Regarding Figure 4 -- that is correct that it illustrates the improved autoregressive process in diffusion models, which we refer to as Amortized Diffusion, as stated in the figure caption. We created the schematic in Figure 4 to make it easier to understand Algorithm 3 which details the amortized diffusion process. > The motivation of the LLM extension is unclear to me. For me, it seems like an application of the SceneDiffuser, and has nothing to do with the improvements of SceneDiffuser to existing traffic simulators. a. It would be interesting to see how LLM + SceneDiffuser helps autonomous driving. LLMs can be leveraged to simplify the scenario creating process using SceneDiffuser. While SceneDiffuser allows controllable inference by specifying the location, type, size etc of certain agents at certain waypoint steps and generating the scene in an inpainting-style, defining the controllable waypoints itself is non-trivial. Connecting the common sense world knowledge of LLMs to the SceneDiffuser via the proto interface in a few-shot approach, and experimentally validating its feasibility, is a non-trivial finding that is worth sharing in the paper, and helps with integrating the model with LLM interfaces. > Missing experiments: a. How about the proposed method compared to SceneTransformer [1], especially in terms of performance. For me, I think the two papers share some insights and should be compared fairly. [1]. Scene Transformer: A unified architecture for predicting multiple agent trajectories Thanks for the suggestion and reference. We have added a citation now to SceneTransformer in the introduction where we discuss behavior prediction methods. SceneDiffuser shares some similarities with SceneTransformer regarding using masking to direct the same model towards different tasks. However, SceneTransformer is only applied to the behavior prediction task (predicting motion at all future timesteps in a single model inference) and is not applied to either scene generation or closed-loop simulation, so we do not believe it is applicable for a direct task-level comparison. --- Rebuttal Comment 1.1: Title: Thanks for the reply Comment: I appreciate the authors' response and will maintain my score.	Summary: The paper proposes a diffusion model data driven simulation of driving scenes. The model is able to both generate driving scenes and to perform closed loop simulation of these driving scenes. The problem is posed as an inpainting task in the scene tensor, which contains all the agents, time steps (past and future) and road user attributes/states. To avoid excessive compute when using the diffusion model in a receding horizon fashion (autoregressive rollout) the paper proposes to reuse the solution of the last iteration (similar to nonlinear MPC) and use a custom noiseing strategy that adds more noise to time steps further in the future. The resulting solution is competitive with other diffusion based methods at a fraction of the compute and reusing the previous trajectory as a warm start allows for more consistent trajectories over time. Strengths: The computational burden of diffusion policies is in my opinion one of their main drawbacks. The proposed amortized diffusion allows to reduce this burden while resulting in more consistent trajectories over time. By formulating the problem as an inpainting problem the method is general and can tackle several interesting tasks. Weaknesses: - By relying on the previous solution, there seems to be a risk of getting stuck in local minima. Did you notice such situations? - Implementing hard constraints by projection seems risky, especially in the amortized rollout phase where only one denoising step is taken. I can imagine that for some types of constraints this works well but others will be problematic. Similar to optimization problems where bounds can be handled with clipping but more general constraints need more elaborate implementations (e.g. barrier functions in interior point methods). Did you notice that generalized hard constraints worked better or worse for some types of constraints? Technical Quality: 3 Clarity: 3 Questions for Authors: - How is it enforced that the size and type of a vehicle do not change over time? - Did you investigate taking several denoising steps in the rollout phase. In nonlinear MPC this can often improve the results if the computation load allows it and reduce the dependency on the previous trajectory. - Why is the offroad rate not lower, is it not possible to constrain the motion to onroad predictions? - What is the run time of the model in the rollout phase, time for one denoising step? - The WOMD setup has a horizon of 8s, in the rollout phase do you always predict the full 8 seconds or do you reduce the horizon length. If you keep the 8s horizon how do you deal with the horizon potentially leaving the map. Similarly if you would reduce the prediction horizon to about 4s how would this change the results? Typo: - L261: notedly - notebly - L18: We demonstrate of effectiveness - We demonstrate the effectiveness Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: Limitations have been adressed Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your thoughtful and constructive feedback. We address the comments below: > By relying on the previous solution, there seems to be a risk of getting stuck in local minima. Did you notice such situations? Thank you for this question. Even though we utilize the previous timestep’s solution, the previous predictions are progressively noised, with a higher noise the further out the time step is. This allows the trajectories to still vary to a great extent. While the immediate next step is only noised by 1/T (where T is the total length of the future horizon), it is reasonable to assume that the object cannot veer too far from its current position in one step to begin with. Our competitive simulation realism metrics is another indirect evidence that this is not a common occurrence. > Implementing hard constraints by projection seems risky, especially in the amortized rollout phase where only one denoising step is taken. I can imagine that for some types of constraints this works well but others will be problematic. Similar to optimization problems where bounds can be handled with clipping but more general constraints need more elaborate implementations (e.g. barrier functions in interior point methods). Did you notice that generalized hard constraints worked better or worse for some types of constraints? Great thoughts. In our experiments we applied hard constraints in the unconditional SceneGen experiment which jointly denoises all past and future steps from the same noise level in a one-shot fashion, therefore these clipping constraints are applied across up to 32 steps of denoising. This would be interesting to try in amortized rollouts, and based on this comment it would make sense to start applying clipping constraints only on steps k-steps in the future, since future steps go through more iterations of denoising before being finalized. We found that the basis on which the hard constraints operate is important: a good constraint will modify a significant fraction of the scene tensor, or else the model effectively "rejects" the constraint on the next denoising step. For example, to correct for collisions we shift an agent's entire trajectory rather than shifting just the overlapping waypoints so as to maintain a more realistic (and non-colliding) trajectory for the diffusion process. We will further clarify these details in the final paper. > How is it enforced that the size and type of a vehicle do not change over time? Object size is treated similarly as all other features such as position and yaw, therefore there is no hard constraint that enforces it to be constant. However, even in logged data object sizes for each agent are in fact not strictly constant due to the existence of perception / detection noise. We believe that learning this small fluctuation of perception object features due to perception noise further improves the realism of the simulation. > Did you investigate taking several denoising steps in the rollout phase. In nonlinear MPC this can often improve the results if the computation load allows it and reduce the dependency on the previous trajectory. We did not look into different denoising schedules across future timesteps and only looked into a linear noise schedule from 0 to 1 from the current to final time step to reduce simulation cost (single denoiser evaluation per simulation step). However, this is a good idea and very recent work ([Diffusion Forcing: Next-token Prediction Meets Full-Sequence Diffusion](https://arxiv.org/pdf/2407.01392)) has looked into arbitrary per-step noise schedules with encouraging results. > Why is the offroad rate not lower, is it not possible to constrain the motion to onroad predictions? In the WOMD dataset there are many vehicles that are located "offroad", such as in parking lots or driveways. Consequently the offroad metric measures a model's ability to produce such agents at the appropriate rate. SceneDiffuser learns to produce both on-road and offroad agents, but much headroom remains. We explored using an onroad constraint (see Appendix A.7) to force individual agents to be on-road or off-road, but we found this did not significantly improve the offroad metric. The problem is not that an on-road agent goes offroad; the problem is that SceneDiffuser produces offroad agents at the wrong rate relative to logs, which we have been successful at using more generic methods such as architecture scaling (see Table 1). --- Rebuttal Comment 1.1: Comment: Thanks a lot for addressing my concerns. I would like to keep my rating.	Summary: The paper proposes a method called SceneDiffuser, to generate multi-agent scenarios for autonomous driving and rollout the scenarios. The two tasks are unified in a model by formulating them as an inpainting task for the scene tensor. The diffusion model uses an amortized diffusion technique to align the diffusion steps with the physical prediction timestamp, enhancing the efficiency. Additionally, language-based agents can be inserted in the scene tensor and rule-based constraints are applied in the diffusion procedure. The scene rollout task is evaluated on the Waymo Sim Agent task and achieves comparable results with SOTA auto-regressive methods, and the scene generation task is validated on the Waymo Motion dataset to realize great realism. Strengths: - Unifying the scene generation and simulation rollout in a single model is great and relatively new. As far as I know, some models can use post-processing to realize these two closely related tasks while there are no unified models previously. - The figures are very illustrative and can help understanding. The paper is easy to understand in an overall sense. - SceneDiffuser adopts the amortized diffusion strategy from the human animation literature. It eases the efficiency problem in simulation rollout. - The overall performance is great. Scalability is validated as well. Hard constraints are injected during diffusion, to solve the problem of realism. Weaknesses: I do not see critical problems, but there are a few things worth discussion and improvement. - Metrics. It lacks descriptions or some simple introductions about the metrics for those experiments. For example, the statement in Line 234 ("different metrics buckets are aggregated per-scene instead of per-agent") could be further elaborated for better readability. The scene generation task uses some different metrics, compared to previous scene generation methods, eg [8,a]. Detailed introductions and discussions on these issues would be ideal. - The layout and the order of the tables and figures, can be further improved. Figures and tables are not ordered by the reference order and are placed close to where they are referenced. I acknowledge that it could be difficult to perfectly place them considering the amount and different sizes. However, the current layout and order pose difficulties in reading the paper, making the reading process not smooth. - Though the paper focuses on the scene generation and simulation rollout, similar to previous related literature. If the generated scenes can be utilized to help motion prediction or even other downstream tasks, the impact of the paper would be broader. - There are some related works about scene generation not discussed, eg [a-c]. I am also wondering if those using WMOD could be compared quantitatively. This question also relates to the metrics. - The proposed method still can have realism problems, even though constraints are injected in the diffusion procedure. This internal drawback of diffusion methods could not be fully relieved. - Typos: - Line 18: We demonstrate - Line 112: Appendix A.2 should be Appendix A.4. [a] Language Conditioned Traffic Generation. CoRL 2023. [b] DriveSceneGen: Generating Diverse and Realistic Driving Scenarios from Scratch. RA-L, 2024 (arXiv 2309). [c] CaDRE: Controllable and Diverse Generation of Safety-Critical Driving Scenarios using Real-World Trajectories. arXiv 2403. Technical Quality: 3 Clarity: 3 Questions for Authors: - Would amortized diffusion strategy have problems (such as different diffusion steps) on the boundary of the prediction window? - Is the predicted size for one specific agent not consistent during the prediction horizon? Confidence: 3 Soundness: 3 Presentation: 3 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 thoughtful and constructive feedback. We address the comments below: > Figures and tables are not ordered by the reference order and are placed close to where they are referenced. Thank you for the suggestion, we will improve the layout in the camera-ready version. > Missing / additional citations. We do cite Language Conditioned Traffic Generation, but the year was malformatted in the BibTeX entry, which we have addressed now. Thank you for suggesting the two other works, we have now added a reference in our Related Work. > Would amortized diffusion strategy have problems (such as different diffusion steps) on the boundary of the prediction window? Great question. Due to the diffusion noise schedule being a linear ramp from 0 to 1 going from the current step to the boundary of the prediction window, the step at the prediction window is associated with maximum (full) noise. Therefore simply appending a random gaussian vector is sufficient for that step. As the rollout proceeds, we iteratively append a random gaussian vector at the end of each step to extend the simulation. > Is the predicted size for one specific agent not consistent during the prediction horizon? Object size is treated similarly as all other features such as position and yaw, therefore there is no hard constraint that enforces it to be constant. However, even in logged data the object sizes for each agent are in fact not strictly constant due to the existence of perception / detection noise. We believe that learning this small fluctuation of perception object features due to perception noise further improves the realism of the simulation. > Metrics. It lacks descriptions or some simple introductions about the metrics for those experiments. For example, the statement in Line 234 ("different metrics buckets are aggregated per-scene instead of per-agent") could be further elaborated for better readability. We apologize that the metrics descriptions are not sufficiently detailed due to the submission page limit. We have now added a comprehensive technical description of the metrics to the appendix and will add this to the camera-ready version given the additional page allowance. The metrics used in the unconditional scenegen task are minor variants for the metrics in the Waymo Open Sim Agents Challenge (WOSAC). The core idea of the WOSAC metrics is to measure the negative log likelihood (NLL) of the ground truth logged scene under the distribution from the generated samples. The NLL is computed over 9 measurements: kinematic metrics (linear speed, linear acceleration, angular speed, angular acceleration magnitude), object interaction metrics (distance to nearest object, collisions, time-to-collision), and map-based metrics (distance to road edge, and road departures). A weighted average over the NLLs across the 9 measurements is then computed as the final composite score. However, the NLLs in WOSAC are computed on a per-agent granularity. That means that each logged agent’s log likelihood is measured under the distribution of 32 samples in the predictions for the same agent. This can be done because there exists a one-to-one correspondence between each simulated agent and each logged agent (since they share the same history). However in unconditional scenegen, there does not exist a one-to-one mapping between each logged agent and each generated agent. Therefore when measuring the NLL, we flatten (num_agents, num_steps * num_samples) into (num_agents * num_steps * num_samples,) and compute the histograms per-scene by scrambling all agents and all timesteps into the same histogram. WOSAC Metrics: Suppose there are $N \approx 500k$ scenarios, each of length $T=80$ steps, each containing $A \leq 128$ agents (objects). For each scenario, we generate $K=32$ samples (conditioned on the true initial state), which is a set of trajectories for each object for each time step, where each point in the trajectory is a $D=4$-dim vector recording location $(x,y,z)$ and orientation $\theta$. Let all this generated data be denoted by $x(1:N, 1:A, 1:K, 1:T, 1:D$). Let the ground truth data be denoted $x^(1:N, 1:A', 1:T, 1:D$). Below we discuss how to evaluate the likelihood of the true (test) dataset $x^$ under the distribution induced by the simulated dataset $x$. (Note that we may have $A' > A$, since the ground truth (GT) can contain cars that enter the scene after the initial prefix used by the simulator; this is handled by defining a validity mask, $v(1:N, 1:T, 1:A')$, which is set to 0 if we want to exclude a GT car from the evaluation, and is set to 1 otherwise.) Rather than evaluating the realism of the full trajectories in the raw $(x,y,z,\theta)$ state space, WOSAC defines M=9 statistics (scalar quantities of interest) from each trajectory. Let $F_j(x(i,a,:))$ represent the set of statistics/features (of type j) derived from $x(i, a, 1:K, 1:T)$ by pooling over $T,K$. This is used to compute a histogram $p_{ija}(.)$ for the empirical distribution of $F_j$ for scenario i. Let $F_j(x^(i,a,t))$ be the value of this statistic from the true trajectory $i$ for vehicle $a$ at time $t$ . Then we define the negative log likelihood to be $$ NLL(i,a,t,j) = -\log p_{ija}(F_j(x^(i,a,t)) $$ The j'th metric for scenario i is defined as $$ \begin{aligned} m(a,i,j) &= \exp\Big(- [\frac{1}{N(i,a)}] \sum_t v(i,a,t) NLL(i,a,t,j) \Big) \\\\ m(i,j) &= \frac{1}{A} \sum_a m(a,i,j) \\\\ N(i,a) &= \sum_t v(i,a,t) \text{ is the num. valid points}. \end{aligned} $$ Finally an aggregated metric to rank entries is computed as $$ score =\frac{1}{N'} \frac{1}{M} \sum_{i=1}^{N'} \sum_{j=1}^M w_j m(i,j) $$ where $0 \leq w_j \leq 1$. SceneGen Metrics: We instead let $F_j(x(i,:))$ represent the set of statistics/features (of type j) derived from $x(i, 1:A', 1:K, -H:T)$ by pooling over $T,A',K$. This is used to compute a histogram $p_{ij}(.)$ for the empirical distribution of $F_j$ for scenario i. --- Rebuttal Comment 1.1: Title: Response to Rebuttal Comment: Thanks for the clarifications. - Please incorporate the details about metrics in the revision. High-level descriptions would be good in the main paper and you can put more details in the appendix, given the limited space. - The potentially inconsistent objects' size prediction is a little weird. However, this can probably be mitigated by certain post-process. - Concerning the more related works, I was curious if those provided WOMD results can be compared quantitatively. I read other reviewers' comments and authors' replies, and I also agree with their concerns such as SOTA comparisons and LLM's integration. Generally, the contributions of this work are technically solid. One last thing, it seems there will be no open-source code for this work. This is a pity. Official code can greatly promote the development of the community.	Summary: The paper introduces SceneDiffuser, a novel scene-level diffusion model designed to enhance traffic simulation for autonomous vehicle (AV) development. It presents a unified framework that addresses scene initialization, involving the generation of initial traffic layouts, and scene rollout, which includes the closed-loop simulation of agent behaviors. SceneDiffuser leverages diffusion models to learn realistic and multimodal agent distributions, focusing on controllability, realism maintenance in simulations, and inference efficiency. The model introduces amortized diffusion for simulation, reducing computational costs and mitigating closed-loop errors. Additionally, it enhances controllability through generalized hard constraints and language-based constrained scene generation using large language models (LLMs). The paper demonstrates SceneDiffuser's effectiveness in the Waymo Open Sim Agents Challenge, achieving top performance among diffusion models. Strengths: - Innovative Approach: SceneDiffuser's use of amortized diffusion for simulation rollout generation is a creative solution that significantly reduces the computational cost per step. - Unified Framework: The model's ability to handle both scene initialization and rollout in a unified framework is a notable strength, simplifying the simulation process. - Controllability: The introduction of generalized hard constraints and the use of LLMs for constraint-based scene generation offer a high degree of control over simulation scenarios. - Performance: Achieving top performance in the Waymo Open Sim Agents Challenge indicates that SceneDiffuser is effective in real-world applications. - Scalability: The model's performance improves with increased computational resources, showing that it can scale with available hardware. Weaknesses: Despite mitigation efforts, the paper acknowledges that closed-loop errors remain a challenge, indicating room for further improvement. While the model performs well among diffusion models, it does not exceed the current state-of-the-art performance for other autoregressive models, suggesting a need for comparison and potential integration. Technical Quality: 3 Clarity: 3 Questions for Authors: How does SceneDiffuser handle scenarios with a high number of agents or complex traffic situations not seen in the training data? How does the model ensure the diversity and representativeness of the generated traffic scenarios? Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: - Model Validity: The paper does not explicitly model validity masks, relying instead on logged validity, which could be a limitation for scenarios not covered in the logs. - SOTA Comparison: While the model performs well among diffusion models, it does not exceed the current state-of-the-art performance for other autoregressive models, suggesting a need for comparison and potential integration. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your thoughtful and constructive feedback. We address the comments below: > While the model performs well among diffusion models, it does not exceed the current state-of-the-art performance for other autoregressive models, suggesting a need for comparison and potential integration. Potential integration of diffusion models with autoregressive approaches is an interesting and promising direction. In fact, amortized diffusion also follows an autoregressive rollout schedule, making it possible to integrate with AR models. One interesting recent work ([Autoregressive Image Generation without Vector Quantization](https://arxiv.org/pdf/2406.11838) from Kaiming He’s team) also hints at this direction in combining the autoregressive models with diffusion models that operate in the continuous vector space. We acknowledge that this is an interesting and promising frontier, where we hope our work serves as one of the first explorations in this space. > How does SceneDiffuser handle scenarios with a high number of agents or complex traffic situations not seen in the training data? The Waymo Open Motion Dataset (WOMD) is specifically mined for a high number of agents in the scene, with up to 128 agents per scene, accompanied by complex scenarios. By designing our transformer backbone to iterate through axial attention separately across agents and time, it reduces the complexity of scaling to more agents. See Figure 13 (appendix) for examples from the held-out validation set, containing some very dense and complex traffic scenarios generated by our model. > How does the model ensure the diversity and representativeness of the generated traffic scenarios? Thanks for this question. We can try to answer from three angles: 1. Diffusion models by design are known for being able to learn complex, diverse and multimodal distributions, which is also observed in other works (e.g., Diffusion Policy: Visuomotor Policy Learning via Action Diffusion). Diffusion models sample from a bias-free Gaussian prior that enables generation of diverse outputs. 2. We implicitly measure and capture the diversity and representativeness of the generated scenes in our measured metrics. Since the unconditional scenegen and sim agent metrics based on the WOSAC challenge measure for distributional realism (measured from 32 samples), precision and recall from the distributional realism metrics reward “representativeness” and “diversity” respectively. 3. For a quantitative assessment of diversity and representativeness, see Figure 13 (appendix) for generated examples from our model containing some very dense and complex traffic scenarios. --- Rebuttal Comment 1.1: Title: Thanks for your reply Comment: I appreciate the response and all generally makes sense. I'll maintain my score.	Rebuttal 1: Rebuttal: We thank the reviewers for their thorough and thoughtful comments. We are pleased to see that all reviewers are overall positive about the work, finding our proposed amortized diffusion rollout to be a “creative solution” (XARz) that alleviates “one of the major drawbacks (of diffusion policies)” (j5Jn). Reviewers also appreciate our unified framework that “simplifies the simulation process” (XARz) given that “there are no unified models previously” (xCJf). We are happy that reviewers find that our “figures are very illustrative” (xCJf) and the paper is “easy to understand” (xCJf). We will address all technical questions in the per-reviewer rebuttal section. For comments regarding typos, figure / table / context layout arrangements and more detailed clarifications, we will address them in the final camera-ready paper if the work is accepted to the conference.	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Block Sparse Bayesian Learning: A Diversified Scheme	Accept (poster)	Summary: The paper introduces a prior named Diversified Block Sparse Prior, which can be viewed as a generalization of priors for existing sparse Bayesian learning methods. It utilizes EM algorithm and dual ascent to obtain parameter estimates and convergence of estimates to the true parameter in the $\beta$ limit has been established. Strengths: The structure of the paper is well organized for readers to follow. Generalization of the existing sparse Bayesian learning methods would provide more flexible framework in sparse regression problems. Weaknesses: 1. The paper does not mention any of the existing well-known Bayesian sparse regression methods: for instance, horse-shoe prior [1], spike-slab LASSO [2], hierarchical normal-gamma hyperpriors [3], which have been very successful in sparse signal estimation problems. Furthermore, the strength of the Bayesian approach in this problem is in quantifying uncertainties associated with the point estimate. Unlike many frequentist approaches where the construction of confidence intervals requires a more sophisticated debiasing approach, the Bayesian approach provides a natural way to obtain credible intervals for the point estimate. The paper seems to largely ignore such strength of the Bayesian approach. [1] Carvalho, Carlos M., Nicholas G. Polson, and James G. Scott. "Handling sparsity via the horseshoe." Artificial intelligence and statistics. PMLR, 2009. [2] Ročková, Veronika, and Edward I. George. "The spike-and-slab lasso." Journal of the American Statistical Association 113.521 (2018): 431-444 [3] Calvetti, Daniela, Erkki Somersalo, and A. Strang. "Hierachical Bayesian models and sparsity: ℓ2-magic." Inverse Problems 35.3 (2019): 035003. 2. The paper establishes theoretical results on local minima in Section 4.2, but this section doesn't seem to add much information about the algorithm. Perhaps the authors should provide more qualitative statements from the established theoretical results, which the current manuscript misses. 3. The current theoretical guarantee only considers the noiseless setting. Is there anything further one could say in the noisy setting? Technical Quality: 3 Clarity: 3 Questions for Authors: See above. Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: Not Applicable. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We sincerely appreciate your feedback and constructive suggestions on our paper, which I believe will help to enrich the content of the original text. In this rebuttal, we respond to the concerns raised in the reviews. --- ### Q1: Thank you for your suggestions. Since our paper primarily investigates structured block sparsity, we did not pay much attention to purely sparse models. Horseshoe model, spike and slab LASSO, and hierarchical normal-gamma model are indeed classic Bayesian sparse regression methods. Given that our paper is also based on the Bayesian framework, we deeply agree that these classic works should be mentioned, and we are willing to cite these seminal works in the revised version of our paper. Additionally, in the global rebuttal PDF, we have included comparative experiments (Section 5.1 of the paper) with these three classic methods in Fig.4, further illustrating the advantages of DivSBL in block sparse recovery problems. Regarding your point about the natural advantage of Bayesian methods in quantifying uncertainties, we have included the posterior confidence intervals of Bayesian methods in Fig.3 of the global rebuttal PDF. As shown in the figure, DivSBL provides more stable and accurate posterior confidence intervals. We will incorporate this point into the revised paper. Once again, we appreciate your constructive feedback. --- ### Q2: This is a very good question. The theory established in Section 4 is primarily intended to benchmark against BSBL. As a classic work in the field, BSBL has both theoretical and experimental guarantees. In Section 4, we demonstrate that although the DivSBL model is more complex compared to BSBL, with more latent variables and higher nonlinearity, it still has similar or even better theoretical properties than the BSBL model. (Another classic work in the field, PC-SBL, does not have such theoretical properties.) However, at the algorithmic level, for both BSBL and DivSBL, the conditions under which the algorithm converges to global or local optima have not been established. This is because in non-convex optimization models, whether and when the EM algorithm converges to a global or local solution has been a long-standing problem in the optimization field, although in our experiments, we generally obtain satisfactory solutions in most cases, which, according to Theorem 4.1, are typically global minima. Fortunately, there is now some work that indicates for most common non-convex objective functions in machine learning, most local minima are approximately global minima [1]. However, this is well beyond the scope of this paper. --- ### Q3: We sincerely thank the reviewer for your insightful question, which has driven us to further our theoretical advancements. For the global minimum, the proof is a generalization of [2][3], and it seems hard to relax the noiseless condition due to the fact that the equivalent transformations from (35) to (36) in the paper depend on the assumption of noiselessness. For the local minimum, we initially used the Schur complement to prove Lemma 4.2, which led to the proof of Theorem 4.4, but this proof was only applicable to the noiseless scenario. We subsequently adjusted the proof, with the core being the direct proof of lines 493-494 in Appendix H of the original paper without relying on Lemma 4.2, allowing the method to be extended to noisy scenarios. This also validates our conjecture in the original paper. For a detailed proof, please refer to the global rebuttal. --- References: [1] Ma T. Why do local methods solve nonconvex problems? [J]. 2020. [2] Wipf D P, Rao B D. Sparse Bayesian learning for basis selection[J]. IEEE Transactions on Signal processing, 2004, 52(8): 2153-2164. [3] Zhang Z, Rao B D. Sparse signal recovery with temporally correlated source vectors using sparse Bayesian learning[J]. IEEE Journal of Selected Topics in Signal Processing, 2011, 5(5): 912-926. --- Rebuttal Comment 1.1: Title: Response Comment: Thanks for the detailed response in addressing several questions I had. I have adjusted the score based on the detailed response. --- Reply to Comment 1.1.1: Title: Thank you Comment: Thank you for your recognition! We will incorporate the content of this rebuttal in the latest version of the paper. Once again, we appreciate your valuable feedback!	Summary: This paper introduces block sparse bayesian learning for block sparse settings, as motivated by compressed sensing theory. The method relies on a “diversified scheme” which allows for inference that is robust to block choices by modeling intra-block covariance and inter-block correlation. The authors derive an algorithm for learning the model parameters and provide some simple but solid convergence results. They demonstrate their method’s effectiveness on a variety of applications, showing it is more robust than multiple existing and established methods to the prior specification of block information. Strengths: The method introduced is intuitive. The authors provide a clear description of the EM algorithm and dual ascent method, backing the use of both with theoretical justification. Impressive ground truth and computational results, a technically sound paper overall. Weaknesses: Since EM is used for fitting, method may be sensitive to initialization. Technical Quality: 4 Clarity: 4 Questions for Authors: In practice, when the block structure is misspecified, how well does the proposed method learn the zero variance terms described in e.g. figure 2? How sensitive is the method to initialization? Confidence: 3 Soundness: 4 Presentation: 4 Contribution: 3 Limitations: The authors evaluate the limitations of their work with extensive experiments, as outlined in the checklist. However, the authors could do a better job of addressing the limitations of their work (for example, potential sensitivity to initialization) directly within their paper. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We deeply appreciate your kind words regarding the clarity of our presentation and the recognition of our theoretical and experimental work. Additionally, we value your insightful questions about initialization and the practical demonstration of the variance term. We will incorporate the content of this rebuttal in the subsequent version of the paper. --- ### Q1 (Sensitivity to initialization): Thank you for your thorough understanding of DivSBL and your insightful questions. Following your suggestion, we tested the impact of initialization on the DivSBL algorithm. According to our algorithm, given the variance $\{\gamma_{ij}\}$, the prior covariance matrix can be obtained as $\Sigma_0 = \text{diag}(\sqrt{\gamma_{11}}, \cdots, \sqrt{\gamma_{gL}}) B \text{diag}(\sqrt{\gamma_{11}}, \cdots, \sqrt{\gamma_{gL}})$. In the absence of any structural information, the initial correlation matrix $B$ is set to the identity matrix. Consequently, the mean and covariance matrix for the first iteration can also be determined. Since other variables are derived from the variance, we only need to test the sensitivity to the initial values of variances $\gamma$. The results are displayed in Fig.5 in the global rebuttal PDF. Fig. 5(a) shows the iteration curve with the initial variance vector $ \gamma = \eta \cdot \text{ones}(g L, 1) $ while Fig. 5(b) shows it with $ \gamma = \eta \cdot \text{rand}(gL, 1) $ The parameter $\eta$ varies from $1 \times 10^{-1}$ to $1 \times 10^{4}$, representing different initial variance values. We observe that while the initialization could affect the convergence rate to some extent, the algorithm's overall convergence is assured. --- ### Q2 (Variance learning): This is a very good question. The variable selection at each position is determined by the shrinkage of the variance at that position. Through variance shrinkage, DivSBL can eventually find the true block structure, making the method robust to the block size. Based on your constructive questions, we illustrate the structure of the variance learned at different preset block sizes, as shown in Fig.2 in the global rebuttal PDF. We find that, regardless of whether the block size is small, medium, or large, DivSBL consistently shrinks to the true block as expected, which is an achievement other block-based algorithms cannot consistently match. --- Rebuttal Comment 1.1: Comment: Thank you to the authors for thoroughly addressing questions and running extensive experiments in the rebuttal stage. --- Reply to Comment 1.1.1: Title: Thank you Comment: Thank you for your recognition! We will incorporate the additional experiments into the latest version of the paper. Once again, we appreciate your valuable feedback!	Summary: The authors propose a hierarchical bayesian model for sparse inverse problems where sparsity is structured in blocks. The authors propose a diversified block sparse prior using a structured covariance taking into account both intra block and block-to-block correlations. They propose an EM algorithm to solve the problem, showcase some thereotical properties in noiseless settings and illustrate the performance of their model with synthetic and real datasets. Strengths: - Self contained paper - Novel and simple model with both theoretical and applied contributions - The illustration used to provide the intuition are not easy to understand - The theoretical findings are not well motivated / explained and seem out of place / space fillers. - The presentation of the paper could be significantly improved (figures hard to read, tiny fonts) Weaknesses: - The illustration used to provide the intuition are not easy to understand - The theoretical findings are not well motivated / explained and seem out of place / space fillers. - The presentation of the paper could be significantly improved (figures hard to read, tiny fonts) Technical Quality: 2 Clarity: 2 Questions for Authors: 1. Paragraph 2.1.1 should be explained better. I fail to see how the proposed structured covariance would lead to the diversified sparsity (intra block/extra block) regardless of the predefined blocks. But if the method is robust to the chosen blocks, what is their effect then ? Why not let the method discover the blocks by itself ? 2. I fail to see how the proposed method can recover accurate sparsity structures regardless of the predefined blocks. I do not find fig2 helpful in this regard. In both conditions (white/pink) the recovered gamma_i are close to 0 ? 3. I believe in L95 there should be gL*(L+1)/2 constraints ? 4. Is there an intuition behind selecting the constraint function psi ? 5. Where does the toeplitz correction come from ? What is the impact of this step on the convergence of the EM algoritm ? Is this step necessary ? 6. Since the main contribution of the paper is the structured sparsity in groups, in the experiments I would expect the group lasso to perform very well when the groups are known and fixed. Which is not the case here. Is that due to a poor hyperparameter setting ? - typo: L137 a diversified solution - typo: L176 the diversified block sparse prior, the following global Confidence: 3 Soundness: 2 Presentation: 2 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 feedback and constructive suggestions on our paper, which we believe will help enrich the content of the original text. In this rebuttal, we respond to the concerns raised in the reviews. --- ### Q1: This is a very good question. Block-based methods require a predefined block size and then estimate based on these blocks. Traditional block-based methods are sensitive to predefined block sizes, as they estimate each block as either all zero or all non-zero. If the block size is misspecified, the method can produce significant errors. In our approach, by diversification, each variable is controlled by a corresponding variance term (while in BSBL, all elements within a block are controlled by a single variance term). Variable selection is based on individual variance shrinkage, avoiding the situation where all elements within a block are simultaneously zero or non-zero, thus making the method robust to the block size. Although our method still requires a predefined block size, which is necessary because we need to learn a correlation matrix $B_i$ with a determined dimension, the predefined block size acts more like an initial point in DivSBL. Through variance shrinkage, DivSBL can eventually find the true block structure, as you mentioned. You can refer to Fig. 2 of the global rebuttal PDF, where regardless of whether we choose a small, medium, or large block size, our method can ultimately identify the true block positions through variance shrinkage, which other block-based methods (like BSBL) do not possess. --- ### Q2: We apologize for the confusion. In Figure 2 of the paper, the ~0 in the pink area indicates that $ \gamma_i $ is non-zero (not close to zero), while the 0 in the white area indicates that $ \gamma_i $ is zero. We want to convey that through diversified variance, we can exclude white areas in predefined blocks via variance shrinkage, thereby adaptively finding the true blocks (i.e., the pink areas), as shown in Fig. 2 of the global rebuttal PDF. In BSBL, all elements within a block share the same $ \gamma $, which means the elements within a block are estimated to be either all zero or all non-zero simultaneously. Interestingly, if we formulate group Lasso in a Bayesian approach, as suggested in [1], it could be found that all elements in the same block also share a common variance in the prior. That’s why traditional block-based methods have this simultaneous zero or non-zero issue. Our insight is that the key to leveraging block information lies in learning the correlation matrix $ B_i$, rather than having the elements within a block share a common variance parameter. --- ### Q3: Yes, although they are of the same order of magnitude, considering the symmetry of the correlation matrix, the number of constraints should be $ \frac{gL(L+1)}{2} $. Thanks for your correction. --- ### Q4: This is a very good question. Reference [2] documents that if correlation matrices $B_i$ of different blocks are not constrained, it could lead to overfitting. Therefore, a strong constraint $ B_i = B $ is used, meaning that each block has the same correlation matrix to avoid overfitting. Figure 7 in the paper shows that the unconstrained algorithm (green line, Diff-BSBL) is faster initially but suffers from significant error increase later due to overfitting. On the other hand, algorithms with strong constraints (black and blue lines, DivSBL without diversified correlation & BSBL) are slower initially but achieve better accuracy later. Our motivation is to develop an algorithm that achieves both faster speed and better accuracy. Thus, our contribution lies in proposing a weak constraint framework and providing both explicit and implicit formats for choosing $ \psi $, which allows the correlation matrix of each block to retain some similarities while preserving their individual specificities. As shown by the red line (DivSBL) in the figure, DivSBL is faster in the early stages and achieves higher accuracy in the later stages. We believe that there might be better ways to select $ \psi $, and we leave this as future work. --- ### Q5: Thank you for your insightful question. The step of Toeplitz correction originates from BSBL [2] and is necessary, since we need to ensure that $ B_i$ maintains a correlation matrix structure during updates. Therefore, after updating $ B_i $, it needs to be projected onto a correlation matrix. Toeplitz correction provides a feasible and sufficiently simple way to do this, although it does result in some loss of correlation information. We believe that more complex projection methods could be considered, but this is beyond the scope of this paper. --- ### Q6: Thanks for your question. In all of our experiments, the size and location of the blocks are unknown to the algorithm and the classic CVX toolbox is used for solving group Lasso. For block-based methods, we agree that if the blocks are known and fixed, the methods perform well. However, since block information is unknown in real scenarios, block-based methods require preset block information, to which traditional methods are very sensitive, as shown in Figure 4 of the paper. Our contribution lies in addressing the sensitivity of block-based methods to preset block information via diversification. This way, even if our preset block information is not accurate, we can still adaptively identify the true blocks by variance shrinkage, as shown in Fig.2 of the global rebuttal PDF. We further included experiments on the joint effect of noise and the number of observations, demonstrating the advantages of our method in block sparse recovery, as shown in Fig.1 of the PDF. --- References: [1] Casella G, Ghosh M, Gill J, et al. Penalized regression, standard errors, and Bayesian lassos[J]. 2010. [2] Zhang Z and Rao B D. Extension of SBL algorithms for the recovery of block sparse signals with intra-block correlation. 2013.	Summary: In this work, the authors propose a novel prior called Diversified Block Sparse Prior towards a new framework to address the problem of recovery of block sparse signals. They provide theoretical and experimental justification as a proof of the efficacy of their work. Strengths: The authors propose a novel diversified block sparse prior which allows for a diversified variance and a diversified correlation. Such a prior can be used to encode/learn the knowledge of DAGs. An EM based solution is derived. Weaknesses: This area of research is quite old, and hence, any result that comes about tends to have flavors of several previous works. While the results here are relevant for a journal, I do not find anything exciting in the work which is worth publishing at Neurips. Overall the impact of the work is poor. However, in a stand-alone manner, these are some of the weaknesses: 1. The length of the block is assumed constant across the blocks. Although the authors claim that the corresponding entries will be zero or non-zero, the model will be forced towards solutions that have a constant non-zero block size. 2. Lack of sample complexity results: when we introduce new variables into any existing set-up (as compared to B-SBL, the variance here is G_iB_iG_i, which is twice as many parameters) we expect the number of measurements to be larger. Noise also impacts sample complexity. Hence, it is essential to analyse their joint effect on the sample complexity. 3. Local and global minima results hold in no-noise scenarios: The noisy scenario is presented only as a conjecture. 4. Although EM iterations are used, a closed form solution for B_i is not available. Authors propose the ascent approach for estimating B_i. This impacts the estimation process, but it has not been clarified. 5. It is not clear from the experimental settings as to what leads to better results of the proposed algorithm. The algorithm displays better performance in spite of having to estimate additional parameters in G and B. This is possible only if the number of measurements increases. More experimental results based on the ratio, m/p where m denotes the number of observations and p denotes the sparsisity is required. Technical Quality: 3 Clarity: 3 Questions for Authors: 1. What is the additional burden due to the introduction of diversified prior. Plots of m/p to substantiate the above. 2. How should the proofs change to include noise? 3. How does your method compare with PC-SBL, to be added into 2.1.3. 4. What is the error in estimating B_i in the synthetic case? Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: This method is effective only with signals that have constant block-size. No sample complexity results are available. Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thanks for your valuable questions on our paper. In this rebuttal, we respond to the concerns raised in the reviews. --- ### Q1 (Constant block size): Thanks for your question. Since the block locations and sizes are unknown in real-world scenarios, block-based methods require a predefined block size to perform estimations. Our observation is that traditional block-based methods are sensitive to the predefined block information because they estimate the elements within a block to be either all zero or all non-zero. As you mentioned, these traditional models will be forced towards solutions that have the constant non-zero predefined block size, leading to significant errors if the block size is misspecified. In our approach, by diversification, each variable at a position is controlled by a variance term. The variable selection at each position is determined by the shrinkage of the variance at that position. This addresses the simultaneous zero or non-zero issue, thus making the method robust to the block size. Although our method still requires a predefined block size, which is necessary because we need to learn a correlation matrix $B_i$ with a determined dimension, the predefined block size acts more like an initial point in DivSBL. Through variance shrinkage, DivSBL can eventually find the true block structure. We have further added visualization experiments related to Figure 4 in Section 5.2 of the paper, where the true signal block sizes are highly non-uniform. You can refer to Fig. 2 in the global rebuttal PDF, where regardless of whether we choose a small, medium, or large block size, our method can ultimately identify the true block positions through variance shrinkage, which other block-based methods (like BSBL) do not possess. --- ### Q2 (Sample complexity): This is a very good question. We agree that incorporating too many latent variables could be burdensome for recovery. DivSBL involves $n+g$ latent variables (since the correlation matrix $B_i$ for each block retains only one AR parameter through Toeplitz projection), which is a reasonable number in the Bayesian framework. For instance, the Bayesian Fused Lasso model in [1] involves $2n$ latent variables but is still a classic method in structured sparse learning. Here, our observation is that BSBL involves $g+1$ latent variables (under the strong constraint where $B_i = B$ for each block). This number of latent variables is too few (even fewer than the $n$ latent variables in SBL), making BSBL unable to effectively capture the prior covariance structure. Since elements within a block share a common variance parameter in the BSBL model, they are estimated to be either all zero or all non-zero simultaneously, making the method highly sensitive to the preset block information, as shown in Figure 4 of our paper and Fig. 2 of the global rebuttal PDF. We have added experiments in Fig.1 of the global rebuttal PDF showing the joint impact of observations and noise on the algorithms. Our method remains stable even when observations is close to the number of non-zero elements, supporting our argument: in terms of representing the prior covariance structure, it is not that DivSBL is over-parameterized, but rather that BSBL is under-parameterized. --- ### Q3 (Theoretical results in noisy case): Thanks for your constructive question. For the global minimum, the proof is a generalization of [2], and it seems hard to relax since the equivalent transformations from (35) to (36) in the paper depend on the assumption of noiselessness. For the local minima, we subsequently adjusted the proof, allowing the method to be extended to noisy scenarios. This also validates our conjecture in the paper. For a detailed proof, please refer to the global rebuttal. --- ### Q4 (A closed-form solution in EM): Thanks for your question. As documented in [2], the subproblems of the EM algorithm have close form solutions both in the unconstrained case and under strong constraints. Strong constraints are used to avoid overfitting. Our contribution lies in proposing a weak constraint framework and provide both explicit and hidden formats for choosing $\psi$. Subproblems of the EM algorithm with explicit constraints require iterative solving via the dual ascent method, while subproblems with hidden constraints have a closed-form solution for $B_i$, as demonstrated in Proposition 3.1. We also provide comparative experiments in Appendix D to demonstrate the effectiveness of algorithm with hidden constraints. --- ### Q5 (PC-SBL): Thank you for your insightful question. The prior in PC-SBL is $p(x_i\|\alpha_{i-1},\alpha_{i},\alpha_{i+1}) = \mathcal{N}(x_i;0,(\alpha_{i} + \beta \alpha_{i-1} + \beta \alpha_{i+1})^{-1}).$ This pattern-based method, which uses variance coupling between elements rather than learning correlation, differs from block-based DivSBL. Hence, it is not a special case of DivSBL in Section 2.1.3. In summary, our proposal of the DivSBL was not aimed at unifying SBL and its variants, nor was it our main contribution. The diversification of variance and correlation matrix had clear motivations and resolved the longstanding sensitivity issue of block-based methods. --- ### Q6 (Error in estimating $B_i$): Thanks for your question. The correlation matrices $B_i$ in the model are latent variables. Given a block sparse signal $x$, it could be generated by arbitrary correlation matrix $B_i$ of any dimension, hence there is no ground truth for $B_i$ in block sparse recovery. The latent variables $B_i$ are introduced here to better exploit block sparse information, but ultimately, only the target signal $x$ is used to measure errors. --- References: [1] Casella G, et al. Penalized regression, standard errors, and Bayesian lassos[J]. 2010. [2] Zhang Z, Rao B D. Sparse signal recovery with temporally correlated source vectors using sparse Bayesian learning[J]. 2011.	Rebuttal 1: Rebuttal: # Global Rebuttal --- ## 1. Experimental Setup in Global Rebuttal PDF ### Fig.1: The test data in Fig.1 is sourced from the Audioset described in Section 5.3 of the paper. This audio data contains approximately 90 non-zero elements ($K=90$), which constitutes about 20% of the total dimensionality ($N = 480$). Therefore, we start the test measurements with a sampling rate ($M/N$) of a same 20%. In this scenario, $M/K$ is roughly 1 and increases with the sampling rate. Concurrently, the signal-to-noise ratio (SNR) varies gradually from 10 to 50. The phase transition diagram illustrates that DivSBL performs well at more extreme sampling rates and is better suited for lower SNR conditions. ### Fig.2: Figure 2 visualizes the posterior variance learning on the signal from Section 5.2 of the paper to demonstrate DivSBL's ability to adaptively identify the true blocks. The block sizes of the three non-zero blocks are 100, 40, and 30, and the algorithms are tested with preset block sizes of 20 (small), 50 (medium), and 125 (large), respectively, to show how each algorithm learns the blocks when the block structure is misspecified. The first row of each subplot shows the distribution of non-zero elements in the original signal, while the subsequent rows display the posterior variance learned by the comparative algorithms. As expected, DivSBL is able to adaptively find the true block through diversification learning and remains robust to the preset block size, validating our discussion in Figure 2 of the paper. ### Fig.3 & Fig.4: Figures 3 and 4 present experiments on the test signal from Section 5.1 of the paper. Based on the reviewers' valuable suggestions, we have included posterior confidence intervals of the Bayesian methods to better demonstrate the natural advantage of Bayesian models in quantifying uncertainties. Additionally, we have added comparative experiments of recovery errors (NMSE & Correlation) with the horseshoe model, spike & slab LASSO, and hierarchical normal-gamma model for 500 random runs in Fig.4, further illustrating the advantages of DivSBL in block sparse recovery problems. ### Fig.5: The experiment in Fig.5 tests the sensitivity of DivSBL to initialization on the signal data from Section 5.1 of the paper. Initial variances are set to $\gamma = \eta \cdot \text{ones}(g L, 1)$ and $\gamma = \eta \cdot \text{rand}(gL, 1)$ with the scale parameter $\eta$ ranging from $1 \times 10^{-1}$ to $1 \times 10^{4}$. The results show that while initialization could affect the convergence speed to some extent, the algorithm's overall convergence is assured. --- ## 2. The Proof of Local Minima in Noisy Scenario We sincerely thank the reviewers for your insightful questions, which have driven us to further our theoretical advancements. Your valuable feedback has been instrumental in enhancing the depth and rigor of our work. We subsequently adjusted the proof, with the core being the direct proof of lines 493-494 in Appendix H of the original paper without relying on Lemma 4.2, allowing the method to be extended to noisy scenarios. We found that the constraint (a.2) with noise can be proved convex with respect to $Z$ and $\sqrt{\gamma} \otimes \sqrt{\gamma}$ directly. The proof is as follows: ### Proof We can equivalently transform the constraint (a.2) with noise into the following: $$ Z \succeq \Phi \Sigma_0 \Phi^T + \beta^{-1} I \Longleftrightarrow \forall \omega \in \mathbb{R}^m, \quad \omega^T Z \omega \geq \omega^T \Phi \Sigma_0 \Phi^T \omega + \beta^{-1} \omega^T \omega. $$ The LHS $\omega^T Z \omega$ is linear with respect to $Z$. And for the RHS, $\omega^T \Phi \Sigma_0 \Phi^T \omega + \beta^{-1} \omega^T \omega = q^T \Sigma_0 q + \beta^{-1} \omega^T \omega$, where $q = \Phi^T \omega$, and $\Sigma_0$ can be reformulated as: $$ \Sigma_0 = \text{diag}(\sqrt{\gamma_{11}}, \ldots, \sqrt{\gamma_{gL}}) \tilde{B} \text{diag}(\sqrt{\gamma_{11}}, \ldots, \sqrt{\gamma_{gL}}) = \begin{bmatrix} {\gamma_{11}} \tilde{B}\_{11} & \sqrt{\gamma_{11}} \sqrt{\gamma_{12}} \tilde{B}\_{12} & \ldots & \sqrt{\gamma_{11}} \sqrt{\gamma_{gL}} \tilde{B}\_{1N} \\\\ \vdots & \vdots & & \vdots \\\\ \sqrt{\gamma_{gL}} \sqrt{\gamma_{11}} \tilde{B}\_{N1} & \sqrt{\gamma_{gL}} \sqrt{\gamma_{12}} \tilde{B}\_{N2} & \ldots & {\gamma_{gL}} \tilde{B}\_{NN} \end{bmatrix} $$ Therefore, RHS: $$ \sum_{i=1}^{N} \sum_{j=1}^{N} q_i q_j \tilde{B}\_{ij} \sqrt{\gamma_{i}} \sqrt{\gamma_{j}} + \beta^{-1} \omega^T \omega = \text{vec}(q q^T \odot \tilde{B})^T (\sqrt{\gamma} \otimes \sqrt{\gamma}) + \beta^{-1} \omega^T \omega $$ which is linear with respect to $\sqrt{\gamma} \otimes \sqrt{\gamma}$. In conclusion, $Z \succeq \Phi \Sigma_0 \Phi^T + \beta^{-1} I$ is convex with respect to $Z$ and $\sqrt{\gamma} \otimes \sqrt{\gamma}$, which can conclude the proof in Theorem 4.4 in the noisy case ($\forall \beta$). Pdf: /pdf/219ae34bb27cc0b77639c401a1710c15b2155c67.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Capturing the denoising effect of PCA via compression ratio	Accept (poster)	Summary: In this paper, the authors propose a novel metric called compression ratio to capture the effect of PCA on denoising which can significantly reduce the distance of data points belonging to the same community while reducing inter-community distance relatively mildly. They try to explain this phenomenon through both theoretical proofs and experiments on real-world data. In addition, they design a straightforward algorithm that could be used to detect outliers and provide many experimental results to demonstrate its superiority over existing methods. Strengths: 1. the paper studies an important question that how to characterize the improvement of dimension reduction via PCA in denoising and clustering. 2. the proof part is solid and sound 3. the experiment part is rich and convincing, validating the theoretical analysis part Weaknesses: The paper only conduct experiments on single-cell RNA-seq, which is not convincing. Results on more datasets are expected. Technical Quality: 3 Clarity: 3 Questions for Authors: Can more metric comparison be included such ARI? Table 3 the middle 2 columns (Purity) they are the same, I guess one is 5% and another one should be 10% instead of 5%? Confidence: 3 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 thank the reviewer for their valuable comments. Please find our response below. Regarding only using single-cell data: We first note that single-cell is indeed a very important data-type with various applications in immunology, neuroscience, and others. The Science Journal placed it as the breakthrough of the year in 2017. Also, many machine learning papers use single-cell data primarily for experiments, including recent NeurIPS papers [1,2] Additionally, we have tested that the compression ratio phenomenon of PCA is widely present in high dimensional noisy data. For example, we ran our experiments on a certain AFLP dataset [1]. Furthermore, this phenomenon can also be observed in popular image datasets such as MNIST and F-MNIST if they are artificially corrupted with high variance noise. Although we observed the compression ratio gap on these datasets, they do not have natural outliers. Hence, we did not include the compressibility results due to the space constraints of NeurIPS papers. By contrast, single-cell data is a very good fit for high-dimensional noisy data with natural outliers. Some erroneous cells are the results of mixtures of different cell types or cells disproportionately affected by noise, which makes this datatype an ideal candidate for our outlier detection method. Overall, we are also interested in testing more high-dimensional noisy datasets with natural outliers. If the reviewer has such datasets in mind, please let us know, and we will be happy to test more. Other clustering metric: We can surely show improvements in other clustering metrics, such as the ARI. Following the reviewer’s recommendation, we ran these experiments and observed that our method provides the second-best rank for ARI. Here, we want to note that ARI seems not to give an accurate picture of the clustering outcome if the clusters have varied sizes, and indeed, all of the outlier detection methods had weaker improvements in the ARI metric compared to both NMI and purity. As a summarizing step, we calculated the ranks across different metrics (NMI, ARI, and purity), and our method (variance of compression) had the best overall rank by a significant margin. For example, for dimension k-1, we had a rank of 2.8, whereas the next best rank was 3.7. On a separate note, we will fix the heading of the table as pointed out by the reviewer (yes, the right column is for 10% purity). [1] Gong, Jing, et al. "xTrimoGene: an efficient and scalable representation learner for single-cell RNA-seq data." NeurIPS2023. [2] Palma, Alessandro, et al. "Modelling single-cell RNA-seq trajectories on a flat statistical manifold." NeurIPS 2023 AI for Science Workshop. 2023. ------ We hope this answers the reviewer's questions, and we will be happy to answer any other queries they have.	Summary: This paper introduces compression ratio, defined as the ratio of pre-and-post-PCA distances for a pair of observations, for outlier detection tasks. The authors demonstrated that this metric could capture the effect of PCA on high-dimensional data with moderate noise and proposes that points with lower variance of compression ratio and do not share a common signal with others are more likely to be outliers. The proposal was validated in both simulations and on real-world scRNA-seq datasets. Strengths: 1. The authors provided a detailed statistical setup for the problem and provided theoretical guarantees of components of the algorithm. 2. The idea is quite simple and elegant 3. The simulation shows that with moderate noise, the proposed method achieves good outlier removal methods. Weaknesses: 1. More robustness/sensitivity analysis would be needed to help understand how widely applicable this simple ratio is. 2. The current real data application is not well-motivated: while identifying potentially mislabeled cell types are interesting, these are often better treated as deconvolution and/or mixture model problems. Technical Quality: 3 Clarity: 3 Questions for Authors: 1. In Figure 1, why is the variance of compression achieving moderate to low ranks? 2. The simulated outliers seem to come from a convex combination of existing clusters — have the authors considered more general outlier cases? 3. I would encourage the authors to provide more simulation results with higher dimensionality (right now it uses d=1,000 < n=3,000)? 4. On the selection of dimension for PCA, it looks like choosing anywhere from k to 2k (where k is the true number of “community”) is not too bad — in practice is there any advice and guidance on choosing k in the first place that performs reasonably? 5. From Algorithm 1, it seems like returning these indices requires at least doing O(n^2) distance after performing PCA — adding the theoretical and empirical time complexities on some of these datasets would benefit this method's users. 6. I would encourage the authors to compare the results on benchmark datasets used for outlier removal, especially since that is the primary application highlighted. Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: Detailed in questions. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for their valuable comments. Please find our response below. Motivation behind real-world application: We thank the reviewer for their input. First, we observe that such mixture model approaches are predominantly used in data with access to bulk-RNA seq data, which can be less complex than single-cell RNA seq data [1,2]. More importantly, we note that the highly cited work [3] laid down a standard pipeline for single-cell RNA seq data. Here, preprocessing is followed by clustering, and then the clustering is used to find differentially expressed genes (DEG) in the data (i.e., features that have predominantly high values in one cluster compared to other clusters). In such cases, a better separation of the underlying data can be beneficial in better DEG detection. As our outlier removal improves the performance of clustering algorithms such as PCA+K-Means, we hope it may be of interest and use to bioinformaticians. Answer to questions Weaker performance in Figure (1): We start by noting an observation from the outlier detection survey paper we referenced (HHH+22) that the success of an outlier detection algorithm depends on how closely the assumption behind the algorithm matches that of the dataset. In our paper, we theoretically studied our outlier detection algorithm in the case where outliers are generated as random mixtures of community centers further perturbed by noise, which is essentially the same as random mixtures of the points in the communities. Figure 1(b) is for a different kind of outliers. Here, outlier points are generated by adding a “higher variance noise” to the corresponding community center compared to normal points for that community. Note that this is an outlier model different from the one we theoretically study. In fact, outlier detection methods like LOF are known to have a very good performance in such settings (HHH+22). We wanted to showcase that our method can be competitive even when the outlier model differs from our theoretical model. We hope this will further increase confidence in our outlier detection method. Types of outliers: As we have noted above, apart from the outlier model where outliers are convex combinations of points in the communities (which we study theoretically), we also provide results for the case where outliers are points with higher variance noise (which we present in Figure 1(b)). Apart from that, we also test our method on a large set of single-cell data. Simulations for d>n: Following the recommendation by the reviewer, we also ran experiments with d>n by setting d=4000 and n=2000. We obtained identical performance as the ones shown in the paper. In fact, for the higher noise case, our outlier detection performance was comparatively even better than the other methods. We shall add this result to the paper. Choice of PCA-projection dimension: We did not consider this question in this paper. This is indeed an important question. In our experience, simple techniques such as elbow plots on the eigenvalue of the covariance matrix seem to be a good technique for obtaining a good choice. Additionally, there exists a large body of work on choosing the correct PCA dimension for noisy high-dimensional data. Run-time complexity: Indeed, calculation of all O(n^2) distances is necessary for obtaining the variance, bringing the time complexity to O(n^2*d). For the datasets we consider, our algorithm runs under 3 minutes, with it running under 5 seconds for the smaller datasets (less than 1000 points). We also want to point out that the distance calculations are highly parallelizable. Furthermore, theoretically we can improve this runtime significantly in our model. For each point, we may sub-sample a few points O(sqrt(n) log n) and then calculate the compression ratio with these points to obtain the variance of compression. This would reduce the run-time to only consider n^{1.5} log n distances. Empirical verification of such speedups is a future direction. [1] Song, Liyang, et al. "Mixed model-based deconvolution of cell-state abundances (MeDuSA) along a one-dimensional trajectory." Nature Computational Science 3.7 (2023): 630-643 [2] Chu, Tinyi, et al. "Cell type and gene expression deconvolution with BayesPrism enables Bayesian integrative analysis across bulk and single-cell RNA sequencing in oncology." Nature Cancer 3.4 (2022): 505-517 [3] Heumos, Lukas, et al. "Best practices for single-cell analysis across modalities." Nature Reviews Genetics 24.8 (2023): 550-572. ----- We hope this answers the reviewer's questions, and we will be happy to answer any other queries they have.	Summary: This paper studies the denoising effect of PCA using a novel metric called "compression ratio". The metric is defined as the ratio of the pre and post-PCA between two points. The authors note that when the dataset has a community structure, outlier points tend to have a flatter distribution of compression ratios w.r.t other data points, whereas inlier points have a larger compression ration w.r.t to other intra-community data points. This insight is used to design a simple outlier-detection algorithm for data with community structure. Under certain assumptions on the data distribution, the authors show that this outlier identification algorithm succeeds with a constant probability. The authors also provide many experimental results on both synthetic and real-world datasets to show that their proposed methods outperform existing algorithms. Strengths: - The paper studies a problem of good interest and provides a clean, well-motivated solution. - The theoretical results are interesting Weaknesses: - Because of the theoretical nature of the paper, there are many assumptions such as knowing the number of outliers, and assumptions on the noise distribution. These assumptions do not always hold in real-world data. Technical Quality: 3 Clarity: 3 Questions for Authors: - In Figure 1, it seems like the proposed method (Variance of compression) performs worse than most other methods. Can the authors provide more information regarding Figure 1b? - Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: See questions and weaknesses. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for their valuable comments. Please find our answers below. Regarding the theoretical assumptions: Our theoretical setting is a generalization of several popular unsupervised models, such as the Gaussian mixture models and the stochastic block model. The noise distribution we consider is SubGaussian with very high variance. Such distributions capture noise observed in many real-world scenarios, such as datasets with bounded entries (as all bounded variables are subGaussian). Next, we note that our outlier detection algorithm does not need knowledge of the number of outliers. We prove that if the data has outliers in the random mixture model setting, these outliers will have the lowest variance of compression. Regarding the weaker performance in figure 1(b): We start by noting an observation from the outlier detection survey paper we referenced (HHH+22) that the success of an outlier detection algorithm depends on how closely the assumption behind the algorithm matches that of the dataset. In our paper, we theoretically studied our outlier detection algorithm in the case where outliers are generated as random mixtures of community centers further perturbed by noise, which is essentially the same as a random mixture of the points in the communities. Figure 1(b) is for a different kind of outliers. Here, outlier points are generated by adding a “higher variance noise” to the corresponding community center compared to normal points for that community. Note that this is an outlier model different from the one we theoretically study. In fact, outlier detection methods like LOF are known to have a very good performance in such settings (HHH+22). We wanted to showcase that our method can be competitive even when the outlier model differs from our theoretical model. We hope this will further increase confidence in our outlier detection method. ------ We hope this answers the reviewer's questions, and we will be happy to answer any other queries they have.	Summary: The paper proposes a new measure called ‘compression ratio’ to determine how effectively PCA compresses data. For subspace clustered data the authors show that if the signal directions for each cluster are well-separated, the compression ratio is larger for within clusters than compared to between clusters. The paper also proposes a method for outlier detection through this compression ratio. Strengths: The paper theoretically shows that for clustered data that are well separated and each cluster centroid is situated in a subspace, not representable by the span of centroids, the compression within clusters is greater than compressions between clusters, implying the formation of tight clusters in the reduced low-dimensional representation. Weaknesses: 1. The assumptions in the paper are quite strong in my opinion. Especially the assumption of nearly orthonormal cluster centroids is unrealistic for low-dimensional data ($n \gg d$) where PCA is usually applied. 2. The outlier detection algorithm requires a run of the PCA to find the compression ratio. However, it is well known that PCA is not at all outlier robust. In that case how are the compression ratios reliable? The theoretical guarantees in Theorem 2.8 does not seem to match this intuition. Is this guarantee only an artefact of the restrictive assumption on the subGaussianity of the outliers? Technical Quality: 2 Clarity: 2 Questions for Authors: 1. Usually, it is common practice to calculate the information lost in PCA based on the ratio of the sum of the eigenvalues. How does the compression ratio relate to the variance explained? A clarification regarding this is warranted. 2. How do the authors manage to run vanilla PCA on single-cell RNAseq data on which $d \gg n$? Do they use a different version of the PCA? 3. How does the method compare to other robust PCA techniques? What are the advantages of their proposal compared PCA-based custering methods such as IF-HCT-PCA? Jiashun Jin. Wanjie Wang. "Influential features PCA for high dimensional clustering." Ann. Statist. 44 (6) 2323 - 2359, December 2016. https://doi.org/10.1214/15-AOS1423 Also see my questions in the weakness section. Confidence: 4 Soundness: 2 Presentation: 2 Contribution: 2 Limitations: Yes, limitations are discussed. Flag For Ethics Review: ['No ethics review needed.'] Rating: 3 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for their review. Please find our responses below. Comments regarding weaknesses: Regarding unrealistic conditions of centers: The reviewer comments that the assumption of centers being nearly orthonormal is unrealistic for the case of n>>d (where n is the number of data points and d is the dimension). This is an incorrect evaluation of our theoretical contribution in our understanding. First, we point out that our assumption can be interpreted as each center (there are $k$ centers in total) being not a linear combination of others. This assumption is much weaker than nearly orthonormal. Our assumption covers many natural benchmark models, such as the stochastic block model. Secondly, even the realizability of this weaker condition has no connection with the comparative values of n and d. Outlier detection in PCA: As the reviewer pointed out, PCA is not robust to outliers in all scenarios. In this paper, we mainly focus on high-dimensional noisy data, which we present in the random mixture vector model with subGaussian noise. First, we observe the compression ratio phenomenon of PCA in simulation and all the datasets that we consider. Then, we use this phenomenon to detect outliers in this model. Furthermore, The overall performance of our outlier detection algorithm on a large set of real-world datasets is a strong support of its efficacy. Answer to questions: Q1) Regarding “explained variance”: In this paper, the compression ratio is defined on k-dimensional PCA projection and the amount of information retained is dependent on factors such as k and the variance of the noise in each community. Among our datasets, the top k singular values range from 3%-10% of the sum of the singular values, depending on the noise level of the datasets. There is a very weak correlation between this value and compressibility phenomena. Q2) The vanilla PCA algorithm works for any rectangular matrices, and as such, we do not need to use a different method for d>>n and n>>d. Q3) The goal of the paper is to analyze the “compressibility” of PCA itself, and as such, we do not focus on other PCA variants. It is an interesting future direction to see if similar compressibility phenomena are observed in other variants of PCA, and we thank the reviewer for their suggestion. Regarding the PCA based clustering method: Please note that we do not propose a clustering algorithm in this paper. Rather, we use the compression ratio metric to observe the denoising effect of PCA in noisy high-dimensional data with underlying community structure. Next, we use this metric to design an outlier detection algorithm. Therefore, comparisons with PCA-based clustering methods are not relevant to the paper. ------ We hope this answers the reviewer's questions, and we will happily answer any other queries they have. --- Rebuttal Comment 1.1: Title: Response to Authors Comment: Thank you for the detailed rebuttal. However, I still have some reservations regarding the assumptions as they are quite strong and does not hold for practical senarios. For example the assumption won't hold for $k > d$. Additionally, if I understand correctly, the subgaussianity of the outliers appears to be crucial for the theoretical guarantees, potentially excluding cases with unboundedly large outliers. This undermines the purpose of developing of being outlier-robust. Please correct me if I’m mistaken. Given that the paper also proposes an outlier-robust PCA and evaluates its effectiveness through clustering performance, I believe it should be compared with similar recent methods, such as IF-HCT-PCA and other robust PCA techniques. Unfortunately, the current experimental setup does not seem to address such comparisons. Thus, I am inclined to keep my scores as is. --- Rebuttal 2: Comment: As we mentioned in our paper (even abstract, first sentence of the second paragraph), our main focus in this paper is high-dimensional noisy data. Here $k$ is the number of clusters and $d$ is the dimension of vectors. In single-cell data, $k$ is usually smaller than $50$ and $d$ is usually larger than $20000$. For another example, in popular image data sets such as MNIST and F-MNIST, $k=10$ and $d=784$. The condition $d\gg k$ is also true for many many other domains. In the case of $k\geq d$, we believe PCA or spectral algorithms are not the correct approaches. For example, many spectral algorithms (including PCA) projected the high-dimensional data into $\Theta(k)$ dimensional vectors in applications to data/models with $k$-clusters. If $k\geq d$, we believe the projection will remove some useful information. See the link for spectral clustering https://en.wikipedia.org/wiki/Spectral_clustering . If the reviewer insisted that our algorithm failed in low-dimensional data, then we agree with the reviewer and have nothing to discuss with, since $k\geq d$ is not in our consideration. Also, in the entirety of our paper, we only say that our algorithm is robust under the choice of the projected dimension, and it is very different from the concept of robust PCA. Using the compression ratio of PCA as an outlier detection algorithm has no connection to robust PCA. We are not sure why the reviewer connected our result with robust PCA. Please see the link of robust PCA (https://en.wikipedia.org/wiki/Robust_principal_component_analysis).	null	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Fair GLASSO: Estimating Fair Graphical Models with Unbiased Statistical Behavior	Accept (poster)	Summary: The article explores the issue of achieving fairness in Gaussian Graphical Models (GGMs), particularly in the presence of biased data. Such biases can lead to unfair behavior in the models. To address this issue, the authors propose two bias metrics aimed at achieving statistical similarity across groups with different sensitive attributes. Based on these metrics, the authors introduce a regularized graphical lasso method called Fair GLASSO, designed to obtain sparse Gaussian precision matrices with unbiased statistical dependencies across different groups. The authors also propose an efficient proximal gradient algorithm to obtain these estimates and analyze the tradeoff between fairness and accuracy. Strengths: （1）The authors are the first to propose definitions of fairness and bias metrics applicable to graphical models. （2）Through theoretical analysis and experiments, the effectiveness of Fair GLASSO in mitigating bias while maintaining model accuracy is demonstrated. （3）The method is compared with various existing approaches, showcasing Fair GLASSO's advantages in reducing bias and improving accuracy Weaknesses: （1）The implementation of the algorithm relies on complex matrix operations, which may pose high computational costs in practical applications. （2）Although the experiments used multiple datasets, the variety and scale of these datasets are still limited, possibly not fully representing all practical application scenarios. （3）There are some formatting issues in the paper, such as unnumbered equations on page 23. Technical Quality: 3 Clarity: 3 Questions for Authors: (1) Can the authors provide a detailed explanation for the choice of these two bias metrics? Specifically, how do these metrics capture fairness better than other potential metrics? (2) Can the authors provide a detailed breakdown of the computational complexity for each step of the Fair GLASSO algorithm? (3) How does the proposed Fair GLASSO method perform on non-Gaussian data? Have the authors considered extensions or modifications to handle such cases? (4) The method relies on certain assumptions (e.g., bounded spectrum, equal group sizes). How sensitive is the performance of Fair GLASSO to violations of these assumptions? (5) What specific evaluation metrics were used to compare the performance of Fair GLASSO with other methods? Are these metrics the most appropriate for assessing both fairness and accuracy? (6) Can the authors provide more details on the real-world datasets used, specifically the nature of the sensitive attributes and the relevance of fairness in those contexts? (7) The paper contains some unnumbered equations, such as those on page 23. Can the authors clarify the reasons for this and provide the necessary numbering for easier reference? Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 4 Limitations: (1) Although the paper discusses the efficiency of the Fair GLASSO algorithm, a more detailed analysis or discussion of the impact of complexity on practical applications would be better. For example, discussing potential scalability issues with larger datasets or in real-time applications could be very helpful. (2) The paper relies on certain assumptions, such as bounded spectrum and equal group sizes. Including a sensitivity analysis for these assumptions would be beneficial. (3) The paper could provide more concrete examples or case studies demonstrating the application of Fair GLASSO in real-world scenarios, beyond synthetic and small-scale examples. (4) Discuss the ethical implications of using Fair GLASSO in these fields. Emphasize the importance of stakeholder engagement and continuous monitoring to ensure that the implementation does not inadvertently harm the groups it aims to protect. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: # Rebuttal for fwTq: We greatly appreciate your positive feedback along with your valuable questions and suggestions. We hope that our responses below maintain your positive assessment. > Answer to Question 1. Thank you for your question. For graph-based works, the predominant choice of bias metric is demographic parity (DP). Thus, we approach the nascent task of graphical model estimation with a familiar bias metric to verify our approach with established measurements. However, our formulation is suited to other bias metrics such as equalized odds (EO), defined in the global response. While both DP and EO are popular fairness definitions, we cannot compute EO for the true precision matrix since it is conditioned on the ground truth connections. As the crux of our theoretical results relies on measuring the bias in the true precision matrix, we choose DP as our bias metric. > Answer to Question 2. We present a brief analysis for bias metric $H\_\\mathrm{node}(\\mathbf{\\Theta})$, but a similar analysis holds for other penalties such as $H(\\mathbf{\\Theta})$. The first step of Algorithm 1 is a proximal gradient step. Computing the gradient requires an inverse $( \\mathbf{\\Theta} + \\epsilon \\mathbf{I} )^{-1}$ and product $\\mathbf{A} \\mathbf{\\Theta}\_{\\bar{\\mathcal{D}}}$, both incurring $\\mathcal{O}(p^3)$ operations. The gradient step and soft-thresholding enjoy entry-wise computations with complexities $\\mathcal{O}(p^2)$. The projection step onto the set of positive semidefinite matrices involves an eigendecomposition of $\\dot{\\mathbf{\\Theta}}^{(k)}$ with complexity $\\mathcal{O}(p^3)$. Finally, the step size update $t^{(k)}$ only requires scalar operations, and the accelerated update of $\\check{\\mathbf{\\Theta}}^{(k+1)}$ involves $\\mathcal{O}(p^2)$ operations, so they can be neglected. If accepted, we will include these additional details in the revised version of the manuscript to strengthen its clarity. > Answer to Question 3. In Table 2 of our manuscript, we estimate real-world networks from real data, such as the discrete graph signals of the School and Friendship social networks. Thus, we empirically observe satisfactory performance even when observations are non-Gaussian, as queried by the reviewer. However, you also ask an important question: can Fair GLASSO be extended to non-Gaussian graphical models? Gaussianity specifies the loss in the objective of Fair GLASSO, but we may consider other distributions in the optimization problem, such as the Ising negative log-likelihood. Such a substitution requires altering our theoretical results, and in future work we will explore the fairness-accuracy relationship for non-Gaussian distributions. > Answer to Question 4. We thank you for this question. If accepted, we will provide a detailed discussion on the assumptions for Fair GLASSO. Here, we share a brief summary. First, AS1 merely defines the cardinality of the support of the true precision matrix. For the spectrum of the true covariance matrix $\\mathbf{\\Sigma}\_0$, eigenvalues with finite magnitudes as in AS3 is reasonable for any practical setting. AS2 may be violated for a rank-deficient $\\mathbf{\\Sigma}\_0$. However, letting $\\epsilon>0$ addresses both theoretical and implementation concerns, where $\\mathbf{\\Sigma}\_0$ need not be positive definite for convergence or the error bound. As would be expected, the error bound becomes perturbed based on the magnitude of $\\epsilon>0$. The final assumption can be relaxed to require only that no group vanishes as $p\\rightarrow\\infty$. If a group vanishes, then edges cannot achieve perfect balance across all pairs of groups, which will result in a lower bound on the second term of the error upper bound. Moreover, we present additional simulations in the attached document illustrating how the assumptions affect performance. > Answer to Question 5. Our metrics for error and bias are described more thoroughly in Appendix G. We employ the normalized squared Frobenius error, a standard metric for network inference works. We follow similar intuition for bias, where we normalize measurements to compare biases across networks without being affected by changes in graph size or edge weights across graphs. > Answer to Question 6. In real-world social network analysis, common network characteristics such as homophily can lead to negative outcomes across gender in both social and academic settings [A4]. Hence, the School, Friendship, and Co-authorship networks require scrutiny with respect to fairness, where gender is a critical consideration. For demonstrative purposes, we use publication type as the sensitive attribute for Co-authorship as an example of data with more than two groups. Additionally, biases in recommendation systems can reproduce and even exacerbate existing harmful stereotypes [A5]. The MovieLens dataset, a common benchmark for fair graph machine learning, exemplifies our ability to form unbiased models from networks used for recommendation systems. If our work is accepted, we will include this relevant discussion in the final version. > Answer to Question 7. Thank you for asking about the reasons for our choice. We followed a common approach of numbering equations to which we refer, which serves to provide lighter notation. However, we agree with the reviewer that numbering all equations may better facilitate the understanding of our results. If the reviewer deems it necessary, we will gladly make this change upon acceptance of this work. We also appreciate your valuable suggestion regarding further discussion of ethical implications, and we will augment our broader impact discussion if accepted. --- Rebuttal Comment 1.1: Title: Fair GLASSO: Estimating Fair Graphical Models with Unbiased Statistical Behavior Comment: I would like to thank the authors for their detailed responses, clarification, and additional results. Most of my questions are solved and I raise my score. --- Reply to Comment 1.1.1: Title: Thank you for your thorough review Comment: We thank the reviewer again for your perceptive questions and comments. It is clear that you read our paper in detail, and we greatly appreciate your thoroughness.	Summary: The authors propose a method for estimating Gaussian graphical models that are fair. To do this, the methodology uses Fair GLASSO, a regularized loss for estimating the precision matrix of the GGM which is fair with respect to sensitive attributes. The authors also provide theoretical results regarding the asymptotic errors of the estimated precision matrix. Strengths: - Overall, the paper is well written. - The methodology developed is sound and supported by theoretical results. - The experimental results show that the derived method is effective in practice. Weaknesses: - Please define modularity and "partial correlations within and across groups" for completeness. - Theorem 1 provides asymptotic results in terms of p, but it would be more interesting to derive results which are asymptotic in the number of data points n. Usually, the number of nodes are fixed and the number of datapoints increases. - It would be interesting for authors to investigate how the results change when the assumptions are violated. - Also, is n fixed even as p increases to infinity in the result above? In this case, won't the covariance matrix become uninvertible when p > n? - The results should also include a pareto frontier between error and bias when the regularization parameters vary (but p and n are fixed) Technical Quality: 3 Clarity: 3 Questions for Authors: See the weaknesses section Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The authors should elaborate on the limitations of the proposed methodology a bit more. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: # Rebuttal for V8H3: We thank you for your thorough review and detailed questions. We are grateful for your kind words regarding the strengths of our work. > Answer to Weakness 1. Group-wise modularity is computed as in reference [19] of the paper, that is, $$ Q(\\mathbf{\\Theta}) = \\sum\_{a=1}^g \\frac{\\mathbf{z}\_a^\\top \\mathbf{\\Theta}\_{\\bar{\\mathcal{D}}} \\mathbf{z} }{2s} - \\sum\_{a=1}^g \\left(\\frac{\\mathbf{z}\_a^\\top \\mathbf{\\Theta}\_{\\bar{\\mathcal{D}}} \\mathbf{z} }{2s}\\right)^2, $$ where $s$ denotes the number of nonzero entries in $\\mathbf{\\Theta}$. To estimate partial correlation, we apply graphical lasso without a bias penalty, and entries of the resultant precision matrix denote estimates of partial correlation for every pair of variables. We thank you for your comment. We agree that these definitions are necessary for completeness. We will add more detailed versions of these definitions in the revised paper. > Answer to Weakness 2. Your point is well taken, and we clarify the meaning of the theoretical result. The result in Theorem 1 holds with high probability as either $n$ or $p$ increase; it is the probability of the error bound holding that converges to 1 as $p$ increases to infinity. We understand that this presentation appears vague. Thanks to your question, we will state this fact more clearly in the final version if accepted. > Answer to Weakness 3. Thank you for this comment. For lack of space, we outline the effects of violating our assumptions here, but we will provide a comprehensive discussion in the updated paper if accepted. We also provide empirical demonstrations of the assumptions on estimation performance in the attached document, described in the global response. Observe that since AS1 has no restrictions on permissible values of $s$, AS1 merely defines the number of edges in the true graphical model. AS2 and AS3 bound the eigenvalues of the true covariance matrix $\\mathbf{\\Sigma}_0$. In realistic settings, these eigenvalues will have finite magnitudes as in AS3, but the covariance may indeed be rank deficient, violating AS2. Theoretically, this affects the log-determinant bound in equation (18) of our paper, as we cannot finitely bound the difference above with the reciprocal of the smallest eigenvalue. However, in such a case, we may instead consider Theorem 1 with $\\epsilon > 0$. We then obtain a similar error bound, albeit perturbed by the value of $\\epsilon$, that is, the magnitude of $\\epsilon$ increases with the number of zero-valued eigenvalues of $\\mathbf{\\Sigma}_0$. Finally, AS4 can be relaxed to require only that group sizes be asymptotically similar, so no group vanishes as $p\\rightarrow\\infty$. If a group vanishes, then the error bound will contain persistent terms corresponding to average edge magnitudes of the remaining groups, which cannot be balanced in connection across all groups. > Answer to Weakness 4. As in our response to your Question 2, we note that our theoretical results do not require that $n$ be fixed. Moreover, you are correct that with insufficient samples, the empirical covariance matrix may not be invertible. Indeed, a major advantage of graphical lasso is that it is suitable in a low sample regime. The sparsity penalty implements prior assumptions of parsimonious entries in the precision matrix to supplement inadequate information in the sample covariance matrix. > Answer to Weakness 5. We appreciate your valuable suggestion. We propose the following approach to show conditions on parameters $\\mu_1$ and $\\mu_2$ to guarantee Pareto optimality of Fair GLASSO. Say that we assume that our Fair GLASSO estimate $\\mathbf{\\Theta}^$ has error $\\\|\\mathbf{\\Theta}^ - \\mathbf{\\Theta}_0\\\|_F^2 = \\delta$ for some $\\delta > 0$. For any feasible precision matrix $\\mathbf{\\Theta} \\in \\mathcal{M}$ such that $\\\|\\mathbf{\\Theta} - \\mathbf{\\Theta}_0\\\|_F^2 \\leq \\delta$, we wish to determine the selection of $\\mu_1$ and $\\mu_2$ that guarantees $H(\\mathbf{\\Theta}^) < H(\\mathbf{\\Theta})$, that is, that we have a Pareto optimal estimate $\\mathbf{\\Theta}^$. Our proposed approach is to exploit the optimality of $\\mathbf{\\Theta}^$, which yields $$ \\mu\_2 \\left( H(\\mathbf{\\Theta}) - H(\\mathbf{\\Theta}^) \\right) \\geq \\mathrm{tr}(\\hat{\\mathbf{\\Sigma}}(\\mathbf{\\Theta}^-\\mathbf{\\Theta})) + \\log \\det \\mathbf{\\Theta} - \\log \\det \\mathbf{\\Theta}^ + \\mu\_1 \\left( \\\| \\mathbf{\\Theta}^*\_{\\bar{\\mathcal{D}}} \\\|\_1 - \\\| \\mathbf{\\Theta}\_{\\bar{\\mathcal{D}}} \\\|\_1 \\right), $$ from which we derive bounds on $\\mu_1$ and $\\mu_2$ to ensure that the right-hand side is positive. If our paper is accepted, we will provide the full version of the above Pareto optimality result, as requested by the reviewer. We appreciate your high standards regarding our paper. We will indeed elaborate on the limitations of our proposed work, the intuition of which your questions have helped us to develop.	Summary: Traditional graphical models may reinforce existing biases present in the data. This paper introduces a novel approach to ensure that the learned graphical models are fair across different groups or demographics. Strengths: - The authors develop a penalty method that adds a fairness penalty to the GLASSO objective. - As the added penalty is smooth, the authors develop a FISTA-type method to solve the optimization problem with an $\ell_1$ nonsmooth term. Objective includes Gaussian graphical model loss + fairness penalty term + $\ell_1$ penalty term. - The authors provide experiments on both real and synthetic datasets, demonstrating the efficacy of their methods. - The paper is generally well-written and has a good synthetic empirical investigation. Weaknesses: - My main concern is that the proposed fair graphical model is essentially a joint graphical model widely studied in the existing literature. Please see below (Questions) for further clarification. - The proposed penalty functions are already studied in the existing graph fairness literature. Specifically, both fairness penalty functions $H(\Theta)$ and $H_{\text{node}}(\Theta)$ are from [15, 18], except that the authors replaced $\| \cdot \|$ with $( \cdot )^2$; for example, please refer to Eqs (1) and (2) in [18]. - Since $H (\Theta)$ and $H_{\text{node}}(\Theta)$ are smooth functions, the authors apply FISTA-type methods for graphical models. As FISTA and its variants are already explored in graphical models and their theoretical analyses are already provided [R2], Algorithm 1 simply applies to the smooth $f$ and nonsmooth $\ell_1$ term. Thus, the theoretical contribution of Theorem 2 is limited. - Estimation guarantees in Theorem 1 follow from existing literature on graphical model estimation, except that the authors need to handle $H(\Theta)$ and $H_{\text{node}}(\Theta)$ in the proof of Theorem 1. For example, the proof of trace difference, log-determinant difference, and sparsity penalties is identical to Theorem 1 of [32]. - In real experiments, the ground truth of the graph is used to generate the data, and then a fair graph is estimated. However, I am concerned that this might not be considered as real experiments since, in real scenarios, the precision matrix for graphical model estimation is indeed unavailable. In addition, it is not clear that these real datasets are suitable for Gaussian graphical models, as they should consist of binary numbers (e.g., interactions between people as nodes would be 0/1). This raises questions about the applicability of the method in real-world scenarios. Technical Quality: 2 Clarity: 2 Questions for Authors: - How does the proposed method differ from the joint graphical lasso [R1, R3, R4, R5], which borrows strength across the groups within graphical models that share certain characteristics, such as the locations or weights of nonzero edges? Specifically, under AS4 and since $Z$ is an indicator matrix, $H(\Theta)$ and $H_{\text{node}}(\Theta)$ are identical to the fused penalty term widely used in the joint estimation of joint graphical models; see for example [R4]. If you run joint graphical lasso [R1, R3, R4, R5], do they give similar results to yours? - What is the difference from existing FISTA methods for graphical models; see for example [R2]. Can you clarify how the Hessian of $f$ in the FISTA section is positive definite? It would be good if you could clarify how the rate changes with the eigenvalue of $\nabla^2 f$. - What is the the key difference in bounding the trace difference, log-determinant difference, and sparsity penalties compared to Theorem 1 of [32] and existing joint estimation of graphical models [R1, R3, R4, R5]? - Can you clarify what are samples and nodes for your dataset? For example, what is the data matrix $X$ for the friendship experiment? - Do these datasets resemble real-world applications of the proposed Gaussian graphical models, considering that i) they include a ground truth graph and ii) nodes of social networks have binary associated samples (e.g., 0/1 interactions between people)? Additional References - [R1] Pircalabelu, Eugen, and Gerda Claeskens. "Community-based group graphical lasso." Journal of Machine Learning Research 21.64 (2020): 1-32. - [R2] Oh, Sang, Onkar Dalal, Kshitij Khare, and Bala Rajaratnam. "Optimization methods for sparse pseudo-likelihood graphical model selection." Advances in Neural Information Processing Systems 27 (2014). - [R3] Guo, Jian, et al. "Joint estimation of multiple graphical models." Biometrika 98.1 (2011): 1-15. - [R4] Danaher, Patrick, Pei Wang, and Daniela M. Witten. "The joint graphical lasso for inverse covariance estimation across multiple classes." Journal of the Royal Statistical Society Series B: Statistical Methodology 76.2 (2014): 373-397. - [R5] Ma, Jing, and George Michailidis. "Joint structural estimation of multiple graphical models." Journal of Machine Learning Research 17.166 (2016): 1-48. Confidence: 4 Soundness: 2 Presentation: 2 Contribution: 2 Limitations: N/A Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: # Rebuttal for QDSi: We sincerely thank you for your review and your kind words. We appreciate your insightful comments and how you link our approach to existing works. > Answer to Question 1. Thank you for your interesting question. Your observation is key; similar to group lasso or joint graph inference methods, we optimize group-wise submatrices of the precision matrix, but our formulation differs subtly with important consequences for fairness. Joint graph inference methods such as [R1], [R4], and [R5] assume each graph lies on the same node set, where we may treat each submatrix of $\\mathbf{\\Theta}$ for every group pair as a different graph. Our topological fairness only requires that the support and signs of edges are balanced on average across all group pairs. However, joint graph inference yields similar sparsity patterns for all submatrices, which is far more restrictive than balancing edges in expectation. Moreover, the group lasso penalties in [R3], [R4], and [R5] can achieve fairness in support, but they ignore the signs of the edges, thus they cannot balance correlation biases. Thus, existing group lasso or joint graph learning approaches are either too restrictive or do not consider both kinds of graphical model bias. In contrast, our fairness metrics can balance structure in both sparsity patterns and signed edges. > Answer to Question 2. The main differences between our approach and other graphical model FISTA algorithms lie in (i) the fairness penalty in the objective function; (ii) the constraints for positive semidefinite precision matrices; and (iii) the type of convergence analysis. We first note that our Fair GLASSO algorithm and the work in [R2] have different objective functions and thus different gradient updates. Moreover, while [R2] solves an unconstrained optimization problem, we require projection onto the feasible set after soft-thresholding. On top of this, we guarantee convergence of the optimization variable, which is stronger than guaranteeing convergence of the objective function, as is done for [R2] and classical FISTA algorithms. To show that the Hessian of $f$ is positive semidefinite (PSD), here we supplement the proof of Theorem 2 (Appendix F). Note that $f$ can be split as $f = f\_1(\\mathbf{\\Theta}) + R\_H(\\mathbf{\\Theta})$, and recall that $\\mathbf{\\Theta}$ is PSD and $\\epsilon > 0$. Then, from (39), it follows that the Hessian of $f\_1(\\mathbf{\\Theta})$ is PSD since it is given by the Kronecker product of two PSD matrices. Next, note that the terms $R\_H(\\mathbf{\\Theta})$ promoting fairness are convex, so their Hessian is also PSD, rendering the Hessian of $f$ PSD. Finally, the convergence rate in Theorem 2 depends on the Lipschitz constant $L$ and the strong convexity constant $\\alpha$, respectively associated with the largest and smallest eigenvalue of the Hessian of $f$. Thus, it follows that increasing the smallest eigenvalues or decreasing the largest eigenvalues of the Hessian will improve the rate of convergence, and the converse is also true. Based on the feedback provided, we will highlight these relevant distinctions in the revised manuscript. > Answer to Question 3. You are correct that the proof is similar to that of the original result in [32]. Since our proof is not limited by space, we aim to provide a self-contained result with enumerated steps for clarity, which can increase accessibility for audiences outside of statistics. We are also careful to identify the effects of bias mitigation. For example, the trace and sparsity differences do adhere to the proof in [32]. However, the log-determinant difference in (18) of our paper deviates slightly from the original due to the additional bias term in the right-hand side of equation (13) in our manuscript versus equation (8) in [32]. Moreover, our goal differs from [R1], [R3], [R4], and [R5], which show the effects on error when graphical lasso is modified to improve performance, while we formalize the tradeoff between accurate estimation versus unbiased solutions. > Answer to Question 4. For Karate club, School, Friendship, and Co-authorship, nodes represent individuals, while MovieLens nodes represent movies. Regarding samples, the Karate club dataset is the only one without real graph signals, so we generate synthetic Gaussian data given the ground truth network. MovieLens graph signals represent movie ratings. Edges in the Co-authorship network denote collaborations, and we use keyword frequencies as signals. Finally, for both the School and Friendship datasets, the edges represent pairwise student interactions over all time, and the graph signals are sums of interactions over windows of time, that is, the graph signals represent time-varying node degrees as interactions vary. Detailed descriptions of the real datasets can be found in the Appendix, and we will augment Table 3 to include the interpretation of nodes and signals. > Answer to Question 5. Your concern is warranted since real data simulations validate our approach in practical scenarios. Social network analysis is a common application of graphical models, but often no ground truth graph exists. However, we must confirm the effectiveness of Fair GLASSO. The Friendship and School datasets thus demonstrate our method for realistic applications, which we can verify with ground truth graphs. Critically, we emphasize that the Karate club dataset is the only real network for which we generate synthetic graph data. All other real-world datasets are each accompanied by a set of real graph signals. For example, the social networks possess real discrete graph signals, yet we still observe satisfactory performance in Table 2 of our paper. We hope this assuages your concern about the realism of our simulations. We sincerely thank you for your feedback, and we will refer to your thoughtful comments to clarify our method upon updating the manuscript. --- Rebuttal 2: Title: Response to Rebuttal by Authors Comment: I appreciate the authors' response. Below are my replies to your response. 1. In my opinion, the fair Glasso presented in this paper is indeed a variant of a graphical model with a group penalty, and further investigation with different choices of penalty formulations is needed. I also respectfully disagree with the statement that "group lasso penalties can achieve fairness in support, but they ignore the signs of the edges, thus they cannot balance correlation biases" without providing experimental or theoretical results. Indeed, there are variants of group penalties that show improvement in support recovery for sign-coherent groups. For example, (https://arxiv.org/pdf/1103.2697). 2. I believe an extensive discussion on the novelty of the method in the introduction, regarding both the penalty and the optimization method (FISTA for GLasso), is needed. For example, the phrases "For this purpose, we propose ..." and "we also propose a stronger alternative metric" in Lines 127 and 134 should be rephrased to explicitly mention that these penalties are from previous works such as [15, 18]. Further, the use of FISTA for smooth + $\ell_1$ objectives, as well as graphical lasso, is standard, and the convergence analysis in Theorem 2 follows from existing literature. 3. In my opinion, having no space limits does not allow us to repeat others' proofs. I recommend that the authors remove the identical parts (e.g., trace difference, log-determinant difference, and sparsity penalties) and frequently reference the modified parts of the estimation proof (e.g., from Theorem 1 of [32]). 4. I still did not receive a response to my question, "What is the data matrix $X$ for the Karate Club, School, and Friendship datasets?" Is this data matrix generated using the ground truth graph, or is it available as real data for graph estimation? I don't think the statement "For both the School and Friendship datasets, the edges represent pairwise student interactions ..." answers my question. If I understand correctly, you are using this edge information to construct the ground truth graph, but it is not clear to me what $X$ in Eq. (4) represents for these datasets and how you constructed it. Also, I am uncertain whether these datasets (Karate Club, School, and Friendship datasets) are suitable for Gaussian graphical models, or whether another form of graph learning method should be applied. Do we have good literature on applying GLasso to these datasets, or should we consider using another type of graph learning? --- Rebuttal Comment 2.1: Title: Addressing additional comments from Reviewer QDSi Comment: 1. Your point is well taken; indeed modifications of group lasso penalties are plentiful, including those that consider signs of entries. However, as you rightly noted, these metrics show improvement in support recovery, but this is a different goal than promoting balanced connections. In particular, the cooperative-Lasso penalty promotes parsimonious estimates while accounting for sign, but it does not aim to mitigate differences of groups of entries. The fairness metrics for graphs take the difference of weighted sums of edges rather than promoting group-wise sparsity. Due to lack of space and time, we save a theoretical and empirical comparison of these penalties with topological DP for the revision of this paper, if accepted. 2. Thank you for your suggestion. We will make these necessary changes regarding the novelty upon acceptance. 3. We understand your point. If deemed necessary, we can certainly remove redundant derivations such as the sparsity and trace differences. 4. We apologize if the explanation of the graph signals in our response seemed ambiguous. We observe student interactions over time, and each graph signal is a window of time. The signal value for one student at a given window is the number of interactions in which that student participated. Regarding the social network datasets, indeed these are typically equipped with discrete graph signals as is the case for the datasets shown in this work. Empirically, we observe satisfactory performance even when assuming Gaussianity. However, in future work, we aim to generalize fair graphical models beyond Gaussianity, such as Ising models, which do account for discrete signals. We thank you again for your detailed comments. We truly appreciate how invested you are in our work. We hope that you find these answers satisfactory.	Summary: The paper introduces Fair GLASSO, a method for estimating Gaussian graphical models (GGMs) that addresses biases in data with respect to sensitive nodal attributes. The authors propose two bias metrics to promote fairness in statistical similarities across different groups, leading to the development of Fair GLASSO, a regularized graphical lasso approach. The paper also presents a proximal gradient algorithm for efficient estimation. Theoretical analysis shows the tradeoff between fairness and accuracy, and empirical results validate the effectiveness of the proposed method on both synthetic and real-world data. Strengths: 1. Novel contribution in defining fairness for graphical models and proposing methods to estimate fair GGMs. 2. Thorough theoretical analysis including error bounds and convergence guarantees. 3. Comprehensive empirical evaluation on both synthetic and real-world datasets. 4. Proposed method can improve both fairness and accuracy in certain scenarios, especially when the underlying graph is fair but the data is biased. 5. Clear explanations and intuitive visualizations of concepts and results. Weaknesses: 1. This work is limited to Gaussian graphical models and may not be able to generalize to other types of graphical models such as ising model or covariance model. 2. The fairness focus is mainly focusing on demographic parity and this may not be the optimal in relality. It would be better to explore other fairness definitions even though the authors claim that other definitions of group fairness can be similarly adapted. 3. Some of the real-world datasets use synthetic signals, which may limit the real-world applicability of those specific results. 4. The method introduces additional hyperparameters such as $\mu_1$ and $\mu_2$ that need to be tuned. Technical Quality: 3 Clarity: 3 Questions for Authors: 1. How sensitive is the method to the choice of hyperparameters $\mu_1$ and $\mu_2$? 2. How would the approach extend to non-Gaussian graphical models? 3. How you considered other fairness metrics beyond demographic parity? 4. How does the computational complexity scale for very large graphs (e.g. millions of nodes)? Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: 1. Only applicable to Gaussian graphical models. 2. Focuses solely on group fairness via demographic parity. 3. May not generalize well to more general graph structures. 4. Theoretical guarantees assume specific conditions on the true precision matrix and group sizes. 5. Limited exploration of the trade-offs between fairness and accuracy across different scenarios. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: # Rebuttal for pQPd: We are grateful for your positive review and clear questions. Indeed, your review helps us clarify the utility of our approach beyond conceptual discussions. We are glad to hear that you find our work novel, thorough, and comprehensive. > Answer to Question 1. Thank you for your question. Indeed, as with many graphical lasso modifications, we require selection of appropriate weights for additional penalties. Figures 1 and 2 of the attached document present Fair GLASSO performance as hyperparameters $\\mu_1$ and $\\mu_2$ vary when estimating a fair or unfair precision matrix, respectively. Observe that when the true precision matrix is unfair, increasing $\\mu_2$ encourages a fairer estimate and thus increases the error. Moreover, smaller values of $\\mu_2$ yield greater bias for the unfair setting in Figure 2 than the fair setting in Figure 1. While a larger $\\mu_2$ decreases the bias in both settings, the effect is greater in Figure 2 for a true precision matrix that is unfair. As hyperparameter tuning is a highly practical consideration, we will add these results to the final version if accepted. > Answer to Question 2. Your question allows us to clarify the flexibility of our bias metrics for graphical model estimation. Indeed, Gaussianity is widely used for its ubiquity and appealing statistical properties, yielding copious theoretical guarantees that we exploit for our results. However, note that Gaussianity only dictates the loss to be minimized, thus any optimization-based graph learning approach is amenable to our fairness penalties. Moreover, our FISTA algorithm is still applicable under other distributions as long as the associated loss is convex and differentiable, such as the negative log-likelihood of the Ising model that you mentioned. > Answer to Question 3. You raise an excellent point; notions of fairness may differ by application, thus consideration of other definitions is critical. Since fair graphical model estimation is a novel task, we follow the custom of existing graph fairness works that employ demographic parity (DP). However, the penalty for Fair GLASSO is flexible and allows for other bias metrics. Moreover, as long as the chosen fairness penalty is convex and differentiable, our convergent FISTA algorithm remains applicable. Consider for instance the following adaptation of equalized odds (EO), $$ \\mathbb{P}[ \\Theta^\_{ij} \~\|\~ [\\mathbf{\\Theta}\_0]\_{ij},Z\_{ia}=1, Z\_{ja}=1 ] = \\mathbb{P}[ \\Theta^\_{ij} \~\|\~ [\\mathbf{\\Theta}\_0]\_{ij},Z\_{ia}=1, Z\_{jb}=1 ] ~\\forall a,b\\in[g], $$ where $\\mathbf{\\Theta}^$ denotes an estimate of the true precision matrix $\\mathbf{\\Theta}\_0$, and $\\mathbf{Z}$ is the group membership indicator matrix. Note that graphical EO is conditioned on the true precision matrix. Thus, we can measure biases in estimated precision matrices but not the true one. For this reason, we emphasize DP for group fairness since a measure of bias in the true precision matrix is critical to our theoretical interpretation of the fairness-accuracy tradeoff. > Answer to Question 4.* While we show estimation of graphs on the order of 1000 nodes, the complexity indeed scales more than linearly with the number of optimization variables, thus our approach may not be viable for millions of nodes. However, existing works can efficiently estimate very large graphical models, potentially under additional assumptions [A1,A2,A3]. We can combine these approaches with our proposed fairness metrics, although we may lose our guarantee of convergence. > Answer to Weakness 3. Finally, we wish to clarify a concern you expressed in Weakness 3. We stress that Karate club is the only real network for which we generate synthetic graph signals; all remaining real-world datasets possess data that are not synthetically generated. Indeed, as you noted, we wish to demonstrate the viability of Fair GLASSO in realistic settings, such as social networks with non-Gaussian data. We thank the reviewer for your questions. You pinpointed vital practical concerns that are crucial to address in order to continue exploring fair graph learning in realistic scenarios. --- Rebuttal Comment 1.1: Title: Concerns from Reviewer QDSi Comment: Thank you for your detailed response. Most of my previous concerns are basically addressed. However, after taking a look at Reviewer QDSi's comments, I have some additional concerns as follows. (1) The main concern is about novelty. According to Reviewer QDSi's comment, the fairness penalty functions appear to be very similar to those in [15,18]. While you've clarified some differences from existing joint graphical models, the core idea still appears to be a variation on well-studied concepts. The modifications to balance sparsity patterns and signed edges, while interesting, do not seem to constitute a substantial leap forward in fair graph learning. (2) As for the technical contribution, the adjustments to the FISTA algorithm, including the constrained optimization and convergence guarantees, are incremental improvements rather than fundamental innovations. The theoretical analysis, while thorough, largely follows established approaches in graphical model estimation. (3) Your focus on demographic parity limits the broader applicability of the method. As noted in your response about equalized odds, adapting to other fairness metrics introduces additional complexities that are not fully addressed in the current work. Based on these new concerns, I believe this paper still needs improvement and I will drop my score from 6 to 5. --- Reply to Comment 1.1.1: Title: Addressing additional concerns from Reviewer pQPd Comment: Thank you for bringing up your additional thoughts. (1) We completely understand your point that these previous works have contributed greatly to the analysis of fair network connectivity. The primary contribution of our work is the theoretical and empirical analysis of fair topologies of signed graphs, in particular, graphical models encoding conditional dependence. While [15,18] are seminal to fair graph signal processing, neither work can address the effects of fairness on graph topology when permitted to alter both sparsity and edge signs. In particular, the work in [15] aims to design graph filters for fair graph signal processing. An analogous task is performed in [18], which is restricted to balancing edges only by magnitude, while we further provide theoretical analysis for how fair graph learning affects the topology, a critical aspect of fairness for data science. Moreover, we note that the $\ell_2$ norm gives fairer outcomes even when edge sign is not considered, as group pairs are balanced overall as opposed to the $\ell_1$ norm which may favor balancing some pairs of groups over others. (2) Indeed, the advantages of FISTA for graphical model estimation is well known. While our analysis is inspired by existing works, we aim to show that not only are the convex fairness penalties amenable to efficient algorithms with well-understood performance guarantees, we also are able to provide a stronger guarantee that our algorithm converges with respect to the estimation variable, which is stronger than previous works' results on convergence of the objective function. (3) Fair methods aim to mitigate negative outcomes due to potentially hidden external influences such as stereotypes, thus we believe that thorough analysis is critical and aligned with the purpose of developing fair methods. We provide the first theoretical analysis of the effect of imposing fairness for graph estimation using a well-established notion of topological fairness. Indeed, the focus of this work is learning fair graphical models, while the comparison of fairness metrics for graphs warrants separate investigation since many fairness metrics in machine learning have not yet been adapted to the graph setting. Such an analysis of fairness metrics ought to be applied to tasks beyond graph learning and is thus out of scope of this paper. We thank you again for your comments, and we truly appreciate your high standards.	Rebuttal 1: Rebuttal: # Global We would like to thank the reviewers for their quality comments and perceptive questions about our work. Below we detail the main topics discussed both in the following responses and to be added to the revised paper should it be accepted. We provide additional discussion of Fair GLASSO to clarify its flexibility and novelty. Thanks to the questions by reviewer QDSi, we emphasize the novelty of our method and FISTA algorithm. We also highlight the flexibility of Fair GLASSO; our choices of demographic parity and Gaussianity are convenient for our theoretical analysis but are flexible to alternatives, as inquired by reviewers pQPd and fwTq. For example, we may instead measure bias in graphical models via Equality of Odds (EO), which we may define as $$ \mathbb{P}[ \Theta^\_{ij} \~\|\~ [\mathbf{\Theta}\_0]\_{ij},Z\_{ia}=1, Z\_{ja}=1 ] = \mathbb{P}[ \Theta^\_{ij} \~\|\~ [\mathbf{\Theta}\_0]\_{ij},Z\_{ia}=1, Z\_{jb}=1 ] ~\forall a,b\in[g], $$ where $\mathbf{\Theta}^$ denotes an estimate of the true precision matrix $\mathbf{\Theta}_0$, and $\mathbf{Z}$ is the group membership indicator matrix. In the attached document, we provide additional simulations to demonstrate Fair GLASSO behavior under hyperparameter tuning and violation of assumptions. Figures 1 and 2 of the attached document present Fair GLASSO performance as hyperparameters $\mu_1$ and $\mu_2$ vary when estimating a fair or unfair precision matrix, respectively. Observe that when the true precision matrix is unfair, increasing $\mu_2$ encourages a fairer estimate and thus increases the error. Moreover, smaller values of $\mu_2$ yield greater bias for the unfair setting in Figure 2 than the fair setting in Figure 1. While a larger $\mu_2$ decreases the bias in both settings, the effect is greater in Figure 2 for a true precision matrix that is unfair. We elaborate on the theoretical implications of violating the assumptions for Theorem 1, as requested by reviewers V8H3 and fwTq. Moreover, we provide additional simulations in Figure 3 of the attached document where the precision matrix varies in sparsity (AS1), the true precision matrix is rank-deficient (AS2), and the group sizes vary (AS4). Figure 3a shows the classical graphical lasso result, where as the precision matrix grows denser, estimation error suffers, particularly when the sparsity penalty weight $\mu_1$ is larger. In Figure 3b, we demonstrate the effects of a low-rank ground truth precision matrix on estimation performance. Indeed, the use of $\epsilon>0$ permits low-rank estimates, and we observe relatively robust error for different values of $\epsilon$. Finally, Figure 3c shows that as the ratio between two groups becomes small, that is, the precision matrix becomes unfair due to imbalanced groups, error increases as we impose fairness, particularly for larger $\mu_2$. We again thank the reviewers for taking the time to provide thorough evaluations of our submission. We hope that you find our responses satisfactory. References in Author Responses: - [A1] C.-J. Hsieh, M. A. Sustik, I. S. Dhillon, P. K. Ravikumar, and R. Poldrack, "BIG & QUIC: Sparse Inverse Covariance Estimation for a Million Variables", in Advances in Neural Information Processing Systems, 2013. - [A2] T. Yao, M. Wang, and G. I. Allen, "Fast and Accurate Graph Learning for Huge Data via Minipatch Ensembles", arXiv preprint arXiv:2110.12067, 2021. - [A3] X. Wang, J. Ying, and D. Palomar, "Learning Large-Scale $MTP_2$ Gaussian Graphical Models via Bridge-Block Decomposition", in Advances in Neural Information Processing Systems, 2023. - [A4] C. Avin, Z. Lotker, Y. Nahum, and D. Peleg, "Modeling and Analysis of Glass Ceiling and Power Inequality in Bi-populated Societies", in International Conference and School on Network Science, 2017. - [A5] A.-A. Stoica, C. Riederer, and A. Chaintreau, "Algorithmic Glass Ceiling in Social Networks", in International World Wide Web Conference*, 2018. Pdf: /pdf/ed2640abc0102077ee7b1f13e08a0e8151e9534d.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Reconstruction of Manipulated Garment with Guided Deformation Prior	Accept (poster)	Summary: The paper aims to recover garments that are manipulated instead of worn. The method first generates the UV mappings from point clouds, followed by ISP to recover the complete mapping. A diffusion model is used to extract the deformation priors and guide the recovery from UV mappings to 3D mesh. Experiments show that the proposed method delivers lower reconstruction errors and outperforms the baselines. Strengths: * This method is able to recover garments in a more general and complex poses. * The proposed model achieves robust performance as shown in the experiments. Weaknesses: 1. This method seems to be garment-specific design, or even topology-depend. For example, to recover the shirt and pants, one need to train different models to recover the garments, leading to limited generalisation abilities. 2. While the ground truth may include too much details, i.e. too many wrinkles, and even looks a bit noisy, the recovered garments are oversmooth. The proposed model fails to recover high frequency details of the garments. Technical Quality: 2 Clarity: 2 Questions for Authors: 1. Are the recovered garments meshes able to be used for further animations? 2. How to connect the edges in the recovered mesh from point clouds? Are the edges fixed or dynamically connected? Since the point clouds do not include any information about the connectivities, how to define the edges? 3. In the qualitative results, such as Figure 5, the recovered garments seem to be smoother than the ground truth. Is this because of the “auto smooth” option during rendering? Could you provide some visual results of the smoothed ground truth garments? 4. What is the averaged number of points for different garments? Is the model able to deal with large number of points? 5. While the proposed method is able to handle garments in more complex poses, is it possible to compare with other baselines using the garments worn by the human body, e.g. the quantitative and qualitative results on CLOTH3D dataset? Confidence: 4 Soundness: 2 Presentation: 2 Contribution: 3 Limitations: Please refer to the weaknesses and questions. Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your valuable reviews. To provide a context, we would first like to briefly describe our pipeline. Given the point cloud, we first map each point to the UV space using the UV mapper. This yields a sparse UV map and a sparse panel mask. We then use Eq. (10) to fit the optimal latent code $\textbf{z}^$ for the ISP model from the sparse panel mask. Note that with $\textbf{z}^$, we can recover a complete panel mask and a rest-state garment mesh that defines the vertices and faces of the garment. Then, we leverage the diffusion model to recover the complete UV map, utilizing the sparse UV map and the complete panel mask as the guidance in the reverse diffusion process. This being said, below is the actual response to your comments. 1. Garment-specific design. Our approach is not specific to a particular garment. However, due to the challenging nature of the task where only a partial garment is observed, we consider category-level garment reconstruction as in much prior art such as GarmentNets [27] and GarmentTracking [2]. Since a folded shirt and a pair of folded trousers can exhibit similar shapes as shown in Fig. 2 of the attached PDF file, we need to use different models for them. 2. The recovered garments are smooth. The qualitative results in our paper are rendered without smoothing. Both the ground truth meshes and our reconstructed meshes are visualized in their raw form. The fact that our reconstructions seem smoother than the ground truth meshes can be attributed to the tendency of neural networks to learn low-frequency functions [Rahaman2019], which yields smooth reconstructed UV maps. Furthermore, our guided denoising process finds the expected reconstructions $\hat{x}$ given observations $y$ and the starting noise $ x_T $, where $\hat{x} = E(x\|y,x_T) = \sum_x xP\lbrace x\|y, x_T\rbrace$. In areas where the data is missing, it provides only weak guidance and the reconstructions are naturally smooth. In future work, we will explore methods to enhance our diffusion model to capture finer details. 3. Are the recovered garments meshes able to be used for further animations? Yes, our recovered meshes can be used for animation and simulation directly. In Fig. 3 of the attached PDF file, we show the simulated results for the recovered shirts using Blender, where we drop them onto a horizontal bar. 4. How to connect the edges in the recovered mesh from point clouds? We do not compute edges for the point cloud to generate the garment mesh. Instead, we use Eq. (10) to fit the optimal latent code $\textbf{z}^$ for ISP model from the sparse panel mask. Using $\textbf{z}^$ alongside the ISP meshing process, we reconstruct a garment mesh in rest state as illustrated in the bottom-right of Fig. 2 of the main paper. This mesh defines the vertices and faces of the garment. To reconstruct the garment in the observed deformed state, we update the vertex positions by $\textbf{V}=\mathcal{M}[u,v]$, where $\mathcal{M}$ is the recovered UV map and $(u,v)$ is the corresponding UV coordinate of $\textbf{V}$. 5. What is the averaged number of points for different garments? Is the model able to deal with large number of points? The averaged numbers of points provided by VR-Folding dataset [2] are 30K for Shirt/Pants/Skirt and 27K for Top. However, instead of using all points, we randomly sample 4000 of them as the input. Therefore, we are able to handle large number of points. 6. Garments worn by the human body. Using ISP model to recover on-body garments has been shown to work in [1,40]. Consequently, we focus on the more challenging task of recovering garments not being worn. Our method differs from [1, 40] by utilizing a diffusion model as the deformation prior and leveraging UV mapping along with the proposed fitting method (Sec. 3.3 and 3.4) to recover complete garment meshes from partial point clouds. With appropriate training data, our method can also handle garments worn on the human body. However, due to time constraints, we are unable to present results for this specific scenario. ## References N. Rahaman, A. Baratin, D. Arpit, F. Draxler, M. Lin, F. Hamprecht, Y. Bengio, and A.Courville. On the spectral bias of neural networks. In International Conference on Machine Learning, 2019. --- Rebuttal Comment 1.1: Comment: Dear Reviewer J5PZ, As the discussion period is approaching its end, we would like to ask if you have any questions or comments regarding our rebuttal. Thank you again for your time and consideration.	Summary: The pape addresses the challenge of accurately reconstructing the 3D shape of garments that are manipulated rather than worn. The authors leverage the Implicit Sewing Patterns model and introduce a diffusion-based deformation prior to recover 3D garment shapes from incomplete 3D point clouds. The method maps these points to UV space, generates partial UV maps, and uses a reverse diffusion process to produce complete UV maps and 2D to 3D mappings. The approach demonstrates superior accuracy compared to previous methods, especially in handling large non-rigid deformations. Strengths: The focus on reconstructing manipulated garments rather than worn ones addresses a significant gap in current research, as most existing methods assume garments are worn and thus have less complex deformations. Combining ISP with a diffusion-based deformation prior is a strong methodological contribution, enabling the modeling of complex deformations that were previously challenging to capture. Weaknesses: The accuracy of the reconstruction heavily depends on the quality of the input point clouds. Incomplete or noisy point clouds might still pose a challenge. Technical Quality: 3 Clarity: 3 Questions for Authors: Can this method handle noisy or highly sparse point clouds effectively, and have you tested its robustness in such scenarios? Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: While the method shows promise, its ability to generalize across a wide variety of garment types and materials without retraining is not fully explored. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your appreciation of our work. We address your questions and comments as follows: 1. Handling noisy or highly sparse point clouds. To evaluate performance under noisy conditions, we add per-point Gaussian noise to the input data, varying the standard deviation. As shown in Fig. 1 (b) of the attached PDF file, the results on the Folding Pants subset indicate that reconstruction error increases with noise levels; however, the errors remain relatively low across different noise levels. Additionally, the evaluation of real-world data in Sec. 4.4 demonstrates the robustness of our method, even when the input point cloud, generated using Nerf, is noisy and inaccurate. Regarding sparsity, the captured points are generally dense in visible areas. Instead of using all available points, we randomly sample 4000 points from them as the input. We also evaluate the influence of point quantity on reconstruction quality by analyzing errors with varying input point numbers on the Folding Pants subset. The results, shown in Fig. 1 (a) of the attached PDF file, reveal that while a reduction in points leads to increased error, we maintain a relatively low error margin even with only 2000 points. 2. Generalization across a wide variety of garment types and materials without retraining is not fully explored. Due to the challenging nature of our task where only a portion of the garment is observed, we consider category-level garment reconstruction as in prior art GarmentNets [27] and GarmentTracking [2]. However, we acknowledge the reviewer's point that investigating the generalization across types and materials is an important direction for future work. --- Rebuttal Comment 1.1: Comment: Thank you for your thorough and detailed responses to my questions and comments. I appreciate the additional experiments and analysis you provided to address my concerns. Regarding the handling of noisy or highly sparse point clouds, I appreciate the effort to evaluate your method's performance under varying levels of Gaussian noise and with different quantities of input points. It is encouraging to see that your method maintains relatively low reconstruction errors even as noise levels increase and point quantities decrease. The robustness demonstrated on real-world data also strengthens the confidence in your approach. On the topic of generalization across a wide variety of garment types and materials, I understand the challenges associated with reconstructing garments when only a portion is observed. While category-level reconstruction is a reasonable approach given these challenges, I agree that exploring the generalization capabilities across different garment types and materials is an important direction for future research. I appreciate your acknowledgment of this point and openness to further investigate it. Overall, I commend the contributions of your work and the thoroughness of your rebuttal. My overall assessment and rating of the paper will remain the same. --- Reply to Comment 1.1.1: Comment: Thank you for your commendation of our contributions!	Summary: This paper presents a method for reconstructing folded and crumpled garments from point cloud data. It uses the implicit sewing pattern (ISP) model to represent the 3D shape in 2D uv-maps. The proposed method converts a 3D point cloud to sparse uv-maps and corresponding masks for front and back side using an encoder structure followed by a MLP. The incomplete masks are filled and used to guide the completion of the uv-maps via a diffusion process. Finally, the deformed mesh can be recovered from the filled uv-map. Strengths: This paper improves state-of-the-art reconstruction of point cloud data for folded garments in visual quality as well as 3D accuracy. Notably, this is done while no prior knowledge of the garment geometry is needed. The usage of a diffusion network to fill the sparse 2D data of the ISP model is a clever idea and matches the network characteristics very well. Weaknesses: The comprehensibility of the paper could be improved by discussing the different parts of the pipeline in order and clearly pointing out the result of each stage and its purpose for the next stage. Some intermediate results for different scenes might be helpful to follow the pipeline. Technical Quality: 3 Clarity: 2 Questions for Authors: How many points do the input point cloud contain? Did you test how many points are necessary and how accurate do they have to be to produce a high-quality reconstruction? Confidence: 3 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: The limitations are just mentioned very briefly. Some quantitative evaluation on the number of intersections in the reconstructed mesh or more animated reconstructions would show how large these limitations are. An analysis might even benefit the method as e.g. the number of intersections seems to be low based on the qualitative results. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank you for your acknowledgement of our contribution in manipulated garment reconstruction. Below are our responses to your comments and questions. 1. Comprehensibility. Thank you for pointing this out. At the end of each stage and to enhance comprehensibility, we will revise our paper and refer the reader to the intermediate results in our main framework figure (Fig. 2 of the main paper). 2. How many points do the input point cloud contain? We use 4000 points randomly sampled from the captured point clouds as the input. To evaluate the influence of point quantity, we analyze the reconstruction errors by varying the number of points used as input on the subset of Folding Pants. The results are reported in Fig. 1 (a) of the attached PDF file. A reduction in points correlates with increased error. However, even with 2000 points, we maintain a relatively low error margin. We will include this experiment in our final version of the paper. 3. How accurate do the points have to be to produce a high-quality reconstruction? To evaluate the influence of input point noise, we add per-point Gaussian noise to the input with varying standard deviation. Fig. 1 (b) of the attached PDF file shows the results on the subset of Folding Pants. It illustrates that as the noise level rises, so does the reconstruction error; nonetheless, the errors remain relatively low across different noise levels. We will include this experiment in our final version of the paper. Additionally, the evaluation of real-world data in Sec. 4.4 of the main paper also demonstrates the robustness of our method, where the input point cloud is generated using Nerf which is noisy and inaccurate. 4. Quantitative evaluation on the number of intersections or more animated reconstructions. In Table 1 of the attached PDF file, we evaluate the intersections of our reconstructions and compare them with those of GarmentTracking [2] using the ground-truth initialization. We compute the average ratio of faces with intersection as the evaluation metric. Notably, our results exhibit fewer intersections compared to GarmentTracking on Pants, Top and Skirt. We will revise our paper to include this evaluation and more reconstruction results.	null	null	Rebuttal 1: Rebuttal: We would like to thank all reviewers for their valuable suggestions and constructive comments. We have carefully considered and addressed each of the suggestions and questions raised. We will incorporate these suggestions into our revised paper. The attached PDF file includes the following additions: - figures of error curves under varying numbers of points and noise levels as suggested by Reviewers 2QwG and 4mMP; - a table of intersection evaluation as recommended by Reviewer 2QwG; - illustrative examples for Reviewer J5PZ. Once again, we sincerely thank all reviewers for their expertise and the time they spent in reviewing our paper. Pdf: /pdf/a38da3ee7985e1aa0593de893811ec2f9634144e.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Graph-based Unsupervised Disentangled Representation Learning via Multimodal Large Language Models	Accept (poster)	Summary: This paper introduces a bidirectional weighted graph-based framework, to learn factorized attributes and their interrelations within complex data. The authors proposed a β-VAE based module to extract factors as the initial nodes of the graph, and leverage the multimodal large language model (MLLM) to discover and rank latent correlations, thereby updating the weighted edges. Experiments demonstrate evidence of effective performance in disentanglement and reconstruction. Strengths: This paper integrates the VAE with multimodal large language model, which provides strong interpretability via the open-world knowledge of the large language models/multimodal models. Weaknesses: * As a generative model, β-VAE is extensively discussed with many useful variants. While this work heavily borrows the existing advances of β-VAE, I would respect ground-breaking findings or improvements on this model (e.g., closed-form derivation of the feature distribution z after employing a graphical model). Otherwise speaking about absolute performance, I expect a standard diffusion model can easily outperform β-VAE and most of its variants (And authors should include comparison and discussion with diffusion models, even it is less likely that the proposed method can outperform, but insights on what β-VAE is lacking would be insightful, although it’s less meaningful in the era of diffusion model). * Related to above, the technical novelty and motivation of this work is limited since the current model can be easily understood as the combination of β-VAE and Large Multimodal models. There is less strong justification while this combination is optimal rather than other obvious choices (e.g., integrating a vision-language model, or diffusion+MLLM (since diffusion models are also trained with variational inference)). Author should either provide strong justification (better if theoretical) or more empirical validation showing the proposed framework is optimal than other obvious variants to enhance their motivation and novelty. * Line 148, it is obvious that z dos not follow multivariate normal, and author proposed Eq. 4 as the solution. Surprisingly, the author only showed the derivation of this equation (which is trivial in my view) in the appendix, with no justification why this is optimal. Why α=1? Or how strong is this assumption? Is the resulting objective still convex? What is the distribution of z under the new objective? Overall the authors imposed made many conditions in the ease of derivation with many justifications missing. * The authors only used GCN to learn the graph representation, which ruled out many other prominent choices (E.G., GAT, gatV2, GIN, GTN, GraphSAGE). authors should conduct thorough ablation study to select the optimal GNN architecture. * As an applied paper, it is less acceptable that codes are not released in the current phase. As many papers release their codes in anonymous GitHub repos and recently there are higher requirements of reproducibility and codeavilability in top venues. We also need to check the overall soundness of the empirical implementation. Technical Quality: 2 Clarity: 2 Questions for Authors: * For the bidirectional weighted graph, it is unclear why this is a good choice. From my knowledge, a causal DAG would be a better choice to represent the interrelation of the entities, and there are many works (e.g., [1]) available deriving the closed-form distributions of the features under this assumption. [1] BayesDAG: Gradient-Based Posterior Inference for Causal Discovery. NIPS 2023. Confidence: 4 Soundness: 2 Presentation: 2 Contribution: 2 Limitations: The authors addressed some limitations of their works. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We greatly appreciate your insightful comments and commit to refining our manuscript based on your suggestions. Below, we address all your concerns. W1: Why not replace $\beta$-VAE with advanced generative models R1: Thanks for your insightful comments to help us improve our work. Firstly, we would like to discuss our standpoint on using other generative models, especially the Diffusion you mentioned. In our framework, the core of $\beta$-VAE based encoder $E_{sem}$ is to extract and initialize disentangled latent factors. This important perception block cannot be ideally replaced by Diffusion or other non-DRL generative models, as they do not produce an orthogonal and disentangled latent space, and thus can not comprehend and extract disentangled factors (even though some of them are also trained with variational inference). Contrary to replacing $\beta$-VAE with the Diffusion (or other variants) as the semantic encoder, we tend to integrate it as the decoder $D_{rec}$. This integration capitalizes on the superior generative abilities of the Diffusion model to improve the reconstruction fidelity of our framework. Concomitantly, the enhanced perceptual capacity of our model can, in turn, refine the generative process of the Diffusion, thereby establishing a synergistic, mutually beneficial closed-loop. We are currently implementing this feature. However, should time constraints arise, we promise to at least include an extra discussion section to cover these content. W2: Lacking technical novelty and the justifications of technical combinations R2: First, we must emphasize that the technical novelty and motivation of this work is: 1) We are first to leverage the commonsense reasoning of MLLMs to discover and rank the semantic interrelations for DRL; 2) We propose a novel and practical disentanglement framework built upon β-VAE and MLLMs, with a bidirectional graph architecture, specifically designed to learn the interrelations between independent factors. The naive combination of diffusion+MLLM could not achieve the same purpose of learning relation-aware representations, thereby facilitating practical and controllable disentanglement. This shortfall arises because Diffusion models are not designed for disentanglement, as they do not produce an orthogonal and disentangled latent space. Therefore, it is hard to directly compare our proposed method with the combinations you mentioned. W3: Unclearness of equations and justifications in Section 3.1 R3: It's appreciated for your valuable comments. We apologize for not detailing the assumptions in the manuscript, and we promise to expand both the paper and the appendix to clarify these conditions and justifications explicitly. Specifically, regarding the question "Is the resulting objective still convex?", we assumed that the model is upper bounded by the norm of its gradient, which satisfies the Polyak-Lojasiewicz (PL) condition, thus ensuring the suboptimality of the model. The PL condition is weaker than (strong) convexity, meaning it can be applied in a broader range of scenarios. Existing models such as L1-regularized linear regression and logistic regression have been proven to satisfy this condition, which supports our decision to use logistic regression for gradient fitting. The assumption that $\alpha$=1 can be achieved by controlling the ratio of real samples to latent space samples. In the preliminary stage, we have tested model performance across a spectrum of hyper-parameters $\alpha$. Our empirical findings revealed a notable degradation in the quality of generated images when $\alpha$ was below 0.2 or above 5.5. Conversely, the KID metric exhibited stable consistency at $\alpha$=1 for most scenarios. And for your last concern: Given our utilization of the discriminator for gradient fitting, the distribution of $z$ under the new objective does not affect the final optimization procedure. Consequently, we did not delve into the new distribution properties of $z$. W4: Authors should conduct thorough ablation study to select the optimal GNN architecture R4: Thanks for your suggestions. We will consider potentially prominent graph choices with experimental proof, provided they can be optimized within our framework in an unsupervised manner. W5: Authors should release their code R5: Sure, we have released our project and sent the anonymous GitHub link to the AC as required. We highly welcome fellow researchers to follow and help improve our work. Q1: For the bidirectional weighted graph, it is unclear why this is a good choice. R6: Thank you for the feedback. As described in Section 2.2 and Figure 1, we analyzed the reasons for proposing DisGraph for embedding knowledge instead of using a causal graph: 1) the causal relationship is often overly simplistic, typically represented as binary and impractical. However, in practice, paired variables commonly exhibit bidirectional influence, each impacting the other to varying degrees. For example, an increase in "age" can positively influence "baldness", whereas increased "baldness" does not significantly affect "age" in return; 2) Causal learning approaches are designed to model an event based on causal inference. However, our setting, akin to most DRL approaches, is to model the scenario within the observed image. When considering the interrelations between observed vision attributes, the binary causal relation are inadequate. Furthermore, we conduct the comparison results with a causal model DEAR in Section 4.1, to show the experimental superiority of our choice. Regarding your comments, we recognize that the detailed explanations of our advantages over structured DRL (Hierarchical DRL, Causal DRL, etc.) were not sufficiently clarified. We commit to refine this aspect in our revision. --- Rebuttal Comment 1.1: Comment: I thank the authors for their response. However, I think my messages were poorly delivered and many of my intended points were lost when the authors summarize my comments. Sorry to say but the authors are just reiterating their main contributions and strengths of their methods instead of utilizing this chance to address the key concerns. Some cases to illustrate: 1. For W2 I was asking why this combination is optimal to all non-trivial combinations. The proper way should be listing some potential non-trivial combinations and show (better with experiments) why these combinations would underperform. This would greatly enhance the motivations of this work. Sadly, the authors just restate their contributions and novelty and choose only one example (diffusion+MLLM) to illustrate, which is less convincing. 2. For W1, why not replace the $\beta$-VAE with advanced generative models is just one of my questions, while my major point is why diffusion-based models are included as a baseline. The authors have 7 days and I think it shouldn't be difficult to perform an image-generation experiment with a standard diffusion model. The author should also address this question on absolute generation performance, and how much the proposed method is worse than (if any) the standard diffusion model to sacrifice for the interpretability. These empirical evaluations should be performed to more holistically evaluate the proposed method. I am open to challenges if I am wrong. But I cannot give a higher score based on the current version of the manuscript and authors' rebuttal. I think the authors should be candid when rephrasing the reviewers' comments, and make sure that every point raised is addressed properly. --- Reply to Comment 1.1.1: Comment: Thanks for your quick and patient feedback. We apologize for our misunderstandings regarding your comments and hope to address your concerns effectively in this renewed discussion. 1: We would like to address your concerns of the optimal combination from both experimental and theoretical perspectives: 1) Experimentally, we have conducted extra experiments focusing on relation-aware disentanglement among typical DRL+MLLM/VLM combinations. The results are illustrated in the attached PDF accordingly: Table 1 \| Combinations\| Results\| Brief Comments\| \| --- \| --- \| --- \| \| $\beta$-VAE + GLM-4v \| Figure A3 (in attachment) \| Producing counterfactual and anomalous results.\| \| FactorVAE + GPT-4o\| Figure A5 (in attachment) \| Suffering from inferior reconstruction quality.\| \| $\beta$-TC-VAE+ GPT-4o\| Figure A5 (in attachment) \| Failing to learn attributes effectively.\| \| $\beta$-VAE+ GPT-4o\| Figure A5 (in attachment) \| Current combination with most stable and effective performance\| \|The optimal selection of MLLM\| Figure A1 (in attachment) \|GPT-4o outperforms others on attribute identification (also see Figure 6 in paper)\| The visualization results demonstrate that the current combination yields the most stable and effective outcomes. We have also performed comparative experiments on generation quality metrics to evaluate the model performance (please refer to Table 2). 2) Theoretically, to our knowledge, these results can be attributed to the straightforward and effective design of the $\beta$-VAE. Since our model just leverages the DRL model to extract and initialize semantic factors, extensional designs can lead to instability (e.g., extra MLP classifier and discriminator in FactorVAE; the inflexible penalty in TC-$\beta$-VAE; the embedding codebook in VQ-VAE, etc.). These components, while potentially beneficial in certain contexts, may introduce unnecessary complexity and reduce the stability in our setting for relation-aware disentanglement. The exclusion of non-DRL combinations (Diffusion, GAN, etc. + MLLMs) from disentanglement capability comparisons, is due to their inability to generate orthogonal and disentangled latent spaces,* as detailed in R1. However, the comparisons of generation quality are conducted involving DRL and non-DRL models, for evaluating the model trade-off between generation and interpretability (see next response).* 2. According to your response, we have included Diffusion and GAN models as the baselines in the generation quality experiments as shown in Table 2. Table 2 \| Model\| CelebA (64x64)\| \| CelebA (256x256) \| \| \| --- \| --- \| --- \| --- \| --- \| \| \| FID $\downarrow$\| KID x $10^3$ $\downarrow$ \| FID $\downarrow$\| KID x $10^3$ $\downarrow$ \| \| FactorVAE + GPT-4o\| 112.08 \| 101.54 \| 126.58 \| 130.12 \| \| $\beta$-TC-VAE + GPT-4o \| 68.17 \| 62.90 \| 91.45 \| 87.22 \| \| GEM (Ours) \| 46.05 \| 48.32 \| 50.93 \| 51.01 \| \| Vanilla VAE \| 53.39 \| 51.48 \|56.82 \| 61.26 \| \| StyleGAN2 (40k steps)\| 12.94\| 9.20\| 18.02 \| 19.55 \| \| DDPM (Diffusion, $T$ = 1k)\| 8.56\| 6.56 \| 15.93 \| 10.01 \| \|DDIM (Implicit Diffusion, $T$ = 1k)\| 10.04 \| 8.15 \| 16.24 \| 13.62 \| \| Stable Diffusion (fine-tuning)\| 7.72 \| 7.22 \| 10.63 \| 9.17 \| Due to time constraints, we present the results on the CelebA dataset, and we promise to provide comprehensive evaluations in the manuscript. Even though our model achieved superior performance among DRL approaches, an inevitable trade-off between reconstruction and disentanglement remains, resulting in decreased reconstruction quality compared to image generation models (GAN, Diffusion, etc.). Since our model is oriented towards interpretability, we consider this trade-off acceptable (see Lines 253-257 in the paper). However, it is insightful to leverage the advantages of both DRL and non-DRL models within a mutually beneficial closed-loop architecture (as detailed in R1), and we will make efforts to improve our work in this direction. We are open to further discussions if you have any unresolved concerns. And we will conduct a comprehensive evaluation and analysis according to your concerns and discussion.	Summary: Researchers introduced a bidirectional weighted graph-based framework to explore factorized attributes and their interrelations within complex data. They proposed a -VAE module for extracting initial factors and utilized a multimodal large language model (MLLM) to uncover latent correlations and update weighted edges. Integrating these modules enabled their model to achieve superior unsupervised disentanglement and reconstruction performance, inheriting interpretability and generalizability from MLLMs. Strengths: 1. The paper introduces a graph-based approach to model interrelationships within complex data, aiming to integrate background knowledge into Deep Reinforcement Learning (DRL). I find this idea novel and intriguing. 2. The paper presents a rigorous framework with clear exposition and straightforward methodology, making it accessible and easy to understand. Weaknesses: 1. The paper lacks significant innovation at the neural network and algorithmic levels. While the introduction of DisGraph and its optimization methods is proposed to be effective, insufficient explanation is provided regarding why they work. Strengthening this aspect of the description would enhance the paper's persuasiveness. 2. The paper could provide a brief explanation of some methods used, such as the Somers' D algorithm, even if included in an appendix. Currently, this aspect appears somewhat incomplete. 3. An explanation of the update mechanism for the entire model at the end of Section 3 would be beneficial. Technical Quality: 3 Clarity: 2 Questions for Authors: 1. How is the effectiveness of DisGraph ensured? What problems could arise if errors are introduced into DisGraph? Confidence: 4 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 greatly appreciate all of your valuable suggestions, which play a pivotal role in enhancing the quality of our paper. Below we address all your concerns. W1&W3: Detailed explanations of the optimization mechanism for the entire model R1: Thanks for your feedback. We promise to enhance our manuscript with more detailed explanations of the model's optimization mechanism. Below, we offer a concise explanation of the optimization mechanism for clarity: During the training, the optimizable parameters of the encoder $E_{sem}$, DisGraph $G$ and decoder $D_{rec}$ are denoted as $\phi$, $\gamma$ and $\theta$, respectively. And the optimization objectives can be formulated as follows: $L_{gem}$ ($\phi$, $\gamma$, $\theta$) = $D_{\mathrm{KL}}(q_{\phi}(x, z)$,$p_{\gamma,\theta}(x, z))$, $L_{dis} = -D_{\mathrm{KL}}\left(q_{\phi}(\mathbf{z}\|\mathbf{x}) \\|\| p_{\theta}(\mathbf{z})\right) $ $L_{total} = \lambda_{gem} L_{gem} + \lambda_{dis} L_{dis} + \lambda_{adv} L_{adv} $ where the specific optimization processes can be formulated as: $\nabla_{\theta} L_{gem}(\phi,\gamma,\theta) \overset{x=D_{\theta}(z)}{=} -E_{z\sim q(z)}\nabla_{x}\left[\log\left(\frac{p_{\theta,\gamma}(x,z)}{ q_\phi(x, z)}\right)\right]\nabla_{\theta}x$ $\nabla_{\phi} L_{gem}(\phi,\gamma,\theta) \overset{z=E_{\phi}(x)}{=} E_{x\sim p(x)}\nabla_{z}\left[\log\left(\frac{p_{\theta,\gamma}(x,z)}{ q_\phi(x, z)}\right)\right]\nabla_{\phi}z$ $\nabla_{\gamma} L_{gem}(\phi,\gamma,\theta) \overset{z=G_{\gamma}(z_{dis})}{=} E_{x\sim p(x)}\nabla_{z}\left[\log\left(\frac{p_{\theta,\gamma}(x,z)}{ q_\phi(x, z)}\right)\right]\nabla_{\gamma}z$ Furthermore, the optimization objective of the discriminator can be expressed as: $L_{adv} = L(D) = \frac{1}{N} \left[ \sum\limits_{i=0; (x_i, z_i) \in E_\phi}^{N} \text{softplus}(-D(x_i, z_i)) + \sum\limits_{i=0; (x_i, z_i) \in D_\theta}^{N} \text{softplus}(D(x_i, z_i)) \right]$ where $$D^(x,z)=\log\left(\frac{p_{\gamma, \theta}(x,z)}{q_{\phi}(x,z)}\right)$$. The discriminator $D$ can be used to fit $D^$ to achieve gradient estimation and complete the training. You may also check the R1and R3 for Reviewer d3xR, for insights into the framework's definitions and workflow. W2: A brief explanation of some methods used, such as Somers' D algorithm, will be beneficial R2: Thanks for your suggestions. We will meticulously integrate comprehensive definitions and clarifications of all employed functions. Specifically, for the Somers' D algorithm you referenced, we provide the subsequent example to enhance your understanding. Suppose we have the sample dataset $S=\{(1,2),(3,1),(2,3)\}$: \| Variable \| Pairs \| Value \| \|--------------\|--------------------------------\|-------\| \| $N_c$ \| (1,2) vs (2,3) \| 1 \| \| $N_d$ \| (1,2) vs (3,1) and (2,3) vs (3,1) \| 2 \| \| $T_y$ \| None \| 0 \| Somers' D indicator can be calculated as follows: $ D =\frac{N_c-N_d}{N_c+N_d+T_y} = \frac{1 - 2}{1 + 2 + 0} = -\frac{1}{3} $ This obtains a value of approximately -0.33, signifying a negative correlation between variables $X$ and $Y$. This calculation demonstrates that the Somers' D metric is straightforward to calculate and is particularly applicable to ordinal variables. Furthermore, Somers' D is asymmetric and capable of distinguishing bidirectional relationships between variables. These characteristics make it highly suitable for integration into our model. Q1: How is the effectiveness of DisGraph ensured? What problems could arise if errors are introduced into DisGraph? R3: To ensure the effectiveness of DisGraph, we perform an ablation experiment by disabling the DisGraph (see Figure 7 in Section 4.5). Since completely removing DisGraph is infeasible due to its role in embedding bidirectional weighted relations, we alternatively utilize an initial version of DisGraph without the updating module $E_{gnn}$. Refer to the top-left in Figure 7, where the model, using an initial Graph, exhibits weakened or inaccurate relational awareness (e.g., the relation between "Bald" and "Gender" weakens). This observation demonstrates the effectiveness of DisGraph. Regarding your second question, to our knowledge, the errors in interrelation identification from MLLMs may lead to counterfactual outcomes. For example, applied with a less capable MLLM that does not recognize the positive correlations between "banana" and "yellow" or "age" and "white hair", the model may obtain a red banana or a white hair baby learned from the errors introduced into DisGraph (refer to the counterfactual results by a weaker MLLM in Figure A3 of the attachment). In our perspective, even advanced MLLMs (e.g., GPT-4o) can exhibit a certain bias. To enhance robustness of GEM, we are investigating potential improvements both within the MLLM (e.g., data pre-processing, bias-aware modules, and knowledge editing) and externally (e.g., weight redistribution, debiasing modelling, and modifications to decoding strategies). --- Rebuttal Comment 1.1: Comment: Thank you to the author for providing a thorough response to my question. I believe it has addressed my concerns regarding DisGraph. I will raise the score I have given and consider the paper to be an excellent one.	Summary: To achieve fine-grained, interpretable and unsupervised disentangled representation learning (DRL), this paper proposes a new framework by integrating $\beta$-variational autoencoder ( $\beta$-VAE), multimodal large language model (MLLM) and graph learning into a single pipeline. Experimental results show that the proposed framework can achieve a better trade-off in the capability of disentanglement and quality of reconstruction than the evaluated baselines under different datasets. Strengths: The strengths of the paper are listed as follows. 1. The paper is well-motivated. Figure 1 clearly illustrates the limitations of the existing works in DRL and the advantages of the proposed framework, which clearly shows the motivation of the paper. 2. This paper provides a thorough and insightful summarization of the related work in DRL, which highlights the contribution of the proposed framework. 3. It is great that the authors could provide detailed and diverse qualitative results in the section of experiments. It can give the readers a more clear view to understand the effect brought by the proposed framework. Weaknesses: The weaknesses of the paper are listed as follows. 1. It would be better if the authors could first formulate the problem as an optimization problem mathematically before introducing the details of the method to solve the problem. In the problem formulation, the input, output, constraints and objectives should be clearly defined. 2. In the proposed framework, the input to the decoder $D_{rec}$ is not from the normal distribution but from the variable extracted from DisGraph. It is a critical point that needs to be highlighted in Figure 2. However, it is missing in Figure 2. 3. Some technical details are not clear as listed below. A. The input to the decoder $D_{rec}$ is not from the normal distribution but from the variable extracted from DisGraph. But how to make this process differentiable for end-to-end training is unclear. B. It is not clear how to train the graph learner in an unsupervised way. What is the loss function? What is the dimension of the node feature? Moreover, how to update the adjacency matrix of the DisGraph given the updated weights of the GNN? C. In Figure 2, it is not clear about the usage of a set of extra images input to the landmark function. 4. It would be better if the authors could use some metric to quantify the disentanglement capability of the DRL algorithms and show the quantitative results to evaluate the proposed framework and the baselines. 5. It would be better if the authors could provide a more intuitive explanation of the loss function they designed. What is the usage of each term within the loss function? Why can they address the limitations of the existing challenges of DRL? Technical Quality: 3 Clarity: 2 Questions for Authors: The questions of the paper are listed as follows. 1. Is Equation (2) instead of Equation (1) the fundamental objective of vanilla VAE? 2. What are the differences among $p_{\theta}(z\|x)$, $p_{\theta}(x\|z)$ and $p_{\theta}(z)$? Why can they share the same parameters $\theta$? 3. Why can the MLLM have the capability to provide accurate attribute scores given the multimodal input provided by the framework? 4. If it has been proved that unsupervised DRL is impossible without extra prior, why does the proposed unsupervised framework work? What is the extra prior or inductive bias here? 5. Could you please give more explanation about why is the proposed algorithm to obtain the impact scores between the pair of attributes reasonable? 6. What are the potential use cases of the disentanglement capability from DRL? Confidence: 3 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: The limitations are shown in the section of Weaknesses and Questions. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We value your insightful feedback and will refine our manuscript accordingly. Here, we address each of your concerns. W1: Detailed definitions of the model R1: Thanks for your suggestions. We will detail the model's parameters, definitions, and optimization strategies in revision. Here, we present a brief overview of for clarity: \| Component \| Input \| Output \| \|------------------\|--------------------------------------------\|------------------------------------------\| \| Encoder $E_{sem}$ \| Image $x \in \mathbb{R}^{n \times n}$ \| Disentangled latent variable $z_{dis} \in \mathbb{R}^{pre}$ \| \| DisGraph $G$ \| Disentangled latent variable $z_{dis} \in \mathbb{R}^{pre}$ \| Correlation-involved latent variable $z \in \mathbb{R}^{pre}$ \| \| Decoder $D_{rec}$ \|Correlation-involved latent variable $z \in \mathbb{R}^{pre}$ \| Reconstructed image $\hat{x} \in \mathbb{R}^{n \times n}$ \| where $pre$ is the pre-defined dimensionality for all latent variables. During training, the optimizable parameters of the encoder $E_{sem}$, DisGraph $G$ and decoder $D_{rec}$ are denoted as $\phi$, $\gamma$ and $\theta$, respectively. And the optimization objectives can be formulated as follows: $L_{gem}$ ($\phi$, $\gamma$, $\theta$) = $D_{\mathrm{KL}}(q_{\phi}(x, z)$,$p_{\gamma,\theta}(x, z))$, $L_{dis} = -D_{\mathrm{KL}}\left(q_{\phi}(\mathbf{z}\|\mathbf{x}) \\|\| p_{\theta}(\mathbf{z})\right) $ $L_{adv} = L(D) = \frac{1}{N} \left[ \sum\limits_{i=0; (x_i, z_i) \in E_\phi}^{N} \text{softplus}(-D(x_i, z_i)) + \sum\limits_{i=0; (x_i, z_i) \in D_\theta}^{N} \text{softplus}(D(x_i, z_i)) \right]$ $L_{total} = \lambda_{gem} L_{gem} + \lambda_{dis} L_{dis} + \lambda_{adv} L_{adv} $ In the revised total loss, as distinct from the manuscript's version, we partition the original $L_{dis}$ into two components: $L_{gem}$ for reconstruction and $L_{dis}$ for disentanglement. W2: Missing details in Figure 2 R2: Thanks for your thorough review. We have updated Figure 2 to highlight the input distribution of $D_{rec}$ accordingly. W3_A: How to make it differentiable for end-to-end training in the model R3: Based on the latent variable $z_{dis}$ from encoder $E_{sem}$, we generate $n$ nodes, each representing one of the $n$ semantic attributes. In practice, each node mirrors $z_{dis}$'s dimensionality but isolates the $i$-th attribute by masking all dimensions except the $i$-th, thereby to learn the $i$-th attribute. These nodes, combined with interrelations from $P_{rel}$, form the DisGraph, which outputs the embedding matrix $T$. This matrix is utilized to calculate $z$ by averaging each volume, subsequently decoded by $D_{rec}$ to reconstruct the image with our loss functions. All aforementioned modules are differentiable. W3_B: Unclearness of the Graph learner training R4: As described in Line 195, we follow the instructions by Liu et al. to unsupervisedly train the graph learner. Specifically, the adjacency matrix are updated within $E_{gnn}$, by the Structure Bootstrapping Mechanism and Multi-view Graph Contrastive Learning. W3_C: Unclearness in Figure 2 about Landmark R5: In this work, we only apply off-the-shelf landmark models for data pre-processing, which does not require any extra data in the databases. We will accordingly clarify it in Figure 2. W4: Disentanglement metrics R6: Our research emphasizes incorporating attribute interrelations, where enhancing disentanglement is not our primary objective (refer to R4 to Reviewer qyA4). However, to address your concern, we have conducted extra experiments as shown in Figure A4 in the attachment. W5: Explanations of the loss function R7: We have detailed our loss functions in R1. Regarding your final concern, our approach addresses DRL’s limitations by: 1) contributing to a more practical paradigm; 2) balancing reconstruction and disentanglement abilities by adjusting $\lambda_{gem}$ and $\lambda_{dis}$. Q1: Is Equation (2) the fundamental objective of vanilla VAE? R8: Equation (2) represents the objective function of the $\beta$-VAE, while Equation (1) represents the likelihood estimation for vanilla VAE. Q2: Justifications of parameters $\theta$ R9: We adopt the original VAE notations: $p_{\theta}(z)$ implies $z$ follows a standard normal distribution without parameters. In $p_{\theta}(z\|x)$ and $p_{\theta}(x\|z)$, $\theta$ denotes decoder parameters. $p_{\theta}(z\|x)$ is used solely for theoretical derivation of the variational lower bound, with no parameter sharing in practice. Q3: Why can MLLMs provide accurate scores? R10: Theoretically, the impressive capabilities of MLLMs, especially in realistic AI generation, reveal that they can comprehend real-world concepts at a certain level, informed by in-depth studies (see Section 2.3); Experimentally, our evaluations of SOTA MLLMs confirm their reliability (see Section 4.4 and Figure A1 in attachment). Q4: Reliance on unsupervised DRL R11: Refer to the R2 for Reviewer qyA4, the DRL branch extracts and initializes latent factors. Although these factors exhibit partial independence, this limitation is acceptable as their interrelations will be refined and updated by the MLLM branch and DisGraph. Hence, our model does not require any external supervision or priors. Q5: Explanations on interrelations determining R12: For determining the interrelationships between two attribute scores from MLLMs, we employ correlation analysis algorithms (e.g., Somers' D). Due to spatial constraints, please refer to R2 for Reviewer SQvd for the details of this part. Q6: Potential applications R13: Our practical and relation-aware DRL framework can be applied in domains like AI-generated content, explainable AI, medical imaging, robotics, and autonomous vehicles. --- Rebuttal Comment 1.1: Comment: Thanks for the detailed rebuttal from the authors. I think it solved most of my concerns. Given the feedback, I think a thorough revision should be made for the final publication. So please remember to make the revisions you promised for the final version of the paper. I have raised my score for this paper.	Summary: The paper presents a novel framework that integrates β-VAE with multimodal large language models within a graph structure, DisGraph, to enhance disentangled representation learning. This approach allows for effective handling of complex and interdependent data attributes in an unsupervised manner. The model dynamically updates relationships between attributes, improving disentanglement and interpretability compared to traditional methods. Extensive experiments demonstrate its superior performance in both disentanglement and reconstruction. Strengths: 1. The paper successfully integrates β-VAE with multimodal large language models (MLLMs) within a graph-based framework, which is a novel approach. 2. The use of a graph-based approach to model the relationships among attributes addresses a significant gap in existing DRL methods. 3. The experiments are well-designed, covering various aspects of the model’s performance. Weaknesses: 1. The paper would benefit significantly from clearer writing and better organization. The paper occasionally uses technical terms and concepts without adequate definitions or explanations. 2. While the paper addresses the unrealistic assumption of statistical independence in many DRL methods, the solution proposed still relies heavily on the disentanglement abilities of β-VAE, which itself often presupposes some level of independence or weak dependence among latent variables. 3. Also, the reliance on pre-trained multimodal large language models might introduce biases from these models into the disentangled representations. 4. A deeper theoretical analysis of why and how the inclusion of interrelations leads to better disentanglement would be valuable. Technical Quality: 3 Clarity: 2 Questions for Authors: 1. How are the generated node embeddings T generated by DisGraph associated with the losses introduced in Section 3.1? Confidence: 4 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: We greatly appreciate your insightful comments and commit to refining our manuscript based on your suggestions. Below, we address all your concerns. W1: The paper would benefit significantly from clearer writing, organization and explanations R1: Thanks for your suggestion, we promise to enhance the manuscript on the writing style and structural organization. In addition, we will ensure that all technical concepts presented in the paper are associated with clear and comprehensive definitions or derivations (e.g., Somers’ D algorithm). W2: The heavy reliance on the disentanglement abilities of β-VAE, which itself often presupposes some level of independence or weak dependence. R2: Thanks for your insightful comments. We wish to re-emphasize the key of our work: To move beyond the unrealistic independence assumption of traditional DRL, we propose a more logical and practical DRL paradigm that involves the bidirectional interrelations between attributes. In this framework, $\beta$-VAE branch is only employed to extract and initialize latent factors. The weak dependence or partial independence among initial factors is acceptable, as their interrelations will be subsequently determined, overwritten, and updated by the proposed MLLM branch and DisGraph. In this way, our method aligns more closely with real-world dynamics and offers broader applicability. W3: Reliance on pre-trained multimodal large language models might introduce biases R3: Our framework is based on the belief that MLLMs, including their future iterations, are sufficiently robust to comprehend logical rules of reality (e.g., aging brings wrinkles, sunrise brings light, etc.). These rules are represented as interrelations between entities. On this basis, we have corroborated the efficacy of MLLMs using ground truths to affirm their effectiveness in straightforward scenarios (see Section 4.4 and Figure A1 in the attachment). However, we totally agree with you that even the most powerful MLLMs (e.g., GPT-4o) can exhibit bias on limited pre-training data. To address this, we are exploring potential solutions from both within the MLLM (e.g., data pre-processing, bias-aware module, knowledge editing, and etc.) and from our end (e.g., weight redistribution, debiasing modelling, decoding strategy modification and etc.). W4: A deeper theoretical analysis of why and how the inclusion of interrelations leads to better disentanglement would be valuable R4: Thanks. It is really meaningful and interesting to discuss "what is a better disentanglement". If it means the better performance on independently decomposing factors, then the inclusion of interrelations might not seem beneficial; however, if it refers to a better performance/practicality for real and complex scenarios, our disentanglement paradigm excels by statistically capturing the logical rules of real world. Specifically, the inclusion of interrelations can be beneficial in model generalizability, counterfactual reasoning and practical usages. We will further conduct analysis and discussion on this point in the manuscript, through both theoretical analysis and experimental investigations. Q1: How are the generated node embeddings T generated by DisGraph associated with the losses? R5: Our apologies for the unclear descriptions. In brief, DisGraph generates the embedding matrix $T$ based on updated parameters to derive the latent variable $z$ through the aggregation of node embeddings. $z$ is subsequently decoded by $D_{rec}$ to reconstruct the image within the bounds of our loss functions. We welcome your reference to the R1 for Reviewer d3xR for a comprehensive discussion of the model's loss functions and workflow. --- Rebuttal 2: Comment: Thank you for your continued efforts. We have provided comprehensive rebuttals and tried to address the concerns raised in your reviews. Please take the time to review if possible, if you have any further questions or require additional clarification, please let us know and we welcome discussions in any format . Thanks again. Title: Hope for your further comments --- Rebuttal Comment 2.1: Title: Official Comment by Reviewer qyA4 Comment: I thank the authors for their responses. I will raise my score.	Rebuttal 1: Rebuttal: Dear reviewers, First of all, we would like to thank all reviewers for their time and efforts in reviewing this paper. These insightful comments are really helpful in guiding to improve the manuscript. *We have made our efforts to meticulously address each concern raised by the reviewers. Please refer to separate responses for details. We have also attached a one-page PDF to support our responses.* We hope that the responses sufficiently address the reviewers' concerns. And we are open to further discussions if there be any unresolved issues. Finally, we promise a careful revision of the manuscript according to these comments and discussions. We have released our code online (as attaching external links is not allowed, we have sent an anonymous GitHub link to the AC as required), and hope our work can provide valuable insights to the community. Sincerely yours, Authors Pdf: /pdf/5807e21e72c867f2be5cfd29277f128aa7e6bb19.pdf	NeurIPS_2024_submissions_huggingface	2,024	Summary: Objective The paper presents a novel framework for disentangled representation learning, which aims to identify and separate the underlying factors of variation in complex data. The primary goal is to enhance the interpretability and robustness of data perception and generation models. Methodology The proposed method integrates a β-VAE (Variational Autoencoder) with a bidirectional weighted graph framework and utilizes Multimodal Large Language Models (MLLM) to discover and rank potential relationships between factors. This integrated approach ensures fine-grained, practical unsupervised disentanglement. Contributions 1. Innovative Framework: Combining β-VAE with MLLM and a bidirectional weighted graph for enhanced disentangled representation learning. 2. Fine-Grained Disentanglement: Achieves more detailed and practical separation of data factors. 3. Improved Interpretability: The model inherits the interpretability and generalization capabilities of MLLMs. 4. Robust Evaluation: Shows superior performance in terms of disentanglement and reconstruction quality on benchmark datasets. Strengths: Originality. The paper presents a unique combination of β-VAE and Multimodal Large Language Models (MLLM) within a bidirectional weighted graph framework. This novel integration allows for capturing and ranking complex relationships between factors, addressing limitations in previous methods. Quality. The methodology is rigorous, with well-designed components and thorough evaluations on the CelebA and LSUN datasets. The use of Graph Neural Networks (GNNs) for optimizing the DisGraph demonstrates a high level of sophistication and effectiveness. Clarity. The paper is well-organized and clearly written, with detailed explanations and helpful diagrams. Each component of the framework is logically explained, making the complex methodology accessible to readers. Significance. The framework enhances interpretability and robustness in disentangled representation learning, with practical implications for image generation and AI explainability. It sets a new direction for future research. Weaknesses: 1. Dependence on MLLM: The framework heavily relies on Multimodal Large Language Models (GPT-4) to discover and rank relationships between factors. This dependence can be problematic if the MLLM is not sufficiently trained on relevant data or if it introduces biases present in its training corpus. Additionally, relying on a single score from MLLM may not be sufficiently convincing, making this step overly dependent on the accuracy and reliability of MLLM. Despite the evaluations in section 4.4, which assess the accuracy of the scores, having specific guidelines or principles for MLLM scoring would be more convincing than relying solely on a single score. 2. Lack of Detailed Attribution: While the paper introduces a novel framework, it lacks detailed explanations on how each latent representation specifically maps to distinct attributes. This can make it challenging to understand and interpret the exact role of each variable in practical applications. Technical Quality: 3 Clarity: 3 Questions for Authors: 1. I did not fully understand how the paper finds the correspondence between the latent representations output by the Encoder and the semantic attributes. For example, in Figure 1, how do the latent representations obtained through the Encoder correspond to attributes such as hat, eyes, etc.? Could you provide a detailed explanation of this process? 2. In the step where MLLMs are used to evaluate attributes (Figure 3), is there a specific principle guiding the MLLM to score the attributes? For instance, what is the difference when the MLLM scores the same attribute as 2, 3, or 4? Additionally, what would the results be if other MLLMs mentioned in your related work section were used for scoring instead of relying solely on the GPT-4 series? 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: We greatly appreciate your insightful comments and commit to refining our manuscript based on your suggestions. Below, we address all your concerns. W1: Dependence on MLLM R1: Thanks for the insightful comments. First, we would like to clarify that our model leverages the commonsense knowledge embedded in MLLMs to predict interrelations. This is predicated on the assumption that MLLMs, including their future iterations, are powerful and reliable enough to comprehend the physical rules of the real world (e.g., aging brings wrinkles, sunrise brings light, etc.). To substantiate the reliability, we evaluate the scores from SOTA MLLMs with ground truths, as detailed in Section 4.4 and Figure A1 in the attachment. Nevertheless, we totally agree with your comments, that a solitary score is not convincing enough to represent MLLMs' knowledge. Towards it, two perspectives of considerations are undertaken: 1) enhancing the prompting guidelines to have more informative outputs (e.g., likelihood probabilities, multi-level categorical outputs, averaged iterative scores and etc.); 2) interpreting lightweight bias mitigation modules with certain prior knowledge (e.g., [1] and [2]). [1]Hauzenberger et al., Modular and on-demand bias mitigation with attribute-removal subnetworks, 2023. [2]Kumar et al., Parameter-efficient modularised bias mitigation via AdapterFusion, 2023. W2: Lack of Detailed Attribution R2: Thanks. Actually, it is a frequent question why unsupervised DRL models possess the ability to align specific attributes. We provide a brief discussion here and will offer a comprehensive explanation in the revision. To address your concern, we need to analyze it from the information-theoretic perspective. As per the Information Bottleneck (IB) theory [3], constraining the information input to the DRL model (e.g., by the penalty coefficient $\beta$ in $\beta$-VAE), inherently enables the model to identify and learn the most representative factors for successful reconstruction. For instance, when trained on the Shapes3D (a collection of simple, synthetic objects) with a merely three-dimensional latent variable, the model tends to learn the most critical factors which are observed to be "object colour", "object shape", and "background shape". These attributes are aligned in the three dimensions, organized in order of their contribution to reconstruction. Similarly for facial images, the model spontaneously learns and organizes the most informative attributes (e.g., hair, gender and etc.) in the disentangled dimensions. In addition, in our framework, we employ a landmark detection for pre-processing, extracting pivotal object features and discarding image redundancies via cropping and resizing. It further helps the mapping of each latent representation to unique attributes. [3] Burgess et al., Understanding disentangling in $\beta$-VAE, 2018. Q1: I did not fully understand how the paper finds the correspondence between the latent representations output by the Encoder and the semantic attributes R3: In the response for W2, we have clarified that for a collection of data, the most informative attributes will be unsupervisedly learned by the $\beta$-VAE and sequentially aligned across several dimensions. It highlights the role of $\beta$-VAE branch to disentangle and initialize the attributes. Nevertheless, these initialized attributes need a further human observation to extract textual concepts for subsequent MLLM prompting. Q2: Is there a specific principle guiding the MLLM to score the attributes? For instance, what is the difference when the MLLM scores the same attribute as 2, 3, or 4? What would the results be if other MLLMs were used for scoring? R4: In the paper, Figure 3 illustrates the specific guiding principle, which prompts MLLMs to classify one attribute into multiple degrees on its own judgement. Specifically, it assigns scores ranging from 0 to 5 for each attribute, where 0 indicates the attribute’s absence, and 5 denotes its highest expression. For example, for scoring attribute ''smile", MLLMs tend to assign a score of 0 for the absence of a smile and a score of 5 for a full laugh, according to the statistical distribution they have learned from extensive data. Towards your 2nd question, we wish to further clarify: since the goal of the MLLM branch in GEM is to discover the interrelations, the statistical relativity between two attributes is of primary concern, rather than the absolute scores for the individual attribute (see Figure A2 in the attachment). For example, given a collection of facial images, it is acceptable if the scores of "age" and "bald" exhibit a positive correlation, even if the specific score values are fluctuating. Addressing your final concern, we believe that a less capable MLLM would hinder the learning of attribute interrelations. We substantiated this by replacing GPT-4o with the inferior GLM and assessing the outcome. Figure A3 in the attachment demonstrates that GLMs' limited perceptual capacity yielded counterfactual outcomes. Therefore, the MLLM bias mitigation methods mentioned in R1 are valuable. --- Rebuttal Comment 1.1: Comment: In general, I am satistifed with the author feedback. As reflected in my score, the paper has its merits, and is above the acceptance bar in my opinion.	null	null	null	null	null	null
Improving self-training under distribution shifts via anchored confidence with theoretical guarantees	Accept (poster)	Summary: This paper presents Anchored confidence (AnCon), a novel self-training algorithm to improve test-time accuracy under distribution shifts. AnCon modifies the standard self-training algorithm by adding a temporal ensemble regularization. This regularizer is constructed by the consistency of temporal ensembles weighting with their predictive confidences. This intuitively helps the model avoid the "early-learning phenomenon", i.e., the model exploiting noisy labels after initially learning clean labels. Contributions include: 1. A new algorithm for memorizing past ensemble predictions to avoid the "early-learning phenomenon", enhancing self-training performance under sequential distribution shifts. 2. In terms of theory, the authors provide a rigorous theoretical analysis for the upper bound of the test-time error of the proposed temporal ensembles by concentration inequality in Theorem 3.1. Inspired by Knowledge Distillation (KD), they also design an upper bound of the expected cross-entropy loss between the temporal ensembles and the optimal value in Theorem 3.2. 3. Extensive experiments confirm the hypothesis that the proposed algorithm can improve self-training performance regarding test-time accuracy and calibration under distribution shifts across different hyperparameter choices. Strengths: - This paper is very well-written and clear to understand the important aspects of the algorithm. - Although the temporal ensemble weighing technique reminds me of similarities with Early learning regularization (ERL) in discount factor from past predictions, I still like the AnCon in general because of a novel of high-quality uncertainty estimation behavior in neural network self-training. - Similar to ERL, AnCon is also more computationally efficient than non-parametric techniques and standard sampling-based Deep Ensembles. - The theoretical contribution of this paper is good, yielding a solid AnCon algorithm. Specifically, under mild assumptions, Theorem 3.1 and 3.2 formally explain why AnCon works and how temporal ensemble regularizers can contribute to improving self-training under covariate shifts (details in Contribution 2). - Experiments show a significant improvement of the standard self-training algorithm across different distribution shifts like artificial corruptions and real-world domain shifts. - The robustness of the proposed model across different settings is also confirmed across different hyperparameter choices of coefficient regularizer $\lambda$ in Eq. 1 and discount factor $\beta$ in Eq. 3, different proportional weighting schemes for $w_m(x)$ in Eq. 3, and different soft-hard predictions for $p(y\|x,\theta_i)$ in Eq. 2. Weaknesses: - Regarding the proposed algorithm: compared with the standard self-training, AnCon requires pre-defining the regularizer $\lambda$ and the discount factor for the temporal ensembles $\beta$. - Regarding the theory: Theorem 3.1 requires $\bar{p}(x;\mathbf{c}_{0:m}) \geq 1/2$, i.e., at least 50% accuracy on average for the temporal ensembles. This is a quite strong assumption. - Regarding the experiments: (1) The quantitative results in all tables are reported without the standard deviation and significant tests; (2) The improvement in calibration is shown without any theoretical evidence. Fig. 3 (a) only shows ECE without the reliability diagram, making it hard to assess the correlation between the accuracy and uncertainty of softmax’s probability; (3) Lacks of comparison with other baselines, e.g., many baselines [1] in UDA could be added to compare in Appendix C. - Others that are mentioned by the authors: the challenge of self-training methods under distribution shifts and the violation of average correct predictions in self-training. - Miscellaneous: (1) Although assumptions A.1, A.2, and A.3 are mild and have been cited, I believe it is still worth discussing how they are realistic with the paper's setting; (2) Some mathematical notations are vague and perhaps need to be polished (e.g., $f(x;\theta)$ or $f_k(x;\theta)$ in L-78, how $\bar{f}(\cdot)$ in Eq. 1 connect to the Def. $\bar{f_k}(\cdot)$ in Eq. 2, $\hat{\mathbb{E}}$ in Eq. 3 seems not to be defined, the same notation $\sigma$ for different $\sigma_*^2$ in Theorem 3.2 and perhaps the softmax $\sigma_k(x;\theta_i)$ in L-339, more in Question 2); (3) I find it quite hard to follow acronyms without links, I would recommend using \usepackage[acronym]{glossaries} so readers can smoothly follow the paper; (4) Some Figure’s x-y-titles are tiny, e.g., Fig. 3 (b). Technical Quality: 3 Clarity: 4 Questions for Authors: 1. The connection of AnCon with KD is not clear to me. The pseudo label $\hat{Y}(x;\theta)$ in self-training with AnCon and the true label $Y(X)$ in L-163 ($Y(x)$ in L-74) are completely different because $Y(X)$ is unobservable while $\hat{Y}(x;\theta)$ is model’s prediction. So in Section 3.3, the statement in L-165-166 to connect AnCon with KD is still wrapping my head. In particular, why AnCon's pseudo-label can be considered as $Y(x)$ (perhaps the true label $Y(X)$ in L-163)? Also, I am curious about why Eq. (40) can lead to Eq. (41), i.e., how we can bound the norm of gradient loss $\|\|\nabla l(\theta_{m,t}) - \nabla \tilde{l}(\theta_m)\|\|^2$ by the $Err(\hat{Y};\theta_{m})$ while this upper bound related the true label $Y(X)$? 2. Some questions for clarification: is $\delta$ in L-83 $\in [0,1]$? $\sum_0^m$ or $\sum_0^{m-1}$ in Eq. 3? $\theta_k$ or $\theta_m$ in $Err_{XY}(\cdot)$ in L-184? $\mathbf{w}\_{1:m}$ or $\mathbf{w}_{0:m}$ in RHS Eq. in L-186? 3. Compared with ELR which computes the temporal ensembles by the logit vector $f(x;\theta_i)$ only in L-83, the proposed algorithm requires computing $\mathbb{E}\_{x\in X}\max_{k\in [K]}f_k(x;\theta_i)$ in Eq. 3, does this causes a higher computational demand? 4. Can you generate a reliability diagram [2] to show the overconfidence and underconfidence of methods? I think this could be easier to assess how your method can improve the model's uncertainty quality. 6. In the testing of different weighting schemes in Fig. 4 at Section 4.4, have you considered the setting of a uniform weighting for $\mathbf{w}$, i.e., set Eq. 2 to $\bar{f_k}(x;\theta_{0:m},\mathbb{w}_{0:m}):= \sum_i^m p(y=k\|x;\theta_i)$? This is a simple setting but no longer temporal ensembles by discount factors, and also not standard (vanilla) self-training. I am quite curious about this result. 5. Do the authors think your proposed method can work in other sequential decision-making, e.g., bandits, RL, bayesian optimization, active learning, etc.? If yes, could you please give some comments? Otherwise, could you please raise some challenges? References: [1] Fang et al., Source-Free Unsupervised Domain Adaptation: A Survey, arXiv, 2023. [2] Guo et al., On Calibration of Modern Neural Networks, ICML, 2017. Confidence: 4 Soundness: 3 Presentation: 4 Contribution: 3 Limitations: Please see my comments on the Weaknesses. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We sincerely appreciate Reviewer hP9c's insightful suggestions and thoughtful comments. We are pleased that Reviewer hP9c acknowledges our core technical contributions to showing the effectiveness of high-quality uncertainty estimation in the temporal ensemble for improving self-training with solid theoretical and empirical results. Below, we have carefully addressed Reviewer hP9c’s valuable comments, which we believe significantly improve our work. (Unfortunately, due to the number of comments from Reviewer hP9c, our rebuttal addresses only Weaknesses. We will post the remaining responses to Questions in the official comment and apologize for any inconvenience.) _Note: [G#] is the reference for the global responses._ W1: Yes, but we hold a positive view on using the provided default hyperparameter values in diverse distribution shift scenarios. Specifically, we note that the single configurations ($\lambda=0.3$ and $\beta=0.9$) work well for 105 numbers of different distribution shifts with varying difficulties. Also, the performances are shown to be not drastically affected by changes in the hyperparameter values. Finally, we kindly refer to [G4 in the global response] for more detailed explanations of our rigorous hyperparameter selection procedure and its strong practical implications. W2: We kindly refer to [G1] for the validity of the assumption of $ \bar{p}(x; c_{0:m}) $ made in Theorem 3.1. Also, we note that AnCon’s strong empirical performance can be preserved even if the condition is violated as discussed in [G3]. W3-1: Thank you for pointing out the important missing details in the error bars. In the original version, we opted to omit the variance terms because the variance is not particularly large for any method (e.g., on average 0.96 for OfficeHome), which gives statistical significance at a P-value < 5%. However, in order to prevent concerns about the statistical significance, we have added P-values for each table. W3-2: Thanks for the great suggestion that can help readers to understand the uncertainty estimation behavior of AnCon. Following the Reviewer hP9c’s insightful suggestion, we have analyzed the reliability diagram. As widely known in the literature, all self-training methods turn out to be overconfident. However, as shown in Figure R5, AnCon relaxes the overconfident behavior, which can be inferred from its better ECEs in the manuscript (e.g., Table 5). W3-3: To clarify, AnCon aims to solve the source-free domain adaptation (SFDA) and test-time adaptation (TTA) problems, not the unsupervised domain adaptation (UDA) problem wherein the labeled source domain dataset is available during the adaptation. The unavailability of any reliable labeled samples in SFDA and TTA makes more challenging learning scenarios, which involve early learning phenomenon and model collapse under severe distribution shifts (cf. Figure 1 (a)). Therefore, the UDA methods would not be directly comparable to AnCon. Also, we note that the chosen baselines show state-of-the-art performances in general settings (cf. [G5 in the global response]). W4: Kindly see [G3] for the unique and significant performance gains from AnCon in challenging distribution shift scenarios, wherein the average correct predictions assumption is violated. W5-1: As Reviewer hP9c commented, regularity conditions in Assumptions A.1, A.2, and A.3 are mild but essential for most theoretical studies with convergence analyses. Assumptions A.1 and A.2 can trivially hold under bounded parameter values that can be guaranteed by optimizing neural networks with finite iterations under a gradient or weight clipping. Assumption A.3 holds for infinite-width neural networks, i.e., the neural tangent kernel (NTK) regime (Charles & Papailiopoulos, 2018). Given that the gradient descent training dynamics of neural networks can be well approximated by NTK (Jacot et al., 2018), the PL condition can be generally regarded as a mild assumption. We fully agree with Reviewer hP9c’s suggestion and have added these discussions to “Appendix A.1 Assumptions.” Charles, Z., & Papailiopoulos, D. (2018). Stability and generalization of learning algorithms that converge to global optima. In ICML. Jacot, A., Gabriel, F., & Hongler, C. (2018). Neural tangent kernel: Convergence and generalization in neural networks. In NerIPS. W5-2: Thanks for the valuable clarifying questions! $ f_k(x; \theta) $ is right; $ \bar{f}(x) := (\bar{f}_1(x), \bar{f}_2(x), \cdots, \bar{f}_K(x)) $; $ \hat{E} $ is the Monte-Carlo estimator with mini-batch samples; we have introduced $ \sigma^{2}(\bar{\theta}) $ for the variance of stochastic gradient of $\bar{f}$; finally, we introduce a new notation for the softmax as $\phi$ instead of $\sigma$ to avoid the confusion. W5-3/4: Thanks for the great suggestions. We have added links for all acronyms and increased the font size for all small figures. --- Rebuttal 2: Title: Responses to questions Comment: Q1-1: We inadvertently caused confusion to Reviewer hP9c on the connection between AnCon and knowledge distillation (KD). To be clear, we do not intend to treat the pseudo label $ \hat{Y} $ as the true label $ Y $ since this reduces the theoretical rigor of our work. Indeed, we clearly state the bias coming from pseudo labels in the optimality gap in Theorem 3.2. Also, we state that “the gradient is biased due to the usage of pseudo labels and the generalized temporal ensemble” in Line 168-169. The purpose of this connection is to show how AnCon can reduce the variance of stochastic gradients in the self-training scenario through the partial variance reduction theory by interpreting our generalized temporal ensemble as the teacher network. In order to avoid any confusion, we have changed Lines 165-169 as follows: “”” … , where the generalized temporal ensemble is the teacher network $ f^{(t)} $ with a notable difference that the pseudo label $ \hat{Y} $ is used instead of the true label $ Y $ which requires careful analysis for studying the optimality. The purpose of this connection is to perform a convergence analysis of AnCon by modifying the partial variance reduction theory [31], as given below. We note that the usage of pseudo labels, instead of the true label, and the generalized temporal ensemble result in an inherently biased gradient estimator. Therefore, the convergence analysis requires special treatments for handling the biased gradient, unlike typical supervised learning settings in self-distillation literature. “”” Q1-2: It can be derived by using the law of total expectation with the random event $ 1(Y(X) = \hat{Y}(X)) $ and then applying the bounded support assumption, which we have added to Line 678. Q2-1: If this refers to Line 125 in Eq 3, yes due to the recursion. Q2-2: It is \sum_{0}^{m}, which means the current average confidence is taken into account because the exponential moving average is introduced to avoid the computation of the expectation with respect to all samples. Q2-3: Thank you so much for your careful review and pointing out the type. It is $\theta_m$ because $Err_{XY}(\hat{Y}; \theta_{m,0})$ is an error rate of pseudo label under parameter $\theta_m$. Q2-4: Thanks again for pointing out the typo. This is $ w_{0:m} $ because the generalized temporal ensemble includes the initial model prediction. (After very careful review, we have found other typos in Line 178, Line 179, Line 674, which we corrected). Q3: AnCon has almost the same computational complexity as ELR, and the confusion of Reviewer hP9c would be due to our undefined notation of $ \hat{E}[c(X; \theta_i)] $ which is a Monte-Carlo approximation of $ E[c(X; \theta_i)] $ with mini-batch samples $ \xi $. Specifically, Eq (2) for storing previous predictions is the same as with storing the previous logit vector in ELR ($ K \times N $ numbers). Also, Eq (3) can be efficiently implemented by using softmax output values during the training process which are already computed for computing the self-training loss. Thus, Eq. (3) requires storing only a single number with the computational cost of adding $ B $ numbers. In order to prevent the confusion, we have added the above discussion in Line 131. Q4: Kindly see the response to the weakness. Q5: As per Reviewer’s insightful comment, we have tested the undiscounted vanilla temporal ensemble (UVTE) method, which results in 4.2\% of reduction of accuracy on average. Intuitively, UVTE does not work well because memorizing all predictions, which involve highly inaccurate ones, can result in a low-quality temporal ensemble. Indeed, this is well illustrated in Figure R3 where the UVTE would not take advantage of gathering more samples due to inclusion of more incorrect predictions compared to AnCon. We believe this new result further highlights the importance of uncertainty awareness for the temporal ensemble in self-training, which is consistent with our theoretical results in Theorems 3.1 and 3.2. Q6: Thank you for the insightful question that made us think about the non-trivial extension of AnCon. Extending AnCon to sequential decision-making scenarios presents significant challenges as they involve the fundamentally different mechanisms. In sequential decision-making, leveraging observed rewards and balancing exploitation and exploration are core aspects (e.g., constructing the upper confidence bound of the reward in the bandit problem), unlike in self-training. Therefore, the main challenges for applying AnCon to this setting would be defining rewards and incorporating exploration strategies into pseudo label generation. As it holds great significance, we mark this extension as an important future direction. --- Rebuttal Comment 2.1: Comment: I thank the authors for the detailed rebuttal, especially for clarification for Q1 and new results in Q4-5. I keep my original rating for this paper. Since other reviewers also need clarification on the typos, I hope the authors can carefully revise the notation in the final version of the paper. Good luck! --- Reply to Comment 2.1.1: Comment: Thank you for your thoughtful review and for acknowledging the clarifications and new results we provided. We fully understand the importance of clear notation, which we have significantly improved thanks to the reviewers’ suggestions. We will carefully revise the notation and correct any typos in the final version of the paper. Thank you again for your insightful comments throughout the review process!	Summary: The paper aims to improve self-training, a common technique used for learning on unlabeled data (with iteratively generated pseudo labels), when it is applied to scenarios with distribution shifts. The proposed approach, Anchored Confidence (AnCon), essentially applies label smoothing on the pseudo labels with the ensemble prediction of the models obtained from previous iterations (temporal ensemble) to achieve better temporal consistency and improve the quality of the pseudo labels. Theoretical analysis is provided on the benefits of using temporal ensemble and the connection to ensemble knowledge distillation in the linear case. Empirically, when AnCon is shown both effective and stable when combined with a few orthogonal baselines such as Self-training and GCE under settings such as unsupervised domain adaptation (Sec. 4.1), robustness against label corruption (Sec. 4.2), calibration, etc. (Sec. 4.3). Strengths: 1. The main paper is well-written and pleasant to read. 2. The paper effectively modifies and adapts Early Learning Regularization (ELR) to the setting of self-training under distribution shifts with both theoretical justification and empirical evidence. The theoretical derivations are generally rigorous with assumptions clearly stated. 3. The connection to self-distillation helps to better understand the approach. 4. The empirical and ablation studies are comprehensive and clearly discuss a few critical criteria such as model selection, hyperparameter, and calibration. Weaknesses: 1. Empirically, the approach improves over various baselines when being added, but what about the existing SoTA baselines for unsupervised domain adaptations, which seem relevant to this work. Besides, it seems rather odd to only report the results in Sec. 4 with non-optimal $\lambda=0.3$, as the sensitivity analysis in Figure 2(a) clearly prefers much larger $\lambda$. 2. A critical assumption in the theorems is that the teacher (temporal ensemble) has a sufficiently good performance. It will be helpful to justify this with more empirical evidence. 3. Non-trivial typos: In line 149, $x$ is already used in the main theorem, so may want to change $x$ to $z$ to avoid confusion, and this issue also occurred on 643 with $m$, which might have already caused major problems in proof (see below in Question 3) 4. Minor typos: Line 667, Proof of Lemma A.4, Eq. (31), $k$ should be written as $mq$; Some references from NeurIPS 2024 should be 2023. 5. There might be some mistakes in the theorem proofs. See below in Questions 3 and 4. Technical Quality: 3 Clarity: 3 Questions for Authors: 1. The pseudo label $\tilde{Y}$ is actually also part of the smoothing vector from $\bar{f}$. I wonder how necessary it is to separate $\tilde{Y}$ out as its purpose is to increase the weight of the most recent model, or whether there is a more unified notion to describe the proposed approach with just $\bar{f}$. 2. In Theorem 3.1, the random events of model predictions from different iterations $i, j$ are assumed to be independent. How realistic is the assumption given that the model is trained based on the labels given by the previous iterations? 3. Throughout the paper, $m$ is already defined as the number of models, but the proof of Theorem 3.1 assigns $m = Q(x;c_{0;m})/2$, which is the number of sufficiently confident predictions for $x$ made by the $m$ models. I don’t think it’s appropriate to assign $m$ something else here as it is already defined. If you fix the notation of $m$ (of $q \cdot m$) in Eq. (29) and Eq. (31), Lemma A.4, the bound may look a bit more complex, because the $m$ in Eq. (30) cannot be assigned to a different value. Please clarify. 4. Moreover, in line 152, the paper claims $\bar{f}$ is asymptotically correct, but it is unclear to me if the probability on the L.H.S. of Eq. (6) still goes to 0 when $m \rightarrow \infty$ after fixing the aforementioned problem with $m$. Please clarify. 5. Theorem 3.1 studies the asymptotic correctness of the temporal ensemble with large $m$. The experiments mostly show the AnCon under 20 epochs. How does the performance change when more epochs are added? Is it still consistent with the theoretical implications? Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The authors have discussed the limitations in Section 6. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We sincerely thank Reviewer qtUp for the insightful suggestions and constructive comments, which have significantly improved the clarity of our paper. We are glad that the reviewer enjoyed reading our paper and acknowledged our principled improvements over the existing temporal consistency methods with theoretical guarantees and attractive properties. In our response below, we have addressed the questions and comments. _Note: [G#] is the reference for the global responses._ W1-1: To clarify, AnCon aims to solve the source-free domain adaptation (SFDA) and test-time adaptation (TTA) problems, not the unsupervised domain adaptation (UDA) problem wherein the labeled source domain dataset is available during the adaptation. The unavailability of any reliable labeled samples in SFDA and TTA makes more challenging learning scenarios, which involve early learning phenomenon and model collapse under severe distribution shifts (cf. Figure 1 (a)). Therefore, the UDA methods would not be directly comparable to AnCon. Also, we note that the chosen baselines show state-of-the-art performances in general settings (cf. [G5 in the global response]). W1-2: Our suboptimal choices of hyperparameters are due to our rigorous and practical hyperparameter choice setting, and we kindly refer to [G4] for detailed explanation on the hyperparameter selection procedure and its strong practical implication. W2: Thanks for pointing out the significance of the assumption made in Theorem 3.2, which asserts that "AnCon is at least better than vanilla self-training." However, the assumption is required only for deriving the final bound in Eq (7) to gain more insights about the impact of the generalized temporal ensemble's quality on the suboptimality of self-training. Rather, the core message of Theorem 3.2 that “AnCon is at least better performance than the vanilla self-training” holds _without_ this assumption. Specifically, in Eq. (13) on page 15, $ N(\lambda^\dagger) / N(0) $ corresponds to the ratio between the last term of Eq. (12) under AnCon and the vanilla self-training. Crucially, this ratio is less than or equal to 1, supporting the central message without the assumption. Thanks to the Reviewer qtUp’s insightful question, we have separated the statement of Theorem 3.2 into two parts and modified the discussion in Lines 187-190 (Kindly see the comment below for the final form) to avoid the initial confusion and emphasize that AnCon guarantees at least better performance than the vanilla self-training can hold without such assumption. W3: Thanks for pointing out the notation mistake. Since the argument of the function $ \xi $ is an arbitrary scalar, we have changed $ x $ to $ z $ in Line 149. We have changed the index notation of $ m $ in the Lemma A.4. to $ o $. These notational changes do not invalidate the proof. Regarding the confusion from the index notation, kindly see the response to Q3. W4: Thanks for pointing out the minor typos! We have changed $ k $ by $ m \cdot q $ and fixed typos for the references. W5: Kindly see the responses to Q3 and Q4. Q1: Thanks for suggesting to unify the notation of the generalized temporal ensemble $ \bar{f} $ and the pseudo label $ \hat{Y} $ that might be clearer than the current notation. Despite careful thoughts, unfortunately, we do not see any feasible way to unify the notation without sacrificing the insights and clarity that our current notation can provide. Specifically, our separate notation enables clear explanations of the selective temporal consistency (cf. Eq (2)) that is only involved in $ \bar{f} $. Also, the notation can intuitively explain the role of $\bar{f}$ that regularizes the pseudo label $ \hat{Y} $ through label smoothing, which makes the discussions in Lines 105-115 and the connection between AnCon and knowledge distillation clearer. Finally, there are points that require discussion solely on either of them (e.g., when referring to the accuracy of pseudo labels in Line 145 and Line 184; when discussing the quality of the generalized temporal ensemble in Theorem 3.1). Given the above reasons, we hope that Reviewer qtUp could agree with the advantage of separating notation for the pseudo label and the generalized temporal ensemble. Q2: Thanks for highlighting the validity of the assumption in Theorem 3.1. Here, we emphasize the important aspects of the assumption: the assumption is based on the “conditional” independence between temporal correctness given that the current prediction on a sample is relatively confident. This is grounded in the strong correlation between accuracy and confidence across a wide range of scenarios. Another way to understand this assumption is that the previous history of predictions is summarized in the random event whether the prediction is confident or not. We further remark that the validity of this assumption could be reinforced by strong empirical support for Eq. (6), as shown in Figure R3. Q3: Thanks for pointing out the unclear notation for the supporting lemma. The number of random Bernoulli samples $m$ in the Lemma A.4 (which we change to $o$) is not used in the other parts. Therefore, all other parts remain the same, except Line 624 which refers to this lemma is changed to “... due to Lemma A.4 with $ p_i = P(Y(x) = \hat{Y}(x; \theta_i)) $, $ o = Q(x; c_{0:m}) $, and $ q= 1/2 $.” Q4: We kindly refer to [G2] for the clarification of the notion of asymptotic convergence. Also, we note that [G2] presents the important implication of Eq. (6) in the non-asymptotic region, i.e., monotonic improvement of quality of the generalized temporal ensemble, with strong empirical evidence. Q5: As explained in [G2], we kindly refer to Figure R3 that shows monotonic improvements over 100 epochs of quality of the generalized temporal ensemble under diverse distribution shifts scenarios, being consistent with Theorem 3.1. --- Rebuttal Comment 1.1: Title: Reviewer Response Comment: Thank you for the responses for addressing my concerns including the asymptotic convergence w.r.t. $Q$ and the choice of hyperparameters. For W3 and Q3: In Eq. (30), $m$ is the number of models. In Eq. (31), you set $t = \log \frac{k}{m\bar{p}}$, is this $m$ the number of model or the new $o$? Let’s suppose $m$ is changed to $o$, such that $t=\log \frac{q}{\bar{p}}$ here, then the bound in Eq. (31) may look like $\exp(oq-m\bar{p}-oq\log\frac{q}{\bar{p}})$ with both $m$ and $o$ inside. I think this should affect the bound in Theorem 3.1 as the number of models $m$ would appear. It’s better for the authors to show a more complete derivation after fixing the notations. --- Rebuttal 2: Title: Detailed changes as per the response to W2 Comment: “”” Assume $ l(\theta) $ satisfies $ L $-smoothness, $ \mathcal{L} $-expected smoothness, and $\mu$-Polyak-Lojasiewicz (PL) condition (cf. Assumptions A.1, A.2, and A.3). For $\gamma \leq \tfrac{\mu}{4 \mathcal{L} \cdot L}$ and a carefully chosen $\lambda$ (cf. Lemma A.6), it holds that $$ Eq. (12) $$ Further, if $\mathbf{w}_{0:m}$ such that {...}, i.e., the teacher has a sufficiently good performance, the optimality gap becomes $$ Eq. (7) $$ where $l^*$ {...} . “”” (here we could only refer equation number and use {...} to represent the repetitive equations since the MathJax cannot display the equations properly.) Modified discussion in Lines 187-190: “”” In Theorem 3.2, we remark that the vanilla self-training ($ \lambda=0 $) results in the maximum value of the last term in Eq. (12), which is the neighborhood size of the stochastic gradient descent, while having the same first two terms. In other words, the result suggests that AnCon is at least better than vanilla self-training under the mild regularity conditions. Furthermore, under the assumption of a sufficiently good performance temporal ensemble, we gain valuable insights on the design of $ w_{0:m} $: aiming for … “”” --- Rebuttal 3: Title: Further clarification Comment: Thanks for reading the authors' rebuttal and asking a further clarifying question. The confusion of Reviewer qtUp is noted. In our changed notation, all $ m $ in Lemma A.4. are changed to $ o $, which is the number of random Bernoulli samples. We remark that Lemma A.4 is a supporting lemma, which means that the semantics of notations are independent of other parts of the paper (i.e., none of the quantities in Lemma A.4, including Eq. (30), is interpreted as the number of models). Therefore, all $ m $ notations in Lemma A.4 are changed to $ o $. Then, the right-hand side of Eq. (31) is $ o q - o \bar{p} - o q \log \frac{q}{\bar{p}} $, which is obtained by $M(t) = exp( o \bar{p} (exp(t) - 1))$ and $ t = log \frac{q}{\bar{p}} $. From the above, Eq. (29) is $ p(S_o \leq q o) \leq exp(o (q - \bar{p} - q \log \frac{q}{\bar{p}}) ) $. Therefore, applying this inequality to Theorem 3.1 with $ p_i = p(Y(x) = \hat{Y}(x; \theta_i)) $, $ o = Q(x; c_{0:m}) $, and $ q = 1 / 2 $ proves the last inequality in Eq. (11). We hope this clarifies why there is no mistake in the proof and that the confusion arose from the same notation used in the supporting lemma and other parts of the paper. We sincerely appreciate Reviewer qtUp's thorough review and attention to detail. --- Rebuttal Comment 3.1: Title: Reviewer Response Comment: Thanks for the clarification. I apologize for mistakenly thinking $m$ for $S_m$ should not be updated to $o$. Now everything is clear! The other two reviewers are also generally positive about the contribution of this work, with minor similar concerns about the assumption of $\bar{p}(x;c_{0:m}) \geq 1/2$. Considering the soundness of theoretical analysis and the empirical advantages, I believe this paper will greatly contribute to the research on self-training and test-time adaptation. I have raised my score to 6 for acceptance :) --- Reply to Comment 3.1.1: Comment: Thank you for taking the time to revisit our explanation. We're glad that the clarification resolved the initial confusion regarding the notation. Also, we appreciate your positive evaluation of our work and your consideration of the theoretical analyses and empirical results. Your insights have been so much helpful in improving the clarity and rigor of our paper!	Summary: the authors propose a novel approach to enhance self-training for test-time adaptation (TTA) or source-free domain adaptation (SFDA) in neural networks facing distribution shifts. The core idea revolves around a method called Anchored Confidence (AnCon), which uses temporal ensembles and label smoothing to improve the accuracy and robustness of pseudo labels generated during self-training. This method aims to address the challenge of filtering incorrect pseudo labels, a common issue under distribution shifts, without incurring significant computational overhead. Theoretical guarantees and extensive experiments validate the efficacy of AnCon in diverse distribution shift scenarios. Strengths: * the paper provides rigorous theoretical analyses to support the proposed method. It shows that the generalized temporal ensemble with prediction confidences is asymptotically correct and that label smoothing can reduce the optimality gap. * The method does not require additional forward passes or neighborhood searches, making it computationally efficient compared to existing techniques. * experimental results demonstrate improvements in self-training performance across distribution shift scenarios. Weaknesses: * The novelty of the paper is limited! (The integration of temporal consistency and ensembles for self-training under distribution shifts) Although the method shows good empirical results on small datasets, there may be scenarios or datasets where the performance gains are less pronounced, which are not extensively discussed. * The success of the method is somewhat dependent on the quality of the initial model parameter $\theta_0$. If the initial model is significantly biased or underperforming, the improvements might be limited. Technical Quality: 3 Clarity: 3 Questions for Authors: * The paper claims that the generalized temporal ensemble with prediction confidences is asymptotically correct. Can you provide a detailed proof or further elaboration on the conditions under which this asymptotic correctness holds? Specifically, what assumptions about the data distribution or model convergence are necessary to guarantee this property? * The theoretical analysis suggests that label smoothing can reduce the optimality gap in self-training. Could you explain the underlying mechanism of how label smoothing achieves this reduction? Additionally, what are the theoretical bounds on the optimality gap with and without label smoothing, and how do these bounds depend on the hyperparameters of the smoothing technique? * How does AnCon perform on highly imbalanced datasets or with extreme distribution shifts? * What are the specific hyperparameter settings used in the experiments, and how sensitive is the method to these settings? * Can the proposed method be integrated with other advanced TTA or SFDA techniques, and what would be the potential benefits or drawbacks? * How does the method handle concept shifts, where p(Y\|X) changes between the training and test distributions? * are there any specific types of neural network architectures or tasks (e.g., vision, NLP) where AnCon performs exceptionally well or poorly? Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: Please see the questions and the weaknesses. My current decision on this paper is borderline (reject/accept). I look forward to the authors' rebuttal to address the following questions and concerns, which will help in making a final decision. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We sincerely thank Reviewer fUqB for the valuable suggestions and comments. We are glad that the reviewer acknowledges our rigorous theoretical analyses, efficient algorithm development, and effective performances of AnCon under different distribution shifts scenarios. We believe that addressing the valuable comments further improves our paper, which we hope can effectively address any concerns of Reviewer fUqB. * [G#] is the reference for the global responses. (Unfortunately, due to the number of comments from Reviewer fUqB, our rebuttal addresses parts of responses. We will post the remaining responses in the official comment and apologize for any inconvenience.) W1: Thank you for highlighting the novelty aspect of our paper. As Reviewer fUqB noted, promoting temporal consistency is a well-established framework in self-training algorithms. However, our contribution lies in demonstrating that "uncertainty-awareness" enhances the effectiveness of temporal consistency under distribution shifts. Specifically, Theorem 3.1 shows that uncertainty awareness improves the quality of temporal ensembles proportional to the number of temporally confident predictions. Additionally, Theorem 3.2 and Corollary 3.2.1 illustrate that "AnCon" reduces the optimality gap of self-training, which can be further improved by a high-quality, uncertainty-aware teacher. Crucially, such high-quality teachers are driven by our simple thresholding rule (Eq. (3)) with theoretical guarantees (Theorem 3.1). The significant theoretical contribution has not been studied and would not be possible by just incorporating the temporal consistency through ensemble as shown in Figure R6. In order to help readers to conceptualize the core theoretical contributions of the paper, we have the following discussion to Line 199. ‘’’ Furthermore, we highlight the significance of AnCon’s uncertainty awareness for improving effectiveness of temporal consistency in self-training. Specifically, from the result of Theorem 3.1, $g^{KL}(w_{0:m})$, thereby the optimality gap of the self-training, can be further reduced by collecting more confident samples, while guaranteeing the condition $\bar{p}(c_{0:m}) \geq 0.5$. Therefore, it is important to collect high-quality predictions for matching the condition, which would be hard to satisfy under other temporal ensemble mechanisms (cf. Figure R3). ‘’’ W2: Kindly see [G3 in the global reference] that explains the unique and significant performance gains from AnCon in challenging distribution shifts scenarios. W3: Thank you for pointing out concerns regarding the dependency on the initial model parameter. As Reviewer fUqB conjectured, we have rigorously shown the impact of initial model performance on the sub-optimality of AnCon and the vanilla self-training method (cf. $l(\theta_0) - l^$ and $Err(\hat{Y}; \theta_0)$ in Corollary 3.2.1). Crucially, in Corollary 3.2.1, both AnCon and the self-training method can improve by reducing the initial optimality gap $l(\theta_0) - l^$ as the number of inner and outer iterations $T \cdot (m+1)$ increases, which is why we need “adaptation” if the performance deteriorates under severe distribution shifts. Finally, we kindly refer to [G3] for the discussion of empirical results supporting this argument. Q1: We gently remind Reviewer fUqB that the asymptotic convergence on inputs on which $ f $ produces infinitely many relatively confident predictions is rigorously proven in Theorem 3.1 with explicitly stated assumptions. We also kindly refer to [G1] for the discussion about validity of assumptions and [G2] for the empirical evidence. Q2: This is actually rigorously proven in Theorem 3.2, a core technical contribution of our work, as discussed in Lines 187-199. Specifically, “the underlying mechanism of how label smoothing achieves this reduction” is through connecting AnCon with the self-distillation. Crucially, this connection enables the adoption of the partial variance reduction theory, which can show that the generalized temporal ensemble reduces the neighborhood size of SGD. Our convergence analysis provides the optimality gap in Eq. (7), with the maximum gap occurring in self-training without label smoothing (cf. Line 187-188). This demonstrates that AnCon is at least better than vanilla self-training (cf. Line 189). Additionally, AnCon further improves the optimality gap by reducing $g^{KL}(w_{0:m})$, which explains the effectiveness of selective temporal consistency. Q3: The impacts of severe distribution shifts typically result in a poorly performing initial model, which can significantly reduce the effectiveness of self-training methods like AnCon. However, as discussed in our response to W3, AnCon successfully improves poorly performing initial model parameters under severe distribution shifts, unlike other self-training methods. Further, following Reviewer fUqB’s suggestion, we performed additional experiments in the highly class imbalance scenario. This setting is significant as effective methods like oversampling are not applicable in self-training, yet they largely impact self-training performance. In the new experiments, we compare AnCon with ELR and vanilla self-training under a heavy-tailed class imbalance with an imbalance ratio of up to 65 times. As shown in Figure R2, AnCon's effectiveness is well-preserved under severe class imbalance scenarios. In summary, we believe AnCon would show promising performances in multiple challenging self-training scenarios. Q4: Kindly see [G4] for the detailed explanation of our rigorous hyperparameter selection procedure and its significant practical implications. We also kindly refer to “Section 4.3.2. Robustness to the choice of hyperparameters” which shows the stable performances of AnCon even under arbitrary choices of hyperparameters. --- Rebuttal 2: Title: Responses to Q5 and Q6 Comment: Q5: We kindly refer to “Section 4.1” for the integration of AnCon with state-of-the-art SFDA technique (NRC) and TTA technique (GCE). We also kindly refer to [G5 in the global response; GLOBAL SOTA] for conceptualizing the state-of-the-art performance levels of considered baselines. Regarding potential benefits, AnCon differs from state-of-the-art methods in handling noisy pseudo labels under distribution shifts. Specifically, NRC filters incorrect predictions based on local consistency, while AnCon uses temporal consistency. Combining NRC and AnCon leverages pseudo labels that are both locally and temporally consistent, resulting in significant performance improvements over NRC or Self-Training + AnCon (cf. Table 1). In addition, GCE reduces the impact of wrong pseudo labels rather than finding them. Applying GCE to AnCon minimizes the effects of potentially wrong but temporally consistent pseudo labels, which can be implied by the performance of GCE + AnCon compared to GCE or Self-Training + AnCon (see Table 1). In summary, AnCon can complement existing state-of-the-art methods by handling noisy pseudo labels fundamentally differently. Q6: We kindly remind Reviewer fUqB that the concept shift is out of the scope of our work as stated in Line 71. Also, we note that addressing concept shifts in the self-training scenario without labels is questionable, as even detecting such shifts without feedback on predictions through shifted labels in a principled manner is impossible (e.g., Lu et al., 2018). - Lu et al. (2018). Learning under concept drift: A review. IEEE T-KDE. Q7: We appreciate the curiosity of Reviewer fUqB about extending AnCon to various neural network architectures and tasks. Indeed, our theory and algorithm for AnCon are broadly applicable as AnCon is independent of specific neural network architectures or dataset structures, unlike methods that rely on batch normalization statistics or random image augmentations. At the same time, being agnostic to architectures and data structures make it inherently hard to make rigorous theoretical statements on the extensibility. Therefore, affirmative conclusions about the extension of AnCon would require large-scale comprehensive experiments with careful design of explorative strategies, which is beyond the scope of this paper. Moreover, even if AnCon performs suboptimally in certain architectures or tasks, this does not invalidate (1) our theoretical contribution of showing how uncertainty-aware temporal consistency improves self-training under distribution shifts and (2) our algorithmic contribution of designing an effective temporal ensemble mechanism without necessitating computationally heavy processes such as additional forward passes or neighborhood searches. In summary, while we acknowledge the potential benefits of further explorations, we believe our current focus provides a solid foundation for understanding AnCon's impact and effectiveness. --- Rebuttal Comment 2.1: Title: Official Comment by Reviewer fUqB Comment: I have carefully reviewed the feedback from other reviewers, considered the author’s rebuttal, and followed the ensuing discussion. I appreciate the authors' thorough responses, particularly their clarifications on W1 and answering my questions. Assuming that the insights from these discussions will be included in the final paper, I recommend the paper for acceptance as it provides interesting insights and has the potential to contribute to the ML community and I will raise my score from 5 to 7. --- Reply to Comment 2.1.1: Comment: Thank you for your careful review and for taking the time to consider our rebuttal and the feedback from other reviewers. We greatly appreciate your acknowledgement of our efforts to clarify W1 and address your questions. We will ensure that the insights from these valuable discussions are thoroughly incorporated into the final version of the paper. Thank you once again for your thoughtful evaluation and support!	null	null	Rebuttal 1: Rebuttal: G1: On the validity of the on-average assumption In Theorem 3.1, we made an assumption that $ \bar{p}(x; c_{0:m}) > 0.5 $, which we argue is not strong because of its dependence on the confidence thresholds $ c_{0:m} $. Specifically, $ \bar{p} $ is measured only for relatively confident predictions (cf. Line 144-145). This means that the assumption can hold by controlling the confidence threshold (cf. $ c_{0:m} $ in Theorem 3.1) at the expense of loosening the upper bound in Eq. (6) as mentioned in Line 156-157. For a concrete example, we have added Figure R1 that explains both (1) the average accuracy can be higher than 50% in the challenging setting where the pseudo label accuracy is below 50% and (2) $ \bar{p} $ can be further increased by increasing the confidence threshold (e.g., select 90th-quantile). G2: Further elaborations of Theorem 3.1 In Theorem 3.1, the convergence holds for the asymptotic region of the number of confident predictions over iterations $ Q(x; c_{0:m}) $, not the number of iterations $ m $; that is, the inputs on which the neural network produce relatively confident predictions infinitely many times as the number of iterations goes to infinity. Further, we remark that the bound monotonically decreases as $ Q(x; c_{0:m}) $ increases. This means that the generalized temporal ensemble can provide high-quality learning signals for self-training in non-asymptotic regions through the “uncertainty-aware” temporal consistency that helps to satisfy the condition $ \bar{p}(x; c_{0:m}) > 0.5 $. Specifically, as shown in our new figures (cf. Figure R3), our generalized temporal ensemble’s accuracy tends to increase by a margin significantly as the number of confident samples increases, being consistent with our theory. We note that this monotonic improvement would not be the case for the temporal ensemble without uncertainty-awareness and vanilla self-training, which highlights the importance of ‘selectivity’ for constructing the temporal ensemble. To clarify the notion of asymptotic convergence and monotonic improvement, we have changed Line 151-152 as follows: “”” The result says that as long as the expected accuracy for relatively confident predictions is at least 50% on average over iterations, $ \bar{f}(x; \theta_{0:m}, w_{0:m}) $ is asymptotically correct on $ x $ such that $ Q(x; c_{0:m}) \rightarrow \infty $ as $ m \rightarrow \infty $. Besides, we remark that the error rate of the generalized temporal ensemble monotonically decreases as $ Q(x; c_{0:m}) $ increases if the iteration on-average accuracy condition holds. “”” Also, in Line 143, we have added “for samples where the neural network tends to be relatively confident during the self-training” after “asymptotically correct.” G3: On performance of AnCon under severe distribution shifts Performance gains over a poorly performing initial parameter through self-training are shown in our extensive experiments. Specifically, in challenging scenarios where the initial model trained on the source domain significantly deteriorates, AnCon significantly improves performance, unlike vanilla self-training. This aligns with our theoretical results in Theorems 3.1 and 3.2. For example, in VisDa-2017 (Table 6), while the initial model accuracy is 38.71%, AnCon and self-training improve it to 71.11% and 67.77%, respectively. Additionally, for Shot, Impulse, and Gaussian corruptions with the most extreme shift intensity of 5, where the initial model achieves accuracies of (3.04%, 1.76%, 2.12%), AnCon achieves (22.56%, 26.56%, 25.85%) (cf. Table 11). This striking improvement, compared to vanilla self-training and ELR, underscores the importance of AnCon's uncertainty-aware temporal consistency scheme. G4: On rigorous hyperparameter selection procedure and its practical implication We perform hyperparameter selection without labels instead of looking at the test performance and selecting the best value which is data snooping and can result in overly optimistic performances that are hard to reproduce. Therefore, even though we found (and were not surprised about) that the found hyperparameters were sub-optimal during the sensitivity analysis, we opted to maintain our realistic hyperparameter selection setting. Another point we should mention is our choice of fixing single hyperparameter values across diverse settings that include 105 numbers of distribution shift scenarios. Of course, even under our aforementioned realistic hyperparameter selection setting, tuning hyperparameters for each scenario could result in better performances. However, we opted to fix the hyperparameter values for all scenarios, considering that in practice the environments (e.g,. Data, distributions, features) change frequently and thus tuning each time is very expensive. By doing so, we believe that we do not report overly optimistic performances of AnCon obtained under settings that are abstracted to the practice. We hope this can resolve Reviewer qtUp’s question on the sub-optimal choice of the hyperparameter value. G5: On performances of baseline methods In this work, we apply AnCon to two baseline methods, NRC and GCE. While their ideas are simple, these methods are frequently cited as achieving state-of-the-art performances in recent literature (cf. Karim et al., 2023 CVPR; Press et al., 2023 NeurIPS; Rusak et al., 2022 TMLR). The basic intuitions behind these baselines—promoting local consistency and reducing the impact of wrong pseudo labels—are dominant principles in SFDA and TTA literature. To the best of our knowledge, no significantly better methods than these baselines exist without including computationally heavy methods such as ensembles. Therefore, we believe AnCon's compatibility with these baselines demonstrates its compatibility with state-of-the-art methods, and including other similar methods would provide only marginal additional insights. Pdf: /pdf/432f58b32b18d4f1a8f41217c3350a6da07f7f72.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Parameterized Approximation Schemes for Fair-Range Clustering	Accept (poster)	Summary: The authors study the fair range clustering problem, where facilities are associated with multiple demographic labels, forming intersecting groups. They impose both lower and upper bounds on the number of cluster centers chosen from each label. For both $k$-median and $k$-means clustering objectives, they present a $1 + \epsilon$ approximation algorithm when the underlying metric space is Euclidean. The key contribution of this work is leveraging the properties of Euclidean metric spaces to improve approximation ratios while maintaining similar running times as for general metric spaces, specifically fixed-parameter tractable (FPT) in parameters $k$ and $\ell$. The authors make use of the techniques and results that are known the literature, but it is still challenging to stitch the pieces together to obtain a solution and formally prove all the claims, which the authors have successfully managed to do. I have verified proofs in sufficient detail and cannot find anything wrong or incorrect. It is possible that I may have missed something. The writing can be simplified by clearly explaining the figures and explicitly stating that Figure 2 applies only to clients. It took me some time to realize that the facility set does not undergo the same transformation, as the coreset applies only to clients. Also it was difficult to understand precisely what the authors refer to as the annular region in Figure 1a (this was only clear after reading Section 4.2, and discretisation of distances). In a nutshell, the approach works by first reducing the high-dimensional space to lower-dimensions, present $1 + \epsilon)$ FPT algorithm in lower-dimensions and show that this solution translates to a $ 1 + O(\epsilon)$ FPT approximation in higher dimensions. Strengths: This work has significant theoretical contributions, offering new insights into a known difficult clustering problem variant, where earlier works have extensively investigated and established the computational complexity of the problem. Weaknesses: Similar to earlier work by Thejaswi et al. (2022), the presented FPT algorithms may not scale practically, given that the exponential factors are large. In theory, dimension reduction and coreset constructions are expected to introduce a minimal $\epsilon$ factor of distortion in distances. However, in practice, creating smaller-sized coresets often requires a larger $\epsilon$, which limits the practical scalability of algorithms. Also the achieved approximation factors in practical applications may be significantly larger than the theoretical claims. Even though the theoretical contributions are good, I would suggest that the authors put an effort to perform (at least some) experimental evaluations when submitting to an applied conference such as NeurIPS. Technical Quality: 3 Clarity: 3 Questions for Authors: The extension from considering only lower bound requirements to including both lower and upper bound requirements is straightforward in the work of Thejaswi et al. 2022. In their work, see Lemma~5.2, which exhaustively lists/enumerates all feasible constraint patterns satisfying the lower bound requirements, and this can be extended to enumerate feasible constrained patterns that satisfy both lower and upper bound requirements. Consequently, all algorithmic findings of diversity-aware clustering (with lower bound requirements) would extend from this adaptation to fair-range clustering (with lower and upper bound requirements), although the authors themselves do not explicitly assert this claim, the extension is immediate. Do you agree with this, or do you hold a different viewpoint? Line 52-54: This statement is not accurate. The reduction presented by Thejaswi et al. (2021) from diversity-aware $k$-median to matroid median problem shows that any algorithm for matroid median can effectively handle the scenario with disjoint facility groups. Consequently, this reduction yields a $7.081 + \epsilon$ approximation for the disjoint facility groups case, as further detailed in Theorem~7.1 of Thejaswi et al. (2024) preprint on ArXiv this also yields a FPT($k$) algorithm with 1 + 2 e^{-1} approximation. Do you hold a different viewpoint on this? Figure 1(a): The caption does not clearly explain the significance of the two circles around the client. It would be beneficial to explicitly specify these details. Are these circles representing the distance defined by the authors in Lines 228-229 on Page 6 (as a consequence of discretisation of distances)? please clarify. Confidence: 5 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: In the broader impact section authors have briefly mentioned the potential social impact of their work. Flag For Ethics Review: ['No ethics review needed.'] Rating: 8 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for the thoughtful comments. We summarize our responses in the following. Q1: Regarding the extension from diversity-aware clustering to fair-range clustering. Response: Thanks for pointing this out. Following your guidance, we found that when $k$ and $\ell$ (i.e., the maximal number of opened facilities and the number of demographic groups) are fixed parameters, it is straightforward to extend an algorithm for diversity-aware clustering to fair-range clustering, based on the method for enumerating feasible constraint patterns given in the work of Thejaswi et al. (2022). We will clarify this in the revised version. Q2: Regarding the reduction to the matroid median problem. Response: Sorry for the incomplete description of related work. Thejaswi et al. (2021) demonstrated that the diversity-aware clustering problem can be reduced to the matroid clustering problem when the demographic groups are disjoint and the sum of lower bounds associated with the groups equals $k$. It was also indicated that this reduction can be extended to the fair-range clustering problem with an $O(k^{\ell-1})$ multiplicative overhead in the running times of the algorithms. We will clarify this reduction and the corresponding approximation results in the part of related work in the revised version. Q3: Figure 1(a): The caption does not clearly explain the significance of the two circles around the client. It would be beneficial to explicitly specify these details. Are these circles representing the distance defined by the authors in Lines 228-229 on Page 6 (as a consequence of discretisation of distances)? Please clarify. Response: In Lines 228-229, we introduce a set of annuli centered at $c_i$ by discretizing the distances from the facilities to $c_i$. Each annulus is defined such that its outer radius is $1+\varepsilon$ times its inner radius. The circles shown in Figure 1(a) represent the outer and inner circles of the annulus involving $f^_i$ (i.e., the facility corresponding to the leader $c_i$). This will be clarified in the revised version. Q4: Regarding the explanation of Figure 2.* Response: Sorry for the unclear presentation. In the revised version, we will include a description of the process illustrated in Figure 2. Additionally, we will enhance the clarity of the data-reduction algorithm by explaining the roles of JL-transform and coreset construction. --- Rebuttal 2: Title: Response to rebuttal Comment: Thank for your responses. I agree with the authors' replies and will update my evaluation accordingly. However, the authors have not addressed the identified weaknesses. If they acknowledge these issues, they should discuss them in the revised version of the paper. If they disagree, I recommend presenting counterarguments to address these concerns. --- Rebuttal Comment 2.1: Title: Thank you Comment: Many thanks for reading our response and appreciation of our work. In the revised version, we will carefully discuss the practical impact of the work according to your comments. On one hand, we will further illustrate the widespread consideration of Euclidean data in practical clustering tasks, underscoring our work's contribution to revealing different approximability of the Euclidean version of the problem, especially in the context of the larger tight ratios in general metric spaces. On the other hand, when a constant loss in the approximation ratio is acceptable, small coresets for $k$-median and $k$-means clustering can be constructed using fast bi-criteria approximation algorithms (such as the ones based on $k$-means++ [1]). By allowing a sacrifice in the approximation ratio, we believe that our coreset-based adaptation of the JL-transform has the potential to accelerate existing heuristics in high-dimensional Euclidean spaces, including those proposed by Thejaswi et al. (2022). [1] Ankit Aggarwal, Amit Deshpande, and Ravi Kannan. Adaptive Sampling for $k$-Means Clustering. In Proc. of APPROX-RANDOM 2009: 15-28	Summary: The paper presents fixed-parameter approximation schemes for the fair-range k-median and k-means problems in Euclidean spaces, parameterized by both the number of facilities and labels. The results improve on existing results, which could only achieve constant-ratio approximation. The main technique used is a data-reduction technique to reduce the dimensionality, combined with an algorithm for low-dimensional spaces. Strengths: 1. The paper presents an FPT APX-scheme for very important clustering problems. 2. The approximation results improve on the current best results. 3. The results are theoretically solid and technical. Weaknesses: 1. The techniques are not novel. 2. The results are purely theoretical, with no experimental results provided. Technical Quality: 3 Clarity: 3 Questions for Authors: Did you consider any other notions of fairness, based on other constraints (e.g., related to clients)? Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: Lack of experimental work. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for the thoughtful comments. We summarize our responses in the following. Q1: Did you consider any other notions of fairness, based on other constraints (e.g., related to clients)? Response: Thanks for the question. For the fair clustering problem where clients are partitioned into different demographic groups and the proportion of each group in each cluster is constrained, it is known that a variant of the algorithm stated in Lemma 3 yields small-size coresets [1]. By replacing the algorithm in Lemma 3 with this variant, one can generalize our data-reduction method (Algorithm 1) to address the clustering problem with the fairness constraint imposed on clients. Consequently, we believe that the ideas in the paper have the potential of being applicable to the client-constrained case. We will add this intuition and related work on the client-constrained fair clustering problem in the revised version. [1] Sayan Bandyapadhyay, Fedor V. Fomin, and Kirill Simonov. On Coresets for Fair Clustering in Metric and Euclidean Spaces and Their Applications. In Proc. of ICALP 2021: 23:1-23:15 Q2: Regarding the novelty of the work. Response: Some aspects of the work are built upon existing methods, such as Johnson-Lindenstrauss transform and the construction of coresets and nets. However, leveraging these well-known techniques to improve upon the previously known constant-factor approximation ratios in Euclidean spaces is non-trivial. To achieve this goal, we give a novel approach for exploring the properties of the Euclidean metric in the context of the fair-range clustering problem. This includes partitioning the solution search space into small cells and carefully balancing the number of cells (which affects the running time) with the distance from each facility opened in an optimum to the center point of the cell it belongs to (which affects the approximation ratio). In our revised version, we will make the ideas that distinguish the work clearer in the introduction. Q3: Regarding the nonexistence of experimental work. Response: Our research focuses on the theoretical aspect of the fair-range clustering problem, demonstrating an upper bound of $1+\varepsilon$ on the parameterized approximation ratio in Euclidean spaces. Considering the significant attention received by the hardness and approximability of the problem [2,3,4], we believe that gaining this new understanding of its approximability is of independent interest. [2] Suhas Thejaswi, Ameet Gadekar, Bruno Ordozgoiti, and Aristides Gionis. Diversity-Aware Clustering: Computational Complexity and Approximation Algorithms. CoRR abs/2401.05502, 2024 [3] Zhen Zhang, Junfeng Yang, Limei Liu, Xuesong Xu, Guozhen Rong, and Qilong Feng. Towards a Theoretical Understanding of Why Local Search Works for Clustering with Fair-Center Representation. In Proc. of AAAI 2024: 16953-16960 [4] Sèdjro Salomon Hotegni, Sepideh Mahabadi, and Ali Vakilian. Approximation Algorithms for Fair Range Clustering. In Proc. of ICML 2023: 13270-13284 --- Rebuttal Comment 1.1: Comment: Thank you for your response. I will keep my score. --- Reply to Comment 1.1.1: Title: Thank you Comment: Many thanks for reading our response and continued support.	Summary: - This paper studies fair range clustering, which aims to ensure that cluster centers are not dominated by specific demographic groups. - It focuses on fair range clustering using the 1-norm and 2-norm distance metrics. - The paper proposes an algorithm with three internal steps: (i) data reduction to low-dimensional space, (ii) obtaining fair centers in the low-dimensional space, and (iii) transforming the centers back to the original high-dimensional space. - The authors theoretically demonstrate that the algorithm can be computed in Fixed Parameter Tractable (FPT) time. Strengths: - The problem considered in this paper allows each center (facility) to include multiple demographics, whereas a previous work considers a single demographic label for each center. - The proposed algorithm can be computed in FPT-time. - The algorithm is theoretically applicable to high-dimensional data. Weaknesses: 1. The writing and presentation are complex, making it difficult for non-experts to follow. It assumes readers are very familiar with fair range clustering. 2. The paper focuses too much on techniques used to derive the algorithms, lacking intuitive explanations about how the algorithm works. 3. The introduction should better justify the necessity of fair range clustering. It should include related works on (conventional) fair clustering [A, B, C] and their key differences to highlight the significance of fair "range" clustering. 4. The data reduction mechanism lacks novelty, appearing to be a direct consequence of combining Lemmas 3, 4, and 5, which were not developed by the authors. 5. The link mapping $\phi$ between low-dimensional space and high-dimensional space, which is a key component of the proposed algorithm, is theoretically valid (through Lemmas 4 and 5), but practical construction methods are not discussed. 6. Numerical analysis is missing. Given existing works on fair clustering [A, B, C] or fair range clustering [D] with numerical results on real data, appropriate experiments are necessary. 7. (Minor) line 451: second -> third, line 454 : third -> fourth [A] Fair Clustering Through Fairlets https://dl.acm.org/doi/pdf/10.5555/3295222.3295256 [B] Fair Algorithms for Clustering https://proceedings.neurips.cc/paper_files/paper/2019/file/fc192b0c0d270dbf41870a63a8c76c2f-Paper.pdf [C] Variational Fair Clustering https://arxiv.org/abs/1906.08207 [D] Fair k-Center Clustering for Data Summarization https://proceedings.mlr.press/v97/kleindessner19a/kleindessner19a.pdf Technical Quality: 3 Clarity: 2 Questions for Authors: 1. What is the intuitive definition of “core set”? 2. What is the role of the core set in data reduction? 3. The authors mention that Thejaswi et al. [2022] showed limits of approximation order in a general metric space (lines 73-77). How is the approximation order improved when considering Euclidean space rather than a general metric space? 4. Is $\tilde{\mathcal{S}^*}$ in line 504 defined? If not, what is its definition? Confidence: 3 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: 1. It is not confirmed that the proposed algorithm can be applied to real scenarios. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for the thoughtful comments. We summarize our responses in the following. Q1: What is the intuitive definition of ''core set''? Response: Thanks for the question. A ''core set'' is a small subset of the client set. For any feasible solution, its costs on the original instance and reduced instance (where the client set is replaced by the core set) are approximately the same. Constructing a core set and using it to reduce the instance can significantly enhance computational efficiency while ensuring that the solutions closely match those obtained from the full client set. We will clarify this in our revised version. Q2: What is the role of the core set in data reduction? Response: In data reduction, constructing a core set helps to reduce the size of the client set: We replace the client set with a smaller core set. This has the following two effects. (1) When invoking Lemma 5 with the client set as input, we can map the instance into a low-dimensional space without significantly altering the distance between each pair of client and facility. Here, the dimension is logarithmically related to the number of clients. By reducing the number of clients using a core set, we can significantly lower the dimension. (2) We construct the solution based on the ''leaders'' (i.e., the clients closest to the facilities opened in an optimal solution) within the client set. Replacing the original client set with the core set allows us to identify these leaders in FPT time. We will clarify the role of the core set in our revised version. Q3: The authors mention that Thejaswi et al. [2022] showed limits of approximation order in a general metric space (lines 73-77). How is the approximation order improved when considering Euclidean space rather than a general metric space? Response: The properties of the Euclidean metric allow us to carefully partition the space. We can thus restrict the solution search space to a more refined range, and thereby break through the lower bound on the approximation ratio that applies to general metric spaces. Specifically, our algorithm partitions the search space into smaller cells, ensuring that each facility opened in an optimum is close to the center point of the cell it belongs to. Consequently, we can identify a nearly-optimal solution by enumerating the subsets of center points of the cells. We will describe this idea in Section 1.1 of the revised version. *Q4: Is $\tilde{\mathcal{S}}^{}$ in line 504 defined? If not, what is its definition?** Response: The notation $\tilde{\mathcal{S}}^$ should be $\tilde{\mathcal{H}}^$, which denotes an optimal solution to $\tilde{\mathcal{I}}$. Sorry for the typo. Q5: Regarding the presentation. Response: Thanks for pointing out the issues with the presentation. We apologize for being unable to response to each issue individually due to the space constraint. We will carefully correct the typos and reorganize the content in the revised version. First, we will clarify the intuitive ideas of our algorithms, including the roles of Lemmata 3, 4, and 5, as well as the partitioning of the solution search space. Second, we will add related work on conventional fair clustering, and underline the significance of fair range clustering by highlighting its important roles in applications where the centers are required to fairly represent the demographic groups. Q6: The data reduction mechanism lacks novelty, appearing to be a direct consequence of combining Lemmas 3, 4, and 5, which were not developed by the authors. Response: JL-transform (Lemmas 4 and 5) has been widely utilized in clustering problems. However, given that most previous works directly use this transform to construct an $O(\log n)$-dimensional space, we think it is somewhat unexpected that this transform, combined with a coreset-construction method (Lemma 3), yields an $O(\log k+\log\log n)$-dimensional space. This allows us to partition the solution search space into sufficiently small cells. Furthermore, given that there are algorithms for constructing coresets for the fair clustering problem where the fairness constraint is imposed on the clients [1], our idea for data reduction has the potential of being applicable to this problem as well. [1] Sayan Bandyapadhyay, Fedor V. Fomin, and Kirill Simonov. On Coresets for Fair Clustering in Metric and Euclidean Spaces and Their Applications. In Proc. of ICALP 2021: 23:1-23:15 Q7: Regarding the practicality of the mapping $\phi$. Response: The coreset-construction algorithm in Lemma 3 runs in linear time, and one can easily trade off the size of the constructed coreset against its approximation guarantee. Moreover, it is built upon random sampling and is simple to implement. Thus, we believe that our coreset-based adaption of JL-transform is quite practical. Q8: Regarding the nonexistence of experiments. Response: In line with recent advancements in hardness and approximability of fair range clustering [2,3,4], our research focuses on theoretical aspects, breaking through the lower bound in general metric spaces and providing the first FPT approximation scheme under the Euclidean metric. Given the widespread consideration of Euclidean data in fair range clustering problems, we believe that gaining such a new understanding of the problem's approximability in Euclidean spaces is of intrinsic value. [2] Suhas Thejaswi, Ameet Gadekar, Bruno Ordozgoiti, and Aristides Gionis. Diversity-Aware Clustering: Computational Complexity and Approximation Algorithms. CoRR abs/2401.05502, 2024 [3] Zhen Zhang, Junfeng Yang, Limei Liu, Xuesong Xu, Guozhen Rong, and Qilong Feng. Towards a Theoretical Understanding of Why Local Search Works for Clustering with Fair-Center Representation. In Proc. of AAAI 2024: 16953-16960 [4] Sèdjro Salomon Hotegni, Sepideh Mahabadi, and Ali Vakilian. Approximation Algorithms for Fair Range Clustering. In Proc. of ICML 2023: 13270-13284 --- Rebuttal Comment 1.1: Title: Thank you for the responses Comment: I appreciate the authors' rebuttal responses. In light of these responses, I will raise the score. However, I suggest further improvements to the presentation, especially for non-experts. Specifically, it would be beneficial to (1) clarify the definition and necessity of fair range clustering in the earlier parts of the paper, (2) provide intuitive explanations of key techniques (e.g., the definition of the coreset, how to find $\phi$), and (3) offer a detailed exposition of Algorithm 2, as mentioned by other reviewers. --- Reply to Comment 1.1.1: Title: Thank you Comment: Many thanks for raising the score and your further insightful guidance. We will carefully improve the presentation in the revised version, making our work more understandable according to your guidance.	Summary: The paper deals with the problem of fair-range clustering in Euclidean metric spaces. In fair-range clustering, one is given a set of clients and a set of possible facilities. Every facility is associated with a subset of $\ell$ many classes. The goal is to pick up to $k$ many facilities such that a given clustering objective is minimized with respect to the chosen facilities as centers under the side constraint that the number of facilities that are associated with a certain class lies $i$ within a given interval $[\alpha_i,\beta_i]$, for all $i\leq \ell$. The clustering objectives considered here are the $k$-Median and the $k$-Means objective. The authors propose FPT $(1+\epsilon)$-approximations for both problems with parameters $k$ and $\ell$. Their approach essentially works by first mapping the input to an Euclidean space of lower dimension and computing a coreset. For such a low-dimensional weighted instance, they give an algorithm that computes a near-optimal approximation on the modified instance. In the end, they translate the solution back to a solution for the original instance by returning the pre-image of the injective mapping from the transformation step. Strengths: This is a well-written and clear paper with a good contribution. There already existed optimal FPT($k$,$\ell$)-algorithms for the two considered problems matching known lower bounds. In this paper, the authors manage to break the barriers for general metric spaces when restricting to Euclidean metric spaces by giving near-optimal $(1+O(\epsilon))$-approximation algorithms for the Euclidean setting. Weaknesses: Apart from the Questions mentioned later, I only have minor comments. I am willing to increase my score to "accept" when addressing the questions. _Comments to the authors:_ - please provide a citation for the results mentioned in the abstract (lines 9-10) - please define $\tau$ and $\ell$ in the preliminaries - are Lemma 1 and Lemma 2 needed somewhere in the main body of the paper? Otherwise, they could be transferred to the appendix - figure 1: please provide an explanation of the different symbols (small circles = clients, squares = facilities?) - l. 171: what do you mean by "distance parameter"? - why is the upper bound stated in equation (2) meaningful? How does it help in bounding $\delta_{\max}^{\rho}$ if it contains $\delta_{\max}^{\rho}$? - how are the annuli guessed if the possible radii depend on the maximal distance within an optimal solution in lines 229,230? When looking at the proof of Lemma 8, it becomes obvious that the value of $\delta_{\max}^{\rho}$ is guessed. Please also provide this information in the text. - In general, is a bit difficult to recognize which are the parts that are guessed in Algorithm 2. If I understood correctly, the rings $A_i$ are guessed (which includes guessing the leader $c_i$, the radius of the annulus, which is based on guessing $\delta_{\max}^{\rho}$, and the set $L_i$), the color coding is done randomly, and the feasible solution of lowest cost is again guessed (lines 15-16 in Algorithm 2). It would be helpful to specifically state which things have to be guessed in the text. - It is not specified how the values are chosen randomly in line 9 of Algorithm 2, resp. lines 249-253 (Uniformly at random?). Please make this more formal. - it does not become entirely clear to me how the feasible solution is chosen in lines 15-16 in Algorithm 2. Are you iterating over all possible subsets of $S$ and only then check whether the subset contains at most $k$ elements? This seems a bit wasteful. Why would it not be enough to choose one facility from every ring? It would be helpful if you write this part in lines 258-259 a bit clearer. _Language, Typos & Layout_ - 112: "number" -> "numbers" - 216: I guess that "see Appendix [...]" belongs in the next line - 223: "denotes" -> "denote" - 229, 230: Why do you use $\\|f-c_i\\|^{\rho}$ instead of $\delta^{\rho}(f,c_i)$ here? - it might increase readability if you restate Theorem 1 where it is proven Technical Quality: 3 Clarity: 4 Questions for Authors: - line 9 of Algorithm 2 assigns every facility an integer at random. This makes your algorithm a randomized algorithm and influences the result of Lemma 9. As Lemma 9 is used in the proof of Theorem 1, Theorem 1 should also mention that this guarantee holds with high probability. Please clarify. - What is the motivation for using first the original Lindenstrauss transform and then the stronger version in the second step? Why do you not need the stronger transform in the first step? Confidence: 4 Soundness: 3 Presentation: 4 Contribution: 3 Limitations: Yes, the authors clearly state the limitations (fixed-parameter tractability with parameters $k$ and $\ell$, restriction to Euclidean metric spaces) in the abstract. In Section 6, they also state considerations to make when using their results for practical applications. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for the thoughtful comments. We summarize our responses in the following. Q1: Regarding the randomness of Algorithm 2. Response: Thanks for pointing this out. The probability that Algorithm 2 yields the desired $(1+\varepsilon)$-approximation solution is the same as the probability that inequalities in Lemma 9 hold. In our revised version, we will modify Theorem 1 and its proof to clarify the randomness of our algorithm and the associated success probability. Q2: What is the motivation for using first the original Lindenstrauss transform and then the stronger version in the second step? Why do you not need the stronger transform in the first step? Response: The motivation for using the original transform in the first step is primarily driven by computational efficiency: Although the stronger transform guarantees that the distance similarity between the original space and its low-dimensional mapping is preserved over a broader range, it involves semidefinite programming and has a higher time complexity. In the first step, we use the union of clients and facilities as the input for the dimension-reduction method, aiming to map the instance to a space whose dimension is independent of $d$ (the dimension of the original space). This mapping needs to preserve the distance between each pair of points in the input set, without considering the points outside this set. Both the original and stronger transforms can achieve this goal. However, we choose the original transform because it has a lower time complexity. In the second step, we use a coreset of size $(k\log n)^{O(1)}$ as the input for the dimension-reduction method, aiming to map the instance to the desired $O(\log k+\log\log n)$-dimensional space. Here, we need to preserve the distance between any point in the coreset and any facility (outside the coreset). Due to the requirement of preserving distances over a broader range than in the first step, we choose the stronger transform in this step. We will elaborate on the above intuition in our revised version to enhance the understanding of Algorithm 1. Q3: Regarding the presentation. Response: We thank the reviewer for pointing out the typos and issues with the presentation. We will carefully correct these in our revised version. We apologize for being unable to response to each typo and presentation issue individually due to the space constraint. Q4: Line 171: what do you mean by ''distance parameter''? Response: The distance parameter denotes the parameter ''$\lambda$'' in Definition 2 and Lemma 6. As this parameter decreases, the constructed net becomes larger, causing our algorithm to take more time, but the opened facilities selected from the net more closely approximate the optimal ones. We will make this clear in the revised version. Q5: Why is the upper bound stated in equation (2) meaningful? How does it help in bounding $\delta^\rho_{\max}$ if it contains $\delta^\rho_{\max}$? Response: We construct annuli centered at the leaders. Since the left-hand side of equation (2) is the maximum radius of the annuli (recall that the distance from each facility in the annulus $A(i,j)$ to the leader $c_i$ is at most $\epsilon(1+\epsilon)^{j}\delta^\rho_{\max}n^{-1}$ and $j\in\\{0,\cdots,\lceil\epsilon^{-2}\log n\rceil\\}$), and the right-hand side denotes the maximum distance among the facilities in $\tilde{H}^$ to their corresponding leaders, equation (2) implies that each facility in $\tilde{H}^$ is involved in one of the annuli. This suggests that enumerating over $j\in\\{0,\cdots,\lceil\epsilon^{-2}\log n\rceil\\}$ to identify an annulus $A(i,j)$ that contains the optimal opened facility $f_i^$ is feasible. We will clarify this in the revised version. Q6: How are the annuli guessed if the possible radii depend on the maximal distance within an optimal solution in lines 229, 230? When looking at the proof of Lemma 8, it becomes obvious that the value of $\delta^\rho_{\max}$ is guessed. Please also provide this information in the text.* Response: We guess the value of $\delta^\rho_{\max}$ by examining the distance between each pair of client and facility. We need to enumerate $n^{O(1)}$ items in this process, which introduces a $n^{O(1)}$ multiplicative overhead in the running time of the algorithm. We will make this clear in the revised version. Q7: Regarding the parts that are guessed in Algorithm 2. Response: Algorithm 2 guesses the rings $A_i$ by enumerating the possible values of $c_i$, $L_i$, $\delta^\rho_{\max}$, and the integer $j\in\\{0,\cdots,\lceil\epsilon^{-2}\log n\rceil\\}$ satisfying $f^_i\in A(i,j)$, iteratively performs color coding and guesses a successful iteration (which exists with constant probability), and selects the solution with lowest cost from the candidate set. We will clarify this in the description of Algorithm 2 in the revised version. Moreover, we will include an algorithm that formally describes how to construct the set $\mathbb{A}$ of possible values for $\\{A_1, \cdots, A_k\\}$, rather than providing it implicitly in the proof of Lemma 8. Q8: It is not specified how the values are chosen randomly in line 9 of Algorithm 2, resp. lines 249-253 (Uniformly at random?). Please make this more formal.* Response: Sorry for the informal presentation. The color of each facility is chosen uniformly at random in step 7. We will make corresponding modifications in the revised version. Q9: Regarding the selection of the feasible solution in lines 15-16 of Algorithm 2. Response: Indeed, merging the sets of candidate opened facilities selected from the $k$ rings and enumerating the subsets of the union $S$ to find feasible solutions is unnecessary. It is sufficient to separately construct $k$ sets of candidates based on the rings and select one opened facility from each set. We will make corresponding modifications in Algorithm 2 and its description. --- Rebuttal Comment 1.1: Comment: Thank you for the detailed response. All my questions are resolved and I will increase my score accordingly. --- Reply to Comment 1.1.1: Title: Thank you Comment: Many thanks for reading our response and your positive rating.	Rebuttal 1: Rebuttal: We greatly appreciate the reviewers for the in-depth reviews, which have significantly helped us in improving our work. Below, we provide detailed responses to the comments.	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
OPUS: Occupancy Prediction Using a Sparse Set	Accept (poster)	Summary: The paper presents OPS, a novel framework for occupancy prediction in autonomous driving. It formulates the task as a direct set prediction problem, using a transformer encoder-decoder architecture to predict occupied locations and classes simultaneously. This approach eliminates the need for explicit space modeling or complex sparsification. The main results of the paper demonstrate that the OPS framework outperforms previous state-of-the-art methods in occupancy prediction on the Occ3D-nuScenes dataset. It achieves superior RayIoU scores, a metric designed to address the overestimation issues of the traditional mIoU metric. The paper also includes an ablation study highlighting the effectiveness of the various strategies incorporated in OPS, such as adaptive re-weighting, consistent point sampling, and coarse-to-fine prediction. These strategies contribute to improved performance, particularly in terms of mIoU and RayIoU. Strengths: - [S1] Clarity: The paper is well-written and easy to follow. The problem formulation, methodology, and experimental results are clearly presented. Overall, the figures are informative and complement the text well. - [S2] Quality: The proposed OPS framework is thoroughly described, and the experimental results on the Occ3D-nuScenes dataset shows merits of the proposed method in terms of RayIoU. The ablation studies further validate the contribution of each component in the framework. Weaknesses: - [W1] Technical soundness: The paper proposes to use Chamfer distance as the main objective function, which is known to be sub-optimal. Although several strategies including FocalLoss, coarse-to-fine refinement have been proposed, it makes the system overly complicated and potentially unfair for comparison. For example, it is unclear whether the baseline methods can benefit from the proposed strategies as well. Please comment this in the rebuttal. - [W2] Limited Evaluation: The experimental evaluation is solely conducted on the Occ3D-nuScenes dataset. While this is a standard benchmark, evaluating the method on additional datasets, such as SemanticKITTI or Waymo Open Dataset, would provide a more comprehensive assessment of its generalizability and robustness. - Reference: [NewRef1] Occ3D: A Large-Scale 3D Occupancy Prediction Benchmark for Autonomous Driving - [W3] mIoU Performance: - [W3.1] Although OPS excels in RayIoU, its performance on the mIoU metric lags behind some dense models. Given that mIoU is a widely used metric in occupancy prediction, addressing this weakness would make the method more appealing to a broader audience. In comparison, RayIoU is only introduced in a recent paper that has not been peer reviewed. - [W3.2] As the paper is focusing on autonomous driving applications, it is unclear whether mIoU performance can cause safety-critical problems for downstream tasks such as behavior prediction and planning. It would be good to discuss this aspect in the rebuttal and next version of the paper. - [W3.3] In Table 3, the reference number for FB-OCC is wrong. - [W4] Lack of Qualitative Analysis: While the paper provides some visualizations, a more thorough qualitative analysis of the predictions would be insightful. Analyzing failure cases, comparing predictions across different classes and distances, and examining the impact of the proposed strategies on the quality of predictions would provide a deeper understanding of the method's strengths and weaknesses. Technical Quality: 2 Clarity: 3 Questions for Authors: Please check the weakness section, especially W1 and W3. Confidence: 4 Soundness: 2 Presentation: 3 Contribution: 2 Limitations: Yes, the limitations have been discussed 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 insightful comments. We have carried out experiments on Occ3D-Waymo, detailed in the global response to all reviewers. Our results underscore the generalizability of our OPS. We have also corrected the reference number for FB-Occ in Tab.3. Below are our responses to other specific concerns: - [W1] Chamfer distance is sub-optimal. As stated in lines 46-52 and Sec.C in the appendix, the Hungarian algorithm is optimal but not scalable for the occupancy task. In spite of the sub-optimal property, Chamfer distance is justified by its computational efficiency and satisfactory outcomes accroding to our experiments. - [W1] Proposed strategies lead to complicated system. We introduce four strategies in total, as shown in Tab.2. The re-weighting losses does not alter model structures. CPS is computationally similar to the sampling scheme in SparseBEV[1]. The coarse-to-fine approach, meanwhile, streamlines the computation in the initial phases. Therefore, these strategies do not complicate the system building on top of SparseBEV. - [W1] Unclear if the baseline methods can benefit from the proposed strategies. - The re-weighted CD loss and CPS are tailored to our set prediction framework and are not directly applicable to other occupancy prediction methods. - The coarse-to-fine scheme is also adopted by CTF-Occ[4] and SparseOcc[2]. However, each method has its uniquely crafted designs, which are not intended for external use. - Regarding the classification loss, our main baselines, SparseOcc[2] and FB-Occ[3], incorporate more complex designs than our re-weighted focal loss. SparseOcc, for instance, integrates focal and Dice losses, while FB-Occ sums up four distinct classification losses. We are not sure if their performances can be improved by simply replacing their focal loss with ours, given the composite nature of their loss functions. - [W1] Proposed strategies lead to potentially unfair comparison. Strategies not exclusively tailored for OPS (CD loss and CPS), have comparable or even more complex alternatives in SparseOcc. In addition, we humbly believe that the entirety of the strategies and other components should be evaluated together for a single approach. Therefore, we respectfully assert that the comparisons are fair. - [W3.1] mIoU vs. RayIoU. - Our mIoU are further enhanced: As detailed in the general response, OPS-L(8f) now achieves 36.14 mIoU, marking a 3.74 improvement over our prior submission and 6 mIoU lead over SparseOcc (8f). The gap between dense and sparse methods has been largely reduced to 3 mIoU. - RayIoU also matters: RayIoU, introduced by SparseOcc[2], has gained acceptance through peer review at ECCV and is utilized in recent literature[2,5,6] and a CVPR workshop[7]. As illustrated in their Fig.4, Fig.5 and Sec. 4.1, the mIoU can be hacked by predicting a thicker surface, a common occurrence with dense methods trained on visibility masks. This could account for the higher mIoU observed in dense methods, despite poorer visualizations. In contrast, RayIoU is not vulnerable to that over-estimation. - [W3.2] Relatively low mIoU performance may cause safety-critical problems. Please refer to our global response. - [W4] More qualitative analysis. We thank the reviewer for the kind suggestion and have incorporated additional analysis into our draft. Here are the key points: - Failure cases: As shown in Fig.3 and Fig.8, a common OPS failure mode is the prediction of scattered and discontinuous surfaces at long distances. Another is the presence of holes in predicted driving surface, a phenomenon also observed in SparseOcc due to the sparsity properties. - Impact of proposed strategies: Tab.4 demonstrates the impact of our proposed strategies. Tab.3, Tab.6 and Tab.7 examine other facts that could affect model performance. Fig.4 Fig.5 and Fig.6 uncover some underlying mechanisms of the proposed OPS. - Predictions across different distances: We report the RayIoU of FB-Occ and OPS at different ranges in the following table. It is evident that OPS demonstrates a more pronounced advantage in nearby areas than at far distances. This could be attributed to the phenomenon pointed out by SparseOcc: dense approaches tend to overestimate the surfaces, especially in nearby areas. \|model\|overall\|0-20m\|20-40m\|>40m\| \|-\|-\|-\|-\|-\| \|FB-Occ\|33.5\|41.3\|24.2\|12.1\| \|OPS-L\|41.2\|49.10\|31.15\|13.73\| - Predictions across different classes: The per-class RayIoU results are presented as follows. OPS outperforms FB-Occ across all classes. The top 5 most improved classes are driving surfaces, other flats, sidewalks, man-made structures, and vegetation, indicating the background categories can benefit most from our model. \|Method\|others\|barrier\|bicycle\|bus\|car\|c.veh.\|motor.\|ped.\|cone\|trailer\|truck\|surface\|flat\|sidewalk\|terrain\|manmade\|vege.\| \|-\|-\|-\|-\|-\|-\|-\|-\|-\|-\|-\|-\|-\|-\|-\|-\|-\|-\| \|FB-Occ\|5\|44.9\|26.2\|59.7\|55.1\|27.9\|29.1\|34.3\|29.6\|29.1\|50.5\|44.4\|22.4\|21.5\|19.5\|39.3\|31.1\| \|OPS-L\|10.9\|46.2\|29.6\|65.5\|58.4\|29.7\|31.1\|35.8\|33.8\|34.7\|52.7\|68.6\|37.3\|35.1\|37.5\|50.1\|43.1\| [1] Sparsebev: High-performance sparse 3d object detection from multi-camera videos, CVPR23. [2] Fully sparse 3D panoptic occupancy prediction, ECCV24. [3] Fb-occ: 3d occupancy prediction based on forward-backward view transformation, arXiv23. [4] Occ3d: A large-scale 3d occupancy prediction benchmark for autonomous driving, Neurips24. [5] CascadeFlow: 3D Occupancy and Flow Prediction with Cascaded Sparsity Sampling Refinement Framework. [6] Panoptic-FlashOcc: An Efficient Baseline to Marry Semantic Occupancy with Panoptic via Instance Center, arXiv24. [7] The Autonomous Grand Challenge at the CVPR 2024 Workshop.	Summary: This paper focuses on the sparsity property in occupancy prediction, given that most voxels are occupied. In order to reduce computation costs on empty voxels, this paper introduces a set prediction paradigm to explicitly model sparsity. OPS, the proposed framework, utilizes the encoder-decoder architecture to jointly reconstruct and classify point clouds. Chamfer distance is used as the supervision. For experiments, OPS outperforms state-of-the-art occupancy methods by 4.9 RayIoU. Strengths: 1. Good motivation. The introduction of sparsity as the representation of scenes is with a great motivation. 2. Novel architecture. Using the point cloud + set prediction approach for occupancy is novel, elegant, and makes sense. 3. Strong performance. The proposed OPS with RayIoU achieves significantly better performance and inference speed compared to the current state-of-the-art. Although the authors mentioned the current limitation is the need for longer epochs, it is not a major issue, as most set-prediction methods face this challenge. Weaknesses: 1. Error citation. I think the "sparseocc" mentioned frequently in this paper should be [1], instead of [2]. [1.] Fully sparse 3D panoptic occupancy prediction [2.] SparseOcc: Rethinking Sparse Latent Representation for Vision-Based Semantic Occupancy Prediction 2. Is there a typo in Line 245? The query count for OPS-tiny is only 0.6k, while for OPS-S, OPS-M, and OPS-L, the query counts are as high as 12K, 24K, and 48K respectively. 3. If the query count is as high as 48K, self-attention would not be able to handle such a large query size. How did the authors manage to do this? The design details are not elaborated on. 4. Since the authors have replaced the basic representation of occupancy with point cloud, they should discuss the differences with point cloud forecasting tasks, such as 4D-Occ [3] and ViDAR [4], especially ViDAR paper which also constructs point clouds from visual images. Discussions on [3] and [4] are suggested to be included in the main paper. [3.] Point Cloud Forecasting as a Proxy for 4D Occupancy Forecasting [4.] Visual Point Cloud Forecasting enables Scalable Autonomous Driving. Technical Quality: 3 Clarity: 2 Questions for Authors: See Weakness. Confidence: 4 Soundness: 3 Presentation: 2 Contribution: 2 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 the valuable feedback and feel honored for being approbated on our motivation, novelty and performances. Below, please find our responses to the weaknesses: - Error citation. Thanks for bringing this to our attention. We have thoroughly reviewed the cited works and identified an incorrect citation in line 71, which has been duly corrected. In the remaining instances (lines 35, 88, 92, 122, 239, 243, 268, 274, and Tab.1), we have confirmed that the correct paper[1] has been cited. - Typos in line 245. We appreciate the reminder and have made the corrections. The query numbers for OPS-S, OPS-M, and OPS-L are indeed 1.2K, 2.4K, and 4.8K. The small number of queries is a key factor for the fast inference speed of OPS. More detailed configurations of different models can be found in Tab.5 in the appendix. - Discussions on point cloud forecasting tasks. We have included comparisons between OPS and works[2,3] in the appendix. Regrettably, due to page limits, we were unable to incorporate this discussion into the main text. [1] Fully sparse 3D panoptic occupancy prediction, ECCV24. [2] Point cloud forecasting as a proxy for 4d occupancy forecasting. CVPR23. [3] Visual point cloud forecasting enables scalable autonomous driving, CVPR24. --- Rebuttal Comment 1.1: Title: Response Comment: Thanks for the authors' rebuttal. I will maintain my rate. --- Reply to Comment 1.1.1: Comment: We sincerely thank the reviewer for maintaining the positive assessment of this paper. We will include the details mentioned in the rebuttal in the revised version.	Summary: This paper considers the problem of occupancy prediction from multi-view images for autoonomous driving. One of the main challenges in the occupancy prediction task is the high computational demand incured by discretizing the 3d space. Traditional methods typically predict the occupancy of each voxel individually and assign it a semantic class. The key idea of this work if to reduce computational burden by formulating occupancy prediction as a set prediction task. The authors employ the Chamfer distance in the loss term and propose a novel point sampling process, termed Consistent Point Sampling, to make the SparseBEV decoder applicable. In experiments on the Occ3d-nuScenes dataset, their method demonstrates superior performance with regard to the RayIoU metric while being computationally more efficient than the state-of-the-art methods. Strengths: I believe the proposed general approach is interesting and the work seems well evaluated (to the extent that I can judge). The paper is largely well-written and seems easily understandable for someone working in that space. I also want to applaud the authors for committing to making their code publicly available. Weaknesses: This topic seems to be traditionally mainly covered in Computer Vision venues. And while the contribution of this work may also be of interest to the ML community, the writing needs to provide more background and context to be more accessible to the NeurIPS community. E.g. the readers at NeurIPS may not be familiar with the broader tasks and some more specialized architectures such as SparseBEV. The work contains numerous writing and grammar issues. Some examples are mentioned in the minor comments section below. However, the work should undergo a careful proofread in its entirety. Some of the mathematical notation seems off. E.g. {$\mathbb{P}^g,\mathbb{C}^g$} is denoted as a set containing two sets while it is treated as a set cotaining tuples of point locations and semantic classes. Some more minor math notation issues are given in the comments below. The first bullet point in the contribution list is somewhat broad and focuses more on the properties of the method. It does not mention some of the new key technical ideas underlying the method such as CPS. I would recommend fully rephrasing the contribution list and focusing on what is technically new (or at least for the first time applied in the context of occupancy prediction). Simply mentioning that there are several strategies that are introduced to boost performance makes the reader wonder what these strategies are. Minor Comments: * l.3 "discretize 3D environment" -> "discretize the 3D environment" * l.33/34 "Alternative sparse latent representations has been explored" -> "Alternative sparse latent representations have been explored" * l. 37 What is meant by "necessitating complex intermediate designs and explicit"? Complex architecture? * l.42/43 "Our OPS eliminates" should be "Our method eliminates" or "OPS eliminates" * l.48 "unable to tacke tremendous voxels" maybe something like "unable to handle a very high number of voxels" * l.69/70 "all our model configurations easily surpass all prior arts" -> "all our model variants easily surpass all prior work". * l.83 "This task recently becomes a foundational perception task in autonomous driving" -> "This task has recently become a foundational perception task for autonomous driving" * Consider using $N_g$ instead of $N^g$ for the number of occupied voxels in ground truth. The latter looks like $N$ to the power of $g$. Same for all other occurrences of $g$ in a superscript. * If $\mathbf{c}^g$ denotes a semantic class, it should not be defined as element of $\mathbb{R}$. This is not necessarily wrong but may be confusing as it is likely represented as an integer if not a one-hot vector? * Using $N$ to represent the number of semantic classes may be confusing given that $N^g$ is used to represent the number of occupied ground truth voxels. Technical Quality: 3 Clarity: 2 Questions for Authors: * From the writing, it is not really clear to me, whether some of the competing methods are also set based? I would not see why the Hungarian algorithm would be needed otherwise. If those methods are set-based, the writing might clarify this. From the abstract it seems like competing approaches perform classification of each voxel individually. * In the right most panel of fig 2, why is "Consistent Point Sampling" written in a green box while everything else is in grey? * What is meant by a set of learnable queries? Are these simply the queries that would be used in the traditional transformer except that they are now learned? Confidence: 3 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: To the extent that I can understand it, the authors have properly addressed the limitations of this work. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for constructive suggestions and feedback. We will release our full code and models once the paper is made public. Below are our responses to specific comments: - Writing issues. We greatly appreciate meticulous suggestions on grammar and notations, which indeed help elevate paper's quality. We have revised our draft accordingly and will conduct a comprehensive proofreading to ensure clarity and precision. - Providing more background and context. Thanks for the advice. We will enrich the background descriptions in sections of related works, methodology, and appendix. For specified architectures in SparseBEV[1], we will provide explanations to guide readers to the original paper, delineating which modules are newly designed and which are adapted from SparseBEV. - Details about compting methods. As mentioned in lines 74-75, OPS is the first set-based approach for occupancy prediction. All baselines perform voxel-wise classification, resulting in predictions that are inherently ordered according to the physical locations of voxels, thus differing from set-based methods whose predictions are unordered. We will provide further clarification on this distinction in Section 4.2. - Why the Hungarian algorithm would be needed. The primary challenge of a set-based approach lies in associating the unordered prediction set with ground-truths. As detailed in lines 46-52, while the Hungarian algorithm is effective for association in object detection, it is not suitable for occupancy prediction, which motivates development of OPS. - Consistent Point Sampling in Fig.2. We highlight the "consistent point sampling" in Fig.2, as it is newly introduced in OPS. Other components, such as "adaptive mixing," are inherited from SparseBEV[1]. We will clarify this in the caption. - Learnable queries. The learnability of queries in Transformers is contingent upon the specific application. In standard Transformers for tasks such as machine translation, queries are derived from the input data and are not learnable. However, in many Transformer-based models (e.g., SparseBEV[1] and DETR[2]), queries are initialized randomly and are optimized during training. They enable the model to dynamically focus on various aspects of the input data. [1] Sparsebev: High-performance sparse 3d object detection from multi-camera videos, CVPR23. [2] End-to-end object detection with transformers, ECCV20. --- Rebuttal Comment 1.1: Comment: I appreciate the authors responses and continue to see the work on the accept side although I am not yet sure I will be able to raise my scores as some of the suggested changes are hard to judge without a full new review. --- Rebuttal 2: Comment: We sincerely appreciate the reviewer's time and effort in offering insightful feedback and keeping a positive assessment of this paper. Due to the NeurIPS policy, we are unable to provide the reviewer with our revised version of this paper. We feel regretful for the inconvenience, but have indeed incorporated the reviewer's valuable suggestions into our new draft.	Summary: This paper introduces OPS, a novel framework that treats occupancy prediction as a set prediction problem. The approach leverages a transformer encoder-decoder architecture and Chamfer distance loss to align predicted and ground-truth points. The model improves performance with strategies like coarse-to-fine learning, consistent point sampling, and adaptive re-weighting. OPS achieves superior RayIoU and faster FPS compared to state-of-the-art methods on the Occ3D-nuScenes dataset. In summarize, this paper is technically sound and shows strong and convincing performance on a commonly used dataset. Strengths: 1. This paper formulates occupancy prediction as a sparse set prediction problem, which is technically sound and interesting. Indeed, predicting a sparse set introduces several efficiency and memory benefits, as long as a significant performance improvement. 2. Several proposed techniques, including coarse-to-fine learning, consistent point sampling, and adaptive re-weighting, are effective and have the potential to generalize to even other methods. Also, these techniques are validated by extensive ablation studies on the nuScenes dataset. 3. Experiments are carefully designed and adequate ablation studies are provided, though only on the nuScenes split. Weaknesses: 1. In a high level, the proposed method is similar to SparseOcc, although implementation details can be different. 2. Although this method has strong performance on Occ3D-nuScenes dataset and several ablation studies are provided, I am still concerned that this method can overfit to this relatively small dataset. Can authors provide further evidences on the Occ3D-Waymo split? Technical Quality: 3 Clarity: 3 Questions for Authors: 1. Can authors provide results on the Waymo split? Or at least can authors provide a convincing explanation why such experiments cannot be conducted on Waymo? As far as I know, Occ3D-Waymo is on a par with Occ3D-nuScenes in terms of data scale, thus computation should not be a significant concern. 2. Can authors comment on the difference between SparseOcc and OPS? I'd like to understand both the detail differences and the high-level differences. Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: No potential negative societal impact is detected by reviewer. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for the insightful comments. Please refer to the global response to all reviewers for our experiments on Occ3D-Waymo. In summary, the proposed OPS demonstrates its generality with superior mIoU results and fast inference speed. Below, we discuss the differences between SparseOcc and OPS: - View perspective of occupancy prediction. The fundamental difference lies in the perspective of occupancy prediction. As depicted in lines 33-37 and 122-130, all previous methods, including SparseOcc, treat occupancy prediction as a standard classification task. OPS, however, pioneers a set prediction viewpoint, offering a novel, elegant, and end-to-end sparsification approach, as pointed out by Reviewer Zbj3. - Multi-stage vs. end-to-end sparsification procedure. SparseOcc generates sparse occupancy by gradually discarding voxels through multiple stages. The discarding of empty voxels at early stages is irreversible, leading to obvious cumulative errors, as detailed in lines 276-280 and illustrated in Fig.3. Conversely, OPS circumvents complex filtering mechanisms by directly predicting a sparse set, resulting in more coherent outcomes. - Detailed model design. In terms of a more detailed perspective of the structure, there are also many differences such as - Query number: In Occ3D-Nuscene, SparseOcc necessitates 32K queries in its final stage. OPS, by comparison, operates with a mere 0.6K-4.8K queries for occupancy prediction, capitalizing on its flexible nature and contributing to its fast inference. - Coarse-to-fine procedure: SparseOcc's coarse-to-fine strategy involves progressively filtering empty voxels and subdividing occupied voxels into finer ones. In contrast, OPS interprets coarse-to-fine as the escalation in number of predicted points across stages. - Sampling process: The feature sampling in SparseOcc is deterministic, with each query anchored to a specific location. In contrast, the query locations are learnable in OPS. Therefore, we propose consistent point sampling to dynamically and efficiently gather features from input images. - Learning objective: Our learning target encompasses predicting both semantic classes and occupied locations, simultaneously. The latter is a new objective introduced by OPS, achieved through a modified Chamfer distance loss. In conclusion, we believe that SparseOcc and OPS are markedly different in both fundamental and detailed designs. --- Rebuttal Comment 1.1: Comment: Thank you for providing these responses! They address my questions and I'll keep my positive evaluation of this paper. --- Rebuttal 2: Comment: We sincerely thank the reviewer for the positive evaluation of this paper. We will further improve our revised version based on the reviewer's comments.	Rebuttal 1: Rebuttal: We sincerely thank the reviewers for their constructive comments and are privileged by their praise regarding our motivation (5U1g, TqRW, Zbj3), novelty (Zbjs), writing (TqRW, iFoi), and experiments (5U1g, Zbj3). We'd like to first mention that OPS performances have further improved since our last submission, as detailed in the table below. In a nutshell, all OPS(8f) variants achieve substantial boosts in mIoU (+2.64 to +3.90) and RayIoU (+1.77 to +2.27). These improvements result from tuning hyperparameters and fixing post-processing, without altering any network structures. All our codes and checkpoints are well-organized and will be released once the paper is made public. \|\|mIoU\|RayIoU\|newmIoU\|newRayIoU\| \|-\|-\|-\|-\|-\| \|OPS-T(8f)\|30.6\|35.9\|33.24(+2.64)\|38.40(+2.50)\| \|OPS-S(8f)\|31.2\|37.3\|34.24(+3.04)\|39.07(+1.77)\| \|OPS-M(8f)\|31.7\|38.0\|35.60(+3.90)\|40.27(+2.27)\| \|OPS-L(8f)\|32.4\|38.9\|36.14(+3.74)\|41.17(+2.27)\| Experiments on Occ3D-Waymo. We'd like to clarify the comments about Occ3D-Waymo from reviewers 5U1g and iFoi. Initially, our draft did not evaluate OPS on the Occ3D-Waymo, as it is not commonly used as a standard benchmark for vision-centric approaches. The only vision-based method we found with reported results on this dataset is the Occ3D paper, which evaluates BEVDet, TPVFormer, BEVFormer, and the newly proposed CTF-Occ. During the rebuttal phase, we trained the OPS-L (1f) on 20% of the dataset for a fair comparison with these baselines. Despite not fine-tuning the training configurations, OPS-L already achieves 19.0 mIoU at 8.5 FPS, outperforming the baseline methods. We are grateful for the reviewers' suggestions and will incorporate the results into our revised draft. \|\|mIoU\|RayIoU\|FPS\|general\|vehicle\|bicyclist\|ped.\|sign\|tfc.light\|pole\|Cons.cone\|bicycle\|motorcycle\|building\|vegetaion\|Treetrunk\|road\|sidewalk\| \|-\|-\|-\|-\|-\|-\|-\|-\|-\|-\|-\|-\|-\|-\|-\|-\|-\|-\|-\| \|BEVDet\|9.88\|-\|-\|0.13\|13.06\|2.17\|10.15\|7.80\|5.85\|4.62\|0.94\|1.49\|0.0\|7.27\|10.06\|2.35\|48.15\|34.12\| \|TPVFormer\|16.76\|-\|-\|3.89\|17.86\|12.03\|5.67\|13.64\|8.49\|8.90\|9.95\|14.79\|0.32\|13.82\|11.44\|5.8\|73.3\|51.49\| \|BEVFormer\|16.76\|-\|4.6\|3.48\|17.18\|13.87\|5.9\|13.84\|2.7\|9.82\|12.2\|13.99\|0.0\|13.38\|11.66\|6.73\|74.97\|51.61\| \|CTF-Occ\|18.73\|-\|2.6\|6.26\|28.09\|14.66\|8.22\|15.44\|10.53\|11.78\|13.62\|16.45\|0.65\|18.63\|17.3\|8.29\|67.99\|42.98\| \|OPS-L\|19.00\|24.7\|8.5\|4.66\|27.07\|19.39\|6.53\|18.66\|6.41\|11.44\|10.40\|12.90\|0.0\|18.73\|18.11\|7.46\|72.86\|50.31\| Safety concerns. Our OPS-L(8f) has achieved a state-of-the-art RayIoU of 41.17, outperforming the previous sparse model SparseOcc[1] by 6.07 and the dense model FB-Occ[2] by 7.7. The mIoU gap between sparse and dense methods is also reduced from 8.5 (in SparseOcc) to 3.0. However, as noted by Reviewer iFoi, the implications of this gap on safety remain ambiguous. This concern is particularly pertinent in the context of autonomous driving, and we would like to clarify this as follows: - Risks of dense predictions. The biggest issue of dense predictions is the huge discrepancies between evalutation metrics and real-world scenarios. As shown in Fig.1 in the attached one-page pdf, evaluation metrics only consider voxels within the camera visiblity mask, which is derived from camera parameters and ground truth. Detailed precedure for generating the mask can be found in Occ3D[3]. However, in real-world applications, we can only produce view mask based on camera intrinsics and extrinsics, failing to filtering out over-estimated voxels. From this example and and Fig.3 in our paper, dense methods can misidentify occupied voxels, even close to the ego vehicle. These errors are overlooked during evaluation but pose significant safety hazards in real-world scenarios. In contrast, OPS suffer much less from this issue as it does not over-estimate occupancy. - The depth errors of OPS is much smaller than FB-Occ. In Fig.2 in the attached one-page pdf, we compare the depth errors of FB-Occ and OPS along camera rays. OPS demonstrates lower depth errors across all scenes, despite its relatively low mIoU performance. Given the significance of the first occupied voxel for safety, OPS's precision in this regard enhances safety rather than detracting from it. This aligns with Fig. 9 in SparseOcc, which shows that training FB-Occ without the camera visiblity mask results in poorer mIoU but lower errors. In conclusion, while it is necessary to minimize the mIoU gap between sparse and dense methods, our analysis indicates that mIoU might not fully represent potentially hazardous situations. Therefore, it would be more rational to take both mIoU and RayIoU into consideration for the occupancy task. [1] Fully sparse 3D panoptic occupancy prediction, ECCV24. [2] Fb-occ: 3d occupancy prediction based on forward-backward view transformation, arXiv23. [3] Occ3d: A large-scale 3d occupancy prediction benchmark for autonomous driving, Neurips24. Pdf: /pdf/0926e6bbbed1e89aedb5de967419d6f7f3bde497.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Learn more, but bother less: parameter efficient continual learning	Accept (poster)	Summary: The paper presents a new parameter-efficient method for continual learning in LLMs. The method focuses on two aspects of continual learning: (1) Catastrophic forgetting and (2) Forward transfer. To address catastrophic forgetting the gradient update of the current task is performed on the orthogonal space of previous tasks. To address forward transfer, they propose to initialize the new SVD parameters of the current task using a combination of previous tasks via learned coefficients. The method is tested on two benchmarks with three task orders. An ablation is provided for each proposed component. The method is compared to another parameter-efficient method for CL, variations of the proposed method, some basic baselines (MTL, standard finetuning), and few previous CL methods on standard architectures. Strengths: - Unlike most methods which focus on forgetting, the method addresses forward transfer as well. - The method shows improvement in accuracy over a recent parameter-efficient method. - Ablation and analysis of the proposed components and hyperparameters are provided. Weaknesses: - Despite that forgetting is one of the main aspects addressed by the paper, it is not evaluated and no forgetting metric is reported. - Some very related works are missing [1,2]. - Some design choices/observations are not clear, see the questions section. - Minor: Paper needs proofread. Suggestions for a few improvements are below: - L149: “since the the” - Section 3.1: A description of O-LoLA is missing in the baselines section - L 84 description of triplet could be provided here for clarity. - 3 rows (out of 4) from Table 3 are already presented in Table 2 - Since the parameters of previous tasks are kept frozen, I am not sure whether forgetting is the right terminology or one should use interference (since forgetting is avoided by design somehow) [1] Yu, Jiazuo, et al. "Boosting continual learning of vision-language models via mixture-of-experts adapters." Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2024. [2] Liang, Yan-Shuo, and Wu-Jun Li. "InfLoRA: Interference-Free Low-Rank Adaptation for Continual Learning." Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2024. Technical Quality: 3 Clarity: 3 Questions for Authors: - Is the training performed in two stages? One for determining sensitivity parameters and one for training the task? - Do you assume that the task identity is not available at the test time? If yes, is the input image at the test time forwarded to the sum of the SVD of all tasks? - In Table 3, it is not clear to me why NLNB -CL is better than L-CL and B-CL, any thoughts on that? - Do the same observations in Table 3 hold for the other benchmark? - Figure 3 shows that excluding Sigma leads to better performance, I am wondering what could be the reasons behind this and why you don’t consider doing this in your proposed approach. - How is your method compared with the mentioned works above? Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: Limitations and societal impact are not discussed. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your detailed feedback on our paper. We have thoughtfully addressed your insights and concerns, and hope our responses offer the necessary clarity on the issues raised. > Q1: Training stage Thanks for your interest. Yes, first we initialize the SVD parameters using sensitivity-determined important parameters for the new task (injecting knowledge), then fine-tuning the new task in orthogonal subspaces. > Q2: Task identity not available at test time? If yes, is the input image at the test time forwarded to the sum of the SVD of all tasks? Thank you for raising the concern. (1) Yes, task identity is not available at test time. (2) Inputs are forwarded through the whole model, including previously learned SVDs. We will make it clear in the subsequent revision. > Q3: Performance of NLNB-CL, L-CL and B-CL Thanks for your interest in this observation. As we discussed this result in section 3.3, NLNB-CL, while neither initializes nor employs gradient projection, performs slightly better on average testing accuracy but important to note that it does NOT achieve the best performance in any specific task order. - Inherent adaptive capabilities: pre-trained model with low-rank SVD matrices may have inherent adaptive capabilities or rely on other compensatory mechanisms, making performance more stable on average. This stability might lead to slightly better average testing accuracy compared to L-CL and B-CL. - Orthogonal subspace in B-CL: it preserves previous tasks' subspaces, retaining knowledge from previous tasks but somehow hindering optimization for new tasks, leading to suboptimal performance. - Knowledge transfer in L-CL: it emphasizes knowledge transfer, potentially disrupting previously learned subspaces, which may affect results. > W4.4 \& Q4: Table 3 Thank you for raising the concern. No, Table 3 does not hold for the other benchmark. The reason we showed Table 3 separately is to compare each component (stage) clearly. We will remove Table 3 to avoid confusion due to repeated information in Table 2. > Q5: About excluding Sigma Thanks for your interest. Excluding Sigma and Including Sigma are different initialization strategies. Since the initialization of LB-CL idea is to learn previous tasks' important subspaces, constructed by triplets, if without $\boldsymbol{\Sigma}_i$, only doublets $\{\boldsymbol{U}_i,\boldsymbol{V}_i\}$ cannot fully represent these subspaces. We consider excluding Sigma as an initialization strategy, which can be used as an improvement strategy in implementation. We will clarify this in the revision. > W2 \& Q6: Compare with the mentioned works above Thank you for pointing out these related works. We appreciate the opportunity to compare our method with them. - Model Focus: [1] proposes a CL framework for a specific vision-language model, pre-trained CLIP, with Mixture-of-Experts (MoE) adapters. [2] proposes a LoRA-based continual learning method for a pre-trained Vision Transformer (ViT). However, our approach is for large language models and not a specific large language model. - Method: - [1] uses MoE to dynamically activate the most related experts (adapters) by routers for a task, but the number of experts $N_{E}$ in the vision-language model is predefined and fixed, limiting flexibility and potentially affecting learning new tasks when none of the experts have the required knowledge. However, our approach uses a low-rank SVD matrix per task, learning tasks separately and mitigating forgetting. - [2] algorithm not only stores previous LoRA parameters but also additionally stores gradient subspaces of previous tasks. Our approach initializes new task subspaces using previous SVD matrices without storing extra components, making it more memory-efficient. Also, large pre-trained models mainly fine-tune within a specific low-rank subspace, encapsulating crucial model update directions. - Dataset: [1] and [2] use image datasets, while our approach is applied to text (natural language) datasets. While [1] and [2] provide CL methods to vision-language models, our method offers a scalable and effective approach to CL in large language models, proven in NLP tasks. We are committed to including these related works and comparisons in the subsequent revision. > W1: Evaluating forgetting and its metric Thank you for mentioning this important aspect. We followed existing continual learning methods by evaluating model's performance primarily by average testing accuracy, which provides a good measure of how well the model performs on all tasks. In subsequent revisions, we will include additional metrics such as forward transfer score, backward transfer score, and forgetting metrics to offer a more thorough understanding of the model's behavior in CL. > W4.1: Typo Thanks for pointing out it. We will correct the typos in the subsequent revision. > W4.2: Description of O-LoLA in baselines section Thanks for pointing out this point. We will describe it in the subsequent revision, such as "O-LoRA: incrementally train new tasks in an orthogonal subspace while fixing the LoRA matrices of previous tasks." > W4.3: Description of triplet Thanks for mentioning this point. We will describe triplet in the subsequent revision in L 84, such as "a singular value and its corresponding vectors". > W4.5: About catastrophic forgetting Catastrophic forgetting occurs when a neural network learns new tasks, inadvertently overwriting or conflicting with knowledge of earlier tasks thus reducing performance. This is critical in continual learning, as it undermines the principle of consistently accumulating knowledge without negatively impacting prior learning. We compared NLNB-CL (only keeps SVD matrices of previous tasks frozen) with LB-CL. Results show performance degradation in NLNB-CL when learning new tasks, highlighting the need to address both forgetting and interference. --- Rebuttal Comment 1.1: Title: Official comment by Reviewer qwD9 Comment: Thank you for your response. Some of my concerns have been addressed. I encourage the authors to consider the points raised by all reviewers in the revised version. I am leaning towards keeping my original score. --- Reply to Comment 1.1.1: Comment: Thank you for considering our responses. We are happy some of our answers were satisfying, and we promise that we will gladly incorporate the valuable and constructive comments raised by all reviewers in the revised version. We are also pleased to offer further clarification to make sure your remaining concerns are resolved.	Summary: This paper introduces LB-CL, a continual learning algorithm designed to tackle the issues of catastrophic forgetting and forward knowledge transfer. The approach integrates orthogonal low-rank SVD decomposition and sensitivity-based parameter initialization. The orthogonal subspace learning component addresses catastrophic forgetting by ensuring the SVD decompositions of different tasks remain orthogonal. The sensitivity-based initialization enhances forward transfer by optimizing parameter initialization weights. Comprehensive experiments across multiple representative datasets demonstrate that LB-CL outperforms many existing methods. Strengths: The paper introduces a novel approach that combines sensitivity-based knowledge transfer with orthogonal subspace learning, a unique method in the context of continual learning for LLMs. The methodology is rigorously developed and supported by comprehensive experimental evaluations, demonstrating the effectiveness of LB-CL against existing state-of-the-art methods. The experimental results robustly support the claims, showing that LB-CL outperforms state-of-the-art methods on standard continual learning benchmarks. Weaknesses: 1. The paper does not sufficiently clarify the advantages and necessity of the proposed SVD decomposition over existing methods like LoRA. 2. The paper does not provide experiments to demonstrate the sensitivity of the method to the order of tasks. 3. The paper does not address whether the classification head is distinguished by task-ID during inference. 4. The paper's experimental section lacks a thorough comparison with other common initialization methods, which makes it difficult to assess the superiority of the proposed initialization strategy. 5. The computational complexity and scalability of maintaining orthogonal subspaces for a growing number of tasks are not addressed. As the number of tasks increases, the computational overhead may become prohibitive. Technical Quality: 2 Clarity: 3 Questions for Authors: Could you provide more details on why SVD decomposition is preferred over LoRA and what specific advantages it offers? Have you tested the sensitivity of LB-CL to the order in which tasks are presented? How might task order impact the performance of the method? How does the method perform when tasks are highly similar and distinguishing features overlap? Does the orthogonality constraint still effectively prevent forgetting in such cases? During inference, does the model require the task-ID to be known? If so, how does this affect the practicality and flexibility of LB-CL? The choice of rank in the low-rank SVD decomposition significantly impacts performance. How is this rank chosen optimally and how sensitive is the method to this hyperparameter? Confidence: 4 Soundness: 2 Presentation: 3 Contribution: 2 Limitations: * Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your constructive feedback on our paper. We truly appreciate the time you invested in the review. We have carefully considered your insights and addressed the highlighted concerns. We hope our responses provide clarity on the matters raised. W1 & Q1: About advantages and necessity of the proposed SVD decomposition preferred over LoRA Thanks for your interest. SVD decomposition offers key advantages: (1) singular values are important for identifying the relationship between singular vectors in the orthogonal matrices, evaluating the importance of triplets ($\{\boldsymbol{U}_i,\boldsymbol{\Sigma}_i,\boldsymbol{V}_i\}$) efficiently, while $\boldsymbol{A}$ and $\boldsymbol{B}$ of LoRA are not orthogonal, making the doublets $(\{\boldsymbol{A}_i,\boldsymbol{B}_i\})$ dependent with each other and discarding the doublets can result in greater variation from the original matrix. (2) SVD matrix easily evaluates the importance of its components, making it more flexible, for example, SVD only masks singular values for pruning and maintains singular vectors, while LoRA may prune all elements if it is measured as unimportant, hindering reactivation. We will highlight this comparison in the subsequent revision. W2 & Q2 & Q3: Sensitivity to task order Thank you for your question. We have tested LB-CL's sensitivity to different task orders in original version of our paper. Table 2 (page 7) shows average testing accuracy for 3 different task orders in each CL benchmark. Let's revisit results on the standard CL benchmark for clarity: *Task Order 1:* dbpedia$\rightarrow$amazon$\rightarrow$yahoo$\rightarrow$agnews *Task Order 2:* dbpedia$\rightarrow$amazon$\rightarrow$agnews$\rightarrow$yahoo *Task Order 3:* yahoo$\rightarrow$amazon$\rightarrow$agnews$\rightarrow$dbpedia \| Method \| Order 1 \| Order 2 \| Order 3 \| \|------------\|-------------\|-------------\|-------------\| \| LB-CL \| 76.9% \| 76.5% \| 76.8% \| Results indicate a moderate sensitivity to task order. Achieving task order-invariance is challenging in continual learning, as the order of tasks can affect model performance. For example, learning Task A before Task B might yield different results compared to learning Task B before Task A. Q4 & Q5: Perform when similar tasks and overlapping features, and whether prevent forgetting? Thank you for raising this comment. (1) Our approach uses weighted triplets to transfer knowledge. When previous tasks are highly similar with distinguishing overlapping features for the new task, these tasks' important triplets for the new task are also similar. We use weighted scores for these triplets, constructing the new SVD matrix accordingly. (2) In such cases, the orthogonal gradient subspace is the intersection of these weighted triplets orthogonal subspaces, making the new task gradient orthogonal update to effectively prevent forgetting. W3 & Q6 & Q7: During inference, does the model require task-ID to be known? Thanks for mentioning this point. No, during the inference, we don't require task-ID. We use explicit instructions or demonstrations during training, injecting knowledge into the new SVD matrix, enabling the model to generalize well and handle unseen tasks efficiently. We are committed to emphasizing this in our subsequent revision. Q8: Choice of rank in low-rank SVD decomposition and how sensitive is the method to rank? Thanks for your interest. In Table 4 of original version of our paper (page 9), we compared average testing accuracy for different ranks of the low-rank SVD matrix. Let's revisit results for clarity: \| r-dim \| Order1 \| Order2 \| Order3 \| Std. \| \|------------\|------------\|-----------\|-----------\|-----------\| \| 2 \| 76.7 \| 77.2 \| 75.2 \| 0.85 \| \| 4 \| 77.0 \| 76.8 \| 75.9 \| 0.48 \| \| 8 \| 76.9 \| 76.5 \| 76.8 \| 0.17 \| \| 16 \| 77.4 \| 76.0 \| 75.5 \| 0.80 \| \| Std \| 0.25 \| 0.44 \| 0.60 \| \| It shows that in our scenarios, increasing rank does not significantly improve performance, and differences between ranks 2 and 16 are not significant. In our experiments, we used rank 8 for its smallest standard deviation, indicating consistent performance across different orders. W4: Comparison with other common initialization methods Thank you for your valuable feedback. We acknowledge the importance of thoroughly comparing our proposed initialization strategy with other common methods in continual learning to better assess its effectiveness. In our experiments, we compared our initialization strategy with a standard random initialization, using NLNB-CL as a baseline. This approach involves freezing SVD matrices of previous tasks and using a new randomly initialized SVD matrix for new tasks. This comparison highlighted our method's improvements. We are committed to providing a thorough evaluation of different initializations in subsequent revision, such as model-agnostic meta-learning. W5: Computational complexity and scalability of maintaining orthogonal subspaces Thanks for your insightful comment. As the number of low-rank SVD matrices grows, we merge updates into the initial parameters to mitigate GPU memory inflation, maintaining computational feasibility and preventing excessive memory usage. While our approach has shown effectiveness in empirical evaluations, its performance and scalability with a large number of tasks, such as hundreds, need further study. We will further focus on optimizing techniques and improving scalability to ensure practical use in extensive continual learning applications. --- Rebuttal Comment 1.1: Title: Official Comment by Reviewer aBm6 Comment: Thank you for the positive response. Most of my doubts have been addressed. Therefore, I will keep my original rating. --- Reply to Comment 1.1.1: Comment: Thank you for checking our responses. We’re glad that most of your concerns have been addressed. We are also more than happy to make more clarifications that could address any remaining concerns and potentially increase the score.	Summary: This paper proposes the Learn More but Bother Less Continual Learning (LB-CL) algorithm for Continual Learning (CL) of Large Language Models. Unlike previous research, this paper introduces the idea of using SVD-based low-rank matrices to inject knowledge learned from previous tasks into new tasks, thereby enhancing plasticity during the CL process. Additionally, it suggests a method for learning in an orthogonal subspace to prevent forgetting of previous tasks. Experimental results on various text classification datasets demonstrate that the proposed algorithm outperforms existing algorithms. Furthermore, various ablation studies and analyses experimentally show the role and effectiveness of each component of the proposed algorithm. Strengths: The strengths of this paper are as follows: 1. The paper is well-written and easy to read overall. In particular, the explanation of the proposed algorithm in Section 2, "Generalization and Forgetting Tradeoff of Low-rank Finetuning," and Section 2.1 is seamlessly integrated, making it easy to understand the motivation and ideas behind the proposed algorithm in a natural flow. 2. The idea of Knowledge Extraction and Injection using SVD-based low-rank matrices adapters in CL to utilize knowledge from previous tasks for learning new tasks is novel and innovative. 3. The proposed algorithm demonstrated superior performance compared to existing algorithms in experiments conducted on various text classification benchmark datasets. 4. The extensive ablation studies and analyses experimentally validated the role and effectiveness of each component of the proposed algorithm, making this section particularly interesting to read. Weaknesses: LB-CL is motivated by O-LoRA and proposes a similar idea (Section 2.2: Training in Orthogonal Subspaces). Although the proposed algorithm achieves state-of-the-art performance in various experiments, the performance improvement over the previous SOTA algorithm, O-LoRA, is not very substantial (e.g., an average improvement of 1.3% on standard CL benchmarks and 0.4% on a large number of tasks). While LB-CL introduces additional ideas for knowledge transfer, this might increase the overall cost of the algorithm. Therefore, to verify the superiority of LB-CL over O-LoRA, it is necessary to compare the computation costs of these algorithms (e.g., training time, number of training parameters, or FLOPS). Additionally, I have identified the following corrections that need to be made while reading the paper: 1. Line 192: It seems that Eq.5 should be corrected to Eq.7. 2. Line 224: It would be beneficial to include a brief explanation of O-LoRA under the 'Baselines' section. Technical Quality: 4 Clarity: 3 Questions for Authors: I find LB-CL proposed in this paper is somewhat novel. However, due to the similarity with the existing algorithm in certain aspects and the lack of significant performance improvement compared to the existing algorithm, I believe additional experiments and analysis are needed to properly validate the merits of the proposed idea. Please check the Weakness Section for more details. Confidence: 4 Soundness: 4 Presentation: 3 Contribution: 3 Limitations: There is no potential negative societal impact of this paper. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your appreciation and excellent summary of our work. We also appreciate the time and effort you dedicated to reviewing our research. We have addressed your questions and concerns below: > W1: Line 192: It seems that Eq.5 should be corrected to Eq.7. Thanks for your correction. Yes, Eq.5 should be corrected to Eq.7. > W2: Line 224: It would be beneficial to include a brief explanation of O-LoRA under the ’Baselines’ section. Thanks for your suggestions. We will include the explanation of O-LoRA should be briefly explained in the 'Baselines' section, such as "O-LoRA: incrementally train new tasks in an orthogonal subspace while fixing the LoRA matrices of previous tasks." in the subsequent revision. > Q: Computation cost comparison Thanks for your insightful suggestions. Exp.Details: We conduct computation cost comparisons on 4 NVIDIA A6000 GPUs and compare training costs between O-LoRA and LB-CL on task order 1 from the standard CL benchmark with T5-large model. \| Method \| GPU Memory \| Num of training params/task \| \|------------\|----------------\|---------------------------------\| \| O-LoRA \| 24.82 GB \| $r(m+n)$ \| \| LB-CL \| 28.28 GB \| $r(m+n)+r$ \| Discussion: - The GPU memory footprint of the two methods is quite close. - For the number of training params, we compare the trainable params within one layer. $r$ is the SVD matrix rank and LoRA rank, $m$ is the input dimension of the layer, and $n$ is the output dimension of the layer. Since $r \ll \min(m, n)$, the number of training params of two methods is also close. - LB-CL implementation computation cost is slightly more than O-LoRA. First, the orthogonal gradient update itself takes extra cost. Second, our code implementation computation cost is mainly incurred by DeepSpeed, a deep learning optimization library developed by Microsoft designed to train large-scale models efficiently. While we use DeepSpeed's `ZeRO stage 2' for efficient memory management, it currently does NOT support extracting gradients during training, as noted on their GitHub page. This limitation requires us to write an additional gradient computation module for orthogonal gradient update, increasing training costs. We plan to optimize our code implementation to reduce these costs. Additional merits: ROUGE (Recall-oriented Understudy for Gisting Evaluation) is a set of metrics designed to evaluate the quality of summaries by comparing them with reference summaries, which are widely used in natural language processing (NLP) tasks. ROUGE scores measure the overlap between the predicted and reference summaries, indicating how well the model-generated summaries capture the essential content of the reference summaries. We compare Average ROUGE-L scores (measures the longest common subsequence between the predicted and reference summaries, capturing sentence-level structure similarity) between O-LoRA and LB-CL on the standard CL benchmark: \| Method \| Order 1 \| Order 2 \| Order 3 \| \|------------\|-------------\|-------------\|-------------\| \| O-LoRA \| 0.7868 \| 0.7759 \| 0.7902 \| \| LB-CL \| 0.8169 \| 0.7994 \| 0.8090 \| It shows that the ROUGH-L scores of LB-CL achieve performance improvements across all three task orders of the Standard CL benchmark compared to O-LoRA, demonstrating the effectiveness of LB-CL. Furthermore, the following table presents the average accuracy in Order 1 with different numbers of seed samples, which illustrates that LB-CL is more flexible and can achieve higher accuracy. We ultimately chose 8 seed samples in the original version of our paper because the variance across the 3 task orders was the least, as shown in Figure 4 of the original version of our paper (page 8). \| # Seed Sample \| 4 \| 8 \| 16 \| 64 \| \|-------------------\|---------\|---------\|----------\|----------\| \| LB-CL \| 76.78% \| 76.90% \| 77.16% \| 77.32% \| We greatly appreciate your insightful feedback. Based on your valuable suggestions, we will include this computation cost analysis and provide a more detailed comparison of computation costs with other different algorithms. Additionally, we will incorporate the additional merits as discussed and include additional metrics such as the forward transfer score to offer a more thorough understanding of the model's behavior during continual learning in the experimental section of the subsequent version. --- Rebuttal Comment 1.1: Comment: Thank you for providing the author response. Almost all of my concerns have been addressed, so I keep my initial score 'weak accept'. --- Reply to Comment 1.1.1: Comment: Thank you for reviewing our responses. We appreciate your feedback and are glad that we could address almost all of your concerns. If you have any remaining questions or need further clarification, we are more than willing to provide additional clarification.	Summary: This paper presents a novel approach to continual learning for large language models (LLMs). The proposed method, LB-CL, incorporates parameter-efficient tuning using low-rank subspace learning and orthogonal subspace projection to mitigate catastrophic forgetting. The study leverages incremental SVD-based low-rank matrix parameters for fine-tuning LLMs across a sequence of tasks. Comprehensive evaluations on benchmark datasets demonstrate the superiority of LB-CL over existing state-of-the-art methods in continual learning. Strengths: 1. The use of incremental SVD-based low-rank matrix parameters and orthogonal subspace projection do address key challenges in continual learning such as catastrophic forgetting and efficient knowledge transfer. 2. The method is rigorously evaluated on multiple benchmark datasets, providing strong empirical evidence of its effectiveness. The baseline compared with this paper includes the latest papers published in 2024. 3. The paper includes an in-depth analysis of parametric knowledge transfer dynamics, initialization strategies, and the impact of seed samples on model performance, contributing to a deeper understanding of continual learning in LLMs. Weaknesses: 1. The paper does not provide open access to the code and datasets used, which may hinder reproducibility and wider adoption of the proposed method. 2. The method in this paper is similar to O-LoRA [1] and has some improvements over O-Lora. This paper claims that "O-LoRA does not explicitly address knowledge transfer across different tasks." However, there is no specific evaluation in the experimental part of this paper to prove that the improvement of this paper on O-LoRA can improve "knowledge transfer across different tasks". 3. In the past, there have been some continual learning methods based on orthogonal subspaces in non-LLM fields, such as [2] and [3]. This paper does not point out the core differences between this method and these previous methods. Is this method just an application of past methods in the fields of LLM and LoRA? [1] Wang, Xiao, et al. "Orthogonal subspace learning for language model continual learning." arXiv preprint arXiv:2310.14152 (2023). [2] Chaudhry, Arslan, et al. "Continual learning in low-rank orthogonal subspaces." Advances in Neural Information Processing Systems 33 (2020): 9900-9911. [3] Farajtabar, Mehrdad, et al. "Orthogonal gradient descent for continual learning." International Conference on Artificial Intelligence and Statistics. PMLR, 2020. Technical Quality: 3 Clarity: 3 Questions for Authors: see Weaknesses Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: see Weaknesses Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We sincerely appreciate your thorough review as well as constructive feedback. Your comments have been extremely helpful. We have carefully addressed each of your concerns and provided detailed answers to your questions below: > W1: About open access to the code and datasets We strongly agree with the importance of reproducibility and accessibility of our experiments and appreciate your suggestion. We have shared our code and datasets via an anonymized link with the Area Chair in a separate comment to maintain anonymity during the review process, per NeurIPS author response guidelines, which will be made public ultimately. > W2: About specific evaluation on the improvement due to "knowledge transfer across different tasks" Thank you for raising this comment. To specifically demonstrate the importance of knowledge transfer, we have conducted a detailed analysis of the influence of each component of our approach—initialization (knowledge transfer) and orthogonal gradient update—on overall performance in the original version of our paper. Table 3 presents the average testing accuracies under three scenarios: - (1) No initialization (no knowledge transfer) and no orthogonal gradient update, called NLNB-CL: This baseline scenario helps establish the effectiveness of our basic model without any enhancements for knowledge transfer or gradient management. - (2) Only initialization (only knowledge transfer), called L-CL: In this scenario, we focus on the impact of knowledge transfer. The results show an improvement in average testing accuracy, indicating that initializing new tasks with knowledge from previous tasks helps the model learn more effectively. - (3) Only orthogonal gradient update, called B-CL: This scenario isolates the effect of the orthogonal gradient update mechanism. The results demonstrate how managing gradient directions reduces interference between tasks, leading to better retention and performance. These three different scenarios demonstrate the importance of individual ingredients, which can show our approach improves the knowledge transfer across different tasks, compared to O-LoRA. > W3: About core differences between this method and these previous continual learning methods based on orthogonal subspaces in non-LLM fields? Is this method just an application of past methods in the fields of LLM and LoRA? Thank you for mentioning this point. We are happy to clarify the core differences between our method and previous methods and explain why our approach is not merely an application of past methods but a tailored solution for parameter-efficient continual learning in large language models (LLMs). We list the core differences in the following discussion: Replay-based Approach in [2]: - Method: [2] (Chaudhry et al.) use a memory buffer to store previous task data and replay it during the training of new tasks. It divides a random orthogonal space into several subspaces and allocates these subspaces one-to-one to each task with pre-defined orthogonal projections. - Limitations: Storing and replaying previous data can become impractical for large-scale models due to memory constraints and data privacy concerns. - Our Approach: We do not store any previous data, thereby ensuring data privacy and making our method more scalable for LLMs. Instead, we leverage the inherent low-rank structure of the model to manage orthogonal subspaces without relying on data replay. Gradient Storage in [3]: - Method: [3] (Farajtabar et al.) propose Orthogonal Gradient Descent (OGD), which stores a set of gradient directions in memory for previous tasks and projects new task gradients onto these stored orthogonal directions. - Limitations: Storing gradient directions for large-scale models is memory-intensive and impractical, especially as the number of tasks increases. - Our Approach: We avoid storing previous task gradients. Instead, we utilize low-rank subspaces to project new task gradients. This method is more memory-efficient and suitable for parameter-efficient continual learning in LLMs. In summary, both methods mentioned ([2] and [3]) involve storing either data or gradients, while our work addresses the unique challenges of parameter-efficient continual learning in LLMs by avoiding data and gradient storage, leveraging low-rank approximations, and ensuring data privacy. Our work is not just an application of past methods in the field of LLM and LoRA. We believe these core differences highlight the innovation and practicality of our approach. We will highlight these differences in the subsequent version. --- Rebuttal 2: Title: Please check authors' rebuttal Comment: Dear reviewer, Please check authors' rebuttal they have made the effort to respond to your concerns. AC	Rebuttal 1: Rebuttal: Dear Reviewers, We greatly appreciate your insightful feedback and valuable suggestions. We have provided specific responses to each reviewer’s questions separately. We sincerely thank you for your contributions to improving our work. If there are any further concerns or queries, we are fully prepared to address them. Thank you for your time and effort.	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Mutli-Armed Bandits with Network Interference	Accept (poster)	Summary: The paper explores regret minimization in multi-armed bandits subject to interference. At each time, the learner assigns one of A treatments to each of the N arms. The observed per-arm response is subject to interference – ie, it depends on the assignments of all the other arms. This work studies the setting of s-sparse interference, where only the assignment of s "neighbors" of the arm affect its outcome. The paper's main theoretical contribution is to use discrete Fourier analysis to rewrite this problem as a linear bandit, then solve that bandit using tools from the linear bandits literature. An explore-then-commit algorithm is proposed that achieves a high-probability regret bound of (T A^s)^(⅔), with only logarithmic dependence on N. Strengths: This paper provides a novel formulation of bandits-with-interference as a linear bandits problem using discrete Fourier analysis. The problem is well-motivated by e-commerce applications, and the methods developed are to my knowledge novel. The paper is well-written, and provides thorough exposition of the results. Weaknesses: It took me a long time to realize that the effects were being estimated on a per-subset basis – ie, that chi^{a_i}(B(n)) is an indicator vector for the subset a_i intersected with the neighborhood of n. Originally I thought that chi^{a_i}(B(n)) =1 for all subsets of a_i, so I was very confused why we didn't have to worry about dependence among the entries of chi. If the authors can think of any way to clarify the exposition, I would greatly appreciate it. This is probably obvious to someone who is more familiar with Boolean Fourier analysis, but your readers may not be. This paper is very well-written. One thing that was missing from the exposition was an explanation of what the Fourier analysis buys us in this setting. What did the Fourier approach allow you to do in this problem that was not available using previous methods (for example, methods people have applied to combinatorial bandits)? From reading your appendices, I think the answer might be that the orthogonality of the basis functions makes it easy to bound the precision of theta. If you could clarify this it would help your method be adopted by a wider audience. Technical Quality: 4 Clarity: 3 Questions for Authors: I'd like to make sure I understand the notation in this paper. Could the authors please provide, for a small toy example, numerical examples of the following vectors from Algorithm 1? $\bf{a_i}$ in Line 2, $\bf{\chi}(\bf{a_t})$ in Line 3, $\bf{\chi^{a_i}}(\mathcal{B}_n)$ in Line 5. This paper makes a novel contribution of translating the "MAB-with-interference" problem to a linear bandits problem using Fourier analysis. I don't understand why you can't then use existing solutions from the linear bandits literature to solve your problem, and take regret rates from there, instead of rederiving the rates for your own algorithm. Could you please clarify why you cannot apply the linear bandits results mentioned in the introduction to your problem? Confidence: 4 Soundness: 4 Presentation: 3 Contribution: 3 Limitations: The model in the paper is extremely general: a unit's outcomes are dependent on the assignments of all of its neighbors, with no lower-order structure. As a result, the performance of the algorithm scales exponentially in the degree s. In reality I would expect the outcome to depend on lower-order interactions than s. I wonder if the authors have considered what would happen if they allowed the degree of the graph to exceed the order of interactions in the potential outcomes function, as in [1]. In this case a single assignment would give you information on multiple lower-order interaction coefficients. I imagine this would improve the performance of your algorithm significantly in the case where d << s, but the problem will get harder to analyze because the X vectors in your algorithm will now have correlations among the A^s elements of a single row. This will make bounding the singular values of X more difficult. If you have space, I would love to see some discussion of how applicable your Fourier Analysis techniques are to these types of stronger modeling assumptions on the potential outcomes. [1] Cortez, Mayleen, Matthew Eichhorn, and Christina Yu. "Staggered rollout designs enable causal inference under interference without network knowledge." Advances in Neural Information Processing Systems 35 (2022): 7437-7449. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Weaknesses: _It took me a long time to realize that the effects were being estimated on a per-subset basis – ie, that chi^{a_i}(B(n)) is an indicator vector for the subset a_i intersected with the neighborhood of n. Originally I thought that chi^{a_i}(B(n)) =1 for all subsets of a_i, so I was very confused why we didn't have to worry about dependence among the entries of chi. If the authors can think of any way to clarify the exposition, I would greatly appreciate it. This is probably obvious to someone who is more familiar with Boolean Fourier analysis, but your readers may not be._ Thank you for helping us improve the exposition of our paper! We provide a simple example of (a) binary action embeddings and (b) the corresponding Fourier embeddings below. We will also revise the paper to reflect this example. $\textbf{Binary action embedding}$. Consider $N$ units with 2 arms ($\mathcal{A} =2$), and a network graph $\mathcal{G}$ such that each unit $n$ is connected to one other unit, i.e., $\mathcal{G}$ has maximum degree 2. An action $\mathbf{a} = (a_{1}, \ldots a_{N}) \in \\{0,1\\}^N$, will induce the binary embedding $\mathbf{v}(\mathbf{a}) = (v(a_1), \ldots v(a_N)) \in \\{-1,1\\}^N$ where $v(a_i) = 1$ if $a_i$ is 1 and -1 if $a_i = 0$. For example, if $\mathbf{a} = (0,1,1 \ldots 1)$, then $\mathbf{v}(\mathbf{a}) = (-1,1,\ldots,1)$. $\textbf{Fourier embedding}$. For any subset of units $ S \subset [N]$, the Fourier character $\chi_{S}(\mathbf{v}(\mathbf{a})) = \prod_{i \in S} v(a_i)$. For instance, if the action $\mathbf{a} = (0,1,1 \ldots 1)$ as above, and the subset $S = \\{1,2\\}$, the Fourier character $\chi_{\\{1,2\\}}(\mathbf{v}(\mathbf{a})) = v(a_1) \times v(a_2) = -1$. The vector of Fourier characteristics $\boldsymbol{\chi}(\mathbf{a}) = (\chi_{S}(\mathbf{v}(\mathbf{a})) : S \subset N) \in \\{-1,1\\}^{2^N}$ is the concatenation of all Fourier characters for all subsets. $\textbf{Fourier coefficient}$. Since each unit $n$ is only connected to one other unit $m$, unit n's neighborhood $\mathcal{N}(n) = \\{n,m\\}$ for a unit $m \neq n$. For unit $n$, the blocks $\mathcal{B}(n)$ are the indices of $\mathbf{v}(\mathbf{a})$ corresponding to treatments of units in $\mathcal{N}(n)$. For our network graph $\mathcal{G}$, $\mathcal{B}(n) = \\{v(a_n), v(a_m)\\}$. The subsets $S \in \mathcal{B}(n) = \\{\phi, \\{n\\}, \\{m\\}, \\{n,m\\} \\}$ correspond to the non-zero coefficients of unit n's Fourier coefficient $\boldsymbol{\theta}_{n} \in \mathbb{R}^{2^{N}}$. _This paper is very well-written. One thing that was missing from the exposition was an explanation of what the Fourier analysis buys us in this setting. What did the Fourier approach allow you to do in this problem that was not available using previous methods (for example, methods people have applied to combinatorial bandits)? From reading your appendices, I think the answer might be that the orthogonality of the basis functions makes it easy to bound the precision of theta. If you could clarify this it would help your method be adopted by a wider audience._ The Fourier basis provides a natural sparse linear representation of the network interference which is not easily done in other bases. To see this, we continue the example from the point above. Since $\boldsymbol{\theta}_{n}$ is 4-sparse, the reward $r_n (\mathbf{a}) = \langle \boldsymbol{\theta}_n, \boldsymbol{\chi} (\mathbf{a}) \rangle$ for unit $n$ can be represented using 4 Fourier characters: $\\{\chi\_{\phi}, \chi\_{n}, \chi\_{m}, \chi\_{\\{n,m\\}} \\}$. This representation captures sparsity unlike a 'one-hot' representation where the reward for unit $n$ can be represented as $r_n (\mathbf{a}) = \sum\_{\mathbf{a}' \in \\{0,1\\}^N}r_n(\mathbf{a}') \mathbf{1}[\mathbf{a} = \mathbf{a}']$. This one-hot basis also linearly expresses the reward but requires $2^N$ indicator basis vectors to do so. It is precisely this sparse linear representation induced by the Fourier basis that allows our bounds to scale with $2^s$ rather than $2^N$. Questions: _This paper makes a novel contribution of translating the "MAB-with-interference" problem to a linear bandits problem using Fourier analysis. I don't understand why you can't then use existing solutions from the linear bandits literature to solve your problem, and take regret rates from there, instead of rederiving the rates for your own algorithm. Could you please clarify why you cannot apply the linear bandits results mentioned in the introduction to your problem?_ We note that once we have mapped the network bandit problem into the corresponding Fourier basis, we still do not directly have a standard linear bandit problem. In particular, we are consider $N$ separate, simultaneous linear bandit problems (one for each unit), each with $\mathcal{A}^s$ possible actions. An additional aspect of our analysis is the aggregation of information over the various units to produce an estimate for the global average reward function. --- Rebuttal Comment 1.1: Comment: Thank you for the detailed response.	Summary: The paper addresses the challenge of online experimentation in the presence of network interference, which is common in applications like e-commerce and clinical trials. The authors propose a multi-armed bandit (MAB) problem where a learner assigns actions (e.g., discounts) to units (e.g., goods) over fixed and known rounds to minimize regret while considering the interference across units. However, naively applying canonical MAB methods (e.g., the upper-confidence-bound algorithm) will lead to regret with the exponential dependence on the number of units. The main challenge of the paper is the exponentially large action space (each unit has \|A\| actions and thus \|A\|^n in total per round). The sparsity structure of the interference (each unit can only be affected by at most s neighboring units) implies that the effective action space for each unit can be a lot smaller. The paper designs an encoding scheme and an algorithm based on this observation. They show that the optimal regret in both $T$ and $\|A\|$ can be obtained. Strengths: I think the paper proposes an interesting problem to study. The problem is practical, well-motivated and mathematically elegant.The sparsity structure is also common and reasonable to assume. I enjoy reading the paper and learning about the problem. The transformation to the linear space of functionals is interesting. It leads to the use of statistical bounds in high-dimensional statistics to be applied, which gives tight regret bounds. I also like the use of LASSO to identify the interference strucuture. I believe this method may be of independent interest. The algorithm and the theoretical results are presented clearly. The proof is written carefully and easy to read. Weaknesses: Although the formulation is interesting, the algorithm design and analyses seem quite standard. After transforming to the functional space, it becomes the MAB problem with effectively $\|A\|^s$ arms. The ETC algorithm and the analysis of the estimation error as well as the regret have been studied in the literature. I wonder if the formulation alone is sufficient as the contribution of the paper. Technical Quality: 3 Clarity: 3 Questions for Authors: The paper takes an agnostic approach to the network structure. This is the strength of the algorithm. However, I wonder if there is room for the network structure. For example, it doesn't seem possible for the algorithm to incorporate some network information such as clusters and stars. Is it possible to adapt the algorithm to certain graphs? ETC is known to be not rate-optimal. I wonder why the authors don't use LinUCB algorithmsin linear bandit at the first place. The problem can be viewed as linear bandit with a very large space, correct? In Step 10 of Algorithm 1, how can the optimization problem be solved in practice given the large space? Confidence: 5 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: See Questions. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Weaknesses: _Although the formulation is interesting, the algorithm design and analyses seem quite standard. After transforming to the functional space, it becomes the MAB problem with effectively $A^s$ arms. The ETC algorithm and the analysis of the estimation error as well as the regret have been studied in the literature. I wonder if the formulation alone is sufficient as the contribution of the paper._ We believe there are several main contributions to our paper outside of the formulation, which we enumerate below. - First, as mentioned in the reviewer’s comment, the Fourier embedding of the unit-specific rewards is non-obvious and hasn’t been considered before in related literature. - Second, once we have performed the transformation using the discrete Fourier transform, the problem is not just a MAB instance with $A^s$ arms, but rather $N$ simultaneous multi-armed bandit instances, each having $A^s$ arms. Thus, an additional step we must take in our argument (and a step that isn’t considered in more classical approaches to ETC) is that we must aggregate our confidence sets for unit-specific reward functions into a corresponding confidence set for the global reward. - Third, we also provide a sequential elimination style algorithm which can obtain improved dependence on the time horizon $T$ in the regret bound. In particular, this style of algorithm gets the same dependence on $T$ as a UCB algorithm would. Questions: _The paper takes an agnostic approach to the network structure. This is the strength of the algorithm. However, I wonder if there is room for the network structure. For example, it doesn't seem possible for the algorithm to incorporate some network information such as clusters and stars. Is it possible to adapt the algorithm to certain graphs?_ In our paper, we consider a minimal assumption setting in which all we know is a bound on the size of the neighborhood of each unit. We opt not to make additional structural assumptions on the network (e.g. clusters, stars, etc.) for the sake of simplicity and generality. We believe that better regret rates may be able to be achieved by making structural assumptions (for instance, in this case we may be able to regress against low-degree polynomials in the Fourier space), but this is outside of the scope of the paper. _ETC is known to be not rate-optimal. I wonder why the authors don't use LinUCB algorithms in linear bandit at the first place. The problem can be viewed as linear bandit with a very large space, correct?_ In the setting of unknown network structure (Section 5 of our paper), the given dependence on the time horizon $T$ is optimal (i.e. no algorithm can generally achieve dependence better than $O(T^{2/3})$). See [1] for details, as the authors construct a lower bound. In the setting of known network interference (Section 4 of our paper), we actually provide a sequential-elimination algorithm (Algorithm 3 in Appendix D) that obtains optimal regret dependence on the time horizon T (a rate of $O(T^{1/2})$). While we could additionally consider a UCB-style algorithm, this would likely be more difficult to analyze, and wouldn’t improve the regret rate, at least with respect to the time horizon $T$ (sequential elimination and LinUCB achieve the same rate). We re-emphasize that, even after mapping to the frequency space, we still are not in a vanilla linear bandit problem — we are actually in a setting where there are $N$ simultaneous, related bandit instances. _In Step 10 of Algorithm 1, how can the optimization problem be solved in practice given the large space?_ Computing the optimal action is equivalent to just finding the maximum in a large list (a trivial optimization problem for modern computers). We note that at this point in the algorithm there are no constraints on the selected action. [1] Botao Hao, Tor Lattimore, and Mengdi Wang. High-dimensional sparse linear bandits. Advances in Neural Information Processing Systems, 33:10753–10763, 2020. --- Rebuttal Comment 1.1: Comment: Thanks for the detailed response. I don't have further comments and remain positive of the paper. --- Reply to Comment 1.1.1: Comment: Thanks for the response. We believe we have addressed the primary concerns mentioned in the review. Is there anything else we can clarify to improve the score?	Summary: The paper investigates a multi-armed bandit problem on a set of units that affect the rewards of each other. A trivial solution will have an exponential regret in the number of units, so using sparsity assumptions on the affecting neighborhood, the authors present an algorithm with regret that is only exponential in the sparsity coefficient. The authors present algorithms both for the case that the affecting neighborhood is known to the agent and the case that it is unknown. Strengths: * The paper presents and solves a useful problem in practice * The theory is sound and the methods are original for network MAB, specifically learning the orthonormal coefficients is clever Weaknesses: On the one hand, Algorithm 1 performs well only when $N$ is very large (otherwise its better to use Algorithm 3), but it also has a running time of $\Omega(N)$, so it seems bad either way. Not sure why the focus is not on Algorithm 3 instead. Technical Quality: 4 Clarity: 3 Questions for Authors: * it seems you did not use the correct format for the submission (as their are no line numbers), make sure you correct this * in the definition of "Linear Fourier expansion", should be $S \subset$ instead of $S \in$, right? * In your algorithms, can you clarify the running time of finding the minimizing coefficient vector? * In Theorem 4.1, should be $\mathcal{A}$ instead of $A$? Confidence: 4 Soundness: 4 Presentation: 3 Contribution: 3 Limitations: The authors properly address the limitations of their work. Flag For Ethics Review: ['No ethics review needed.'] Rating: 8 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Weaknesses: _On the one hand, Algorithm 1 performs well only when $N$ is very large (otherwise its better to use Algorithm 3), but it also has a running time of $\Omega(N)$, so it seems bad either way. Not sure why the focus is not on Algorithm 3 instead._ We chose to focus Section 4 on Algorithm 1 due to its simplicity and its similarity to the algorithm in the unknown interference structure case. We agree that Algorithm 3 likely offers a bound on regret in most parameter settings. For the final draft, we have added additional exposition about Algorithm 3 in Section 4 to better contrast the two approaches to regret minimization. In particular, we have added a theorem statement following the theorem statement for the “explore then commit” style algorithm. Questions: _Various typos and formatting issues_ Thank you for pointing out the various typos and the issue with our paper's formatting. We have corrected these issues for the final draft of the paper. _In your algorithms, can you clarify the running time of finding the minimizing coefficient vector?_ The runtime of finding the minimizing coefficient vector (i.e., $\hat{\mathbf{\theta}}_n$) is equivalent to solving an ordinary least squares or Lasso for $N$ units when the graph structure is known and unknown respectively. There exists efficient gradient-based algorithms for solving these linear programs. We note that our algorithms are designed such that each of these linear programs can be solved in parallel for each unit independently which significantly reduces runtime. --- Rebuttal Comment 1.1: Comment: Thank you for the response, I will keep my score positive.	Summary: This article studies the multi-armed bandit (MAB) problem under unit interference. This unit inference problem is often considered in offline settings. This article extends it to online settings with a linear regression solution based on discrete Fourier features. Two Explore-Then-Commit algorithms are proposed to minimize regret under known and unknown interference, respectively. Finally, the algorithms are tested on some numerical simulations. Strengths: 1. The paper is relatively well-written and easy to follow. 2. It is interesting to study the interference problem in online settings 3. The linear regression solution based on Fourier features seems novel. Weaknesses: 1. The paper lacks real examples to demonstrate the combination of online experimentation and interference. Perhaps the combination is as natural as the paper suggests. For example, In online experimentation, after every action, it may take some time for the interference to occur. If we measure the outcome right after the action, it may provide no information about the effect of interference on the reward. 2. The paper should discuss Assumption 2 more. For example, the upper bound s needs to hold for all units n. Suppose s is very large or small. It is unclear how this affects the algorithms presented later. 3. It is unclear if we can apply the offline methods under interference to online settings. Maybe we could use these methods to estimate the reward function at every step and then take action by maximizing the reward function. Technical Quality: 3 Clarity: 3 Questions for Authors: N.A. 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: Weaknesses: _The paper lacks real examples to demonstrate the combination of online experimentation and interference. Perhaps the combination is as natural as the paper suggests. For example, In online experimentation, after every action, it may take some time for the interference to occur. If we measure the outcome right after the action, it may provide no information about the effect of interference on the reward._ A concrete example is given by online bidding in advertisement; the “agent” here is a centralized platform that coordinates at each round bids coming from N advertisers. Advertisers submit bids and compete in an auction: winning advertisers get to display the ad. Treatments here correspond to different pricing schemes imposed by the platform. For example, two different treatments might correspond to different reserve prices imposed on advertisers (e.g., a higher or lower premium paid at ad-display time). The reward function measures the downstream conversions driven by ads. Here, it is natural to assume that the reward for one advertiser will only be impacted by the behavior (impacted by the treatment) of a subset of the total population of advertisers, e.g., direct competitors. _The paper should discuss Assumption 2 more. For example, the upper bound s needs to hold for all units n. Suppose s is very large or small. It is unclear how this affects the algorithms presented later._ Our algorithms leverage knowledge of the sparsity (or at least an upper bound on the sparsity s) in determining the length of the exploration period. As noted in Remark 4.6 in [1], we can select the length of the exploration period to be _independent_ of the sparsity, but we will pay an additional cost in regret of $O(A^{s/3})$. We have added a comment noting this in the appropriate sections. If one is concerned about practical applications of our algorithms, cross-validation can be used to select the length of the exploration period, as outlined in our remark at the end of Section 4. We also note that such sparsity assumptions are common in both network causal inference literature and the high-dimensional statistics literature. _It is unclear if we can apply the offline methods under interference to online settings. Maybe we could use these methods to estimate the reward function at every step and then take action by maximizing the reward function._ We note that the goals of problems considered in the offline setting are not the same as those considered in the online setting. In the offline setting, the goal of the learner is typically to (a) estimate some sort of treatment effect in the presence of network interference and (b) produce a confidence interval/set for the parameter estimate. The experiments designed to accomplish these tasks often involve uniform/random exploration over the entire time period, and thus would yield linear regret. In the online setting, we want to minimize regret. While we do estimate the underlying global reward functions, this is just a nuisance parameter in our setting. What we really care about is (a) quickly discovering a (nearly) action and (b) exploiting this action over many time steps. This difference is what necessitates different algorithms. [1] Botao Hao, Tor Lattimore, and Mengdi Wang. High-dimensional sparse linear bandits. Advances in Neural Information Processing Systems, 33:10753–10763, 2020.	Rebuttal 1: Rebuttal: We would like to thank the reviewers for the time spent reviewing our work. We greatly appreciate the feedback and will use it to improve our work. We want to clarify that we view our primary contributions to be the following. - A framework for studying multi-armed bandits in the presence of network interference under minimal structural assumptions. - An embedding our this framework into a setting of $N$ parallel linear MAB instances using aspects of discrete Fourier analysis. - Simple explore-then-commit and sequential elimination style algorithms that can be used to obtain small regret. In addition, several reviewers noted that our exposition on the aspects of Fourier analysis necessary for our results was a bit dense. We provide a simple example of (a) binary action embeddings and (b) the corresponding Fourier embeddings below. Further, we describe how the Fourier representation naturally captures our sparse network interference assumption unlike other potential representations. This example can be found in the reviews below, but we discuss it here for convenience. We will also revise the paper to reflect this example. $\textbf{Binary action embedding}$. Consider $N$ units with 2 arms ($\mathcal{A} =2$), and a network graph $\mathcal{G}$ such that each unit $n$ is connected to one other unit, i.e., $\mathcal{G}$ has maximum degree 2. An action $\mathbf{a} = (a_{1}, \ldots a_{N}) \in \\{0,1\\}^N$, will induce the binary embedding $\mathbf{v}(\mathbf{a}) = (v(a_1), \ldots v(a_N)) \in \\{-1,1\\}^N$ where $v(a_i) = 1$ if $a_i$ is 1 and -1 if $a_i = 0$. For example, if $\mathbf{a} = (0,1,1 \ldots 1)$, then $\mathbf{v}(\mathbf{a}) = (-1,1,\ldots,1)$. $\textbf{Fourier embedding}$. For any subset of units $ S \subset [N]$, the Fourier character $\chi_{S}(\mathbf{v}(\mathbf{a})) = \prod_{i \in S} v(a_i)$. For instance, if the action $\mathbf{a} = (0,1,1 \ldots 1)$ as above, and the subset $S = \\{1,2\\}$, the Fourier character $\chi_{\\{1,2\\}}(\mathbf{v}(\mathbf{a})) = v(a_1) \times v(a_2) = -1$. The vector of Fourier characteristics $\boldsymbol{\chi}(\mathbf{a}) = (\chi_{S}(\mathbf{v}(\mathbf{a})) : S \subset N) \in \\{-1,1\\}^{2^N}$ is the concatenation of all Fourier characters for all subsets. $\textbf{Fourier coefficient}$. Since each unit $n$ is only connected to one other unit $m$, unit n's neighborhood $\mathcal{N}(n) = \\{n,m\\}$ for a unit $m \neq n$. For unit $n$, the blocks $\mathcal{B}(n)$ are the indices of $\mathbf{v}(\mathbf{a})$ corresponding to treatments of units in $\mathcal{N}(n)$. For our network graph $\mathcal{G}$, $\mathcal{B}(n) = \\{v(a_n), v(a_m)\\}$. The subsets $S \in \mathcal{B}(n) = \\{\phi, \\{n\\}, \\{m\\}, \\{n,m\\} \\}$ correspond to the non-zero coefficients of unit n's Fourier coefficient $\boldsymbol{\theta}_{n} \in \mathbb{R}^{2^{N}}$. $\textbf{Fourier basis captures sparsity}$. Since $\boldsymbol{\theta}_{n}$ is 4-sparse, the reward $r_n (\mathbf{a}) = \langle \boldsymbol{\theta}_n, \boldsymbol{\chi} (\mathbf{a}) \rangle$ for unit $n$ can be represented using 4 Fourier characters: $\\{\chi\_{\phi}, \chi\_{n}, \chi\_{m}, \chi\_{\\{n,m\\}} \\}$. This representation captures sparsity unlike a 'one-hot' representation where the reward for unit $n$ can be represented as $r_n (\mathbf{a}) = \sum\_{\mathbf{a}' \in \\{0,1\\}^N}r_n(\mathbf{a}') \mathbf{1}[\mathbf{a} = \mathbf{a}']$. This one-hot basis also linearly expresses the reward but requires $2^N$ indicator basis vectors to do so. It is precisely this sparse linear representation induced by the Fourier basis that allows our bounds to scale with $2^s$ rather than $2^N$.	NeurIPS_2024_submissions_huggingface	2,024	Summary: This paper introduces a Multi-Armed Bandits framework to address the challenge of online experimentation with network effects. Specifically, the authors consider a learner sequentially assigning one type of $\mathcal{A}$ actions to $N$ units over $T$ periods to minimize the regret. The reward from each unit depends not only on the action it received but also on the actions its neighbors received, i.e., there is interference across the underlying network of units. The contribution of this paper is as follows: - Using Boolean encoding and Fourier series of Boolean functions, the authors re-express the reward function of each unit as a linear function of the Fourier basis. Then, they propose a simple 'explore-then-commit' style algorithm to address the challenge of the MAB problem with network interference. - With known interference, i.e., the underlying neighbors of each unit are known by the learner, the authors show that their proposed 'explore-then-commit' type algorithm possesses a sublinear regret in $T$ and $N$. - With unknown interference, the authors use LASSO to estimate the parameters on the Fourier basis, and establish a similar sublinear regret. The authors also argue the scaling of $T$ in their regret bound cannot be improved. - Numerical simulations validate the effectiveness of the proposed algorithms and show they outperform the UCB baseline. Strengths: - The paper is very clear and well-written. - The analysis is sound and well-discussed for all the limitations - The discrete Fourier decomposition requires a deep understanding and keen observation of the problem. - Although the algorithm follows a simple 'explore-then-commit' style, the analysis is non-trivial and possesses theoretical and technical difficulties. - The regret is both sublinear in $N$ and $T$, and also $\mathcal{A}^s$ where $s$ is the degree of neighbors. Weaknesses: - I feel it's not common to see $\mathcal{A}$ to denote a number rather than the action set. - The Boolean encoding of the actions is not well-discussed. - In Fig 2(b), it seems that the regret stops accumulating when $T$ is larger enough. Is it true? Could you give a discuss why it happens? - There are some typos of notations, for example, on page 4, (2) Simple orthonormal basis, the authors used $\mathcal{F}_{bool}$. Technical Quality: 4 Clarity: 3 Questions for Authors: The authors studied the interference over the underlying network of units, I wonder if it's possible to consider the impact over time, i.e., the reward may rely on previous actions that its neighbors received, for example, the impact decays exponentially over time. Confidence: 3 Soundness: 4 Presentation: 3 Contribution: 3 Limitations: The limitations are well addressed. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Weaknesses: _The Boolean encoding of the actions is not well-discussed._ Thank you for helping us improve the exposition of our paper! We provide a simple example of (a) binary action embeddings and (b) the corresponding Fourier embeddings below. Further, we describe how the Fourier representation naturally captures our sparse network interference assumption unlike other potential representations. This example can be found in the response to all reviewers above, but we discuss it here for convenience. We will also revise the paper to reflect this example. $\textbf{Binary action embedding}$. Consider $N$ units with 2 arms ($\mathcal{A} =2$), and a network graph $\mathcal{G}$ such that each unit $n$ is connected to one other unit, i.e., $\mathcal{G}$ has maximum degree 2. An action $\mathbf{a} = (a_{1}, \ldots a_{N}) \in \\{0,1\\}^N$, will induce the binary embedding $\mathbf{v}(\mathbf{a}) = (v(a_1), \ldots v(a_N)) \in \\{-1,1\\}^N$ where $v(a_i) = 1$ if $a_i$ is 1 and -1 if $a_i = 0$. For example, if $\mathbf{a} = (0,1,1 \ldots 1)$, then $\mathbf{v}(\mathbf{a}) = (-1,1,\ldots,1)$. $\textbf{Fourier embedding}$. For any subset of units $ S \subset [N]$, the Fourier character $\chi_{S}(\mathbf{v}(\mathbf{a})) = \prod_{i \in S} v(a_i)$. For instance, if the action $\mathbf{a} = (0,1,1 \ldots 1)$ as above, and the subset $S = \\{1,2\\}$, the Fourier character $\chi_{\\{1,2\\}}(\mathbf{v}(\mathbf{a})) = v(a_1) \times v(a_2) = -1$. The vector of Fourier characteristics $\boldsymbol{\chi}(\mathbf{a}) = (\chi_{S}(\mathbf{v}(\mathbf{a})) : S \subset N) \in \\{-1,1\\}^{2^N}$ is the concatenation of all Fourier characters for all subsets. $\textbf{Fourier coefficient}$. Since each unit $n$ is only connected to one other unit $m$, unit n's neighborhood $\mathcal{N}(n) = \\{n,m\\}$ for a unit $m \neq n$. For unit $n$, the blocks $\mathcal{B}(n)$ are the indices of $\mathbf{v}(\mathbf{a})$ corresponding to treatments of units in $\mathcal{N}(n)$. For our network graph $\mathcal{G}$, $\mathcal{B}(n) = \\{v(a_n), v(a_m)\\}$. The subsets $S \in \mathcal{B}(n) = \\{\phi, \\{n\\}, \\{m\\}, \\{n,m\\} \\}$ correspond to the non-zero coefficients of unit n's Fourier coefficient $\boldsymbol{\theta}_{n} \in \mathbb{R}^{2^{N}}$. $\textbf{Fourier basis captures sparsity}$. Since $\boldsymbol{\theta}_{n}$ is 4-sparse, the reward $r_n (\mathbf{a}) = \langle \boldsymbol{\theta}_n, \boldsymbol{\chi} (\mathbf{a}) \rangle$ for unit $n$ can be represented using 4 Fourier characters: $\\{\chi\_{\phi}, \chi\_{n}, \chi\_{m}, \chi\_{\\{n,m\\}} \\}$. This representation captures sparsity unlike a 'one-hot' representation where the reward for unit $n$ can be represented as $r_n (\mathbf{a}) = \sum\_{\mathbf{a}' \in \\{0,1\\}^N}r_n(\mathbf{a}') \mathbf{1}[\mathbf{a} = \mathbf{a}']$. This one-hot basis also linearly expresses the reward but requires $2^N$ indicator basis vectors to do so. It is precisely this sparse linear representation induced by the Fourier basis that allows our bounds to scale with $2^s$ rather than $2^N$. _In Fig 2(b), it seems that the regret stops accumulating when T is larger enough. Is it true? Could you give a discuss why it happens?_ The regression algorithm (either OLS in the case of Algorithm 1 or the Lasso in the case of Algorithm 2) estimates the unknown global reward function with a high-degree of accuracy at the end of the exploration phase. In more detail, we have that (with high probability) $\|\widehat{r}(a) - \bar{r}(a)\| < \epsilon$ for all actions $a$, where $\epsilon$ is some small value denoting the width of the confidence interval. In the case that the suboptimality gap (i.e. the gap in reward between the best and second best action) is smaller than $\epsilon$, we are guaranteed to select the optimal action. That is, we incur zero regret during the exploitation phase. Questions: _The authors studied the interference over the underlying network of units, I wonder if it's possible to consider the impact over time, i.e., the reward may rely on previous actions that its neighbors received, for example, the impact decays exponentially over time._ We believe investigating the effects of an entire history of treatments on the current period is both interesting and practically-relevant. Given that the current approach for estimating rewards depends heavily on the unknown, unit-specific reward functions being fixed over the rounds of interaction, additional machinery would almost surely need to be developed to handle this generalization. Here is perhaps one possible approach: - If the dependence of present reward (say in round $t$) on historical treatments decays geometrically, it may be possible to “extend” the action space to tuples of actions played over the past $s$ rounds (i.e. tuple of the form $(a_t, a_{t - 1}, \dots, a_{t - s})$. We can then suffer some “truncation” error for ignoring the given treatments in rounds $t -s -1, t-s -2$, etc. This truncation error can be computed based on the geometric rate of decay, and $s$ can likely be chosen with respect to the time horizon $T$ to obtain small regret. Additionally, machinery from the reinforcement learning literature may be applicable to handling time-dependent rewards. We note that both aforementioned approaches fall outside of the scope of this paper, and thus we leave them for future work. --- Rebuttal Comment 1.1: Comment: Thanks for the response. I will keep my positive score.	Summary: The paper tackles a multi-armed bandit problem where there is interference that can be modeled by a network. The interference model assumes that a unit's treatment effect is affected by the treatments assigned to its neighbors in the network model. This interference model implies that in the worst case there are $\mathcal{A}^{N}$ possible combination of arms to be pulled each round which makes the regret minimization analysis difficult using existing techniques. To tackle this challenge, the paper studies the sparse network interference model and uses discrete Fourier analysis to show the unit-specific reward can learned using sparse linear regression-based algorithms. They provide a regret minimization algorithm for the setting where the interference model is explicitly known and for the setting where it is unknown. They conclude the paper numerical simulations to corroborate their theoretical findings. Strengths: The paper is well-written with ample discussion of the background, notation, set-up, theorems, and relation to existing work. As a result the paper is easy to understand and able to highlight its contributions. Contribution-wise, the paper considers a relevant multi-armed bandit with interference setting and is able to consider a richer class of actions compared existing work. The assumption that the interference network is sparse seems reasonable and intuitive given the real-world settings discussed in the paper. The regret bounds presented seem intuitive and are able to effectively leverage the sparse network structure. The paper's contributions provide a good generalization of network interference that can be used in future work. Weaknesses: One potential weakness of the paper is that it provides limited proof sketches on results related leveraging the sparse network. Intuition on how the proof technique works may be useful for readers interested in utilizing similar assumptions for future research. The paper also only briefly touches upon settings where the graph is partially observed. The prescribed solution in these settings is to use the fully observed algorithm if "all" the neighbors of the unit are observed and to use the unobserved algorithm if the neighbors are not observed. It still seems unclear what should happen if only "some" of the neighbors are observed. Perhaps additional detail can be added to clarify. Technical Quality: 3 Clarity: 4 Questions for Authors: 1. Does the sparse network model effectively capture interference effects that decay depending on how related two units are? For example, unit $i$ is weakly related to units $1, \dots, K$ so that the arm assignment for one these units has a small effect, but aggregated over all $K$ units has a large effect. 2. If only a portion of neighbors is revealed for unit $i$, do you use Algorithm 1 or Algorithm 2? Confidence: 2 Soundness: 3 Presentation: 4 Contribution: 3 Limitations: Authors have adequately addressed limitations. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Weaknesses: _One potential weakness of the paper is that it provides limited proof sketches on results related leveraging the sparse network._ We agree that a proof sketch would help the reader better understand our algorithm and its convergence. If accepted, we will use the additional page to add brief proof sketches following the theorem statements. _The paper also only briefly touches upon settings where the graph is partially observed. The prescribed solution in these settings is to use the fully observed algorithm if "all" the neighbors of the unit are observed and to use the unobserved algorithm if the neighbors are not observed. It still seems unclear what should happen if only "some" of the neighbors are observed. Perhaps additional detail can be added to clarify._ If only some of the neighbors are observed, or if the practitioner has any doubt about whether a given edge is present in the graph/network, it is likely best practice to use the Algorithm 2 (i.e. the algorithm for the fully-unobserved graph case). We note that both in theory and in our simulations, the performance of this algorithm is not much worse than that of Algorithm 1. Moreover, we emphasize that neither the fully or partially observed settings have been studied before this paper. While it may be possible to derive algorithms for particular forms of unobserved structure, it falls outside of the scope of our work. We have added clarification about this point in the paper. Questions: _Does the sparse network model effectively capture interference effects that decay depending on how related two units are?_ Our paper considers a worst-case setting in which the reward/outcomes associated with each unit can depend arbitrarily on the treatments assigned to its neighbors. We believe that better regret rates are possible if additional structure is assumed, e.g. that the reward satisfies a “bounded difference” property and is not very sensitive to a change in treatment for any given individual unit. Deriving algorithms that can leverage additional structural assumptions is likely a non-trivial task, so we leave it for future work. _If only a portion of neighbors is revealed for unit i, do you use Algorithm 1 or Algorithm 2?_ In this case, the learner should use Algorithm 2. --- Rebuttal Comment 1.1: Comment: I appreciate the response and the clarifications. I will keep my positive score.	null	null	null	null
MoEUT: Mixture-of-Experts Universal Transformers	Accept (poster)	Summary: Motivated by the superior generalization performance of Universal Transformers (UT) demonstrated in other works, this paper addresses the compute efficiency problem of this architecture. While UT decreases the parameter count drastically by sharing parameters across layers, vanilla UT underperforms dense transformers on typical NLP tasks. It is unclear how to efficiently scale the parameter count of the UT, as scaling a single layer to compensate for the loss of parameters would result in computational costs beyond those of standard transformers due to increased layer width. First, this paper explores Mixture-of-Experts (MoE) techniques to efficiently scale the parameters of the UT. Due to sparse expert activation, MoE can scale up the parameter count without drastically increasing the compute requirements. Since simply scaling the parameter count with MoE layers does not yield the expected performance gains, the authors propose two additional innovations: Layer grouping—where parameters are shared within groups of layers instead of across all layers—and Peri-layernorm—where layer normalization is applied only before linear projections that are followed by sigmoid or softmax activation functions. At a high level, my understanding is that the proposed MoEUT architecture essentially interpolates between a dense transformer without shared layers and a UT with completely shared layers. MoEUT can learn to reuse the same experts for each layer (or group), which corresponds to vanilla UT, or it can learn to use completely different, non-overlapping experts at each layer, resembling a standard transformer. Strengths: Overall it is an interesting paper, the proposed method is (conceptually) simple, sound and well motivated. I especially like that authors also included zero-shot downstream task evaluation in the empirical section. Originality: the paper builds on existing knowledge in a meaningful way. It uses existing MoE technique to efficiently increase capacity of UT, which is not a new idea as it had already been proposed in the SUT paper (as aknowledged and discussed by the authors). It adds two additional ideas that seem to have a positive effect on the performance: layer grouping and "peri-layernorm". Yet, as discussed in chapter 5, also layer-grouping has been investigated in prior works. Quality & Clarity: overall, the claims of the paper are supported by evidences. The paper is adequately written, though chapters 2.1 and 2.2 might be dense for readers unfamiliar with the two architectures the authors build upon. The arguments are mostly clear with some exceptions (see Questions). Significance: good. the paper addresses relevant problem and makes a moderate contribution to the field. This work has the potential to influence subsequent studies on scaling UT architectures. Weaknesses: At a high level, my main concern is the following: given that MoEUT effectively interpolates between a standard transformer and vanilla UT, do the authors think that MoEUT would still keep the advantage of vanilla UT when it comes to systematic generalization? Beyond that, I have some additional questions/doubts that I list in the questions part. Technical Quality: 3 Clarity: 3 Questions for Authors: - ll. 28 - 29: the fact that UT shines in systematic generalization baselines does not make it a more "general" architecture, does it? In contrary, UT imposes the requirement of parameter sharing across layers, which can be see as an additional inductive bias, which could be potentially learned by the standard transformer from the data. - Chapter 3: I am a bit confused by the fact that σ-MoE underperforms the dense transformer baseline in parameter-matched setting. (Fig.4a), which seem to be in contradiction with the results from the σ-MoE paper. Why is it the case? - l. 172: my understanding from the related literature is that relative positional encoding is essential to enable systematic generalization in UT. Why do authors decide to use RoPE positional encodings here? - l. 219: "We note that SUTs have not been evaluated previously on any language modeling tasks." -- the original SUT was evaluated on e.g. English-German translation task, Is it not a language modelling task? - ll. 319 - 322: Authors talk about importance of comparing parameter-matched MoE and dense models. IT would be useful if they could explain why parameter-matched setting is important (as compared to compute matched) - ll. 287 - 299: Does "column" refer to individual token representations throughout the layers in transformer? Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: Authors adequately address the limitations in chapter 5. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We would like to thank the reviewer for the valuable review and for positive comments on the methodology of the paper. Please find our responses as follows: > .. given that MoEUT effectively interpolates between a standard transformer and vanilla UT, do the authors think that MoEUT would still keep the advantage of vanilla UT when it comes to systematic generalization? We can confirm that: we evaluated MoEUT with G=2 on the publicly available dataset of [1] for learning random knowledge graphs. Similarly to Fig. 14 in the appendix of [1], our model learns ~70% OOD generalization. In contrast, the standard Transformers completely fail. > the fact that UT shines in systematic generalization baselines does not make it a more "general" architecture, does it? In contrary, UT imposes the requirement of parameter sharing across layers, which can be see as an additional inductive bias, which could be potentially learned by the standard transformer from the data. We would first like to clarify that UTs are in principle strictly more general than parameter equivalent standard transformers: they could assign Nparams/Nlayers of their weights to each layer deterministically and simulate a standard Transformer. In this sense, UTs are not at all a “restricted version” of the standard Transformers. That said, the reviewer’s remark regarding the standard Transformer and learning layer-sharing from the data is a valid point. In practice with finite amounts of data, however, learning such behavior purely from data is very inefficient, if not impossible. A good illustration of this is compositional tasks. Transformers typically learn to solve compositional tasks by allocating each step/function to each layer. In realistic settings, not all compositional combinations are present in the dataset, thus, certain functions are only learned in certain layers; causing failures to generalize on unseen compositions. In fact, [1] rigorously analyzes this in synthetic knowledge graphs, unveiling that transformers use early layers for resolving the first hop, and later layers to resolve the second. However, the knowledge about rarely-seen compositions will be only available in the early layers, thus they can’t be composed with others. [2] shows similar issues on LLama3-70b on real world problems. > I am a bit confused by the fact that σ-MoE underperforms the dense transformer baseline in parameter-matched setting. (Fig.4a), which seem to be in contradiction with the results from the σ-MoE paper. Why is it the case? Please note that our baselines are much stronger than those reported in the 𝜎-MoE paper: on C4, we achieve a perplexity of 13.4 using 244M parameters vs. 17.79 reported by the 𝜎-MoE paper using 266M. This difference comes from two modifications. First, the 𝜎-MoE paper follows the experimental protocol of Transformer XL: we used their official 𝜎-MoE codebase, but improved their baseline by using RoPE and no XL cache. Second, they use dropout in the FFN layers of their baseline, and ‘expert dropout’ in the 𝜎-MoE. Here we disabled all dropouts in all our models as we use sub-epoch training. This resulted in perplexity improvements with a higher gain for the baseline than for 𝜎-MoE. > Why do authors decide to use RoPE positional encodings here? RoPE is a form of relative positional encoding and is used by most modern LLMs, like LLama. Given its popularity, we considered it the best choice. > "We note that SUTs have not been evaluated previously on any language modeling tasks." -- the original SUT was evaluated on e.g. English-German translation task, Is it not a language modelling task? We can soften or remove this claim, since it depends a lot on how one approaches the problem. Translation tasks (like many NLP tasks) can be formulated as an LM task, but in practice, the translation benchmarks (used in the original SUT paper) and those for evaluating LLMs (used in ours) are very different in important ways. The former is an isolated task where people explicitly train models on a dedicated translation dataset (even a specific encoder-decoder architecture is often used instead of generic decoder-only auto-regressive models). This makes translation benchmarks somewhat easier in the sense that very small, specialized models perform pretty well (e.g., the Transformer baseline used in the SUT paper only has 65M parameters; while their biggest SUT also only has 110M params). > IT would be useful if they could explain why parameter-matched setting is important (as compared to compute matched) The parameter-matched setting is crucial to evaluate the model’s expressiveness in the LLM tasks where the number of parameters has a high impact on the model performance. We consider this setting to be particularly important to evaluate the true expressiveness of MoEs compared to their dense counterparts. While the compute-matched setup has values when considering certain practical settings, it gives an “unfair” advantage to MoEs in terms of comparison, as we can easily add extra parameters to an MoE without significantly increasing compute requirements. Here we wanted to show that our MoEUT is capable, even without considering such an advantage, by evaluating its pure expressiveness in the more challenging parameter-matched setting. > Does "column" refer to individual token representations throughout the layers in transformer? Yes, it does. We thank the reviewer for pointing out this ambiguity and will improve the clarity in the final version. We believe our response above resolves all the concerns that the reviewer has raised. If the reviewer finds our response useful, please consider increasing the score. Thank you very much. [1] Wang et al: Grokked Transformers are Implicit Reasoners: A Mechanistic Journey to the Edge of Generalization [2] Biran et al: Hopping Too Late: Exploring the Limitations of Large Language Models on Multi-Hop Queries --- Rebuttal Comment 1.1: Comment: I would like to thank the authors for their comprehensive replies. I appreciate that the authors tested MoEUT on systematic generalization tasks (learning random graphs), making the method even more convincing. --- Reply to Comment 1.1.1: Comment: Thank you very much for your response! We are glad to hear that the reviewer found our response useful!	Summary: This paper introduces a novel application of the mixture of experts (MoE) architecture within both the MLP and attention modules of the Universal Transformer network. The integration of MoE is further complemented by an innovative sequence-level routing regularization technique, which the authors argue enhances training stability. Additionally, the paper proposes the incorporation of layer grouping and a new layer normalization scheme, aimed at boosting model performance. Compared with baselines, the proposed MoEUT can achieve better perplexity with the same number of parameters and obtain competitive performance in various downstream tasks. Strengths: 1. The paper demonstrates the efficacy of incorporating the Mixture of Experts (MoE) architecture into a shared-layer Transformer network, highlighting its potential to improve performance. 2. By integrating the MoE model with layer grouping and a novel layer normalization approach, the proposed model achieves superior results in language modeling tasks compared to standard Transformers. 3. Visualization of the results reveals significant specialization across different layers, with each layer showing a distinct preference for particular experts, indicating effective learning and specialization within the network. Weaknesses: 1. The relationship between the MoE network architecture, the proposed layer grouping strategy, and the novel layer normalization technique appear to be undefined. Clarification on how these components synergize within the model would enhance understanding of their collective impact on performance. 2. While the author suggests that the $\sigma$-MoE model exhibits instability during training, this assertion is not substantiated with empirical evidence. Providing experimental results or a more detailed analysis to support this claim would strengthen the argument. 3. The current ablation study does not sufficiently demonstrate the effectiveness of the proposed method. Expanding the ablation study to include a broader range of experiments and comparative analyses could offer a more comprehensive evaluation of the individual contributions of the proposed enhancements. Technical Quality: 2 Clarity: 3 Questions for Authors: 1. Layer Grouping and Novel Layer Norm Performance Contribution: - Do the layer grouping and the novel layer normalization contribute independently to the performance improvements observed, or are these contributions specifically related to the architecture of the Mixture of Experts (MoE) network? 2. Impact of Improved Sequence Level Routing Regularization on Training Stability: - Does the implementation of improved sequence-level routing regularization enhance the training stability of the model? 3. Distinct Contributions of MoE Variants in MoEUT: - Given the implementation of MoE within the MoEUT framework (specifically in the MLP and attention mechanisms), how does each variant individually affect the model's overall performance? 4. Impact of Excluding MoE on Performance: - If the MoE design is omitted, allowing layer grouping and “peri-layernorm” to independently influence the model, what is the anticipated impact on performance? Additionally, is the integration of layer grouping and “peri-layernorm” with the proposed MoE architecture necessary for achieving the observed benefits? 5. Comparative Analysis of MoEUT and SUT: - In addition to perplexity comparisons, it is suggested that a direct comparison between MoEUT and SUT (Sparse Transformer) should also be conducted across the downstream language modeling tasks presented in Table 1. This would provide a more comprehensive understanding of their relative performances. Confidence: 4 Soundness: 2 Presentation: 3 Contribution: 2 Limitations: The authors adequately discuss the limitations and do not have the potential negative societal impact. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We would like to thank the reviewer for their valuable time reviewing our work. We would like to respond to the concerns raised by the reviewer as follows. > … . Clarification on how these components synergize within the model would enhance understanding of their collective impact on performance… > Do the layer grouping and the novel layer normalization contribute independently to the performance improvements observed, or are these contributions specifically related to the architecture of the Mixture of Experts (MoE) network? > If the MoE design is omitted, allowing layer grouping and “peri-layernorm” to independently influence the model, what is the anticipated impact on performance? Additionally, is the integration of layer grouping and “peri-layernorm” with the proposed MoE architecture necessary for achieving the observed benefits? We would first like to draw the reviewer’s attention to the fact that we have dedicated ablation studies on the effect of layer grouping in Fig. 6 and the effect of different layer normalizations in Fig. 8 independently of each other for our MoE-based model. We demonstrated that both help. Testing these on the naive UTs without MoE in a systematic/fair way is not easy precisely because of the challenge of scaling the naive UTs (the very problem we address in this work): they are prohibitively slow and use too much memory for any interesting scale. Given that MoE is anyway necessary to scale up UTs, it seemed natural to focus on evaluating these methods for the MoE-based UTs. Also intuitively, we have no reason to believe that the contributions of these methods would be very different for UTs because the original motivations of these methods are based on UT’s properties, and they are unrelated to the use of MoE (e.g., peri-layernorm is motivated by the residual norm growth caused by parameter-sharing across layers; see A.2). > The current ablation study does not sufficiently demonstrate the effectiveness of the proposed method. Expanding the ablation study to include a broader range of experiments and comparative analyses could offer a more comprehensive evaluation of the individual contributions of the proposed enhancements. We believe that the ablation studies presented in the current paper sufficiently cover the most important aspects to justify our design choice within MoEUT. Please see Fig 6 for the effect of routing, Fig 8 for comparing pre/post/peri layernorm, Fig 13 for the effect of d_expert, and Fig 14 for the effect of K. As we explained above, conducting further ablations on the naive UTs without MoE is not reasonable because of their scale inefficiency. If the reviewer still thinks there are any other ablations that are critically missing, we would appreciate it a lot if the reviewer could suggest concrete ideas. Thank you. > While the author suggests that the 𝜎-MoE model exhibits instability during training, this assertion is not substantiated with empirical evidence. Providing experimental results or a more detailed analysis to support this claim would strengthen the argument. … Does the implementation of improved sequence-level routing regularization enhance the training stability of the model? Yes, without sequence-level routing regularization, larger models suffer from an expert collapse and they diverge. We found it uninformative to include training loss curves exploding to infinity in the appendix, but if the reviewer thinks that would be interesting for the readers, we can include them in the appendix of the next version of the paper. > In addition to perplexity comparisons, it is suggested that a direct comparison between MoEUT and SUT (Sparse Transformer) should also be conducted across the downstream language modeling tasks presented in Table 1. This would provide a more comprehensive understanding of their relative performances. Thank you for pointing this out. We extended our downstream task evaluations to SUT and “SUT without ACT” (in the meanwhile, we identified that the “ACT” component of SUT, which is a fundamental component of SUT, is detrimental to its performance here). These results show that MoEUT achieves 18-33% increases (8.7-12.2 points) over SUT. Removing ACT from SUT improves its downstream performance as well, but MoEUT remains consistently better, with 7-11% increases (3-5.1 points) on average across our tasks, model sizes, and pretraining datasets. \| Dataset \| #params \| Model \| PPL \| LAMBADA \| BLiMP \| CBT \| HellaSwag \| PIQA \| ARC-E \| Average \| \|----\|----\|----\|----\|----\|----\|----\|----\|----\|----\|----\| \| C4 \| 44M \| MoEUT \| 18.30 \| 23.2% \| 78.2% \| 81.1% \| 29.2% \| 61.3% \| 33.5% \| 51.1% \| \| \| 44M \| SUT \| 40.50 \| 1.2% \| 65.3% \| 51.1% \| 26.4% \| 57.8% \| 31.9% \| 39.0% \| \| \| 44M \| SUT w.o. ACT \| 21.51 \| 18.1% \| 72.8% \| 66.3% \| 27.5% \| 59.1% \| 32.5% \| 46.0% \| \| \| 244M \| MoEUT \| 13.24 \| 30.6% \| 79.7% \| 85.3% \| 35.7% \| 65.2% \| 36.4% \| 55.5% \| \| \| 244M \| SUT \| 20.05 \| 20.5% \| 71.0% \| 68.5% \| 28.2% \| 60.1% \| 32.7% \| 46.8% \| \| \| 244M \| SUT w.o. ACT \| 14.58 \| 27.8% \| 77.0% \| 75.9% \| 32.7% \| 63.2% \| 35.5% \| 52.0% \| \| PES2O \| 44M \| MoEUT \| 11.09 \| 13.1% \| 68.7% \| 69.6% \| 28.3% \| 55.1% \| 31.4% \| 44.4% \| \| \| 44M \| SUT \| 25.04 \| 0.5% \| 59.2% \| 38.1% \| 26.2% \| 55.0% \| 31.1% \| 35.0% \| \| \| 44M \| SUT w.o. ACT \| 12.68 \| 11.7% \| 66.5% \| 53.9% \| 28.0% \| 56.1% \| 31.5% \| 41.3% \| \| \| 244M \| MoEUT \| 8.52 \| 19.4% \| 73.5% \| 77.4% \| 30.1% \| 56.3% \| 35.6% \| 48.7% \| \| \| 244M \| SUT \| 20.44 \| 0.5% \| 60.9% \| 42.8% \| 26.7% \| 55.3% \| 33.0% \| 36.5% \| \| \| 244M \| SUT w.o. ACT \| 9.31 \| 16.8% \| 71.9% \| 64.8% \| 28.8% \| 57.3% \| 34.8% \| 45.7% \| We will add this to the updated version of our paper. We believe our response above resolves all the concerns that the reviewer has raised. If the reviewer finds our response useful, please consider increasing the score. Thank you very much. --- Rebuttal Comment 1.1: Title: Official Comment by Reviewer ZbxN Comment: I extend my gratitude to the authors for their detailed responses. To fully grasp the efficacy and interplay of the proposed components, I anticipate an exploration of the performance for MoEUT without PeriLN and vice versa. Such results would provide a clearer understanding of these elements. Moreover, I am keen to understand how MoEUT and PeriLN complement each other, suggesting that their integration is not merely coincidental but inherently synergistic. The authors have addressed my concerns to some extent, therefore I would like to increase my score. Should the authors further elaborate on these aspects, specifically by demonstrating the independent and combined effects of MoEUT and PeriLN, I am inclined to further improve their score. --- Reply to Comment 1.1.1: Comment: We are very thankful for the increased score! We are glad to hear that the reviewer found our response useful! We agree with the reviewer that analyzing PeriLN in more detail would be a very useful additional experiment for our paper. First, we would like to emphasize that one direction of such comparison is already part of the paper: we analyze the effect of different layer norm variants on MoEUT in Figure 8 of the paper. The reverse direction is missing: We do not have experiments with PeriLN on standard (naive) UTs. We tried to run such experiments upon the suggestion of the reviewer. We would like to emphasize that this is very resource intensive: we need at least 8 A6000-level GPUs to make the experiment fit in the memory even for our tiny, 44M naive UT model. Unfortunately, we found that naive UTs experience residual blowups and become unstable during training. Such blowup does not happen in MoEs, possibly because the number of simultaneously active channels/attention heads is limited to a much smaller number than in naive UTs, where all of them can be active at the same time, resulting in significantly greater residual norm growth. We added an additional regularization on the norm of the residual, which delayed the blowup significantly, but it still happened at around 20% of the training completed. Until that point its behavior was as we predicted: naive UT with PeriLN outperformed naive UT without PeriLN (using PreLN instead). We are happy to finalize these experiments, search for a stable solution, and add them to the final version of the paper, but since naive UT is a completely novel setting that we have not examined so far, unfortunately, the remaining time is not enough for us to do it during the rebuttal. We would like to thank the reviewer again for his efforts to improve the quality of our paper and for his thoughtful suggestions!	Summary: This paper focuses on the problem of inefficient parameter-computation ratio in Universal Transformers (UT). UT shares parameters across layers but reduces the parameter count significantly. One naive approach is to scaling up the layer size, however, cannot be easily achieved due to the prohibitive computational resource requirements. MoEUT, the proposed approach, exploits MoE architecture in both attention and feed forward layers to address this issue. To achieve the similar performance as the standard Transformers, the authors first introduce layer grouping, which allows non-shared weights among the layers within a group. Second, they remove the layernorm in the main data path in standard Transformer to avoid gradient flow and add layernormaround the residual connections. Experiments shows MoEUT outperforms standard Transformers slightly while incurring less compute and memory costs. Strengths: 1. The idea of exploiting MoE to address the parameter-compute ration in Universal Transformers is interesting. MoE itself incorporates ideas of expert sharing among similar tokens. It is an intuitively reasonable combination. 2. Sound explanations of the rationale of designing layer grouping and peri-layernorm are presented in the paper together with cited works to further support the claims. 3. The evaluation and analysis are comprehensive with deep dive to the design components. Weaknesses: 1. The claim of using significantly less compute and memory should be further supported by evaluation numbers. Though Table 4 have presented detailed training hardware information of the experiments reported in the paper, it is very hard to determine the quantitative computation and memory costs. A general number like GPU hours, GPU duty cycles, DRAM utilization or costs in terms of dollars would be a much better indicator rather than existing presentation. 2. In Section 2.1, it is mentioned the load balancing loss is now considered for each sequence due to the loss explosion issue when applying on the entire batch. I may not fully understand the difference here and why full batch balancing loss would cause explosion while sequence-level won't. Further elaboration or evaluation could be helpful in explaining this. Technical Quality: 3 Clarity: 3 Questions for Authors: It seems the number of experts is very large as a default setting in the evaluation. What if the total number of experts is just, let's say, 8 or 16 and k is 1 or 2, similar like the sparsely-activated MoE, how the performance would change? Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: Limitations are addressed in the paper and there is no negative societal impact of this work. 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 valuable review and for many positive comments on the methodology of our paper. Please find our responses as follows: > The claim of using significantly less compute and memory should be further supported by evaluation numbers. Though Table 4 have presented detailed training hardware information of the experiments reported in the paper, it is very hard to determine the quantitative computation and memory costs. We will update Table 4 in the final version if the paper is accepted, to include the total GPU-hours (N_GPU * duration in the current table) for better readability. Comparing memory this way is nontrivial, as it does not scale linearly with the number of GPUs, as we are using simple data-parallel training. However, here are some direct comparisons on identical hardware for the 244M parameter models that allow directly comparing them on identical hardware, showing that MoEUT is much faster and uses less memory than the alternative UT variants: \| Model \| Time / training step \| Memory usage/GPU \| \| ---- \| ---- \| ---- \| \| Dense \| 443 ms/iter \| 9.2 Gb \| \| Naive UT \| 3559 ms/iter \| 25.9 Gb \| \| MoEUT \| 772 ms/iter \| 9.0 Gb \| \| SUT \| 1344 ms/iter \| 23.4 Gb \| We measured the training iteration time and memory usage on 8 V100 32Gb GPUs. Here one “iteration” corresponds to an effective batch size of 64x1024 tokens for all models. The training iteration time was measured by using a batch size for each model that fits GPUs; models require either 1 or 2 gradient accumulation steps to achieve the effective batch size depending on their memory requirement. We measured the training time right after initialization and a warmup period. The memory usage is measured using 2 grad accumulation steps for all models for a fair comparison. Note that around ~3Gb of memory is used by the model parameters and optimizer state on each GPU. > I may not fully understand the difference here and why full batch balancing loss would cause explosion while sequence-level won't. We cannot provide a mathematical proof here, but we do have one hypothetical but intuitive explanation. If the balancing is done at the batch level, the experts can specialize in different sequence types. Since the batches are sampled randomly, the “variance” of utilization rate between the active experts used in different forward passes might vary highly. Some experts may specialize in rare sequences, thus they will be rarely trained, resulting in a “slow expert collapse”. When they are reactivated at a much later stage of training, they may cause sudden loss explosion as their training “stage” lags behind that of other more frequently used experts. On the other hand, if the balancing is done on a sequence level, the model is encouraged to use various experts in each sequence, eliminating some of this variance. This still allows some expert specialization, because the balancing is relatively weak. Using a significantly larger batch size would probably also stabilize the training, but it is prohibitively expensive with our resource budget. It seems like a useful next step for better-resourced teams, and so we will emphasize this in our next version. > What if the total number of experts is just, let's say, 8 or 16 and k is 1 or 2, similar like the sparsely-activated MoE, how the performance would change? This is an excellent question. In our experiments, we found K=1 performed significantly worse than K > 1. In order to match the MACs of the dense model, the number of experts should be at least K*N_layers, otherwise the activated experts would be “wider” than the FFN of the baseline. Furthermore, to keep the number of parameters constant, d_expert should be significantly increased. We study the effect of increasing expert size (d_expert) in Fig. 13 in the appendix, while keeping K constant. Increasing the expert size is detrimental. Decreasing K would have an additional negative effect. We analyze this independently of K in Fig 14. If the reviewer thinks additional experiments could add value to the paper, we can run an experiment with some of our MoEUT methods in a max-d_expert configuration and K=2 to see the effects of pushing these parameters to the extreme. These questions are extremely valuable for us and will enable us to improve our paper. Thank you very much. --- Rebuttal Comment 1.1: Comment: Thank you very much for addressing my concerns. They are really helpful. I will maintain my current rating. --- Reply to Comment 1.1.1: Comment: Thank you very much for your response! We are glad to hear that the reviewer found our response useful!	Summary: The paper suggests to use Sparse MoEs together with Universal Transformers to overcome the parameter-count limitation that the latter have when parameters are shared over consecutive layers. In particular, the work suggests to use $\sigma$-MoEs (that use sigmoid activation function in the router, rather than the more popular softmax activation), and use fine-grained experts (selecting many small experts over a large pool, rather than one or two large ones over a smaller pool). The goal is to make Universal Transformers competitive on language modeling tasks, where they haven’t excelled in the past (presumably due to the smaller parameter count, compared to dense models of the same time complexity). Two important novelties that are introduced are Layer Grouping in UTs (this allows to chose the degree of parameter sharing across layers in the UT), and relocating the LayerNorm operations (called PeriLayerNorm, as opposed to pre and post LayerNorm). The paper includes experiments on several pretraining tasks (C4, peS2o, SlimPajama) and zero-shot evaluation on several downstream tasks. In both cases, the results achieved by MoEUT are competitive with a standard dense transformer with the same number of parameters, and often slightly better. Strengths: - The presentation of the work is excellent. From the motivation, to the explanation of the proposed method, related works, and the description of the experiments. - The main experiments show that the goal of making UTs competitive with standard dense transformers in language modelling tasks was achieved. - Many additional ablation experiments were conducted to try to explain how experts are selected across different layers, and tokens. - An effort was put on implementing reasonable baselines such as $\sigma$-MoEs and Sparse UTs. - The paper clearly states current limitations (e.g. not the most efficient implementation, which results in experiments that are 2x slower than the dense counterpart). Weaknesses: - The proposed method matches dense transformers on language modeling, but it’s barely better. This begs the question: why using MoEUTs then, rather than the simpler baseline? The answer could be better MAC efficiency at the same memory cost, but this is not clearly represented in Table 1 (and as the authors point out, it’s actually slower due to implementation limitations). - The perplexity reported for Sparse UTs is alarmingly high. The paper mentions that proper hyperparameter tuning was done, but I’m wondering if the authors reached out to the SUT authors to make sure that everything was implemented correctly. - A similar thing happens with $\sigma$-MoEs, which performs worse than the dense baseline when matching the parameter count, and most troubling barely better when matching MACs. ------- Edit after rebuttal: The authors addressed most of my concerns in the rebuttal. Given their response to my and to other reviewers' comments, I'm increasing my score to "Accept". Technical Quality: 3 Clarity: 4 Questions for Authors: - In figure 10 and 11, do the expert indices correspond to the experts in the attention or in the feed-forward part of the block? Do the trends differ across the two? Confidence: 5 Soundness: 3 Presentation: 4 Contribution: 3 Limitations: No negative societal impact particular to this work, in my opinion. 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 their insightful review and for the positive comments on the clarity and methodology of the paper. Please find our responses as follows: > The proposed method matches dense transformers on language modeling, but it’s barely better. This begs the question: why using MoEUTs then, rather than the simpler baseline? Our goal is to pave the way towards a general model that can be used for LM but is also good at systematic generalization, eventually arriving at foundation models that are more trustworthy and data efficient. In this paper, we address a single step toward that goal: we present a way to overcome the long-standing efficiency limitations of UTs (which are known to generalize better than standard transformers), which have prevented their scaling to sizes required for LLMs. > it’s actually slower due to implementation limitations It is true that our current proof-of-concept kernel is slower than a standard transformer despite requiring fewer flops, but we believe this can be mostly mitigated by better kernels. Even with the current kernels, our method is significantly faster than a naive UT or the next best UT baseline, SUT, and for most of our experiments naive UTs are not viable to run because of their memory usage and speed (see time/memory usage measurements below). Rather than replacing Transformers, we are advocating for more research on Universal Transformers with our method for larger scales. Note additionally that we investigated these models in a parameter-matched setting because we were interested in comparing their expressiveness. The number of parameters in our MoEUT can be increased very cheaply (as with other MoEs), and it is possible to achieve significantly better perplexity for marginally higher compute, potentially justifying the wall-clock time slowdown even with the current kernels. (We use a parameter-matched setup instead of this because this would give an unfair advantage to our MoEUTs compared to the baselines). Speed/memory usage of different models, showing that MoEUT is much faster compared to naive UT and SUT and uses less memory: \| Model \| Time / training step \| Memory usage/GPU \| \| ---- \| ---- \| ---- \| \| Dense \| 443 ms/iter \| 9.2 Gb \| \| Naive UT \| 3559 ms/iter \| 25.9 Gb \| \| MoEUT \| 772 ms/iter \| 9.0 Gb \| \| SUT \| 1344 ms/iter \| 23.4 Gb \| We measured the training iteration time and memory usage on 8 V100 32Gb GPUs. Here one “iteration” corresponds to an effective batch size of 64x1024 tokens for all models. The training iteration time was measured by using a batch size for each model that fits GPUs; models require either 1 or 2 gradient accumulation steps to achieve the effective batch size depending on their memory requirement. We measured the training time right after initialization and a warmup period. The memory usage is measured using 2 grad accumulation steps for all models for a fair comparison. Note that around ~3Gb of memory is used by the model parameters and optimizer state on each GPU. > The perplexity reported for Sparse UTs is alarmingly high We confirmed via personal communication through a colleague that SUT does not work well for LM. We used the official code of the authors, with minimal modification required to adapt it to our codebase. Additionally, we conducted some ablations on the SUT models, and we found that the main cause of the bad performance is the ACT used by their model (which was presented as a fundamental building block of SUT). By disabling ACT, the gap between MoEUT and SUT is much smaller, while MoEUT remains consistently better: \| Dataset \| Model Size \| Baseline \| MoEUT \| SUT w.o. ACT \| SUT \| \| --- \| --- \| --- \| --- \| --- \| --- \| \|C4\| 44M \| 18.9 \| 18.2 \| 21.5 \| 40.5 \| \| \| 244 M \| 13.3 \| 13.2 \| 14.5 \| 20.0 \| \| peS2o \| 44M \| 11.5 \| 11.1 \| 12.7 \| 25.0 \| \| \| 244M \| 8.6 \| 8.5 \| 9.3 \| 20.4\| > A similar thing happens with 𝜎-MoEs, which performs worse than the dense baseline when matching the parameter count. Please note that our baselines are much stronger than those reported in the 𝜎-MoE paper: on C4, we achieve a perplexity of 13.4 using 244M parameters vs. 17.79 reported by the 𝜎-MoE paper using 266M. This difference comes from two modifications. First, the 𝜎-MoE paper follows the experimental protocol of Transformer XL: we used their official 𝜎-MoE codebase, but improved their baseline by using RoPE and no XL cache. Second, they use dropout in the FFN layers of their baseline, and ‘expert dropout’ in the 𝜎-MoE. Here we disabled all dropouts in all our models as we use sub-epoch training. This resulted in perplexity improvements with a higher gain for the baseline than for 𝜎-MoE. > In figure 10 and 11, do the expert indices correspond to the experts in the attention or in the feed-forward part of the block? Those expert indices correspond to the feed-forward part. We will clarify this in the final version. Thank you for pointing this out! We believe our response above resolves all the concerns that the reviewer has raised. If the reviewer finds our response useful, please consider increasing the score. Thank you very much. --- Rebuttal Comment 1.1: Comment: I thank the authors very much for their detailed response to my comments, and the other reviewers' comments as well. In particular, I appreciate very much the fact that the authors made the effort to fairly reproduce the baselines, and contacted the authors to make sure that they were correctly represented. Thus, given that I feel that my concerns have mostly been addressed, I will increase the score and recommend the acceptance of the paper. --- Reply to Comment 1.1.1: Comment: Thank you very much for the increased score! We are glad to hear that the reviewer found our response useful! Thank you again for your valuable feedback!	null	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
OneBit: Towards Extremely Low-bit Large Language Models	Accept (poster)	Summary: This paper presents OneBit, a framework for quantizing large language models (LLMs) to 1-bit weight matrices. Unlike existing methods that rely on 4-bit or 8-bit quantization to avoid severe performance degradation, OneBit introduces a novel 1-bit parameter representation and an effective parameter initialization method based on matrix decomposition. Strengths: - This paper proposes an aggressive compression method, exploring the feasibility and challenges of compressing LLMs to 1-bit. This is a highly meaningful research direction, and similar work should be encouraged for publication. However, I have some concerns about this approach, which I will detail in the questions section. - The paper is well-organized and well-written. - The experiments compare the proposed method with current popular low-bit quantization methods and demonstrate superior results. Additionally, the experiments address an important question in the current LLM research field: whether to use quantized large models or directly use smaller models. Weaknesses: - Entropy Encoding: Intuitively, 1-bit compressed models should be suitable for entropy encoding. Previous work has demonstrated that quantized LLMs still have compressibility [1,2]. Have the authors tried using popular entropy encoders to further compress these weights? - Inference Calculations: During inference, do g and h participate in the calculations? Does this mean that 1-bit net is not entirely integer-based computation? Does each layer have its own G and h? - Dequantization: Is dequantization required between layers during inference? - Knowledge Distillation (KD): In line 191, it is mentioned that KD does not use LM loss. Why is that? - Comparison with 1.58bitnet: Have the authors considered comparing their method with 1.58bitnet [3]? - Table 2 Details: Does Table 2 show the performance of W1A16 or W2A16? If it is W2A16, where is the performance of W1A16 reported? Why are there no experimental results for 16B and 60B models in Table 2? I suspect that extreme quantization has a more detrimental effect on larger models. - Comparison in Figure 3: Figure 3 compares the performance of 1-bit quantized 7B models with smaller models. Are these smaller models in full precision? How would the results compare with 8-bit smaller models? - Code Availability: Will the code be open-sourced? - Minor Issues: Figures 3 and 4 are not clear when printed in gray-scale. References: [1] Mao Y, Wang W, Du H, et al. On the compressibility of quantized large language models. arXiv preprint arXiv:2403.01384, 2024. [2] [2] Hershcovitch M, Choshen L, Wood A, et al. Lossless and Near-Lossless Compression for Foundation Models[J]. arXiv preprint arXiv:2404.15198, 2024. [3] Ma S, Wang H, Ma L, et al. The Era of 1-bit LLMs: All Large Language Models are in 1.58 Bits[J]. arXiv preprint arXiv:2402.17764, 2024. Technical Quality: 3 Clarity: 3 Questions for Authors: See above. Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: See above. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We appreciate the time and effort you have invested in reviewing our paper. Question 1: "Have the authors tried using popular entropy encoders to further compress these weights?" This maybe a great intuition! Theoretically, a model quantized to 1-bit does have the potential for further compression using entropy coding. In fact, we are currently exploring this possibility, and it holds independent research value. Question 2: "During inference, do g and h participate in the calculations? Does this mean that 1-bit net is not entirely integer-based computation? Does each layer have its own G and h?" Yes. The FP16 vectors g/h participate in the calculation during inference. Our proposed 1-bit net structure is indeed not entirely integer-based. The core of our idea is the minimal use of floating-point and their substantial benefits. Finally, each Linear layer has its own G and h. Question 3: "Is dequantization required between layers during inference?" No. Dequantization is not required between layers during inference, because the original weight have been entirely converted into a quantized matrix W and two floating-point vectors g/h. Question 4: "Why is it mentioned that KD does not use LM loss in L191?" We specifically mention in the paper that LM loss is not used to ensure accurate description and facilitate reproducibility of our results. The reason for not using LM loss is that this loss does not demonstrate beneficial effects in our experiments. Question 5: "Have the authors considered comparing their method with Bitnet-b1.58?" BitNet-b1.58 is a work slightly later than ours, aiming to propose a possible 1-2 bit model structure (examining the performance of training from scratch), which differs from model quantization that transforms a "pre-trained model" into a low-bit representation. However, we are also curious whether the BitNet-(1b/1.58b) structure can be used for quantizing existing models, and we have discussed the relevant results of BitNet-1b in Appendix A.5 and Fig. 6. BitNet-b1.58 is also similar to this. The conclusion shows that, compared to BitNet, our model structure achieves stable ability transfer and training process, whereas BitNet-(1b/1.58b) fails to converge during quantization-aware distillation. Question 6: "1. Does Table 2 show the performance of W1A16 or W2A16? If it is W2A16, where is the performance of W1A16 reported? 2. Why are there no experimental results for 16B and 60B models in Table 2? I suspect that extreme quantization has a more detrimental effect on larger models." 1. Table 2 compares our method with four baselines: FP16, GPTQ, LLM-QAT, and OmniQuant. FP16 represents the non-quantized model, serving as the upper bound for all methods’ capabilities. As the first 1-bit weight quantization method, our approach, OneBit, uses W1A16 quantization. The baselines GPTQ, LLM-QAT, and OmniQuant use a W2A16 quantization level. 2. Due to the limitation of computational resources, we are currently unable to perform experiments on larger scale models, although we have been trying to get the resources. However, our existing results indicate an exciting trend: "the larger the model, the smaller the performance gap between the FP16 precision and the W1A16 quantized model." This conclusion is mentioned in lines L238~L240 of our paper. Question 7: "Figure 3 compares the performance of 1-bit quantized 7B models with smaller models. Are these smaller models in full precision? How would the results compare with 8-bit smaller models?" Yes, the smaller models are in full FP16 precision. The conclusion is that our 1-bit quantized model is better than the similar scaled full precision model. As the upperbound, the full precision model is better than the same 8-bit smaller models. Hence, we can directly conclude that our 1-bit quantized model is better than the 8-bit smaller models. Question 8: "Code Availability: Will the code be open-sourced?" We have submitted the core OneBit Linear Layer python code in the supplemental material to NeurIPS. Additional, all the code, data, and checkpoints are fully open-sourced on other platforms. They will be made completely public after the peer review process is concluded. Question 9: "Minor Issues: Figures 3 and 4 are not clear when printed in gray-scale." Thank you for your reminder and suggestions! We will reconsider their line styles, colors, and plotting methods, and make adjustments in the revised version. We look forward to hearing from you and hope to address any concerns you may have about our work. Please let us know if you have any further questions. --- Rebuttal Comment 1.1: Comment: Thank you for the clarification and new sensitivity analysis. I will keep my score. --- Reply to Comment 1.1.1: Comment: Thank you very much for your continued review. We are grateful for your positive feedback and the time you have devoted to evaluating our work. Please don’t hesitate to reach out if there are any further questions or points of discussion. We remain at your disposal for any additional clarifications.	Summary: This paper explores an innovative 1-bit quantization framework for Large Language Models (LLMs) to significantly reduce their memory and computational demands. Traditional methods face severe performance drops with reduced bit-width; however, this paper introduces a novel quantization and initialization approach that maintains at least 81% of the original model’s performance, even with extreme bit-width reduction. The proposed method, which includes a specialized matrix decomposition and parameter initialization, demonstrates strong performance and robustness in experiments, establishing a new direction for deploying LLMs on resource-constrained environments. Strengths: The paper is easy to follow. The proposed method shows good performance, achieving at least 81% of the unquantized model’s efficacy, a significant achievement given the drastic reduction in model complexity and size. Weaknesses: A significant issue discussed in the paper is the lack of a specialized CUDA kernel for optimizing binary operations, which hinders accurate evaluation of the additional computational costs associated with the two FP vectors $\mathbf{a}$ and $\mathbf{b}$. This limitation complicates the assessment of their impact on overall performance. Furthermore, despite the inclusion of $\mathbf{a}$ and $\mathbf{b}$, there remains a considerable performance decline compared to FP16 models, challenging the practical applicability of this approach in real-world settings. Technical Quality: 3 Clarity: 3 Questions for Authors: 1. The experiments described in Section 4.3 may not provide an appropriate comparison. Assessing the proposed method alongside directly training smaller models or utilizing low-rank decomposition to minimize parameter counts involves fundamentally different approaches to reducing model size. Additionally, the proposed method incorporates knowledge distillation, which is not employed in the baseline methods being compared, potentially skewing performance comparisons. 2. An essential ablation study is notably absent from the discussion. The proposed method incorporates two additional floating-point vectors, $\mathbf{a}$ and $\mathbf{b}$, for binary quantization. Yet, the impact of these vectors on performance enhancement remains unclear, highlighting a gap in the evaluation of the method’s effectiveness. 3. To offer a more comprehensive evaluation, I recommend including assessments on generative tasks, such as code generation. This would provide deeper insights into the versatility and practical applicability of the proposed method across different domains. Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The authors have discussed the limitations of their study. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We appreciate the time and effort you have invested in reviewing our paper. Weakness: "It might lack specialized CUDA kernel for optimizing binary operations and the additional computational costs associated with the two FP vectors a and b may be not clear. Moreover, the performance decline challenging the practical applicability in real-world settings." - For CUDA kernel and inference time: The potential advantage of our method benefits from a special multiplication, *INT1(W) FP16(A)*, in which the traditional FP16FP16 can be quickly and efficiently replaced by setting the sign bit of FP16 activation. For example, we have W=(0.1, -0.3, -0.2) and A=(0.8, 0.2, 0.7), and traditional WA maybe 0.10.8+(-0.3)0.2+(-0.2)0.7 and it can be quantized to Pos(0.8)+Neg(0.2)+Neg(0.7). Here Pos(·) represents the machine instruction for setting the sign bit of a floating-point number to '+', while Neg(·) represents the opposite. Unfortunately, since this computation method is not yet perfectly supported at the GPU hardware level, we cannot demonstrate how fast OneBit truly is on the device by carefully designing CUDA kernel. All experiments have been conducted using FP16 format containing only ±1 for simulation. We provide an possible efficient implementation of the OneBit Linear Layer in the supplemental material (with parallel tensor computation). If we simply simulate INT1 using FP16 format, the inference time is approximately 1.2x that of the original model. In fact, thanks to the broadcasting mechanism of tensors, the element-wise multiplication of matrices and vectors can be performed very quickly. Therefore, the additional vector incurs minimal time overhead. If we aim for extreme space compression, i.e., expanding the compressed weight during inference, the inference latency is approximately 2.2x that of the original model. It is worth noting that most weight-only quantization studies introduce additional inference latency. Additionally, we sincerely hope that our work, along with recent similar efforts, will encourage device providers to support this faster computation method at the hardware level. - For practical applicability: Even though our proposed quantization is lossy compression, we strive to demonstrate its practical value in this paper. In Section 4, we show our method’s excellent performance on benchmarks by comparing it with strong baselines. In Appendix A.4, we demonstrate the practicality of our method through SFT and instruction-following tests. Moreover, compared to contemporaneously published method [1], our approach proves to be superior in both effectiveness and capability, underscoring the research and practical value of our method. Question 1: "The proposed quantization method and training smaller models or utilizing low-rank decomposition are different approaches, and their comparison may not appropriate. Additionally, comparing with the baselines, which not employe knowledge distillation, may be appropriate as well." We understand the reviewer's concern. It is important to clarify that our comparisons with these different compression methods are not intended to defeat them, but rather to demonstrate the model’s capabilities from another perspective—specifically, that it performs better than smaller models of the similar scale. Therefore, we did not include this comparison as the main result in Sec 4.2, but rather as a separate subsection, "Problem Solving Ability". Additionally, regarding the second concern, firstly it is crucial for us to compare with strong baselines in model quantization, regardless of the methods they employ. Among the baselines we selected, there are also methods based on knowledge distillation (training), such as LLM-QAT [2], which was once a strong baseline. Please refer to Sections 4.1 & 4.2. Question 2: "An essential ablation study is notably absent from the discussion. The impact of these vectors a/b on performance enhancement remains unclear." In fact, the comparison with BitNet is essentially an ablation study concerning the a/b vectors, as the main difference between our model structure and BitNet lies in the introduction of the FP16 a/b vectors. Due to space limitation, the main discussion is placed in Appendix A.5, with the conclusions only presented in Sections 5.2 & 5.3 of the main text. We will address this issue in the revised version. From the discussion in A.5, we demonstrate that, once these two vectors are deleted (BitNet), the 1-bit weight W-only model fails to converge during quantization-aware distillation. Hence, our model structure (with a/b vectors) achieves stable ability transfer and training process, which demonstrate its necessity. Question 3: "Including generative tasks would provide deeper insights into the versatility and practical applicability of the proposed method across different domains." Thank you for your valuable suggestions! We will consider adding more examples of generative tasks in the revised version's Appendix to demonstrate the practical value of our method. We look forward to hearing from you and hope to address any concerns you may have about our work. Please let us know if you have any further questions. Reference: [1] Huang W, Liu Y, Qin H, et al. BiLLM: Pushing the Limit of Post-Training Quantization for LLMs[C]//Forty-first International Conference on Machine Learning. 2024. [2] Liu Z, Oguz B, Zhao C, et al. LLM-QAT: Data-free quantization aware training for large language models[J]. arXiv preprint arXiv:2305.17888, 2023. --- Rebuttal 2: Title: Official comments by Reviewer mFhw Comment: Thank you to the authors for rebuttal and the clarifications provided. Based on your responses, I remain inclined to keep the score. --- Rebuttal Comment 2.1: Comment: Thank you very much for your continued review. We are grateful for your positive feedback and the time you have devoted to evaluating our work. Please don’t hesitate to reach out if there are any further questions or points of discussion. We remain at your disposal for any additional clarifications.	Summary: This paper proposes OneBits, a novel quantization-aware training methodology for 1-bit large language models (LLMs). OneBits introduces two key contributions for training 1-bit models. First, it presents a new 1-bit binary quantization linear design that separates the weight matrix into sign and value components. The sign is packed into INT1, while the value is decomposed using a 1-rank decomposition factor added to the linear operation. Second, to train the 1-bit models in the linear layers of BitNets, OneBits modifies the traditional quantization-aware training (QAT) method by augmenting the cross-entropy loss function with an additional term for the reconstruction error of each layer, resulting in the final objective loss function. Using the proposed approach, OneBits is applied to various decoder-only LLM models. The comparisons between OneBits (W1A16) and other methods like LLM-QAT, AWQ, and OmniQuant (W2A16) demonstrate that OneBits achieves superior performance in common sense reasoning tasks. Strengths: - The paper proposes a final objective loss function that combines the final cross-entropy loss with the reconstruction error of each layer using a Quantization-aware Knowledge Transfer method. The effectiveness of incorporating the reconstruction error is demonstrated through an ablation study (Table 6). - Unlike the traditional 1-bit linear design in BitNet, the authors introduce a new 1-bit binary quantization linear design that includes scaling factors (g/h) for each input/output channel of the weight matrix. They also propose an initialization method from a pretrained model using Sign-Value Independent Decomposition (SVID). - To initialize the scaling factors (g/h) for each input/output channel, the paper explores various 1-rank decomposition methods for value in SVID, including Singular Value Decomposition (SVD) and Non-negative Matrix Factorization (NMF). Experimental results indicate that the 1-rank decomposition of value using NMF is more effective than SVD. Weaknesses: - While the paper demonstrates zero-shot performance in terms of PPL and CSR, it lacks experiments on how the same model maintains performance in few-shot scenarios, such as the MMLU benchmark. - If the quality of this generated data is poor, it could negatively impact the performance of the OneBit LLM. The paper does not clearly explain why self-generated data was used instead of public datasets like C4. - The analysis of OneBit LLM's benefits in terms of inference latency and throughput relative to accuracy is insufficient. A detailed examination of these metrics would provide a more comprehensive understanding of the advantages of using OneBit LLM. Technical Quality: 2 Clarity: 3 Questions for Authors: - While the OneBit method has demonstrated independent evaluation of zero-shot and few-shot performance, showing effectiveness compared to LLM-QAT and OmniQuant, it does not provide evidence of a single OneBit model performing well in both zero-shot and few-shot scenarios simultaneously. It would be valuable to present combined performance results, such as including MMLU results in Table 2 for a comprehensive comparison. - When comparing the quality of output generated by OneBit LLM to other models using metrics like AlpacaEval, what trends or patterns emerge regarding the quality of generated data? Confidence: 4 Soundness: 2 Presentation: 3 Contribution: 2 Limitations: Since OneBit LLM is applied only to weights, this method is likely to be effective in improving latency and throughput, particularly in scenarios involving small batch sizes during the generation phase. In this paper, activation quantization has not been considered, and further research in this area is necessary to optimize performance. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We appreciate the time and effort you have invested in reviewing our paper. Weakness 1: "It might lack a few-shot benchmark result such as MMLU." Although few-shot evaluation is not a necessary component in most model quantization research [1,2,3], we still evaluated the 5-shot performance of OneBit-7B on MMLU in Sec. 4.3. Please refer to Sec. 4.3 and Fig. 3(b). Weakness 2: "Poor self-generated data may negatively impact the performance of OneBit. The reason for using it instead of public dataset C4 is not clearly explained." Here we follow LLM-QAT (L204) to perform knowledge distillation. In LLM-QAT [5], the authors have demonstrated the effectiveness of using self-generated data, which provide a comprehensive coverage of sample-able tokens. Using external data may introduce bias. In fact, in terms of content, the quality of self-generated data (which we have open-sourced on other platforms) is indeed inferior to the carefully cleaned real data. However, it can maximize the ability transfer of the FP16 teacher in the student model. We take Llama-7B and PPL as examples to compare the effects of the two types of data, where C4 has the same amount of data after sampling as the self-generated data. \| data source \| Wiki2 \| C4 \| \| -- \| -- \| -- \| \| sampled-C4 \| 15.01 \| 12.29 \| \| self-generated \| 10.19 \| 11.40 \| Weakness 3: "A detailed examination of inference latency may be insufficient." The potential advantage of our method benefits from a special multiplication, *INT1(W) FP16(A)*, in which the traditional FP16FP16 can be quickly and efficiently replaced by setting the sign bit of FP16 activation. For example, we have W=(0.1, -0.3, -0.2) and A=(0.8, 0.2, 0.7), and traditional WA maybe 0.10.8+(-0.3)0.2+(-0.2)0.7 and it can be quantized to Pos(0.8)+Neg(0.2)+Neg(0.7). Here Pos(·) represents the machine instruction for setting the sign bit of a floating-point number to '+', while Neg(·) represents the opposite. Unfortunately, since this computation method is not yet perfectly supported at the GPU hardware level, we cannot demonstrate how fast OneBit truly is on the device. All experiments have been conducted using FP16 format containing only ±1 for simulation. We provide an possible efficient implementation of the OneBit Linear Layer in the supplemental material. If we simply simulate INT1 using FP16 format, the inference time is approximately 1.2x that of the original model. If we aim for extreme space compression, i.e., expanding the compressed weight during inference, the inference latency is approximately 2.2x that of the original model. It is worth noting that most weight-only quantization studies introduce additional inference latency. Additionally, we sincerely hope that our work, along with recent similar efforts, will encourage device providers to support this faster computation method at the hardware level. Question 1: "It would be valuable to present combined performance results, such as including MMLU results in Table 2." Thank you for your suggestion! We did not take this for 2 reasons: first, other than OmniQuant, the W2A16 baselines perform poorly on MMLU. Second, we wanted to compare our method’s performance in general knowledge using MMLU, hence we included it in Section 4.3. Question 2: "What trends or patterns emerge regarding the quality of generated data comparing to other models?" As shown in PPL (Tab.2) and the content in Tab. 5, OneBit can fluently output content as long as it has not forgotten the knowledge in that domain, showing no significant difference from the original model. However, once OneBit forgets the knowledge of a certain domain, it tends to output a minimal number of tokens followed by '\n', and then stops outputting. Limitation: "Activation quantization has not been considered, and further research in this area is necessary to optimize performance." To date, weight quantization [1,4] and weight-activation[2,3,5] quantization remain 2 distinct research paths. The reason and difficulty lie in the fact that activation quantization also compromises the model’s capabilities, with significant compression of activations causing severe degradation of the model’s performance. Therefore, the strongest baseline for W-quantization is currently W1A16, while WA-quantization can generally achieve W4A4. We are working towards further compressing activations, but we think that not considering activations may not be a limitation. We look forward to hearing from you and hope to address any concerns you may have about our work. Please let us know if you have any further questions. Reference: [1] Frantar E, Ashkboos S, Hoefler T, et al. OPTQ: Accurate quantization for generative pre-trained transformers[C]//The Eleventh International Conference on Learning Representations. 2022. [2] Xiao G, Lin J, Seznec M, et al. Smoothquant: Accurate and efficient post-training quantization for large language models[C]//International Conference on Machine Learning. PMLR, 2023: 38087-38099. [3] Shao W, Chen M, Zhang Z, et al. OmniQuant: Omnidirectionally Calibrated Quantization for Large Language Models[C]//The Twelfth International Conference on Learning Representations. 2024. [4] Lin J, Tang J, Tang H, et al. AWQ: Activation-aware Weight Quantization for On-Device LLM Compression and Acceleration[J]. Proceedings of Machine Learning and Systems, 2024, 6: 87-100. [5] Liu Z, Oguz B, Zhao C, et al. LLM-QAT: Data-free quantization aware training for large language models[J]. arXiv preprint arXiv:2305.17888, 2023. --- Rebuttal Comment 1.1: Title: Invitation to Participate in the Discussion Period Comment: Thank you very much for your review. We have provided detailed responses to your question. If you could participate in the discussion period, we would be very grateful again. --- Rebuttal Comment 1.2: Title: Response from Reviewer gg38 Comment: Thank you for your considerate response. While most of my concerns have been addressed, I still believe it is important to examine how the gap between Zero-shot and Few-shot performance changes before and after applying OneBits to the public LLM models in Table 2. When performing QAT from scratch, as with OneBits-7B, I believe that training with at least a similar number of tokens to what is suggested by the Chinchilla-optimal is necessary to observe a reliable trend. However, considering that Figures 3(a) and 3(b) show that OneBit-7B achieves performance comparable to the 1B-scale model, which was trained with a larger amount of data, and that OneBit demonstrates a meaningful performance improvement over other quantization methods on public LLMs, I have decided to raise my score from 4 to 5. --- Reply to Comment 1.2.1: Comment: Thank you very much for your continued review. We are grateful for your positive feedback and the time you have devoted to evaluating our work. Please don’t hesitate to reach out if there are any further questions or points of discussion. We remain at your disposal for any additional clarifications.	Summary: This paper proposes OneBit, which quantizes the LLM weight matrices to 1-bit and achieves good performance and improved convergence speed by using two additional vectors with FP16 per one linear layer. Strengths: 1. This paper is generally well-written and easy to follow. 2. The memory required for the model part is less than other methods. 3. Their methods nicely outperforms other methods in many tasks. Weaknesses: 1. It will be great if they compare with other one-bit based quantization methods such as BitNet. 2. I recommend authors to add empirical results for larger models like Llama-70b. Technical Quality: 3 Clarity: 3 Questions for Authors: 1. Would it be possible to compare the inference speed of this method and other methods? I am curious about the potential delay in inference caused by using additional FP16 vectors. Confidence: 4 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 appreciate the time and effort you have invested in reviewing our paper. Weakness 1: "It will be great if they compare with other one-bit based quantization methods such as BitNet." Converting the "pre-trained model" into a low-bit representation is the focus of almost all research on model quantization [1,2,3], and we also follow this point. BitNet, as another well-known work, differs from model quantization by proposing a possible model structure with 1-bit weights (they focus on training low-bit model from scratch). Therefore, BitNet and our model quantization essentially address different research problems. In fact, we are also curious whether the BitNet structure can be used for quantizing existing models, and we have discussed the relevant results in Appendix A.5 and Fig. 6. The conclusion shows that, compared to BitNet, our model structure achieves stable ability transfer and training process, whereas BitNet fails to converge during quantization-aware distillation. Hence, we cannot provide benchmark results of BitNet in the main text. Weakness 2: "I recommend authors to add empirical results for larger models like Llama-70b." Due to the limitation of computational resources, we are currently unable to perform experiments on 70B-scale models, although we have been trying to get the resources. However, our existing results indicate an exciting trend: "the larger the model, the smaller the performance gap between the FP16 precision and the W1A16 quantized model." This conclusion is mentioned in lines L238~L240 of our paper. Question: "Would it be possible to compare the inference speed of this method and other methods? I am curious about the potential delay in inference caused by using additional FP16 vectors." It is possible to compare the inference speed of ours with FP16 baseline. In a 4k-length inference test, if the weights are simulated in FP16 format containing only ±1, the OneBit model, which includes FP16 vectors, takes approximately 1.2x the duration of Llama-7b without these vectors. In fact, thanks to the broadcasting mechanism of tensors, the element-wise multiplication of matrices and vectors can be performed very quickly. Therefore, the additional vector incurs minimal time overhead. We look forward to hearing from you and hope to address any concerns you may have about our work. Please let us know if you have any further questions. Reference: [1] Frantar E, Ashkboos S, Hoefler T, et al. OPTQ: Accurate quantization for generative pre-trained transformers[C]//The Eleventh International Conference on Learning Representations. 2022. [2] Xiao G, Lin J, Seznec M, et al. Smoothquant: Accurate and efficient post-training quantization for large language models[C]//International Conference on Machine Learning. PMLR, 2023: 38087-38099. [3] Liu Z, Oguz B, Zhao C, et al. LLM-QAT: Data-free quantization aware training for large language models[J]. arXiv preprint arXiv:2305.17888, 2023. --- Rebuttal Comment 1.1: Comment: Thank you for your rebuttal and clarification. I remain inclined to accept this work and will maintain my score of 6. --- Reply to Comment 1.1.1: Comment: Thank you very much for your continued review. We are grateful for your positive feedback and the time you have devoted to evaluating our work. Please don’t hesitate to reach out if there are any further questions or points of discussion. We remain at your disposal for any additional clarifications.	null	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Approximation Rate of the Transformer Architecture for Sequence Modeling	Accept (poster)	Summary: This study investigates a Jackson-type approximation rate for single-layer Transformers with one head, and compares their ability with RNNs, another nonlinear sequence-to-sequence map. Strengths: - The literature overview is concise - The Jackson-type approximation rate for the Transformer is derived for the first time Weaknesses: The main theorem (Theorem 4.2) sounds trivial because the bound is a combination of the definitions of complexities $C^\alpha$ (Sobolev smoothness) and $C^\beta$ (Barron bound). The universality of Eq.8 (Theorem A.3) may sound non-trivial, but it is obtained by rewriting the Kolmogorov representation of continuous function (from Theorem A.1), which is much a stronger (but only existential) result. It could be non-trivial if the authors could provide a similar bound in a constructive manner without using the magic argument of Kolmogorov. Technical Quality: 2 Clarity: 2 Questions for Authors: - Can the author provide a similar bound in a constructive manner without using the Kolmogorov theorem? - Given a dataset, how to estimate $\alpha$ and $\beta$? Confidence: 3 Soundness: 2 Presentation: 2 Contribution: 2 Limitations: n/a Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: 1. The main theorem (Theorem 4.2) sounds trivial because the bound is a combination of the definitions of complexities $C^\alpha$ (Sobolev smoothness) and $C^\beta$ (Barron bound). - Firstly, we need to clarify that $ C^\alpha $ is not a Sobolev smoothness term. It is defined as the POD rank of the temporal coupling term $ \rho $ (Line 181 - Line 195). To the best of our knowledge, our approximation rate results (Theorem 4.2) have no similar results previously. - Theorem 4.2 should not be dismissed as trivial. For Theorem 4.2, our analysis sheds light on the distinct roles of the feed-forward and attention components. The feed-forward component aims to approximate both the pointwise functions $F$ and $f$, as well as the POD bases of the temporal coupling component $\rho$. We substantiated the validity of our findings numerically in Section 5, demonstrating the existence of low-rank structures in Transformer approximations. - Additionally, Theorem 4.2 provides insights into the differences between Transformers and traditional sequence modeling architectures like RNNs, discussed in Section 6. The complexity measures defined Section 4 are unaffected by permutation but is influenced by temporal mixing. This contrast implies the fundamental distinction of Transformers and RNNs in handling temporal relationships. In Section 6.1 we show that the RNN is proficient in handling temporal relationships with strong temporal ordering structure. While for relationship with minimal temporal ordering, the Transformers works better. Section 6.2 explores how temporal mixing can impact Transformer performance, whereas RNNs remain unaffected. - Defining appropriate complexity measures and approximation spaces is crucial in approximation theory, offering insights into hypothesis spaces. A well-chosen approximation space can illuminate the capabilities of the hypothesis space. Referring to recent studies [1] and [2], which consider targets of the form $H_t(x) = \sum \rho(s)x(t-s)$, various complexity measures are defined for $\rho$ considering the architectures. In RNNs [1], these measures account for the smoothness and decay rate of $\rho$, whereas in CNNs [2], they focus on the sparsity of $\rho$. Different architectures reveal distinct approximation capabilities: RNNs excel with smooth and fast-decaying targets, while CNNs are effective with sparse targets. Our results also provides insights of the Transformer architectures, which are discussed in Section 5 and Section 6. [1] Li, Zhong, et al. "Approximation and optimization theory for linear continuous-time recurrent neural networks." Journal of Machine Learning Research 23.42 (2022): 1-85. [2] Jiang, Haotian, Zhong Li, and Qianxiao Li. "Approximation theory of convolutional architectures for time series modelling." International Conference on Machine Learning. PMLR, 2021. 2. Given a dataset, how to estimate $\alpha$ and $\beta$ ? - Estimating $\alpha$ and $\beta$ directly from a dataset based on their definitions can be challenging. However, empirical estimation is feasible by training models of varying sizes on the dataset. In Section 5.1, we discuss how to estimate $\alpha$ in detail. The main idea is train models with varying $m_h$ and fit the error curve with $\frac{1}{m_h^\alpha} + c$ for an estimation of $\alpha$. It is important to highlight that insights derived from approximation results hold greater significance than exact values of approximation bounds. Specifically, in Section 6, we discuss the strengths and limitations of Transformers compared to RNNs, leveraging these approximation insights for discussion. 3. Can the author provide a similar bound in a constructive manner without using the Kolmogorov theorem? - The approximation bound in Theorem 4.2 is independent of the Kolmogorov theorem. The Kolmogorov theorem is only used in Theorem 4.1 to establish that form (8) is general enough to represent any continuous target. The approximation bound in Theorem 4.2 considers targets of the form (8) where $F$, $f$, and $\rho$ are assumed to be general continuous function with finite complexity measures and not restricted by the Kolmogorov representation. Consequently, the results in Theorem 4.2 are not depend on the Kolmogorov theorem. --- Rebuttal 2: Comment: Thank you for your clarifications. I will keep my score as is. > The approximation bound in Theorem 4.2 is independent of the Kolmogorov theorem. If so, it's misleading that Theorem 4.1 is put inside the Section 4.2, and it's even better if the paper is written completely without Kolmogorov. --- Rebuttal Comment 2.1: Comment: Thanks for your response. We would like to clarify again that the purpose of Theorem 4.1 is to ensure that the target space considered in form (8) is large enough to represent any continuous sequence-to-sequence functions. We want to confirm that this target space is not restrictive. Then, in Theorem 4.2, we consider target functions of the form in (8) with regularities to develop the approximation rates. The Kolmogorov method is a proof technique for Theorem 4.1, there may also be other methods to prove the theorem, but this should not affect the results and logic flow of the paper.	Summary: This paper introduces a novel concept of complexity measures to construct approximation spaces for single-layer Transformers with one attention head, providing Jackson-type approximation rate results for target spaces that possess a representation theorem. Strengths: - The results in this paper are presented within a general framework using rigorous and elegant mathematical tools, offering a solid theoretical foundation for researchers interested in approximation. - Their hypothesis of singular value decay pattern regarding the target space can be validated through the experiments detailed in Section 5. Furthermore, the hypothesis underscores the crucial role of pairwise coupling and low-rank structure. Weaknesses: The results presented are limited to 2-layer single-head Transformers, which restricts their applicability and insights into more common models such as multi-layer multi-head Transformers. Technical Quality: 3 Clarity: 2 Questions for Authors: - How can the results be generalized to analyze multi-layer multi-head Transformers? Will such generalization provide new insights or understanding? - Although the discussion on the parameters' dependence on rank is provided, the factor $\tau^2$ in the RHS of the inequality in Theorem 4.2 appears suboptimal for approximating long sequences. - It seems that much of the relevant literature on the approximation power of Transformers has been omitted. For example, [1][2][3]. [1] Giannou et al (2023). Looped Transformers as Programmable Computers. [2] Bai et al (2023). Transformers as statisticians: Provable in-context learning with in-context algorithm selection. [3] Wang \& E (2024). Understanding the Expressive Power and Mechanisms of Transformer for Sequence Modeling. Confidence: 4 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: See Weaknesses. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: 1. How can the results be generalized to analyze multi-layer multi-head Transformers? Will such generalization provide new insights or understanding? - Firstly, our rate still applies to multi-layer and multi-head Transformers, serving as an upper bound. This is because our single-layer, single-head architecture represents the simplest form of multi-layer, multi-head Transformers. However, increasing the number of layers and heads can potentially yield more refined bounds. Theoretical analysis of the relationship with depth and the number of heads requires consideration of a more intricate approximation space, which includes defining suitable target form with complexity measures that account for depth and the multi-head structure. - While our theoretical results are based on simplified architectures, empirical verification in Section 5 and Section 6 confirms that these insights (be specific) hold for multi-layer architectures as well. In Section 5, we demonstrated the existence of low-rank structures in multi-layer Transformer architectures. Section 6 discuss both the strengths and limitations of Transformers compared to RNNs. We verified our statements regarding general multi-layer and multi-head structures. 2. Although the discussion on the parameters' dependence on rank is provided, the factor $\tau^2$ in the RHS of the inequality in Theorem 4.2 appears suboptimal for approximating long sequences. - The quadratic scaling of Transformers in sequence length is a well-known issue. The factor of $\tau^2$ arises because the size of attention matrix scales as $O(\tau^2)$ with the sequence length,leading to quadratic scaling in computation time. This scaling also affects approximations, as described by Equation (43), where the approximation of the attention matrix involves both temporal directions $t$ and $s$, resulting in approximation errors that scale with $\tau^2$. 3. It seems that much of the relevant literature on the approximation power of Transformers has been omitted. For example, [1][2][3]. - [1] considers a special setting regarding expressiveness, demonstrating that Transformers can represent any computer program. [2] and [3] explore target relationships with certain special structures. Thank you for highlighting these references. We will include them in the related work section. [1] Giannou et al (2023). Looped Transformers as Programmable Computers. [2] Bai et al (2023). Transformers as statisticians: Provable in-context learning with in-context algorithm selection. [3] Wang & E (2024). Understanding the Expressive Power and Mechanisms of Transformer for Sequence Modeling. --- Rebuttal Comment 1.1: Comment: Thank you for your clarifications. I will maintain my score.	Summary: The study explores the theoretical aspects of Transformer architectures in sequence modeling, particularly focusing on approximation rates for sequence-to-sequence relationships. A representation theorem is established, introducing novel complexity measures that analyze interactions among input tokens, culminating in a Jackson-type approximation rate estimate for Transformers. Strengths: This study enhances the understanding of Transformer's approximation rate and gives concrete comparisons with traditional models like recurrent neural networks. Weaknesses: The paper deviates from the standard Transformer architecture by requiring a neural network layer before the attention mechanism to implement the Kolmogorov Representation Theorem, potentially inheriting the theorem's limitations. Technical Quality: 3 Clarity: 3 Questions for Authors: Q1. In the context of POD, it is my understanding that having rho with fast decaying singular values allows for the complexity measure of H to be constant. However, this paper employs a specific construction to derive equation (22) for sigma(rho) as mentioned in line 492. Could we still say that rho has fast decaying singular values in this case? Please provide a specific explanation. Q2. It's unclear how to construct the F1 function that realizes equation (25). Could you explain in detail? Q3. I cannot understand the flow from equation (22) to (25). Eequation (24) (f(x_t)+sum_s f(x_s)) is constructed using equation (22), which is realized by using a specific attention, and then f(x_t) is removed in equation (25). Why not just construct an attention, average pooling, that constitutes sum_s f(x_s) in Eq. (22)? Q4. Theorem A.3 states that n=tau * (2 * tau * d+1)+1. However, looking at equation (23), it appears that the output of f is only (2 * tau * d+1)-dimensional. Where does n=tau * (2 * tau * d+1)+1 need to be? Q.5 Considering the theoretical framework presented here which inherits limitations from the Kolmogorov representation theorem, could you specify what limitations might arise in the class of functions approximated by the model? It is worth noting that identifying these limitations does not detract from the contributions of this paper. Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The paper deviates from the standard Transformer architecture by requiring a neural network layer before the attention mechanism to implement the Kolmogorov Representation Theorem, potentially inheriting the theorem's limitations. Flag For Ethics Review: ['No ethics review needed.'] Rating: 8 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: 1. The paper deviates from the standard Transformer architecture by requiring a neural network layer before the attention mechanism to implement the Kolmogorov Representation Theorem, potentially inheriting the theorem's limitations. - For our proposed architecture (5), the term $\hat h = \hat f \circ x$ is fed into the attention component, where $\hat f$ is a feed-forward network. This assumption is not particularly restrictive. Our architecture (5) can be viewed as a specific "slice" of the standard Transformer architecture. The standard Transformer follows a pattern of "Atten->FFN->Atten->FFN->...". Our formulation can be seen as focusing on the "FFN->Atten->FFN" part within this structure. 2. In the context of POD, it is my understanding that having rho with fast decaying singular values allows for the complexity measure of H to be constant. However, this paper employs a specific construction to derive equation (22) for sigma(rho) as mentioned in line 492. Could we still say that rho has fast decaying singular values in this case? Please provide a specific explanation. - Line 492 pertains to the proof of Theorem 4.1, demonstrating the equivalence of Equation (8) with the continuous function space $\mathcal C=C(\mathcal X^{(E)}, \mathcal Y)$. The proof is constructive, involving a specific construction of $\rho$ at Line 492. It is essential to emphasize that this construction is designed specifically for the proof of Theorem 4.1. When assuming a target in the form of Equation (8), we do not assume $\rho$ to have any specific form. - For Theorem 4.2, we do not assume $\rho$ is fixed like the construction presented in Line 492. In Theorem 4.2, the target $H$ adopts the structure of Equation (8), where $\rho \in C(\mathcal I \times \mathcal I, \mathbb R)$ is a general continuous function that have finite complexity $C_1^{\alpha}$. Since $\rho$ is not restricted to a specific form, different target $H$ may correspond to varying patterns of singular value decay and thus different complexity measures. 3. It's unclear how to construct the F1 function that realizes equation (25). Could you explain in detail? Firstly, for clarity, Equation (24) should be defined as $u(t) = f(x(t)) + \sum_{s=1}^\tau f(x(s))$. Next, it is observed that each $u(t)$ resides within disjoint cubes since $b_t$ are assumed to be distinct. Consequently, $F_1$ can be defined separately on each disjoint cube. For each $t$, the expression $F_1(u(t))$ is governed by Equation (25). Moreover, $u(t)$ is $n$-dimensional, where $u_i(t)$ denotes its $i$-th component. 4. I cannot understand the flow from equation (22) to (25). Eequation (24) (f(x_t)+sum_s f(x_s)) is constructed using equation (22), which is realized by using a specific attention, and then f(x_t) is removed in equation (25). Why not just construct an attention, average pooling, that constitutes sum_s f(x_s) in Eq. (22)? - To clarify, Equation (24) should be defined as $u(t) = f(x(t)) + \sum_{s=1}^\tau f(x(s))$. Equation (25) does not remove $f(x_t)$; rather, it is an intermediate definition of $F$ in Line 500. - The proof aims to align the functions $F$, $f$, and $\rho$ in Equation (8) with Equation (18). Specifically, $\rho$ is defined at Line 492, and $f$ is given by Equation (23). The function $F$ is constructed as $F(u) = F_2 \circ F_1((\tau+1)u)$, where its definition is decomposed into two distinct functions for clarity. By substituting these expressions for $f$ and $F$ into Equation (22), the proof achieves an exact correspondence with Equation (18). 5. Theorem A.3 states that n=tau * (2 * tau * d+1)+1. However, looking at equation (23), it appears that the output of f is only (2 * tau * d+1)-dimensional. Where does n=tau * (2 * tau * d+1)+1 need to be? - Thanks for pointing out. This is indeed a typo, the correct formula should be $n=(2 * \tau * d+1)$. 6. Considering the theoretical framework presented here which inherits limitations from the Kolmogorov representation theorem, could you specify what limitations might arise in the class of functions approximated by the model? It is worth noting that identifying these limitations does not detract from the contributions of this paper. - A techniqual limitation of the function space arises because a given $H$ may correspond to different sets of $F$, $f$, and $\rho$, implying non-uniqueness of the form (8). This aspect is reflected in the definitions of complexity measures in (10), (12), and (13), where we take the infimum over all possible $F$, $f$, and $\rho$. - In Section 6, we also discuss limitations arising from target form (8). Proposition 6.2 states that permutation of input sequences does not alter the complexity measures, suggesting that temporal ordering is insignificant within this function space. This implies that Transformers excel in handling sequential relationships with minimal temporal dependencies, as detailed in Section 6.1. However, the complexity of the function space can be significantly influenced by temporal mixing. As discussed in Section 6.2, this indicates that the performance of Transformers can be adversely affected by straightforward temporal mixing manipulations. To summary, these intrinsic structural limitations also implies approximation limitations of the Transformers. --- Rebuttal Comment 1.1: Comment: Thank you for the response. I will raise my score.	null	null	null	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Video Diffusion Models are Training-free Motion Interpreter and Controller	Accept (poster)	Summary: This paper introduces a new Motion Feature (MOFT) that can effectively capture motion information in video diffusion models. The authors reveal that robust motion-aware features already exist in video diffusion models, allowing to encode comprehensive motion information with clear interpretability. They present MOFT, which can be extracted without the need for training and is generalizable across diverse architectures. Strengths: - Training-free strategy effectively extracts motion information encoded in the features of the video diffusion model, demonstrating its ability to capture and leverage the inherent motion representations learned by the model. - The method presents a clean and straightforward solution for extracting motion encoding from video diffusion models, making it a ready and practical technique for various applications involving motion analysis or synthesis. Weaknesses: - The paper lacks clarity on the training process. While it claims to be training-free, it defines loss functions for other tasks (Equations 3 and 4). It would be helpful to clarify which stages are trained and which are not. - The PCA analysis is based on a small number of videos (only 2 videos in Figure 2), which limits the generalizability of the results. - While the motion in the qualitative videos looks good, the differences compared to other alterations appear subtle and hard to recognize. Other methods show too poor results, were they tuned correctly? - The paper should report the runtime and resolution for better understanding of the method's computational requirements and output quality. - The idea is heavily inspired by DIFT and utilized for video applications, then novelty seems limited. Technical Quality: 3 Clarity: 2 Questions for Authors: Clarification needed: - Figure 1: a. It is unclear whether the motion feature in 1(a) is extracted semantically or spatially. Clarification is needed on how the similarity with other videos in 1(b) is calculated. Additionally, an explanation of what the higher score represents and why motion features from different videos could influence each other would be helpful. b. In 1(c), the motion direction seems to be manually defined. If so, why does the paper state that MOFT serves as guidance for controlling motion direction? If MOFT controls the motion, what is the source video for that motion? - Figure 6: Why the comparison is presented in the form of a point for DIFT and a segment for MOFT. Confidence: 5 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: Limitations are addressed adequately. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We are grateful for your valuable input. Please see the detailed responses to each of your concerns listed below. W1: Clarification on the training process > The paper lacks clarity on the training process. It would be helpful to clarify which stages are trained and which are not. Optimization does not necessarily mean training. "Training-free" means that we do not need to optimize model parameters during the training stage. Instead, the loss function is used to optimize the latent at each denoising step during the inference stage, which is a common technique to guide the diffusion process [1, 2]. We will add this clarification in the new version. Please refer to the pseudo-code in the global response for the details of the optimization process. W2: Clarification for the number of videos in PCA > The PCA analysis is based on a small number of videos (only 2 videos in Figure 2), which limits the generalizability of the results. In Figure 2, PCA analysis is based on six videos, with indices 1 and 2 showing the same motion in different videos. We do not consistently use the same pair of videos to demonstrate that our observations are not tied to specific videos. Although the sample size is small, our results show that PCA-filtered motion channels are robust to the number of videos. Table 2 in the attached PDF compares channel similarity between PCA results from 6 and 20 videos, showing high similarity in filtered motion channels, indicating PCA's robustness. Table 3 further confirms that motion fidelity and image quality metrics are also robust to the number of videos used. W3: Clarification on the qualitative comparison > While the motion in the qualitative videos looks good, the differences compared to other alterations appear subtle and hard to recognize. Other methods show too poor results, were they tuned correctly? In the qualitative comparison with other methods, we focus on challenging cases for existing methods. In these cases, other methods often struggle: for example, DragNUWA [3] typically only moves part of the object, and Gen-2 [4] frequently generates unnatural movements. Our method, however, performs well and generates natural motions even in these challenging scenarios. We do not need to fine-tune these methods; instead, we directly test their results using publicly available code or APIs. W4: Report on the runtime and resolution > The paper should report the runtime and resolution for better understanding of the method's computational requirements and output quality. Our results are at a resolution of 512x512 and 16 frames unless otherwise specified. We use DDIM with 25 denoising steps for each sample. It takes approximately 3 minutes to generate one sample on an RTX 3090 GPU. We will include this information in the revision. W5: Clarification on the novelty > The idea is heavily inspired by DIFT and utilized for video applications, then novelty seems limited. The inspiration from DIFT lies in the high-level research style, as both works analyze diffusion features. However, our motivations, contributions, and techniques are distinct: - Motivation: We aim to decompose motion features from video diffusion features for better motion understanding and control, unlike DIFT which targets semantic correspondence in image diffusion models. - Contribution: MOtion FeaTure (MOFT) is the first to reveal rich motion information in video diffusion features, using a straightforward and innovative approach. DIFT shows diffusion features can capture semantic correspondence. - Technique: MOFT uses a novel PCA-based strategy to extract motion-aware features, while DIFT directly uses intermediate features without further processing. Q1-1: Clarification on the motion feature The motion feature in 1(a) is extracted following Eq. 2. The extracted feature contains spatial dimension, but the feature of a point location captures temporal motion of that point instead of semantics. The heatmap in 1(b) is calculated by the cosine similarity between the MOFT at the red dot in 1(a) and the MOFT of all points in 1(b), expressed as: $M=cosine(M_a,M_b)$, where $M\in \mathbb{R}^{H×W}$ is the output heatmap, $M_a \in \mathbb{R}^{C}$ is the MOFT of one point in the source image, and $M_b\in \mathbb{R}^{H\times W\times C}$ is the MOFT of all points in the target image. $H$, $W$ and $C$ are height, width and channel number, respectively. We use only one frame to calculate the similarity and for visualization. Higher scores indicate greater motion similarity. For example, higher scores in the man’s region (last case in 1(b)) show that the man’s motion direction matches the reference (red dot) in 1(a), both moving left. This method also allows us to manipulate MOFT to alter motion direction. Q1-2: Clarification on the motion signal We need to transfer manually defined motion directions to MOFT for the motion optimization target, otherwise the optimization is not feasible. For obtaining the target MOFT, we offer two methods: - Synthesized from manually defined motion directions (as shown in Fig. 7(c) and 7(d)), which is the case discussed in this question. Details of this process are described in Line 175-179 of the paper. - Extracted from the reference source video (Fig. 7(a) and 7(b)). Q2: Clarification on Figure 6 The similarity heatmaps serve different purposes in each method. In DIFT, the similarity heatmap shows semantic similarity between points in the target and source images, focusing on a one-to-one correspondence to find the most accurate match. In MOFT, the heatmap represents motion similarity between points in the target image and a reference point in the source image. Here, the heatmap visualizes regions with similar motion rather than finding a single best match. We visualize their effects at different time steps to highlight the MOFT works better at the earlier denoising stage, instead of direct comparisons on effects. --- Rebuttal Comment 1.1: Comment: Thank you to the authors for the detailed response. A few points remain unclear to me, including the optimization process solely on the latent representation. I could not fully verify and be convinced on this point. However, I understand the limitations of conveying technical details thoroughly in a written response. If possible, I would suggest the authors conduct additional samples that transfer longer and more complex motions, such as multipoint, circular, or periodic motions. Considering the strengths and applicability of this work, I am happy to increase my rating to "Borderline Accept". I hope the authors will soon release the code so that other researchers can build upon this work to push forward the field. --- Reply to Comment 1.1.1: Title: Response by authors Comment: Thank you for the quick reply and positive response. We appreciate your feedback and are happy to clarify any remaining points. The optimization process on the latent representation is not a novel technique. It has been widely used in image and video editing tasks, such as DragDiffusion [1] and SMM [2]. Our focus is on proposing a method to extract motion information as the optimization target. We will include more challenging cases in the final version and will release the code for further exploration by the research community. Thank you again for your time and consideration. [1] Shi Y, et al. Dragdiffusion: Harnessing diffusion models for interactive point-based image editing, CVPR 2024. [2] Yatim D, et al. Space-time diffusion features for zero-shot text-driven motion transfer, CVPR 2024.	Summary: The paper introduces a training-free framework for understanding and controlling motion in video diffusion models. The key innovation is the MOtion FeaTure (MOFT), which is derived by removing content correlation and filtering motion channels from pre-trained diffusion model features. MOFT provides a training-free way to encode and manipulate motion information, offering high interpretability and generalizability across various architectures. The framework demonstrates competitive performance in generating natural and faithful motion, with applications in video motion control and point-drag manipulation. Strengths: 1. Training-free Approach: The framework does not require additional training, leveraging pre-trained diffusion models to control motion, significantly reducing resource requirements. 2. Interpretability: MOFT offers a clear and interpretable way to understand and manipulate motion information in video diffusion models. 3. Generalizability: The method is applicable across various video generation models, demonstrating versatility and robustness. Weaknesses: Scalability to Longer Videos: The proposed method's scalability to longer videos or higher resolutions is not adequately explored. Complexity of MOFT Extraction: Removing content correlation and filtering motion channels may be complex and require fine-tuning for optimal results. Experiments: The text prompts used for quantitative experiments and user studies are unclear, and 56 case studies are insufficient to validate effectiveness. Technical Quality: 3 Clarity: 3 Questions for Authors: Providing a detailed description or pseudocode for MOFT extraction would aid in understanding its practical implementation and reproducibility. Have you tested MOFT's scalability for generating longer videos or higher-resolution outputs? What challenges, if any, did you encounter, and how did you address them? Additionally, how does this method handle more complex object control, such as multi-object scenarios with different categories and sizes? Confidence: 5 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: The author have discussed limitations in Supp. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your insightful review. You will find detailed responses to each of the points you raised below. W1: Scalability to longer videos and higher resolutions > Scalability to Longer Videos: The proposed method's scalability to longer videos or higher resolutions is not adequately explored Thanks for your suggestions. We've added experiments showing that our methods can be directly generalized to higher resolutions and longer videos. In Figure 3(a) of the attached PDF, we demonstrate that PCA can clearly separate videos with different motions based on their diffusion features from Open-Sora [5], an open-source video generation model capable of producing long videos. In Figure 3(b), we show that our methods can be applied to higher resolutions (768×768) and longer videos (205 frames on Open-Sora). W2: Clarification on MOFT extraction and optimization process > Complexity of MOFT Extraction: Removing content correlation and filtering motion channels may be complex and require fine-tuning for optimal results. The extraction of MOFT is both straightforward and efficient, requiring only a subtraction operation and mask indexing, thereby adding minimal time to the overall process. Our method does not require fine-tuning of model parameters. Instead, it only involves efficient optimization during the inference stage, which is a common technique in image and video editing to guide the generation process [2,6,9]. For further clarification on the optimization process, please refer to the pseudo-code in the global response. W3: Clarification on user studies > Experiments: The text prompts used for quantitative experiments and user studies are unclear, and 56 case studies are insufficient to validate effectiveness. We have added the prompts for the test in the appendix, some of them are shown below. - b&w photo of 42 y.o man in black clothes, bald, face, half body, body, high detailed skin, skin pores, coastline, overcast weather, wind, waves, 8k uhd, dslr, soft - a rabbit, forest, haze, halation, bloom, dramatic atmosphere, centred, rule of thirds, 200mm 1.4f macro shot - a white deer in the snow, cartoon, centred - a man surfing in the sea, RAW photo, subject, (high detailed skin:1.2), 8k uhd, dslr, soft lighting, high quality, film grain, Fujifilm XT3 - a car turns in the winter, 8k uhd, dslr, soft - photo of coastline, rocks, storm weather, wind, waves, lightning, 8k uhd, dslr, soft lighting, high quality, film grain, Fujifilm XT3 - night, old house, post apocalypse, forest, wind, rocks, 8k uhd, dslr, soft lighting, high quality, film grain - ... User study usually does not include samples with the scale of quantitative evaluation due to the labor consumption. 56 case studies are common numbers in user studies (~18 samples for each method). For example, Dragondiffusion [6] (ICLR 2024 , 16 samples for each method), Rerender-A-Video [10] (Siggraph Asia 2023, 8 samples for each method), FateZero [11] (ICCV 2023, 9 samples for each method) Q1: Challenges and solutions in this work > What challenges, if any, did you encounter, and how did you address them? The main challenge lies in the extraction of MOFT. Unlike DIFT, which directly uses intermediate features as the Diffusion Feature (DIFT) because it encodes rich semantic information, video diffusion features entangle various types of information, including semantic and motion information. Decomposing motion information from these features is not straightforward. Fortunately, our proposed method effectively localizes and extracts motion features, inspired by recent works on understanding video latents [8]. In addition, we want to highlight that the contribution of this paper extends beyond the technical aspects; it also discloses the finding that motion-aware features naturally exist in video diffusion models and provides a clear interpretation of how video diffusion features encode motion information. Q2: Solutions for complex cases > Additionally, how does this method handle more complex object control, such as multi-object scenarios with different categories and sizes? Our method can be naturally applied to multi-object scenarios involving different categories and sizes, thanks to the excellent generalization ability of video generation models. In multi-object scenarios, we employ multiple masks and use different optimization targets for these masked regions, enabling effective multi-object control. We will include more complex cases in the final version. --- Rebuttal Comment 1.1: Comment: Dear Reviewer, Please reply to the rebuttal if your concerns are addressed. AC. --- Rebuttal Comment 1.2: Comment: Thanks for the response and further experiments, which have addressed my main concerns. My original rating remains unchanged. --- Reply to Comment 1.2.1: Title: Response by authors Comment: Thank you for your positive feedback and for acknowledging that our response addressed your main concerns. We are keen to resolve any remaining issues and would be grateful if you could let us know if there are specific aspects that need further improvement. We hope that our response can fully address your concerns and positively influence your rating.	Summary: This paper investigates the relationship between the features of video diffusion models and the motion in the generated videos. By extracting motion features and using them as guidance, training-free motion control can be achieved. Strengths: 1. The technical aspects of this paper are clear and it is easy to read. 2. The proposed method can achieve training-free motion control for video generation. 3. The framework can be applied to different forms of control signals. Weaknesses: 1. From Fig. 6, it is hard to draw the conclusion that "MOFT can provide more valid information than DIFT at the early design stages". 2. The analysis experiments in the method section only focused on very simple motions, such as pan up, down, left, and right, without discussing more complex and realistic motions. 3. The generated motions presented in the experiment section are also mostly very simple. 4. The experiments lack comparisons with existing methods. Comparisons with other methods were only made in the point drag mode. Technical Quality: 3 Clarity: 3 Questions for Authors: Please refer to the waknesses. Confidence: 5 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: The limitations are discussed while the potential negative societal impact is not discussed. But I don't think this discussion is necessary. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We appreciate your thoughtful feedback. I've provided detailed responses to each of your concerns below. W1: Clarification on the conclusion from Fig. 6 > From Fig. 6, it is hard to draw the conclusion that "MOFT can provide more valid information than DIFT at the early design stages". From Figure 6, we observe that at early denoising steps (e.g., time step 800), DIFT struggles to provide valid information as the semantic correspondence is wrong. In contrast, MOFT delivers a relatively high score in the corresponding motion region (the rabbit's head), which benefits motion control. This observation is further validated by Figure 4 in the supplementary material. Note: The similarity heatmaps serve different purposes for each method. In DIFT, the heatmap represents semantic similarity, whereas in MOFT, it represents motion similarity. Therefore, we do not directly compare the heatmaps between DIFT and MOFT at the same time steps. Instead, we visualize their effects at different time steps to highlight that MOFT performs better at the earlier denoising stages. W2: Reasons for using simple motion in analysis experiments > The analysis experiments in the method section only focused on very simple motions, such as pan up, down, left, and right, without discussing more complex and realistic motions. We select simple motions in the analysis experiments for two reasons: (1) Simplifying the analysis allows for clearer insights. (2) It is sufficient to filter out motion channels. Motion features obtained in this way generalize well to more complex motions because complex motions are composed of simple ones, i.e., different simple motions occurring at different times and spaces combine to form complex motions. W3: Presented motions are not simple > The generated motions presented in the experiment section are also mostly very simple. In Figure 8 and the supplementary webpage, we showcase complex motions, including camera motion control, motion control of multiple objects, different motion frequencies and directions, etc. These examples cover common aspects of motion control, such as those in Motionctrl [12], SMM [2], and Cameractrl [13]. We welcome suggestions for additional test cases from the reviewers. W4: Comparisons with existing methods > The experiments lack comparisons with existing methods. Comparisons with other methods were only made in the point drag mode. In addition to comparisons using the point drag mode, we also evaluate our approach against SMM [2], a method that extracts intermediate features for motion control. To make the comparison more comprehensive, we include a qualitative comparison on motion transfer tasks with methods [2,14] (please refer to Fig.1 and Table 1 of the attached PDF), demonstrating our ability to achieve a superior balance between motion fidelity and text alignment. This improvement is attributed to our innovative motion decomposition designs. Beyond these comparisons, we emphasize that our approach offers deeper insights into motion interpredictions in video diffusion features. --- Rebuttal Comment 1.1: Title: Thanks for your rebuttal. Comment: The authors have addressed most of my concerns. I decide to keep my initial positive rating. --- Rebuttal 2: Comment: Dear Reviewer, Please reply to the rebuttal if your issues are addressed. AC.	Summary: This paper presents a training-free method for motion control in video diffusion models and explores the interpretability of features within these models. The authors demonstrate through experiments that principal components of the features, extracted using PCA, contain motion information. They propose a pipeline that eliminates content correlation information from the features, filters motion channels, and optimizes the initial latent input in the diffusion model's UNet. Strengths: - The paper effectively demonstrates the potential of internal features in video diffusion models to capture motion information. - The use of PCA to eliminate irrelevant information is well-justified. - The proposed training-free method can be applied to various manipulation scenarios, including reference-based and drag-based control. Weaknesses: - In Section 3, the authors discuss the challenge of extracting motion information from diffusion features due to their encapsulation of other data types, such as semantic and structural correlations. The paper lacks a detailed explanation of "content correlation information" (section 3). It is unclear whether this term encompasses semantic, structural, appearance, background, lighting, or other information. - Figure 6 contrasts the video motion control capabilities of DIFT and MOFT. It is recommended that identical sample images be used and their similarity heatmaps be compared, thereby better visualizing the capability gap between DIFT and MOFT. - The optimization process of the latent in Section 4.1 could be more clearly explained, particularly the settings from references [31; 41]. - A more descriptive caption for the Motion Control Pipeline (Figure 5) and a clearer title for the caption of Figure 6 are advised for better comprehension. Technical Quality: 2 Clarity: 3 Questions for Authors: Q1. After eliminating content correlation information, does the feature retain any information other than motion? If so, could this residual information affect video generation? Q2. Figure 6 illustrates how the ability to track motion varies with generation steps. Is it possible to manipulate features from earlier generation steps to achieve better results? Confidence: 4 Soundness: 2 Presentation: 3 Contribution: 2 Limitations: Not included. While the research demonstrates the potential of training-free methods to encode motion information, it remains unclear whether the proposed method completely eliminates motion-correlated information or retains any motion-irrelevant information. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your constructive comment. The detailed responses regarding each concern are listed below. W1: Explanation of content correlation information > In Section 3, the authors discuss the challenge of extracting motion information from diffusion features due to their encapsulation of other data types, such as semantic and structural correlations. The paper lacks a detailed explanation of "content correlation information" (section 3). It is unclear whether this term encompasses semantic, structural, appearance, background, lighting, or other information. This component is inspired by VideoFusion [8], which demonstrates that decomposing video latents into shared latents among all frames and per-frame residual latents enhances video generation. The shared latents, to which we refer as content correlation information, encompass shared aspects such as semantic content and appearance. In contrast, the residual latents primarily capture motion information, which also can be interpreted as deformation in structure. Building on this insight, we designed a content correlation removal process to remove shared information while preserving motion information. The effectiveness of this approach is validated in Figure 2. We will clarify this term in the revision. W2: Identical sample images in Figure 6 > Figure 6 contrasts the video motion control capabilities of DIFT and MOFT. It is recommended that identical sample images be used and their similarity heatmaps be compared, thereby better visualizing the capability gap between DIFT and MOFT. Thank you for your valuable input. We have added the corresponding images, and you can find the results from identical images in Figure 2 in the attached PDF, which supports our conclusions. It is important to note that the heatmaps in DIFT and MOFT represent different contents: semantic similarity in DIFT and motion similarity in MOFT. Therefore, even though the same images are used, the heatmaps cannot be directly compared side by side. Instead, we visualize their effects at different time steps to highlight that MOFT is more reliable at the earlier denoising stage. W3: Explanation of the optimization process of the latent > The optimization process of the latent in Section 4.1 could be more clearly explained, particularly the settings from references [31; 41]. Thank you for the suggestion. We will explain this more clearly in the revision. Please refer to the global response for the pseudo-code of the optimization process. W4: Revision for the captions > A more descriptive caption for the Motion Control Pipeline (Figure 5) and a clearer title for the caption of Figure 6 are advised for better comprehension. (MOFT v.s. DIFT) Thank you for your suggestion. We will include the following revisions: Revised caption of Figure 5: In one denoising step, we get the intermediate features and extract MOFT from it with content correlation removal and motion channel filter. We optimize the latents to alter the sampling process with the loss of masked MOFT and reference MOFT. For the detailed motion control process, please refer to the pseudo-code. Revised title of Figure 6: Effects of DIFT and MOFT on different denoising time steps. Q1: Clarification on the residual information > After eliminating content correlation information, does the feature retain any information other than motion? If so, could this residual information affect video generation? As illustrated in Fig. 2 of the main paper, after removing content correlation information, videos with entirely different appearances but identical motion directions cluster closely together (e.g., Right 1 and Right 2). This suggests that motion information is the primary component retained in the feature. Additionally, results presented in Figure 7 and the supplementary material further demonstrate that reference videos have minimal influence on appearance, lighting, or other semantic aspects. Thus, the residual information beyond motion has a negligible effect on video generation. Q2: Manipulating features from earlier generation steps > Figure 6 illustrates how the ability to track motion varies with generation steps. Is it possible to manipulate features from earlier generation steps to achieve better results? Good idea! We do manipulate the features from earlier generation steps. We manipulate features from earlier generation steps for two primary reasons: 1. MOFT provides valid motion information early in the generation process, allowing us to manipulate the motion effectively. 2. The motion in the generated videos is established during the early generation steps, necessitating manipulation at these stages. However, at the very beginning of the generation process, MOFT does not offer a very clear motion pattern. Therefore, we typically apply optimization at 850 to 500 denoising time steps for a 1000-timestep denoising process. The inclusion of limitations We've described the limitations in the Supplementary due to the limited space of the main paper. --- Rebuttal Comment 1.1: Comment: Thanks for the response. My primary concerns are solved and I would like to recommend acceptance on the condition that the authors would make all the necessary changes into the next version. --- Reply to Comment 1.1.1: Title: Response by authors Comment: Glad to know that your primary concerns are solved. We will definitely integrate changes mentioned in the responses in the next version (and also changes mentioned by other reviewers), as we have already provided the detailed change contents in response to w1, w2, w3, w4, q1, q2, and in the attached PDF (w2). Given that the policy of NeurIPS does not allow editing the paper before the final decision, we respectively hope that your positive attitude toward this work could be reflected in the final rating. --- Rebuttal 2: Comment: Dear Reviewer, Please reply to the rebuttal if your issues are addressed. AC.	Rebuttal 1: Rebuttal: We are grateful to the reviewers for your thorough, insightful, and constructive feedback. We are pleased that the interpretability and clarity of MOFT have been recognized (Reviewers P4uW, vDWU) and that the technical soundness of our paper has been acknowledged (Reviewers zi7R, zmG9, P4uW, vDWU). We also appreciate the recognition of MOFT's versatility and its potential for diverse applications (Reviewers zi7R, zmG9, P4uW, vDWU), as well as the effectiveness of our training-free approach (Reviewers zi7R, zmG9, P4uW, vDWU). We have addressed each of your comments with care and have provided detailed clarifications in our responses and the attached PDF. Please refer to the responses below for further details. Thank you for your commitment. We eagerly anticipate your continued feedback and hope that you find the responses to be satisfactory. --- Following is the pseudo-code of the optimization process since some reviewers raise the common question. Algorithm: Optimization process Input: noisy latents at timestep t $z_t$, region mask $S$, reference MOFT $MO^g$, the network $\epsilon_{\theta}$, Motion Channel Mask $C$, learning rate $\eta$. Output: optimized latents $z_t^{new}$. Begin $X=\epsilon_{\theta}(z_t)$ $\triangleright$ Get intermediate feature $X$ from the network Given $C$, extract MOFT $MO$ by Eq. 2 in the main paper Given $S$, $MO^g$, $MO$, get the loss $l$ by Eq. 3 in the main paper Optimize $z_t$ by $z^{new}_t = z_t - \eta \frac{\partial l}{\partial z_t}$ Return $z_t^{new}$ End --- Reference: due to the rebuttals' character limit, we've placed the references for all rebuttals below. [1] Shi Y, et al. Dragdiffusion: Harnessing diffusion models for interactive point-based image editing, CVPR 2024. [2] Yatim D, et al. Space-time diffusion features for zero-shot text-driven motion transfer, CVPR 2024. [3] Yin S, et al. Dragnuwa: Fine-grained control in video generation by integrating text, image, and trajectory. arXiv 2023. [4] Gen-2, https://runwayml.com/research/gen-2. [5] Zheng Z, et al. Open-Sora: Democratizing Efficient Video Production for All. [6] Mou C, et al. Dragondiffusion: Enabling drag-style manipulation on diffusion models. ICLR 2024. [7] Ouyang W, et al. I2VEdit: First-Frame-Guided Video Editing via Image-to-Video Diffusion Models. arXiv preprint 2024. [8] Luo Z, et al. Videofusion: Decomposed diffusion models for high-quality video generation, CVPR 2023. [9] Shi Y, et al. Dragdiffusion: Harnessing diffusion models for interactive point-based image editing, CVPR 2024. [10] Yang S, et al. Rerender a video: Zero-shot text-guided video-to-video translation. SIGGRAPH Asia 2023 Conference Papers. [11] Qi C, et al. Fatezero: Fusing attentions for zero-shot text-based video editing, ICCV 2023. [12] Wang Z, et al. Motionctrl: A unified and flexible motion controller for video generation, ACM SIGGRAPH 2024 Conference. [13] He H, et al. Cameractrl: Enabling camera control for text-to-video generation, arXiv preprint 2024. [14] Gen-1, https://runwayml.com/research/gen-1. Pdf: /pdf/ad1e7f762f2fbf242f290fe1a639fd192cd5eff0.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Learning-to-Cache: Accelerating Diffusion Transformer via Layer Caching	Accept (poster)	Summary: This paper proposes a method to accelerate DiT model inference using layer caching strategy. By utilizing feature interpolation, the non-differentiable layer selection problem is transformed into a differentiable optimization problem. The routing matrix $\beta$ is learned to indicate whether the features of a certain layer at the current timestep can be reused from the cached features of the same position in the previous timestep. Extensive experimental results demonstrate the effectiveness of this method in accelerating DiT model inference and also shed light on the redundancy of layers in current DiT models. Strengths: 1. Learning-to-Cache (L2C) transforms the non-differentiable layer selection problem into a differentiable optimization problem through interpolation, which is a clever transformation and forms the basis for optimizing the subsequent routing matrix $\beta$. 2. It is meaningful to explore how to apply feature caching mechanisms to DiT models for inference acceleration. The experimental results of the paper also demonstrate the effectiveness of the method. Compared with simply reducing NFE and previous feature caching methods, L2C achieves better performance. 3. This paper is well-organized and well-written; Weaknesses: My main concern lies in the scalability of this method: 1. L2C requires training for different DiT models and diffusion schedulers, which limits the potential applications of this method; 2. This paper reports experimental results on DiT and U-ViT series models, but does not experiment on text-to-image models based on the DiT architecture (e.g., Pixart-$\alpha$[1]). Is it because training on large-scale text-image pairs dataset is too costly? 3. The paper does not report specific training costs time; 4. Compared to the original inference process, will L2C increase additional memory due to routing matrix $\beta$ overhead and feature caching? [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 weakness Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: Limitations are discussed briefly, but could be touched upon in more detail. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We sincerely appreciate the valuable feedback and constructive suggestions. Thanks so much for taking time and effort to review our paper. > W1: L2C requires training for different DiT models and diffusion schedulers, which limits the potential applications of this method Thank you for your insightful question. The training cost of L2C is low because only the router matrix is updated, leaving the model parameters unchanged. For example, in PixArt-XL-2 with a 512 resolution, only 840 parameters need to be trained, taking just 3 hours on 8 A5000 GPUs. We consider this training overhead to be relatively small; using a distillation approach to compress a small model typically requires significantly more resources, such as 4 A100 GPU days for BK-SDM [1]. [1] BK-SDM: A Lightweight, Fast, and Cheap Version of Stable Diffusion. ECCV24. _________________ > W2: No experiment on text-to-image models based on the DiT architecture (e.g., Pixart). Is it because training on large-scale text-image pairs datasets is too costly? Thanks for the valuable suggestion. Here we show the experimental results on PixArt-XL-2-512x512. * Training Cost: The training cost for this experiment is approximately 3 hours on 8 A5000 GPUs, using around 200,000 images for training. We utilized the first 200,000 samples from the SAM-LLaVA-Captions10M dataset. The router matrix converges and achieves optimal performance with 200,000 samples. We also tested with 400,000 samples but observed no performance gain, as the router does not change with additional training samples. * Generation Quality: We test our method on the validation set of COCO2014 (30k) and COCO2017 (5k). The results, shown in the table below, indicate that our method outperforms the approach using fewer steps in DPM-Solver. We provide some qualitative examples in Figure 5 of the attached PDF. * What the router learns: We have observed some intriguing patterns in the router, as illustrated in Figure 1 of the attached PDF. The cross-attention block displays significantly more temporal redundancy compared to other types of modules, such as self-attention and MLP. In addition, this router has the unique feature of not being cacheable at intermediate steps. We believe these specific patterns can also guide the future design of model architecture, helping to eliminate unnecessary computations. \| Method \| NFE \| Activate Layer Ratio in Cache Steps \| Latency(s) \| SpeedUp \| Training Cost(h) \| FID (COCO2017)↓ \| FID (COCO2014)↓ \| \|------------\|-----\|----------------------\|---------\|---------\|------------------\|-----------------\|-----------------\| \| DPM-Solver \| 20 \| 100\% \| 2.14 \| 1.00x \| - \| 32.51 \| 27.14 \| \| DPM-Solver \| 14 \| 100\% \| 1.51 \| 1.41x \| - \| 33.79 \| 28.40 \| \| L2C \| 20 \| 31.3\% \| 1.52 \| 1.41x \| 3.3 \| 32.36 \| 27.39 \| _________________ > W3: The paper does not report specific training costs time; We apologize for missing this important experimental detail. Here, we report the training cost for each experiment. We use ImageNet for training, and in all cases, convergence is achieved in less than one epoch. The experiments are conducted on 8 A5000 GPUs. We would add this training cost to our next version of the manuscript. Thanks so much for pointing this out. \| Model \| DiT-XL/2 \| DiT-XL/2 \| DiT-XL/2 \| DiT-XL/2 \| DiT-L/2 \| DiT-L/2 \| U-ViT-H/2 \| U-ViT-H/2 \| \|----------------------\|----------\|----------\|----------\|----------\|---------\|---------\|--------------\|--------------\| \| NFE \| 50 \| 20 \| 10 \| 50 \| 50 \| 20 \| 50 \| 20 \| \| Resolution \| 256 \| 256 \| 256 \| 512 \| 256 \| 256 \| 256 \| 256 \| \| Sampler \| DDIM \| DDIM \| DDIM \| DDIM \| DDIM \| DDIM \| DPM-Solver-2 \| DPM-Solver-2 \| \| Training Cost (Hour) \| 7.2 \| 5.0 \| 2.5 \| 8.1 \| 7.0 \| 1.5 \| 5.7 \| 3.0 \| _________________ > W4: Compared to the original inference process, will L2C increase additional memory due to routing matrix overhead and feature caching? * For Routing Matrix: The routing matrix has a very small number of parameters, calculated as $steps \times layers \times block\\_per\\_layer$. In our experiments, the largest router, used for DiT-XL/2 with 50 sampling steps, contains 1,400 parameters ($25 \times 28 \times 2$), resulting in an extra memory overhead of just 2.8KB (using FP16 for inference). * For Feature Caching: Yes, L2C needs extra overhead for feature caching. As the cache in the computer system and KV-Cache in LLM, L2C trades space for time by storing intermediate results in VRAM, leading to additional memory overhead. Below is the additional overhead observed in the DiT model. We believe there is still room for optimization of the memory overhead in feature caching. Thanks for raising this critical issue. \| Method \| Memory \| \| -- \| -- \| \| DiT-XL/2 \| 3905 MiB \| \| DiT-XL/2 with L2C\| 4831MiB \| --- Rebuttal Comment 1.1: Comment: Dear Reviewer NP2z, We sincerely appreciate the time and effort you have dedicated to reviewing our work. We greatly appreciate your thoughtful review of our work and we are looking forward to hearing your feedback. To address your concerns regarding the scalability of our method, we have conducted additional experiments, including: 1. Experimental results on PixArt, alongside the comparison results with the few-step DPM-Solver. 2. Showing that the training cost for the router remains within an acceptable range. We are grateful for your attention to our rebuttal and are committed to addressing any additional concerns you might have. Thank you once again for your thoughtful consideration. Best regards, Authors of submission 1630	Summary: This paper introduces L2C, a novel approach that dynamically caches computations in diffusion transformers, significantly reducing the computational load. L2C leverages the repetitive structure of transformer layers and the sequential nature of diffusion, optimizing caching decisions to produce a static computation graph. Experimental results show that L2C outperforms existing methods like DDIM and DPM-Solver, as well as prior cache-based techniques, at the same inference speed. Strengths: - The writing is easy-to-follow - The motivation is strong. There exists many redundancy and the authors bypass it in a smart way Weaknesses: I am not an expert in this area. There is no obvious weakness as far as I can tell Technical Quality: 3 Clarity: 3 Questions for Authors: See Weaknesses Confidence: 2 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: Thank you very much for your review of our manuscript. We appreciate your time and effort in evaluating our work. It is encouraging to hear that you like our work and that no obvious weaknesses have been found. If you have any questions where you think further detail or explanation might be beneficial, we would be happy to address them. Thank you again for your valuable time and feedback.	Summary: The paper presents Learning-to-Cache (L2C), a method to accelerate diffusion transformers' inference by caching redundant computations across timesteps. A learnable router dynamically determines which layers can reuse calculations from previous timesteps. L2C can eliminate up to 93.68% of computations in specific steps (46.84% overall) in models like U-ViT-H/2 with minimal performance loss. Strengths: - The proposed caching method for the diffusion process is novel and provides acceptable speed-up without requiring retraining or fine-tuning of the model weights, only adding a few learnable parameters. - The paper introduces a straightforward learnable optimization process to identify redundancies in the diffusion process. - The proposed router is time-dependent but input-invariant, enabling the formation of a static computation graph for inference. - The paper is well-written and easy to understand. The figures and result tables are easy to follow and comprehensive, offering clear visual representations and supporting the text. Weaknesses: - The paper's contribution is incremental, primarily introducing a learnable router that determines what computations to reuse from previous timesteps. It would benefit from offering more innovations and deeper insights to significantly advance the field. - The improvement in speed-up is very similar to DeepCache, which does not require any training. There are some minor mistakes in the text, such as a typo in line 233 where "maximum" is misspelled as "mamimum." Technical Quality: 4 Clarity: 4 Questions for Authors: - Step distillation techniques, which typically involve few or just one step, have successfully accelerated the diffusion process with minimal impact on output quality. Can the proposed model be integrated with distilled models to achieve additional speed-up on top of the improvements gained from distillation? - You have proposed training only the router parameters while freezing the model parameters. Is there any benefit to fine-tuning and optimizing both the model parameters and the router parameters together? - What are the implications if the diffusion main loss function is used to train the router? Confidence: 5 Soundness: 4 Presentation: 4 Contribution: 3 Limitations: Since the goal is to speed up inference, it should be discussed whether this method can be combined with other acceleration techniques, such as step distillation. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We extend our gratitude for your insightful feedback and suggestions > W1: The paper's contribution is incremental. It would benefit from offering more innovations and deeper insights We greatly value your suggestion that we need to offer more profound insights in this paper. Beyond introducing a new method, we aim to share the following key insights to advance the field: (1) Theoretical explanation of the caching-based method: In Section 3.2\&3.3 and Appendix, we reveal that fast samplers and cache mechanisms represent different levels of reuse. Unlike previous heuristic-based approaches like DeepCache, our work establishes a theoretical connection and build the clear relationship between cache and fast solvers. This not only clarifies their relationship but also enhances the reliability of caching-based methods by providing theoretical support. (2) Insights from the special patterns in the learned routers: L2C reveals intriguing patterns in the learned routers (refer to Figures 1, 2, 3 and 4 in the attached PDF). In U-ViT (Figure 2), the intermediate layers can be entirely cached, whereas the early and later layers play a crucial role. We also add one experiment on PixArt-XL-2 and for PixArt, the temporal redundancy in the cross-attention layer (Figure 1.b) is notably pronounced, with over 94\% of layers (265 out of 280) being eligible for caching.These findings can be leveraged not only to accelerate model inference but also to guide the design of model architectures. To summarize, we aim to move beyond heuristic methods in designing the cache mechanism, incorporating performance guarantees and providing more theoretical interpretability for this special cache mechanism in accelerating the diffusion models. This has not been explored before and we think is important for this area. ___ > W2: The improvement in speed-up is very similar to DeepCache. Thanks for your insightful quesion. We compare our approach with DeepCache, focusing primarily on generation quality under the same acceleration ratio. Our method improves the FID from 2.70 to 2.64, using the same model and parameters, indicating a superior caching mechanism compared to DeepCache. Additionally, DeepCache is limited to U-ViT due to it is bound to the u-shaped structure, making it inapplicable to models like DiT and PixArt. However, L2C is versatile and can be applied to all these models. \| Methods \| NFE \| Latency(s) \|Speedup \|FID↓ \| \|--\|--\|--\|--\|--\| \| DPM-Solver \| 20 \|7.60 \|1.00x \| 2.57 \| \| DeepCache \| 20 \|4.68 \|1.64x \| 2.70 \| \| Faster Diffusion \| 20 \|5.95 \| 1.29x \| 2.82 \| \| L2C (ours) \| 20 \| 4.62 \|1.67x \| 2.64 \| ___ > Q1\&Limitation: Can the proposed method be combined with step distillation? Thank you for your constructive suggestion. We built our algorithm on the distilled PixArt-XL-2-512x512, employing a 4-step LCM scheduler. The table below presents our results, which are compared against the 3-step LCM. The learned router is visualized in Figure 4 of the attached PDF. From our experiments, our method achieves approximately 1.28x acceleration, successfully caching 78 out of 168 blocks. Consistent with the results on PixArt with 20 NFEs, cross-attention remains the most redundant component in the denosing sequence. \| Method \| NFE \| Cache Layer Ratio \| Latency(s) \| Speedup \| FID (COCO2017)↓ \| FID(COCO2014)↓ \| \|--\|--\|--\|--\|--\|--\|--\| \| PixArt-XL-2 + LCM \| 4 \| - \|0.96 \| 1.00x \| 34.52 \| 29.60\| \| PixArt-XL-2 + LCM \| 3 \| - \|0.73 \| 1.32x \| 34.77\| 29.72\| \| PixArt-XL-2 + LCM + L2C\|4\|78/168 \|0.75\|1.28x \| 34.45 \| 29.26 \| ____ > Q2: Optimizing both the model parameters and the router parameters Thanks for your great suggestion. We show the comparison results if optimizing the model parameters and the routers together: \| Method \| Cache Layer Ratio \| Latency(s) \| Speedup \| IS \| FID↓ \| sFID↓ \| Precision \| Recall \| Training Cost↓ \| \|--\|--\|--\|--\|--\|--\|--\|--\|--\|--\| \| DDIM20 \| - \| 2.87 \| 1.00x \| 223.49 \| 3.48 \| 4.89 \| 78.76 \| 57.07 \| - \| \| DDIM15 \| - \| 2.17\| 1.32x \| 205.97 \| 5.07 \| 6.07 \| 76.26 \| 55.65 \| \| Router \| 333/560 \| 2.09 \| 1.37x \| 219.85 \| 4.01 \| 5.22 \| 78.28 \| 55.73 \| ~40 GPU Hour \| \| Router&Model \| 331/560 \| 2.09 \| 1.37x \| 213.34 \| 3.87 \| 5.00 \| 77.83 \| 57.84 \| ~66 GPU Hour \| \|\|\| \| DDIM10 \| - \| 1.43 \| 1.00x \| 158.31 \| 12.38 \| 11.22 \| 66.78 \| 52.82 \| - \| \| DDIM9 \| - \| 1.29 \| 1.11x \| 140.85 \| 16.57 \| 14.21 \| 62.28 \| 49.98 \| - \| \| Router \| 107/280 \| 1.17 \| 1.22x\| 147.77 \| 14.63 \| 10.96 \| 64.30 \| 51.65 \| ~20 GPU Hour \| \| Router&Model \| 107/280 \| 1.17 \| 1.22x\| 134.87 \| 14.02 \| 12.43 \| 64.92 \| 52.37 \| ~41 GPU Hour \| \|\| The conclusion is that, yes, optimizing both the model and the router enhances the model's performance, as evidenced by slight improvements in FID and sFID. However, this optimization process requires additional time to train and fine-tune both components. We will include this experiment in our revised manuscript and thanks again for your inspiring suggestion. ____ > Q3: what if the diffusion main loss function is used to train the router? Thank you for your insightful question. We have adjusted the training loss accordingly, and the results are presented in the table below. We selected baselines with a very similar acceleration ratio for comparison. The results indicate that using the original diffusion loss makes it more challenging for the router to learn, resulting in slightly worse image quality compared to the distillation loss used in our submission. \| Method \| Cache Layer Ratio \| Latency \| Speedup \| IS \| FID↓\| sFID↓\|Precision \| Recall \| \|--\|--\|--\|--\|--\|--\|--\|--\|--\| \| DDIM-20 \| - \| 2.87\| 1.00x \| 223.49 \| 3.48 \| 4.89 \| 78.76 \| 57.07 \| \| DDIM-15 \| - \| 2.17 \| 1.32x \| 205.97 \| 5.07 \| 6.07 \| 76.26\| 55.65 \| \| Original Loss \| 295/560 \| 2.18 \| 1.32x \| 217.23 \| 3.97 \| 5.11 \| 77.83 \| 57.05 \| \| Our Loss \| 300/560 \| 2.16 \| 1.33x \| 223.41 \| 3.70 \| 4.91 \| 78.88 \| 56.36 \| --- Rebuttal Comment 1.1: Comment: Dear Reviewer FT6Q: Thank you for your valuable feedback on our work. Your constructive comments on our work are invaluable, and we genuinely hope to get feedback from you. Regarding the weaknesses you mentioned, we include the corresponding experiments as follows: 1. Experimental results when applying Learning-to-Cache to 4-step LCM on PixArt. 2. Generation quality compared with other cache-based methods (DeepCache, Faster Diffusion) 3. Experimental results when optimizing both the model parameters and the router parameters 4. Experimental results using the original diffusion loss. Your feedback is incredibly important to us, and we sincerely thank you for considering our rebuttal. We are more than happy to discuss them if you have any further concerns or questions. Thank you again for your time and effort to review our work and looking forward to your response. Best Regards,  Authors of submission 1630	null	null	Rebuttal 1: Rebuttal: Dear Chairs and Reviewers, We deeply appreciate your thoughtful comments and the time you have dedicated to reviewing our paper. Attached is a pdf containing the following: * Visualizations of learned routers in different models * Generated images compared with the baseline. We look forward to the opportunity to discuss this further with you. Many thanks for your kind attention. Best regards,  Authors of submission 1630 Pdf: /pdf/c523972e3a525fb13c311ad38b1c374f71fd12cd.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Ctrl-X: Controlling Structure and Appearance for Text-To-Image Generation Without Guidance	Accept (poster)	Summary: This paper presents a training-free and guidance-free method for controllable image/video generation with structure and appearance control. Specifically, Ctrl-X injects structural and appearance features directly into the noised samples via cross-attention. Compared with other baselines for structural and appearance control, the proposed method achieves good appearance alignment and structure presentation. Strengths: The proposed method is a good complement to training-based and guidance-based controllable visual generation methods. Experiment results also shown the effectiveness of the proposed method. Weaknesses: - It looks like the generated images/videos are a little bit painting style. I guess this is caused by injecting structure features directly without training/fine-tuning. - The training-based baselines are not very strong. Combining two existing models (e.g., ControlNet+IP-Adapter, T2I-Adapter+IP-Adapter) might not be a fair comparison, since they are not specifically designed for both appearance and structure control. I would suggest compare structural preservation ability with ControlNet (SD1/2/3, SDXL) and T2I-Adapter, and then compare appearance control ability with IP-Adapter. Technical Quality: 2 Clarity: 3 Questions for Authors: My understanding is that for training-free methods, we are making a trade-off between control quality and training computation cost. There exists some efficient training-based methods for controllable generation [1,2]. A natural question is: compared with such training-based method, is the training-free property good enough for us to use Ctrl-X? [1] Ran, Lingmin, et al. "X-adapter: Adding universal compatibility of plugins for upgraded diffusion model." Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2024. [2] Lin, Han, et al. "Ctrl-Adapter: An Efficient and Versatile Framework for Adapting Diverse Controls to Any Diffusion Model." arXiv preprint arXiv:2404.09967 (2024). Confidence: 3 Soundness: 2 Presentation: 3 Contribution: 2 Limitations: NA Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your time and feedback on our work. We address your suggestions and concerns below. You can find the referred figures in the PDF attached with the “global” response. Tables can similarly be found in the main body of the “global” response. Painting style generation results. Our proposed method works for any domain. Many realistic and non-painting samples generated are included in Figure 1, 4, 5 and Supplementary Figures 10, 11 in the paper. We will update the paper to make everything clear. Moreover, many samples in the attached rebuttal PDF also have realistic generation results—if the base model (e.g., SDXL) can generate realistic results for a prompt (which SDXL almost always can), then our method can, too. Comparing with training-based baselines for individual structure or appearance control. Thanks for the suggestion! For appearance-only control, we compare Ctrl-X (by dropping structure control) against IP-Adapter in Figure 4, where Ctrl-X displays better appearance alignment than IP-Adapter for both the subjects and backgrounds. For structure-only control, we compare Ctrl-X against both training-based baselines (ControlNet and T2I-Adapter) and training-free baselines (FreeControl, Plug-and-Play, etc.) in our Appendix, specifically Figure 10 and Table 3 in the paper Appendix. Additionally, we present additional experimental results with Uni-ControlNet [1], a ControlNet-based model trained to control structure and appearance at the same time. We report the user study and quantitative results in Tables 1 and 2. Ctrl-X is significantly ahead of Uni-ControlNet in terms of human preference for overall fidelity, indicating our method’s ability to balance structure and appearance control. Moreover, though Uni-ControlNet has better DINO self-sim, it struggles to balance structure preservation with appearance transfer with worse DINO-I scores, which is echoed by the user study. Trade-off between training-time and quality. Thanks for the thought-provoking discussion starter. Ctrl-X provides a training-free and optimization-free method that achieves a delicate balance between structure control and appearance transfer. Though the argument that adapters have made it less necessary to train control modules from scratch is totally valid, the training cost (or backpropagation cost for guidance-based methods) cannot be ignored as we need to backpropagate through new models that will only get bigger. For example, Ctrl-Adapter [2] is trained on 200K images—paired data for any condition that Ctrl-X supports is difficult to gather at this scale. Also, FreeControl (being guidance-based) requires ~44GB of VRAM on SDXL to run, compared to Ctrl-X’s 11.5GB VRAM usage (Table 3). The flexibility of training-free methods is also important, as Ctrl-X works with a large range of structure control signals (including higher-level conditions like bounding box and pose skeleton as shown in Figure 3), which training-based methods are limited by, as training requires paired data difficult to gather for in-the-wild conditions like 3D mesh, point cloud, etc. Thus, Ctrl-X’s training-free property has many upsides that may not necessarily make it a “trade-off.” Of course, training-based methods still excel at the specific tasks they are trained for—a canny ControlNet, for example, is great at canny-image-conditioned generation. However, their limited flexibility makes the “trade-off” of Ctrl-X’s training-free nature a lot more appealing, as Ctrl-X works for a much wider range of applications, condition types or models. This may be closer to what we ultimately want for “controllable generation,” that is, humans can use any (visual) medium to influence generative models’ outputs. [1] Shihao et al. “Uni-ControlNet: All-in-One Control to Text-to-Image Diffusion Models.” NeurIPS 2023. [2] Lin, et al. “Ctrl-Adapter: An Efficient and Versatile Framework for Adapting Diverse Controls to Any Diffusion Model.” arXiv:2404.09967.	Summary: This paper proposes a training-free framework (Ctrl-X)to control the structure and appearance when diffusion generation without any training. The method does not need much more inference time cost or GPU resource cost. The insight is that diffusion feature maps capture rich spatial structure and high-level appearance from early diffusion steps sufficient for structure and appearance control without guidance. The experiments demonstrates superior results compared to previous training-based and guidance-based baselines (e.g. ControlNet + IP-Adapter [4, 5] and FreeControl [2]) in terms of condition alignment, text-image alignment, and image quality. Strengths: 1. The method is novel and the motivation is clear. 2. The writing is good and easy to follow. Weaknesses: The main concern to me is the performance of the proposed method. 1. The authors do not provide any User Study results. They only show the quantitative results evaluated by DINO Self-sim and DINO-CLS, which are not widely used. In supp, they report the results in CLIP score, LPIPS in Table 3. From the result shown in Table 3, the proposed method gets a bad performance compared to others. For example, Ctrl-X gets the worst Self-sim performance. 2. The qualitative comparison is also unsatisfactory. For example, in Figure 5, I observe that ControlNet+ IP-Adapter gets a better result than Ctrl-X, e.g, the 3rd rows. Technical Quality: 3 Clarity: 3 Questions for Authors: See the weaknesses. Confidence: 5 Soundness: 3 Presentation: 3 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 time and feedback on our work. We address your suggestions and concerns below. You can find the referred figures in the PDF attached with the “global” response. Tables can similarly be found in the main body of the “global” response. Performance of Ctrl-X, qualitative evaluation. Thanks for your suggestion of conducting a user study to prove the superior performance of Ctrl-X. We report the user evaluation in Table 1. We randomly selected 15 sample pairs from our dataset and then assign each sample pair to 7 methods: Splicing ViT Feature, Uni-ControlNet, ControlNet + IP-Adapter, T2I-Adapter + IP-Adapter, Cross-Image Attention, FreeControl, and Ctrl-X. We invited 10 users to evaluate pairs of results, each consisting of our method, Ctrl-X, and a baseline method. For each comparison, users assessed 15 pairs between Ctrl-X and each baseline, based on four criteria: “the quality of displayed images,” “the fidelity to the structure reference,” “the fidelity to the appearance reference,” and “overall fidelity to both structure and appearance reference.” We collected 150 comparison results for between Ctrl-X and each individual baseline method. We reported the human preference rate, which indicates the percentage of times participants preferred our results over the baselines. The user study demonstrates that Ctrl-X outperforms training-free baselines and has a competitive performance compared to training-based baselines. Moreover, we have included more qualitative Ctrl-X experiments on more challenging conditions (Figure 1), higher-level conditions (Figure 3), appearance- and structure-only control (Figures 4 and 5) in the PDF attached in the “global” response. Performance of Ctrl-X, quantitative evaluation. We respectfully disagree that DINO self-sim score is “not widely used.” The DINO self-sim score has been employed by previous works (InstructPix2Pix [1], Pix2Pix-Zero [2], Plug-and-Play [3], FreeControl [4]) to evaluate the similarity between the global structures of two images. Additionally, we do not think that “Ctrl-X has a bad performance.” Ctrl-X consistently achieves high fidelity to both structural and appearance references, and it performs better in terms of DINO self-sim and DINO-I scores compared to ControlNet + IP-Adapter and Cross-Image Attention. There is, in fact, a trade-off between structure consistency (DINO self-sim) and appearance similarity (DINO-I), as these are competing metrics—increasing structure preservation corresponds to worse appearance similarity, as shown in Figure 2 where we ablate Ctrl-X structure and appearance schedules. Single metrics are not representative of overall method performance, which is why we survey overall fidelity in our user study (Table 1), where Ctrl-X achieved the best overall fidelity. We will add examples to illustrate this trade-off in the camera-ready version. For the evaluation of appearance similarity, we re-evaluated all generated samples using the DINO-I score, which has been employed by appearance customization works such as DreamBooth [5], P+ [6], and Break-A-Scene [7]. The results are reported in Table 2. The DINO-I score computes the cosine similarity between the DINO [CLS] embeddings of two images, while our original DINO-CLS directly computes the mean square error of these embeddings. This new evaluation metric further demonstrates our promising performance compared to both training and training-free baselines. [1] Brooks et al. “InstructPix2Pix: Learning to Follow Image Editing Instructions.” CVPR 2023. [2] Parmar et al. “Zero-shot Image-to-Image Translation.” SIGGRAPH 2023. [3] Tumanyan et al. “Plug-and-Play Diffusion Features for Text-Driven Image-to-Image Translation.” CVPR 2023. [4] Sicheng et al. “FreeControl: Training-Free Spatial Control of Any Text-to-Image Diffusion Models with Any Condition.” CVPR 2024. [5] Ruiz et al. “DreamBooth: Fine Tuning Text-to-Image Diffusion Models for Subject-Driven Generation.” CVPR 2023. [6] Voynov et al. “P+: Extended Textual Conditioning in Text-to-Image Generation.” arXiv:2303.09522. [7] Avrahami et al. “Break-A-Scene: Extracting Multiple Concepts from a Single Image.” SIGGRAPH Asia 2023. --- Rebuttal Comment 1.1: Title: Thank you for the response Comment: Thanks for the detailed response. Most of my concerns have been well-addressed. I have raised my rating from 4 to 5.	Summary: This paper introduces a method for controllable generation using diffusion models. The approach is designed as a training free technique for 1) structure/layout controlled generation (like e.g. controlNet) and 2) appearance transfer. The approach leverages manipulation of attention mechanisms and information transfer from reference images to the generative image. Authors evaluate their methods in multiple settings, and compare to state of the art related work, showing that their approach can achieve similar performance to more expensive alternatives. Strengths: The paper is, for the most part, well written and well grounded in the related literature. Relevant related works are well references, and works from which ideas are borrowed are acknowledged. The main benefit of the work is its fully training-free nature, which can offer more flexibility when generating images with different types of controls. The proposed methodology is relatively simple, leaving room for future improvements. Another benefit is the fact that the method can do both appearance and structure control, while related works often focus on a single one. Experiments show promising results, with a performance similar to FreeControl, but without inference time optimization steps. Some ablations experiments are provided, in an effort to analyse the different components of the model. Weaknesses: The main limitation of the work is the limited methodological novelty. The tools employed are not very novel: the structure transfer simply uses the method proposed in [34], while attention map manipulation is very commonly used for structure control (e.g. for editing methods such as prompt-to-prompt). Another noticeable limitation, highlighted in Figure 9a, is the lack of flexibility with regards to using appearance OR structure control. Results show that appearance control is required when performing structure control, requiring to generate a separate appearance image. This can increase generation cost, and reduces control over the content of the image, as the appearance image is simply controlled by a prompt. While the training free nature of the approach allows to use different types of structure images, the approach seems limited to control types with exact edge definition. Higher-level constraints like pose or bounding boxes do not appear to be an option with this type of method. While the experiments on video generation are interesting, I would recommend that the authors focus more space on structure-only generation (as in the appendix) and expand the ablation and limitation experiments. For example, studying the impact on the quality of generated appearance image for structure-only generation would be beneficial. Technical Quality: 3 Clarity: 3 Questions for Authors: -Can the methodology handle pose or bounding boxes types of controls? If not, are there modifications that can be done to achieve this? -Can the method handle images with more than one subject? All object centric experiments (structure + appearance) show generation with a single object, often at the center of the image. How does the approach perform with more complex images ? -In certain settings, conditions appear to be too strong and can affect image quality (e.g. figure 11, dog image). The benefit of guidance/inference is that one can control the influence of a structure image, offering more flexibility. Is there a way to adjust the influence of a structure image in this approach? Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: One experiment in figure 9 shows one limitation of the proposed approach. However, as pointed out in above sections, there are several additional points that should be discussed (flexibility, single subject, loose controls, etc). For some of these, additional experiments could have allowed to understand the behaviour of the methodology more clearly. Broader impact is adequately discussed. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you very much for the in-depth reading of our paper and the helpful comments. Our responses are listed below. You can find the referred figures in the PDF attached with the “global” response. Tables can similarly be found in the main body of the “global” response. Model extension to multiple object generation. Great suggestion! We conduct an additional experiment that involves multiple subjects in both the structure and appearance images, as seen in Figure 1. We tested Ctrl-X and ControlNet + IP-Adapter with two objects (house and tree) and three objects (dog, plant, and chair). Ctrl-X captures strong semantic correspondence between different objects and achieves balanced structure and appearance alignment. On the contrary, the training-based baseline often fails to maintain the structure and/or transfer the subjects’ appearance. Adjust the influence of structure images. Thanks for the suggestion! We present a new experiment that ablates different combinations of appearance and structure control schedules in Figure 2. Doing so changes the influence of the structure and appearance images on the output, making cross-class structure-appearance pairs (e.g., horse normal map with puppy appearance) look more realistic. Limited to lower-level control types. We present our experiments with new higher-level condition types: bounding boxes and human pose skeletons in Figure 3. Ctrl-X can handle these sparser and higher-level conditions by decreasing the structure schedule, making our method applicable to other higher-level control types, too. Limited methodological novelty. Indeed, Ctrl-X is inspired by previous literature on training-free structure control and appearance customization. However, we suggest the reviewer consider how our work advances guidance-free controllable text-to-image generation. Existing guidance-based methods have limited structure condition types and/or only handles either structure control or appearance control. Also, they require backpropagation through T2I/T2V which are only getting increasingly larger. In comparison, Ctrl-X enables fully disentangled control of structure and appearance while being fast and cheap in terms of inference time and GPU memory usage (Table 3). Moreover, whereas guidance-based methods are sensitive to guidance weights for each score function, Ctrl-X is more robust to its control schedules—in fact, the schedules can be varied to change the influence of the structure and appearance images (Figure 2). Compared to the training-based [34], where the query and key for attention come from trained embeddings, Ctrl-X directly uses the query and key within Stable Diffusion’s self-attention layers by exploiting the spatial correspondence property of self-attention observed by us and also prior training-free works. Thus, our method re-frames appearance control as a local style transfer task achieved by spatially-aware normalization of intermediate features. These techniques allow Ctrl-X to achieve multi-subject generation (Figure 1) and higher-level conditions like bounding box and pose (Figure 3) in an all-in-one method which none of our baselines can achieve. We believe our training-free and guidance-free method's disentanglement of structure control and appearance control, along with its flexibility and robustness, is novel, and we hope our method's utilization of attention layers is useful to the community—especially as visual generation moves towards transformer-based architectures. Lack of flexibility with regards to using appearance OR structure control. Thanks for the observation. Ctrl-X is specifically designed to solve the combined controllable generation by disentangling control from given structure and appearance images. Our baselines show that achieving a good balance between structure alignment and appearance transfer is often difficult, training-free or not. Thus, Ctrl-X aims to provide a solution for that. However, Ctrl-X can achieve appearance-only control by simply dropping structure control (and thus not needing to generate a structure image), as shown in Figure 4, displaying better appearance alignment for both the subject and background than the training-based IP-Adapter. Indeed, for structure-only control Ctrl-X needs to generate an appearance image, but Table 3 shows that the additional inference latency cost is not high and the peak GPU memory usage is in fact lower than ControlNet + IP-Adapter and T2I-Adapter + IP-Adapter as there are no additional modules. Plus, with multi-subject generation, we believe control over the content of the image can be achieved by simply providing an appearance image. Impact of generated appearance image quality on structure-only generation. We present structure-only generation samples alongside their jointly generated appearance images (equivalent to vanilla SDXL generation) in Figure 5. There is minimal quality difference between the generated appearance images and appearance-transferred output images, indicating that Ctrl-X’s appearance transfer does not greatly impact image quality. Thus, the output quality of Ctrl-X only grows as its base model’s quality improves.	Summary: This article presents Ctrl-X, a simple method for T2I diffusion models to control structure and appearance without additional training or guidance. Specifically, it uses feature injection and spatially-aware normalization in the attention laters to align the given structure and appearance. Doing so, Ctrl-X achieves training-free and guidance-free generation in both image and even videos. The effectiveness of Ctrl-X is demonstrated through experimental results on the collected benchmark, underscoring the model's capability. Strengths: Strengths 1. The technical elaboration of the proposed method is clear. 2. The motivation for the proposed method is straightforward. The insight of the paper is practical. Overall, I appreciate the high-level idea of this paper. 3. The evaluations conducted on the provided benchmarks provide evidence of the effectiveness of the proposed methods. However, there are some concerns regarding the experimental results, which will be further discussed in the weaknesses section. Weaknesses: Weaknesses 1. Model extension I am curious whether this method can do multiple object generation. For example, given two object sketches/cannies in one picture, and two object appearances in another picture, can this framework automatically match the most suitable appearance and structure alignment for the two objects, thereby generating the picture? 2. Comparisons on latency Since the paper claims that other training-free models significantly increase computing time and require more GPU memory. It is suggested to add another table on comparing computing resources and inference latency. Technical Quality: 4 Clarity: 4 Questions for Authors: Shown as above Confidence: 4 Soundness: 4 Presentation: 4 Contribution: 4 Limitations: The paper has included this part in the conclusion section and checklist. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your positive feedback! We address your questions/concerns below. You can find the referred figures in the PDF attached with the “global” response. Tables can similarly be found in the main body of the “global” response. Model extension to multiple-subject generation. Great suggestion! We conduct an additional experiment that involves multiple subjects in both the structure and appearance images, as seen in Figure 1. We tested Ctrl-X and ControlNet + IP-Adapter with two objects (house and tree) and three objects (dog, plant, and chair). Ctrl-X captures strong semantic correspondence between different objects and achieves balanced structure and appearance alignment. On the contrary, the training-based baseline often fails to maintain the structure and/or transfer the subjects’ appearance. Report peak GPU memory and inference latency. Thanks for your suggestion. We report the inference latency and peak GPU memory usage in Table 3, re-tested on a single NVIDIA H100 GPU for a fair comparison. Ctrl-X (SDXL) is slightly slower than training-based baselines yet is significantly faster than training-free baselines and Splicing ViT Features. Moreover, Ctrl-X has lower peak GPU memory usage than SDXL training-based methods and significantly lower memory than SDXL training-free methods. (We note that Uni-ControlNet and Cross-Image attention uses the base model SD v1.5, which is ~4–5x faster and uses ~3x more memory compared to SDXL. Splicing ViT Features also trains its own much smaller custom model.)	Rebuttal 1: Rebuttal: We thank all the reviewers for their time and extensive reading of our paper. We are grateful that reviews find our paper “clear” (tSTQ, DRHE, 6fgc), our method effective (tSTQ, YZfZ), and our experiments promising (DRHE). Responses to individual reviewers are addressed below each review. Any referenced figures can be found in the attached one-page PDF on the “global” author rebuttal here (which contain additional experiments and samples). Any referenced tables are included below. Please let us know if you have any additional questions or concerns! --- For all quantitative and qualitative experiments in the below tables, we use SDXL as the base model whenever possible (ControlNet + IP-Adapter, T2I-Adapter + IP-Adapter, FreeControl, Ctrl-X); otherwise, we use the method's implemented/trained base model (SD v1.5 for Uni-ControlNet and Cross-Image Attention, custom model for Splicing ViT Features). Table 1: User study. Average user preference of result quality, structure fidelity, appearance fidelity, and overall fidelity. We follow the setting of the user study from DenseDiffusion [1], where the human preference percentage showcases how often the participants preferred Ctrl-X over the baselines below. Ctrl-X consistently outperforms training-free baselines and is competitive with training-based ones, especially overal fidelity, showcasing Ctrl-X's ability to balance structure and appearance control. \| Method \| Result quality ↑ \| Structure fidelity ↑ \| Appearance fidelity ↑ \| Overall fidelity ↑ \| \| :--- \| :---: \| :---: \| :---: \| :---: \| \| Splicing ViT Features \| 95% \| 87% \| 56% \| 78% \| \| Uni-ControlNet \| 86% \| 17% \| 96% \| 74% \| \| ControlNet + IP-Adapter \| 46% \| 61% \| 41% \| 50% \| \| T2I-Adapter + IP-Adapter \| 74% \| 53% \| 67% \| 58% \| \| Cross-Image Attention \| 95% \| 83% \| 83% \| 83% \| \| FreeControl \| 64% \| 48% \| 79% \| 74% \| \| Ctrl-X (ours) \| - \| - \| - \| - \| Table 2: Updated quantitative evaluation. Updated quantitative evaluation with Uni-ControlNet and DINO-I appearance metric instead of DINO [CLS]. We use DINO-I following DreamBooth [2], which is the cosine similarity between the DINO ViT [CLS] tokens of the appearance and output images, where higher indicates better appearance transfer. Note that Splicing ViT Features scores are extremely high because it is trained per-image-pair and optimizes the loss between DINO features directly, as mentioned in our paper. \| Method \| Self-sim: Natural image ↓ \| DINO-I: Natural image ↑ \| Self-sim: ControlNet-supported ↓ \| DINO-I: ControlNet-supported ↑ \| Self-sim: New condition ↓ \| DINO-I: New condition ↑ \| \| :--- \| :---: \| :---: \| :---: \| :---: \| :---: \| :---: \| \| Splicing ViT Features \| 0.030 \| 0.907 \| 0.043 \| 0.864 \| 0.037 \| 0.866 \| \| Uni-ControlNet \| 0.038 \| 0.555 \| 0.074 \| 0.574 \| 0.053 \| 0.506 \| \| ControlNet + IP-Adapter \| 0.068 \| 0.656 \| 0.136 \| 0.686 \| 0.139 \| 0.667 \| \| T2I-Adapter + IP-Adapter \| 0.055 \| 0.603 \| 0.118 \| 0.586 \| 0.109 \| 0.566 \| \| Cross-Image Attention \| 0.145 \| 0.651 \| 0.196 \| 0.510 \| 0.195 \| 0.570 \| \| FreeControl \| 0.058 \| 0.572 \| 0.101 \| 0.585 \| 0.089 \| 0.567 \| \| Ctrl-X (ours) \| 0.057 \| 0.686 \| 0.121 \| 0.698 \| 0.109 \| 0.676 \| Table 3: Timing and computing resources. Preprocessing time, inference time, and peak GPU memory of all methods. We re-test timing and add peak GPU memory usage of all methods on a single NVIDIA H100 GPU. Preprocessing time refers to method portions that are not the final sampling steps (e.g., feature extraction, inversion, etc.). Ctrl-X is slightly slower than training-based baselines yet significantly faster than training-free baselines and Splicing ViT Features. Moreover, Ctrl-X has lower peak GPU memory usage than SDXL training-based methods and significantly lower memory than SDXL training-free methods. (We note that Uni-ControlNet and Cross-Image attention uses the base model SD v1.5, which is ~4–5x faster and uses ~3x more memory compared to SDXL. Splicing ViT Features also trains its own much smaller custom model.) \| Method \| Preprocessing time (s) \| Inference latency (s) \| Total time (s) \| Peak GPU memory usage (GB) \| \| :--- \| :---: \| :---: \| :---: \| :---: \| \| Splicing ViT Features \| 0.00 \| 1557.09 \| 1557.09 \| 3.95 \| \| Uni-ControlNet \| 0.00 \| 6.96 \| 6.96 \| 7.36 \| \| ControlNet + IP-Adapter \| 0.00 \| 6.21 \| 6.21 \| 18.09 \| \| T2I-Adapter + IP-Adapter \| 0.00 \| 4.37 \| 4.37 \| 13.28 \| \| Cross-Image Attention \| 18.33 \| 24.47 \| 42.80 \| 8.85 \| \| FreeControl \| 239.36 \| 139.53 \| 378.89 \| 44.34 \| \| Ctrl-X (ours) \| 0.00 \| 10.91 \| 10.91 \| 11.51 \| [1] Kim et al., Dense Text-to-Image Generation with Attention Modulation, ICCV 2023. [2] Ruiz et al. “DreamBooth: Fine Tuning Text-to-Image Diffusion Models for Subject-Driven Generation.” CVPR 2023. Pdf: /pdf/fd3f832362ddce6f69a3459579a442b7392cca98.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Constrained Adaptive Attack: Effective Adversarial Attack Against Deep Neural Networks for Tabular Data	Accept (spotlight)	Summary: This paper aims to study the problem of finding adversarial examples for tabular datasets. Different from attacking image models or text models, attacking tabular models requires finding adversarial examples which are legal, which do not violate the relation between features. Moreover, it also requires to tackle both numerical and categorical features. Strengths: 1. The studied problem is important and under less investigation compared to adversarial attacks in CV and NLP. 2. The paper is well written and easy to follow. 3. The experiment analysis is convincing and sufficient. Weaknesses: However, I still have concerns on this paper. Specifically, many terms / techniques used in the method are not originally proposed by this paper. For example, 1. In terms of the main objective (as discussed in Section 3.1), one key step to let adversarial examples satisfy the feature constraints (in Eq.1 and Eq.2) is to translate into a differentiable function. However, this is proposed by the previous work Simonetto et al, 2021. 2. In terms of the solving algorithm (as discussed in Section 4.1), the author propose CAPGD, which seems a fine-tuning / lightweight modification of the previous method CPGD. This also limit the technical contribution of this paper. 3. Finally, the author claims trying both CAPGD (proposed in this paper) and MOEVA (previous work) and BF* (previous work) can improve the attack successful rate. Overall, I do not hesitate about the effectiveness of combining these strategies for solving the attack problem. Instead, I am concerned of the originality and the significance of the work. Besides, although the authors discussed the reasons on why differentiable models are considered in this paper, I still believe that undifferentiable models like XGBoost is one important branch of models for solving the tabular data classification tasks. I encourage the authors also investigate possible solutions for undifferentiable models. Technical Quality: 3 Clarity: 3 Questions for Authors: Plz see the weakness. Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: I didn't see such a discussion. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your review. We appreciate that you acknowledge the importance of the problem and the quality and persuasiveness of our analysis. We will address below your doubts about the originality and significance of our work. W1 - Existing differentiable function: We acknowledge that integrating the constraints as a differentiable penalty function is not novel in this work and was proposed by CPGD [33]. Nevertheless, the results in [33] (confirmed in Table 2 of our paper) indicate that leveraging the constraints penalty function is not sufficient to achieve high effectiveness with gradient-based attacks. An attack that only uses a differentiable penalty such as CPGD remains ineffective in the challenging datasets we address. Thus, the need for the novel mechanisms we introduce in CAPGD and CAA. W2 - CAPGD novelty: We understand your concern regarding the similarities between CPGD and CAPGD, being both gradient attacks where the constraints are included as penalty functions. However, we respectfully disagree for the following reasons: (1) Compared to the previous attack, CPGD, our new attack CAPGD introduces 4 novel mechanisms to increase the effectiveness of the attack: the repair operator, the adaptive step, the momentum, and multiple initialization. We demonstrate the effectiveness and complementarity of each component. For instance, removing the constraints repair operator, a novelty of this paper, reduces the effectiveness of the attack by up to 24.1 robust accuracy points. CAPGD significantly increases the effectiveness of gradient-based attacks on 3/4 datasets, while preserving the efficiency advantage of gradient-based attacks w.r.t. search attacks. (2) Designing CAPGD is not intuitive. The literature on adversarial attacks proposed many mechanisms to improve their effectiveness, including random sampling, reinitialization, adaptive steps, and revert to best, and the first challenge was to identify which mechanisms are relevant to our use case, namely which mechanisms are compatible and beneficial to the constraints satisfaction objective. In particular, we found out that combining all the mechanisms in the literature was not optimal, and we achieved the best performances without reverting to the example with the higher loss when the step size changes. We provided in Appendix B.1 a study of the components of CAPGD and their complementarity. We hope this clarifies our argument on why CAPGD is not a straightforward improvement of CPGD. We are open to further discussion and would be happy to elaborate on any points if needed. W3 - Applying a combination of attacks: We appreciate your concern regarding the design of our meta-attack CAA. Nevertheless, we respectfully believe that its design represents a significant contribution for two reasons: (1) By applying a combination of complementary and strong attacks, we aim to become the standard for evaluating the robustness of models to adversarial attacks in Tabular Machine Learning. Identifying both "complementary" and "strong" attacks for a meta-attack is not straightforward. We presented in Table 1 of our manuscript 10 attacks proposed for Tabular Machine Learning. Some are gradient-based and others are search-based. We first identified which attacks natively support all the constraints, and which could eventually be extended. We ended with 2 gradient attacks CPGD (native support) and LowProFool (extension needed), and two search attacks BF* and MOEVA. Next, we demonstrated that our new attack CAPGD subsumes CPGD and LowProfool and that MOEVA subsumes BF. Then we needed to validate the complementarity of CAPGD and MOEVA (Figure 2 of our manuscript). Finally, we confirmed with an extensive evaluation (Table 3 of our manuscript) that our new CAA attack combining MOEVA and CAPGD still preserves the benefits of each (efficiency of CAPGD and effectiveness of MOEVA). Each step required formal analysis, extensive engineering, and exhaustive experiments. (2) Meta-attacks, that combine existing attacks are an active line of research. In Computer Vision, AutoAttack by Croce et al.[12] is a meta attack combining existing attacks (APGD+FAB) to benefit from the complementarity of search and gradient attacks. The attack has revolutionized the research of robustness assessment in computer vision and led to a significant improvement of novel defense mechanisms. We strongly believe that CAA will be as impactful for Tabular Machine Learning as AutoAttack, especially as it was carefully designed to achieve both efficiency for simple cases and effectiveness for challenging cases and has very limited hyper-parameters. Thank you once again for your constructive feedback, we will update the final manuscript according to your feedback to better showcase the significance of our meta-attack. W4 - Undifferentiable models:* We agree that tree-based models such as XGBoost are in many settings outperforming Deep Neural Network (DNN) architectures. DNN architectures are catching up, in particular for large datasets as demonstrated in [5], hence the need to evaluate their robustness. However, we also argue that CAA is relevant to any model (including tree-based models) with two settings: - in transferability, by generating adversarial examples on a surrogate model and evaluating their success rate on the target (tree-based) model, - by applying CAA (through the search-based component MOEVA that is model agnostic). In the common author response (C3), we provide an empirical study for both settings and show that CAA remains effective against random forest and XGBOOST models. We will also update the appendix in the final version of the paper with a discussion on undifferentiable models. --- Rebuttal Comment 1.1: Comment: We thank the reviewer's response. I agree with the reviewer that this method is potential to be served as a good baseline strong attack in the related literature, thanks to the authors' effort on trying different strategies for performance improvement. It is also insightful to see the transferability of attacking between different types of models. Thus, I increase the rating to 5. --- Reply to Comment 1.1.1: Comment: We thank you for your response and positive feedback on our extended analysis and new results. We appreciate that you have increased your score to 5 and are happy to provide any additional insight or answer any interrogation you may have to fully satisfy your requirements for a clear acceptance of our work.	Summary: This paper introduces two novel adversarial attacks, specifically designed to target the evasion of deep neural networks (DNNs) in classification tasks involving tabular data satisfying real-world constraints. The first attack, CAPGD, is a gradient-based method that enhances the constrained PGD (CPGD) attack proposed in [33] by incorporating improvements from the APGD definition [12], such as the addition of momentum and an optimized step size selection. The second attack, CAA, combines the efficient but less effective CAPGD with another search-based attack, MOEVA, which is more effective but less efficient regarding the computational time required to perform the attack. The extensive experimental evaluation on four tabular datasets and five DNNs for tabular data demonstrates that CAPGD significantly improves the success rate of generating successful adversarial examples compared to CPGD. Furthermore, CAA achieves a reasonable trade-off between efficacy and computational efficiency, offering higher attack efficacy than CAPGD and requiring less computational time than MOEVA. Strengths: I find this paper particularly compelling as it proposes a new evasion attack against deep learning models for tabular data with real constraints that clearly outperforms the other state-of-the-art proposals. The paper demonstrates two key strengths: - Despite the two proposed attacks are improvements and combinations of existing approaches to generate realistic attacks, they are based on reasonable and novel observations. In particular, the design of CAA is motivated by the evidence that CAPGD and MOEVA are complementary. These attacks significantly outperform the state-of-the-art CPGD [33]. - The experimental analysis is comprehensive and convincing. The experiments are performed on 5 different deep learning models employed to classify tabular data on 4 different datasets with variable number of constraints. Both the accuracy and efficiency of the attacks are evaluated. Furthermore, additional results are shown varying the maximum perturbation and the value of important parameters of the attacks are shown. Finally, an ablation study shows the impact of each improvement introduced in CAPGD. Weaknesses: Even though the proposal is good, I think that some weaknesses about the presentation of the proposal and the analysis of the results need to be addressed in the final version of the paper: The description of CAPGD should be improved: the description of CAPGD can be enhanced by better explaining the role of the repair operator. Specifically, the authors mention that constraints of the form $f = \psi$ are enforced at every iteration by the repair operator. However, it is not clear whether applying this operator at every iteration guarantees the generation of an adversarial example that satisfies all dataset constraints and the maximum perturbation constraint by the end of the execution. This is a crucial property, as the attack cannot be tested if it does not satisfy the constraints, potentially wasting the time required to generate the attack. The depth of the analysis of the results should be improved: the depth of the analysis of the results can be improved by discussing particular results to understand their causes and how to mitigate these cases. For instance, CAPGD and MOEVA fail to generate adversarial examples on the CTU dataset for 2 out of 5 models (Table 3 and results in the Appendix). This failure may be due to the high number of constraints (360) considered for this dataset, since the two attacks are more effective on the other datasets for which at most 30 constraints are considered. It would be interesting to evaluate the efficacy of the two attacks by varying the number of constraints considered for the CTU dataset, to better highlight the limitations of the proposed attacks. Additionally, CAA generates less effective attacks with higher epsilon values (Figure 5b), and MOEVA generates less effective attacks with a higher number of iterations (Figure 7b). Even though these results are sporadic, they are counterintuitive, as the search space for adversarial examples increases with higher epsilon and more mutation rounds. A detailed discussion of these phenomena would provide valuable insights. The limitations section is missing: the paper should include a limitations section summarizing the limitations of the presented attack algorithms and their evaluation. For example, the evaluation is performed only against an $L_2$ attacker, whereas other norm-based or synthetic attackers could have been considered. The attacks may not work well against specific datasets and models when $\epsilon$ is small. While these limitations are reported in the paper, they are scattered throughout. A dedicated section would clarify these points. Typos and inconsistencies: there are some typos and inconsistencies in the notation, such as: - $R_\Omega$ in Eq. 3 is not defined when the equation is presented. - $x^{(k+1)}$ -> $x^{(k-1)}$ in Eq. 7. - The classifier is represented by $H$ in Algorithm A.2, but $h$ is used in the main body of the paper. Additionally, $X$ appears twice in the function in line 3 of Algorithm A.2. Correcting these typos and inconsistencies will improve the clarity and readability of the paper. Finally, another weakness is more generic: The proposed attacks are really specific: the paper is proposing two effective algorithms to forge realistic evasion attacks against deep learning models used for classifying tabular data, an under-explored setting. I think that the contribution is appreciable. However, the chosen setting may limit the impact of the results, since, at the best of my knowledge, tree-based models continue to be the state-of-the-art for classification tasks on tabular data [a]. [a] Ravid Shwartz-Ziv and Amitai Armon, Tabular Data: Deep Learning is Not All You Need, Information Fusion Volume 81, May 2022, Pages 84-90 Updates after the authors' response The authors have provided a satisfying response addressing all the concerns that I have raised as weaknesses. The authors are willing to introduce the findings provided in the response in the next version of their paper, as far as I understood. Moreover, they will also include a dedicated limitations section and correct the typos. Technical Quality: 4 Clarity: 3 Questions for Authors: - Is CAPGD guaranteed to generate an attack that satisfies the dataset and perturbation constraints at the end of execution? - CAPGD and MOEVA may be unable to generate adversarial examples in specific settings (see results on two models on the CTU dataset in Table 3). What is the reason? Could it be due to the high number of constraints of the dataset? How does the success rate of the two attacks vary considering different numbers and types of constraints (linear and nonlinear)? - Why may CAA and MOEVA show a smaller success rate when considering higher epsilon values and a higher number of rounds (see Figures 5b and 7b)? Confidence: 4 Soundness: 4 Presentation: 3 Contribution: 3 Limitations: The authors should sum up the limitations of their proposals in a specific section in the paper. The negative societal impact is discussed by the authors who claim that their work may give birth to new and stronger defenses. Finally, the experimental and implementation details have been extensively documented. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your support and your insightful feedback. We appreciate your comments towards improving the quality of the paper. We clarify and answer your concerns below. W1/Q1 - Explaining the role of the repair operator. Is CAPGD guaranteed to generate an attack that satisfies the dataset and perturbation constraints at the end of execution? The repair operator's role is to ensure equality constraints are satisfied during optimization. While equality constraints are included in the penalty function, optimization alone does not achieve exact equality of feature values. The repair operator addresses this by setting the value of the left-hand side of an equation to match the evaluation of the right-hand side in each iteration. It maintains other dataset constraints such as bounds, mutability, and feature types but does not ensure other relational constraints are met. The operator can violate maximum perturbation constraints, yet at each iteration, the perturbation is corrected back within the allowed maximum. This approach has been shown to improve the success rate of CAPGD, as demonstrated by our ablation study in Table 7. W2/Q2 - Attacks fail to generate adversarial examples on CTU for 2/5 models. Is it the high number of constraints? Impact of different numbers and types of constraints ? Thank you for raising this comment. Indeed, CTU dataset exhibits a large number of constraints compared to the other datasets, and some are particularly challenging. We show in the common answer (C1) that these constraints are harder to optimize. W2/Q3 - CAA epsilon values - Why may CAA show a smaller success rate when considering higher epsilon values? Thank you for pointing out the pattern in Fig5b. Indeed, CAA's performance can decrease with higher budgets. We provide below a complementary analysis of this behavior. We investigated the case of augmenting the EPS budget of CAA on LCLD dataset with STG model. We found that when augmenting the EPS budget from 1 to 5, the success rate of CAPGD drops from 27.1% to 0.4% and is not entirely balanced by MOEVA's improvement from 4.3% to 12.4%. The drop in CAPGD performance is caused in almost all cases by the violation of boundary constraint after the repair operator when the repair operator fixes the constraints of the type A = B / C. Each of these features is defined in the dataset with their respective maximum and minimum values. Given Max(B) and Min(C), the repair operator will lead to Max(A) = Max(B) / Min( C), however in the definition of the dataset proposed by Simonetto et. al. [33], Max (A) is lower than Max(B) / Min( C). Hence our repair operator contradicts the boundary constraint definitions. This phenomenon appears only for large perturbations. This violation should be solved by fixing the dataset's definition of the boundary constraints to take into account the feature relationships. We have included in the limitation section of our paper (in the final version, and in the author's response above C3) a discussion on the quality of the constrained datasets available and the coherence between their boundary constraints and their feature constraints. W2/Q3 - MOEVA Iterations - Why may MOEVA show a smaller success rate with a higher number of generations? MOEVA is a multi-objective genetic algorithm. An inherent problem of multi-objective optimization is the trade-off between the objectives. If all solutions in the population are on the Pareto front, the algorithm must decide which solutions to discard for the next iteration, potentially discarding a valid adversarial example in our case. Figure 1 in the Author's response PDF shows the evolution of the success rate of MOEVA with the number of iterations in the same settings as in Figure 7b for TabTransformer. We find that the success rate reaches a maximum at 100 iterations. We argue that valid adversarial examples were discarded when the search continued to 1000 iterations. To confirm our hypothesis, we run the same experiment with a 10 times larger search population, such that more solutions are preserved at each iteration. We observe that in this setting, MOEVA converges slower (due to less selection pressure) but the success rate strictly increases with the number of generations. Increasing the population size also increases the execution time (by 3.4x in this case), due to the selection operator overhead. Our approach CAA aims at minimizing the memory and computation overheads while maximizing the success rate, and CAA can be tuned to lead to lower robust accuracy with more iterations if the search space is expanded (for example with larger populations). We thank you for this remark and we have introduced a discussion on the impact of the population size in the appendix. W3 - Limitation sections: Thank you for this suggestion. We added a limitation section in the common author response (C4), and to the updated paper for the final version. W4 - Typos: Thank you for pointing this out, we have corrected them for the final version. W5 - The proposed attacks are specific: We agree that tree-based models are in many settings outperforming Deep Neural Network (DNN) architectures. DNN architectures are catching up, in particular for large datasets as demonstrated in [A], hence the need to evaluate their robustness. However, we also argue that CAA is relevant to any model (including tree-based models) with two settings: - in transferability, by generating adversarial examples on a surrogate model and evaluating their success rate on the target (tree-based) model, - by applying CAA (through the search-based component MOEV, which is model agnostic). In the common author response, we provide an empirical study for both settings and show that CAA remains effective against random forest and XGBOOST models. [A] Borisov et al. "Deep neural networks and tabular data: A survey. 2021. --- Rebuttal 2: Title: Compliments to the authors for their high-quality response. Comment: I sincerely thank the authors for their wide and deep response. Their points sound reasonable and clarify the open points that I raised in the review. I hope that the authors will discuss their new results in the next version of their paper. I have only an observation about the results in Table 3 of the attached PDF. It seems to me that attacking STG is difficult independently of the considered constraints since its robust accuracy is always 95.3%. Understanding if the model is really robust or if a better attack is needed could be an interesting future work. I will modify my review to acknowledge your response and improve my score, given the depth of your analysis and dedication you have shown in your response. --- Rebuttal Comment 2.1: Comment: We thank you for your praise of our rebuttal and we are happy to see you increase your score following our answers. To answer your observation on Table 3 on the author's response PDF. We confirm that STG architecture is the hardest to attack both with gradient and search attacks. We show consistent robustness of STG in Table 3 of our main submission across all the datasets. STG [A] is a novel architecture that implements an embedded nonlinear feature selection method by introducing the stochastic gates to the input layer (the feature space) of a neural network. The randomness introduced on the fly to select the features for training and inference significantly hinders evasion attacks, both gradient and search attacks. There is a similar phenomenon in the benchmark by Croce et al. for computer vision (Robustbench). In their evaluation of AutoAttack, they clearly "rule out classifiers which have (1) zero gradients with respect to the input, (2) randomized classifiers, and (3) classifiers that use an optimization loop at inference time" [B]. Contrary to their benchmark, we decided to cover one architecture per family of mechanisms from the Tabular ML literature, including stochastic mechanisms (STG belongs to categories 2 and 3 discarded in Robustbench). In Table 3 of our main paper, while we demonstrate that STG is the most robust, our study uncovers some cases where STG robust accuracy could still be significantly decreased with CAA (LCLD, URL), while other datasets will be challenging targets for future research (CTU). We appreciate your feedback on this pattern and the discussion it raises. In the appendix, we described the mechanisms of each architecture but did not connect the mechanisms with the observed robustness. Following your insight, we will also update this section to explain how each mechanism could impact the robustness (a complete verification of each mechanism impact would be a natural follow-up for dedicated papers). Thank you again for this discussion and the points you raised. They have significantly improved our final version. [A] Yamada, Yutaro, et al. "Feature selection using stochastic gates." ICML, 2020. [B] Croce et al. "Robustbench: a standardized adversarial robustness benchmark."(NeurIPS, 2021).	Summary: The paper proposes two adversarial attack methods targeting deep learning models for tabular data. The two methods are: CAPGD (Constrained Adaptive Projected Gradient Descent) and CAA (Constrained Adaptive Attack). CAPGD is a modification based on constrained PGD with step size adjusting, repair operator, additional random initialization, and momentum. CAA is a combination of CAPGD and MOEVA (Multi-Objective Evolutionary Adversarial Attack), which is a search-based attack method. The two methods are combined by iteratively applying the two with CAPGD first. The authors demonstrate the effectiveness of these attacks across five architectures and four datasets. Strengths: Strengths: 1. Clarity: The motivation and rationale behind the proposed algorithms are clearly presented in a logical order. 2. The paper provides an extensive empirical evaluation of the proposed attacks across multiple datasets and architectures, showcasing their superiority in terms of effectiveness and computational efficiency. Weaknesses: Weakness: 1. Lack of novelty and contribution: CAPGD is modified base don CPGD with a series of commonly used optimization techniques. CAA is a combination of CAPGD and MOEVA, which was proposed by a previous work. 2. The implementation of CAA, involving the combination of CAPGD and MOEVA, might be complex and resource-intensive, which could limit its practical applicability in some settings. 3. Lack of evaluation against defense mechanisms: Section 5.4 briefly discussed potential defense mechanisms, Madry’s adversarial training, which was proposed six years ago. There have been many works proposed since then. It is not fair to say that it is the only reliable defense against evasion attacks. Minor: • On page 1, line 30, “This raises anew the need to study …”. Maybe it should be “This raises a new need to study …”? Technical Quality: 2 Clarity: 3 Questions for Authors: NA, see above. Confidence: 4 Soundness: 2 Presentation: 3 Contribution: 2 Limitations: No discussion found for limitation. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your feedback. We appreciate the opportunity to clarify and address any misunderstandings. We will address each of your points one by one and welcome further discussion on these issues. W1 - Lack of novelty and contribution. CAPGD is modified based on CPGD. CAA is a combination of CAPGD and MOEVA: We agree that the core intuitions behind the improvements of CAPGD and CAA are elegant and not particularly complex, but we would like to point out that: (1) the literature on adversarial attacks proposed many mechanisms to improve their effectiveness, including random sampling, reinitialization, adaptive steps, and revert to best, and the first challenge was to identify which mechanisms are relevant to our use case, namely which mechanisms are compatible and beneficial to the constraints satisfaction objective. In particular, we found out that combining all the mechanisms in the literature was not optimal, and we achieved the best performances without reverting to the example with the higher loss when the step size changes. We provided in Appendix B.1 a study of the components of CAPGD and their complementarity. In addition, we also proposed new iterative repair mechanisms that were not explored in previous work and demonstrated their effectiveness. Hence, CAPGD is not a straightforward improvement of CPGD. (2) meta attacks, that combine existing attacks are also an active line of research. In Computer Vision, AutoAttack by Croce et al.[12] is a meta attack combining existing attacks (APGD+FAB) to benefit from the complementarity of search and gradient attacks. The attack has revolutionized the research of robustness assessment in computer vision and led to a significant improvement of novel defense mechanisms. We believe CAA will be as impactful for Tabular Machine Learning as AutoAttack, especially as it was carefully designed to achieve both efficiency for simple cases and effectiveness for challenging cases and has very limited hyper-parameters. We strongly argue that both attacks required significant design, engineering, and experimentation to find the optimal mechanisms and attacks to combine, and we have demonstrated that our techniques represent a significant leap forward for the community. W2 - The implementation of CAA might be complex and resource-intensive, which could limit its practical applicability in some settings: Thank you for raising this critical aspect of robustness evaluation. The implementation of CAA brings marginal overhead in terms of implementation, given that the constraint evaluation runs on CPU and is parallelized. In addition, we have carefully evaluated the impact of CAA in terms of runtime. Compared to the closest attack in terms of performance, MOEVA, CAA is significantly cheaper and faster to run. In Table 3, we showed that CAA is up to 5 times faster than MOEVA, and is always less expensive to run than MOEVA on 4 datasets. The only case where CAA is marginally more resource intensive is on CTU, but the overhead is between 7.76% and 13.74%, respectively for VIME and TabNet architectures. Thank you for opening this discussion, we will incorporate it in the final manuscript within a limitation section (cf common authors's response, C4). We discuss there the cases where CAA could be more expensive, and will suggest good practices for practitioners to use CAPGD and CAA to their fullest potential. W3 - Lack of evaluation against defense mechanisms: There have been many works proposed since Madry Adversarial Training. It is not fair to say that it is the only reliable defense against evasion attacks: Thank you for raising this critical point. There may have been a misunderstanding as we do not claim that Madry's Adversarial Training (AT) is the only reliable one, but that AT with all its improvements is. Since then, the robustbench benchmark [A] has continuously updated its leaderboard with new defenses, but all the effective ones are based on adversarial training and some data augmentation mechanisms. Some have proposed AT + Cutmix [B], others AT + Generative models (for example with 20M synthetic data [C]). To validate the effectiveness of CAA on stronger defenses we have implemented 5 new synthetic data for Tabular ML in combination with Adversarial Training: AT + TVAE [D], AT + WGAN [E], AT + TableGAN [F], AT + CT-GAN [D] and AT + GOGGLE [G]. We evaluated CAA on these 5 defenses and report in Table 4 of the authors' response PDF the best robustness achieved by these defenses, compared to the robustness by the vanilla Madry AT on all our datasets and models. The results are the average over 5 seeds run to ensure reliable evaluation. Our new extensive experiments show that these new defenses can significantly improve the robustness of the models to CAA, but that our new attack remains effective for URL and LCLD datasets across all architectures, and for WIDS on TabTransformer and STG architectures. Thank you for suggesting this study, we will discuss these new results in the appendix of the final version of the manuscript. [A] Croce et al. "Robustbench: a standardized adversarial robustness benchmark."(2020). [B] Yun et al. "Cutmix: Regularization strategy to train strong classifiers with localizable features." ICCV, (2019). [C] Wang et al. "Better diffusion models further improve adversarial training." ICML. PMLR, (2023). [D] Xu et al. Modeling tabular data using conditional GAN. NeurIPS, (2019). [E] Arjovsky et al. Wasserstein GAN. CoRR, abs/1701.07875, (2017) [F] Park et. al. Data synthesis based on generative adversarial networks. VLDB Endowment, (2018) [G] Liu et al. GOGGLE: Generative modelling for tabular data by learning relational structure. ICLR, (2022) --- Rebuttal Comment 1.1: Title: Summary of our improvements Comment: Dear reviewer, we thank you again for your constructive feedbacks, and your suggestions to improve our work. We would like to highlight that we have addressed during this rebuttal all your concerns and interrogations and we have provided additional insights and results to support our claims. In particular, we have adressed the weaknesses you raised as follows: * W1: Lack of novelty and contribution. => A1: We have elabotated on the complex process of desiging our new CAPGD attack, that required analyzing multiple improvement mechanisms, their interactions, thus leading to only including in CAPGD the most relevant mechanisms. Our CAPGD design is the best that could be achieved for gradient attacks in tabular ML. We also detailed the inception of our new meta-attack, CAA and explained why its design is not straightforward and required the analysis, selection and evaluation of 10 existing attacks. * W2: The implementation of CAA might be complex and resource-intensive => A2: We elaborated on our previous analysis on the computation cost and execution time of CAA compared to MOEVA (Table 3 of our manuscript) and explained that CAA is marginally more ressource-intensive than MOEVA in one over 4 datasets and significantly more efficient than MOEVA in the 3 remaining datasets. * W3: Lack of evaluation against defense mechanisms => A3: We have implemented 5 new defenses using extensive data augmentation and adversarial training. Our new defenses leverage some of the best and most recent generative models of tabular data and required the training of complex generative models to generate 100 times more synthetic examples and achieve the best adversarial training defenses. Our new extensive experiments show that these new defenses can significantly improve the robustness of the models to CAA, but that our new CAA attack remains effective for URL and LCLD datasets across all architectures, and for WIDS on TabTransformer and STG architectures. If you find our answers and discussion satisfactory, we would greatly appreciate it if you could increase your score accordingly. If there are any remaining issues or questions, we would be more than happy to address them before the discussion period ends. Thank you again for your insights and the discussion points you raised.	Summary: This paper considers the evaluation of the robustness of deep learning models applied to tabular data. The authors introduce two novel adversarial attack methods: Constrained Adaptive Projected Gradient Descent (CAPGD) and Constrained Adaptive Attack (CAA). These methods are designed to exploit the vulnerabilities of tabular data models, which often include categorical features, immutability constraints, and feature relationship constraints that are not typically considered in attacks designed for computer vision (CV) or natural language processing (NLP). CAPGD improves on existing gradient-based attacks by incorporating adaptive mechanisms and eliminating the need for parameter tuning, significantly enhancing the success rate and efficiency of generating valid adversarial examples. CAA further combines CAPGD with the Multi-Objective Evolutionary Adversarial Attack (MOEVA), optimizing both effectiveness and computational cost. The paper demonstrates the superior performance of CAA across various datasets and models, suggesting it should become a standard test for evaluating the robustness of tabular models. Strengths: - The paper is well-motivated and logically structured, contributing significantly to advancing adversarial machine learning, particularly in the domain of tabular data. - The proposed CAA method is SOTA on effectiveness and efficiency, making it a good benchmark for testing the robustness of tabular data models, similar to the role of AutoPGD/AutoAttack in computer vision tasks. - The paper includes extensive and systematic experiments, providing solid empirical evidence for the effectiveness of the proposed attacks. Weaknesses: - The paper does not provide a clear explanation of the penalty function in Equation (4). A more detailed clarification is needed to understand how this function is formulated and applied. - The description of constraints in Equations (1) and (2) is somewhat abstract and difficult to interpret. The authors should refine the descriptions of these constraints to improve clarity. Technical Quality: 3 Clarity: 3 Questions for Authors: - Are there any other constraints in tabular data besides categorical features, immutability, and feature relationship constraints? - Why are gradient attacks ineffective on the CTU dataset? - Why is feature engineering necessary for the datasets? Have all four datasets considered in the paper undergone feature engineering? It seems that the WiDS dataset has not undergone feature engineering. Is that correct? 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 for your positive feedback and your praise for the extensiveness and significance of our work in advancing tabular adversarial machine learning. We appreciate your interest and would be happy to provide further explanations to address any questions you have. W1 - Clarification of the penalty function: The penalty function transforms each constraint formulation into a differentiable loss function to be minimized by gradient descent. Let's consider one complex constraint from the LCLD credit scoring use case: The term of the loan can only be 36 or 60 months and the number of open accounts is lower than the number of allowed accounts for this client. Such a constraint can be formally written as (term ∈ {36, 60}) ∧ (open_acc ≤ total_acc). The AND operator ∧ is equivalent to a sum of loss, while the element of set operator c∈{a,b,...} is equivalent to multiple OR operators, that are described as min(\|c-a\|,\|c-b\|,...) in a loss function. Finally, the a≤b operator is equivalent to a min(0,a-b) in a loss function. Hence, the complex constraint translates as the following penalty: min(\|term − 36\|,\|term − 60\|)+ max(0, open_acc − total_acc) Thank you for requesting these clarifications. We will update the final version accordingly and provide a meaningful example for each use case. W2 - Clarification of the Equations (1) and (2): The grammar in equations (1) and (2) are inspired by the work of Simonetto et al. [33] where they demonstrate the completeness of this grammar and its ability to cover all linear constraints. To elaborate on the two equations, equation (1) means that a constraint formula ω can either be an intersection (∧), or a union (∨) of two other constraint formulae ω1, ω2, or ω can be a comparison operator between two values ψ, or ω can be the feature $f$ equals a value of the set {ψ1 ... ψk}. Then equation (2) details the numeric expressions that are supported by the grammar. A numeric expression ψ can be constant, an operation between two other numerical expressions ψ1 and ψ2, or a specific feature f, or the value for f of the clean sample $x_i$. The difference between $f_i$ and $x_i$ is that $f_i$ corresponds to the current value of the evaluated example and $x_i$ corresponds to its original value in the clean example. This seemingly simple grammar allows very large recursive combinations and covers all the relations found in the features of our datasets. In this grammar, the symbol $\in$ represents a type of constraint, and not that $f$ is a value. The constraint $f \in \{ψ_1, ..., ψ_k\}$ is equivalent to $(f=ψ_1) \lor (...) \lor (f=ψ_k)$ Hence we can simplify the grammar as follows: $\omega := \omega_1 \land \omega_2 \mid \omega_1 \lor \omega_2 \mid \psi_1 \succeq \psi_2$ (1) $\psi := c \mid f \mid \psi_1 \oplus \psi_2 \mid x_i$ (2) To improve the readability of these equations, we will include the above detailed explanation in the final manuscript, and we have prepared an exhaustive table, Table 1 of the Author Rebuttal PDF, with examples of each type of constraint of the grammar, with real-world examples, and how they are converted into a penalty function. We will also include this table in the updated manuscript. Q1 - Are there any other constraints in tabular data besides categorical features, immutability, and feature relationship constraints? To the best of our knowledge, the only constraints related to tabular features are the ones we handle: types (including discrete, categorical, and binary), immutability, boundaries (minimum and maximum possible values), and feature relationships. Other constraints could be considered, but they are related to the threat model and the capabilities of the attackers, and hence outside the scope of the study. For example, the constraints on the budget of the attacker and the cost of changing a feature (for example an attacker could not change the feature of his current balance, without having sufficient resources to actually update his real account balance, or to change its address without the cost of moving its real address). Q2 - Why are gradient attacks ineffective on the CTU dataset? Thank you for raising this comment. Indeed, CTU dataset exhibits a large number of constraints compared to the other datasets, and some are particularly challenging. We show in the common answer (C1) that these constraints hinder gradient attacks and are harder to optimize. Q3- Why is feature engineering necessary for the datasets? Have all four datasets considered in the paper undergone feature engineering? You are right, each dataset has been proposed by different research teams with their own pre-processing and feature engineering. We did not run any additional feature engineering. However, some datasets rely heavily on raw measurements, for example, the Botnet CTU dataset with features related to a number of connections in ports and traffic load; or WIDS dataset where the features are numerical biological data (eg. albumin_apache about albumin concentration in g/L). Other datasets were designed by their authors with more feature engineering. In the LCLD credit scoring dataset, some features (grade, subgrade, fico_range_low) are scores computed by Lending Club to grade the customer and the loan, and are the result of feature processing and engineering of raw features. Therefore, the four use cases cover different levels of feature engineering, with datasets as you pointed out requiring little feature engineering (WIDS), and datasets built with more advanced feature engineering (LCLD). Thank you for raising this point. We will update the appendix section related to the dataset and provide clarifications and relevant references to the feature engineering process of each dataset. --- Rebuttal Comment 1.1: Title: Summary of our improvements Comment: Dear reviewer, we thank you again for your constructive feedbacks, and your support of our work. We would like to highlight that we have addressed during this rebuttal all your concerns and interrogations and we have provided additional insights and results to support our claims. In particular, we have adressed your interrogations as follows: * Q1: Are there any other constraints in tabular data besides categorical features, immutability, and feature relationship constraints? => A1: To the best of our knowledge, our work covers all the constraints related to tabular data. * Q2: Why are gradient attacks ineffective on the CTU dataset? => A2: We provided a detailed analysis in the common answer with an analysis of the constraints of CTU. CTU is robust because of the number of constraints and the number of features involved in each constraint. * Q3: Why is feature engineering necessary for the datasets? => A3: We did not run any additional feature engineering on the datasets. Each dataset was designed by a different source and may have required dedicated feature engineering. We were not involved in this step. If you find our answers and discussion satisfactory, we would greatly appreciate it if you could increase your score accordingly. If there are any remaining issues or questions, we would be more than happy to address them before the discussion period ends. Thank you again for your insights and the discussion points you raised.	Rebuttal 1: Rebuttal: We thank the reviewers for their comments. The reviewers agree on the importance of the problem we tackle and are satisfied with the comprehensiveness of our study and analyses. Our work proposes the most effective and efficient attacks for Tabular Machine Learning in constrained domains. Our new attack CAA is up to 5 times faster than the SOTA search attack MOEVA and up to 83% percentage points more effective than the SOTA gradient attack CPGD. To address the reviewers' feedback, we implemented and evaluated 5 new defenses against CAA, provided a generalization study on 2 new models, and analyzed in detail the constraints of the CTU case. These new results are in the attached PDF. We address below the common comments of the reviewers: C1- Novelty of the work (JEHw, aMTd): We would like to clarify that research on adversarial robustness for tabular ML is still in its infancy. Our work investigates how adaptive attacks and meta-attacks can form a new and strong standard for such robustness assessment. In computer vision, comparable endeavors had a significant impact (e.g. AutoAttack [12]) and yielded de-facto evaluation standards (e.g. RobustBench [A]). We aim to push such needed advances for tabular ML, while considering its specificities — i.e. the existence of validity constraints. However, the development of adaptive mechanisms for tabular attacks is not straightforward: blindly combining existing mechanisms (developed for computer vision) yields suboptimal results. Therefore, our work carefully investigates specific adaptations, including a tabular-specific repair mechanism, to form a novel optimized attack (CAPGD). Furthermore, the development of a meta-attack requires careful selection of the baseline methods. We are the first to investigate this question, through extensive experimentation and the demonstration that not all attacks are needed (some attacks are subsumed by others). We reveal that combining CAPGD with MOEVA yields the best comprehensiveness-efficiency trade-off. CAA, the resulting meta attack, therefore acts as the new baseline for adversarial attacks on tabular ML models. C2- Analysis of CTU constraints: (XFcC, 5k6D) CAPGD and MOEVA fail to generate adversarial examples on CTU for 2 out of 5 models. CTU dataset has a large number of constraints compared to the other datasets, and some are particularly challenging. We argue that some of these constraints hinder gradient attacks and are harder to optimize. To confirm our hypothesis and provide additional insights, we split the constraints of CTU based on their type into 4 buckets (Table 2 of the Author Response PDF). First, we ran an ablation study, where we ignored one bucket of constraint at a time. Next, we studied the success rate when we considered each bucket separately. Finally, we reported the impact of the number of constraints to optimize from CG3, the largest bucket. The results in Table 3 show that for gradient attacks, removing one type of constraint is not enough to improve the success rate. Constraints across multiple remaining categories are not satisfied. The individual bucket study confirms that only when considering constraints of type CG2 alone, CAPGD improves its success rate (in VIME and TabNet). When only considering CG3 constraints, reducing the number of constraints improves the success rate (by reducing robust accuracy from 95.3% when considering 100% of CG3 constraints to 84.5% and 43.0% respectively when considering 50% and 10% of the constraints). We hope this fine-grained constraint analysis addresses the interrogations of reviewers #XFcC and #5k6D, and confirms that for CTU dataset, both the number of constraints and the complexity of individual constraints make the constrained adversarial optimization challenging for gradient attacks. Thank you for pointing out this pattern, we will extend the appendix with a section dedicated to the aforementioned analysis of the constraints of CTU. C3- Generalization of our approach to shallow/tree models: (5k6D, aMTd) We train Random Forests (RF) and XGBOOST models to achieve the best performance on our datasets and we present in Table 5 of the attached PDF, the robust accuracy of both models against CAA for the four datasets in two settings: (1) Direct attack where CAA (using its search component MOEVA) attacks directly the RF and XGBOOST models, and (2) Transfer attacks, where we craft the examples on our deep learning (DL) models and evaluate them in the RF and XGBOOST models. Our new study shows that (1) DL models of our study achieve comparable clean performance to the shallow models, (2) both RF and XGBOOST models are vulnerable to direct CAA attacks (down to 9.1% of robust accuracy on LCLD XGBoost), and (3) CAA attacks on DNN transfer to RF (down to 5.3% robust accuracy) and XGBoost (down to 9.4% robust accuracy) models. This study confirms the relevance and significance of our attacks on tabular models, including undifferentiable models. C4- Dedicated "Limitations" section: (All) We have scattered the limitations of our approaches across the paper and we summarize them for completeness. - Marginal overhead of CAA: In settings where CAPGD fails to attack tabular models, CAA can exhibit a computation overhead (<14%) compared to MOEVA. However, in 4/5 evaluated settings, CAA is faster than MOEVA (up to 5 times). - CAPGD effectiveness with complex constraints: CAPGD effectiveness drops when increasing the constraint's complexity such as the number of constraints or the number of features involved in each constraint. - Coherence of constraints: The mechanisms of CAA assume that the constraints definitions are sound. Incoherences between boundary constraints and feature relation constraints can lead to invalid adversarial examples with large EPS budgets. We will introduce both the study of tree-based models and the dedicated limitation section in the final version of the paper. Pdf: /pdf/5f95b6fcacfd49103dfdf078ba15850631a22bd2.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Prospective Representation Learning for Non-Exemplar Class-Incremental Learning	Accept (poster)	Summary: This paper aims to solve the catastrophic forgetting in non-exemplar class-incremental learning. The authors propose Prospective Representation Learning (PRL) to prepare representation space for classes in later tasks in advance. Such forward compatible method first squeezes the embedding distribution of the current classes to reserve space for forward compatibility with future classes, then makes the new class features away from the saved prototypes of old classes. Extensive experiments are performed to demonstrate that the method is effective. Strengths: 1. The paper is easy to understand and follow. 2. The reported performance of the proposed method seems good, especially in TinyImageNet. 3. The illustration of the method is clear. Weaknesses: 1. The novelty of the method could be one of the concerns. There are previous works considering forward-compatible incremental learning [1,2]. The embedding space reservation is not a new concept, which has been proposed in [2]. This paper lacks related works and discussion on the advantages over other forward compatible methods and comparison with them. 2. Lack of evaluation on large datasets like Imagenet1000. [1] Shi et al. Mimicking the Oracle: An Initial Phase Decorrelation Approach for Class Incremental Learning. [2] Zhou et al. Forward Compatible Few-shot Class-Incremental Learning. Technical Quality: 3 Clarity: 3 Questions for Authors: 1. What are the advantages of PRL over other forward-compatible methods? 2. Can you provide the evaluation results on large datasets? Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: The paper has a section of limitation. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your constructive feedback! We hope the following responses can address your concerns. --- W1 & Q1: What are the advantages of PRL over other forward-compatible methods? A1: First, unlike previous works, PRL targets CIL in exemplar-free scenarios (NECIL). NECIL requires the algorithm to learn a unified model without access to any data from previous tasks, which means that the commonly used memory buffers are not available thus more challenging. Second, compared to previous works, PRL considers how to resolve conflicts between new and old classes during the incremental phases, in addition to reserving space in the initial phase. Zhou et al [2] also mentioned that such conflicts need to be taken into account when it transforms into a CIL problem (i.e., there are enough instances of the new classes). Compared to the work of Zhou et al [2], which presupposes unseen classes by mixing instances from the initial task, our approach improves the forward compatibility of the model without interfering with the learning of the initial task itself. The reference works you provided are inspiring to our research. We will add a discussion of the works on forward-compatible incremental learning in the final version of our paper. --- W2 & Q2: Lack of evaluation on large datasets like Imagenet1000. A2: The following table compares the average incremental accuracies of the different methods for the 10 phases setting on ImageNet-1k. We will provide more experimental results on ImageNet-1k in the final version of the paper. \| \| &ensp; PASS &ensp; \| &ensp; SSRE &ensp; \| &ensp; SOPE &ensp; \| &ensp; POLO &ensp; \| &ensp; NAPA-VQ &ensp; \| &ensp; PRL (Ours) &ensp; \| \| --- \| :---: \| :---: \| :---: \| :---: \| :---: \| :---: \| \| Accuracy (%) \| 55.90 \| 58.12 \| 60.20 \| 61.53 \| 54.21 \| 62.74 \| We are looking forward to answering any follow up questions during the discussion period. --- Rebuttal Comment 1.1: Title: Thank You for the response Comment: The authors' response resolves most of my concerns, I decide to raise my score. --- Reply to Comment 1.1.1: Title: Official Comment by Authors Comment: Thank you for taking the time to read our response and increasing your score! We are glad to hear that our response addressed your concern.	Summary: This work introduces a Prospective Representation Learning (PRL) scheme to prepare the model for handling conflicts of the balance between the old and new classes in Non-exemplar class-incremental learning (NECIL). The author proposes to squeeze the embedding distribution of the current classes in the base phase and make the new class features away from the saved prototypes of old classes in the incremental phase, improving the balance of old and new classes in the existing NECIL baselines. Strengths: 1. This work proposes the Prospective Representation Learning (PRL) scheme to solve the balance problem between old and new classes in NECIL tasks. 2. The proposed PRL scheme is plug and play, making it convenient to combine with other models. Weaknesses: 1. Few analysis was conducted on the loss weight α in formula 14. 2. There are some grammar or writing errors in the text, such as the repeated appearance of the "propose" on line 111. Technical Quality: 3 Clarity: 2 Questions for Authors: 1. Why not perform Preemptive Embedding Squeezing (PES) on new classes during the incremental phase? Will this not cause overlap in the feature space of the new classes? 2. What does the $L_{IIC}$ of Formula 9 indicate? I do not find the corresponding explanation. (ps: I guess the author may have mistakenly wrote $L_{PES}$ as $L_{IIC}$) 3. What do the old class prototypes of formula 11 and the potential spatial features of formula 12 specifically refer to, and is there a relationship between them? Confidence: 3 Soundness: 3 Presentation: 2 Contribution: 2 Limitations: None Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you so much for the insightful questions! We will revise our manuscript accordingly and address your questions below. --- W1: Few analysis was conducted on the loss weight α in formula 14. A1: We set $\alpha_1=10$, $\alpha_2=10$ , and $\alpha_3=2$ by default. Due to rebuttal limitations, the experimental results are shown in the pdf file attached to the Author Rebuttal. In Eq.14, $\alpha_1$ and $\alpha_2$ are common in previous NECIL methods and represent the weights of distillation loss and prototype loss, respectively. The main role of these two loss functions is to maintain the pre-existing knowledge of the model. Therefore, as shown in Fig.(d) and Fig.(e), as $\alpha_1$ and $\alpha_2$ get larger, the optimization of the model will be biased towards maintaining stability, resulting in the model performing better on the old task and worse on the new task. For the consideration of comprehensive performance, we set $\alpha_1 = 10$ and $\alpha_2=10$ for PRL. Then $\alpha_3$ controls the loss of the Prototype-Guided Representation Update (PGRU) proposed in this paper. In Figure (c), as $\alpha_3$ increases PGRU comes into play. The effect of growing $\alpha_3$ on the overall performance fluctuates, which may be caused by overly strict constraints on the learning of new class representations. Overall, our algorithm is relatively robust to the choice of hyperparameters. --- W2 & Q2: Some grammar or writing errors. A2: Thank you for pointing out our error. As you guessed, $\mathcal{L}_ {IIC}$ was a writing error, and should actually be $\mathcal{L}_ {PES}$. We will carefully scrutinize the main text and the appendix, and ensure such errors are eliminated in the final version of the paper. --- Q1: Why not perform Preemptive Embedding Squeezing (PES) on new classes during the incremental phase? Will this not cause overlap in the feature space of the new classes? A3: First, going into the incremental phase, the main problem faced by the model shifts from adjusting the relationship between new classes to dealing with the overlap between the new classes and the old ones, especially in the absence of samples from the old classes. We therefore propose Prototype-Guided Representation Update (PGRU) to alleviate this problem. Due to the shift of the main problem, the improvement from performing PES in the incremental phase is not obvious. We further reflect on this issue. This could be caused by the fact that as incremental learning goes on and on, the number of new classes is relatively small compared to the old ones. Therefore we try to increase the number of classes in the incremental phase for our experiments on CIFAR-100. In the following table, we performed only one incremental phase and set the number of classes $C$ in the incremental phase to 5, 10, 20, and 50, respectively. It can be seen that the effect of PES is gradually apparent when the number of new classes increases. \| \|C=5\|C=10\|C=20\|C=50\| \|---\|:---:\|:---:\|:---:\|:---:\| \|w/ PES\|80.97\|79.10\|77.78\|73.96\| \|w/o PES\|80.84\|79.05\|77.34\|73.37\| Certainly, the ratio of the number of new classes to the number of old classes naturally decreases as the tasks learned by the model accumulate, so we only employ PES in the initial phase. Previous work [1] that considered forward compatibility also optimized the learning of the model only in the initial phase. Second, in the incremental phase, due to the sufficient number of samples in the new classes, the cross-entropy loss also makes the features of the new classes distinguish from each other and reduce the overlap of the new classes. --- Q3: What do the old class prototypes of formula 11 and the potential spatial features of formula 12 specifically refer to, and is there a relationship between them? A4: We have described the old class prototypes and the features in the potential space in Sections 3.2 (line154-158) and Section 3.3 (line195-200), respectively. At the end of each phase, a prototype is computed and saved for each class of the current task. As shown in Eq.4, the prototype is usually the average of all the features of the class. This is widely used in existing NECIL methods [2, 3]. The potential spatial features refer to features $\mathcal{P}_ {\phi_ t}(\mathcal{F}_ {\theta_ {t-1}}(x^i))$ that have been projected, where $x^i$ denotes the sample of the current class, $\mathcal{F}_ {\theta_ {t-1}}(x^i)$ is the feature extracted by the teacher model (the model trained from the previous phase). Old class prototypes cannot be updated after saving due to the absence of old class data. Since the teacher model $\mathcal{F}_ {\theta_ {t-1}}$ is frozen, $\mathcal{F}_ {\theta_ {t-1}}(x^i)$ also does not change in the current phase of training. Therefore, we introduce a projector $\mathcal{P}_ {\phi_t}$ to project the prototypes $\boldsymbol{p}^c$ and $\mathcal{F}_ {\theta_ {t-1}}(x^i)$ into a potential space. Optimizing the projector via Eq.11 can change the relationship between $\boldsymbol{p}^c$ and $\mathcal{F}_ {\theta_ {t-1}}(x^i)$ in the potential space thus avoiding the new class features to be too close to the region where the old class prototype is located. Eq.12 is to align the features $\mathcal{F}_ {\theta_ {t}}(x^i)$ extracted by the current updated model $\mathcal{F}_ {\theta_ {t}}$ with the potential spatial features $\mathcal{P}_ {\phi_ t}(\mathcal{F}_ {\theta_ {t-1}}(x^i))$ that have been adjusted by the projector. We will optimize the expression to make this clearer in the final version. --- Reference: [1] Shi et al. Mimicking the Oracle: An Initial Phase Decorrelation Approach for Class Incremental Learning. [2] Zhu et al. Prototype augmentation and self-supervision for incremental learning. [3] Shi et al. Prototype reminiscence and augmented asymmetric knowledge aggregation for non-exemplar class-incremental learning. --- We are looking forward to answering any follow up questions during the discussion period. --- Rebuttal Comment 1.1: Title: Official Comment by Authors Comment: Dear reviewer SYbV, We thank you sincerely for your time and effort in reviewing our manuscript and providing valuable suggestions. We have provided detailed responses to your questions and hope that they adequately address your concerns. If you need further clarification or have any other questions, please feel free to discuss them with us! We are more than willing to continue our communication with you. We would greatly appreciate it if you would update the rating by synthesizing other reviewers' comments as well as our responses. --- Rebuttal 2: Title: Responses to Comment by Reviewer SYbV Comment: Thank you for your response. We suppose that you may have misunderstood our response and our experiments in rebuttal. Our proposed PES aims to construct a better initial embedding space. Therefore, in our initial submitted version, PES is only performed in the first phase. We have done extensive experiments in our submitted version (Table 2 and Figure 3) to demonstrate the effectiveness of this manner. We also list the results in the following. Results demonstrate that PES can significantly improve the forward compatibility of model since it reserves space to prepare for future classes. For continual learning on incremental new classes, to make new classes embedded in the space previously reserved, PES was not included in the incremental phase in our submitted version. \| \| CIFAR-100 (5 phases) \| CIFAR-100 (10 phases) \| CIFAR-100 (20 phases) \| TinyImageNet (5 phases) \| TinyImageNet (10 phases) \| TinyImageNet (20 phases) \| \| --- \| :---: \| :---: \| :---: \| :---: \| :---: \| :---: \| \| baseline \| 69.25 \| 68.52 \| 65.93 \| 55.04 \| 54.15 \| 51.65 \| \| baseline w/ PES \| 70.57 \| 69.64 \| 67.58 \| 57.08 \| 55.84 \| 53.58 \| In the first round of review, as you suggested, we add experiments that using PES in the incremental phase, shown in the rebuttal, which lead your misunderstandings. The results have verfied that adding PES in the incremental phase indeed does not bring in further improvement. It means that our original design in submitted version is reasonable and effective. We do not need PES in the incremental phase. We hope this response clarifies your misunderstandings.	Summary: This paper focuses on non-exemplar class-incremental learning, specifically addressing the challenge of balancing old and new classes. The author introduces Prospective Representation Learning (PRL), which involves constructing a preemptive embedding squeezing constraint to allocate space for future classes. Additionally, the author proposes a prototype-guided representation update strategy. Strengths: 1.The Preemptive Embedding Squeezing (PES) constrains the current class space to prepare for accommodating future new classes. 2.The Prototype-Guided Representation Update (PGRU) strategy ensures that features of new classes remain distinct from prototypes of old classes in the latent space. 3.The writing is clear. 4.The paper includes extensive experiments. Weaknesses: 1.What is the meaning of IIC in equation 9? The paper does not explain its meaning; I guess it stands for PES. 2.Many previous works have studied mapping class centers to different subspaces (orthogonal). The paper should compare similar works to highlight the differences and advantages of the proposed method. As indicated by the following references: [1,2,3]. 3.The PASS paper also uses prototype augmentation (and proposes other methods), but your baseline is higher than PASS, especially in TinyImageNet P=20, by almost 10%. The author should explain the advantages of using prototype augmentation in the baseline or provide experimental results without prototype augmentation. 4.In equation 14, there are many hyperparameters, /alpha1,2,3. The author should provide more sensitivity analysis of the hyperparameters to make the experiments more thorough. [1] Chaudhry A, Khan N, Dokania P, et al. Continual learning in low-rank orthogonal subspaces[J]. Advances in Neural Information Processing Systems, 2020, 33: 9900-9911. [2] Guo Y, Hu W, Zhao D, et al. Adaptive orthogonal projection for batch and online continual learning[C]//Proceedings of the AAAI Conference on Artificial Intelligence. 2022, 36(6): 6783-6791. [3] French R M. Dynamically constraining connectionist networks to produce distributed, orthogonal representations to reduce catastrophic interference[C]//Proceedings of the sixteenth annual conference of the cognitive science society. Routledge, 2019: 335-340. Technical Quality: 2 Clarity: 3 Questions for Authors: 1.Many previous works have studied mapping class centers to different subspaces (orthogonal). The paper should compare similar works to highlight the differences and advantages of the proposed method. As indicated by the following references: 1, 2. 2.The PASS paper also uses prototype augmentation (and proposes other methods), but your baseline is higher than PASS, especially in TinyImageNet P=20, by almost 10%. The author should explain the advantages of using prototype augmentation in the baseline or provide experimental results without prototype augmentation. Confidence: 5 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: Thank you for your thoughtful questions! We are glad that you found the paper easy to read and affirm our experiment. We hope that our response below will address your concerns. --- W1: What is the meaning of IIC in equation 9? Is it a writing error? A1: We are sorry for our writing error. It should be $\mathcal{L}_{PES}$ in Eq. 9. We will carefully check and ensure such errors are eliminated in the final version of the paper. --- W2 & Q1: Discussion of the differences and advantages of the method proposed in this paper over previous studies on mapping class centers to different subspaces. A2: First, unlike previous works, PRL targets CIL in exemplar-free scenarios (NECIL). PRL does not need to store exemplars of past tasks to promote subspace orthogonality. Second, previous works start to deal with the conflict between old and new tasks only when a new task arrives. However, due to the lack of samples from old tasks in NECIL, it is intractable to deal with this conflict using only the new task data. Instead, we consider reserving space for unknown new classes in the initial phase to prepare for conflict resolution in advance. The references you provided is enlightening to our research. We will include a discussion of the above methods in the Related Work section. --- W3 & Q2: Explain the advantages of using prototype augmentation in the baseline compared to PASS. A3: Since only one prototype is saved for each class, using one prototype to represent the old class distribution would lack diversity. Prototype augmentation helps to maintain the discrimination between old and new classes and prevents the decision boundary from being biased in favor of the new classes. From the perspective of our paper, both prototype augmentation and the knowledge distillation technique commonly used in NECIL are prompting the model to achieve backward compatibility, i.e., to make the updated model compatible with classes that have already been learned. The PRL proposed in this paper, on the other hand, is prompting the model to achieve forward compatibility, i.e., enhancing the ability of the model to be compatible with unseen classes. Therefore, better performance can be achieved when both forward and backward compatibility of the model are improved. After PASS [1], many other prototype augmentation strategies have been proposed, such as [2, 3]. We adopt the prototype augmentation method called Prototype Reminiscence (PR) from [2] as our baseline, which is described in Section 3.2 (line 162). The experiments in the Appendix (Table 6) also demonstrate that our PRL can be combined with PASS or other methods in a plug-and-play manner and enhance its performance. We complement the performance of PASS combined with PRL on the TinyImageNet dataset in the following table, where 'P' denotes the number of incremental phases. It can be seen that the PRL brings a significant boost to PASS as well. \| \| &ensp; P=5 &ensp; \| &ensp; P=10 &ensp; \| &ensp; P=20 &ensp; \| \| :---: \| :---: \| :---: \| :---: \| \| PASS &ensp;\| 49.55 \| 47.29 \| 42.07 \| \| PASS+PRL &ensp; \| 52.19 \| 50.38 \| 42.63 \| --- W4: More sensitivity analysis of the hyperparameters. A4: We set $\alpha_1=10$, $\alpha_2=10 $, and $\alpha_3=2$ by default. When a sensitivity analysis is performed on one of the hyperparameters, default settings are used for the remaining hyperparameters. Due to rebuttal limitations, the experiment results are shown in the pdf file attached to the Author Rebuttal. The figures in the left column show the effect of changing the value of each hyperparameter on the average incremental accuracy of our method. The figures in the right column show the effect of changing the value of each hyperparameter in the last phase on the accuracy on the new and old tasks, respectively. Among the three hyperparameters in Eq. 14, $\alpha_1$ and $\alpha_2$ are common in previous NECIL methods and represent the weights of distillation loss and prototype loss, respectively. The main role of these two loss functions is to maintain the pre-existing knowledge of the model. Therefore, as shown in Figure (d) and Figure (e), as $\alpha_1$ and $\alpha_2$ get larger, the optimization of the model will be biased towards maintaining stability at the expense of plasticity, resulting in the model performing better on the old task and worse on the new task. It can be seen that as the value of $\alpha_1$ and $\alpha_2$ increases to a certain level its performance improvement on old tasks slows down. Excessively large values of $\alpha_1$ and $\alpha_2$ will bring much less gain on the old task than they will hurt performance on the new task. For the consideration of comprehensive performance and with reference to previous works [1, 3], we set $\alpha_1 = 10$ and $\alpha_2=10$ for our method. Then $\alpha_3$ controls the loss of the Prototype-Guided Representation Update (PGRU) proposed in this paper. In Figure (c), as $\alpha_3$ increases PGRU comes into play. The effect of growing $\alpha_3$ on the overall performance of the algorithm fluctuates, which may be caused by overly strict constraints on the learning of new class representations. Overall, our algorithm is relatively robust to the choice of hyperparameters. We will add a clarification on hyperparameters in the final version. --- Reference: [1] Zhu F et al. Prototype augmentation and self-supervision for incremental learning. CVPR 2021. [2] Shi W et al. Prototype reminiscence and augmented asymmetric knowledge aggregation for non-exemplar class-incremental learning. ICCV 2023. [3] Wang S et al. Non-Exemplar Class-Incremental Learning via Adaptive Old Class Reconstruction. ACM MM 2023. --- We are looking forward to answering any follow up questions during the discussion period.	Summary: The paper proposes a method to deal with incremental classification task in which no exemplars from the previously seen classes can be saved for usage during training on the newly arriving classes. The proposed method squeezes the embedding distribution of the current classes to reserve space for forward compatibility with future classes and reduces the impact of introducing new classes by trying to restrict the embeddings of the new classes in the regions not occupied by the previously seen classes. The method uses the class prototype of the previously seen classes but does not use any exemplars. The method uses Preemptive Embedding Squeezing and Prototype-Guided Representation Update to achieve the above goals. Strengths: The proposed method is based on the premise of compressing the feature space occupied by the previously seen classes to ensure less interference between old and new classes, which sounds logical. The method seems to be clearly written. The proposed method performs well on all the compared datasets. Weaknesses: The paper should include a separate section to discuss the difference between this method and other methods that employ feature space compression for incremental learning. The standard deviation in the results between different runs is not mentioned. Apart from accuracy improvement, does the proposed method involve fewer/more parameters as compared to the other compared methods? Is there any difference in training or testing time for the proposed method as compared to the others. Technical Quality: 3 Clarity: 3 Questions for Authors: The paper should include a separate section to discuss the difference between this method and other methods that employ feature space compression for incremental learning. The standard deviation in the results between different runs is not mentioned. Apart from accuracy improvement, does the proposed method involve fewer/more parameters as compared to the other compared methods? Is there any difference in training or testing time for the proposed method as compared to the others. Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The paper mentions a limitation in that it is not able to rationally allocate the space of base classes since the number and distribution of unknown classes cannot be predicted. However, the authors did not experimentally demonstrate any such issue, which can be possibly done by changing the order of the classes between multiple runs. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your positive response! We are delighted that the reviewer has found our method clear and sound. We have addressed the main points and questions below. --- Q1：Lack of discussion with other methods that employ feature space compression for incremental learning. A1: Thanks to your suggestion, we will add a separate subsection to the Related Work section to discuss methods on feature space compression in incremental learning. --- Q2: The standard deviation of the results between different runs that change the order of the classes. A2: We perform three runs and use a different random seed to set the class order for each run. The table below shows the standard deviation of the three runs, where 'P' denotes the number of incremental phases and 'Tiny' denotes the TinyImageNet dataset. The experiments show that our method is robust to different class orders. \| \|   CIFAR100 (P=5)   \|   CIFAR100 (P=10)   \|   CIFAR100 (P=20)   \| &ensp; Tiny (P=5) &ensp; \| &ensp; Tiny (P=10) &ensp; \| &ensp; Tiny (P=20) &ensp; \| \| --- \| :---: \| :---: \| :---: \| :---: \| :---: \| :---: \| \| PRAKA \| 68.95 \| 69.02 \| 65.71 \| 54.90 \| 53.38 \| 49.93 \| \| NAPA-VQ \| 70.44 \| 69.04 \| 67.42 \| 52.77 \| 51.78 \| 49.51 \| \| PRL (Ours)   \| 71.26$\pm$0.19 \| 70.17$\pm$0.31 \| 68.44$\pm$0.24 \| 58.12$\pm$0.48 \| 57.24$\pm$0.41 \| 54.51$\pm$0.36 \| --- Q3: Comparison on the number of model parameters, training time and testing time. A3: The introduction of a projector in our method introduces additional parameters, but the number of parameters added is minimal compared to the network as a whole. And the forward propagation does not need to go through the projector during the test. The following table shows the model parameters of our method, the training time for one epoch in the last incremental phase and the testing time (on all classes) on CIFAR-100. The experimental results are performed with in the same environment. Model parameters： \| \|   PASS   \|   PRAKA   \|   NAPA-VQ   \|   PRL (Ours)   \| \| :---: \| :---: \| :---: \| :---: \| :---: \| \| Parameters   \| 10.93M \| 11.02M \| 11.18M \| 11.30M \| Testing time: \| \|   PASS   \|   PRAKA   \|   NAPA-VQ   \|   PRL (Ours)   \| \| :---: \| :---: \| :---: \| :---: \| :---: \| \| Test time   \| 1.82s \| 2.38s \| 4.31s \| 1.74s \| Training time for one epoch: \| \| &emsp; P=5 &emsp; \| &emsp; P=10 &emsp; \| &emsp; P=20 &emsp; \| \| :---: \| :---: \| :---: \| :---: \| \| PASS   \| 10.09s \| 5.92s \| 4.81s \| \| PRAKA   \| 7.62s \| 4.27s \| 3.57s \| \| NAPA-VQ   \| 20.06s \| 10.62s \| 6.54s \| \| PRL (Ours)   \| 7.97s \| 4.54s \| 3.55s \| We are looking forward to answering any follow up questions during the discussion period.	Rebuttal 1: Rebuttal: We thank all reviewers for their positive view of our work and valuable feedback. We responded to reviewers' comments in individual replies to each reviewer with references to weakness (W) and questions (Q). In response to the question of Reviewer FnFn and Reviewer SYbV about the analysis of the hyperparameters $\alpha$ in Eq. 14, we have attached a pdf file showing the experiment results. In the pdf file, the figures in the left column show the effect of changing the value of each hyperparameter on the average incremental accuracy of our method; the figures in the right column show the effect of changing the value of each hyperparameter in the last phase on the accuracy on the new and old tasks, respectively. Please let us know if there are additional items or further clarifications/discussions we could address. We will incorporate clarifications and additions, as we specified in our replies, in the final version of our work. Pdf: /pdf/d933f53f522066b4eef673761cfe6e47c11609b6.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
CriticEval: Evaluating Large-scale Language Model as Critic	Accept (poster)	Summary: This work introduces a benchmark for using LLMs are critics. The benchmark covers four settings: 1. Providing feedback 2. Correction of a response with/without feedback 3. Comparison of two responses for a given query 4. Providing meta-feedback (feedback on feedback) Strengths: Extensive experiments across models and setups. Weaknesses: For weakness I would repeat the limitations I list below. Technical Quality: 4 Clarity: 4 Questions for Authors: Did you consider structured generation? Besides positional bias, did you explore any other biases such as bias to length, style or certain words? Did you consider few-shot performance? Confidence: 4 Soundness: 4 Presentation: 4 Contribution: 4 Limitations: Two minor limitations: - As far as I can tell structured generation was not used which has been shown to improve performance - As far as I can tell few-shot performance was not considered. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We really appreciate your valuable suggestions and insightful questions. We will address your concerns as follows. --- Q1: Did you consider structured generation? A1: We appreciate the reviewer’s attention to the details of our evaluation. Structured generation, such as JSON output, is relatively new but crucial for applications of LLMs, and we have not considered it yet. While the structured generation is not used, our conclusions are still reliable due to the same generation settings of all evaluated LLMs. The primary goal of our proposed CriticEval in the current stage is to construct a comprehensive and reliable benchmark for evaluating critique ability. We will supplement discussions about it in the Limitation. Thanks for your valuable suggestions. --- Q2: Besides positional bias, did you explore any other biases such as bias to length, style or certain words? A2: Yes, in addition to positional bias, we have investigated length bias, which is discussed in Section 5.2 (lines 198-200) and Appendix I. Figure 10 (Appendix I) reveals no significant correlation between the count of unique tokens and the Likert scores from GPT-4’s subjective evaluations across three critique dimensions [1,2], likely due to the human-annotated reference critiques used in the prompt. Regarding other potential biases, such as style and specific word preferences, our human annotations haven't observed substantial influence from these factors. --- Q3: Did you consider a few-shot performance? A3: Yes, we have studied the few-shot prompting strategy. However, our results demonstrate that few-shot prompting reduces performance across various LLMs. For example, when using 1-5 examples in objective feedback evaluations, we observed a significant decline in LLMs' performance as the number of examples increased. \|Spearman Correlation\|No Few-shot\|1\|2\|3\|4\|5\| \|-\|-\|-\|-\|-\|-\|-\| \|Llama-3-7B-Instruct\|61.34\|58.13\|54.25\|52.99\|53.23\|50.11\| \|InternLM2-20B-Chat\|69.86\|66.26\|64.99\|63.32\|60.33\|61.72\| This intriguing phenomenon may be due to the complexity of the critique task, where few-shot examples might impede the LLM’s understanding of the evaluated responses. Consequently, CriticEval currently does not utilize few-shot prompting by default. Given the emerging interest in critique ability research, we look forward to future works investigating advanced inference strategies to improve critique ability of LLMs. --- ### References [1] AlpacaEval: An Automatic Evaluator of Instruction-following Models [2] How Far Can Camels Go? Exploring the State of Instruction Tuning on Open Resources --- Rebuttal Comment 1.1: Comment: Thanks for responding to my questions.	Summary: This paper introduces CriticEval, a benchmark designed to comprehensively and reliably evaluate the critique ability of large language models (LLMs). It assesses critique capabilities across four dimensions (feedback, comparison, correction, and meta-feedback) and nine diverse task scenarios, using both scalar-valued and textual critiques for responses of varying quality. The benchmark was constructed using a human-in-the-loop pipeline, with initial critiques generated by GPT-4 and refined by human experts. CriticEval employs both objective metrics and subjective evaluation by GPT-4 with human-annotated reference critiques. Key findings from evaluating 35 LLMs include: GPT-4's high correlation with human judgments when using reference critiques, some open-source LLMs approaching closed-source models in performance, and insights into how critique difficulty varies by task type, response quality, and critique dimension. CriticEval could be used as a comprehensive and reliable tool for assessing LLM critique capabilities. Strengths: - CRITICEVAL evaluates critique ability across multiple dimensions (feedback, comparison, correction, meta-feedback) and diverse task scenarios, providing a more holistic assessment than existing benchmarks. - The benchmark combines GPT-4 generated critiques with human expert refinement and employs both objective metrics and subjective evaluation with human-annotated reference critiques. This approach ensures a more reliable and accurate evaluation of LLM critique abilities. - The paper presents results from evaluating 35 open-source and closed-source LLMs, offering valuable insights into the current state of LLM critique capabilities. It reveals interesting relationships between critique difficulty and factors like task type, response quality, and critique dimension. Weaknesses: - The biggest concern of the dataset is that it relies heavily on GPT-4 for initial critique generation and evaluation. This could introduce a bias favoring models such as GPT-4 and models trained on GPT-4 distilled data. The human-in-the-loop process might not fully mitigate this bias, especially if annotators are influenced by GPT-4's initial outputs. A more diverse set of models or purely human-generated critiques for the benchmark could have provided a more neutral evaluation framework. - The paper doesn't adequately address the scalability of CRITICEVAL for evaluating future language models. Additionally, the reliance on GPT-4 and human experts for evaluation might make it challenging for other researchers to fully reproduce or extend the benchmark. - Insufficient analysis of failure modes: While the paper presents overall performance metrics, it doesn't delve deeply into the specific ways in which models fail at critique tasks. A more detailed error analysis could provide valuable insights into the limitations of current LLMs and guide future research more effectively. - Lack of comparison to human performance: The paper doesn't provide a clear comparison between LLM performance and human performance on these critique tasks. Technical Quality: 3 Clarity: 2 Questions for Authors: How did you evaluate the human's performance during the benchmark construction phase? Confidence: 5 Soundness: 3 Presentation: 2 Contribution: 2 Limitations: Yes Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We really appreciate your valuable suggestions and insightful questions. We will address your concerns as follows. --- Q1：... relies on GPT-4 for evaluation. This could introduce a bias favoring models such as GPT-4 ... A1: Please refer to "Global Response - Overcome Bias of GPT-4 Judge" for more details. In summary, we supply the human-annotated critiques to improve GPT-'s reliability, and experimental results in the meta-feedback dimension have validated its reliability (Section 6.2). --- Q2: ... a more diverse set of models or purely human-generated critiques provide a more neutral evaluation framework. A2: As described in Appendix A.1, human annotators might be influenced by GPT-4' initial critiques. We wish to emphasize that our decision to employ a human-in-the-loop rather than pure human annotation is motivated by two essential considerations (effectiveness and efficiency): #### 1. Human-written Critiques are Not Comprehensive (Effectiveness) Our human annotation reveals that annotators might neglect some apparent or severe issues when writing critiques from scratch, consistent with findings in recent studies [1,2]. Neglecting issues usually leads to low-quality critiques. Specifically, experimental results in Table 2 of Global Response - Fine-grained Failure Modes proves that missing issues in critiques lead to low subjective scores. In contrast, despite the possibility of generating inaccurate critiques, LLMs like GPT-4 offer more comprehensive and detailed critiques [1,2]. By revising LLM's errors by human experts, the final critiques could be more comprehensive and accurate, leveraging the strengths of both human annotators and LLMs [1,2]. As detailed in Appendix G.5, our human annotations exhibit significant revisions (25.22%, 34.83%, and 48.37%) on GPT-4's initial critiques, effectively alleviating potential bias and noise. #### 2. Annotating Critique Task from Scratch Cost A Lot (Efficiency) Writting critiques from scratch is a significant challenge [3,4]. For instance, Shepherd [4] incurred an annotation cost of 8\\$ per sample, leading to over 28,864\\$ and 1,350 work hours to annotate the entire CriticEval, which is unbearable for our project. Thus, we have to employ advanced LLMs to generate draft critiques, followed by human annotation. GPT-4 is chosen because our preliminary studies indicate that it is the most reliable LLM for producing draft critiques, while other LLMs are much worse (Table 2). Consequently, a diverse set of LLMs introduces more noise in draft critiques, bringing more difficulties to human annotators. In conclusion, the human-in-the-loop pipeline achieves the trade-off between annotation cost and quality. We promise to add these details to the revised paper to emphasize the motivation of using the human-in-the-loop pipeline. Thanks for your detailed review and insightful question. --- Q3: The paper doesn't adequately address the scalability of CriticEval ... reliance on GPT-4 and humans make it challenging to reproduce or extend CriticEval A3: Please refer to Section "Global Response - Scalability and Cost" for our explanations. Our explanations reveal that the cost of reproducing and extending CriticEval is comparable to established benchmarks like AlpacaEval and AlpacaFarm. --- Q4: Insufficient analysis of failure modes ... A4: Thanks for your very valuable suggestions. We have conducted coarse-grained and fine-grained analyses of failure modes before. Due to space limitations, we only included the coarse-grained analysis in Section 6.6. To address your concern, we have supplemented our findings in "Global Response - Fine-grained Failure Modes." This supplementary material reveals intriguing phenomena. For example, the most frequent failure modes are missing errors, lacking effective comparison and worse revision than references for feedback, comparison and correction. Besides, inaccurate critiques usually lead to lower subjective scores. The revision that does not follow suggestions in feedback usually leads to the worst performance. We really appreciate your insightful suggestions and the opportunity to address them. --- Q5: Lack of comparison to human performance ... A5: As described in Q1-A1, collecting purely human-annotated critiques is challenging. Thus, human performance is not recorded in the current submission. We agree that human performance is valuable, and we are urgently working on annotating human-generated results on the test set. All annotators have an undergraduate level of education. Due to the massive workload of human annotation, subjective annotations are ongoing, and the objective scores have been provided below: \|\|Feedback (Corr.)\|Comparison (Acc)\|Correction (Pass Rate)\|Meta-Feedback (Corr.)\| \|-\|-\|-\|-\|-\| \|GPT-4\|63.54\|57.33\|69.67\|62.9\| \|Human\|67.69\|60.67\|75.69\|71.36\| Human performance slightly outperforms GPT-4 on four critique dimensions in the objective split. We promise to add full human performance results in the revised paper. Thanks for your valuable suggestions. --- Q6: How did you evaluate human performance during benchmark construction? A6: As briefly described in Appendix G.1, for the textual critiques, the supervisor's (authors) review and revise mechanism ensures the quality of human annotation meets our expectations. For the scalar-based critiques, the supervisors conducted a 5% sample inspection. If the error rate exceeds the threshold, annotators are asked to revise their work until the error rate is lower than the threshold. Besides, the inner-agreement among annotators are computed to make sure their judgments are consistent. --- ### References [1] LLM Critics Help Catch LLM Bugs (OpenAI) [2] Self-critiquing models for assisting human evaluators (OpenAI) [3] AlignBench: Benchmarking Chinese Alignment of Large Language Models [4] Shepherd: A Critic for Language Model Generation --- Rebuttal 2: Title: The Complete Human-level Performance Comment: Dear Reviewer kJKF, We would like to thank you for the thoughtful and constructive feedback and appreciate that you agree on the strengths of our paper. We provided details and analysis to address your concerns during the rebuttal. In this response, we complete the human performance annotation of the subjective tasks on the CriticEval test set, and the overall human-level performance is shown as follows. Note that the cohort and corresponding set of human critiques do not represent the best possible human performance; instead, they represent the capability of annotators selected for this human performance annotation of the CriticEval test set. \|\|Feedback Sub.\|Feedback Obj.\|Comparsion Sub.\|Comparison Obj.\|Correction Sub.\|Correction Obj.\| \|-\|-\|-\|-\|-\|-\|-\| \|GPT-4\|7.84\|63.54\|7.89\|57.33\|7.69\|69.67\| \|Human\|5.61\|67.69\|5.22\|60.67\|6.63\|75.69\| > As described in Section 5, objective scores (Obj.) for feedback, comparison, and correction are correlation, accuracy, and pass rate. Subjective scores (Sub.) for feedback, comparison, and correction are Likert scores (1-10) generated by GPT-4 with human-annotated critiques as references. `Experimental Results:` As shown in the Table above, it can be found that the human level significantly outperforms GPT-4 on the objective task, while it is inferior to GPT-4 on the subjective evaluation. --- Then, we conduct the Quantitative and Qualitative Analysis to understand the human performance in subjective evaluation. ### Quantitative Analysis The distribution of failure modes for humans and GPT-4 is shown in the following tables. The numbers in the tables indicate the frequencies of error types in critiques. The descriptions of failure modes are placed in Table 1 of "Global Response - Fine-grained Failure Modes." \|Feedback\|E1\|E2\|E3\|E4\|E5\|E6\|Other\| \|-\|-\|-\|-\|-\|-\|-\|-\| \|GPT-4\|17.99\|18.71\|16.37\|15.83\|10.07\|14.93\|6.12\| \|Human\|21.18\|24.48\|11.36\|15.27\|9.06\|12.13\|6.52\| \|Comparison\|E1\|E2\|E3\|E4\|E5\|E6\|E7\|E8\|Other\| \|-\|-\|-\|-\|-\|-\|-\|-\|-\|-\| \|GPT-4\|16.67\|11.02\|11.29\|15.59\|4.3\|6.99\|19.35\|12.1\|2.69\| \|Human\|19.71\|15.29\|7.65\|9.51\|3.82\|4.8\|24.9\|11.67\|2.65\| \|Correction\|E9\|E10\|E11\|Other\| \|-\|-\|-\|-\|-\| \|GPT-4\|23.46\|43.83\|21.6\|11.11\| \|Human\|29.38\|36.88\|25\|8.75\| `Experimental Results:` As for the feedback and comparison dimensions, the distribution of E1 (missing issues), E2 (missing suggestions or low-quality suggestions), and E7 (insufficient analysis) in human-written critiques is significantly higher than that of GPT-4. In contrast, the distribution of other errors (most are mistakes in critiques) is much lower. As for the correction dimension, human annotators usually do not follow suggestions in the provided feedback (E9) and generate additional errors (E11). Through communicating with the annotators, we notice that the primary cause of this issue is that some tasks require domain-specific knowledge. The lack of this knowledge among annotators leads to lower-quality corrections. This phenomenon aligns with the findings of recent work [1]. `Conclusion:` The human-written critiques are often less comprehensive than GPT-4, significantly reducing the quality. In contrast, the mistakes in human-written critiques are significantly less than that of GPT-4. This phenomenon is consistent with our preliminary study and recent findings [1], further proving the reasonableness of using the human-in-the-loop pipeline to collect comprehensive and accurate critiques (as described in Q2-A2). ### Qualitative Analysis We inspect the human critiques in the subjective evaluation. We notice that human annotators generally write fewer comments than LLMs, and comments are usually general and brief. Besides, many tasks involve domain-specific knowledge that humans may lack, but GPT-4 excels in (albeit with potential hallucinations). ### Summary We provide the human-level performance for the CriticEval test set. The human performance is better than GPT-4 on the objective split, while it is inferior to GPT-4. `We wish to emphasize that:` Although our first submission lacks pure human performance, our reference critiques obtained through the human-in-the-loop pipeline could serve as very close candidates for the best possible human performance. During the subjective evaluation, the quality score of reference critique is anchored to 8 (overall 1-10 score range), serving as a relative scoring pivot, which is helpful in analyzing the performance gap between LLMs and human. We will supplement experimental results and analysis into our revised paper. We hope these responses address the concerns. We are happy to discuss further comments and suggestions. If the reviewer finds our response adequate, we would appreciate it if the reviewer considers raising the score. ### Reference [1] LLM Critics Help Catch LLM Bugs --- Best Regards, Submission 7061 Authors --- Rebuttal Comment 2.1: Comment: I appreciate the author's response, which slightly resolves my concerns. However, I still have concerns about the bias in pure GPT-4 assisted annotation, which is a fundamental limitation of the methodology. Given the new results, I would like to slightly raise my overall score from 4 to 5. --- Reply to Comment 2.1.1: Title: Response to Reviewer Comment: Dear Reviewer kJKF, We really appreciate your valuable feedback during the review phase, and thank you for raising the overall score assigned to our paper. Although we have made our best efforts, the bias of GPT-4 may still not be completely eliminated. The human-in-the-loop annotation pipeline is the trade-off solution for collecting comprehensive and accurate critiques by considering scalability and reliability. We will discuss it in more detail in the Limitation Section of our revised paper. If you have any further questions or concerns, we are more than happy to address them! Best Regards, Submission 7061 Authors	Summary: The paper addresses the need for a comprehensive evaluation of the critique ability of large language models (LLMs) for self-improvement and alignment with human outcomes. Current evaluation methods are critiqued for their limited scope and reliability. The authors propose CRITICEVAL, a benchmark designed to evaluate LLMs across four critique dimensions: feedback, comparison, correction, and meta-feedback, covering nine diverse task scenarios including NLP, alignment, and reasoning tasks. While CRITICEVAL incorporates human-annotated references to enhance reliability, it heavily relies on GPT-4 for evaluations, raising concerns about generalisability across other LLMs. Evaluations of 35 LLMs demonstrate CRITICEVAL's effectiveness but also highlight the inherent difficulties in critiquing complex tasks and the inverse relationship between critique and response quality. Although promising, the reliance on human annotation and the potential biases introduced by using a single LLM for baseline evaluations could limit its broader applicability. The release of datasets and evaluation tools is a positive step towards fostering further research. Strengths: The work is a very comprehensive study on the critical evaluation problem and provides insight for those who would be in situations where they would want to build better LLM pipelines for use-cases where accuracy is important for fit for use. The exploration of 35 different LLM providers more diversity and incorporating human feedback for quality ranking, it allows for wider evaluation than prior benchmarks. I believe the work is well presented, written and argued. It is a very daunting project to get all the pieces together. It is harder, ironically, to evaluate it just as a paper because of all the moving parts, but the authors evaluations across the LLMs are appreciated. Weaknesses: Even with the mention of incorporating Chinese, I believe there should be a serious discussion on how such evaluation pipelines and datasets would function for low-resource languages (Chinese is not one). Many of the large LLMs have multilingual capabilities and their generation of responses are more likely to have higher error rates and as such being able to do critical evaluation in such use-cases is important. The computational cost and real cost of setting up the CRITICEVAL pipelines should be spelled out. It is not clear if IRB/Ethical clearance was obtained as the checklist response states that IRB would be easy to obtain. This is a concern as such I will be referring this for ethics review. It is appreciated that information was provided in Appendix B and G, but whether IRB was obtained or not should have a clear YES or NO statement. Technical Quality: 3 Clarity: 4 Questions for Authors: 1. How do you protect against errors in the underlying tasks datasets. The explosion of many task evaluation sets, even with the best intentions of researchers means that we have compounding effects of source errors (e.g. in Translation), how would this affect your work and how would you mitigate against it? 2. Ultimately how many people are involved and computational cost of such an exercise as this affects replication ability of this study to cover some of the limitations you hilighted? Confidence: 5 Soundness: 3 Presentation: 4 Contribution: 4 Limitations: The limitations are written in Appendix A. They are clear. Flag For Ethics Review: ['Ethics review needed: Research involving human subjects'] Rating: 8 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We really appreciate your valuable suggestions and insightful questions. Since some of your questions are similar to those of other reviewers, we will describe them in more detail in Global Response. We also provide some summary of these questions under your review comment to make our explanation clear. --- Q1: ... it heavily relies on GPT-4 for evaluations ... The potential biases introduced by using a single LLM for evaluations limit broader applicability. A1: Please refer to "Global Response - Overcome Bias of GPT-4 Judge" for our explanations. In summary, experimental results in the meta-feedback dimension prove the reliability of GPT-4 as a judge, while other LLMs are much worse. Besides, to further improve the reliability of subjective evaluation, GPT-4 is equipped with our human-annotated critiques, which is a trade-off solution for scalability and reliability of subjective evaluation. --- Q2: ... I believe there should be a serious discussion on how such evaluation pipelines and datasets would function for low-resource languages ... A2: Please refer to Section "Global Response - Multilingual Support" for our explanations. In summary, CriticEval could be extended to other low-resource languages at an affordable cost using translation and further human labor. --- Q3: The computational cost and real cost of setting up the CRITICEVAL pipelines should be spelled out. A3: Thanks for your valuable suggestion. Please refer to "Global Response - Scalability and Cost" for more details about the computation and construction cost of CriticEval. In summary, the construction and evaluation cost in CriticEval is comparable to established benchmarks, like AlpacaEval and AlpacaFarm. --- Q4: It is not clear if IRB/Ethical clearance was obtained as the checklist response states that IRB would be easy to obtain ... A4: Thanks for your highly meticulous review. We apologize for any confusion and misunderstanding of the meanings between the human subjects and the crowdsourcing. CriticEval is annotated by crowdsourcing, and no human subjects are studied in our work. Besides, as described in Appendix B, the hourly wage of crowdsourcing is much higher than that of Amazon Mechanical Turk. Thus, our work does not violate the NIPS Code of Ethics. Thank you for bringing this to our attention. --- Q5: How do you protect against errors in the underlying tasks datasets ... how would this affect your work and how would you mitigate against it? A5: We agree that some underlying datasets contain inaccuracies that may lead to compounding effects during evaluation. For example, we have observed some incorrect solutions and reasonings for mathematics and coding questions during our human evaluation process. In our work, to mitigate the effects of such errors, human annotators are instructed to examine each question meticulously, the provided golden answers and the evaluated responses and critiques. They are asked to exclude instances where the golden answers or questions are flawed or incorrect, like wrong solutions to mathematics and coding questions. We promise to supplement more details and cases in the Appendix. Thank you for raising this critical issue, and we appreciate the opportunity to strengthen our work through your valuable comments. --- Q6: Ultimately how many people are involved and computational cost of such an exercise as this affects replication ability of this study to cover some of the limitations you hilighted? A6: Please refer to Section "Global Response - Scalability and Cost" for more details about our explanations. Our explanations reveal that the cost of reproducing and extending CriticEval is comparable to established benchmarks like AlpacaEval and AlpacaFarm, ensuring replication ability for the research community. --- Rebuttal Comment 1.1: Title: Thank you for your resonses Comment: Thank you for your responses.	Summary: This study constructs a comprehensive framework for LLM-based evaluation, encompassing data construction, human/machine annotation, and result analysis. It defines a single evaluation framework that covers various tasks and response types. Although previous studies have evaluated different tasks and response types, they often lacked comprehensive analysis, making it difficult to understand the relationships between various factors during evaluation. This research aims to address this gap. Additionally, it examines the reliability of evaluations based on the types of judge models and target models, as well as the importance of human annotation data. Through extensive experiments and comprehensive analysis, this study demonstrates consistent trends across various tasks and highlights the importance of utilizing human-annotated data in evaluations. Strengths: 1. The proposed framework allows for the evaluation of various tasks and response types. 2. Through various experiments, the high evaluation capability of closed-source LLMs, regardless of response type and task, is confirmed. 3. The importance of human-annotated data is evident, showing consistency regardless of the evaluation model. 4. Additionally, extensive experiments analyze various aspects such as response quality, difficulty, and the capability of reward models as judge models. Weaknesses: 1. One important metric for evaluation models, the ability to revise its generation with critique, is excluded. As mentioned in the paper, there is active research on improving generation performance through LLM’s self-feedback during the inference stage. It is necessary to evaluate each model’s ability to revise existing outputs when provided with critique. 2. Although this study addresses the translation task, it excludes the critique ability in other multilingual contexts. The critique ability of LLMs in various languages other than English is crucial for ensuring diversity, and additional data collection on this aspect seems necessary. Technical Quality: 4 Clarity: 4 Questions for Authors: 1. What is the pattern of score changes when using feedback from other LLMs in Table 5, based on the quality of the feedback from these other LLMs? Confidence: 4 Soundness: 4 Presentation: 4 Contribution: 4 Limitations: Yes, this study clearly mentions its limitations in the conclusion. Flag For Ethics Review: ['No ethics review needed.'] Rating: 9 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We really appreciate your valuable suggestions and insightful questions. Your questions are addressed as follows: --- Q1: One important metric for evaluation models, the ability to revise its generation with critique, is excluded ... It is necessary to evaluate each model’s ability to revise existing outputs when provided with critique. A1: We appreciate the reviewer's insightful comment regarding evaluating the ability to revise generation with critiques. We want to clarify that this capability is a central aspect of our work and has been thoroughly evaluated in our CriticEval benchmark, referred to as the correction ability ($CR$) in our paper. We acknowledge the reviewer's suggestion that "revision" is more precise than "correction" to describe this feature. We will update the terminology accordingly in the revised version of our paper, replacing "correction" with "revision." To further clarify the evaluation of the revision ability in our study, we highlight the following points: 1. Data Collection and Metric for Revision Evaluation: * Section 4.3 (line 155) details the process of collecting reference revisions. * Sections 5.1 (line 189) and 5.2 (lines 194-196) outline the objective and subjective metrics used to evaluate the model’s ability to revise generations. 2. Evaluating Revision Ability: Our evaluation of LLMs’ revision ability encompasses two scenarios: using golden feedback as input and using feedback generated by other LLMs. * Golden Feedback as Input: Subjective scores are computed by comparing the model’s revisions to human-annotated revisions, and the reliability of this subjective evaluation is substantiated in Section 6.2 (Table 4 and lines 240-246). * Feedback from Other LLMs as Input: We also conducted experiments to assess how LLMs perform with feedback produced by others, including themselves. As detailed in Section 6.5 (lines 311-326), we evaluated the average performance of the LLMs using three types of feedback: human-annotated, empty, and self-generated. The results indicate that LLMs face challenges in self-improvement, particularly in complex reasoning tasks. We hope this clarification addresses the reviewer’s concern and demonstrates the comprehensive nature of our evaluation approach. We are grateful for the opportunity to enhance the terminology and presentation of our findings, which we believe will further clarify the contributions of our work. --- Q2: ... it excludes critique ability in other multilingual contexts ... and additional data collection on this aspect seems necessary. A2: Please refer to Section "Global Response - Multilingual Support" for our explanations. In summary, our work is the first step to constructing a comprehensive and reliable evaluation. The multilingual feature is not considered because we mainly focus on the critique ability over common tasks in the current stage. But, the cost of extending CriticEval to other languages is affordable. --- Q3: What is the pattern of score changes when using feedback from other LLMs in Table 5, based on the quality of the feedback from these other LLMs? A3: We apologize for any confusion caused by Table 5 and the related content in Section 6.3. Since feedback and revision performance are entangled, it is essential to investigate how the quality of feedback affects the performance of LLM's revision ability. To explore this, we prompted the InternLM2-20B-Chat and Llama2-70B-Chat models to revise responses from CriticEval using three types of feedback with varying quality levels. To enhance clarity, we have restructured Table 5 as below: the first table presents results from the objective split of CriticEval, and the second table displays results from the subjective split. \| Revision Model \|Source of Feedback\|Feedback Quality (1-10)\|Objective Revision Performance\| \|-\|-\|-\|-\| \|InternLM2-20B\|Llama2-70B\|2.24\|7.15\| \|InternLM2-20B\|InternLM2-20B\|7.53\|10.33\| \|InternLM2-20B\|Human\|8\|50.5\| \|Llama2-70B\|Llama2-70B\|2.24\|5.33\| \|Llama2-70B\|InternLM2-20B\|7.53\|12.47\| \|Llama2-70B\|Llama2-70B\|8\|42.43\| \| Revision Model \|Source of Feedback\|Feedback Quality (1-10)\|Subjective Revision Performance\| \|-\|-\|-\|-\| \|InternLM2-20B\|Llama2-70B\|5.63\|5.71\| \|InternLM2-20B\|InternLM2-20B\|6.85\|5.8\| \|InternLM2-20B\|Human\|8\|7.48\| \|Llama2-70B\|Llama2-70B\|5.63\|5.54\| \|Llama2-70B\|InternLM2-20B\|6.85\|6.32\| \|Llama2-70B\|Llama2-70B\|8\|7.11\| These results indicate that as the quality of the feedback increases, both the objective and subjective revision performance improves. This trend demonstrates that higher-quality feedback is associated with more effective revisions.	Rebuttal 1: Rebuttal: # Global Response We thank all the reviewers for their insightful and valuable comments. Below, we will address some common questions and concerns of reviewers. --- ## 1. Overcome Bias of GPT-4 Judge (kJKF, 2SKd) To mitigate bias of GPT-4 as a judge, our work has made two efforts: ### 1.1 In Construction Phase CriticEval collects high-quality critiques by human-in-the-loop pipeline, where human annotators review and revise GPT-4's initial critiques. The human-annotated revisions for GPT-4's initial critiques are significant (25.22%, 34.83%, and 48.37%), as detailed in Appendix G.5. Besides, the ground-truth answers for challenging tasks are fed to GPT-4 for high-quality draft critiques for GPT-4 (Appendix G.4). Furthermore, we introduce the meta-feedback critique dimension to independently validate GPT-4's evaluation reliability as a judge (Section 6.2 and Table 2). It is purely annotated by humans to evaluate critiques generated by various LLMs, including GPT-4, GPT-3.5-turbo, and two CritiqueLLMs, without the bias of GPT-4. Our results, presented in Tables 2, 3, and 4, show that only GPT-4 with human-annotated critiques achieves a very high correlation with human judgment in meta-feedback, while the others are far behind GPT-4. These results justify GPT-4 as a reliable judge in subjective evaluations and a diverse set of LLMs as judges introduce more noise in draft critiques, bringing more difficulties to human annotators. ### 1.2 In Evaluation Phase Human-annotated critiques serve as reference critiques for subjective evaluation, ensuring GPT-4 does not prefer specific LLMs. Our human annotators haven't observed clear bias towards GPT-4 or LLMs fine-tuned on GPT-4's critiques. Although we have made our best efforts, the bias of GPT-4 may still not be completely eliminated. We emphasize that our evaluation method is a trade-off solution considering the scalability and reliability of the CriticEval subjective evaluation. We look forward to subsequent work that can address and resolve this issue. --- ## 2. Scalability and Cost (kJKF, 2SKd) We notice that reviewers kJKF and 2SKd inquire about the scalability and the cost of CriticEval. Thus, we provide the cost of constructing one task and inferencing one LLM in CriticEval. ### 2.1 Construction Cost The construction cost consists of two parts: 1. Collect Evaluated Responses for All Tasks * Open-source LLMs: a GPU server with 8 A100 (80G) cards is used to generate evaluated responses, and the total GPU hours are 4.26 hours, approximately 82.88\\$ (refer to the price of Alibaba Cloud). * Closed-source LLMs: the average cost for each LLM is 0.89\\$. 2. Generate and Revise GPT-4 Critiques \|For Each New Task\|Cost (\\$)\|Time (hour)\| \|-\|-\|-\| \|Generate Critiques (GPT-4)\|3.09\|-\| \|Human Annotation\|303.53\|53.34\| \|Overall\|306.62\|53.34\| The cost of the human annotation is computed under these settings: * Four human annotators (3 annotators and one supervisor) * 5.69\\$ hourly wage for each annotator (Appendix G.1) * Average 400 samples in one task. In summary, the human annotation cost for one new task is affordable [1]. ### 2.2 Average Computational Cost for One LLM \|Dimension\|Cost of Test set ($)\|Cost of Dev set ($)\| \|-\|-\|-\| \|Feedback\|4.21\|5.09\| \|Correction\|2.11\|2.67\| \|Comparison\|3.62\|5.43\| \|Overall\|9.94\|13.19\| The overall cost of the test and dev set is 13.19+9.94=23.13\\$, comparable to the evaluation cost on the AlpacaEval benchmark (5-15\\$) [2]. Note that these costs are essential for CriticEval, as they guarantee the reliability of critique evaluation. We promise to add these details to the Appendix of our revised submission. --- ## 3. Multilingual Support (Hopm, 2SKd) The primary goal of CriticEval in the current stage is to construct a reliable and comprehensive evaluation for critique ability. We agree that it is essential to study multilingual critiques and intend to broaden CriticEval to include other languages in future work, as described in Section 7 (lines 375-376). Reviewer 2SKd suggests including a serious discussion on how to achieve this goal. The following content briefly introduces our preliminary solution. ### 3.1 Construct Multilingual CriticEval Following the previous work [3], CriticEval could be translated to various languages, especially low-resource languages, with human annotation for revising translation inaccuracies. ### 3.2 Evaluate Multilingual CriticEval While the reliability of objective evaluation could be ensured, the reliability of subjective evaluation is limited by the multilingual capability of the judge model (GPT-4). We recommend back-translating multilingual critiques into English and evaluating them within English CriticEval. --- ## 4. Fine-grained Failure Modes (kJKF) Reviewer kJKF offered valuable suggestions regarding a fine-grained analysis of failure modes. Coarse-grained failure modes have been analyzed in Section 6.6, and the fine-grained analysis is provided in the PDF file. The analysis reveals that the most frequent failure modes are missing errors, lacing effective comparison analysis, and worse revision than references for feedback, comparison, and correction dimensions, respectively. Besides, inaccurate critiques usually lead to lower subjective scores, such as missing crucial errors and incorrect analysis content. The revision that does not follow suggestions in feedback usually leads to the worst performance. --- ### References [1] AlpacaFarm: A Simulation Framework for Methods that Learn from Human Feedback [2] Alpacaeval: An automatic evaluator of instruction-following models [3] Language Models Are Multilingual Chain-of-Thought Reasoners Pdf: /pdf/b8f27b8123624b197f25b21990d52d236e0ac862.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
SpeechForensics: Audio-Visual Speech Representation Learning for Face Forgery Detection	Accept (poster)	Summary: This paper propose audio-visual face forgery detection trained using only real data. During training, audio and visual features are fused by concatenation and then processed by encoder to predict which cluster the feature for each time belong to. During test time, discrepancy between visual and audio for each time indicate the fakeness of the video. Fixed time offset and dynamic time offset are explored to measure the discrepancy. Strengths: 1. With dynamic time offset, this work also considers misalignment happening on the real data. 2. Training with real data only is indeed an interesting direction for detector that can be generalized to unseen deepfakes. Weaknesses: 1. I think [22] is the closest related work as it is also audio-visual deepfake detector trained with only real data. However, I can't find the discussion about the difference between this work and [22] up until experiments (nothing in Introduction and Related Work). And how this work can be better than [2], not only showing in experiments without much discussion on why this work is better. 2. Comparisons with state-of-the-art are mostly with detector using only vision modality which is unfair as fake audio-visual data can have fake-audio-real-visual combination. 3. Many missing audio-visual deepfake detector references and comparisons [a-f] 4. I can't find the training code while also the information (hyperparameter value etc.) in the paper is not sufficient References: [a] Komal Chugh, Parul Gupta, Abhinav Dhall, and Ramanathan Subramanian. Not made for each other-audio-visual dissonance-based deepfake detection and localization. In Proceedings of the 28th ACM international conference on multimedia, pages 439–447, 2020 [b] Zhixi Cai, Kalin Stefanov, Abhinav Dhall, and Munawar Hayat. Do you really mean that? content driven audio-visual deepfake dataset and multimodal method for temporal forgery localization. In 2022 International Conference on Digital Image Computing: Techniques and Applications (DICTA), pages 1–10. IEEE, 2022. [c] Trisha Mittal, Uttaran Bhattacharya, Rohan Chandra, Aniket Bera, and Dinesh Manocha. Emotions don’t lie: An audio-visual deepfake detection method using affective cues. In Proceedings of the 28th ACM international conference on multimedia, pages 2823–2832, 2020. [d] Harry Cheng, Yangyang Guo, Tianyi Wang, Qi Li, Xiaojun Chang, and Liqiang Nie. Voice-face homogeneity tells deepfake. ACM Transactions on Multimedia Computing, Communications and Applications, 2023. [e] Hafsa Ilyas, Ali Javed, and Khalid Mahmood Malik. Avfakenet: A unified end-to-end dense swin transformer deep learning model for audio–visual deepfakes detection. Applied Soft Computing, 136:110124, 2023. [f] Wenyuan Yang, Xiaoyu Zhou, Zhikai Chen, Bofei Guo, Zhongjie Ba, Zhihua Xia, Xiaochun Cao, and Kui Ren. Avoid-df: Audio-visual joint learning for detecting deep-fake. IEEE Transactions on Information Forensics and Security, 18:2015–2029, 2023. Technical Quality: 2 Clarity: 2 Questions for Authors: 1. Is there fusion during test time? 2. Line 127-128: what is modality dropout and how it can allow unimodal input. Why unimodal input is necessary? 3. Are there same $T$ amount of $\gamma$ and the input $\mathbf I$ and $\mathbf A$? The notation $T$ should indicate same number but the illustration in Figure 1 does not imply the same. 4. It is still unclear to me how the knowledge from the training process (CMIIW, predicting the cluster) can transfer to the forgery detection using audio-visual discrepancy. Confidence: 4 Soundness: 2 Presentation: 2 Contribution: 2 Limitations: Limitations are discussed and I concur. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: >Q1:Comparisons with state-of-the-art are mostly with detector using only vision modality which is unfair as fake audio-visual data can have fake-audio-real-visual combination. A1:Thanks for your review. What we want to emphasize is that our experiments have excluded the category of fake-audio-real-visual. So we think the comparisons are fair in this aspect. Thanks again for this comment, we will emphasize this in the experimental settings of ourrevised paper. >Q2:I think [22] is the closest related work as it is also audio-visual deepfake detector trained with only real data. However, I can't find the discussion about the difference between this work and [22] up until experiments (nothing in Introduction and Related Work). And how this work can be better than [2], not only showing in experiments without much discussion on why this work is better. A2:Thanks for your constructive reviews! Regarding the difference between our method and [22], on the one hand, they model only short-term (5 frames) audio-visual synchronization but ignore long-term temporal dependencies. On the other hand, they perform forgery detection by predicting the time offsets between audio and visual modalities. However, with their released code, we found that only fake videos generated by Wav2Lip exhibit distinguish time offset distribution from real videos, refer to our Table 2. And we think that it is a question worthy of further evaluation about whether time offset distribution is a valid forgery feature. >Q3:Many missing audio-visual deepfake detector references and comparisons. A3:Please refer to the "General Response". >Q4:what is modality dropout and how it can allow unimodal input. Why unimodal input is necessary? Is there fusion during test time? A4:Thanks for your careful review. The modality dropout is implemented by setting the frontend embeddings of one of the modality as zero. Since we target to find the inconsistencies between visual and audio representations of fake videos, which requires extracting precise features of visual and audio modalities and avoiding entanglements between them. Therefore, the unimodal input is necessary and these is no feature fusion during test time. >Q5:Are there same $T$ amount of $\gamma$ and the input $\textbf{I}$ and $\textbf{A}$? The notation $T$ should indicate same number but the illustration in Figure 1 does not imply the same. A5: Thanks for your careful review. In the training stage, we only predict the randomly masked sequences, as shown in Figure1. However, we will calculate the label of each frame in advance. Therefore, they are not conflicting. >Q6: It is still unclear to me how the knowledge from the training process (CMIIW, predicting the cluster) can transfer to the forgery detection using audio-visual discrepancy. A6:Thanks for your helpful review. The cluster assignment is generated by applying k-means on the speech representations(lines 129-131).In this way, inputs that belong to the same cluster will be encoded as similar vectors. That is, visual and audio inputs of real videos will be encoded as similar representations. And the audio-visual discrepancies in fake videos will be exposed. --- Rebuttal 2: Comment: Thank you authors for the clear rebuttal, I am increasing my rating to weak accept. I hope the authors will revise to give more clarity to the paper too. About (Q5): then isn't it better not to use $T$ symbol for $\gamma$ in line 132? As the number of $\gamma$ can be different than the number of input. --- Rebuttal Comment 2.1: Title: Thanks very much for the reply! Comment: Many thanks for your careful reviews and valuable advices. We agree with you and will adopt your suggestions in the revised version to make our paper more clear.	Summary: This paper works on audio-visual co-learning for face forgery detection, answering the question of how to extract semantically rich speech-related features to represent detailed lip movements. It is claimed to be the first method where unsupervised learning outperforms the supervised learning method. It is an Strengths: The paper itself presents a nice framework and have a detailed description on how the alignment model was adapted to the context, with certain novel modifications being presented. The experiments, data description, and analysis have been very detailed and thorough. Weaknesses: The main critique I have on the paper is on the novelty and experiments. In terms of the novelty, although face forgery detection itself is new field, CLIP-like architecture itself is not. Apart from the loss function, the reviewer normally would expect more novelties coming from the model architecture refinement. But this is trivial one. In terms of experiments, the unsupervised methods are not fully outperforming the supervised methods, so the reviewer thinks the hypothesis and descriptions of contributions in the abstract is a bit too aggressive - of course, the contributions are still fair. Moreover, the author should present the data used for the compared supervised methods, especially on whether they were trained with similar scale of data - the original CLIP, for instance, acquired massive data to train, and it seems like the case here as well. Technical Quality: 3 Clarity: 3 Questions for Authors: 1. What is the motivation and inspiration the authors had for designing such Siamese like framework? 2. Were the frontends adapted or jointly learned with the whole model as well? How about transformer encoders? 3. There seems are some in-consistency between left and right-hand figures in Fig. 1. If this is only a comparison between conventional methods and one you used for forgery detection, you may state it more clearly in the caption or main text. 4. Do you think the learning capacity of supervised methods is an issue, due to the number of layers, modules or width of the layers? Note, you don't have to do any experiments. This is just for discussion? Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: The authors used face data and working on forgery detection, and the limitations were discussed on the methodologies, without addressing the potential societal impact. The reviewer thinks a short claim would be good. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: >Q1:What is the motivation and inspiration the authors had for designing such Siamese like framework? A1:Thanks for your insightful review! As stated in lines 39-45, we found that lip sequences and audio segments in real videos should convey the same speech contents, while fake videos do not. It inspires us to utilize this framework to perform forgery detection. >Q2:Were the frontends adapted or jointly learned with the whole model as well? How about transformer encoders? A2:Thanks for the careful review. The frontends and transformer encoder are trained together. >Q3:There seems are some in-consistency between left and right-hand figures in Fig. 1. If this is only a comparison between conventional methods and one you used for forgery detection, you may state it more clearly in the caption or main text. A3:Thanks for your valuable feedback! What we need to clarify is that the audio-visual representation learning stage (left-hand figure in Fig.1) is the training stage of our method, while right-hand figures are the forgery detection stage. Thanks again for your careful review, we will describe it more clearly in the caption of the revised version of the paper. >Q4:Do you think the learning capacity of supervised methods is an issue, due to the number of layers, modules or width of the layers? Note, you don't have to do any experiments. This is just for discussion? A4:Thanks for your insightful question! It is indeed an important and interesting problem, and I feel really happy to be asked this question. To the best of my knowledge, the key problem in forgery detection is how to extract discriminative features rather than the learning capacity of models. This is because different forgery methods tend to have different artifact characteristics. However, it is difficult to obtain rich enough forgery data for training models in reality. So, I think the learning capacity of supervised methods is not a crucial issue in this domain.	Summary: The main challenge in face forgery detection is the unsatisfactory generalization in previous detectors. To alleviate this issue, this paper proposes one audio-visual consistency learning framework in the unsupervised learning manner. The important local and global semantic information are learned by the proposed local representation alignment and global information modeling modules. In the test phase, two strategies are proposed to calculate the matching score between visual and audio embeddings. Strengths: 1. Considering the difficulty of obtaining deepfake data, it is a good idea to solve the generalization problem through unsupervised learning methods. 2. The result seems good, and I think the cross-language generalization experiment is interesting. Weaknesses: 1. In lines 72-73, the authors claimed “it is the first unsupervised approach outperforming supervised baselines in this domain”. I think the authors lack of follow-up on the recent works in this domain, such as [R1] and [R2]. 2. The description for the proposed method is too simple. Only lines 123-133 are used to descript the details of the proposed local representation alignment, which is hard for me to understand how to do the local representation alignment and why it can align the representations of visual and audio modalities. Many details are missing. 3. The proposed method and the pre-trained model heavily rely on [53], which makes me feel this paper just apply one existed method to another special field. What is the main contribution of this paper? The novelty needs to be explained more precisely. [R1] Self-Supervised Video Forensics by Audio-Visual Anomaly Detection, CVPR 23. [R2] AVFF: Audio-Visual Feature Fusion for Video Deepfake Detection, CVPR 24. Technical Quality: 3 Clarity: 2 Questions for Authors: In section 4.1, it describes that the region around the mouth is cropped as the input. However, the example shown in figure 4 is the entire face. This inconsistency needs to be addressed to maintain clarity and accuracy in the presentation. Confidence: 5 Soundness: 3 Presentation: 2 Contribution: 2 Limitations: N.A. Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: >Q1:In lines 72-73, the authors claimed “it is the first unsupervised approach outperforming supervised baselines in this domain”. I think the authors lack of follow-up on the recent works in this domain, such as [R1] and [R2]. A1:Thanks for the review. What we want to emphasize is that we compared our method with AVAD[R1], please refer to Table 1 and Table 2 in our manuscript, which is inferior to our method. Moreover, [R2] was not accessible at the time of submission of this paper and we also could not get fair experimental results in our settings since it does not release the source code. For example,[R2] reports experiment results on FakeAVCeleb dataset in the cross-manipulation setting, i.e.,evaluating performance by leaving out one category for testing while training on the rest, while the performance in the cross-dataset setting is unknown. But we provide more comparisons with other multimodal methods. >Q2:The description for the proposed method is too simple. Only lines 123-133 are used to descript the details of the proposed local representation alignment... Many details are missing. A2:Thanks for the valuable review! We apologize for making you feel hard to understand some details of our method. About the local representation alignment, on the one hand, we use a shared transformer encoder to map visual and audio inputs of each frames into a unified feature space (lines 132-133). On the other hand, modality dropout is applied is the training stage (lines 127-128), which means that both unimodal and multimodal inputs will have same labels, that is, all three types of inputs (visual modality, audio modality, and audio-visual modality) will get the same output. In this way , the local representations of visual and audio modalities are aligned. Considering that audio-visual representation learning is researched in the speech recognition task, we allocated more space to introduce the face forgery detection stage instead of representation learning. But according to your review, we will add more introduces about this part in the revised version of the paper. >Q3:What is the main contribution of this paper? The novelty needs to be explained more precisely. A3:Thanks for your review, we think our contributions can be summarized in the following two-folds: 1.Speech representations can serve as strong pseudo labels to perform face forgery detection. 2.By local representation alignment and global information modeling, our method is able to detect both short-range and long-range temporal inconsistencies. While previous methods can only model limited range of temporal information (1s vs ours 16s, refer to line 323-327). >Q4:In section 4.1, it describes that the region around the mouth is cropped as the input. However, the example shown in figure 4 is the entire face. This inconsistency needs to be addressed to maintain clarity and accuracy in the presentation. A4:Thanks for our careful review! Our method takes the mouth region as input, and we will highlight it in figure4 in the revised version of the paper to maintain clarity. [R1] Self-Supervised Video Forensics by Audio-Visual Anomaly Detection, CVPR 23. [R2] AVFF: Audio-Visual Feature Fusion for Video Deepfake Detection, CVPR 24. --- Rebuttal Comment 1.1: Comment: Thank you for your detailed response. I've raised my rating to 4, as many of my minor concerns have been addressed. --- Rebuttal 2: Title: Thanks for the response. Comment: Dear reviewer rUJS, Thank you for your thoughtful feedback. We have carefully considered your comments and would like to provide further clarification on the points you raised. Firstly, we are committed to making comprehensive revisions to improve the clarity and presentation of our paper. Regarding the concern about novelty, we would like to clarify that [53] is for the speech recognition task, instead of using it directly, our approach adapts only the encoder of it to a forgery detection model through the similarity calculation strategies we propose. Our method leverages speech representations of audio and visual signals to perform face forgery detection. This approach demonstrates superior generalization, robustness, and interpretability, offering a novel perspective to this research domain. We greatly appreciate your insights and are eager to address any further specific concerns you may have. Look forward to further discussions! Best regards, The Authors	Summary: This paper proposes SpeechForensics, a unsupervised method for detecting face forgery videos by leveraging audio-visual speech representations. The key ideas are: Learning semantically rich speech representations from both audio and visual modalities on real videos Detecting forgeries by identifying discrepancies between audio and visual speech representations Modeling both local and global temporal information to capture long-range inconsistencies Strengths: Using audio-visual speech representations for forgery detection Unsupervised method that outperforms supervised baselines Interpretable results through visualization and transcription analysis Weaknesses: The method assumes the availability of both high-quality audio and visual data. In scenarios where audio quality is poor or there are discrepancies in synchronization due to encoding errors, the performance will degrade. Limited Scope on Forgery Types: The focus is primarily on forgeries involving discrepancies between audio and visual elements. As such, the technique might not be as effective against forgeries that do not involve speech or where the mouth region is not manipulated. Performance on Silent Videos: The paper mentions a potential degradation in performance in videos with silent segments or noisy audio backgrounds, which could be significant in practical applications. Lacks comparison to some recent audio-visual forgery detection methods Technical Quality: 2 Clarity: 2 Questions for Authors: Could you elaborate on how the method handles significant asynchrony between audio and video, which is common in practical scenarios? How does the method perform on videos with low audio quality or background noise? Could the approach be extended to detect other types of forgeries beyond lip movements? What is the computational cost compared to existing methods? Impact of Audio Quality: How does the quality of the audio track affect the performance of your forgery detection method? Confidence: 5 Soundness: 2 Presentation: 2 Contribution: 2 Limitations: The authors adequately discuss limitations, noting the method's reliance on lip movements and potential issues with extreme samples. They also briefly address broader impacts, acknowledging the potential for an arms race between forgery and detection technologies. The limitations section could be expanded to provide more detailed analysis of failure cases or edge scenarios. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: >Q1:Could you elaborate on how the method handles significant asynchrony between audio and video, which is common in practical scenarios? A1:Thanks for the valuable feedback! The asynchrony between audio and video is indeed common in practical scenarios and we explore two methods,i.e., fixed time offset and dynamic time offset, to handle these asynchronies in the Sec3.2 of our paper. >Q2:Could the approach be extended to detect other types of forgeries beyond lip movements? A2:Thanks for the review. Since our method focus on leveraging speech-related semantic information to perform forgery detection, it can not be directly extended to detect other types of forgeries beyond lip movements, but this is an interesting perspective to be explore. >Q3:Lacks comparison to some recent audio-visual forgery detection methods. A3: Please refer to the "General Response". >Q4:Impact of Audio Quality: How does the quality of the audio track affect the performance of your forgery detection method? How does the method perform on videos with low audio quality or background noise? A4:Thanks for your valuable review. To evaluate the impact of audio quality, we add Gaussian Noise to the audio signals at 5 intensity levels, corresponding to the signal-to-noise ration (SNR) of 40,30,20,15, 10, from low to high. And we think that the performance degradation of our method under noisy audio is within an acceptable range. \| Intensity \| 0 \| 1 \| 2 \| 3 \| 4 \| 5 \| \| :-: \| :-: \| :-: \| :-: \| :-: \| :-: \| :-: \| \| AUC(%) \| 99.0 \| 98.8 \| 98.0 \| 96.9 \| 94.8 \| 91.2 \|	Rebuttal 1: Rebuttal: We sincerely appreciate all reviewers' efforts in reviewing our paper and giving insightful comments and valuable suggestions. As suggest by the reviewers, we provide more comparisons with multimodal methods on the FakeAVCeleb dataset under the cross-dataset setting. And we would like to include them in our revised manuscript to further improve our paper. \| Method \| MDS[1] \| VFD[2] \| AvoiD-DF[3] \| AVAD[4] \| Ours \| \| :-----------: \| :-----------:\| :-----------: \| :-----------:\| :-----------: \| :-----------: \| \| \| Supervised \| Supervised \| Supervised\| Unsupervised \| Unsupervised \| \| AUC(%) \| 76.7 \| 82.5 \| 85.8 \| 85.0 \| 99.0 \| If you have any further concerns, please don’t hesitate to let us know. Thanks again for your reviews. [1]Komal Chugh, Parul Gupta, Abhinav Dhall, and Ramanathan Subramanian. Not made for each other-audio-visual dissonance-based deepfake detection and localization. In Proceedings of the 28th ACM international conference on multimedia, pages 439–447, 2020. [2] Harry Cheng, Yangyang Guo, Tianyi Wang, Qi Li, Xiaojun Chang, and Liqiang Nie. Voice-face homogeneity tells deepfake. ACM Transactions on Multimedia Computing, Communications and Applications, 2023. [3] Wenyuan Yang, Xiaoyu Zhou, Zhikai Chen, Bofei Guo, Zhongjie Ba, Zhihua Xia, Xiaochun Cao, and Kui Ren. Avoid-df: Audio-visual joint learning for detecting deep-fake. IEEE Transactions on Information Forensics and Security, 18:2015–2029, 2023. [4] Chao Feng, Ziyang Chen, and Andrew Owens. Self-supervised video forensics by audio-visual anomaly detection. CVPR2023.	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
TransVIP: Speech to Speech Translation System with Voice and Isochrony Preservation	Accept (poster)	Summary: This paper presents an end-to-end framework for speech-to-speech translation that preserves speaker and voice characteristics while leveraging unsupervised training. The authors also refine the speech tokenizer by distilling semantic information and enhance the sampling mechanism to support textless NAR acoustic modeling. Strengths: The authors have made significant improvements throughout the S2ST pipeline, resulting in a solid contribution. They have also conducted experiments with various datasets and compared their results to those of capable models such as Seamless for S2ST and Encodec for Codec, achieving reasonable improvements. Although some of the experimental results are mixed, given the limited computational resources (only 32 GPUs) and datasets (only 5k hours), the improvements are still impressive and demonstrate the effectiveness of the proposed methods. Weaknesses: 1. The paper is well-written and informative, but it covers a wide range of topics, which can make it overwhelming to read. The introduction and subsequent sections could be restructured to better emphasize the different contributions. For example, the introduction covers four bullet points, where the first two are modeling designs for S2ST and the last two are Codec related. Then in the method section (sec 3), everything is presented together. It would be helpful to dissect section 3 into two main sections and add pointers from the introduction sections to improve clarity. Additionally, consider adding visualizations for the distillation strategy in the main content to further illustrate the proposed methods. 2. My major concern with the proposed framework is the inference speed. It would be helpful to include an analysis of the inference speed of the proposed architecture, as the use of an autoregressive decoder for predicting Codec tokens may significantly slow down the process, even with deduplicated units. Technical Quality: 3 Clarity: 2 Questions for Authors: 1. Following up on my second point in weaknesses, could you provide some comparisons with the UnitY system or others in terms of inference speed? Additionally, there are several direct S2ST translation works [1,2,3] that utilize non-autoregressive modeling on the CVSS dataset, and it might be worth comparing with such methods. 2. I am a little confused about Figure 2's target clip encoding. What is the motivation for using that representation for the [sep] token? From your description (lines 116-120), I do not find any mention of the use of the target speech clip. Can you explain why the pooled representation of that clip is used and what happens during inference when such clips do not exist? [1] Lee et al., (2022). Direct speech-to-speech translation with discrete units [2] Huang et al., (2023). Transpeech: Speechto-speech translation with bilateral perturbation [3] Tan et al., (2024). DiffNorm: Self-Supervised Normalization for Non-autoregressive Speech-to-speech Translation Confidence: 4 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: No concerns on the limitations. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We sincerely appreciate your efforts in reviewing our paper and providing us with valuable, constructive feedback. The detailed responses are listed below. R1. About presentation (Weakness 1) We will reorganize the paper, particularly by dividing section 3 into two main subsections and adding pointers from the introduction to improve clarity. With an additional page allowed in the main content of the final version, we will also consider adding visualizations to further illustrate the proposed methods. R2. About inference speech (Weakness 2, Question1) Your concern about inference speed is valid. Generally, the inference speed for AR models is slower than that of non-AR models. To address this, we have conducted an analysis of inference speed. The RTF (real-time factor) for our model architecture is close to 1, while that of seamless expressive (with NAR T2U modeling) is 0.3, as measured on an Nvidia A6000 GPU with fp16. We believe that the inference speed could be improved by 2 to 4 times by leveraging Grouped Code Modeling, as proposed in VALL-E 2 (https://arxiv.org/pdf/2406.05370). Our current application scenario is video dubbing, which can be done on the cloud and offline. Therefore, inference speed has not been thoroughly investigated in this study. R3. Clarifying target clip encoding (Question 2) The pooled representation of the target clip serves as the acoustic prompt that the generation of the first layer codec can condition on. It is similar to the acoustic prompt in Vall-e, except we use only one token instead of a token sequence for acoustic prompting. The benefit of using a single token is that it creates an information bottleneck, preventing too much semantic information from passing through. This way, we hope the model can learn purely acoustic/speaker-related information. We will clarify this in the revised version. In response to your question about what happens during inference when such clips do not exist, our ablation study results presented in Table 3 indicate that the speaker similarity suffers. Without this prompt, the first layer codec will produce a neutral voice, and the NAR model will struggle to convert it to the target voice. --- Rebuttal Comment 1.1: Title: Official Comment by Reviewer JYog Comment: Thanks authors for clarifying a few points mentioned in my review and provide additional data points on the inference speed. I will maintain my score and evaluation.	Summary: This paper proposes a end-to-end speech translation framework that adds several improvements to the existing textless encoder decoder speech translation architectures. Strengths: 1. There are several interesting ideas in this paper, such as the isochrony embedding and layer beam search. 2. The proposed method out-performs one of the previous SOTA on En-Fr translation tasks. Weaknesses: 1. The writing needs to be improved. There are some typos here and there (e.g. line 280 page 7). And the writing clarity can be improved. 2. There is a lack of ablation study to investigate how much does each design choices affect the model performance. 3. The evaluation has only been performed on translation tasks between En and Fr. It's not clear if the model will perform well between other language pairs, especially between English and non-European languages. 4. For isochronic translation, the model can either choose to translate as usual and then adjust the speech rate to fit into the timing boxes, or the model can be more smart in translating in the optimal way to reflect the isochrony constraint. I couldn't find any discussion regarding this aspect in this paper. Technical Quality: 3 Clarity: 2 Questions for Authors: See weaknesses. Confidence: 4 Soundness: 3 Presentation: 2 Contribution: 2 Limitations: Adequately discussed. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We sincerely appreciate your efforts in reviewing our paper and providing us with valuable, constructive feedback. The detailed responses are listed below. R1. About improving writing and clarity (Weakness 1) We will reorganize the paper, include ablations in the main section, revise the unclear writing and conduct a thorough proofread. These revisions will appear in the updated version. R2. About few ablation study (Weakness 2) We have presented the ablation studies, such as w/ and w/o acoustic embedding, the choice of different codec, w and w/o text BPE and Layer Bean Search in NAR acoustic model. Due to the limited space for the main content, we had to present the ablation studies in the appendix. We will also add an ablation study related to isochrony preservation in the revised version. In this study, we compared our model with the following three baselines. We will report the ASR-BLEU, SLC_p (Speech Length Compliant, as defined in the paper), and Overlap ratio (i.e., speech overlap between the reference and the hypothesis) as follows. \| \| ASR-BLEU \| Overlap \| SLC_0.2 \| SLC_0.4 \| \|---\|---\|---\|---\|---\| \| No IC \| 30.81 \| 0.689 \| 0.63\| 0.87 \| \| Dec IC\| 30.51 \| 0.748 \| 0.75 \| 0.90 \| \| Dec IC + FPI \| 30.45 \| 0.766 \| 0.77\| 0.91\| \| Enc IC (Proposed) \| 30.62 \|0.784 \|0.82\| 0.95\| where 1. No Isochrony control (No IC). 2. Isochrony control on the decoder (Dec IC). This involves adding the Isochrony embedding to the input of the encoder as another positional embedding. We implemented the method from ref [1] in our system. 3. Isochrony control on the decoder with future pause information (Dec IC + FPI). This is an improvement over above 2. In addition to the distance to the global end and VAD information, two extra pieces of information are encoded: the distance to the next pause and the number of pauses in the future. We implemented the method from ref [2] in our system. Ref: [1] Y. Wu, et al. “VideoDubber: Machine Translation with Speech-Aware Length Control for Video Dubbing,” AAAI, 2023. Ref: [2] P. Pal, et al. “Improving Isochronous Machine Translation with Target Factors and Auxiliary Counters”, Interspeech, 2023. Please let us know if more ablation studies should be added. R3. About evaluation on more language-pairs (Weakness 3) We will validate the method with an additional language pair in future work. Our model is built on a multi-lingual Seamless model, and we believe the proposed methods can be extended to other language pairs, including those between English and non-European languages. The main hurdle to this kind of extension investigation is the availability of publicly accessible data. R4. About the discussion on isochronic translation (Weakness 4) We will add discussions regarding isochronic translation as follows in the revised version. The conventional method for isochronic translation involves first translating as usual and then adjusting the speech rate to match the length of the source speech. This approach ensures that the translation quality is not compromised by isochronic control. However, for long videos with multiple utterances, an inconsistent speaking rate can significantly affect the naturalness of the translated speech. We aim to use isochrony control to translate optimally by considering both the timing boxes and the speech rate in real application scenarios. Both should align with the source speech. In our proposed method, the generation of both text and speech is conditioned on global isochrony information. Our experimental results also show that this approach can improve ASR-BLEU score compare to Isochrony control on decoder, meaning the model is more confident and accurate in the generation and make less error like repetition and truncation. Finally, we would like to express our gratitude once again for your time and effort in reviewing our paper. Considering the interesting ideas, SOTA performance, adequate ablation studies, and improved presentation of our paper, we would greatly appreciate it if you could consider increasing your score. --- Rebuttal Comment 1.1: Comment: Thanks for the rebuttal. I would suggest to at least put part of the ablation studies as part of the main paper as they are very important. I am a bit reluctant to raise my score now since a lot has been promised in the "updated version" of the paper which I haven't seen yet. I will consider raising the score once I read that. --- Rebuttal 2: Comment: Dear Reviewer ujH4, Thank you for your suggestions. We appreciate you are considering raising your score. However, due to the review rule, we cannot send you a revised pdf on the system. We also fully understand your reluctance. Let’s try our best to include the revision within this 5,000-character comment box. Otherwise, we will have to ask AC how we can send you an updated version anonymously. With an additional page allowed in the main content of the final version, we will include the following on that page. Ablation Studies 1. Acoustic Embedding We compared the inference with and without acoustic embedding and presented the results in Table 3. Without the acoustic embedding, speaker similarity scores decreased by 0.040 in French-English (Fr-En) translations and by 0.032 in English-French (En-Fr) translations. Additionally, there was a slight decline in the AutoPCP scores. Tabel 3. Ablation on the acoustic embedding in the joint translation model. \| \| ASR-BLEU \| BLEU \| SIM \| A.PCP \| Nat.\| \| :-----\| :----: \| :----: \| :----: \| :----: \| :----: \| \|TransVIP Fr-En \| 32.60 \| 35.34 \| 0.320 \| 2.49 \| 3.19 \| \| - A.Embed \| 32.47 \| 35.18 \| 0.280 \| 2.45 \| 3.23 \| \|TransVIP En-Fr \| 27.28 \| 33.02 \| 0.395 \| 2.67 \| 3.40 \| \| - A.Embed \| 26.84 \| 33.15 \| 0.362 \| 2.45 \| 3.46 \| 2. Choice of Codec We compared training TransVIP using different codecs: SpeechTokenizer [9] and our SASC. In this study, the joint translation model was trained with a subset containing only CVSS-T Fr-En uni-direction data. For the NAR acoustic model, SASC uses 16 codec layers, while SpeechTokenizer uses 8 layers, as it only has an 8-layer version. With both codec we have trained a full system(AR+NAR) with CVSS-T data only. The results are presented in Table 4. Compared to SpeechTokenizer, the model trained with SASC exhibits superior performance in all aspects. Most notably, the speaker similarity improved by 0.04, from 0.226 to 0.264, aligning with the improvement in codec re-synthesis results. Tabel 4. Ablation on the Choice of Codec \| Codec Model \| ASR-BLEU \| BLEU \| SIM \| SLC 0.2 \| SLC 0,4 \| Nat.\| \| :-----\| :----: \| :----: \| :----: \| :----: \| :----: \| :----: \| \| SpeechTokenizer \| 29.81 \| 34.18 \| 0.226 \| 0.76 \| 0.93 \| 3.02 \| \| SASC \| 30.62 \| 34.30 \| 0.264 \| 0.82 \| 0.95 \| 3.09 \| 3. NAR Acoustic Model We conducted two comparisons. Firstly, we compared the performance of a NAR acoustic model with and without text input, i.e., using BPE as input. Secondly, we assessed the inference results with and without the utilization of the Layer Beam Search (LBS) algorithm to determine its impact on performance enhancement. The results are presented in Table 5, where it indicates that the textless model consistently outperforms the model with text input across all metrics of ASR-BLEU, speaker similarity, and naturalness. Moreover, employing LBS yields superior results compared to greedy decoding. Tabel 5. Ablation on the BPE and Layer Beam Search \| NAR Model \| ASR-BLEU \| SIM \| Nat. \| \| :-----\| :----: \| :----: \| :----: \| \|NAR w/o text \| 32.60 \| 0.320 \| 3.19 \| \| - LBS \| 32.30 \| 0.309 \| 3.17 \| \| NAR w/ text \| 31.52 \| 0.307 \| 3.10 \| \| - LBS \| 31.03 \| 0.298 \| 3.09 \| 4. Isochrony Control We compared our proposed Isochrony control method with and without using and other strategies, and presented the results in Table 6, where it demonstrates that our approach achieves the best performance in terms of BLEU score and isochrony evaluation metrics. Tabel 6. Ablation on the isochrony control strategy \| \| BLEU \| Overlap \| SLC_0.2 \| SLC_0.4 \| \|---\|---\|---\|---\|---\| \| No IC \| 30.81 \| 0.689 \| 0.63\| 0.87 \| \| Dec IC\| 30.51 \| 0.748 \| 0.75 \| 0.90 \| \| Dec IC + FPI \| 30.45 \| 0.766 \| 0.77\| 0.91\| \| Enc IC (Proposed) \| 30.62 \|0.784 \|0.82\| 0.95\| where a. No Isochrony control (No IC). b. Isochrony control on the decoder (Dec IC). This involves adding the Isochrony embedding to the input of the encoder as another positional embedding. c. Isochrony control on the decoder with future pause information (Dec IC + FPI). This is an improvement over (b). In addition to the distance to the global end and VAD information, two extra pieces of information are encoded: the distance to the next pause and the number of pauses in the future. Furthermore, we have made several improvements to the paper. We employ a professional proofreading service to fix typos and improve the writing. We add a discussion on isochronic translation, as shown in our previous response. We also rewrite several paragraphs such as the acoustic encoder to make it easier to understand the design and to make the structure clearer Please let us know if you have any further concerns. best regards, Authors --- Rebuttal Comment 2.1: Comment: Thanks for the material. I decided to raise my score by 1. --- Rebuttal 3: Comment: Dear Reviewer ujH4, We have checked with AC, and there isn't a way to send an updated paper. Therefore, we can only use the official comment box for any updates. In fact, most of the ablation studies have already been included in the appendix of the submitted version (please refer to the page14-16). We have revised them and moved them to the main content in the updated version. Further suggestions and concerns are welcome. Each time, we can leverage this 5,000-character comment box to address them. Thanks! Best, Authors	Summary: This paper proposes TransVIP, a speech to speech translation model with voice and isochrony preservation, i.e. pauses and segment durations are preserved between the source and the target, for example for automatic dubbing applications. The proposed model architecture is modular, with multiple encoders for semantic, acoustics and isochrony information, intermediate text output, a non auto regressive acoustic model to generate a sequence of codes which are then decoded to produce a waveform. Contributions include the modular architecture trained end to end, the model capabilities, in particular isochrony preservation. Experiments show that the proposed approach is either competitive with or outperforms a strong baseline (SeamlessExpressive) on translation quality, speaker and prosody similarity while substantially improving isochrony preservation. Strengths: * This is important research work with important applications such as automatic dubbing, especially since most of the research on speech to speech translation does not emphasize isochrony preservation. * The proposed architecture is novel * The empirical results are positive and compare to a strong baseline Weaknesses: * The empirical evaluation could be improved: validate the method in one more language pair and optionally compare to cascaded solutions. * In terms of presentation, the paper could be more self contained and include ablations in the main part of the paper vs the appendix. The paper could also benefit from proofreading (there are quite a few typos). Technical Quality: 3 Clarity: 2 Questions for Authors: “acoustic information(A)”: the title only talks about voice preservation but the evaluation also measures prosody preservation. Could the authors clarify which components of the model are specifically designed to preserve prosody? Confidence: 4 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: The authors acknowledge that only the French-English pair is involved but we still consider this a weakness for a translation related paper. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We sincerely appreciate your efforts in reviewing our paper and providing us with valuable, constructive feedback. The detailed responses are listed below. R1. About empirical evaluation (Weakness 1) We will validate the method with one more language pair in future work. Additionally, to compare to cascaded solutions, we will add the results of cascaded ST + TTS solutions as follows, \| \| ASR-BLEU \| BLEU \| SIM \| AutoPCP \| Rate \| Pause \|SLC_0.2 \| SLC_0.4 \| Nat. \| \|---\|---\|---\|---\|---\|---\|---\|---\|---\|---\| \| ST + StyleTTS (Fr->En) \| 33.57 \| 34.58 \| 0.173 \| 2.74 \| 0.33 \| 0.51 \| 0.56 \| 0.85 \| 3.25 \| \| TransVIP (Fr->En) \| 32.60 \| 35.34 \| 0.320 \| 2.49 \| 0.55 \| 0.44 \| 0.70 \| 0.91 \| 3.19 \| \| ST + VALLE-X (En->Fr) \| 22.50 \| 34.89 \| 0.418 \| 2.87 \| 0.27 \| 0.54 \| 0.65 \| 0.89 \| 3.32 \| \| TransVIP (En->Fr) \| 27.28 \| 33.02 \| 0.395 \| 2.67 \| 0.45 \| 0.65 \| 0.81 \| 0.99 \| 3.40 \| where 1) ST is Seamless Expressive Speech-to-Text translation model 2) We evaluated cascaded system by using TTS model from StyleTTS (open sourced) and VALLE-X (implemented) and reported the better one in terms of objective measurements. R2. About presentation (Weakness 2) We will reorganize the paper, include ablations in the main section, and conduct a thorough proofread. These revisions will appear in the updated version. R3. About prosody preservation(question1) Our framework has not been explicitly designed to preserve prosody. Therefore, prosody is not purposefully maintained but is preserved alongside the voice feature. We have kept the metric in the paper to provide a comprehensive comparison with Seamless. Recently, we have observed an increase in the use of explicit prosody modules in zero-shot TTS. We may consider adding one in future work. --- Rebuttal Comment 1.1: Title: thanks + questions Comment: Dear Authors, Thank you for the additional experiments! I rechecked my review scores which were already quite high so I'm not planning to modify them. For completeness, it may be good to include both ST + StyleTTS and ST + VALLE-X for both directions. In an updated version, it would also be interesting to discuss the strengths and weaknesses of both systems since the proposed approach is not outperforming the baseline in all categories. Can you clarify why the trend for BLEU is the reverse of the trend for ASR-BLEU? Best, --Reviewer kQBQ --- Reply to Comment 1.1.1: Comment: Dear reviewer kQBQ, Thanks again for your appreciation! As for the cascade system result, we currently do not have a TTS system that performs well in both English and French. This version of ValleX does not perform well in English and StyleTTS is only capable of English. So we have to use two separate models for different directions. By the time of the final version, we will probably be able to have an updated version of ValleX and report the performance in both directions. Different model's strengths and weaknesses are good points for discussion. The StyleTTS is trained on a clean but small LibriTTS dataset. So its audio is clean, and the ASR-BLEU is high, but speaker similarity is poor. On the other hand, ValleX is trained on large real data. Therefore its speaker and prosody similarity is high but ASR-BLEU and noise resistance are poor (The performance drops when the input prompt is noisy). Our system reached a balance between similarity and ASR-BLEU, surpassing the Seamless baseline in most metrics with limited data. I think this can also explain the reversed trend in BLEU and ASR-BLEU. The margin between BLEU and ASR-BLEU reflects how accurately the model pronouns the word. StyleTTS is an accurate baseline while ValleX is not that accurate, resulting in the reversed trend. I hope this solves your puzzle and thanks again for your review. best regards, Authors	Summary: The paper introduces TransVIP, a novel speech-to-speech translation system designed to maintain both the speaker's voice characteristics and isochrony during the translation process. TransVIP simplifies the complex task of speech-to-speech translation (S2ST) by breaking it down into two sequential subtasks while retaining an end-to-end framework. It conditions the generation of the target speech not just on semantic information, but also on isochrony and acoustic details extracted from the source speech. The paper demonstrates the effectiveness of TransVIP through experiments on French-English translation, showing superior performance compared to state-of-the-art models. Strengths: 1. The motivation is interesting. The recent studies have paid attention to voice preservation during speech-to-speech translation (S2ST), and this paper further proposes to preserve the isochrony information for ideal speech translation effects. This may provide useful insights for future work. 2. The paper decouples the S2ST model into multiple modules and offers several significant innovations. 3. The proposed method achieves new state-of-the-art performance. Weaknesses: 1. The title may not be fully representative, as only a part of the innovation focuses on voice and isochrony information preservation. As shown in Section 3, only the first subsection is closely related to the title. While the latter subsections present good innovations, the overall relevance among them could be strengthened. 2. The experimental comparison is limited. This paper focuses on voice and isochrony preservation, but does not provide any comparison with related work, like VALL-E X and PolyVoice. As Seamless does not consider voice information, the real advantage of voice preservation is unclear. 3. This paper proposes multiple innovations with many techniques. However, there are few ablation studies to analyze the individual components. There is also a lack of in-depth analysis on the design choices for voice and isochrony preservation. Technical Quality: 3 Clarity: 2 Questions for Authors: The paper is difficult to read, as some technical details are missing, making it challenging to fully understand the design. For example, it is unclear how the acoustic encoder learned from scratch can be expected to extract the desired acoustic information. Confidence: 4 Soundness: 3 Presentation: 2 Contribution: 2 Limitations: Not applicable Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We sincerely appreciate your efforts in reviewing our paper and providing us with valuable, constructive feedback. The detailed responses are listed below. R1. About not fully representative title (Weakness 1) Thank you for acknowledging the numerous innovations presented in our paper. We will refine the title or add a subtitle to encompass as many aspects as possible. R2. About limited experimental comparisons (Weakness 2) We are always eager to compare our work with related research to verify the effectiveness of our proposed methods. However, most works, such as PolyVoice and MSLM-S2ST, neither have open-sourced models/codes nor matched language pairs for investigation. As we know, S2ST is a complicated system, and reproducing others' entire systems is both challenging and unaffordable. Moreover, we need to point out that Seamless does consider voice information. According to its technical report (https://arxiv.org/pdf/2312.05187), they explicitly encode the speaker and prosody information into the speech generation process. Additionally, the Seamless team leveraged far more data for training than we did. Therefore, we already leveraged a very strong baseline to compare with our model. We will also add following results from cascaded system (ST+TTS) as a comparison to our model. \| \| ASR-BLEU \| BLEU \| SIM \| AutoPCP \| Rate \| Pause \|SLC_0.2 \| SLC_0.4 \| Nat. \| \|---\|---\|---\|---\|---\|---\|---\|---\|---\|---\| \| ST + StyleTTS (Fr->En) \| 33.57 \| 34.58 \| 0.173 \| 2.74 \| 0.33 \| 0.51 \| 0.56 \| 0.85 \| 3.25 \| \| TransVIP (Fr->En) \| 32.60 \| 35.34 \| 0.320 \| 2.49 \| 0.55 \| 0.44 \| 0.70 \| 0.91 \| 3.19 \| \| ST + VALLE-X (En->Fr) \| 22.50 \| 34.89 \| 0.418 \| 2.87 \| 0.27 \| 0.54 \| 0.65 \| 0.89 \| 3.32 \| \| TransVIP (En->Fr) \| 27.28 \| 33.02 \| 0.395 \| 2.67 \| 0.45 \| 0.65 \| 0.81 \| 0.99 \| 3.40 \| where 1) ST is Seamless Speech-to-Text translation model 2) We evaluated cascaded system by using TTS model from StyleTTS (open sourced) and VALLE-X (implemented) and reported the better one in terms of objective measurement. R3. About few ablation studies and in-depth analysis (Weakness 3). We have presented the ablation studies, such as w/ and w/o acoustic embedding, the choice of different codec, w and w/o text BPE and Layer Bean Search in NAR acoustic model. Due to the limited space for the main content, we had to present the ablation studies in the appendix. We will also include an ablation study related to isochrony preservation in the revised version. In this study, we compared our model with the following three baselines. We will report the ASR-BLEU, SLC_p (Speech Length Compliant, as defined in the paper), and Overlap ratio (i.e., speech overlap between the reference and the hypothesis) as follows. \| \| ASR-BLEU \| Overlap \| SLC_0.2 \| SLC_0.4 \| \|---\|---\|---\|---\|---\| \| No IC \| 30.81 \| 0.689 \| 0.63\| 0.87 \| \| Dec IC\| 30.51 \| 0.748 \| 0.75 \| 0.90 \| \| Dec IC + FPI \| 30.45 \| 0.766 \| 0.77\| 0.91\| \| Enc IC (Proposed) \| 30.62 \|0.784 \|0.82\| 0.95\| where 1. No Isochrony control (No IC). 2. Isochrony control on the decoder (Dec IC). This involves adding the Isochrony embedding to the input of the encoder as another positional embedding. We implemented the method from ref [1] in our system. 3. Isochrony control on the decoder with future pause information (Dec IC + FPI). This is an improvement over above 2. In addition to the distance to the global end and VAD information, two extra pieces of information are encoded: the distance to the next pause and the number of pauses in the future. We implemented the method from ref [2] in our system. Ref: [1] Y. Wu, et al. “VideoDubber: Machine Translation with Speech-Aware Length Control for Video Dubbing,” AAAI, 2023. Ref: [2] P. Pal, et al. “Improving Isochronous Machine Translation with Target Factors and Auxiliary Counters”, Interspeech, 2023. Please let us know if more ablation studies should be added. R4. About unclear writing (Question 1) We will revise the paper as clear as possible. For example, we have refined the description as follows to address how the acoustic encoder learned from scratch can be expected to extract the desired acoustic information. Many previous works have adopted a reversed gradient approach to remove semantic information from acoustic features. However, these approaches require an additional decoder and training objective, which increases the training burden. In our work, we use the information bottleneck to train the acoustic extractor. The sum pooling serves as the information bottleneck, preventing too much information, especially semantic information, from passing through. Additionally, we design the system to use part of the target speech as input and predict the other part, making it less likely for the acoustic encoder to learn anything semantically meaningful. This approach integrates seamlessly into the original training process, with no extra modules or loss required. Finally, we would like to express our gratitude once again for your time and effort in reviewing our paper. Considering the multiple innovations, adequate ablation studies, added comparisons and improved presentation of our paper, we would greatly appreciate it if you could consider increasing your score. --- Rebuttal Comment 1.1: Title: Response Comment: Thank you for the detailed clarification and sorry for the late response. While the explanation has addressed most of my concerns, I still feel that the direct comparison to strong voice cloning systems is not sufficient. The voice information is not the primary focus of the Seamless system. Additionally, I believe the title of the paper is an important consideration. The authors should choose a title that is representative of the work presented, to accurately convey the scope and focus of their research. Overall, I will raise my score to 5, as the response has addressed the majority of my initial concerns. --- Rebuttal 2: Comment: Dear Reviewer WU4H We hope we have addressed your questions. Please let us know if you have any further concerns, as the discussion between the reviewers and authors will end soon. Thanks! Best regards, Authors --- Rebuttal 3: Comment: Dear reviewer WU4H, We appreciate your efforts in increasing the rating for our paper. Your suggestions and comments are all valid, and we will address them in either the final version or future work due to the short rebuttal period. Additionally, further suggestions and concerns are welcome until the end of the reviewer and author discussion period. Thanks! Authors	Rebuttal 1: Rebuttal: Dear Reviewers, Thank you for your efforts in reviewing our paper. We greatly appreciate your acknowledgment of our contributions, including multiple innovations, state-of-the-art performance, and important research work. However, we received diverse ratings, ranging from scores of 4 to 7. We noticed that two reviewers who gave the lower scores both had concerns about few ablation studies. In fact, we have presented several ablation studies, such as with and without acoustic embedding, the choice of different codecs, with and without text BPE, and Layer Beam Search in the NAR acoustic model. Due to the limited space for the main content, we had to present these ablation studies in the appendix. If this was one of the reasons for the lower scores, we sincerely hope the reviewers could adjust their scores accordingly. Additionally, we will include new results in the revised version, including: • A comparison with a cascaded system, i.e., ST+TTS. • An ablation study related to isochrony preservation. We will also reorganize the content, include the ablation studies in the main content and conduct a thorough proofread to improve the presentation. Please check the details in the responses to the individual reviewers. Thanks again! Authors	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Concentrate Attention: Towards Domain-Generalizable Prompt Optimization for Language Models	Accept (poster)	Summary: This paper studies prompt optimization methods for finetuning language models. While previous methods mainly concern with in domain performance, this paper brings awareness of the domain generalization issue presented in existing PO methods, under the setting where the target domain is unknown. Two empirical findings that link the domain generality of the prompt to the behavior in attention map are presented regarding this setting. Building on top of these findings, the paper proposes new objectives that account for domain generability for both soft and hard prompt optimization settings. Empirical study on BERT-size transformers and standard NLP datasets reveals that the proposed method achieves fairly consistent and substantial gain over vanilla. Strengths: 1. The paper presents a pioneering study of the domain generalization issue of prompt optimization for PLM finetuning under the more practical setting where the target domain is unknown. 2. The findings connecting the generalization ability of prompts to the attention patterns are interesting and of value to the community. 3. Translating the findings into loss objectives are nontrivial technical challenges, and the paper presents neat solutions to these problems. 4. Empirical gain are fairly substantial and consistent. Weaknesses: 1. The main findings that motivate the proposed method are empirical. The paper can benefit from addressing the intuitions behind why such prompts are more generalizable. 2. The models of choice are mainly small-scale transformers rather than LLMs. It is unclear whether the findings on the attention patterns generalize to bigger models. The paper could benefit from further verifying them on open-source LLMs. 3. Presentation: the in-context citation formats are incorrect. Technical Quality: 2 Clarity: 2 Questions for Authors: Both NLI and sentiment analysis are classification tasks, I wonder if the proposed method generalize to tasks beyond classification? Confidence: 3 Soundness: 2 Presentation: 2 Contribution: 3 Limitations: Yes Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We sincerely thank the reviewer for the constructive comments and feedback. We appreciate that our work is considered “pioneering”, “interesting”, and “neat”. We hope our response can address your concerns. Q1: More intuitive explanation We thank the reviewer for the valuable comment. Our intuition is that more concentration on prompts would lead to less attention on inputs. Thus, domain shifts (change of the domain that inputs are sampled from) cause less negative effect as the model pays more attention to knowledge-intensive prompts instead of constantly changing inputs. Moreover, it is also interesting to investigate the reason why prompts optimized by our method are more generalizable from the perspective of calibration. Calibration refers to the model's ability to provide class probabilities that correspond to its likelihood of being true. A well-calibrated model exhibits better domain generalization ability, as claimed in [1]: > In this paper we highlight a novel connection between multi-domain calibration and OOD generalization, arguing that such calibration can be viewed as an invariant representation. > We use a common metric Expected Calibration Error (ECE) [2] for evaluating the calibration: $$ \mathrm{ECE}=\sum_{m=1}^{M} \frac{\left \| B_{m} \right \| }{n} \left \| \frac{1}{B_{m}}\sum_{i\in B_{m}}\left [ \mathbb{I}(\widehat{y_{i}}= y_{i})-\widehat{p_{i}} \right ] \right \| $$ Here $n$ is the number of samples, $M$ is the number of bins. Each sample has its own label $y_{i}$, predicted label $\widehat{y_i}$, and predicted probability $\widehat{p_i}$. A lower ECE value indicates better calibration. As shown in Table 1, we demonstrate the change in prompt calibration before and after training using our method. We find that our method significantly improves model calibration compared with vanilla method. We infer that good calibration functions as an important factor to avoid significant inductive bias in domain generalization setting, which explains the performance improvement brought by our method. \| Method \| \| Sentiment \| \| \| NLI \| \| \| --- \| --- \| --- \| --- \| --- \| --- \| --- \| \| \| S+M→C \| C+M→S \| S+C→M \| Q+R→W \| W+R→Q \| Q+W→R \| \| Vanilla Prefix \| 0.145 \| 0.160 \| 0.104 \| 0.297 \| 0.193 \| 0.159 \| \| Prefix w both \| 0.128 \| 0.095 \| 0.072 \| 0.206 \| 0.162 \| 0.127 \| Table 1. Expected Calibration Error of Vanilla Prefix Tuning and Prefix Tuning with our method. smaller the better. Q2: Extension to other tasks We would like to thank the reviewer for the valuable comment. We are glad to share that our method is able to successfully be applied on mainstream Large Language Models and question-answering tasks. We validate the effectiveness of our method on Llama-2-7b-chat, Vicuna-7b-v1.5, and Alpaca-7b-wdiff models for improving domain generalization ability of prompts on question-answering tasks. We evaluate our method on ROC, SCT, and COPA datasets from the TRAM Benchmark [3] (referred as R, S, and C for simplicity), covering multiple-choice questions in reading comprehension and commonsense reasoning. The result is shown in Table 2. Experimental results show that our method significantly improves the performance of large models on question-answering tasks across multiple domain generalization settings. For instance, for the Llama-7b model, our method improved the average accuracy of soft prompt generalization and hard prompt generalization comparisons by 1.91% and 2.36%, respectively; similar improvements were observed for Vicuna-7b and Alpaca-7b models, ranging from 1.55% to 2.05% and 1.78% to 1.99% respectively. \| Model \| Method \| S+C->R \| C+R->S \| R+S->C \| Avg Gap \| \| --- \| --- \| --- \| --- \| --- \| --- \| \| Llama-2-7b-chat \| Vanilla Prefix \| 62.32±2.15 \| 66.30±2.30 \| 73.15±2.53 \| - \| \| \| Prefix with both \| 63.70±1.96 \| 68.47±0.97 \| 75.32±1.09 \| +1.91 \| \| \| Vanilla IC \| 63.13±1.25 \| 65.50±1.98 \| 77.59±1.14 \| - \| \| \| IC with both \| 65.13±1.03 \| 68.33±2.13 \| 79.83±0.88 \| +2.36 \| \| vicuna-7b-v1.5 \| Vanilla Prefix \| 67.72±1.79 \| 81.09±2.17 \| 88.97±2.64 \| - \| \| \| Prefix with both \| 68.75±1.04 \| 83.93±1.79 \| 89.76±2.60 \| +1.55 \| \| \| Vanilla IC \| 68.37±2.24 \| 83.23±4.12 \| 90.98±1.99 \| - \| \| \| IC with both \| 69.67±1.58 \| 85.50±5.06 \| 93.39±1.23 \| +2.05 \| \| alpaca-7b-wdiff \| Vanilla Prefix \| 61.52±3.79 \| 70.03±2.88 \| 87.91±2.73 \| - \| \| \| Prefix with both \| 63.89±2.93 \| 72.15±2.07 \| 89.58±2.81 \| +1.78 \| \| \| Vanilla IC \| 60.81±1.14 \| 69.11±2.46 \| 89.66±2.37 \| - \| \| \| IC with both \| 63.16±1.56 \| 70.57±1.95 \| 91.19±2.00 \| +1.99 \| Table 2. Performance comparison of LLMs on multiple-choice task accuracy under MFDG settings. In our global response PDF, we illustrate the Concentration Strength Distribution of prompts in the In-Context Demo format for three 7B-sized language models (Llama, Vicuna, Alpaca) across three different tasks (SA, NLI, MCQA). A common observation is that the concentration strength is stronger in deep layers instead of shallow layers. To be more specific, compared to smaller models (Roberta-large), concentration phenomena occur earlier in larger models. Inductively, we get the conclusion that this phenomenon — higher concentration in deep layers, happens independent of model sizes, tasks or prompts. Q3: In-context Citation Errors We would like to thank the reviewers for reading our work carefully. We sincerely apologize for the in-context citation errors in our paper. We will check and revise these errors in the next version. [1] Wald, Yoav, et al. "On calibration and out-of-domain generalization." Advances in neural information processing systems 34 (2021): 2215-2227. [2] Naeini, Mahdi Pakdaman, Gregory Cooper, and Milos Hauskrecht. "Obtaining well calibrated probabilities using bayesian binning." Proceedings of the AAAI conference on artificial intelligence. Vol. 29. No. 1. 2015. [3] Wang, Yuqing, and Yun Zhao. "Tram: Benchmarking temporal reasoning for large language models." arXiv preprint arXiv:2310.00835 (2023). --- Rebuttal 2: Comment: We sincerely appreciate your valuable feedback and insightful discussion! We hope our response has been helpful to you. As the discussion period is drawing to a close, we warmly welcome any further questions from the reviewer. We would be delighted to provide additional clarification! --- Rebuttal Comment 2.1: Title: Reply to authors Comment: Thank you for your. The newly added experiments on motivation, LLMs, and new tasks help strengthen the paper. I improved my ratings accordingly. --- Reply to Comment 2.1.1: Comment: We sincerely thank the reviewer for the constructive discussions and positive feedback. We will optimize our work in detail based on these suggestions and incorporate the experiments you mentioned into our main paper.	Summary: This paper focuses on improving the domain generalization of prompt tuning methods on LLMs. Specifically, this work claims that the concentration strength and concentration fluctuation of a candidate soft or hard prompt may indicate its generalization ability on new domains. By demonstrating the performance of various prompts with their concentration strength and fluctuation, the authors show that higher concentration strength and lower fluctuation may bring better prompt domain generalization. As a result, this paper proposes new objectives in soft and hard prompt tuning based on these observations. The experimental results show that the obtained prompts achieve better performance on new domains in NLI and sentiment classification tasks. Strengths: 1. The paper is well organized, with very clear problem and methodology formulation, making the proposed approach easy to follow up. 2. The observation on prompt attention concentration and its potential correlation to domain generalization are interesting and may encourage further research on this topic. 3. The proposed objectives for soft and hard prompting methods are generalizable and are compatible with most recent prompting algorithms. Weaknesses: The main weakness of this work is the limited task types in the experiments. Only the sentiment classification and NLI tasks are considered in this work. It will be much better if more evidence or results on broader task types are obtained. Technical Quality: 3 Clarity: 4 Questions for Authors: Have you ever evaluated the effect of prompt attention concentration on any (recent) generative LLMs? Confidence: 4 Soundness: 3 Presentation: 4 Contribution: 3 Limitations: The authors have adequately addressed the limitations of this work. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We sincerely thank the reviewer for the constructive comments and feedback. We appreciate that our work is considered “well organized”, “interesting”, and “generalizable”. We hope our response can address your concerns. Q1: Extension to other tasks We would like to thank the reviewer for the valuable comment. We would like to thank the reviewer for drawing our attention to extending our method to broader applications. We are glad to share that our method is able to successfully be applied on mainstream Large Language Models and question-answering tasks. We validate the effectiveness of our method on Llama-2-7b-chat, Vicuna-7b-v1.5, and Alpaca-7b-wdiff models for improving domain generalization ability of prompts on question-answering tasks. We evaluate our method on ROC, SCT, and COPA datasets from the TRAM Benchmark [1] (referred as R, S, and C for simplicity), covering multiple-choice questions in reading comprehension and commonsense reasoning. The result is shown in Table 1. Experimental results show that our method significantly improves the performance of large models on question-answering tasks across multiple domain generalization settings. For instance, for the Llama-7b model, our method improved the average accuracy of soft prompt generalization and hard prompt generalization comparisons by 1.91% and 2.36%, respectively; similar improvements were observed for Vicuna-7b and Alpaca-7b models, ranging from 1.55% to 2.05% and 1.78% to 1.99% respectively. \| Model \| Method \| S+C->R \| C+R->S \| R+S->C \| Avg Gap \| \| --- \| --- \| --- \| --- \| --- \| --- \| \| Llama-2-7b-chat \| Vanilla Prefix \| 62.32±2.15 \| 66.30±2.30 \| 73.15±2.53 \| - \| \| \| Prefix with both \| 63.70±1.96 \| 68.47±0.97 \| 75.32±1.09 \| +1.91 \| \| \| Vanilla IC \| 63.13±1.25 \| 65.50±1.98 \| 77.59±1.14 \| - \| \| \| IC with both \| 65.13±1.03 \| 68.33±2.13 \| 79.83±0.88 \| +2.36 \| \| vicuna-7b-v1.5 \| Vanilla Prefix \| 67.72±1.79 \| 81.09±2.17 \| 88.97±2.64 \| - \| \| \| Prefix with both \| 68.75±1.04 \| 83.93±1.79 \| 89.76±2.60 \| +1.55 \| \| \| Vanilla IC \| 68.37±2.24 \| 83.23±4.12 \| 90.98±1.99 \| - \| \| \| IC with both \| 69.67±1.58 \| 85.50±5.06 \| 93.39±1.23 \| +2.05 \| \| alpaca-7b-wdiff \| Vanilla Prefix \| 61.52±3.79 \| 70.03±2.88 \| 87.91±2.73 \| - \| \| \| Prefix with both \| 63.89±2.93 \| 72.15±2.07 \| 89.58±2.81 \| +1.78 \| \| \| Vanilla IC \| 60.81±1.14 \| 69.11±2.46 \| 89.66±2.37 \| - \| \| \| IC with both \| 63.16±1.56 \| 70.57±1.95 \| 91.19±2.00 \| +1.99 \| Table 1. Performance comparison of LLMs on multiple-choice tasks under MFDG settings. The last column shows the average gap between test performance on vanilla methods and our methods. Results are averages from 3 runs using different random seeds. Additionally, we would also like to discuss ‘’why our method works well for large generative language models?’’. In our global response PDF, we present the Concentration Strength Distribution of prompts using In-Context Demo across three 7B-sized language models (Llama, Vicuna, Alpaca) on three different tasks (SA, NLI, QA). We observed that all three LLMs exhibit stronger concentration strength in deeper layers compared to shallower layers when confronted with prompts for different tasks. Additionally, we found that this phenomenon occurs earlier in larger models (7B) compared to smaller models like Roberta-large. We speculate that this behavior is related to the alignment stage in pre-training of large models during Supervised Fine Tuning with a large number of prompts. [1] Wang, Yuqing, and Yun Zhao. "Tram: Benchmarking temporal reasoning for large language models." arXiv preprint arXiv:2310.00835 (2023). --- Rebuttal 2: Comment: We sincerely appreciate your valuable feedback and insightful discussion! We hope our response has been helpful to you. As the discussion period is drawing to a close, we warmly welcome any further questions from the reviewer. We would be delighted to provide additional clarification!	Summary: This paper studies the problem of prompt optimziation for domain generalization. Through a pilot experiment, they find that the domain generalization capability is tied to the attention concentration in later layers of the network. Based on this finding, the authors design a set of regularizers to improve both soft and hard prompt optimziation procedures. Empirically, the method is tested on sentiment and NLI tasks. Results demonstrated a reduced generalization gap, and improved performance with the added losses over several prompt optimization methods. Strengths: - The exploration of prompt optimization is a highly important avenue for research as prompt optimization remains an efficient way to fine-tune language models. At the same time, it is improtant to consider the robustness of such approaches and how to improve this. - The paper is overall well-written and flows nicely. The paper highlights the core properties for the findings and main results in the introduction of the paper, constructs an experiment to validate this in Section 3, subsequently intorduces their regularizer, and demonstrates results across two tasks. - The proposed approach is simple to implement and can be applied irrespective of the architecture, as it is only an adjustment of the loss function thus having general applicability. - Authors have conducted thorough ablations studies in the proposed approach in the Appendices particularly around stability, visualizations, and initalizations. Weaknesses: - My biggest concerns with this paper are around the experimental results. The performance improvements in experiments Tables 1 and 2 are small covering only 1-2% improvements over baselines. The paper also does not make comparisons to existing approaches for domain adaptation of prompts such as https://arxiv.org/pdf/2207.07087 https://arxiv.org/pdf/2210.02952 https://arxiv.org/pdf/2305.13954 - Further the paper only explores limited settings including a single architecture, task, and setting. Exploring other modalities (such as vision transformers), additional tasks and settings, or other architectures would help solidify that the proposed approach is more general and would extend beyond the two tasks in this work. - Some minor typos such as hypnosis at line 284, and some hyperparameters seem to be missing from the main text for replication purposes including the value for lambda and how this is selected for the regularizers. Technical Quality: 2 Clarity: 3 Questions for Authors: Results for the proposed approach primarily suggest that the phenomena happens in later parts of the network, In practice, it is not clear without running the experiment, which layers will this be most prevalent and if it is task/prompt dependent. For larger networks, would this happen earlier, or for shallow networks would this not happen at all? Results here may be of interest in relation to the calibration of shallow models and lack thereof for deeper models. Confidence: 3 Soundness: 2 Presentation: 3 Contribution: 2 Limitations: - Proposed approach is only evaluated in fine-tuning settings. This limits applicability to many settings where LLMs are evaluated such as in context learning, or zero-shot. - The proposed approach is evaluated on the Roberta model, whereas there are a number of language models that could be investiinvestigated including the T5 encoder-decoder models, and GPT decoder only models. Do we expect different behaviors based on the architectrues and attention? - The proposed approach is limited only to NLP applications, however could be applied for other variants such as vision transformers and robustness considerations. Would we expect similar trends in other applications. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We sincerely thank the reviewer for the constructive comments and feedback. We appreciate that our work is considered “important”, “well-written”, and “thorough”. We hope our response can address your concerns. Q1: Improvement and additional baselines Improvement: We will try to address the reviewer's concerns about performance improvement in the following points. - The objective of this work is to enhance domain generalization in current prompt optimization methods, not to design a new framework. Our method acts as a plug-and-play module compatible with mainstream prompt optimization methods. As shown in Table 1, it improves performance in 3 soft and 3 hard prompt optimization methods. - Our method modifies the training objective or filter-match strategy within the original framework, so performance is limited by the original model structure or initial prompt set. For example, the quality of the candidate prompt set affects the performance of hard prompt optimization (as shown in Table 1 in our paper). Nonetheless, our method consistently enhances domain generalization with prompts from the same candidate set, demonstrating its effectiveness. Additional Baselines: Following the suggestion of the reviewer, we compare our method with the suggested domain adaptation methods — OPTIMA [1] and GPO [2] and two PEFT methods similar to [3] — IA3 and LoRA. The results are shown in Table 1. Compared with DP2O with both, the best performer in a series of prompt optimization methods piggybacked with our optimization strategy, we find that DP2O with both achieves accuracy improvements of 3.88%, 3.54%, 4.46%, 1.77%, 0.55%, and 3.62% compared to the second-best method in six experimental settings. Although our method still performs best, we would like to highlight that our work improves model performance in domain generalization setting where no information from target domain is available during training while data from target domain is accessible in domain adaptation methods like OPTIMA and GPO. The Introduction section of our paper (line 35-39) discusses the shortcomings of domain adaptation methods, while the Preliminary section (line 87-95) introduces the basic definition of domain generalization problems. The Related Work section (line 472-480) contrasts the differences between these two types of problems. \| Method \| \| Sentiment \| \| \| NLI \| \| \| --- \| --- \| --- \| --- \| --- \| --- \| --- \| \| \| S+M→C \| C+M→S \| S+C→M \| Q+R→W \| W+R→Q \| Q+W→R \| \| IA3 \| 75.64±1.77 \| 72.94±2.15 \| 65.33±1.52 \| 41.32±1.09 \| 52.40±1.79 \| 51.93±1.65 \| \| lora \| 79.52±2.32 \| 80.42±1.89 \| 71.76±2.00 \| 47.26±2.68 \| 53.16±1.73 \| 52.19±2.09 \| \| GPO \| 82.57±1.73 \| 89.32±2.09 \| 83.39±0.88 \| 54.65±0.71 \| 54.77±2.20 \| 55.90±2.65 \| \| OPTIMA \| 85.75±2.77 \| 85.01±4.4 \| 80.61±4.46 \| 53.33±3.26 \| 54.19±2.70 \| 57.65±5.17 \| \| DP2O with both \| 89.63±0.52 \| 92.87±0.33 \| 87.85±0.47 \| 56.42±0.36 \| 55.32±0.33 \| 61.27±0.81 \| Table 1. Performance comparison of text classification task accuracy under MFDG settings. Bold indicates the best result for each column, and underline indicates the second-best result for each column. Results are averages from 3 runs using different random seeds. Q2: Extension to other architectures, tasks and modalities We are glad to share that our method is able to successfully be applied on different architectures like large decoder-only models (Llama-2-7b-chat, Vicuna-7b-v1.5, and Alpaca-7b-wdiff) for additional tasks such as question answering. To be specific, we evaluate our method on ROC, SCT, and COPA datasets from the TRAM Benchmark [3] (referred as R, S, and C for simplicity), covering multiple-choice questions in reading comprehension and commonsense reasoning. The result is shown in Table 2. Experimental results show that our method significantly improves the performance of large decoder-only models on question-answering tasks across multiple domain generalization settings. For instance, for the Llama-7b model, our method improved the average accuracy of soft prompt generalization and hard prompt generalization comparisons by 1.91% and 2.36%, respectively. Similar improvements are observed in Vicuna-7b and Alpaca-7b models, ranging from 1.55% to 2.05% and 1.78% to 1.99% respectively. We would like to clarify that our method is designed for language model, as we stated in the title of this paper. Incorporating other modalities into our method is beyond the scope of our research. We believe exploring the possibility to generalize our method to tasks in other modalities is interesting and we will do it in the future. \| Model \| Method \| S+C->R \| C+R->S \| R+S->C \| \| --- \| --- \| --- \| --- \| --- \| \| Llama-2-7b-chat \| Vanilla Prefix \| 62.32±2.15 \| 66.30±2.30 \| 73.15±2.53 \| \| \| Prefix with both \| 63.70±1.96 \| 68.47±0.97 \| 75.32±1.09 \| \| \| Vanilla IC \| 63.13±1.25 \| 65.50±1.98 \| 77.59±1.14 \| \| \| IC with both \| 65.13±1.03 \| 68.33±2.13 \| 79.83±0.88 \| \| vicuna-7b-v1.5 \| Vanilla Prefix \| 67.72±1.79 \| 81.09±2.17 \| 88.97±2.64 \| \| \| Prefix with both \| 68.75±1.04 \| 83.93±1.79 \| 89.76±2.60 \| \| \| Vanilla IC \| 68.37±2.24 \| 83.23±4.12 \| 90.98±1.99 \| \| \| IC with both \| 69.67±1.58 \| 85.50±5.06 \| 93.39±1.23 \| \| alpaca-7b-wdiff \| Vanilla Prefix \| 61.52±3.79 \| 70.03±2.88 \| 87.91±2.73 \| \| \| Prefix with both \| 63.89±2.93 \| 72.15±2.07 \| 89.58±2.81 \| \| \| Vanilla IC \| 60.81±1.14 \| 69.11±2.46 \| 89.66±2.37 \| \| \| IC with both \| 63.16±1.56 \| 70.57±1.95 \| 91.19±2.00 \| Table 2. Performance comparison of decoder-only LLMs on multiple-choice task accuracy under MFDG settings. [1] Guo, et al. Improving the sample efficiency of prompt tuning with domain adaptation. [2] Li, et al. Robust prompt optimization for large language models against distribution shifts. [3] Tam, et al. Parameter-efficient prompt tuning makes generalized and calibrated neural text retrievers. [4] Wang, et al. Tram: Benchmarking temporal reasoning for large language models. --- Rebuttal 2: Title: Author Rebuttal Part 2 Comment: Q3: Spelling errors and missing hyperparameters: We sincerely appreciate your careful reading. - Spelling errors: We apologize for any ambiguities and typographical errors in our paper. We will incorporate your suggestions in the revision to ensure these errors do not recur. - Missing hyperparameters: We provide specific values of lambda in Appendix B.4 (as shown in Table 5 in our paper). We use a validation set of the same size as the training set to evaluate its selection of different regularizers. We apologize for the lack of this information and will emphasize it in the next version. Q4: Concentration distribution on larger models: We thank the reviewer for the valuable comments. In Appendix C.2, we present the Concentration Strength Distribution of different prompts in the Roberta-large model (355M). In our global response PDF, we illustrate the Concentration Strength Distribution of prompts in the In-Context Demo format for three 7B-sized language models (Llama, Vicuna, Alpaca) across three different tasks (SA, NLI, QA). A common observation is that the concentration strength is stronger in deep layers instead of shallow layers. To be more specific, compared to smaller models (Roberta-large), concentration phenomena occurs earlier in larger models and keeps high in deep layers . Inductively, we get the conclusion that this phenomenon — higher concentration in deep layers, happens independent of model sizes, tasks or prompts. Q5: Evaluation other than fine-tuning We would like to thank the reviewer for the valuable comment. We would like to clarify that in-context learning is one of our baselines for discrete prompt optimization. In our main experiments (Table 1 in our paper), In-Context Demo method provides examples as prompt, which is a classic version of existing in-context learning methods (Line 497). --- Rebuttal 3: Comment: We sincerely appreciate your valuable feedback and insightful discussion! We hope our response has been helpful to you. As the discussion period is drawing to a close, we warmly welcome any further questions from the reviewer. We would be delighted to provide additional clarification! --- Rebuttal Comment 3.1: Title: Reviewer Response to Author Rebuttal Comment: Thank you for the comments and addressing many of my concerns. My primary concerns with the paper were (1) generalizability across models and tasks, and (2) comparisons with existing benchmarks. My concerns with (1) have been addressed with the inclusion of new QA tasks and larger + more recent 7B decoder-only experiments. I believe these would be important to have in the main paper. Regarding (2) I thank the authors for including these experiments, and understand that the proposed approach follows a different line of work from the referenced works. I will increase my score to reflect the additional experiments that have improved the paper. --- Reply to Comment 3.1.1: Comment: We sincerely thank the reviewer for the constructive discussions and positive feedback. We will optimize our work in detail based on these suggestions and incorporate the experiments you mentioned into the main paper.	Summary: This paper investigates the domain generalization ability of prompts for pretrained language models (PLMs). The paper finds that prompts that receive higher attention weights from deeper PLM layers and those with stable attention distributions generalize better across domains. The authors introduce a novel objective called "Concentration" which implements a "lookback" attention from the current decoding token to prompt tokens, aiming to enhance both soft and hard prompt optimization methods. Their experiments demonstrate significant improvements in multi-source domain generalization accuracy—1.42% for soft prompts and 2.16% for hard prompts—while maintaining robust in-domain performance. These findings offer valuable insights into creating domain-generalizable prompts. Strengths: * The paper is well-written. * The authors started with an initial analysis to inform a novel training objective, which is both insightful and methodologically sound. * The proposed method is simple and the authors demonstrate its effectiveness across several classification tasks. Weaknesses: I felt there were several obvious questions left unexplored, noted below, which raise concerns regarding the significance of the paper's contributions. * The authors only experimented with a rather small model, i.e., 355M RoBERTa, which raises concerns about whether the proposed method works with larger model sizes. * The authors focused solely on a classification tasks (sentiment classification and natural language inference). This raises concerns about the proposed approach's applicability and effectiveness for other tasks, like open-ended generation. * Finally, the improvements were shown over rather weak baselines. For example, prompt tuning, particularly with small models and limited training data, is a rather weak approach. I also felt that the authors compared their method against a weak implementation of this baseline, using only 5 soft prompt tokens and a learning rate of $2×10^{−5}$. For reference, the original prompt tuning paper used 100 prompt tokens and a learning rate of 0.3, which they found to be critical for prompt tuning's strong performance and faster convergence. These differences raise concerns about the significance of the proposed method's improvements. Technical Quality: 3 Clarity: 3 Questions for Authors: Please see the Weaknesses above. Confidence: 5 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: The author discussed several limitations of their approaches, including the limited variety of prompts, the focus on a few-shot setting, the restriction of discrete prompt optimization to the input level, and the inapplicability of their methods to generation tasks. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We sincerely thank the reviewer for the constructive comments and feedback. We appreciate that our work is considered “well-written”, “novel”, and “insightful”. We hope our response can address your concerns. Q1: Applicability to larger models and other tasks: We would like to thank the reviewer for drawing our attention to extending our method to broader applications. We are glad to share that our method is able to successfully be applied on mainstream Large Language Models and question-answering tasks. We validate the effectiveness of our method on Llama-2-7b-chat, Vicuna-7b-v1.5, and Alpaca-7b-wdiff models for improving domain generalization ability of prompts on question-answering tasks. We evaluate our method on ROC, SCT, and COPA datasets from the TRAM Benchmark [1] (referred as R, S, and C for simplicity), covering multiple-choice questions in reading comprehension and commonsense reasoning. The result is shown in Table 1. Experimental results show that our method significantly improves the performance of large models on question-answering tasks across multiple domain generalization settings. For instance, for the Llama-7b model, our method improved the average accuracy of soft prompt generalization and hard prompt generalization comparisons by 1.91% and 2.36%, respectively; similar improvements were observed for Vicuna-7b and Alpaca-7b models, ranging from 1.55% to 2.05% and 1.78% to 1.99% respectively. Our research primarily addresses the analysis and optimization of attention patterns from current decoding tokens to prompt tokens (line. 121-122). Thus, long sequence generation (e.g., open-end generation) is beyond the scope of this research, as we admit in Section 7 (line. 323-325). We will explore the possibility to improve domain generalizability on more generative tasks in the future. \| Model \| Method \| S+C->R \| C+R->S \| R+S->C \| Avg Gap \| \| --- \| --- \| --- \| --- \| --- \| --- \| \| Llama-2-7b-chat \| Vanilla Prefix \| 62.32±2.15 \| 66.30±2.30 \| 73.15±2.53 \| - \| \| \| Prefix with both \| 63.70±1.96 \| 68.47±0.97 \| 75.32±1.09 \| +1.91 \| \| \| Vanilla IC \| 63.13±1.25 \| 65.50±1.98 \| 77.59±1.14 \| - \| \| \| IC with both \| 65.13±1.03 \| 68.33±2.13 \| 79.83±0.88 \| +2.36 \| \| vicuna-7b-v1.5 \| Vanilla Prefix \| 67.72±1.79 \| 81.09±2.17 \| 88.97±2.64 \| - \| \| \| Prefix with both \| 68.75±1.04 \| 83.93±1.79 \| 89.76±2.60 \| +1.55 \| \| \| Vanilla IC \| 68.37±2.24 \| 83.23±4.12 \| 90.98±1.99 \| - \| \| \| IC with both \| 69.67±1.58 \| 85.50±5.06 \| 93.39±1.23 \| +2.05 \| \| alpaca-7b-wdiff \| Vanilla Prefix \| 61.52±3.79 \| 70.03±2.88 \| 87.91±2.73 \| - \| \| \| Prefix with both \| 63.89±2.93 \| 72.15±2.07 \| 89.58±2.81 \| +1.78 \| \| \| Vanilla IC \| 60.81±1.14 \| 69.11±2.46 \| 89.66±2.37 \| - \| \| \| IC with both \| 63.16±1.56 \| 70.57±1.95 \| 91.19±2.00 \| +1.99 \| Table 1. Performance comparison of LLMs on multiple-choice tasks under MFDG settings. The last column shows the average gap between test performance on vanilla methods and our methods. Results are averages from 3 runs using different random seeds. Q2: Baselines and Hyperparameter selection We thank the reviewer for the valuable comment. For starters, we would like to claim the objective of this work is not to design a brand-new framework, but to improve domain generalization ability of current prompt optimization methods, as stated in lines. 73-75: > With the principle of concentration §3, we propose two algorithms that could piggyback upon popular prompt optimization methods for both hard and soft prompts to improve the domain generalization ability of prompts. > Thus, prompt tuning, as one of the most popular prompt optimization methods, serves as a good baseline to demonstrate that our proposed objective works well for improving the domain generalization ability within the framework of prompt tuning itself. In addition to prompt tuning, we also try to apply our proposed goal to several stronger baselines (such as Prefix Tuning and P-Tuningv2 for soft prompts, In-Context Demo and DP2O for hard prompts), and it consistently shows excellent performance in improving domain generalization ability of prompts on all experimental settings (as shown in Table 1 in our paper). Additionally, we would like to address the reviewer’s concern in hyperparameter selection. The suggested work [2] (100 prompt tokens and learning rate of 0.3) is based on full training data for the T5 model. In resource-limited scenarios, such settings may lead to severe overfitting issues. We also conduct experiments with the suggested hyperparameters by using T5-base model. The result is in Table 2. We find more prompt tokens and larger learning rate actually degrades performance of prompt tuning in the few-shot setting. We would like to clarify that our hyperparameter setting is similar with [3], where a learning rate of 1e-5 is used to train XLM-RoBERTa-base model in the few-shot setting with 4 soft prompt tokens. \| Method \| \| Sentiment \| \| \| NLI \| \| \| --- \| --- \| --- \| --- \| --- \| --- \| --- \| \| \| S+M→C \| C+M→S \| S+C→M \| Q+R→W \| W+R→Q \| Q+W→R \| \| Vanilla PT \| 55.70±0.98 \| 52.37±2.05 \| 52.67±1.55 \| 41.57±0.93 \| 51.83±0.79 \| 51.70±2.25 \| \| PT with both \| 57.17±0.99 \| 54.80±1.77 \| 53.35±1.73 \| 43.72±1.33 \| 53.46±1.53 \| 53.79±1.47 \| Table 2. Performance comparison of soft prompt learning on classification task accuracy for T5-base model. Results are averages from 3 runs using different random seeds. [1] Wang, Yuqing, and Yun Zhao. "Tram: Benchmarking temporal reasoning for large language models." arXiv preprint arXiv:2310.00835 (2023). [2] Lester, Brian, Rami Al-Rfou, and Noah Constant. "The power of scale for parameter-efficient prompt tuning." arXiv preprint arXiv:2104.08691 (2021). [3] Zhao, Mengjie, and Hinrich Schütze. "Discrete and soft prompting for multilingual models." arXiv preprint arXiv:2109.03630 (2021). --- Rebuttal 2: Comment: We sincerely appreciate your valuable feedback and insightful discussion! We hope our response has been helpful to you. As the discussion period is drawing to a close, we warmly welcome any further questions from the reviewer. We would be delighted to provide additional clarification!	Rebuttal 1: Rebuttal: Global Response to All Reviewers --- We illustrate the Concentration Strength Distribution of prompts in the In-Context Demo format for three 7B-sized language models (Llama, Vicuna, Alpaca) across three different tasks (SA, NLI, QA). A common observation is that the concentration strength is stronger in deeper layers instead of shallower layers. To be more specific, compared to smaller models (Roberta-large), concentration phenomena occurs earlier in larger models and keeps till the deep layers. Pdf: /pdf/c9aa1cd94b3753d97f409364d32e38ba36266527.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Truthful High Dimensional Sparse Linear Regression	Accept (poster)	Summary: The authors present an $\varepsilon$-Bayesian incentive compatible and individually rational $k$-sparse linear regression algorithm with side payments for (almost all) privacy-oriented data providing agents. Remarkably, in the limit $d >> n >> \log d$, the accuracy and the needed budget both vanish. Strengths: The paper tackles an interesting problem, at the heart of data collection for machine learning applications. The algorithms and the proof techniques are important advancements in the understanding of privacy-preserving machine learning with financial compensations to strategic data providers. Weaknesses: The paper already has a lot of different notations, which are easily confusing for the reader. It is thus very important to significantly improve the writing, which is too often extremely hard on the reader: - Isn't the $\Pi_{\tau_\theta}$ the same operator as clipping (lines 2 and 3 of Algorithm 1)? It would make it much easier to read if all identical operators were written in the same way. - The partition $\hat D^0 \cup \hat D^1$ should be presented before its use in line 273. - Assumption 5 has a typo (I guess). It should be $D-i$ rather than $D_j$. There should also be a quantification over $i$ (unless each (c_i, D_i) is iid?). - The "symmetric threshold strategy" is used in the main text without definition (and without even a reference to the appendix!). The paper makes a common ground-truth assumption (same $\theta^$). In practice, this may be unrealistic. Technical Quality: 2 Clarity: 2 Questions for Authors: I don't see Assumption 3 as a generalization of Cummings et al. Given that $\delta \leq 1$, the assumption is essentially equivalent to (at least implied by) $f_i \leq 2c_i \varepsilon^3$, which is more demanding than $f_i \leq c_i \varepsilon^2$. It should be rather presented as a relaxation. Do the authors agree? I don't understand the claim (line 162) that "the one-round communication necessitates a closed-form estimator". Wouldn't any algorithm work? If so, I suggest that the authors merely present their new estimator as a proposal for covariance estimation, with a high-probability inversion guarantee (and even point to Theorem 3 as the end goal). I fail to understand how $\theta^$ can be recovered without assumptions on the thresholds $r$, $\tau_x$, $\tau_y$ and $\lambda_n$. It seems that this should not be possible for arbitrary values of these parameters. Can the authors clarify this? Right now, though I think I mostly understand the algorithm, and its implications in terms of privacy, strategyproofness and individual rationality, its accuracy is a mystery to me, which prevents me from providing a larger score. I would be greatly thankful to the authors if they could help me gain insights into this aspect of their result. Confidence: 2 Soundness: 2 Presentation: 2 Contribution: 4 Limitations: The authors should better stress that (i) Agents' "rationality" is merely on privacy leakage (they are indifferent to the trained model's behavior). (ii) Agents are assumed to have the same labeling function (parameter $\theta^*$). (iii) (Individually rational) agents whose data is too different are more likely removed from the system. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: >W1: Isn't the $\Pi_{\tau_{\theta}}$ the same operator as clipping (lines 2 and 3 of Algorithm 1)? It would make it much easier to read if all identical operators were written in the same way. We wish to thank the reviewer for pointing out this. We will add $\Pi_r$ to Line 2 of Algorithm 1 and unify the rest of the notations. >W2: The partition $\hat{D}^{0} \cap \hat{D}^1$ should be presented before its use in line 273. Yes, we will notate it before its use in the finalized version. >W3: Assumption 5 has a typo (I guess). It should be $D_{-i}$ rather than $D_{j}$. There should also be a quantification over $i$ (unless each $(c_i, D_i)$ is iid?). Yes, there is a typo: $D_j$ should be $D_i$. i.e., the conditional marginal distribution of $c_i$. We are indeed taking the infimum over every data $D_i$. This is not supposed to exclude user $i$. And yes, from Assumption 2 we have that $D_i$ is i.i.d and $c_i$ is also i.i.d because otherwise, the user will be able to gauge other user's payment. >W4: The "symmetric threshold strategy" is used in the main text without definition (and without even a reference to the appendix!). Due to the space limit, we postpone it to Definition 4 (threshold strategy) of Section.A.1 in the Appendix. In game theory, a symmetric threshold strategy might involve players adopting the same threshold for their strategies. We will change the "threshold strategy" to the "symmetric threshold strategy" and move it to the main paper if space allows. >W5: The paper makes a common ground-truth assumption (same ). In practice, this may be unrealistic. We admit that a common underlying parameter $\theta^$ may not be the case in reality. However, in the statistical estimation literature, this is quite normal as we always assume the data are i.i.d. sampled from the same distribution or model. Moreover, current research on truthful and private mechanism design [1, 2] and private statistical estimation [3-5] always need such an i.i.d. assumption. Thus, such an assumption is reasonable. [1] Cummings, Rachel, Stratis Ioannidis, and Katrina Ligett. "Truthful linear regression." Conference on Learning Theory. PMLR, 2015. [2] Qiu, Yuan, Jinyan Liu, and Di Wang. "Truthful Generalized Linear Models." arXiv preprint arXiv:2209.07815 (2022). [3] Varshney, Prateek, Abhradeep Thakurta, and Prateek Jain. "(Nearly) Optimal Private Linear Regression via Adaptive Clipping." arXiv preprint arXiv:2207.04686 (2022). [4] Cai, T. Tony, Yichen Wang, and Linjun Zhang. "The cost of privacy: Optimal rates of convergence for parameter estimation with differential privacy." The Annals of Statistics 49.5 (2021): 2825-2850. [5] Bassily, Raef, et al. "Private stochastic convex optimization with optimal rates." Advances in neural information processing systems 32 (2019). >Q1: I don't see Assumption 3 as a generalization of Cummings et al. Given that $\delta < 1$ , the assumption is essentially equivalent to (at least implied by) $f_i < 2c_i \epsilon^3$ , which is more demanding than $f_i < c_i \epsilon^2$ . It should be rather presented as a relaxation. Do the authors agree?* The authors agree with the reviewer's opinion in this regard. Currently, Assumption 3 is indeed not a generalization of the assumption used in the work of Cummings et al. We will delete the generalization part in our paper. >Q2: I don't understand the claim (line 162) that "the one-round communication necessitates a closed-form estimator". Wouldn't any algorithm work? If so, I suggest that the authors merely present their new estimator as a proposal for covariance estimation, with a high-probability inversion guarantee (and even point to Theorem 3 as the end goal). Here, one-round communication is the protocol that all agents send to the server once and simultaneously. Thus, there are no further interactions, which means not all algorithms work. For example, the based method is not one-round, and it does not work. As there is just one round, the server intuitively needs to aggregate this feedback and get an estimator, which has a closed form. In the final version, if additional pages are allowed, we will move the results of the high-probability inversion guarantee to the main context. >*Q3: I fail to understand how $\theta^{}$ can be recovered without assumptions on the thresholds $r, \tau_x, \tau_y$ and $ \lambda_n$. It seems that this should not be possible for arbitrary values of these parameters. Can the authors clarify this? Yes, indeed these parameters cannot be arbitrary and their values need to be carefully decided. Due to the space limit, we introduce how to tune these parameters in Lemma 22 in the Appendix. In the revised version, we will also state these conditions in our Theorem 3 and Corollary 8 in the main paper for ease of understanding. --- Rebuttal 2: Title: (Continued) Re: Q4 Comment: >Q4: Right now, though I think I mostly understand the algorithm, and its implications in terms of privacy, strategyproofness and individual rationality, its accuracy is a mystery to me, which prevents me from providing a larger score. I would be greatly thankful to the authors if they could help me gain insights into this aspect of their results.** We thank the reviewer for appreciating our contributions. We present the accuracy result in Theorem 3. In the upper bound of Thm.3 there are two terms. The first one is $\tilde{O}(\frac{\alpha^2 n k}{\epsilon^2})$ (we assume the radius $r$ as a constant), where $\alpha$ is defined in Definition 6 is $1-\alpha$. Note that if all agents' cost is less than the threshold, then this term becomes zero. Moreover, as $1-\alpha$ means our participation goal, by choosing the parameter $\alpha$ sufficiently small (as suggested in Corollary 8), it will be dominated by the second term. The second term is $\tilde{O}(\frac{k}{n\epsilon^2})$, which is the cost due to privacy and statistical error. It is notable that even in the standard (non-private) high dimensional sparse linear model, the optimal estimation error is $\tilde{O}(\frac{k}{n})$, which only depends on $\log d$ and the sparsity. As we consider the high dimensional case where $n\ll d$, this bound will be $o(1)$. Thus, our second term is also very small and comparable to the non-private case. --- Rebuttal Comment 2.1: Comment: I thank the authors for their response, which clarified several points. Overall, I believe that the paper would greatly gain from improved writing, which is why I stick with my rating. But I fully recognize the value of their contribution. --- Reply to Comment 2.1.1: Comment: We appreciate the reviewer's recognition and feedback. For the camera-ready version, we will incorporate the requested clarifications and definitions on the additional page to ensure completeness. We will also correct any typos and unify the notation to enhance readability. If our response has addressed your concerns and positively influenced your view of our paper, we kindly ask you to consider revising the score.	Summary: The paper solves the problem of high dimensional sparse regression with subgaussian covariates. Along with doing that they also ensure differential privacy of the data providers. Finally, they also provide a payment scheme that is individually rational and which incentivizes truthfulness. Strengths: The paper provides an algorithm to solve the problem of high dimensional sparse regression with subgaussian covariates. They also make sure that the algorithm also ensures differential privacy of the data providers. Finally, they also provide a payment scheme that is individually rational and which incentivizes truthfulness. Weaknesses: 1) The paper seems to be a slight extension of differentially private logistic regression while also incorporating payments into it which does not seem like a major extension given the earlier works of Fallah et al. or Anjarlekar et al. have incorporated incentive-compatible payment mechanisms in traditional DP settings with Fallah et al. solving the problem for mean estimation while Anjarlekar et al. extending that work for the case of logistic regression. 2) The assumptions made in the paper do not seem practical (for example assumptions 3 and 4) Technical Quality: 3 Clarity: 2 Questions for Authors: 1) It is unclear to me why the authors have used Joint Differential Privacy instead of the original DP definition. Can the authors provide more justification for this? 2) Assumption 3 seems a bit vague. Can the authors clarify the specific structure of the upper bound used in the assumption? It seems more clear to have f(.) which is a monotonically increasing convex function of $\epsilon$. 3) Can the authors clarify more about the practical validity of Assumption 4? 4) A literature survey related to incorporating payments in differentially private models seems incomplete. Some relevant works are as follows [a] Justin Kang, Ramtin Pedarsani, & Kannan Ramchandran. (2024). The Fair Value of Data Under Heterogeneous Privacy Constraints in Federated Learning. [b] Ameya Anjarlekar, Rasoul Etesami, & R. Srikant. (2023). Striking a Balance: An Optimal Mechanism Design for Heterogenous Differentially Private Data Acquisition for Logistic Regression. 5) Can be approach be extended to scenarios incorporating heterogeneous differential privacy? Similarly can the proposed approach work for larger models such as deep neural networks? 6) It would have been better to add some experimental results to highlight how the payments and model error varies with a change in the differential privacy guarantees and other parameters. Confidence: 4 Soundness: 3 Presentation: 2 Contribution: 2 Limitations: NA Flag For Ethics Review: ['No ethics review needed.'] Rating: 3 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: >W1: The paper seems to be a slight extension of differentially private logistic regression while also incorporating payments into it which does not seem like a major extension given the earlier works of Fallah et al. or Anjarlekar et al. have incorporated incentive-compatible payment mechanisms in traditional DP settings with Fallah et al. solving the problem for mean estimation while Anjarlekar et al. extending that work for the case of logistic regression. *We respectfully disagree with the reviewer regarding the contribution of our work compared to the work of Fallah et al. [1] or Anjarlekar et al [2]. Importantly, this paper is not a slight extension of DP logistic regression, and it is totally different from the work you mentioned.* * *Our proposed DP algorithm is not adapted from DP logistic regression or mean estimation literature [1,2].* The work of Anjarlekar et al. [2] is based on the previous literature on objective perturbation, which is an iterative algorithm. And the work of Fallah et al. [1] is based on adding Laplacian to a weighted mean. Compared to them, we developed a new closed-form estimator for sparse linear regression. * *The methods you mentioned cannot solve our problem.* Specifically, it is unknown where the objective perturbation method is suitable for high-dimension sparse linear regression, even if we only consider DP, as the utility will always depend on the dimensionality. the work of Fallah et al. [1] is based on adding Laplacian to a weighted mean, which obviously cannot solve our problem. * We provided theoretical results on individual rationality, Bayesian Nash equilibrium, and the payment budget, which have not been given by previous work Anjarlekar et al. [2]. * While there has been work on incorporating IC payment scheme into DP setting, we want to highlight that *our paper are the first work to study in the high dimensional setting.* High dimensionality gives rise to several consequences: (1) the regularization techniques used by prior work are not applicable, (2) a (novel) covariance matrix estimator is needed to guarantee the invertibility, (3) this assumption precludes the use of the output perturbation mechanism adopted in the previous work and therefore we seek to privatize by sufficient perturbation scheme, which in turn greatly makes our truthful analysis part more complicated. We strongly recommend the reviewer to go through Section.C in the Appendix for a comprehensive understanding and accurate evaluation of our work. [1] Fallah, Alireza, Ali Makhdoumi, Azarakhsh Malekian, and Asuman Ozdaglar. "Optimal and differentially private data acquisition: Central and local mechanisms." Operations Research 72, no. 3 (2024): 1105-1123. [2] Anjarlekar, Ameya, Rasoul Etesami, and R. Srikant. "Striking a Balance: An Optimal Mechanism Design for Heterogenous Differentially Private Data Acquisition for Logistic Regression." arXiv preprint arXiv:2309.10340 (2023). >W2: The assumptions made in the paper do not seem practical (for example assumptions 3 and 4) We made five assumptions throughout the paper. - Assumption 1 is the boundedness of the underlying parameter $\theta^$ and the covariance matrix. As we mentioned in the paper, such assumptions have also been used in existing literature. - Assumption 2 is sub-Gaussianity on the covariate vector and response. Note that such an assumption is natural in the literation of statistical estimation and is weaker than the boundness assumption in [1, 2]. - Assumption 3 is a stronger version of [1]. We mimic their assumption on upper bounding the privacy cost function but instead of quadratic bound, we use cubic bound. This is a bit stronger since our assumption on the distribution of response is more relaxed than prior work and we consider the high dimensional sparse setting. Note that the quadratic bound assumption for $(\epsilon,\delta)$-DP is reasonable, as mentioned in Appendix D of [1]. We would like to point out that the upper bound on the privacy cost function is necessary for truthfulness analysis and it is also reasonable to assume that strategic users have bounded privacy cost functions.* We will leave the problem of how to relax the assumption in future work. - Assumption 4 is the conditional independence of privacy cost coefficient $c_i$ of a user $i$ and the data of the other user's data $D_{-i}$ and cost coefficient $c_{-i}$ given a user's data $D_i$. *This is a practical assumption since in our setting users are also concerned that their payment might be inferred from the privacy cost coefficient.* This also means $c_i$ does not reveal any additional information about the costs or data of any other users. - Assumption 5 is the exponential tail decay of $c_i$ which we adopt from [1, 2]. We believe that each of these assumptions is necessary to carry out the analysis and also reasonable in practice. Please see below for more explanation about Assumption 3 and 4. [1] Cummings, Rachel, Stratis Ioannidis, and Katrina Ligett. "Truthful linear regression." Conference on Learning Theory. PMLR, 2015. [2] Qiu, Yuan, Jinyan Liu, and Di Wang. "Truthful Generalized Linear Models." arXiv preprint arXiv:2209.07815 (2022). --- Rebuttal 2: Title: (Cont'd) Response to Reviewer BxFH' s questions Comment: >Q1: It is unclear to me why the authors have used Joint Differential Privacy instead of the original DP definition. Can the authors provide more justification for this? Full differential privacy requires that all outputs by the mechanism, including the payment it allocates to a user, are insensitive to every user’s input. In our strategic user setting, the payment to every user is supposed to be kept secret. Therefore, it is more natural to assume that the payment $\pi_i$ to each user is only observable by the user $i$ while the estimate $\hat{\theta}$ is publicly observable. This consideration exactly falls into the motivation of Joint Differential Privacy. >Q2: Assumption 3 seems a bit vague. Can the authors clarify the specific structure of the upper bound used in the assumption? It seems more clear to have $f(.)$ which is a monotonically increasing convex function of $\epsilon$. The monotonicity in $\epsilon$ is intuitive: smaller values imply stronger privacy properties. Specifically, $\epsilon = 0 $ indicates the output is independent of user $i$’s data. Moreover, we use cubic term in $\epsilon$ to provide stronger constraints. However, it should be noted that the bounding function $F = c_i (\delta+ 1) \epsilon^3$ is not associated with convexity. In our proof, we also did not use the convexity property. >Q3: Can the authors clarify more about the practical validity of Assumption 4? In Assumption 4, we introduce the privacy cost coefficient $c_i$ as a random variable, sampled from some distribution. As mentioned earlier, the payment $\pi_i$ to each user is supposed to be private and the amount of payment is strongly linked to the privacy cost $c_i$. Therefore, it is very natural to assume that $c_i$ depends on each user's own data $D_i = (x_i,y_i)$ and conditioned on $D_i$, $c_i$ does not reveal any additional information on any other user's cost coefficient or data. Otherwise, a strategic user can use his privacy cost coefficient to infer other users' payments. >Q4: A literature survey related to incorporating payments in differentially private models seems incomplete. Some relevant works are as follows [a] Justin Kang, Ramtin Pedarsani, Kannan Ramchandran. (2024). The Fair Value of Data Under Heterogeneous Privacy Constraints in Federated Learning. [b] Ameya Anjarlekar, Rasoul Etesami, R. Srikant. (2023). Striking a Balance: An Optimal Mechanism Design for Heterogenous Differentially Private Data Acquisition for Logistic Regression. We thank the reviewer for providing the relevant literature to us. We will add them to the related work section. >Q5: Can be approach be extended to scenarios incorporating heterogeneous differential privacy? Similarly can the proposed approach work for larger models such as deep neural networks? Sadly, our current framework is not suitable for extending to other scenarios like heterogeneous differential privacy. This is because our privacy guarantee relies on the Billboard Lemma to broadcast the original DP to JDP, and it is unknown whether there is a heterogeneous version of Billboard Lemma. Meanwhile, designing high-dimensional truthful mechanisms with privacy constraints is an intrinsically hard problem. Our mechanism cannot be directly applied to larger models such as DNNs like many other truthful mechanisms. Given this, we believe that our work has been a leap and paved the way for future research. Please see the above for response to question 6 --- Rebuttal Comment 2.1: Comment: We thank the reviewer for their time and for mentioning the related work which we have not included. We will add these to our paper. If our response has addressed your concerns and positively influenced your view of our paper, we kindly ask you to consider revising the score.	Summary: This paper focuses on mechanism design that incentivizes truthful data reporting while preserving privacy in the context of high dimensional sparse linear regression. The proposed mechanism is $(o(1),O(n^{-Omega(1)}))$-jointly differentially private, provides an estimator that is $o(1)$ accurate, is an approximate Bayes NE where most of the agents report truthfully, asymptotically individually rational, and requires a small payment budget. Strengths: 1. This paper has a very clean presentation despite the complicated problem setting and technical components. 2. The theoretical guarantees are comprehensive, including estimation error, privacy guarantee, truthfulness, individual rationality, and budget. 3. The private estimator is quite interesting. Weaknesses: Currently, each agent only collects one data point. Is it possible to study the free-riding issue as well under the current framework? Technical Quality: 3 Clarity: 3 Questions for Authors: See above Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: See above Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for posing an interesting question. In our setting, we need to assume each user can only manipulate the response. Thus, it is unclear at this point whether our payment scheme can tackle the free-rider issue. We will leave it as a future work. --- Rebuttal Comment 1.1: Comment: Thank you for your reply. I have no more questions.	null	null	Rebuttal 1: Rebuttal: Response to Reviewer BFxH's question 6 about adding experiment >Q6: It would have been better to add some experimental results to highlight how the payments and model error varies with a change in the differential privacy guarantees and other parameters. We wish to underscore that the essence of our contribution is theoretical. We would also like to bring the reviewer's attention to the broader field of truthful mechanism design where the majority does not have experiments. Some preliminary experiment results are provided now and more results will come out in our finalized version. This figure plots the results of our mechanism. It is clear from the figure that when the sample size increases, the error goes down for every value of $\epsilon$. Different privacy budget values $\epsilon$ do make a great difference in error under a small data size regime. When the data size becomes larger, all errors quickly reduce to a very low level. This matches our estimation error $\tilde{O}(\frac{\sqrt{k}}{\sqrt{n}\epsilon})$. Pdf: /pdf/8a88f17cc12ef6b763708662bc60dc8b7afce2c7.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Generalizable Implicit Motion Modeling for Video Frame Interpolation	Accept (poster)	Summary: The authors propose GIMM to effectively model intermediate motions. Three core designs are: normalization over the initial bidirectional flows, motion encoding (spatiotemporal motion latent extraction from flows) and adaptive coordinate-based INR. The framework first extracts bidirectional flows of the input frames via off-the-shelf optical flow models (e.g., RAFT) and normalizes them. Next, a Motion Encoder extracts motion features from the normalized flows. The motion feature maps are forward warped respective to the target timesteps. A Latent Refiner refines the warped motion features, and using the refined motion features, a coordinated-based MLP network predicts the normalized flow maps from the target timestep, which could be reversed to the bidirectional flows of original scales for frame synthesis. This implicit motion modeling framework is first individually trained with reconstruction loss on the predicted flow maps. Once it is pre-trained, a frame synthesis module is attached at the end of GIMM, which is jointly trained in an end-to-end manner with frame reconstruction loss. Strengths: 1. Strong results: the visualized video in the supplementary video and the visualized motions fields look great in quality. 2. To my knowledge, use of INRs for motion modeling in VFI, without training at test time is a novel approach. Weaknesses: 1. Lack of Experiments 1.1 Benchmarks - The authors use the test set from X4K1000FPS [42] and SNU-FILM-arb for evaluation, where SNU-FILM-arb is a dataset introduced by themselves. Although there are diverse public datasets available for evaluation, they do not report the experimental results on the public datasets prevalently used in the field. Namely, Vimeo90k [49] is the most commonly used dataset, which they used for training and evaluation of modeled flows. I wonder the frame interpolation performance on Vimeo90k, as I believe there is no reason not to report them. In addition, I think there could have been other options for arbitrary-timestep frame interpolation benchmarks, e.g., Adobe240fps [52]. The proposed SNU-FILM-arb could be a useful benchmark for future studies, but I think they should have shown the validity of their method with public benchmarks before that. 1.2 Ablation studies I find the ablation studies of their method is a bit limited. The main points of their arguments are not experimentally verified in the ablation studies. I find the ablation studies in Table 2 to be a little off-topic, not focused on the main arguments. - Normalization: although they claim normalization of flows over scales and directions is one of the key designs of the framework in the abstract and introduction, the experimental results on its effectiveness cannot be found in Section 4.2 and Table 2. - Motion encoding: similar to normalization, the experimental studies on the effectiveness of motion encoding cannot be found in the paper. They only show how the Latent Refiner affects the performance, but not the motion encoding process, which is one of the contributions that the authors claim. - Generalizability: The title and the abstract emphasizes the 'generalizability' of the method, but do not show any experiments on generalizability. Although they argue that their method can be smoothly integrated with existing flow-based VFI works, there is no experiment on it. This part especially makes me consider the paper to be a bit over-claimed. 2. Weak Analysis / Explanations This is aligned with my concern aforementioned in 1.2 Ablation studies. The authors do not give a good explanation of the results or try deeper analysis on their main arguments. - Normalization: In the abstract and introduction, the authors claim that normalization of flows are one of the key designs, but neither do they experimentally show or intuitively explain its importance / role. I think there should have been at least an intuitive explanation of its necessity, along with an experimental result supporting it. The authors mention that they perform normalization following IFE[13], but if that is the case simply following prior work, it cannot be a contribution of the paper. Should the authors of the paper claim this to be a contribution, it needs further analysis. - INR: to my understanding, this part is the biggest contribution of the paper. However, I am not very convinced with the use of INRs. To my understanding, the INR takes the 3D coordinate as the input along with the motion latent codes at each pixel. I wonder why the spatial coordinates are necessary, as it will always predict the flow of its own spatial position. Furthermore, in that case, the target timestep t is the only part that would make the difference, which makes me curious why we have to adopt the INR form rather than another form of conditioning mechanism. For instance, I think a conditional U-Net used in the diffusion literature could suffice. The authors do not give a solid explanation of why the INR form is necessary, and I wish to hear a clarified explanation. 3. Presentation I feel that some important details, especially the core designs, are not described sufficiently. For instance, although the INR part is the largest contribution of the method, it is explained with only a couple of lines in the main manuscript, and the supplementary materials does not provide sufficient explanations. My main questions (#2 above & #1 in Questions) rise from the ambiguous description of the INR part. What is the input / output of the INR model, how are the input / output tensors shaped, etc. I had to make assumptions on this part, which made me fundamentally wonder why the INR form is necessary. [52] Su, Shuochen, et al. "Deep video deblurring for hand-held cameras." Proceedings of the IEEE conference on computer vision and pattern recognition. 2017. Technical Quality: 2 Clarity: 2 Questions for Authors: 1. What is the input / output of coordinate-based MLP (INR), and why are the spatial coordinates necessary? - I had a hard time trying to understand this. To my understanding, the motion latent code L_t from the Latent Refiner would have a shape of H x W x D where H, W, D denote height, width and dimension, respectively. According to the main paper and the supplementary, the latent L_t and 3D coordinates x,y,t are concatenated and fed to the SIREN network. In that case, the concatenated representation would have a preserved spatial size of HxW, with each coordinate having different latent code L_t. If that is the case, as mentioned in the weakness section above, I believe there is not much reason to include the spatial (x,y) coordinates as the input of the INR network as the network predicts the latent flow of its own spatial coordinate, and I even wonder why an INR form is necessary. For example, can't it be simply be in a form of a conditional U-Net, with target time-steps given as in diffusion literature? The experiments in Table 2 show that the use of spatial coordinates do affect the performance, but I failed to understand the reason for this. Could there be an explanation on the reason for the increase? There could possibly be some misunderstandings by me and wish for some clarifications, as it is a very important component of the paper. 2. What is the input / output of the Latent Refiner? - According to the Fig.2 of the main paper, the output of the Motion Encoder K_i seems to be fed to the Latent Refiner. However, in the supplementary, Latent Refiner does not seem to take K_i as input, but only the warped motion features only. I wonder what is the right visualization. - In connection to the #1 question above, I understood that the output of Latent Refiner to be of shape H x W x D. I feel that it should be correct, but feel uncertain since there is not much description on it. 3. How is the normalization of flows done? With maximum scalar values? With a large constant value? Or by log-scaling? I wonder how it is done, for the paper to be self-contained. 4. How is the forward-warping method evaluated for motion modeling in Table 1? To my understanding, the backward flows from the target timestep, F_{t->0} and F_{t->1} are used for evaluation. However, forward warping could only provide F_{0->t} and F_{1->t}. which does not sound like a fair comparison. Did the authors use techniques such as flow reversal [48] or complementary flow reversal [42]? 5. I wonder the computational costs of the framework, i.e., number of parameters, runtime, with comparison to state-of-the-art methods. The proposed framework seems to consist of many modules which could possibly require vast computational costs. Confidence: 4 Soundness: 2 Presentation: 2 Contribution: 2 Limitations: Yes, the authors have addressed their limitations. Flag For Ethics Review: ['No ethics review needed.'] Rating: 3 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for the constructive comments. Please find the following for our response. > Q1:The authors use the test set ... I wonder the frame interpolation performance on Vimeo90k,... A1: Due to the word limit, please refer to the global response and A5-2 in our response to Reviewer rbyn. > Q2: ... other options for arbitrary-timestep frame interpolation benchmarks, e.g., Adobe240fps [52]. Thanks for your suggestion. We calculate PSNR on the Adobe240fps following the evaluation settings of IFRNet [24] and use the test split divided by VideoINR [7]. The results are listed below: \| Method \| Adobe240fps (PSNR) \| \| --- \| --- \| \| IFRNet \| 31.08 \| \| AMT \| 30.70 \| \| UPR-Net \| 32.01 \| \| CURE \| 31.64 \| \| EMA-VFI \| 31.26 \| \| GIMM-VFI-R \| *32.31* \| \| GIMM-VFI-F \| 32.33 \| Our method achieves stronger performance. This further illustrates the effectiveness of our method for the arbitrary-timestep VFI task. > Q3: What is the input / output of coordinate-based MLP (INR) A3: We concatenate of the motion latent of $D \times H \times W$ and spatiotemporal coordinates of $3 \times H \times W$ as the input to the INR. The INR outputs the corresponding normalized flow. > Q4: ... why an INR form is necessary ... can't it be simply be in a form of a conditional U-Net, with target time-steps given as in diffusion literature? A4: As described in Section 2, the INRs have effective modeling ability for complex, high-dimensional data and can learn continuous mapping from a set of coordinates to a specific signal. Thus, we are motivated to leverage the INR for continuous motion modeling at arbitrary timesteps. We experiment by replacing the INR with a timestep-conditioned U-Net as in diffusion literature. The results on VTF, VSF and model parameters are listed below: \| Method \| VTF(PSNR) \| VTF(EPE) \| VSF(PSNR) \| VSF(EPE) \| Params \| \| --- \| --- \| --- \| --- \| --- \| --- \| \| GIMM (U-Net) \| 36.96 \| 0.39 \| 29.96 \| 2.90 \| 4.27M \| \| GIMM (INR) \| 37.56 \| 0.34 \| 30.45 \| 2.68 \| 0.25M \| Replacing INR with U-Net results in worse performance, especially on the 6X motion modeling benchmark VSF. This demonstrates the strong continuous modeling ability of INR. Besides, GIMM with INR has a much lighter architecture which improves the efficiency. Therefore, it is necessary and proper to use INR for continuous motion modeling. > Q5: ... the use of spatial coordinates do affect the performance, but I failed to understand the reason for this ... A5: As explained in A4, we are motivated to use INR for its effective modeling ability, learning a continuous mapping from a set of coordinates to a specific signal. The coordinates provide positional information for INRs and help to learn continuous mapping since the coordinates are inherently continuous. In our motion modeling, we aim to model continuous motion between timesteps. The motion refers to dense optical flows, which consist of spatiotemporal changes. Therefore, it is necessary to use spatial coordinates for effective motion modeling. The experiment results in Table 2 demonstrate the necessity in practice. > Q6: why the spatial coordinates are necessary, as it will always predict the flow of its own spatial position. A6: In addition to A5, we would like to further clarify that motion latent code serves as a function space for the implicit representations of different instances. The latent code is used for making INRs generalizable which means no need for test-time optimization. The spatiotemporal coordinates are still required for continuous modeling of spatiotemporal changes, such as dense optical flow in our case. Similar insights are shared in the related literature [5]. > Q7: Generalizability:... A7: As described in Section 2 (page 3) and Section 3.2 (page 4), “generalizability” means the generalizable modeling ability of the generalizable INRs (GINRs) across different instances. Unlike per-instance modeling INRs, GINRs do not require test-time learning. Our GIMM takes the motion latent code as an additional input to the INR and achieves generalizable motion modeling without the need for test-time optimization. A similar definition for generalizability can be found in the referenced paper [23]. > Q8: How is the forward-warping method evaluated for motion modeling in Table 1? A8: The forward-warping method produces 'backward' flows $F_{t→0}$ and $F_{t→1}$ from estimated flows $F_{0→1}$ and $F_{1→0}$ without flow reversal techniques. For example, $F_{t→0}$ can be easily obtained from $F_{t→0}=Fwarp(F_{1→0}\cdot t,F_{1→0}\cdot(1-t))$, where $Fwarp(a,b)$ indicates forward warping the objective $a$ with the referenced motion vector $b$. > Q9: I wonder the computational costs of the framework. A9: Due to the word limit, please kindly refer to the global response. > Q10: How is the normalization of flows done? A10: The normalization process follows IFE[13]. We agree with the reviewer and will delete this part from our key designs in our revised manuscript. > Q11: Motion encoding: … the experimental studies on the effectiveness of motion encoding cannot be found in the paper… A11: Thanks for your suggestion. Due to the word limit, please refer to the global response. > Q12: What is the input / output of the Latent Refiner? A12: The Latent Refiner refiner takes both the motion features and the coarse motion latent (warped motion features) as input and outputs the residual for the coarse motion latent. We will update the figure of Latnet Refiner’s architecture in the supplementary of our revised manuscript. > Q13: Presentation. I feel that some important details, ..., What is the input / output of the INR model, how are the input / output tensors shaped, etc…. A13: Thanks for your suggestion. We will specify more details about the INR in the revised manuscript. --- Rebuttal 2: Comment: Thank you for the detailed response. ### Q1. Vimeo90k My concerns on Vimeo90k has been partially addressed. To make myself clear, my initial concerns on Vimeo90k was raised since I could not understand the main reason for using VTF and VSF as a main benchmark, as it is on flows, which is not the ultimate goal of VFI. Although It could be a benchmark to show that the proposed framework models motion fields properly, I believe it is a limited benchmark, which could only serve as an assistance to frame reconstruction, for deeper analysis on the method, and cannot be a main benchmark for comparing the validity as a VFI method. Yet, the authors seem to use the VTF and VSF as one of the main benchmarks, considering the responses in the rebuttal. I wonder the reason for this, as the performance on flow reconstruction does not necessarily mean better frame interpolation results, although it has a correlation. If the reconstruction performance between the flows and frames perfectly correlate, I think it is reasonable to report the frame reconstruction performance on original benchmarks, rather than reporting the flow reconstruction performance with a modified benchmark.  Could the authors provide further explanations on this matter? ### Q3 - Q6. Necessity of spatial coordinates Thank you for the response. However, I still struggle to understand and agree with the use of spatial coordinates. The authors cite [5] as a work that shares the same insight, but to my understanding, there is a crucial difference to [5]. In [5], the model takes relative spatial coordinates between the query coordinate and the reference latent code as the coordinate input. Let $(x,y)$ be spatial coordinates of an image. The work of [5] is on image super-resolution, and they use coordinates of $(0,0), (0,1), (1,0), (1,1)$ to predict the RGB of $(a,b)$, where $0<a,b<1$. Their INR model uses latent codes at $(0,0), (0,1), (1,0), (1,1)$ along with their corresponding relative coordinates to the query coordinate, $(a,b), (a, 1-b), (1-a, b), (1-a, 1-b)$, respectively, as inputs. Formally, it would be as follows: $z_{(a,b)}^1 = f(z_{(0,0)}, (a,b)), z_{(a,b)}^2=f(z_{(0,1)}, (a, 1-b)), z_{(a,b)}^3 = f(z_{(1,0)}, (1-a, b)), z_{(a,b)}^4 = f(z_{(1,1)}, (1-a, 1-b))$, where $f$ is the INR function. I believe this is meaningful, as the goal of the INR model output is to predict the RGB of a different coordinate to the input latent code. However, according to GIMM’s formula, the INR model predicts the feature of the same position to the motion latent code, of which I think is not necessary. Putting the GIMM formula in the form of equation above, it would be something like this: $Z_{(a,b)} = f(z_{(a,b)}, (a,b))$. The latent code of $(a,b)$ predicts the feature of the same location, different to the formula of LIIF [5]. Here, I do not think the coordinate information of $(a,b)$ is necessary to the function $f$. For further explanation, Eq.2 of [5] takes $x_q - v^$ as the coordinate input of the INR model, whereas I believe the GIMM formula takes $x_q$ itself as the coordinate input. $x_q$ denotes query coordinate and $v^$ denotes the coordinate of reference (key) latent code. This is very different. The authors express continuous mapping using the spatial coordinate inputs, but it still fails to convince me, as this task does not require continuous representation in terms of the spatial dimension, with the input and output sharing the same spatial size. ### Q7. Generalizability Thank you for the clear response. It has been well addressed that the term ‘generalizability’ has been used different with my understanding, and in that case, the use of such term is understandable. However, the main part that caused the confusion and still concerns me is, “Our GIMM can be smoothly integrated with existing flow-based VFI works without further modifications”, which is claimed in the abstract and conclusion. This part has not been shown adequately, without experiments, and I still feel that this part is an overclaimed part. ### Q8. Forward warping Thank you for the clarification. I think it would be better if described in the paper. ### Q2, Q9-Q13. Thank you for the clarification. Although some of my questions have been clarified, the clarified parts are mostly on further description of the method. Yet, I still believe that the current version of the paper contains several overclaims (e.g., necessity of spatial coordinates, generalizability to existing VFI works). --- Rebuttal Comment 2.1: Comment: Dear Reviewer ZRiZ, Thank you for the feedback. Regarding your concerns, we would like to clarify further. Please find the following for our response. > New-Q1: Q3 - Q6. Necessity of spatial coordinates > New-A1: We would like to clarify that it is necessary for GIMM to include spatial coordinates within its input. To make it clearer, we first summarize three important explanations that we made in the rebuttal, numbered 1), 2) and 3) as below: 1)(A4) INRs can effectively learn continuous mappings from a set of coordinates to a specific signal. 2)(A5) Our INR-based method GIMM should include spatial coordinates in its input, since GIMM models dense optical flows between timesteps which contain spatiotemporal changes. 3)(A6) We cite [5] (Please refer to the “Learning implicit function space.” paragraph in Section 2 of [5]) for the shared insight that latent code serves as a function space for the implicit representations of different instances. The latent code is used for making INRs generalizable — free of test-time optimization. The coordinates are the key to learning continuous mapping since they are continuous. According to your feedback, we would like to clarify two points. i) We cite [5] (Please refer to the “Learning implicit function space.” paragraph in Section 2 of [5]) to explain the usage and effects of the latent code in INR. The latent code works as a function space to make the INR generalizable across instances. The latent code alone cannot achieve the best continuous modeling performance for the INRs, as can be observed in Table 2 (page 8). We didn’t cite [5] to discuss the necessity of spatial coordinates. ii) We integrate spatial coordinates with temporal coordinates in our GIMM’s inputs since GIMM is designed to continuously model the spatiotemporal changes of motion. Specifically, GIMM models dense optical flows, which vary in spatial distribution as the timestep changes. For instance, the optical flow associated with a moving ball will occupy different spatial positions at different timesteps. Consequently, we use spatiotemporal coordinates in our GIMM’s INR to enable continuous modeling of spatiotemporal changes. If we exclude spatial coordinates $(x,y)$ from our coordinates $(x,y,t)$, the continuous mapping learned won’t be spatiotemporal, and there is likely to be spatial noise for the predicted flows especially around the occluded regions. According to our Table 2 (page 8), spatial coordinates are proven to be necessary for GIMM’s motion modeling. > New-Q2: Q7. Generalizability and Plug-in ability of our method > New-A2: First of all, to avoid confusion in the response, we would like to clarify that “Generalizable/Generalizability” means the generalizable modeling ability of the generalizable INRs (GINRs) across different instances without requirements on test-time learning. As described in A7 and according to your feedback, your concern about the “Generalizable/Generalizability” term is well-addressed. Regarding your current concern about our model’s plug-in ability on existing flow-based VFI methods, we have conducted experiments during the rebuttal and demonstrated the effectiveness of our GIMM when GIMM is plugged into other VFI methods, such as IFRNet and TTVFI. Please refer to A5-1 in our response to Reviewer rbyn for more details. > New-Q3: Vimeo90k. … I could not understand the main reason for using VTF and VSF as a main benchmark…. > New-A3: We would like to clarify that our main benchmarks are arbitrary-timestep frame interpolation benchmarks, i.e., XTest and SNU-FILM-arb. We perform evaluations on these benchmarks, comparing our GIMM-VFI with VFI methods of different motion modeling strategies (Table 1, page 7) and with state-of-the-art methods (Table 2, page 8). Our core contribution is the GIMM module which performs motion modeling. To assess the modeled motion quality, we use the VTF and VSF as benchmarks. The results of these benchmarks are utilized to demonstrate modules’ motion modeling capabilities and to perform an ablation study on the GIMM module design. Therefore, for questions and justifications on the designs of GIMM, we evaluate the designs on VTF and VSF. --- Rebuttal 3: Title: New response to the feedback (Part 1) Comment: Thanks for your feedback on our response. We would like to clarify your current concerns further. Please find the following for our response. ### Necessity of spatial coordinates First of all, we would like to highlight our explanations of using spatial coordinates, as described in our previous responses. 1) Our GIMM aims to perform continuous motion modeling. The modeled motion is dense optical flows, which are of spatiotemporal changes. Therefore, GIMM aims to continuously model spatiotemporal changes. 2) We use INR to achieve continuous modeling since INR learns continuous mapping. The key fact for INR to learn continuous mapping is that the input coordinates are continuous. 3) Latent code serves as a function space for the implicit representations of different instances [5]. The latent code is not the key to learning continuous mapping. According to the above three points, we clarify that using spatiotemporal coordinates is necessary for our GIMM to continuously model the motion of spatiotemporal changes. We would also further make some specific clarifications according to the current feedback. > Q: The explanations they provided with an example of a moving ball, to my understanding, could make sense in a forward-warping based approach, but not in a backward-warping based approach. > A: We use the moving ball example as a piece of evidence for clarification in our above explanation 1), dense optical flows are of spatiotemporal changes. The spatiotemporal changes exist in all optical flows and all flows are faced with the problem of occlusion. This point is irrelevant to the warping approaches. > Q: According to their method, the latent codes of each spatial position would contain the history of pixels going through the corresponding locations with time, and would already contain the information necessary for their own location, which would only necessitate temporal timestep conditioning. > A: As described in the above explanation 2) and 3), the latent code is used to make INR generalizable. The key to achieving continuous modeling is the coordinates rather than the latent code. The latent code does not assure continuous modeling . Notably, the goal of our method is to continuously model the motion of spatiotemporal changes. Therefore, it is necessary to include spatiotemporal coordinates as the inputs to our INR in GIMM. > Q: If not predicting a flow of position different to the latent code, the spatial coordinate input for INR still seems redundant. > A: The goal of INR is to perform continuous modeling for its target signal, i.e., dense optical flows in our case. Simply using the latent code as input will not make continuous modeling. Since the flows are of spatiotemporal changes, the spatiotemporal coordinates are necessary for continuous modeling. In fact, the usage of spatiotemporal coordinates in INR can also be found in related literature [41]. --- Rebuttal 4: Title: New response to the feedback (Part 2) Comment: ### Plug-in ability > Q: In response A5-1 to the reviewer rbyn, the authors said “Notably, plugging in a better continuous modeling module doesn’t guarantee better model fitting since model fitting requires more on the model’s learning strategies and its overall design.” I think this statement contradicts the claim of their paper, where they say that their method “can be smoothly integrated with existing flow-based VFI works without further modifications”, although they somehow succeeded in integration with existing VFI works. > A: Please consider the full context of the quoted sentence from our response in A5-1. Here is the complete description with the context: “We would like to clarify that our method GIMM focuses on continuous motion modeling, which further enables frame interpolation at arbitrary timesteps. Arbitrary-timestep interpolation relies more on continuous modeling while fixed-timestep interpolation relies more on model fitting at the specific timestep of 0.5. Notably, plugging in a better continuous modeling module doesn’t guarantee better model fitting since model fitting requires more on the model’s learning strategies and its overall design.” We would like to summarize and further clarify the following: 1) Our method aims to perform continuous motion modeling. The continuous modeling ability further enables frame interpolation at arbitrary timesteps. Since the task we focus on is interpolation at arbitrary timesteps, the plug-in ability we referred to is for enhancing the arbitrary-timestep interpolation ability of the existing flow-based VFI works. 2) Arbitrary-timestep interpolation relies more on continuous modeling while fixed-timestep interpolation relies more on model fitting at the specific timestep of 0.5. The quoted sentence is used to explain that a module designed for the arbitrary-timestep interpolation task doesn’t guarantee its performance on the fixed-timestep interpolation task. Therefore, the quoted sentence neither contradicts our claim of plug-in ability nor holds relevance to it. > Q: The integration, for instance, to IFRNet, could have been possible, but not smoothly, as several components of IFRNet are not theoretically aligned well with the proposed method. > A: By integrating GIMM into existing flow-based VFI methods, we mean to use the flows from GIMM to replace the original flows in the VFI methods. For instance, regarding the IFRNet, we simply replace all the flows of IFRNet with the flows predicted by GIMM. We keep the architecture of the IFRNet exactly the same. We believe our operation of simply replacing the flows with ours (from GIMM) can be described as ‘smooth’. The same plug-in operation can also be found in Section 3.3 of the reference [13]. --- Rebuttal Comment 4.1: Comment: ## Plug-in ability 1. In response A5-1 to the reviewer rbyn~ Thank you for the clarifications. I now have understood that the main argument of the sentence was on continuous-arbitrary timestep. This part has been clarified. 2. Integration method However, on the integration with existing VFI works, I cannot agree with the authors. Replacing all the flows of IFRNet with flows by GIMM cannot be said to be smooth integration with existing flow-based VFI methods, in general sense. In that form of integration, it can no longer said to be IFRNet. The integration method described by the authors neglects important components of IFRNet, such as the hierarchical coarse-to-fine estimation of flows, and joint prediction of flows and features based on estimations from the previous stage. The IFRNet model simply becomes a decoder for frame synthesis, given flows from GIMM. It loses many important characteristics of the IFRNet model. Although I cannot figure the precise number, the number of parameters involved would also greatly differ, to my assumption. IFRNet has 5M params, while GIMM-RAFT has 19.8M params. In short, as the integration method the authors explained requires important changes to the original model, I do not think the proposed method can be considered to have a ‘smooth integration’ / ‘plug-in’ ability. If simple replacement of estimated flows on other flow-based VFI methods can be considered ‘smooth integration’, then majority of flow-based VFI methods can also claim the same thing, by replacing estimated flows by each other. In that case, it is no longer a novelty / contribution of the method. The authors cite [13], but the work of [13] do not mention / claim their method to have a great plug-in ability. As part of their framework, they simply use an existing flow-based VFI work for blending / frame synthesis. Given the authors’ response, my concern that this is an overclaim is firm. --- Reply to Comment 4.1.1: Title: Newer response to the feedback (Part 1/2) Comment: Thanks for your timely feedback on our response. We are glad that our previous responses have addressed some of your concerns. For the Integration method of our plug-in ability, we would like to clarify the following. > However, on the integration with existing VFI works, I cannot agree with the authors. Replacing all the flows of IFRNet with flows by GIMM cannot be said to be smooth integration with existing flow-based VFI methods, in general sense … The IFRNet model simply becomes a decoder for frame synthesis, given flows from GIMM. It loses many important characteristics of the IFRNet model. > As described in our previous response, we can simply use the flows from GIMM to replace the original flows in the existing VFI methods to achieve integration. We keep the architecture of the VFI method exactly the same and only the flows are replaced by ours. Take the IFRNet as an example, the IFRNet keeps all of its structures when integrating our GIMM into it. Named the model after integration as “IFRNet+GIMM”, it not only extracts image features of the input images but also predicts masks for warping and synthesising the interpolated frames. Both the hierarchical encoding and decoding part of the IFRNet are well-leveraged in “IFRNet+GIMM”. Therefore, we believe that the important attributes of IFRNet are kept and the integration/module plug-in is smooth. The experiments for the plug-in ability have been conducted in A5-1 of our response to the reviewer rbyn. We provide results with IFRNet as below: \| Method \| SNU-FILM-arb-4X \| SNU-FILM-arb-8X \| SNU-FILM-arb-16X \| \| --- \| --- \| --- \| --- \| \| IFRNet \| 34.88 \| 31.15 \| 26.32 \| \| IFRNet+GIMM \| 36.46 (+1.58dB) \| 32.20 (+1.05dB) \| 27.73 (+1.41dB) \| We believe that the plug-in ability of our GIMM is proven to be effective and easy to realize. > Although I cannot figure the precise number, the number of parameters involved would also greatly differ, to my assumption. IFRNet has 5M params, while GIMM-RAFT has 19.8M params. > It should be noted that 19.8M is the number of parameters for GIMM-VFI-R, our complete interpolation method implemented with RAFT. GIMM-VFI-R contains the RAFT flow estimator, GIMM and the frame synthesis module. When plugging in existing VFI methods, we simply integrate GIMM and optionally integrate the flow estimator if there are no flow estimators used in the VFI methods. In the case of the IFRNet, we integrate GIMM and the flow estimator RAFT. The number of parameters of the integrated module is 5.05M (RAFT of 4.8M plus GIMM of 0.25 M). Besides, it should also be noted that when comparing the performance of an interpolation method, the variant of the best performance is used. Therefore, IFRNet here refers to its best variant IFRNet-L, which has 19.7M parameters rather than 5M. --- Rebuttal 5: Title: Newer response to the feedback (Part 2/2) Comment: > If simple replacement of estimated flows on other flow-based VFI methods can be considered ‘smooth integration’, then majority of flow-based VFI methods can also claim the same thing, by replacing estimated flows by each other. In that case, it is no longer a novelty / contribution of the method. > We would like to clarify that our core module GIMM aims to perform continuous motion modeling. GIMM can take flows between the input frames and predict intermediate flow at any given timesteps. Furthermore, GIMM can also achieve good performance with different flow estimators, which makes it quite flexible. Notably, in Table 3 (page 8, GIMM-VFI-F vs. GIMM-VFI-R), we show that integrating a better flow estimator (FlowFormer [17]) can enhance model performance. To the best of my knowledge, no other existing VFI methods contain a similar module that i) is designed for continuous motion modeling with flows as input and ii) can be augmented flexibly with different flow estimators. Therefore, it is quite impossible or much harder for these existing VFI methods to provide proper continuous motion to achieve the plug-in ability claimed by us. By plugging in GIMM, existing VFI methods can achieve better arbitrary-timestep interpolation performance as proven in A5-1 of our response to the reviewer rbyn. Therefore, we believe that our GIMM is novel and has an effective plug-in ability. > The authors cite [13], but the work of [13] do not mention / claim their method to have a great plug-in ability. As part of their framework, they simply use an existing flow-based VFI work for blending / frame synthesis. > As described in our previous response, the specific operation of plugging in is to use the flows from GIMM to replace the original flows in the VFI methods. We cite IFE[13] because the same operation has been used in it. As described in the “Implicit neural representations.” paragraph in Section 2 (page 3), IFE [13] also considers implicit flow modeling but it focuses on per-instance modeling and it is NOT generalizable. Therefore, a plug-in ability to existing VFI methods across various instances is not claimed in their paper. We believe that IFE[13] does not contradict our claim. --- Rebuttal 6: Comment: Due to the limited discussion period, I leave my response on ones that could be quickly replied first, and may possibly fail to reply to all matters. ## Continuous modeling The authors emphasize the continuous modeling ability. Although their proposed design of using INRs for continuous modeling is novel, there are numerous methods capable of continuous modeling of flows. Many recent works either scale the bidirectional flows using the target timestep, i.e., in forms such as $F_{0 \rightarrow t} = t \times F_{0 \rightarrow 1}$, or use a conditioning method with the target timestep, and this way, continuous modeling of flows is in fact possible [1, 16, 18, 20, 21, 24, 32, 33, 42]. It is acceptable if the authors claim that their continuous modeling is more precise, but the claim that it is impossible for these existing methods to provide continuous motions in a plug-in form is not true. All of the methods cited above are capable of continuous estimation of flow maps at arbitrary timesteps, and their intermediate flows could also be plugged into other frameworks, in the sense of the authors use. Yet, none of these works do not claim their work to have a plug-in ability. Thus it is hard to say that their method has a special plug-in ability. ## IFE [13] > The same plug-in operation can also be found in Section 3.3 of the reference [13]. I belive this statement of the authors implies that [13] uses an plug-in operation, and I think the authors tried to use [13] to support that their plug-in strategy is valid. To my understanding, I think the authors' intention is that [13] do not have a plug-in ability, as their flow modeling method is "not generalizable", and is trained per-instance. However, I rather do not find this part important in the 'plug-in' perspective. If the authors claim 'generalizability' is the important part for plug-in ability, as mentioned above, numerous methods existing could also be said to have a 'plug-in' ability. ## IFRNet The experiments with IFRNet still does not sound to be be a 'smooth integration'. For a method to be easy to be 'plug-and-play' form, a framework needs to be capable of disentanglement. For instance, in flow-based VFI, a method should have explicitly separated parts of flow estimation and frame synthesis, so that the estimated flows can be smoothly replaced. However, IFRNet's contribution is 'joint' prediction of flows and features, which means that the prediction of flows and features could be entangled, and thus I find it awkward to replace the flows by predictions from GIMM. --- Rebuttal Comment 6.1: Comment: Thanks for the timely feedback. We would like to further clarify the following. ### Continuous modeling > … Many recent works either scale the bidirectional flows using the target timestep, i.e., in forms such as $F_{0→t} = t \times F_{0→1}$ … > We would clarify that for many recent VFI methods [18,24,27,50] that perform backward warping operations, e.g., IFRNet, they require bilateral flows $F_{t→0}$ and $F_{t→1}$. We believe there is no reason that $F_{0→t}$ should be used in such scenarios. > …, but the claim that it is impossible for these existing methods to provide continuous motions in a plug-in form is not true. All of the methods cited above are capable of continuous estimation of flow maps at arbitrary timesteps, and their intermediate flows could also be plugged into other frameworks, in the sense of the authors use… > Please quote our complete response. The original sentence is that: “it is quite impossible or much harder for these existing VFI methods to provide proper continuous motion to achieve the plug-in ability claimed by us.” We claim some methods are impossible (As described above, $F_{0→t}$ is not for flow-based VFI methods based on backward-warping) and some methods are much harder to plug in. GIMM focuses on the motion and can take flows between the input frames and predict intermediate flow at any given timesteps. The flows can be easily obtained from pretrained flow estimators. In contrast, the existing VFI methods take the input images as input and predicted flows that may not be appropriate to use in other VFI methods. Therefore, we believe that GIMM has an effective plug-in ability to enhance the existing VFI methods’ ability on arbitrary-timestep interpolation. Notably, this is proven by our experiments in A5-1 of our response to the reviewer rbyn. ### IFE [13] We would like to clarify that our GIMM can be plugged into the existing flow-based VFI methods. The “existing flow-based VFI methods” indicate methods that are able to perform interpolation across instances. Therefore, we believe that this is the reason that IFE[13] does not claim its plug-in ability as it requires performing per-instance optimization. Once more, as described in our previous response, the specific operation of plugging in is to use the flows from GIMM to replace the original flows in the VFI methods. We cite IFE[13] because the same operation has been used in it. ### IFRNet We would like to highlight that when integrating GIMM with IFRNet, we keep the original structure of IFRNet and simply replace its flows with ours. In our experiments, IFRNet+GIMM achieves a performance gain of over 1dB across all the subsets of the SNU-FILM-arb benchmark. Given the description above, GIMM makes IFRNet achieve significant improvements on arbitrary-timestep interpolation with a simple operation of replacing the flows. We believe that this can be evidence that our method can be integrated into the existing flow-based VFI methods, smoothly.	Summary: This paper proposes a plug-and-play Generalizable Implicit Motion Modeling module to refine the optical flow in the task of video frame interpolation. Specifically, this module combines several core components of normalization, motion encoder, latent refiner, and coordinate-based network to achieve implicit motion modeling. Experimental results demonstrate the superiority of the optical flow obtained by the proposed GIMM approach. Strengths: The accuracy of optical flow is an important issue that affects the effectiveness of video frame interpolation. It is valuable for the authors to model more accurate motion through implicit motion modeling. Weaknesses: 1.The K, F, and Z symbols in Equations 6-7 should be labeled in Figure 2. In addition, the description of L150-151 for K is confusing to read, especially F is expressed as the difference between two coordinates. 2.How does Equation 11 get the optical flow of GT? As far as I know, none of the existing VFI datasets have a corresponding optical flow. 3.Table 1 allows for a comparison of some of the methods that model more complex motion than just modeling linear motion, such as QVI, ABME, BMBC. 4.Table 3 should include parameter and runtime comparisons to demonstrate the effectiveness of the GIMM. 5. As a plug-and-play motion modeling module, Table 3, the authors should add GIMM to other existing flow-based VFI methods for a fairer comparison, e.g., ABME, TTVFI, RIFE, and IFRNet. Because the design of the optical flow estimation network and synthesis network used in the different methods are not the same, and the use of a higher performance optical flow estimation network also has a significant performance improvement. In addition, validation on vimeo and UCF101 is necessary. Technical Quality: 3 Clarity: 3 Questions for Authors: I'm most concerned about the efficiency of GIMM and the improvement it brings when plugged into other flow-based VFI methods. Confidence: 5 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: Thank you for the constructive comments. Please find the following for our response. > Q1: The K, F, and Z symbols in Equations 6-7 should be labeled in Figure 2. In addition, the description of L150-151 for K is confusing to read, especially F is expressed as the difference between two coordinates. > A1: Thanks for your suggestion. We will add the K, F, and Z symbols to Figure 2 and reformulate the description of L150-151 in our revised manuscript. > Q2: How does Equation 11 get the optical flow of GT? As far as I know, none of the existing VFI datasets have a corresponding optical flow. > A2: As described in Section 4 (page 6), we utilize Flowformer [17] to produce pseudo-ground truth optical flow for training and evaluation usages. > Q3: Table 1 allows for a comparison of some of the methods that model more complex motion than just modeling linear motion, such as QVI, ABME, BMBC. > A3: Thanks for your suggestion. We would like to clarify that our GIMM focus on continuous motion modeling for arbitrary-timestep interpolation with 2 frames as the input. While QVI takes 4 frames as input and ABME can only predict at the timestep of 0.5, BMBC is the only method that allows for continuous motion modeling and interpolation. Therefore, we extend Table 1 with experiments on BMBC. The results of BMBC’s motion modeling and interpolation compared with GIMM are listed below. \| Method \| VTF (PSNR) \| VTF (EPE) \| VSF (PSNR) \| VSF (EPE) \| SNU-FILM-arb-Hard \| \| --- \| --- \| --- \| --- \| --- \| --- \| \| BMBC \| 28.89 \| 0.95 \| 23.19 \| 8.23 \| 28.51 \| \| GIMM (-VFI-R) \|37.56 \| 0.34 \| 30.45 \| 2.68 \| 32.62 \| Our GIMM outperforms BMBC concerning both motion modeling and interpolation. This further demonstrates the effectiveness of our method. We will add this to Table 1 (page 7), in our revised manuscript. > Q4: Table 3 should include parameter and runtime comparisons to demonstrate the effectiveness of the GIMM. > A4: Please kindly refer to the "Parameters and Runtime" section in the global response. > Q5: As a plug-and-play motion modeling module, Table 3, the authors should add GIMM to other existing flow-based VFI methods for a fairer comparison, e.g., ABME, TTVFI, RIFE, and IFRNet. Because the design of the optical flow estimation network and synthesis network used in the different methods are not the same, and the use of a higher performance optical flow estimation network also has a significant performance improvement. In addition, validation on vimeo and UCF101 is necessary. A5-1: We would like to clarify that our method GIMM focuses on continuous motion modeling, which further enables frame interpolation at arbitrary timesteps. Arbitrary-timestep interpolation relies more on continuous modeling while fixed-timestep interpolation relies more on model fitting at the specific timestep of 0.5. Notably, plugging in a better continuous modeling module doesn’t guarantee better model fitting since model fitting requires more on the model’s learning strategies and its overall design. Therefore, in terms of continuous modeling, we evaluate the plug-in ability of our proposed GIMM on arbitrary-timestep interpolation benchmark SNU-FILM-arb rather than fixed-timestep interpolation benchmarks, such as Vimeo90K and UCF101. Since there is a time limit for the rebuttal, we plug in the GIMM module to two of the representative existing flow-based VFI methods, TTVFI and IFRNet, for the experiment. Particularly, we plug in GIMM with a pretrained flow estimator RAFT to IFRNet, since there is not an existing flow estimator in the model. The results of PSNRs are listed below. \| Method \| SNU-FILM-arb-4X \| SNU-FILM-arb-8X \| SNU-FILM-arb-16X \| \| --- \| --- \| --- \| --- \| \| TTVFI \| 34.48 \| 30.39 \| 26.24 \| \| TTVFI+GIMM \| 35.55 (+1.07dB) \| 31.60 (+1.21dB) \| 27.40 (+1.16dB) \| \| IFRNet \| 34.88 \| 31.15 \| 26.32 \| \| IFRNet+GIMM \| 36.46 (+1.58dB) \| 32.20 (+1.05dB) \| 27.73 (+1.41dB) \| Plugging in the GIMM module results in significant improvements for arbitrary-timestep interpolation. This demonstrates the effectiveness of GIMM for continuous modeling when integrated with existing flow-based VFI works. We will add this experiment to the Supplementary of our revised manuscript. A5-2:In order to prove GIMM-VFI's effectiveness of the overall design for interpolation, we further provide evaluations on Vimeo90K and UCF101. Following EMA-VFI [50], we train GIMM-VFI for fixed-timestep interpolation. For evaluation, we calculate PSNRs and compare our method GIMM-VFI with the aforementioned and other state-of-the-art methods. The results are listed below: \| Method \| Vimeo90K (PSNR) \| UCF101 (PSNR) \| \| --- \| --- \| --- \| \| IFRNet \| 36.20 \| 35.42 \| \| AMT \| 36.53 \| 35.45 \| \| UPR-Net \| 36.42 \| 35.47 \| \| ABME \| 36.22 \| 35.41 \| \| TTVFI \| *36.54\| 35.51* \| \| EMA-VFI \| 36.50 \| 35.42 \| \| CURE \| 35.73 \| 35.36 \| \| GIMM-VFI-R \| *36.54* \| *35.51* \| \| GIMM-VFI-F \| 36.67 \| 35.54 \| Two variants of GIMM-VF with different flow estimators, both achieve competitive performance. This further demonstrates our method's strong interpolation ability. --- Rebuttal 2: Comment: Dear Reviewer rbyn, We sincerely thank you for the review and comments. We have posted our response to your initial comments, which we believe has covered your concerns. We are looking forward to your feedback on whether our answers have addressed your concerns or if you have further questions. Thank you! Authors --- Rebuttal Comment 2.1: Comment: Thanks to the author for providing abundant experiments to solve my problem. In addition, I read the negative comments from reviewer ZRiZ, and I think that although INR has been explored in other areas, it is very appropriate for modelling continuous motion in video. Motion in video is varied, such as uniform motion, acceleration, rotation, etc., and a more generalised Implicit Motion Modeling is worth being accepted. I raise my rating to ACCEPT and I am confident that the authors can improve the problems mentioned by all reviewers in the final version.	Summary: This paper aims to solve the Video Frame Interpolation task. To improve the capability of effectively modeling spatiotemporal dynamics, the paper proposes a Generalizable Implicit Motion Modeling (GIMM) module to leverage the implicit neural fields to estimate the flow field at an arbitrary time step. GIMM takes the spatial coordinates, time, and the latent motion code as the input of an INR, which makes it generalizable to new scenes. Strengths: 1. The idea of using INR to achieve continuous time video frame interpretation is interesting but needs to be well investigated. 2. The performance of arbitrary-timestep interpolation is good. Weaknesses: 1. Novelty: The idea of using time-dependent generalizable INR is not new and has been explored in human motion synthesis [1]. [1] also uses the concatenation of spatial coordinates, time step and motion latent as the input for an INR MLP. Moreover, the way of using INR is very similar to CURE[41] in video interpolation. Can you elaborate more details on the difference between the two methods? It seems the performance improvement over CURE might be attributed to the pre-trained flow estimator. [1]. Wei, Dong, et al. "NeRM: Learning Neural Representations for High-Framerate Human Motion Synthesis." ICLR 2024. 2. Performance: In Table 1, GIMM (-VFI-R) only slightly outperforms a simple "Linear" approach on both Vimeo-Septuplet-Flow (VSF) and SNU-FILM-arb-Hard. Also, in Table 2, without spatial coordinates, the performance slightly drops. Do you even conduct ablation on the time variable? Maybe with only motion code as the input, the performance still remains similar? 3. The method relies on the pre-trained flow estimators, which may lead to a suboptimal solution. 4. Typo: "Latnet Refiner" in Figure 2 caption. Technical Quality: 2 Clarity: 2 Questions for Authors: 1. The paper is easy to read. 2. The paper concatenates the motion latent code and the coordinates as the input to achieve generalizable INR. It seems the latent code dominates the input as it has a higher dimension. Will it make the INR less spatial-sensitive? 3. A follow-up question is why not use meta-learning approaches or INR modulation [6]? Confidence: 4 Soundness: 2 Presentation: 2 Contribution: 2 Limitations: The paper discussed the limitations. Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for the constructive comments. Please find the following for our response. > Q1: Novelty: The idea of using time-dependent generalizable INR is not new and has been explored in human motion synthesis [1]. [1] also uses the concatenation of spatial coordinates, time step and motion latent as the input for an INR MLP. A1: We respectfully disagree with the reviewer that the idea of using time-dependent generalizable INR for motion modeling in Video Frame Interpolation lacks novelty due to the presence of NeRM. Although NeRM and our proposed method GIMM both leverage INR conditioned on coordinates and latent, they are quite different concerning the following main points. 1) GIMM performs the general type of motion modeling in the context of video frame interpolation. Unlike NeRM which focuses on human motion, GIMM models any types of motion that may exist within the input frames. 2) While NeRM synthesizes sparse pose motion at each timestep, GIMM predicts dense motion in the form of optical flow for the usage of interpolation. Consequently, GIMM requires spatial coordinates as the additional input to its INR for better modeling, akin to image-based INRs [5]. In contrast, NeRM only takes temporal coordinates. We plan to include NeRM in our references to enhance the comprehensiveness of our related work section. We will add this discussion in the revised manuscript. > Q2: Moreover, the way of using INR is very similar to CURE[41]... performance improvement over CURE might be attributed to the pre-trained flow estimator. A2: As described in the “Generalizable INRs.” paragraph in Section 2 (page 3), CURE directly learns generalizable INRs from video, while our method leverages generalizable INRs for motion modeling to improve intermediate frame synthesis for flow-based VFI. Besides, we would like to clarify that despite both CURE and our method have leveraged pre-trained flow estimators, i.e., RAFT, CURE still performs linear motion modeling with a strong assumption of motion overlapping that should lead to suboptimal results. As observed from Table 3, our GIMM-VFI-R consistently outperforms the CURE algorithm across all benchmarks, achieving PSNR improvements exceeding 1 dB. Additionally, GIMM-VFI-R effectively handles interpolation at 4K resolution where CURE encounters out-of-memory issues. Furthermore, CURE contains a heavier architecture of 51.28M parameters (31.49M larger than our GIMM-VFI-R) and requires a longer time in inference. > Q3. Performance: In Table 1, GIMM (-VFI-R) only slightly outperforms a simple "Linear" approach on both Vimeo-Septuplet-Flow (VSF) and SNU-FILM-arb-Hard. A3: As observed in Table 1 (page 7), the PSNR of our method is 0.36 dB and 0.20 dB higher than the "Linear" approach on the referred benchmarks, respectively. This improvement is significant, particularly considering that both methods utilize the pretrained flow estimator RAFT. > Q4: Also, in Table 2, without spatial coordinates, the performance slightly drops. A4: As shown in Table 2 (page 8), removing spatial coordinates causes a 0.16 dB drop of PSNR on VTF and a 0.06 increase of End-Point-Error on VSF. This demonstrates the crucial role of spatial coordinates. > Q5: Do you even conduct ablation on the time variable? Maybe with only motion code as the input, the performance still remains similar? A5: As presented in Table 2 (page 8) and analyzed in the “Implicit modeling.” paragraph in Section 4.2 (page 7), direct input motion latent code without using any coordinates results in a 0.52 dB decrease of PSNR on VTF and a 0.13 increase of End-Point-Error on VSF. This highlights the importance of implicit modeling in GIMM. > Q6: The method relies on the pre-trained flow estimators, which may lead to a suboptimal solution. A6: Due to the word limit, please refer to the "Pretrained flow estimator" section in the global response. > Q7: The paper concatenates the motion latent code and the coordinates as the input to achieve generalizable INR. It seems the latent code dominates the input as it has a higher dimension. Will it make the INR less spatial-sensitive? A7: Thank you for the suggestion. We reduce the dimension of motion latent from 32 to 8 and the results on VTF and VSF are listed below: \| Latent Dim. \| VTF(PSNR) \| VTF(EPE) \| VSF(PSNR) \| VSF(EPE) \| \| --- \| --- \| --- \| --- \| --- \| \| 8 \| 37.16 \| 0.35 \| 30.15 \| 2.74 \| \| 32 \|37.56 \| 0.34 \| 30.45 \| 2.68 \| Reducing latent dimension leads to worse performance, with reductions of 0.40dB and 0.30dB in the PSNRs on VTF and VSF respectively. This indicates that a proper choice of a higher dimension, e.g., 32, will help generalizable INR achieve better performance rather than impose negative effects on the implicit modeling. > Q8: A follow-up question is why not use meta-learning approaches or INR modulation [6]? A8: As suggested, we implement the Meta-learning approach [23] for modulating the weights of INR, specifically in modeling motion. We compare its performance on VTF and VSF with our method GIMM, and calculate their parameters. The results are listed below: \| Method \| VTF(PSNR) \| VTF(EPE) \| VSF(PSNR) \| VSF(EPE) \| Param. \| \| --- \| --- \| --- \| --- \| --- \| --- \| \| Meta-learning approach [23] \| 30.19 \| 0.88 \| 24.50 \| 6.80 \| 43.92M \| \| GIMM \|37.56 \| 0.34 \| 30.45 \| 2.68 \| 0.25M \| The Meta-learning approach performs much worse than GIMM while adding more than 170x larger model parameters. > Q9: Typo: "Latnet Refiner" in Figure 2 caption. A9: We will correct the typo in our revised manuscript. --- Rebuttal 2: Comment: Dear Reviewer LUi9, We sincerely thank you for the review and comments. We have posted our response to your initial comments, which we believe has covered your concerns. We are looking forward to your feedback on whether our answers have addressed your concerns or if you have further questions. Thank you! Authors	Summary: The paper proposed a video frame interpolation model, starting from an optical flow, encoding flows to spatial-temporal motion latent. The motion prediction model GIMM, took the encoded initial motion latent to arbitrary-timestep interpolation motions. Finally, the motions are used to predict bilateral flows which can warp with input frames to recover the interpolation result. Strengths: 1. The paper proposed a novel flow estimating model, which can estimate bidirectional flows according to input time steps and input frames' flows. The model can be inserted with any flow-estimating VFI model. 2. Quantitative and qualitative results show that the estimated flows are stable and sharp compared with baseline results. Providing a better interpolation result. Weaknesses: 1. The GIMM starts from pretrained flows, which may limit the network performance. In fact, recent VFI networks still tend to estimate blurry results according to inaccurate flow estimating while facing hard cases. 2. More perceptual quantitative indicators need to be shown in the paper, eg. FID or LPIPS. Technical Quality: 3 Clarity: 3 Questions for Authors: 1. Is the flow normalization model necessary? What are potential temporal inconsistencies mentioned in line 146? 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: Thank you for the constructive comments. Please find the following for our response. > Q1: The GIMM starts from pretrained flows, which may limit the network performance. In fact, recent VFI networks still tend to estimate blurry results according to inaccurate flow estimating while facing hard cases. A1: Please kindly refer to the "Pretrained flow estimator" section in the global response. > Q2: More perceptual quantitative indicators need to be shown in the paper, eg. FID or LPIPS. A2: Thank you for the suggestion. We add the perceptual metrics FID and LPIPS to Table 3 (page 8). We report the best results in boldface and the second best with *Italic boldface. The results are listed below: \| Method \| XTest-2K (LPIPS/FID) \| XTest-4K (LPIPS/FID) \| SNU-FILM-arb-4x (LPIPS/FID) \| SNU-FILM-arb-8x (LPIPS/FID) \| SNU-FILM-arb-16x (LPIPS/FID) \| \| --- \| --- \| --- \| --- \| --- \| --- \| \| RIFE \| 0.126/11.99 \| 0.152/13.52 \| 0.038/6.65 \| 0.072/11.99 \| 0.134/19.82 \| \| IFRNet \| 0.108/23.93 \| 0.164/23.75 \| 0.046/9.92 \| 0.066/11.65 \| 0.115/16.91 \| \| M2M \| 0.098/9.25 \| 0.158/8.67 \| 0.036/5.98 \| 0.061/10.13 \| 0.112/17.37 \| \| AMT \| 0.153/13.92 \| 0.187/13.97 \| 0.072/9.25 \| 0.089/10.34 \| 0.136/14.72 \| \| UPR-Net \| 0.104/10.75 \| 0.154/9.45 \| 0.033/6.09 \| 0.064/9.93* \| 0.111/*16.76* \| \| EMA-VFI \| *0.097* /7.21 \| 0.156/8.61 \| 0.041/7.07 \| 0.074/12.17 \| 0.130/19.58 \| \| CURE \| 0.111/26.42 \| OOM \| 0.035/6.98 \| 0.063/12.72 \| 0.114/22.62 \| \| GIMMVFI-R \| 0.113/6.52 \| *0.149/6.49* \| *0.033/5.89* \| *0.060/9.59* \| *0.110/16.45* \| \| GIMMVFI-F \| 0.103/*6.74* \| 0.142/*6.58* \| 0.031/5.86 \| 0.059/9.95 \| 0.109/16.79 \| Our proposed method GIMM-VFI achieves competitive performance according to these perceptual quantitative indicators. > Q3: Is the flow normalization model necessary? A3: As described in the “Flow normalization” paragraph in Section 3.2 (page 4), the normalization process aligns temporal direction and scales the values of input flows. First, without temporal direction alignment of the inputs, it would be hard to define the direction of the output flow $V_t$. The direction alignment is thus necessary. Second, for the scale operation, we experiment by skipping it and present results on VTF and VSF as below: \| Method \| Scale Operation \| VTF(PSNR) \| VTF(EPE) \| VSF(PSNR) \| VSF(EPE) \| \| --- \| --- \| --- \| --- \| --- \| --- \| \| GIMM \| No \| 32.07 \| 1.28 \| 22.23 \| 10.72 \| \| GIMM \| Yes \|37.56 \| 0.34 \| 30.45 \| 2.68 \| Skipping the scale operation performs much worse than the full GIMM settings across both benchmarks. It is therefore necessary to perform the complete flow normalization operation. > Q4: What are potential temporal inconsistencies mentioned in line 146? A4: The potential temporal inconsistencies refer to the possible bias and noises in the estimated flows between input frames. In order to mitigate their negative impacts on motion modeling, we employ a Motion Encoder (ME) to extract motion features. The ablation experiment on Motion Encoder can be found in the global response. --- Rebuttal 2: Comment: Dear Reviewer d4Ah, We sincerely thank you for the review and comments. We have posted our response to your initial comments, which we believe has covered your concerns. We are looking forward to your feedback on whether our answers have addressed your concerns or if you have further questions. Thank you! Authors	Rebuttal 1: Rebuttal: Dear Reviewers, We would like to thank all reviewers for providing constructive feedback that helped improve the paper. Due to the word limit, we provide explanations and experiments for concerns shared by multiple reviewers in the following. 1. Ablation on Motion Encoder (reviewer d4Ah and ZRiZ) We conducted experiments without the Motion Encoder for a direct comparison. The results of motion modeling are presented below. \| Method \| with ME \| VTF(PSNR) \| VTF(EPE) \| VSF(PSNR) \| VSF(EPE) \| \| --- \| --- \| --- \| --- \| --- \| --- \| \| GIMM \| No \| 37.05 \| 0.42 \| 30.26 \| 2.85 \| \| GIMM \| Yes \| 37.56 \| 0.34 \| 30.45 \| 2.68 \| GIMM implemented with ME produces higher-quality flows, demonstrating that Motion Encoder is indeed helpful for our motion modeling. We will add these results in Table 2 (page 8) of the revised manuscript. 2. Evaluations on Vimeo90K and UCF101 (reviewer rbyn and ZRiZ) We would like to clarify that our method focuses on continuous motion modeling, specifically for the arbitrary timestep interpolation task. Therefore, we didn’t include the evaluations on the fixed timestep interpolation benchmarks Vimeo90K and UCF101 in our submission. However, our proposed method still achieves competitive performance on the fixed-timestep interpolation benchmarks. We report the best results in boldface and the second best with *Italic boldface. \| Method \| Vimeo90K (PSNR) \| UCF101 (PSNR) \| \| --- \| --- \| --- \| \| IFRNet \| 36.20 \| 35.42 \| \| AMT \| 36.53 \| 35.45 \| \| UPR-Net \| 36.42 \| 35.47 \| \| ABME \| 36.22 \| 35.41 \| \| TTVFI \| 36.54* \| *35.51* \| \| EMA-VFI \| 36.50 \| 35.42 \| \| CURE \| 35.73 \| 35.36 \| \| GIMM-VFI-R \| *36.54* \| *35.51* \| \| GIMM-VFI-F \| 36.67 \| 35.54 \| Two variants of GIMM-VF with different flow estimators, both achieve competitive performance. This further demonstrates our method's strong interpolation ability. 3. Pretrained flow estimator (reviewer d4Ah and LUi9) As shown in Table 1 (page 7) and discussed in this paragraph (line 225, page 7), many works [20,32] leverage motion priors from RAFT [45] can achieve better performance than method without motion priors [50]. Notably, our GIMM outperforms existing methods [20,32] that utilize the same motion priors. This demonstrates that VFI methods can significantly benefit from pretrained flow estimators. Our GIMM offers the most substantial improvements. Furthermore, in Table 3 (page 8, GIMM-VFI-F vs. GIMM-VFI-R), we show that integrating a better flow estimator (FlowFormer [17]) can enhance model performance. 4. Parameters and Runtime (reviewer rbyn and ZRiZ) Following RIFE [19], we collect the models of each paper and test them on an NVIDIA V100 GPU with the same hardware for 480P frame interpolation. We report the parameters and runtime of each model and list them as below: \| Method \| Params. (M) \| Runtime (s/f) \| \| --- \| --- \| --- \| \| RIFE \| 10.71 \| 0.01 \| \| IFRNet \| 19.7 \| 0.03 \| \| M2M \| 7.61 \| 0.01 \| \| AMT \| 2.99 \| 0.03 \| \| UPR-Net \| 1.65 \| 0.04 \| \| EMA-VFI \| 65.66 \| 0.08 \| \| CURE \| 51.28 \| 0.98 \| \| GIMMVFI-R \| 19.79 \| 0.25 \| \| GIMMVFI-F \| 30.59 \| 0.29 \| Compared with INR-based interpolation methods, our proposed method performs the fastest interpolation and maintains a relatively light architecture. However, there is still a runtime gap between the INR-based method and the non-INR-based interpolation method, we leave it for future research. 5. Normalization (reviewer d4Ah and ZRiZ) As described in the “Flow normalization” paragraph in Section 3.2 (page 4), the normalization process aligns temporal direction and scales the values of input flows. First, without temporal direction alignment of the inputs, it would be hard to define the direction of the output flow $V_t$. The direction alignment is thus necessary. Second, for the scale operation, we experiment by skipping it and present results on VTF and VSF as below: \| Method \| Scale Operation \| VTF(PSNR) \| VTF(EPE) \| VSF(PSNR) \| VSF(EPE) \| \| --- \| --- \| --- \| --- \| --- \| --- \| \| GIMM \| No \| 32.07 \| 1.28 \| 22.23 \| 10.72 \| \| GIMM \| Yes \| 37.56 \| 0.34 \| 30.45 \| 2.68 \| Skipping the scale operation performs much worse than the full GIMM settings across both benchmarks. It is therefore necessary to perform the complete flow normalization operation. Although normalization is important, the normalization process follows IFE[13]. We agree with reviewer ZRiZ and will delete it from our key designs in our revised manuscript.	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
How does Inverse RL Scale to Large State Spaces? A Provably Efficient Approach	Accept (poster)	Summary: The paper studies IRL in linear MDPs. The authors first demonstrate that the feasible reward set cannot be efficiently learned in large state and action spaces. To address this challenge, they propose a new IRL framework called reward compatibility, where the goal is to learn a classifier that determines whether the expert is approximately optimal for a given reward. Using CATY-IRL, they also introduce a new sample-efficient algorithm for this task, which first explores the MDP via reward-free exploration (RFE) and then evaluates whether a given reward is compatible with the expert's demonstrations. Furthermore, for the tabular setting, they provide a tight minimax lower bound and show that a similar bound also improves on existing lower bounds for RFE. Lastly, the authors propose a novel problem setting of objective-free exploration, which generalizes RFE to arbitrary tasks of interest. Strengths: The paper provides a good and original contribution to the challenging problem of IRL in large state-action spaces. In my opinion, its strengths are: 1. Technical quality: The authors use elegant notation and carefully introduce all symbols. Moreover, clear proofs for all results are provided in the appendix. 2. Sample complexity bounds: The sample complexity of CATY-IRL is thoroughly analyzed for tabular MDPs, tabular MDPs with linear rewards, and linear MDPs. Additionally, a tight minimax lower bound for the tabular setting is given. This lower bound is particularly appreciated, as lower bounds are still rare in the IRL literature. 3. Originality: After proving that identifying the feasible reward set is intractable, the authors introduce the novel problem setting of checking for reward compatibility and provide a sample efficient algorithm for it. Weaknesses: 1. Motivation: While original, the motivation for learning a reward compatibility classifier is not entirely clear to me. I would expect the authors to better explain its usefulness and potential applications. 2. Writing: The paper is not easy to understand on the first read. There are many propositions and theorems, but more emphasis on motivation and intuition building would be beneficial. For instance, a simple example for Proposition 3.1 could help build geometric intuition. 3. Related work: The authors introduce reward non-compatibility as a novel metric for IRL. However, minimizing the suboptimality of the expert is a core idea behind many imitation learning and IRL algorithms, such as GAIL and others. Of course, in the unregularized setting minimizing the suboptimality would lead to trivial solutions. However, I would expect a discussion about similarities and differences to min-max IL/IRL in the main part of the paper. 4. Computational complexity: The authors claim that their algorithm is also computationally efficient, but I couldn't find a discussion about this. 5. This is a minor point, but in line 103 you use but don't introduce the notation $Y^X$ for the set of functions mapping from $X$ to $Y$. Moreover, slightly inconsistently the set of functions from $X$ to $\Delta^Y$ is denoted as $\Delta_X^Y$. Why don't you change the notation to $\Delta_Y^X$? Technical Quality: 4 Clarity: 2 Questions for Authors: How would you apply your algorithm to a real world IRL problem? What is the computational complexity of the classification step? Confidence: 3 Soundness: 4 Presentation: 2 Contribution: 3 Limitations: I think the practical limitations should be discussed more extensively. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the Reviewer for praising our analysis as solid and novel, and for noting the significance of the proposed lower bounds. We answer the Reviewer questions and comments below. ## Weaknesses 1- We divide the answer in two parts. First, we explain why learning a reward compatibility classifier is useful from a technical perspective. Next, we describe some applications. Our ultimate goal is to understand how many samples are necessary for inferring as much information as possible about the expert's reward function $r^E$ from demonstrations. Since the problem is ill-posed (underconstrained) [1,2], i.e., $r^E$ is only partially identifiable from demonstrations [3], we resort to understanding how many samples are needed to infer the constraints characterizing $r^E$, i.e., the feasible set (see Definition 3.1). However, as we demonstrate in Section 3, inferring the constraints, i.e., the feasible set, in Linear MDPs cannot be done either in a sample efficient manner (because of the lower bound in Theorem 3.2), or in a computational efficient manner (because it contains a continuum of functions, see lines 184-186). For these reasons, instead of learning the feasible set (i.e., the set of rewards with $0$ (non)compatibility), we propose to learn the set of rewards with $\Delta$ (non)compatibility (for some $\Delta>0$), and we demonstrate that this task is sample efficient (same upper bound as CATY-IRL, see Theorem 5.1) but not computationally efficient, because, again, the set contains a continuum of functions. Thus, we propose to learn a classifier, which can be seen as a trick for the practical computation of a set of infinite items. Beyond offering a significant characterization of the intrinsic complexity of the IRL problem (see Theorem 5.1 and Theorem 6.1), an algorithm (e.g., CATY-IRL) for learning a reward compatibility classifier can be applied to most common IRL applications, *without suffering from the bias induced by some heuristics* (e.g., margin maximization [1]) or additional assumptions (e.g., entropy maximization [4]). For instance, $(i)$ in the context of designing rewards for RL agents [5], CATY-IRL permits to combine domain knowledge and expert demonstrations by calculating the degree to which some human-designed rewards are compatible with the given demonstrations; $(ii)$ given some rewards candidate at modelling the preferences of the observed agent, obtained for example through human design or some IRL algorithms [1,4], with purposes like imitating or predicting behaviour [6], CATY-IRL permits to discriminate among such rewards based on their level of compatibility with the demonstrations. $(iii)$ In a Reward Learning** [3] setting, CATY-IRL allows us to integrate the constraints provided by various feedbacks (e.g., demonstrations and preferences) based on a soft notion of constraints satisfaction. Finally, $(iv)$ CATY-IRL also allows us to integrate demonstrations from different environments [7] in a soft manner. We will make this point clearer in the paper. 2- The Reviewer can find two examples for Proposition 3.1 in Appendix B.1. We will leverage the additional page to provide more insights and intuition on the propositions and theorems, and to improve the readability of the paper. 3- In common IRL algorithms [6], the goal is to learn a single reward function that minimizes the suboptimality of the expert's policy. In IL algorithms (e.g., [8]), the goal is to learn a policy whose suboptimality w.r.t. the expert's policy suboptimality is minimized under all rewards, since the true reward is unknown. Instead, the goal of our IRL classification algorithm is to minimize the error at estimating the suboptimality of the expert's policy under any reward. In other words, we are not looking for some special reward for which the expert's suboptimality is small, but our objective is to learn the expert's suboptimality under any possible reward function. The insight is that we aim to exploit the entire expressive power of demonstrations from an optimal expert to characterize the whole range of reward functions. We will integrate the section on the related works with this discussion. 4- We thank the Reviewer for having made us notice this issue. Simply put, CATY-IRL is computationally efficient because it exploits a computationally efficient algorithm, RFLin [9], as a sub-routine (see Remark 4.1 in [9] for additional details), and then all other steps require constant time and space to be executed. We will add this comment to the main paper and a detailed analysis of the computational complexity. 5- We thank the Reviewer for the suggestion. We will change it. ## Questions > How would you apply your algorithm to a real world IRL problem? See the comment to the Motivation weakness. > What is the computational complexity of the classification step? The classification step consists in executing a RFE algorithm as sub-routine, and then executing some simple operations that require constant time and space, thus, the computational complexity of the classification step is the same as the RFE sub-routine. Specifically, for Linear MDPs, algorithm RFLin [9] is computationally efficient (see Remark 4.1 in [9]). ## References [1] Ng and Russell. Algorithms for IRL. ICML 2000. [2] Metelli et al. Provably efficient learning of transferable rewards. ICML 2021. [3] Skalse et al. Invariance in policy optimisation and partial identifiability in reward learning. ICML 2023. [4] Ziebart et al. Maximum entropy IRL. AAAI 2008. [5] Hadfield-Menell et al. Inverse Reward Design. NeurIPS 2017. [6] Arora and Doshi. A survey of IRL: Challenges, methods and progress. Artificial Intelligence 2018. [7] Cao et al. Identifiability in IRL. NeurIPS 2021. [8] Ho and Ermon. Generative adversarial IL. NeurIPS 2016. [9] Wagenmaker et al. Reward-free RL is no harder than reward-aware RL in linear MDPs. ICML 2022. --- Rebuttal 2: Title: Post rebuttal comment Comment: Thank you for the thorough response. It mostly clarified my questions, so I decided to raise my score to 7. However, I would have the following follow-up questions /remarks: 1. I think in the definition of the feasible reward set, it should be clarified that for linear MDPs, we are only considering rewards that are parametrized by $\langle \phi(s,a),\theta_h \rangle$. At the moment, the definition just requires $r\in[-1,1]^{S\times A \times [H]}$. 2. What exactly do you mean by "the feasible reward set contains a continuum of rewards"? Since you parametrize the reward using a finite number of features, the set of feasible rewards should be confined within the span of these features (which is a finite-dimensional subspace). 3. Just an observation: In Theorem 3.2, the poor scaling $\Omega(S)$ seems to be related to the fact that we need to visit all states to exclude $\lbrace 0 \rbrace$ as the feasible reward set. I think when we additionally assume that the expert is uniquely realizable for some reward, then the problem wouldn't occur. Do you agree? --- Rebuttal Comment 2.1: Comment: Thank you. We address the Reviewer additional questions/remarks below: > I think in the definition of the feasible reward set, it should be clarified that for linear MDPs, we are only considering rewards that are parametrized by $\langle \phi(s,a),\theta_h \rangle$. At the moment, the definition just requires $r\in[-1,1]^{S\times A \times [H]}$ Definition 3.1 is general and independent of structural assumptions of the MDP, like Linear MDPs. Nevertheless, we agree that we should remark that, for Linear MDPs, we consider just rewards parametrized through the feature mapping $\phi$. We will clarify this point in the paper. > What exactly do you mean by "the feasible reward set contains a continuum of rewards"? Since you parametrize the reward using a finite number of features, the set of feasible rewards should be confined within the span of these features (which is a finite-dimensional subspace). Yes, the feasible set is confined within the span of the features, which is still a continuous space. For this reason, there are infinite rewards inside the feasible set, thus we cannot construct an algorithm that outputs all these rewards. We might construct an algorithm that outputs the constraints defining the feasible set, but then we could use such constraints only for classifying rewards as inside or outside the feasible set. Therefore, we prefer to explicitly implement a classifier. > Just an observation: In Theorem 3.2, the poor scaling $\Omega(S)$ seems to be related to the fact that we need to visit all states to exclude $\lbrace 0 \rbrace$ as the feasible reward set. I think when we additionally assume that the expert is uniquely realizable for some reward, then the problem wouldn't occur. Do you agree? That is an interesting question. We agree with the Reviewer that the additional assumption that there is a single optimal policy $\pi^E$ for the expert's reward $\theta^E$ would simplify the hard instances in the proof of Theorem 3.2, so that the lower bound $\Omega(S)$ would not hold anymore. The intuition is interesting, and even though we are not sure that it gets rid of the $\Omega(S)$ dependence, we think that it might be analysed in future works.	Summary: This paper finds that the feasible reward set cannot be efficiently learned even under linear MDPs. Therefore, the paper proposes a new notion called "reward compatibility" that generalizes the notion of "feasible set" and thereby casts IRL as a classification problem. The paper proposes an algorithm to solve this new classification problem and theoretically show that the sample complexity of the proposed algorithms is independent of state cardinality for linear MDPs. Strengths: 1. This paper proposes a new notion called "reward compatibility" and novelly formulates IRL as a classification problem based on the notion. 2. This paper is theoretically solid, which is also the biggest strength of the paper. Weaknesses: 1. The paper title is a little bit exaggerating. The title is "scale IRL to large state spaces", while what the paper does is to scale one specific kind of IRL, i.e., learning the feasible reward set, to large state spaces. In fact, many other kinds of IRL algorithms can work quite efficiently in continuous state spaces without the linear MDP assumption. For example, maximum likelihood IRL [1] is sample efficient where only one sample is needed for each reward update. I think what the authors mean here is that learning the feasible reward set is difficult in large state space, however, learning feasible reward set is only a kind of IRL, but does not represent all IRL methods. I suggest that the authors change the general terminology "IRL" to some more specific terminologies, given that some other kinds of IRL methods can already scale to large state spaces. 2. The paper uses the terminology "online IRL" to represent IRL that needs to interact with the environment. The paper also adds a footnote to explain this notion. I know that this is to contrast offline IRL. However, it is still confusing because online IRL is already defined in literature [2,3,4], i.e., the IRL setting where the demonstrated trajectories are revealed sequentially. Therefore, I highly suggest the authors to use another terminology to avoid confusion. 3. In example 4.1, the authors mention that the reward function with smaller $\bar{C}(r)$ is more compatible. This can be questionable. For example, suppose $r_2=2 r_1$, then $\bar{C}(r_2)>\bar{C}(r_1)$ if they are both positive. However, can we say that $r_1$ is more compatible than $r_2$? The MDPs are equivalent if we multiply the reward by a constant. Then intuitively, $r_1$ and $r_2$ should be same compatible right? 4. Lack of empirical evaluation. [1] Maximum-likelihood inverse reinforcement learning with finite-time guarantees [2] First-person activity forecasting with online inverse reinforcement learning [3] Online inverse reinforcement learning under occlusion [4] Learning multi-agent behaviors from distributed and streaming demonstrations Technical Quality: 2 Clarity: 2 Questions for Authors: Please see weaknesses. Confidence: 3 Soundness: 2 Presentation: 2 Contribution: 3 Limitations: The limitation is discussed in Section 7. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the Reviewer for praising our theoretical analysis as solid, and for recognizing the novelty of the formulation of IRL as a classification problem, which we believe is an important finding of our work. ## Weaknesses 1- We agree with the Reviewer that the general terminology "Inverse Reinforcement Learning" may be confusing, since it does not reveal the specific IRL formulation considered. Even though previous works on the feasible set have adopted the same general notation [5,6,7,8,9], we agree that a more specific terminology, like "Maximum Likelihood IRL" [1], "Bayesian IRL" [10], or "Maximum Entropy IRL" [11], would be clearer. We will change it to "How does Learning the Feasible Reward Set Scale to Large State Spaces?". 2- Again, we agree with the Reviewer that overloading common IRL terminology may create some confusion. Although "Online IRL" fits the analysed problem setting, we will resort to "Active Exploration IRL", which describes the possibility of exploring the environment, and which is compatible with previous work [7]. 3- Thank you for the interesting question, which allows us to remark a very important point about the interpretation of the notion of reward function in MDPs, and in particular about the scale of the rewards. The MDP is a model, i.e., a simplified representation of reality, which is commonly applied to 2 different kinds of real-world scenarios: $(i)$ problems in which the agent (learner in RL or expert in IRL) actually receives some kind of scalar feedback from the environment, which can be modelled as a reward function; $(ii)$ problems in which the agent does not receive a feedback from the environment, but its objective, i.e., its structure of preferences among state-action trajectories (which trajectories are better than others), satisfies some axioms that permit to represent it through a scalar reward [13,14] (this is referred to as the Reward Hypothesis in literature [12]). There is an enormous difference between scenario $(i)$ and scenario $(ii)$. In $(i)$ the notion of $\epsilon$-optimal policy is well-defined for any fixed $\epsilon>0$, because the reward function is given and, thus, fixed. Instead, in $(ii)$, the notion of reward function is a mere mathematical artifact used to represent preferences among trajectories, whose existence is guaranteed by a set of assumptions/axioms [12,13,14]. As the Reviewer has observed, positive affine transformations of the reward do not affect the structure of preferences represented (see [13] or Section 16.2 of [15] or [16]). Therefore, *in $(ii)$, the notion of $\epsilon$-optimal policy is not* well-defined*, because rescaling a reward function $r$ to $kr$ changes the suboptimality of some policy $\pi$ from $\epsilon$ to $k\epsilon$. In other words, for fixed $\epsilon>0$, any policy can be made $\epsilon$-optimal by simply rescaling a reward $r$ to $kr$ for some small enough* $k>0$. In IRL, this issue is even more influential because, although we are in setting $(i)$, we have no idea on the scale of the true reward function. For this reason, our solution is to attach to any reward $r$ a notion of compatibility $\overline{\mathcal{C}}(r)$ which implicitly contains information about the scale of the reward $r$. Compatibilities of different rewards (e.g., $r_1$ and $r_2$ in the Reviewer example) cannot be compared unless the rewards have the same scale (e.g., $r_1$ and $r_2$ have different scales, thus their compatibilities shall not be compared). It should be observed that in Appendix C.2 we discuss a *notion of compatibility independent* of the scale of the reward. However, we show that it suffers from major drawbacks that make the notion of compatibility introduced in the main paper (Definition 4.1) more suitable for the IRL problem. In conclusion, the answer to the Reviewer's question is no, rewards $r_1$ and $r_2$ should not have the same compatibility, because they have different scales, and the notion of compatibility (i.e., suboptimality) is strictly connected to the scale of the reward**. To carry out a fair comparison of compatibilities, one should rescale the compatibility of each reward based on the scale of the reward. We will make this point clear in the paper. 4- We stress that the contribution of the paper is theoretical and, given the contributions provided, we believe that an empirical validation of the proposed algorithm is out of the scope of this work. ## References [1] Zeng et al. Maximum-likelihood inverse reinforcement learning with finite-time guarantees. NeurIPS, 2022. [2] Rhinehart and Kitani. First-person activity forecasting with online inverse reinforcement learning. ICCV, 2017. [3] Arora et al. Online inverse reinforcement learning under occlusion. AAMAS, 2019. [4] Liu and Zhu. Learning multi-agent behaviors from distributed and streaming demonstrations. NeurIPS, 2023. [5] Zhao et al. Is inverse reinforcement learning harder than standard reinforcement learning? ICML, 2024. [6] Lazzati et al. Offline inverse rl: New solution concepts and provably efficient algorithms. ICML, 2024. [7] Lindner et al. Active exploration for inverse reinforcement learning. NeurIPS, 2022. [8] Metelli et al. Towards theoretical understanding of inverse reinforcement learning. ICML, 2023. [9] Metelli et al. Provably efficient learning of transferable rewards. ICML, 2021. [10] Ramachandran and Amir. Bayesian inverse reinforcement learning. IJCAI, 2007. [11] Ziebart el al.. Maximum entropy inverse reinforcement learning. AAAI, 2008. [12] Sutton and Barto. Reinforcement Learning: An Introduction. 2018. [13] Shakerinava and Ravanbakhsh. Utility theory for sequential decision making. ICML, 2022. [14] Bowling et al. Settling the reward hypothesis. ICML, 2023. [15] Russell and Norvig. Artificial Intelligence: A Modern Approach. 2010. [16] David M. Kreps. Notes on the theory of choice. Westview Press, 1988. --- Rebuttal Comment 1.1: Comment: Thanks for the response. I'll keep my current positive rating.	Summary: Even under the strong assumption implicit in Linear MDPs, the learning of the set of rewards that make the expert’s policy optimal doesn’t scale well. This improves somewhat, if additionally a notion of compatibility of rewards is introduced, because in this way and under these conditions the IRL problem can be seen as a classification task. In this context a number of theoretical results are possible minimax optimality of a thus formulated IRL algorithm, complexity bounds and some contribution to the complexity theory of reward-free exploration. Strengths: Outsourcing some of related work to the appendix seems a good idea here, as the proper introduction is still readable and interesting. However, it may have been an alternative option to move the “original contributions” to the appendix as these are already mentioned in the abstract and in --- the paper. The paper aims at much, and although it delivers, but could be more focused and concise. Weaknesses: “How to” is not really addressed, “How to Scale Inverse RL to Large State Spaces?” should be “How does Inverse RL Scale to Large State Spaces?” The separation of exploration and classification phases may not appear to be a problem at this level of abstraction, but practically this can be a forbidding features of an algorithm. The approach uses a restrictive problem setting, while it could be preferable to attempt to discover any compositional structure or any latent low-dimensional manifolds, as would be the present in any practical problem if the problem can be treated at all at larger scales. No simulation included, although it should be easy provide some illustration, in particular for any worst-case results. Objective-free exploration need more study to receive the attention that it is claimed to deserve, but the current definition probably needs to be more precise. Here (as in most contributions to this conference) the use of display equations is dearly missed. Couldn’t the amount of ink be used to measure the length of the papers? The use of color in the manuscript could be more systematic, if it is encouraged at all. There is too much material in the paper. It may be tempting to publish a systematic study at a conference to reach some visibility, but it creates an imbalance among the contribution and may bias future submission. Technical Quality: 4 Clarity: 3 Questions for Authors: Would objective-free exploration be independent on the linear MDP assumption? Is it needed at all in the present paper? Can you compare to other IRL algorithms? Confidence: 3 Soundness: 4 Presentation: 3 Contribution: 4 Limitations: Practical application is limited, but this is outside the scope of this very impressive paper. Flag For Ethics Review: ['No ethics review needed.'] Rating: 8 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We are glad that the Reviewer found our paper to be impressive and our contribution to be substantial. We provide detailed replies to their questions/comments below. ## Weaknesses > “How to” is not really addressed, “How to Scale Inverse RL to Large State Spaces?” should be “How does Inverse RL Scale to Large State Spaces?” We thank the Reviewer for the observation. We will change it. > The separation of exploration and classification phases may not appear to be a problem at this level of abstraction, but practically this can be a forbidding features of an algorithm. From a theoretical perspective, the separation of the exploration phase from the subsequent phase permits to isolate the challenges of exploration, as mentioned in [1]. In practical applications, we require our learner to be able to actively explore the environment. Since the results of the classification phase are available after the exploration has completed, then any subsequent task has to be postponed. > The approach uses a restrictive problem setting, while it could be preferable to attempt to discover any compositional structure or any latent low-dimensional manifolds, as would be the present in any practical problem if the problem can be treated at all at larger scales. We agree with the Reviewer that Linear MDPs suffer from some limitations if we want to apply them to real-world applications, but we believe that they represent an important initial step toward the development of provably efficient IRL algorithms with more general function approximation structures. > No simulation included, although it should be easy provide some illustration, in particular for any worst-case results. We agree that an empirical validation would be nice, but, as the Reviewer also noted, we are already providing a lot of contributions, leaving no space for experiments unfortunately. > Objective-free exploration need more study to receive the attention that it is claimed to deserve, but the current definition probably needs to be more precise. The formulation of the Objective-Free Exploration (OFE) problem setting (Definition 6.1) is intentionally provided in a general way. The reason is that we aim that this definition will be used as a template for analysing exploration problems, and, thus, it should be instantiated more precisely in the specific problem depending on the tasks to be solved (see Example F.1 in Appendix F). In appendix E.1, we provide more insights on OFE, by identifying two additional problems beyond RL and IRL whose exploration phase can be casted in this scheme. > Here (as in most contributions to this conference) the use of display equations is dearly missed. Couldn’t the amount of ink be used to measure the length of the papers? The use of color in the manuscript could be more systematic, if it is encouraged at all. We agree with the Reviewer that some choices about the layout and the design of the paper may be improved. We will leverage the additional page to improve the readability of the paper. > There is too much material in the paper. It may be tempting to publish a systematic study at a conference to reach some visibility, but it creates an imbalance among the contribution and may bias future submission. We agree with the Reviewer that it may be hard to process all of the contributions we provide. Nevertheless, we believe that they cannot be separated from each other, because it would negatively affect the presentation and the understanding of the paper. ## Questions > Would objective-free exploration be independent on the linear MDP assumption? Is it needed at all in the present paper? Yes, Objective-Free Exploration (OFE) is a problem setting which is independent of specific assumptions on the structure of the MDP (e.g., linear MDP). Although, at first sight, OFE may seem out of scope in this paper, we believe that its formulation is significant as: $(i)$ it provides a unifying exploration framework for RL and IRL problems; $(ii)$ it highlights the efficiency and efficacy of Reward-Free Exploration (RFE) strategies for solving both tasks. Since part of our contribution consists in showing that RL and IRL enjoy the same sample complexity rate (Theorem 5.1, Theorem 6.1, and Theorem 6.2) in tabular problems and the same upper bound in Linear MDPs, the OFE problem setting permits to interpret these results in a unifying and original manner. > Can you compare to other IRL algorithms? Unfortunately, we cannot compare with popular IRL algorithms like margin maximization [2] or entropy maximization [3] (and their variants) because they enforce additional assumptions on the reward function to recover. The IRL algorithms that consider a problem setting analogous to ours are those in [4,5,6,7,8], whose objective is the estimation of the feasible reward set. Nevertheless, all algorithms presented in [4,5,6,7,8] focus on the tabular setting, and they exhibit an explicit dependence on the size of the state space. Thus, they cannot be used for problems with large state spaces. ## References [1] Chi Jin et al. Reward-free exploration for reinforcement learning. ICML, 2020. [2] Ng and Russell. Algorithms for inverse reinforcement learning. ICML, 2000. [3] Ziebart et al. Maximum entropy inverse reinforcement learning. AAAI, 2008. [4] Metelli et al. Provably efficient learning of transferable rewards. ICML, 2021. [5] Zhao et al. Is inverse reinforcement learning harder than standard reinforcement learning? ICML, 2024. [6] Lindner et al. Active exploration for inverse reinforcement learning. NeurIPS, 2022. [7] Lazzati et al. Offline inverse rl: New solution concepts and provably efficient algorithms. ICML, 2024. [8] Metelli et al. Towards theoretical understanding of inverse reinforcement learning. ICML, 2023.	Summary: This paper shows that finding the feasible reward set in IRL needs to sample $\Omega(S)$ number of samples, even when the MDP possesses a linear structure. To enable more efficient scaling with $S$, the authors propose another task in IRL called rewards compatibility: deciding whether $\pi^{E}$ is $\epsilon$-optimal under a given reward $r$. They further use reward-free algorithms to solve such tasks and propose a matching lower bound. As a byproduct, the lower bound also improves the existing lower bounds in tabular reward-free RL. Strengths: The theoretical analysis is solid. In particular, the lower bounds for feasible reward set learning and reward compatibility are novel and significant as they quantify the hardness of these two tasks in IRL. Weaknesses: 1. The reward compatibility framework is not that interesting in my opinion because it requires you to input a reward function, which indeed makes IRL a standard RL problem given that reward. More specifically, the reward compatibility framework is just policy optimization and evaluation of $\pi^E$ under a given reward $r$, which has been studied sufficiently before. 2. The algorithms that the authors propose are also just the existing algorithms in standard RL, so there is no novelty in the algorithm design. Technical Quality: 3 Clarity: 3 Questions for Authors: The lower bound in Theorem 3.2 characterizes the difficulty of identifying the exact feasible reward set. However, in many cases we just want to learn a feasible reward with some desirable properties instead of the whole set. For this setting will the lower bound still hold? Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: None. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We are glad that the Reviewer appreciated the novelty and significance of the lower bound results, and the solidity of the theoretical analysis. Below, we report answers to the Reviewer's comments. ## Weaknesses > The reward compatibility framework is not that interesting in my opinion because it requires you to input a reward function, which indeed makes IRL a standard RL problem given that reward. More specifically, the reward compatibility framework is just policy optimization and evaluation of $\pi^E$ under a given reward $r$, which has been studied sufficiently before. We agree with the Reviewer that, as we demonstrate in the paper (Theorem 5.1 and Theorem 6.2), the rewards compatibility framework turns out to be minimax optimally solvable by a policy optimization and evaluation algorithm in the Reward-Free Exploration (RFE) [1] setting, showing an equivalence of the two problems. However, it should be remarked that the significance and the novelty of the scheme lies in the original formulation and interpretation of the Inverse Reinforcement Learning (IRL) problem, and not in the specific solution technique. Our ultimate goal is to understand the computational and statistical complexity of inferring as much information (i.e., constraints) as possible about the expert's reward function $r^E$ in an approximate setting. Due to the partial identifiability of the IRL problem [2,3,4], as explained in the introduction, common IRL approaches like margin [2] or entropy [5] maximization are heuristically "biased" toward a specific reward function somehow close to $r^E$. For this reason, we resort to the feasible set formulation [4,6], which does not introduce additional assumptions about $r^E$ beyond the optimality of the observed expert policy $\pi^E$. Nevertheless, since the feasible set is inefficient to learn (being a set) in problems with a large state space (see Theorem 3.2), we introduce the notion of rewards compatibility. Ideally, we would like to have an IRL classification algorithm (e.g., some variant of CATY-IRL) that takes in input the problem instance and outputs a binary partition of the space of reward functions into at most $\epsilon$-compatible rewards and at least $\epsilon$-compatible rewards. In practice, due to the impossibility of computing such output (limited computational resources), we develop an algorithm, i.e., CATY-IRL, that potentially can classify all possible rewards, but that actually classifies only the input rewards. > The algorithms that the authors propose are also just the existing algorithms in standard RL, so there is no novelty in the algorithm design. We agree with the Reviewer that the proposed algorithm, CATY-IRL, executes existing RFE algorithms as sub-routines. However, a major contribution of our work is demonstrating that such sub-routines actually solve the IRL classification problem (Definition 4.2) in a minimax optimal manner (Theorem 5.1 and Theorem 6.1), and thus, proving an equivalence between IRL and RFE from the sample complexity viewpoint which has been conjectured in previous works (e.g., Appendix A of [4] or Appendix D of [7]). We will stress this in the final version. ## Questions > The lower bound in Theorem 3.2 characterizes the difficulty of identifying the exact feasible reward set. However, in many cases we just want to learn a feasible reward with some desirable properties instead of the whole set. For this setting will the lower bound still hold? Yes. To see why, as an example, assume you aim to learn only the feasible reward function that satisfies the margin maximization criterion in Equation (6) of [2]. By re-using the same hard instance constructed in the proof of Theorem 3.2, we see that no algorithm can discriminate between policies $\pi^E_1$ and $\pi^E_2$ unless it collects a sample from state $\overline{s}$. Without knowing which policy between $\pi^E_1$ and $\pi^E_2$ is the true expert policy, any algorithm will fail with probability at least $0.5$ in the worst case at outputting an accurate estimate of the reward function, since reward $\theta_1=1$ is the margin maximizer for policy $\pi^E_1$, and $\theta_2=0$ is the margin maximizer for policy $\pi^E_2$, and the distance $d$ (see Equation (1)) between these rewards is exactly $1$. The result follows by observing that we need $\Omega(S)$ samples to spot state $\overline{s}$. To avoid this negative result, we can learn a single $\epsilon$-compatible reward (for some $\epsilon>0$) that satisfies the same margin-maximization criterion, instead of learning the feasible reward that satisfies the criterion. Nevertheless, for the reasons presented in the introduction of the paper, we prefer to be criterion-agnostic, and to learn all the compatible rewards. We will make this point clear in the paper. ## References [1] Chi Jin et al. Reward-free exploration for reinforcement learning. ICML, 2020. [2] Ng and Russell. Algorithms for inverse reinforcement learning. ICML, 2000. [3] Skalse et al. Invariance in policy optimisation and partial identifiability in reward learning. ICML, 2023. [4] Metelli et al. Provably efficient learning of transferable rewards. ICML, 2021. [5] Ziebart et al.. Maximum entropy inverse reinforcement learning. AAAI, 2008. [6] Zhao et al. Is inverse reinforcement learning harder than standard reinforcement learning? ICML, 2024. [7] Lindner et al. Active exploration for inverse reinforcement learning. NeurIPS, 2022. --- Rebuttal Comment 1.1: Comment: Thank you for the rebuttal! I will keep a positive evaluation.	null	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Contextual Active Model Selection	Accept (poster)	Summary: This paper focuses on the online contextual active model selection problem. Specifically, the learner receives an unlabeled data point as a context at each round, and the objective is to adaptively select the best model to predict while limiting label requests. To address this problem, the authors proposed a CAMS method that contains a contextual active model selection algorithm and an active query component. Theoretical results about regret in both adversarial and stochastic settings are provided. Strengths: 1) The problem setting that we need to do a model selection at each around is novel and interesting. 2) Theoretical analysis on both adversarial and stochastic settings is provided. Weaknesses: About the problem setting, I have some concerns and questions: 1) In different tasks, such as image classification, and tabular data, we may have many different pre-trained models. For example, in the image classification tasks, we may choose the deep neural network trained on the ImageNet, or we can also adopt the CLIP model. How to construct the candidate model pool? 2) Given a model pool, in the first round, we have already selected a model. How do we decide whether we need to choose a new model or continue using the previous one? 3) In the proposal, given a new instance, the algorithm needs to run each candidate model on the instance, which requires a lot of computation cost. There are also some methods proposed to assign each model a specification to describe its functionality[1]. Can these methods be combined with the proposal? 4) In many cases, we may need to ensemble multiple models, can the proposal be extended to multiple model selection? [1] Lan-Zhe Guo, Zhi Zhou, Yu-Feng Li, Zhi-Hua Zhou. Identifying Useful Learnwares for Heterogeneous Label Spaces. In: Proceedings of the 40th International Conference on Machine Learning (ICML 2023), Hawaii, 2023. Page: 12122-12131. Technical Quality: 2 Clarity: 3 Questions for Authors: As discussed above. Confidence: 3 Soundness: 2 Presentation: 3 Contribution: 2 Limitations: No Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for the feedback on our work! Below please find our detailed responses to your questions. --- > *Q1:* "In different tasks, such as image classification, and tabular data, we may have many different pre-trained models. For example, in the image classification tasks, we may choose the deep neural network trained on the ImageNet, or we can also adopt the CLIP model. How to construct the candidate model pool?" *A:* Thanks for letting us know your confusion. Ideally, it is beneficial to have diverse models, such as pretrained models with different structures or access to varied data distributions during the pre-training stage. CAMS learns to leverage the unique strengths of these black-box models through an online process, actively querying labels and policies. This approach tailors the queries to different contexts to distinguish the capabilities of the various policies and models. To further address your concerns, we conducted additional experiments using a more recent and complex large-scale dataset, the ImageNet dataset with 1000 categories. We also incorporated six more recent pretrained models, including CLIP, Inception V4, VGG19, and PNASNet. In Fig.16 of the attached global response PDF, we present our studies on cost-effective query experiments with the ImageNet dataset using these newer pretrained models. The results are consistent with our previous findings, demonstrating that CAMS outperforms all baselines. CAMS not only shows significant superiority over both contextual and non-contextual baselines but also achieves the lowest label query cost compared to existing baselines and the current state-of-the-art, ModelPicker [1]. [1] Online Active Model Selection for Pre-trained Classifiers, AISTATS 2021 > *Q2:* "Given a model pool, in the first round, we have already selected a model. How do we decide whether we need to choose a new model or continue using the previous one?" *A:* Thank you for the question. This selection process will be determined by the CAMS algorithm, which is quite dynamic. In each round, CAMS will select a model by considering policy advice regarding the model's performance in the current context. It will choose the model with the highest probability by leveraging advice from multiple experts in a stochastic setting. In an adversarial setting, it will first sample a policy based on the policies' exponential cumulative loss and then sample the model according to the policy's advice distribution. > *Q3:* "In the proposal, given a new instance, the algorithm needs to run each candidate model on the instance, which requires a lot of computation cost. There are also some methods proposed to assign each model a specification to describe its functionality[1]. Can these methods be combined with the proposal?" *A:* Thanks for raising the question. Our work is quite different from the Learnware [1] setting. The main differences include the following: * We treat models and policies as black boxes, whereas Learnware requires assigning a specification SSS to each model, which involves parameters of the reduced model. * CAMS focuses on active querying and cost-effectiveness, which Learnware does not. * We assume that these pretrained black-box models are for the same task but with different expertise, aiming to combine their complementary expertise. In contrast, Learnware assumes models are for different tasks. Therefore, they operate in quite different settings, making it challenging to combine these methods. [1] Identifying Useful Learnwares for Heterogeneous Label Spaces. ICML 2023 > *Q4:* "In many cases, we may need to ensemble multiple models, can the proposal be extended to multiple model selection?" *A:* Thanks for the question. This approach can be adapted for multiple model selection scenarios by modifying the RECOMMEND part (Fig 1, lines 29-39) of the CAMS algorithm. Rather than selecting the top-ranking model for a given instance to query in a stochastic setting, we could simply select a few top candidate models to ensemble the models' predictions. --- We hope these responses adequately address your concerns. We appreciate your feedback and look forward to further discussions. Thank you! --- Rebuttal Comment 1.1: Title: Please update your review and engage with the authors Comment: Dear reviewer, Please provide an update to your review. The authors have provided a quite substantial rebuttal. Please acknowledge that you have read the rebuttal, and please post any questions that you may still have. Also clarify if you want to adjust your score. Many thanks, Your AC. --- Rebuttal 2: Title: Please update your review and engage with the authors Comment: Dear reviewer, Please provide an update to your review. The authors have provided a quite substantial rebuttal. Please acknowledge that you have read the rebuttal, and please post any questions that you may still have. Also clarify if you want to adjust your score. Many thanks, Your AC. PS: Sorry for the double message, but this is now a reply to the review, so I hope this will automatically reach your inbox now. --- Rebuttal 3: Title: Please respond Comment: Dear reviewer, Thanks again for your thoughtful review. As this paper is a bit borderline, I would really like to know if the rebuttal had any affect on your review. Therefore please provide an update to your review and acknowledge that you have read the rebuttal and clarify if you want to adjust your score. Many thanks, Your AC.	Summary: The paper introduces CAMS, an algorithm designed for online contextual active model selection. CAMS minimizes labeling costs by selecting the most appropriate pre-trained models for given contexts and strategically querying labels. The paper provides theoretical analysis of regret and query complexity in both adversarial and stochastic settings. Empirical evaluations on benchmark tasks such as CIFAR10 and DRIFT show that CAMS reduces labeling effort significantly while maintaining or improving accuracy. Strengths: - The integration of a contextual model selection mechanism with an active query strategy is a novel approach that effectively addresses the challenge of selecting the best model for varying data contexts while minimizing labeling costs. - The paper offers a robust theoretical foundation, with detailed proofs and analyses of regret and query complexity. - The empirical results are strong, showing that CAMS significantly reduces labeling effort while maintaining or improving accuracy across various benchmarks, including CIFAR10 and DRIFT. Weaknesses: - The method does not discuss how it handles dynamic updates to the set of classifiers or policies. In practical applications, the set of available models may change over time. The lack of a mechanism to incorporate such updates limits the robustness and adaptability of the proposed solution. - While the datasets chosen provide a range of scenarios, the empirical evaluation could benefit from more recent and complex datasets to better demonstrate CAMS' capabilities. Additionally, the comparisons are primarily with older methods or basic variants, and a broader set of state-of-the-art methods, including recent advances in contextual bandits and active learning, are not fully explored. - Some of the mathematical notations and their explanations are dense and could be clarified further. For instance, the derivation and intuition behind the exponential weighting and the specific choice of ηt could be more thoroughly explained to improve understanding. - The paper does not discuss the stability of empirical results across multiple runs. Given that the evaluation relies on certain stochastic processes, it would be beneficial to report the variance or standard deviation of the results to provide a clearer picture of the method's reliability. Technical Quality: 3 Clarity: 2 Questions for Authors: - How does CAMS handle scenarios where the set of pre-trained classifiers is not fixed or continuously updated? - Can more details be provided on the selection and construction of the policy set used in experiments? - How does the method perform when applied to tasks beyond classification, such as regression or ranking problems? Confidence: 3 Soundness: 3 Presentation: 2 Contribution: 2 Limitations: The author mentions the limited focus on classification and non-uniform loss functions in this work. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your detailed review of our work! We greatly appreciate your recognition of the novelty of our approach, the robust and thorough theoretical foundation, and the strong empirical results of CAMS. Below, you will find our detailed responses to your questions. --- > *Q1:* "The method does not discuss how it handles dynamic updates to the set of classifiers or policies. In practical applications, the set of available models may change over time. The lack of a mechanism to incorporate such updates limits the robustness and adaptability of the proposed solution." *A:* Thanks for raising the question! Yes, this is an interesting setting. In this work, we only consider the scenario of having access to pretrained models. However, in our adversarial setting, the regret bound and query complexity could address your concern and provide performance guarantees for worst-case scenarios, including cases where the available models change over time. > *Q2:* "While the datasets chosen provide a range of scenarios, the empirical evaluation could benefit from more recent and complex datasets to better demonstrate CAMS' capabilities. Additionally, the comparisons are primarily with older methods or basic variants, and a broader set of state-of-the-art methods, including recent advances in contextual bandits and active learning, are not fully explored." *A:* Thanks for raising the question! To address your concerns, we conducted additional experiments using a more recent and complex large-scale dataset, the ImageNet dataset with 1000 categories. We also incorporated six more recent pretrained models, including CLIP, Inception V4, VGG19, and PNASNet. In Figure 16 of the attached global response PDF, we present our studies on cost-effective query experiments with the ImageNet dataset using these newer pretrained models. The results are consistent with our previous findings, demonstrating that CAMS outperforms all baselines. CAMS not only shows significant superiority over both contextual and non-contextual baselines but also achieves the lowest label query cost compared to existing baselines and the current state-of-the-art, ModelPicker [1]. In addition, by comparing our approach with a broader set of state-of-the-art active learning methods, as shown in the following table, we illustrate that the most recent baseline with a setting closest to CAMS is ModelPicker [1]. \| Active Learning Setting \ Algorithms \| Coreset (2017) \| Batch-BALD (2019) \| BADGE (2019); VAAL (2019); ClusterMargin (2021) \| BALANCE (2023); GLISTER (2020) \| VeSSAL (2023) \| Model Picker (2021) \| CAMS \| \|-------------------------------------------\|-------------\|----------------\|-------------------------------\|----------------------\|------------\|------------------\|----------\| \| Streaming, sequential \| × \| × \| × \| × \| × \| ✔️ \| ✔️ \| \| Streaming, batch \| × \| × \| × \| × \| ✔️ \| × \| × \| \| Pool-based, batch \| ✔️ \| ✔️ \| ✔️ \| ✔️ \| × \| × \| × \| [1] Online Active Model Selection for Pre-trained Classifiers, AISTATS 2021 > *Q3:* "Some of the mathematical notations and their explanations are dense and could be clarified further. For instance, the derivation and intuition behind the exponential weighting and the specific choice of ηt could be more thoroughly explained to improve understanding." *A:* The derivation and intuition behind exponential weighting is: 1.Bias towards Better Predictions and effective penalty for poor predictions: It increases the weight of consistently accurate experts, quickly focusing on the best performers and improving overall performance. It significantly reduces the weight of poor predictors, minimizing their influence and maintaining robust decision-making. 2. Balancing Exploration and Exploitation: It balances exploration and exploitation by occasionally giving higher weights to less-explored actions, preventing premature convergence to suboptimal choices. 3. Mathematical Convenience: The exponential function ensures positive, normalized weights and efficient updates, making the algorithm scalable and practical for real-time applications. The specific choice of ηt is a decaying lower bound on query probability to encourage exploration at an early stage, to reveal the true label more often at an early stage to differentiate the different policies and models regardless how different they present the agreement on the label. The choice of exact value of ηt is guided by our theoretical analysis. Our empirical results further validate the effectiveness of ηt. > *Q4:* "The paper does not discuss the stability of empirical results across multiple runs. Given that the evaluation relies on certain stochastic processes, it would be beneficial to report the variance or standard deviation of the results to provide a clearer picture of the method's reliability." *A:* Thank you for the comments. In our experiments, we indeed ran multiple trials for each dataset. Specifically, for the DRIFT dataset, we conducted 100 trials; for the HIV dataset, we conducted 200 trials; for the VERTEBRAL dataset, we conducted 300 trials; for the CIFAR10 dataset, we conducted 10 trials; and for the COVTYPE dataset, we conducted 6 trials. We visualized the results in each plot with a 90% confidence interval (if we approximate the outcomes over multiple trials with a Gaussian distribution, then the confidence interval is approximately proportional to the standard deviation). We will clarify this in the revised manuscript. --- Rebuttal 2: Comment: > *Q5:* "How does CAMS handle scenarios where the set of pre-trained classifiers is not fixed or continuously updated?" *A:* CAMS is primarily designed for pre-trained classifiers. However, it also provides performance guarantees for scenarios where classifiers are not fixed, continuously updated, or exhibit unexpected or adversarial behavior. We have both algorithms and theoretical bounds in adversarial settings to ensure performance in these situations. > *Q6:* "Can more details be provided on the selection and construction of the policy set used in experiments?" *A:* We select and construct policies with the goal of creating a more diversified policy set, incorporating diversity in features, architecture, and behavior. To achieve this, we adopt models with entirely different architectures to learn contextual representations alongside classifier behavior. Ultimately, we combine these policies to form a stronger model selection strategy. > *Q7:* "How does the method perform when applied to tasks beyond classification, such as regression or ranking problems?" *A:* Currently, CAMS only covers classification tasks where the oracle policy provides a label. When the oracle policy provides a regression value or a ranking list, one possible solution is to convert the problem into a classification problem. This could involve marking the true label as the top in the ranking list or identifying the value closest to the true value as the highest. --- We hope our response has addressed your concerns. If you have any further inquiries, please let us know. Thank you! --- Rebuttal 3: Title: Please update your review and engage with the authors Comment: Dear reviewer, Please provide an update to your review. The authors have provided a quite substantial rebuttal. Please acknowledge that you have read the rebuttal, and please post any questions that you may still have. Also clarify if you want to adjust your score. Many thanks, Your AC. --- Rebuttal 4: Title: Please respond Comment: Dear reviewer, Thanks again for your thoughtful review. As this paper is a bit borderline, I would really like to know if the rebuttal had any affect on your review. Therefore please provide an update to your review and acknowledge that you have read the rebuttal and clarify if you want to adjust your score. Many thanks, Your AC.	Summary: This paper proposes a Contextual Active Model Selection (CAMS) method for addressing the problem in the online setting by selecting the optimal pre-trained model for given data points while minimizing labeling costs. CAMS utilizes contextual information to make informed model selection decisions and employs an adaptive query strategy to determine when to request labels, thereby reducing overall labeling efforts. Strengths: - This paper provides very rigorous theoretical guarantees, demonstrating the algorithm's effectiveness through regret and query complexity bounds. - Compared with existing active learning approaches, CAMS's ability to efficiently handle various data distributions/scenarios and contexts makes it particularly useful for real-life applications. Weaknesses: - The effectiveness of CAMS heavily relies on the pre-trained models. CAMS may not perform well if the pre-trained models are diverse or representative enough or have a large domain gap with the target task. - The theoretical guarantee of regret bounds and query complexity in this manuscript, are derived under strong assumptions like stochastic, adversarial settings. - The authors use the cumulative loss as the evaluation metric, it is indeed an overall measure of performance but the normal evaluation metrics like accuracy, precision, and recall should also be considered. Technical Quality: 3 Clarity: 3 Questions for Authors: The author should carefully check if typos exist in the manuscript, e.g., the caption of Table 3, "Eq. (??)". Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: The authors have adequately 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: Thank you for your thorough review of our work! We greatly appreciate your recognition of the rigorous theoretical guarantees provided in this paper, both in terms of regret and query complexity bounds. We are also thankful for your acknowledgment of CAMS as particularly useful for real-life applications, filling the gap in current active learning settings. Below, please find our detailed responses to your questions. > *Q1:* "The effectiveness of CAMS heavily relies on the pre-trained models. CAMS may not perform well if the pre-trained models are diverse or representative enough or have a large domain gap with the target task." *A:* CAMS will generally benefit from the diversity of pretrained models; however, when all the models present a large domain gap with the target task, CAMS will be limited by the combinational optimal performance of current models and policies. To address such concern in the worst case scenario, our adversarial setting provides a worst case performance guarantee when all models have a large domain gap with the target task. > *Q2:* "The theoretical guarantee of regret bounds and query complexity in this manuscript, are derived under strong assumptions like stochastic, adversarial settings." *A:* Thanks for raising the question! Yes, we provide theoretical guarantees of regret bounds and query complexity in both stochastic and adversarial settings. These settings are more like a general setting, not considered to be a strong assumption setting. * Stochastic Settings deal with inherent randomness and probabilistic outcomes, suitable for applications involving natural variability and uncertainty. These models are essential in various real-world applications due to the inherent randomness in many systems. Such as economic forecasting, chemical reaction, and biological population dynamics. * Adversarial Settings involve deliberate attempts to disrupt or manipulate systems, requiring strategies to anticipate and counteract adversarial actions. This paradigm is often used in contexts where there is a deliberate effort to deceive or hinder operations. Real-World applications of adversarial settings: such as recommendation systems etc. > *Q3:* "The authors use the cumulative loss as the evaluation metric, it is indeed an overall measure of performance but the normal evaluation metrics like accuracy, precision, and recall should also be considered." *A:* Thanks for the question! In this work, we follow the online learning literature to report the cumulative loss (as a proxy of the cumulative regret). As the reviewer rightfully suggested, employing other metrics could convey additional information. We would like to note that the cumulative loss is linear to Accuracy, i.e., Cumulative loss = T(1-Accuracy), where T is the total number of queries seen by the algorithm. We further considered additional metrics such as the relative cumulative loss (Fig.4(a)), and query complexity (Fig.3(b)). We will make this clear in the revision. > Q4:* "The author should carefully check if typos exist in the manuscript, e.g., the caption of Table 3, Eq. (??)." *A:* Thank you for pointing out the typo. We have fixed it and will update it in the camera-ready version. --- We hope our response has addressed your concerns. If you have any further inquiries, please let us know. Thank you! ---- --- Rebuttal Comment 1.1: Title: response Comment: Thank you for your response, I decide to keep my attitude towards borderline accept.	Summary: The paper proposes an online active model selection strategy where at each round the learner receives an unlabeled data point as a context to adaptively select the best model to predict while limiting the label requests. Strengths: 1. The paper introduces a model selection procedure that is designed to handle both stochastic and adversarial settings. Apart from that it includes an adaptive query strategy that considers the disagreement among the pre-trained models. 2. The framework is cost-effective through its adaptive query strategy and performs significantly well compared to all the contextual and non-contextual baselines. Weaknesses: 1. Mainstream large-scale datasets such as ImageNet, MS COCO etc. will be ideal to validate the all-around performance of the proposed CAMS framework, especially in the query cost and complexity studies. 2. It will be interesting to check with some of the popular and more recent baselines such as CoreSet[1], BatchBALD[2], BADGE[3] on any of the large datasets mentioned in 1. [1] Sener, O., & Savarese, S. (2017). Active Learning for Convolutional Neural Networks: A Core-Set Approach. ArXiv. /abs/1708.00489 [2] Andreas Kirsch, Joost van Amersfoort, and Yarin Gal. 2019. BatchBALD: efficient and diverse batch acquisition for deep Bayesian active learning. Proceedings of the 33rd International Conference on Neural Information Processing Systems. Curran Associates Inc., Red Hook, NY, USA, Article 631, 7026–7037. [3] Ash, J. T., Zhang, C., Krishnamurthy, A., Langford, J., & Agarwal, A. (2019). Deep Batch Active Learning by Diverse, Uncertain Gradient Lower Bounds. ArXiv. /abs/1906.03671 Technical Quality: 4 Clarity: 3 Questions for Authors: Please refer to the weaknesses section. Confidence: 3 Soundness: 4 Presentation: 3 Contribution: 4 Limitations: The paper is somewhat difficult to read due to its proposal’s components explained in disconnected sections. The framework is not exactly flexible to be applied to regression or segmentation problems. As reported, this is primarily applicable to classification problems. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your detailed review of our work! Below, you will find our detailed responses to your questions. --- >*Q1:* "Mainstream large-scale datasets such as ImageNet, MS COCO etc. will be ideal to validate the all-around performance of the proposed CAMS framework, especially in the query cost and complexity studies." *A:* Thanks for raising the question! To address your concerns, we conducted additional experiments using a more recent and complex large-scale dataset, the ImageNet dataset with 1000 categories. We also incorporated six more recent pretrained models, including CLIP, Inception V4, VGG19, and PNASNet. In Fig. 16 of the attached global response PDF, we present our studies on cost-effective query experiments with the ImageNet dataset using these newer pretrained models. The results are consistent with our previous findings, demonstrating that CAMS outperforms all baselines. CAMS not only shows significant superiority over both contextual and non-contextual baselines but also achieves the lowest label query cost compared to existing baselines and the current state-of-the-art, ModelPicker [1]. In addition to ImageNet, we also conducted a cost-effective experiment on a relatively large dataset, Covtype (580K instances), shown in Fig. 3(e) and Fig. 4 in the main paper. [1] Online Active Model Selection for Pre-trained Classifiers, AISTATS 2021 >*Q2:* "It will be interesting to check with some of the popular and more recent baselines such as CoreSet[1], BatchBALD[2], BADGE[3] on any of the large datasets mentioned in 1." *A:* Please note that CAMS (ModelPicker and the other AL criteria adopted in the paper) is developed under the streaming setting, where data arrives sequentially or online, and the model decides which label to query. Although one can make multiple passes over the data stream, the decision of whether to query a label is dependent only on the collection of existing models (or hypotheses). On the other hand, CoreSet, BADGE, and (Batch-)BALD are all designed as pool-based active learning baselines (where CoreSet represents a diversity sampling strategy, BatchBALD being uncertainty sampling, and BADGE representation a combination of both). The active query strategy that CAMS relies on can be viewed as a customized variant of entropy sampling, applied to the streaming setting. This in principle aligns with BALD, with a key difference in that BALD is designed for the pool-based setting as a greedy uncertainty sampling strategy. However, one cannot readily apply diversity sampling under our (streaming) problem setup. \| Active Learning Setting \ Algorithms \| Coreset (2017) \| Batch-BALD (2019) \| BADGE (2019); VAAL (2019); ClusterMargin (2021) \| BALANCE (2023); GLISTER (2020) \| VeSSAL (2023) \| Model Picker (2021) \| CAMS \| \|-------------------------------------------\|-------------\|----------------\|-------------------------------\|----------------------\|------------\|------------------\|----------\| \| Streaming, sequential \| × \| × \| × \| × \| × \| ✔️ \| ✔️ \| \| Streaming, batch \| × \| × \| × \| × \| ✔️ \| × \| × \| \| Pool-based, batch \| ✔️ \| ✔️ \| ✔️ \| ✔️ \| × \| × \| × \| We also will modify section 2(related works) to address this concern. --- We hope our response has addressed your concerns. If you have any further inquiries, please let us know. Thank you! --- Rebuttal Comment 1.1: Comment: Thanks for your response, I maintain my initial score.	Rebuttal 1: Rebuttal: We would like to thank all reviewers for their effort in assessing our work and for their helpful comments and questions. We will respond separately to each reviewer concerning their individual questions. However, we would like to address one overarching theme from the reviews upfront: the performance and scalability of CAMS on large datasets and our choice of baselines. Our response is as follows: 1. Scalability and robustness of CAMS: To further demonstrate the scalability and robustness of CAMS, we conducted additional experiments on ImageNet and incorporated six more recent pretrained models, including CLIP, Inception V4, VGG19, and PNASNet. The results were consistent with those reported in our original submission, and the new results are provided in the attached PDF. 2. Problem setting and baseline selection: As shown in Table 1, the problem setting of contextual active model selection significantly differs from classical contextual bandits and active learning problems. Therefore, we focused on demonstrating that a novel combination of classical algorithmic components, namely EXP4 (for contextual bandits) and uncertainty sampling (for streaming queries), can elegantly solve this new problem. This problem is practically relevant, as pointed out by several reviewers. 3. Comparison against recent studies in active learning: In addition to Table 1 of our original submission, which showcases the novelty of our problem, we have added another table in the attached PDF to highlight the differences between the active model selection problem and recent studies that explicitly focus on active learning. We hope this justifies our choice of baselines as a fair selection for a well-rounded evaluation framework. We will gladly incorporate all of these aspects in our revised manuscript. Pdf: /pdf/b2357a42934f31c9993fd30136f62ba67c3ba3cf.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
VMamba: Visual State Space Model	Accept (spotlight)	Summary: This paper presents VMamba, a novel vision backbone model inspired by the famous Mamba state-space sequence model. The main contribution of VMamba is its ability to achieve efficient visual representation learning with linear computational complexity. The core of VMamba is the VSS block, which incorporates the 2D-Selective-Scan module (SS2D), thereby extending the Mamba model that is a 1D selective scan good for NLP tasks. With SS2D, we can work nicely with inductive biases associated with 2D image space. VMamba's architecture consists of multiple stages with hierarchical representations (similar to ViT). The authors introduce three model sizes: Tiny, Small, and Base. The VSS blocks replace the S6 module from Mamba with the SS2D module, and further enhancements are made by eliminating unnecessary components and optimizing the architecture for better computational efficiency - using the Triton language. Extensive experiments demonstrate VMamba's promising performance across various visual perception tasks, including image classification on ImageNet-1K, object detection, instance segmentation on MSCOCO, and semantic segmentation on ADE20K. VMamba consistently achieves superior accuracy and throughput compared to existing benchmark models, showcasing its scalability and adaptability to different input resolutions and downstream tasks. Strengths: * 2D-Selective-Scan Module: The introduction of the 2D-Selective-Scan (SS2D) module is a creative solution to bridge the gap between 1D selective scan and 2D vision data. * Comprehensive Experiments: The paper provides extensive experimental results on multiple benchmarks, including ImageNet-1K, MSCOCO, and ADE20K, demonstrating the effectiveness and robustness of VMamba across various tasks. * Clear Explanation: The paper is well-written, with clear explanations. The authors provide detailed descriptions of the architecture, modules, and experimental setups, making it accessible to readers. * Visualization: The use of visualizations, such as activation maps and effective receptive fields (ERF), helps in understanding the SS2D mechanism and the model's behavior, which is very important part of all the ablation studies. * Impact on Visual Representation Learning: VMamba addresses a critical issue in vision models by reducing computational complexity from quadratic to linear, which can significantly impact the field of visual representation learning. Weaknesses: * Limited Comparison with Other SSM-based Models: While the paper does compare VMamba with several benchmark models, it would benefit from a more detailed comparison with other state-space models (SSM) in the vision domain. Specifically, models like S4ND and Vim are mentioned, but the comparisons are somewhat brief. Providing more in-depth analysis and results would strengthen the argument for VMamba's superiority. * Adding more interesting works to Related Work section: There are some interesting works on neuromorphic vision and processing with SSMs that authors should cite and mention: [1] State Space Models for Event Cameras. Nikola Zubić, Mathias Gehrig, Davide Scaramuzza - CVPR 2024, Spotlight [2] Scalable Event-by-event Processing of Neuromorphic Sensory Signals With Deep State-Space Models. Mark Schöne, Neeraj Mohan Sushma, Jingyue Zhuge, Christian Mayr, Anand Subramoney, David Kappel - ICONS 2024 * Generalization to Other Tasks: The experiments focus mainly on standard benchmarks for image classification, object detection, and segmentation. However, it is not clear how well VMamba generalizes to other types of visual tasks such as video analysis, 3D vision, or more complex scene understanding. Including some preliminary results or at least discussions on these aspects could highlight the versatility of VMamba further. * Clarity in Mathematical Derivations: Some of the mathematical derivations, especially in the relationship between SS2D and self-attention, are complex and may not be easily accessible to all readers. Simplifying the explanations or providing more intuitive visual insights alongside the formal derivations could enhance understanding. Also, they are not rigorously mathematically proven. Technical Quality: 4 Clarity: 4 Questions for Authors: - Could you provide more detailed comparisons with other state-space models (SSMs) used in the vision domain, such as S4ND and Vim? Specifically, how does VMamba perform in terms of accuracy, computational efficiency, and memory usage compared to these models? - How well does VMamba generalize to other types of visual tasks beyond image classification, object detection, and segmentation? Have you considered evaluating VMamba on tasks such as video analysis, 3D vision, or more complex scene understanding? How does it scale on these tasks? - How sensitive is VMamba to various hyperparameters? It would be helpful to know if specific hyperparameters are critical to achieving the reported performance and if there are guidelines or best practices for tuning them. - How easily can VMamba be integrated into existing deep learning frameworks and pipelines? Are there any specific requirements or modifications needed for seamless integration? Confidence: 5 Soundness: 4 Presentation: 4 Contribution: 3 Limitations: Authors addressed everything regarding limitations section. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: # Response to Reviewer c4kg We appreciate the reviewer’s thoughtful review and constructive comments. In our responses, we address the following concerns: a detailed comparison with SSM-based methods, the generalizability of VMamba, sensitivity to hyper-parameters, and potential for integration into various frameworks. ### Detailed Comparison with SSM-based Methods In Table 1 of the main submission, we have already compared our method to S4ND [2] and Vim [4] in terms of the number of parameters, train throughput, and the Top-1 accuracy on ImageNet-1K. To provide a more comprehensive evaluation, we additionally conduct comparison on FLOPs and the memory usage, and the results are reported in the following table. Moreover, we also compare the performance (both effectiveness and efficiency) change with increasing input resolution in Figure 1 in the `attachment`. For qualitative comparison, we visualize the ERF of S4ND and Vim, and the results are shown in Figure 2 in the `attachment`. We will include these results and the associated analysis in the revised manuscript. \| Model \| Hierarchical \| Params (M) \| FLOPs (G) \| TP. (img/s) \| Test Mem. (M) \| Train TP. (img/s) \| Train Mem. (M) \| Top-1 (\%) \| \|:---:\|:---:\|:---:\|:---:\|:---:\|:---:\|:---:\|:---:\|:---:\| \|DeiT-S \|False \|22M \|4.6G \|1761 \|582 \|2404 \|4562 \|79.8 \| \|DeiT-B \|False \|86M \|17.5G \|503 \|1032 \|1404 \|9511 \|81.8 \| \|S4ND-ViT-B \|False \|89M \|17.1G \|398 \|2221 \|400 \|15868 \|80.4 \| \|Vim-S \|False \|26M \|5.3G \|811 \|1055 \|344 $\dagger$ (232) \|9056 $\dagger$ (16150) \|80.5 \| \|Swin-T \|True \|28M \|4.5G \|1244 \|3092 \|987 \|9798 \|81.3 \| \|ConvNeXt-T \|True \|29M \|4.5G \|1198 \|2498 \|702 \|9450 \|82.1 \| \|S4ND-Conv-T \|True \|30M \|5.2G \|683 \|3945 \|369 \|18843 \|82.2 \| \|Vanilla-VMamba-T \|True \|23M \|5.6G \|638 \|6042 \|195 \|16452 \|82.2 \| \|VMamba-T \|True \|30M \|4.9G \|1686 \|3064 \|571 \|12394 \|82.6 \| [Performance comparison between VMamba and benchmark methods. $\dagger$ indicates the value is measured with mix-resolution while Vim does not support training with mix-resolution (values in the brackets are results obtained with fp32).] ### Additional Related Studies We thank the reviewer for bringing these inspiring studies to our attention. We will include references to these papers in the revised version. ### Versatility of VMamba Due to our limited computational resources, we have focused on conducting experiments on benchmark tasks in vision modeling. However, we recognize the importance of illustrating the potential of the proposed method in more generalized tasks. A preliminary literature review of recently proposed SSM-based approaches in vision tasks, along with our private communications with researchers in the field, highlights the potential of the 2D selective scan technique (SS2D) introduced in this study. SS2D does not make specific assumptions about the layout or modality of the input data, which allows it to be generalized to various tasks. For example, SS2D can process video data by traversing a spatial-temporal plane of frame patches. To our knowledge, recent studies leveraging scanning patterns analogous to SS2D have shown success in various tasks, including image restoration and multimodal data understanding, in addition to those mentioned in the question. We will add these results to the final version and cite their works if they are published by then. Despite not being inherently prohibited, we anticipate challenges in directly migrating SS2D to diverse downstream tasks due to varying requirements. Bridging the gap between SS2D and these tasks, along with proposing a more generalized scanning pattern for vision tasks, is a promising research direction. We will include this discussion in the revised version, hopefully to provide readers with some inspiration. ### Clarity in Mathematical Derivations Due to limited space, we have included detailed proofs in the appendix and will provide more rigorous and clearer derivations in the revised version. We also recognize the significance of providing more intuitive and accessible explanations, and will include them in the revised version. ### Sensitivity ot Hyper-parameters According to our experience, we have not found any hyperparameter to which VMamba is particularly sensitive. This observation is also supported by the ablation results on single hyper-parameters (initialization approach in Table 11 and activation function in Table 15) as well as different combinations (Tables 12, 13, and 14) included in the Appendix. We conducted additional experiments on the influence of the learning rate, and the results are reported in the following table. We will include this discussion in the revised version. \|Model \|Params (M) \|FLOPs (G) \|lr \| Top 1. (\%) \| \|:--:\|:--:\|:--:\|:--:\|:--:\| \|VMamba-Tiny \|30M \|4.91G \|2e-3 \|82.70 \| \|VMamba-Tiny $\dagger$ \|30M \|4.91G \|1e-3 \|82.62 \| \|VMamba-Tiny \|30M \|4.91G \|5e-4 \|82.16 \| [The performance of VMamba-T with different learning rate. Results marked by $\dagger$ is the default setting used in the submission. All the models here are trained on `[SERVER 2]`.] ### Potential of Integrating into Various Frameworks The core of VMamba lies in the design of the SS2D module, which aims to bridge the gap between 1D sequence scanning and 2D plane traversing, rather than specific architectural configurations. SS2D can function as an end-to-end token mixer, allowing it to be integrated into various mainstream backbone networks in computer vision. Indeed, integrating SS2D into existing frameworks requires additional considerations. One critical aspect is the numerical precision settings in the model, which significantly impact performance and computational speed. Another important factor is the inclusion of normalization layers to stabilize the training process. We will include these points in the revised version to assist researchers who may want to build upon our work. --- Rebuttal Comment 1.1: Comment: 1. Authors did Detailed Comparison with SSM-based Methods along with experiments. 2. They will include works of Zubić et al. and Schoene et al. in the related works section. 3. Authors said that they will discuss more the generalized scanning pattern for vision tasks in the paper as future work, which is very interesting. 4. Authors "have not found any hyperparameter to which VMamba is particularly sensitive". 5. Pretty robust model to the changes in hyperparameters, they did experiments, for example learning rates, which is great. Given that the authors have addressed all my concerns with clear and effective experimental evidence, I am updating my score from Accept (7) to Strong Accept (8).	Summary: This paper transplants the Mamba (Selective State Space Model), a linear complexity model originally designed for 1D language processing, into VMamba to process image data. It introduces the 2D selective scan and various acceleration techniques to facilitate the modeling of 2D data and enhance the speed of the network. The proposed VMamba model is trained and evaluated on a number of representative downstream tasks including ImageNet-1K classification, COCO object detection, and ASE20K semantic segmentation, and it is compared with strong baselines. A range of analyses and visualizations on the theoretical perspectives, design choices, and behavior of the model are also presented. Strengths: 1. VMamba is one of the first papers to attempt using Mamba, one of the most efficient and performant linear complexity models to date, to learn visual data and demonstrate effectiveness. 2. The paper proposes a series of innovations to adapt the original Mamba's 1D sequential scanning to process 2D image data (SS2D) and increase the model's processing speed (image throughput) without compromising performance. 3. In-depth deductions, comprehensive analyses, experiments, and visualizations on design choices, theoretical aspects (e.g., the relationship between SSM and Self-Attention), and model behaviors have been presented, carrying a huge volume of insightful findings that are valuable for future research. 4. The proposed VMamba is compared to representative downstream tasks, including ImageNet-1K classification, COCO object detection, and ASE20K semantic segmentation. It shows comparable or better (and consistent) results to strong baselines (e.g., Swin, DeiT, and the concurrent Vim) and superior efficiency. 5. As a general and simple visual model, the proposed VMamba potentially carries huge extension and generalization potential, which could inspire and impact a wide range of visual research. Weaknesses: I didn’t find any critical weakness in this paper. Apart from some limitations that have already been mentioned by the authors, such as large-scale experiments, training strategies, and hyperparameter search, the only part that I hope the paper can show more results is the ablation of some design choices. For instance, the performance change of removing the entire multiplicative branch, where Table 5 does not show a straight ablation because of more than 1 variable change. This problem also exists in some other tables of some other design choices and hyperparameters. But again, I think neither of these weaknesses is critical. Technical Quality: 4 Clarity: 4 Questions for Authors: Could the authors explain more on the statement in Lines 153-154, “such modification prevents the weights from being input-independent, resulting in a limited capacity for capturing contextual information”? Others: Repetitive reference entries: [50] and [51], [50] and [60]. Confidence: 4 Soundness: 4 Presentation: 4 Contribution: 3 Limitations: The authors adequately discuss the limitations and potential societal impact of this work. This paper also points out several potential improvements and future directions, with which I highly agree. Flag For Ethics Review: ['No ethics review needed.'] Rating: 8 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: # Response to Reviewer ZfkW We appreciate the reviewer’s thoughtful review and positive comments about our study. In the following sections, we address the reviewer’s primary concern regarding the lack of ablation on design choices and clarify several other issues raised. ### More Ablation on Design Choices First of all, we would like to clarify that our primary reason for modifying multiple hyper-parameters simultaneously is to ensure that the number of parameters and FLOPs remain comparable, facilitating a fair comparison between different model variants. In Table 5 (corresponding to Figure 3 (e) in Section 4.3 of the main submission), we detail the configurations used to optimize the overall performance of VMamba, balancing both effectiveness and efficiency rather than isolating the impact of each hyperparameter. However, we sincerely acknowledge the importance of analyzing the significance of each individual hyperparameter and architectural design choice on the overall performance. We plan to conduct more comprehensive experiments to extend the results of experiments isolating each hyperparameter in Table 5, and include those results in future versions of this study. To address the issue mentioned in the reviewer's comment, we have conducted additional experiments to analyze the influence of changing a single variable. The results are reported in the following table. Values for Step (e.1) and Step (e.2) are copied from Table 12 and Table 14 in the appendix, respectively, while Step (d.1) and Step (d.2) present new results obtained during the rebuttal process. \| Model \| d\_state \| ssm\_ratio \| DWConv \| Multiplicative Branch \| Layers \| FFN \| Params (M) \| FLOPs (G) \| TP. (img/s) \| Train TP. (img/s)\| Top-1 (\%) \| \|:--:\|:--:\|:--:\|:--:\|:--:\|:--:\|:--:\|:--:\|:--:\|:--:\|:--:\|:--:\| \|Vanilla-VMamba-T\|16 \|2.0 \|True \|True \|[2,2,9,2] \|False\|22.9M \|5.63G \|426 \|138 \|82.17 \| \|Step(a) \|16 \|2.0 \|True \|True \|[2,2,9,2] \|False\|22.9M \|5.63G \|467 \|165 \|82.17 \| \|Step(b) \|16 \|2.0 \|True \|True \|[2,2,9,2] \|False\|22.9M \|5.63G \|464 \|184 \|82.17 \| \|Step(c) \|16 \|2.0 \|True \|True \|[2,2,9,2] \|False\|22.9M \|5.63G \|638 \|195 \|82.17 \| \|Step(d) \|16 \|2.0 \|False\|True \|[2,2,2,2] \|True \|29.0M \|5.63G \|813 \|248 \|81.65 \| \|Step(d.1) \|16 \|1.0 \|False\|True \|[2,2,2,2] \|True \|22.9M \|4.02G \|1336 $\dagger$\|405 $\dagger$\|81.05 $\ddagger$\| \|Step(d.2) \|16 \|1.0 \|False\|True \|[2,2,5,2] \|True \|28.2M \|5.18G \|1137 $\dagger$\|348 $\dagger$\|82.24 $\ddagger$\| \|Step(e) \|16 \|1.0 \|False\|False\|[2,2,5,2] \|True \|26.2M \|4.86G \|1179 \|360 \|82.17 \| \|Step(e.1) \|16 \|1.0 \|True \|False\|[2,2,5,2] \|True \|26.3M \|4.87G \|1164 \|358 \|82.31 \| \|Step(e.2) \|1 \|1.0 \|True \|False\|[2,2,5,2] \|True \|25.6M \|3.98G \|1942 \|647 \|81.87 \| \|Step(f) \|1 \|2.0 \|True \|False\|[2,2,5,2] \|True \|30.7M \|4.86G \|1340 \|464 \|82.49 \| \|Step(g) \|1 \|1.0 \|True \|False\|[2,2,8,2] \|True \|30.2M \|4.91G \|1686 \|571 \|82.60 \| Details of accelerating VMamba. $\dagger$ and $\ddagger$ indicate the value is obtained from `[SERVER 1]` and `[SERVER 2]`, respectively. All other experiments are conducted on `[SERVER 0]`. ### Clarification of the Statement There is a typo in the mentioned statement, and the correct version is "such modification prevents the weights from being input-dependent, resulting in a limited capacity for capturing contextual information" (i.e., change from "input-independent" to "input-dependent"). We will fix this typo and conduct thorough proofreading to prevent further errors in the revised version. Detailed Explanation of the Referred Statement. S4ND [2] extends S4 [1] to higher-dimensional contexts through a straightforward outer product, with the essential condition being that the SSM in S4 is implemented using 'accelerated convolution'. Specifically, S4 utilizes a global convolutional operation to compute the output of the SSM, denoted as $\mathbf{y}$, given the input data $\mathbf{u}$ and the kernel function $\mathbf{K} = \mathbf{C}e^{\mathbf{A\Delta}}\mathbf{B}$. Efficient computation is achieved if $\mathbf{A}$ has an 'Normal Plus Low-Rank' (NPLR) form and $\Delta$ is constant, enabling the low-rank approximation of $\mathbf{K}$ in the spectral domain, allowing the convolution to be efficiently computed with Fast Fourier Transform (FFT) and Inverse Fast Fourier Transform (IFFT). Conversely, if $\Delta$ is input-dependent or context-aware, the kernel function will no longer maintain a low-rank form in the spectral domain, leading to a substantial increase in the convolution computation time. The efficacy of a recurrent model is significantly limited by its capacity to effectively compress context [3]. By leveraging the task of selective copying and employing Induction heads, Mamba [3] illustrates that LTI models lack content awareness. Consequently, it is concluded that a fundamental principle in developing sequence models is selectivity: the context-aware capability to emphasize or disregard specific inputs within a sequential state. ### Repetitive Reference Entries We will address the issues mentioned in the comment and conduct thorough proofreading to prevent further errors in the revised version. --- Rebuttal 2: Title: Final Rating Comment: Thanks to the authors for providing a thorough and solid response to all my concerns. Based on all the reviewers' comments and the rebuttal, I am happy to keep my rating as a Strong Accept (8).	Summary: ### Summary This paper proposes VMamba, which adopts the recently proposed selective linear state space model, Mamba, in the domain of computer vision. The paper evaluates variants of VMamba on tasks such as image classification, object detection, and semantic segmentation. To improve performance and efficiency, VMamba incorporates several architectural and implementation enhancements. --- post-rebuttal: score 6 -> 7 Strengths: ### Strengths - The writing is simple and clear, quite accessible to readers. - After implementing enhancements, VMamba achieves good performance - computational efficient and quantitatively well-performed. - Additional analysis such as the effective receptive field and relationship between attention and the updates in state space are insightful. Weaknesses: ### Weaknesses - As an architecture exploration paper I don’t see many weaknesses. Technical Quality: 3 Clarity: 3 Questions for Authors: ### Questions 1. Is positional embedding used when encoding the patches? Apologize if this is already state somewhere in the paper. 2. If I understand correctly, Figure 3 for section 4.3 shows that performance improved with smaller d_state and expand ratio. This is quite surprising since one might expect degrading performance when network capacity is reduced. Could you provide any insights into this phenomenon? Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: Yes, the author adequately addressed the limitations. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: # Response to Reviewer dvTH We thank the reviewer for the constructive comments and are glad they appreciate the performance of VMamba. Below, we clarify the reviewer’s concerns regarding the detailed structure and the influence of hyper-parameters on VMamba. ### Usage of Positional Embedding To clarify, VMamba does not use positional embedding. Sorry for any confusion caused, and we will make this clear in Section 4.1 Network Architecture (lines 129-136) of the revised version as follows: "Subsequently, multiple network stages are employed to create hierarchical representations" $\rightarrow$ "Without further incorporating positional embedding, multiple network stages are employed to create hierarchical representations." ### Explanation of Performance Improvement In step (e) shown in Figure 3 for Section 4.3, we manage to save parameters and FLOPs by reducing the expansion ratio and eliminating the entire multiplicative branch. This allows us to increase the number of layers from [2,2,2,2] to [2,2,5,2], resulting in the observed performance improvement. Similarly, in step (g), lowering the expansion ratio enables us to increase the depth of the model with additional layers. For step (f), the performance improvement is due to the larger expansion ratio and the addition of extra DWConv blocks. By using a smaller d\_state value, we keep parameters and FLOPs comparable. We will provide more details on these points in the revised version. Influence of d\_State. In Section H.3 of the Appendix, we explore the impact of adjusting the d\_state parameter on VMamba. Table 12 shows that increasing d\_state from 1 to 4 yields only marginal performance gains while significantly reducing throughput, indicating a substantial negative impact on VMamba's computational efficiency. To mitigate this, we propose lowering the ssm\_ratio parameter to reduce overall network complexity. We find the best performance at (d\_state=8, ssm\_ratio=1.5). Influence of ssm\_ratio. We also analyze VMamba's sensitivity to the ssm\_ratio parameter, with results presented in Table 13 of Appendix H.4. The results clearly indicate that lowering the ssm\_ratio significantly reduces performance but also greatly increases the inference speed. On the other hand, adding more layers boosts performance but also decelerates the model. --- Rebuttal Comment 1.1: Comment: Thank you for the rebuttal. I will raise my score, this is a good paper.	null	null	Rebuttal 1: Rebuttal: # Response to all We thank the reviewers for their thoughtful reviews and constructive suggestions. We’re glad that the reviewers recognized the innovation and influence of the proposed 2D-Selective-Scan (SS2D) module, as well as the extensive experiments and thorough analysis supporting VMamba. In the following, we provide a shared response to common concerns raised by the reviewers, and also include a PDF file (referred to as the `attachment`) with additional experimental results to support our discussion. Additional results are included in the `attachment` (figures) as well as in the separate responses to each reviewer (tables). ### Ablation Study on Hyper-parameters All reviewers have raised concerns regarding the influence of hyper-parameters. Due to the mismatch between our limited computational resources and the extensive range of design choices, we did not initially conduct a comprehensive ablation study on all hyper-parameters, focusing instead on a subset included in the appendix. As suggested by the reviewers, we have now conducted additional experiments on this topic. ### Comparison with SSM-based Models Another focus of the reviewers is the need for a more in-depth comparison between VMamba and SSM-based models, such as S4ND [2] and Vim [4]. We recognize the importance of these comparisons and have conducted additional experiments as suggested. The results include comparisons of FLOPs, visualizations of the Effective Receptive Fields (ERFs), and analyses of the changes in performance (both effectiveness and efficiency) with increasing input resolution. ### Statement on Experiment Platforms Please note that there are slight differences between the platforms we used for the original study and this rebuttal. \| Usage \| CPU \| GPU \| Notation \| \|:--:\|:--:\|:--:\|:--:\| \|Original Work\|AMD EPYC 7542\| 8 $\times$ Tesla A100 GPU\|`[SERVER 0]`\| \|Rebuttal (Testing)\|Intel Xeon Platinum 8358\|Tesla A800 GPUs\|`[SERVER 1]`\| \|Rebuttal (Training)\|Intel Xeon Platinum 8480C\|8 $\times$ Tesla H100 GPU\|`[SERVER 2]`\| We investigate the influence of computational platforms on evaluation results as follows. For `[SERVER 0]` and `[SERVER 1]`, we test the generalizability to inputs with increased spatial resolutions, and the results are shown in the following table. Both training and inference throughput values are measured with a batch size of $32$ using PyTorch 2.2. The training throughput calculations include only the model forward pass, loss forward pass, and backward pass. \| Model \| Image Size \| Params (M) \| FLOPs (G) \| [SERVER 0] TP. (img/s) \| [SERVER 0] Train TP. (img/s)\| [SERVER 1] TP. (img/s) \| [SERVER 1] Train TP. (img/s)\| \|:--:\|:--:\|:--:\|:--:\|:--:\|:--:\|:--:\|:--:\| \|VMamba-Tiny\|$224^2$ \|30M\|4.91G \|1490\|418\|1463\|453\| \|VMamba-Tiny\|$288^2$\|30M\|8.11G \|947 \|303\|952 \|305\| \|VMamba-Tiny\|$384^2$\|30M\|14.41G\|566 \|187\|563 \|187\| \|VMamba-Tiny\|$512^2$\|30M\|25.63G\|340 \|121\|339 \|120\| \|VMamba-Tiny\|$640^2$\|30M\|40.04G\|214 \|75 \|216 \|75 \| \|VMamba-Tiny\|$768^2$\|30M\|57.66G\|149 \|53 \|149 \|53 \| We also compare the differences between VMamba-T trained on `[SERVER 0]` and `[SERVER 2]` in the following table. \| Model \| Params (M) \| FLOPs (G) \| LR \| Top 1. (\%) \| \|:--:\|:--:\|:--:\|:--:\|:--:\| \|VMamba-Tiny [SERVER 0]\|30M\|4.91G\|1e-3\|82.60\| \|VMamba-Tiny [SERVER 2]\|30M\|4.91G\|1e-3\|82.62\| According to the results shown in the above two tables, there is only a subtle difference between the results obtained on `[SERVER 0]` and `[SERVER 1]`/`[SERVER 2]`. Therefore, we disregard the influence of computational platforms and will include results obtained with consistent machines in the revised version. ### Citations: [1] Albert Gu, Karan Goel, and Christopher Re. Efficiently modeling long sequences with structured state spaces. In ICLR, 2021. [2] Eric Nguyen, Karan Goel, Albert Gu, Gordon Downs, Preey Shah, Tri Dao, Stephen Baccus, and Christopher Ré. S4nd: Modeling images and videos as multidimensional signals with state spaces. NeurIPS, 35:2846–2861, 2022. [3] Albert Gu and Tri Dao. Mamba: Linear-time sequence modeling with selective state spaces. arXiv preprint arXiv:2312.00752, 2023. [4] Lianghui Zhu, Bencheng Liao, Qian Zhang, Xinlong Wang, Wenyu Liu, and Xinggang Wang. Vision mamba: Efficient visual representation learning with bidirectional state space model. In ICML, 2024. [5] Ze Liu, Yutong Lin, Yue Cao, Han Hu, Yixuan Wei, Zheng Zhang, Stephen Lin, and Baining Guo. Swin transformer: Hierarchical vision transformer using shifted windows. In ICCV, pages 10012–10022, 2021. Pdf: /pdf/61022f32d77522e8311b67559464124abe13c25b.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Analyzing & Reducing the Need for Learning Rate Warmup in GPT Training	Accept (poster)	Summary: This work explores the benefits of learning rate warmup in neural network training, focusing on the size of model updates via the GPT2 model. It finds that controlling update size in parameter space doesn't fully explain warmup's advantages, but quantifying updates in terms of neural representation changes shows promise. The study also highlights the role of high momentum in warmup and suggests potential methods for reducing the need for manual warmup configuration. Overall, the research provides insights into learning rate warmup's necessity and potential ways to eliminate it in practice. Strengths: The paper addresses an intriguing topic, which aims to present a systematic understanding regarding the LR warmup heuristic from a novel perspective. However, I feel that the authors have attempted to cover too many aspects, which might be challenging to thoroughly demonstrate within the scope of a single conference paper. Weaknesses: 1. I noticed that the authors have not adequately discussed the highly relevant paper, "On the Variance of the Adaptive Learning Rate and Beyond," which addresses some of the questions raised by the authors. Please discuss the unique contributions of your work compared to the variance-based analysis presented in that paper. 2. Although the authors try hard to explain the need for warmup and how to potentially reduce it, I still did not find persuasive answers to the questions posed. The conclusions are primarily based on intuitive narrative explanations and a simple experiment involving GPT-2. Meanwhile, some of the conclusions seem to be evident. For instance, before I read the paper, I could understand the statement "L2 update size is not sufficient to quantify the 'effectively' large updates". The paper lacks convincing evidence to support its claims. Lastly, I recommend that the authors narrow down the scope of the title to accurately reflect the content presented in the paper. 3. The authors use linear transitions to analyze the representation changes, which seems too toy for me. 4. I think the gradient clipping operation may be quite related regarding the authors' idea, as it directly impacts the adaptive LR. Could the authors provide some research here? 5. Regarding the writing of this paper, in my opinion, it is not particularly easy to follow. The organization feels somewhat messy. I think the authors should improve the clarity and structure. For example, including more detailed explanations and transitions between sections. 6. In Figure 1, I observe that the performance may be quite similar when using a lower learning rate. Could the authors specify the lowest learning rate used in your experiments? 7. I found the authors' use of the term "update size" to denote the step size in Adam somewhat confusing. I recommend that the authors use "update step", "adaptive learning rate" or "effective learning rate" instead, as these terms are clearer. Technical Quality: 3 Clarity: 2 Questions for Authors: See Weakness. Confidence: 3 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: I have not found any discussions about the limitations and potential negative societal impact. But in my opinion, this may not be a problem, since the work only focuses on analyzing the warmup heuristic in machine learning. Still, it is highly encouraged to add corresponding discussions. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your review and feedback! W7 Update Size: We want to begin by clarifying this as it is a very important concept for our paper. By “update size” we literally mean “the size of the update”. This can be measured in different ways, for example through the L2 norm of the update, the angular change, or the representation change. We note that this is different from the learning rate, which scales the update size, but does generally not fully determine the update size. For example in SGD the L2 update size depends on the learning rate as well as the norm of the gradient. We specifically use “update size” or “update magnitude” to try to avoid confusion with these other terms that we do not feel capture our intended meaning. W1 Comparison with RAdamW: Thank you for this suggestion for improving our paper. Since RAdamW is a popular method for reducing the need for warmup it serves as a good comparison and contextualization of our work. Figure 1 in the global response shows that the RAdamW modifications are insufficient to eliminate the need for warmup in our setting. [2] suggest that RAdamW is approximately equivalent to 4 steps of SGDM followed by Adam with a special type of built-in warmup whose length is roughly 2/(1-beta2) = 40, which is likely too short in our setting. The analysis in [1] is based on the idea that early in training the second-moment estimates are not accurate (noisy) and can therefore not be trusted to scale the update properly. This could in turn contribute to the need for warmup. We note that without momentum, perfect estimates of the second moment at the current time step would control the expected L2 norm of the update. This relates our approach of looking at the update size to the adaptive learning rate view you seem to favor. We note that although [1] focuses on this issue of counteracting noisy estimates of the second moment, this is not necessary the sole reason warmup is beneficial. This is supported by the fact that both SGD and Lion empirically need warmup in various settings but do not use the second moment at all, indicating there is more to the story. The other aspects we explore relate to the momentum (e.g. the bias correction), weight decay and initialization (the angular updates), and how the gradient diversity affects how quickly the internal representations change (RRC compensation). We don’t believe [1] touches upon any of these to a significant extent. We also use Lion to control the L2 update size, avoiding the issues that [1] focuses on. Both works aim to reduce the need for learning rate warmup but focus on different aspects and take a completely different approach. Overall we therefore believe there is very little overlap in the contributions of these works, and if anything they could be complementary if we were to port our Lion modifications back to AdamW. W2 Title: Yes, we agree that just using GPT instead of neural networks would be more fitting. Thank you for this suggestion. W2 L2 Norm is obvious: We don’t believe this is the case, see both the discussion of gradient clipping and RAdamW which are closely related to this idea and not at all obvious shouldn’t work. We also note that clipping the L2 norm of the update will prevent a network from diverging to infinity, something that is often observed in unstable SGD training where warmup can help. Could you clarify further why you believe this is obvious or provide some reference to prior work that shows this? W3 Linear Transformations: This is of course a simplification compared to full neural networks. However, we believe this already gives interesting insights that are sufficient for our purposes. Specifically, this clearly shows that the parameter update size must be decreased when the gradient diversity is low in order to keep the representation changes small. We are also able to draw the same conclusions as existing works e.g. muP and hyperparameter scaling laws, showing this analysis provides useful results despite its simplicity. We believe a more complicated analysis would not fit within the scope of this paper, which is already on the broad side as you mention. W4 Gradient Clipping: Yes, gradient clipping can directly affect the update size. This is especially true when using SGD without momentum, where gradient clipping is similar to clipping the L2 norm of the update. However, controlling the L2 norm is not sufficient as we show. We believe the other ideas like the angular updates and representation changes are less related (but please clarify if you believe they are). W5 Presentation: Could you be more specific here? We note that some of the other reviewers found the paper to be “very well written” and “well motivated and systematic”, but we are happy to consider any concrete changes you recommend. W6 Range of the sweep: Yes, the performance is similar for smaller learning rates. This is consistent with our main hypothesis that large updates cause the degradation that warmup counteracts. Smaller learning rates result in smaller updates, thus avoiding this issue. The lowest learning rate in this sweep is 3e-4. Please let us know if you have any further questions or suggestions! If you feel we have at least partially addressed your concerns, we would greatly appreciate it if you would consider reevaluating your review score. --- [1] Liyuan Liu, Haoming Jiang, Pengcheng He, Weizhu Chen, Xiaodong Liu, Jianfeng Gao, and Jiawei Han. On the variance of the adaptive learning rate and beyond. In International Conference on Learning Representations, 2020. URL https://openreview.net/forum? id=rkgz2aEKDr. arXiv:1908.03265. [2] Jerry Ma and Denis Yarats. On the adequacy of untuned warmup for adaptive optimization. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 35, pages 8828–8836, 2021. arXiv:1910.04209. --- Rebuttal Comment 1.1: Comment: Thanks for the response. I have no further concerns. Considering the authors' further revisions based on the rebuttal, I vote for acceptance.	Summary: The submission analyzes the underlying reason behind the need for a learning rate warmup in neural network training, focusing on GPT pre-training with AdamW and Lion optimizers. The authors identify three key reasons as to why the initial updates are large: 1. Momentum handling by AdamW, 2. Early updates not correlated with the initial weight magnitudes 3. Correlation between gradients of examples during early training The study introduces modifications to the Lion optimizer to mitigate the first two issues and proposes a method for controlling activation updates to address the third. Overall, I believe the paper's contributions are significant and hence I vote for acceptance. Strengths: * This paper analyzes various metrics that correlate with the benefit of learning rate. * The analysis of the normalized Gradient Descent is insightful and reproduces previously known scaling laws. Weaknesses: * The authors begin by analyzing warmup for Adam and instead of directly modifying Adam, they modify the Lion optimizer. Direct modifications to the Adam optimizer would be more convincing and then moving to Lion would streamline the arguments. * The LionAR algorithm is a much more complex solution than AdamW + warmup. Warmup duration is not a crucial hyperparameter, as a longer warmup duration does not hurt training. * The experiments are performed on a fixed setup: GPT-2 model with 100M parameters trained on a single dataset. To ensure the validity and generalizability of the results, it is crucial to extend the analysis to various model architectures, parameter sizes, and datasets. Technical Quality: 3 Clarity: 3 Questions for Authors: * Which dataset is used for training the model? I don't think it is mentioned anywhere in the paper and its important for reproducing the results. * Can the authors clarify the statement 'This factor is larger if the gradients are negatively correlated, which we empirically observe often happens early in training' on line 110? * Did the authors try Adam with inverse bias correction for the momentum as suggested by equation 1? Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 4 Limitations: See weaknesses Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your review and feedback! Using Adam instead of Lion: We actually experimented with direct modification to Adam originally before moving to Lion. This worked equally well or better than the Lion modifications. However, we realized that at the start of training the gradient norms can change rapidly, specifically decreasing in our setup. This causes the second moment in Adam to be larger than it would otherwise be, resulting in smaller update sizes and essentially giving an additional warmup-like effect. The update size is also affected by the alignment of the gradients in successive steps (through momentum), complicating the control of the update size. The main reason for moving to Lion was that it gives precise control of the update size at a given iteration, eliminating these confounding effects that we found hard to control for in Adam and allowing us to explore the effect of the update size directly. We will edit the manuscript to clarify this, but we acknowledge your point that the use of Lion complicates the story. Complexity of LionAR: This is a fair point, the algorithm for LionAR is more complicated than for AdamW. A significant portion of this complexity comes from trying to transfer the hyperparameters of Adam over to Lion, as well as handling the two types of momentum. This could be removed if we don’t need this which would simplify the algorithm considerably. Then the major difference is additional projection of the weight norm instead of using weight decay. In practice weight decay is also only applied to some parameters which could be expressed with a similar if/else branch. In terms of the optimization dynamics we expect the behavior of LionAR to be much more regular than when using weight decay which could matter more than the complexity of the code overall. That being said, we also agree that warmup is a perfectly fine solution in practice, we primarily want to offer insights into why it is needed. Diversity of the Experiments: We agree and would have liked to showcase a broader range of experiments. We are unfortunately somewhat restricted in our compute budget but have tried to add some simple ablations in the global response. We tried a different dataset (SlimPajama [1]) with the same GPT setup and found similar results. We also tried to change the architecture to a llama2 instead of the GPT2 style we used originally. In this case LionAR already suffices to eliminate the need for warmup without further tricks like the RRC or momentum changes. This is likely due to changes in the critical batch size although the exact reasons for why the architecture affects this are not clear to us. We want to further experiment with larger batch sizes and see if the llama behavior becomes more similar to that of GPT2. Dataset: Thank you for pointing this out. This was an oversight on our part, and we appreciate your thorough review. The dataset we used is OpenWebText [2], the same one referenced in the GPT2 paper and NanoGPT. We will update the manuscript to include this information. Line 110 clarification: We meant correlation over time / between optimizer steps, i.e. that when the gradients of successive steps point in opposite directions they cancel out in the momentum vector. This leads to smaller update sizes in Adam. However, the bias correction assumes that all future gradients will align with the current momentum vector and magnifies the update size accordingly, leading to much larger steps than we would see otherwise. We will edit this to clarify. Adam with inverse bias correction Yes, we did some exploratory experiments with modifications like these as well as removing the bias correction completely. This helps a bit, but overall the effect is too small to make a significant difference for momentum values like 0.9. At best this could result in warmup like effects of maybe 20 steps, which is too small to significantly decrease the no-warmup degradation in our setting. For comparison, see also the RAdamW results in the global response which might give effects similar to 40 steps of warmup which is not sufficient. --- [1]: Soboleva, Daria, Faisal Al-Khateeb, Robert Myers, Jacob R. Steeves, Joel Hestness, and Nolan Dey. "SlimPajama: A 627B Token Cleaned and Deduplicated Version of RedPajama." June 2023, www.cerebras.net/blog/slimpajama-a-627b-token-cleaned-and-deduplicated-version-of-redpajama. [2]: Gokaslan, Aaron, and Vanya Cohen. "OpenWebText Corpus." 2019, Skylion007.github.io/OpenWebTextCorpus. --- Rebuttal 2: Comment: I thank the reviewers for their comments. Most of my concerns have been resolved. I look forward to the updated version of the manuscript.	Summary: In this paper the authors investigate the performance benefits seen from the common practice of learning rate warmup and scheduling, attempt to understand the mechanistic underpinnings of those improvements, and engineer optimizers that mitigate the need for warmup. They conduct experiments using NanoGPT and consider controlling parameter updates, angular updates, and “relative representation” changes to close the gap between warmup and no warmup. Strengths: Warmup length and peak learning rate are certainly some of the most important hyperparameters in large model training, and eliminating the need for a warmup phase would present a significant simplification to training. The paper is well motivated and systematic in its investigation of warmup and proposals to sidestep the necessity of warmup. The RRC is an interesting and promising angle on this question. Weaknesses: The results do not suggest a clear prescription for learning rate scaling or straightforward changes that can be made to initializations or updates. In particular, the RRC is completely dependent on the inputs, but there does not seem to be any discussion or investigation of the effects of the input data. For the NanoGPT experiments there is no mention of what the data is. Presumably training was done with a cross entropy loss, but this is also not mentioned. Technical Quality: 3 Clarity: 3 Questions for Authors: Can the authors provide some discussion about the sensitivity of RRC to variance in the inputs across and within batches? It is also not clear what direction the RRC results are suggesting. An “automatic warmup” that scales the update sizes according to online measurements of the signal-to-noise ratio is still a warmup phase, albeit a more principled way to arrive at what that schedule should look like. To be clear, I don’t think this is a bad thing, but it may be more representative of the results to propose an “adaptive” or “automatic” learning rate scheduler, rather than claim to make progress towards eliminating the need for scheduling. Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: Partially Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your review and feedback! Missing Dataset Information: Thank you for pointing this out! This was an unfortunate oversight on our behalf (and we geatly appreciate your attention to these details). The dataset we train on is the original OpenWebText dataset [1] used in the original GPT2 work. Training is indeed performed via next token prediction using cross entropy with teacher forcing. We will include this in future revisions of the manuscript. RRC Dependency on Data: We have expanded our experiments to include a separate dataset (SlimPajama [2]), obtaining similar results. You are correct that the RRC correction depends on the input data (by design), in a way that controlling the parameter update norm can not. This will vary depending on the data within a batch. The simplest example of this would be if the whole mini-batch consists of the same datapoint repeated. The RRC correction would indicate that we should use a lower learning rate (parameter update size) in this case than if the data has no similarity. However, the RRC correction does not measure the similarity of the data in the input space but rather through the gradient diversity. It therefore not only depends on the similarity of the data within each batch (which shouldn’t vary throughout training) but rather on the similarity of the “learning” to be made from each sequence. This can vary throughout time, for example early in training the model could largely learn syntax, word frequency, and potentially unlearn initialization biases (like maybe outputting the input sample). There is a strong overlap in the “lesson” to be learned from each input sequence in this context, resulting in similarity between the gradients which may be dominated by these simple concepts. Later in training the model could learn more advanced concepts that differ more depending on the semantic content of each sequence, resulting in greater gradient diversity. At this point we can perform larger parameter updates because the contributions of the input sequences do not all line up to change the representations in the same way. Such alignment would lead to large representation changes, which we hypothesized could lead to lasting issues e.g. with the non-linearities. In its current form there is no dependency on the similarity between batches for the RRC correction. We hope that if the data is well shuffled the similarity within each mini-batch also reflects the similarity between batches, otherwise this could lead to issues. Let us know if you believe this kind of conceptual discussion of the RRC would be useful / informative we would be happy to incorporate it into the manuscript. Eliminating Warmup vs Automatic Warmup: This is a fair point and we do indeed refer to the RRC correction as an automatic warmup in lines 41 and 220. Overall we believe the definition of a warmup or a schedule is a bit subjective. For example Adam can be seen as a per-coordinate adaptive scheduler for the vanilla SGD learning rate, but what we refer to as the learning rate schedule does typically not account for this. In the same way an RRC corrected optimizer could eliminate the need for manually specified warmup, but would lead to a warmup like effect in the parameter update size. Using other metrics to measure the update size like the RRC, there would not necessarily be an observable warmup phase (and the learning rate could directly control this update size). Clear Recommendations: We do not touch upon initialization but we do show optimizer modifications (LionAR) and potentially further scaling via the RRC gradient noise correction is sufficient to significantly reduce or eliminate the need for warmup. People could attempt to directly apply these methods in other settings if warmup is undesirable for some reason. However we view the primary contribution of our work to be understanding of how the changes in the update size across time contribute to the need for warmup. We hope this will lead to a better understanding of optimization dynamics, that it could inform practitioners about the length of warmup (by just measuring the same metrics we do), and finally lead to better optimizer design in the future. We take the steps towards the optimizer design with LionAR and the RRC correction, but believe future work could improve upon them. Additional Experiments: Aside from repeating our experiments with a different dataset we have performed several other ablations for additional experimental evidence, see the global response. Please let us know if you have any additional questions! We would also greatly appreciate it if you could inform us whether the additional experiments, proposed modifications, and clarifications at least partially mitigate your concerns. --- [1]: Gokaslan, Aaron, and Vanya Cohen. "OpenWebText Corpus." 2019, Skylion007.github.io/OpenWebTextCorpus. [2]: Soboleva, Daria, Faisal Al-Khateeb, Robert Myers, Jacob R. Steeves, Joel Hestness, and Nolan Dey. "SlimPajama: A 627B Token Cleaned and Deduplicated Version of RedPajama." June 2023, www.cerebras.net/blog/slimpajama-a-627b-token-cleaned-and-deduplicated-version-of-redpajama. --- Rebuttal Comment 1.1: Comment: I thank the authors for their detailed response. They have addressed the points raised in my review and I have increased my score.	Summary: To train current deep neural network architectures, especially transformers, the learning rate of AdamW is usually first linearly increased to reach a peak before it's decreased to zero. The paper analyzes the impact of this so-called warming-up phase on GPT-2 models from the perspective of the update size. As a second contribution, the paper presents some small modifications for the Lion optimizer to mitigate some of the issues encountered in the experiments. Strengths: - The paper is very well written. The experiments are nicely motivated and reasonable. - Warming up the learning rate is arguably common practice for training transformer models, but not well understood. The paper provides some interesting analysis of the matter, which could potentially lead to a more intuitive understanding of the problem and eventually better optimizers. Weaknesses: - The results of the paper are somewhat inconclusive and after reading the paper, I am still not sure about the dynamics during the warming up phase. For example, while controlling angular updates seems to stabilize training to a certain degree, it eventually doesn't lead to better performance. Also, as the paper clearly states, the magnitude of the parameter updates doesn't really account for the gains of the warm-up phase. I am wondering if the paper approaches the problem actually from the right perspective. Having said that, I think the paper still provides some value and might help to stir future research. - While the empirical evaluation is insightful, it's limited to a single architecture and domain. This raises the question of how reliable the results actually are. Technical Quality: 3 Clarity: 4 Questions for Authors: - How sensitive are the results from Section 3 to the type of learning rate schedule? For example, how would Figure 1 look if you used, let's say, a cosine annealing schedule? Confidence: 2 Soundness: 3 Presentation: 4 Contribution: 3 Limitations: I think the paper spells out all its limitations; however, for visibility, it might be better to move the corresponding paragraph from the appendix to the main text. I don't see any negative societal impacts of the work. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your review and feedback! Generalizability of the results: We have added experiments with a different GPT architecture (Llama2) and dataset (SlimPajama), see global response. We find that the results are similar, suggesting some transferability within GPT-style training. Originally we wanted to include more transformer tasks like vision transformers and translation but actually found that warmup did not have a significant impact in our target settings. This likely depends on the batch size among other factors, but instead of exploring this further we decided to narrow the scope to GPTs. We will change the title to reflect this, changing “neural network” to “GPT” as suggested by one of the other reviewers. General Approach: The main takeaway would be that the need for warmup largely arises from poor control of the update size during training. Modified optimizers, especially those that control the angular update size directly, can significantly reduce or eliminate the need. However, ultimately we believe that it is large changes in the internal representations that cause the need for warmup, which can not be fully captured by simple measures of the update size of the parameters. We show that the discrepancy between the parameter update size and representation changes can be linked to the noise in the gradient. We can compensate for this based on measurements of the gradient noise, leading to something like an “automatic warmup” in the parameter update size. The hope is that this will lead to an improved understanding of optimization dynamics and potentially eventual improvements in optimizer design. Controlling the angular updates improves performance without warmup, but we did not really attempt to improve the overall performance with warmup. We note that LionAR is at a bit of a disadvantage since the weight decay value and other settings are inherited from the baseline (not re-tuned) and we constrain the magnitude without any additional mechanism like learnable gains to compensate for this. Cosine Schedule: Thank you for bringing this up, this is something we will clarify further. We reran the AdamW baseline with a cosine schedule and added it to the global response (see left half of top figure). The trapezoidal schedule (aka warmup-stable-decay) we used in the manuscript has been becoming more popular for LLM training since it provides more flexibility in the training duration and can modify the data mixture in the cooldown phase while giving similar results [1, 2]. The reason we opted to use it is that it clearly separates the warmup phase from the rest of training, unlike common variants of the cosine schedule where the length of the warmup simultaneously affects the shape of the rest of the schedule. We wanted to eliminate this as a confounding factor, so that the apparent benefits of warmup were not coming from changes in the cooldown phase. In terms of the gap between warmup and no warmup, the results are very similar. However, in this case the cosine schedule performs marginally better and the learning rate transfers better between different warmup lengths. We believe the latter effect is because the area under the curve is roughly independent of the warmup length for the cosine (because the whole schedule shifts), but not the trapezoidal schedule. Limitations: Yes this is a fair point, we will move the limitations section to the main body in a future version of the manuscript. Please let us know if you have any additional questions! We would also greatly appreciate it if you could inform us whether the additional experiments, proposed modifications, and clarifications at least partially mitigate your concerns. --- [1]: Hu, Shengding, et al. "Minicpm: Unveiling the potential of small language models with scalable training strategies." arXiv preprint arXiv:2404.06395 (2024). [2]: Hägele, Alexander, et al. "Scaling Laws and Compute-Optimal Training Beyond Fixed Training Durations." arXiv preprint arXiv:2405.18392 (2024). --- Rebuttal Comment 1.1: Title: reply to authors Comment: I thank the authors for addressing my comments. I will raise my score and vote for acceptance of the paper	Rebuttal 1: Rebuttal: We would like to thank all the reviewers for their thoughtful reviews and feedback on our manuscript. We will try to address your specific concerns and questions in our individual responses. Here we present additional experimental results with accompanying plots in the pdf: * Figure 1 shows what the baseline plots would look like for a cosine decay schedule (specifically one-cycle cosine without momentum for these experiments). The reason we went with the trapezoidal schedule is that it fully separates the warmup phase from the rest of the schedule unlike in the cosine schedule where the warmup length affects the whole schedule. We wanted to avoid these confounding effects with our choice of the trapezoidal schedule. * Figure 1 also shows the performance of RAdamW [1], a popular optimizer modification for reducing the need for warmup, in the baseline setup. We find that while it helps, it does not eliminate the need for warmup. The analysis of [2] suggest RAdamW functions similar to a 2/(1-beta2)=40 step warmup which seems to roughly match our findings (2% here would be 100 steps). * Figure 2 shows the effects of changing the dataset used in our experiments from OpenWebText [3] to SlimPajama [4]. Overall the results are similar as before, when controlling the L2 norm via LionA warmup is still beneficial, controlling the angular updates via LionAR decreases the gap significantly. The higher momentum LionAR with Nesterov momentum and our momentum correction eliminates the gap fully. The RRC also seems to eliminate the benefit of warmup but still has the same practical limitations as we describe in section 6.1. * Figure 3 shows the effects of changing the architecture from GPT2 to the llama style [5] while keeping the dataset and parameter count (~124m) the same. This includes using SwiGLU activations, RoPE embeddings and RMSNorm. In this case LionAR is able to fully eliminate the need for warmup without any additional tricks like the RRC compensation or momentum corrections. Based on our analysis these additional tricks are likely only needed when the critical batch size is very small initially. In the future we want to rerun these experiments using a larger batch size to verify this, but were not able to do it in time for this rebuttal. * Figure 4 shows the results for a larger 209m parameter llama2 trained on SlimPajama. Overall the results are similar to the smaller llama. We believe these additional experiments can increase the variety of our experimental setup, helping mitigate this limitation somewhat, although an even broader range would of course be preferable. Based on reviewer feedback, we have decided to limit our experimental scope to GPT variants and will change the title of the paper to reflect this, as suggested by one of the reviewers. Previously we wanted to include broader transformer experiments like DeiT and translation but found it hard to identify good setups where warmup has a significant impact but are computationally tractable for us. We found that many of the reference configurations we experimented with use warmup but don’t actually benefit significantly from it. This likely varies across batch sizes and other configuration aspects we found too expensive to tune. --- [1] Liyuan Liu, Haoming Jiang, Pengcheng He, Weizhu Chen, Xiaodong Liu, Jianfeng Gao, and Jiawei Han. On the variance of the adaptive learning rate and beyond. In International Conference on Learning Representations, 2020. URL https://openreview.net/forum? id=rkgz2aEKDr. arXiv:1908.03265. [2] Jerry Ma and Denis Yarats. On the adequacy of untuned warmup for adaptive optimization. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 35, pages 8828–8836, 2021. arXiv:1910.04209. [3]: Gokaslan, Aaron, and Vanya Cohen. "OpenWebText Corpus." 2019, Skylion007.github.io/OpenWebTextCorpus. [4]: Soboleva, Daria, Faisal Al-Khateeb, Robert Myers, Jacob R. Steeves, Joel Hestness, and Nolan Dey. "SlimPajama: A 627B Token Cleaned and Deduplicated Version of RedPajama." June 2023, www.cerebras.net/blog/slimpajama-a-627b-token-cleaned-and-deduplicated-version-of-redpajama. [5]: Touvron, Hugo, et al. "Llama 2: Open foundation and fine-tuned chat models." arXiv preprint arXiv:2307.09288 (2023). Pdf: /pdf/c56ffbcb3a9c9232a6a6dcf3c3a5c311cf50c4d7.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
CYCLO: Cyclic Graph Transformer Approach to Multi-Object Relationship Modeling in Aerial Videos	Accept (poster)	Summary: This work focuses on the VidSGG task. Specifically, it built a new UAV-based VidSGG dataset named AeroEye, and also further propose a CYCLO approach for using cyclic attention over the VidSGG task. Strengths: 1. The paper is well-written and easy to follow. 2. From my perspective, a high quality dataset and large scale dataset is of critical imporantance over the VidSGG area. I thus appreciate the effort by the authors. Weaknesses: (See the questions section below) Technical Quality: 2 Clarity: 3 Questions for Authors: Overall, while I tend to accept this work, I still have the following concerns and suggestions w.r.t. the current version of the submission: (1) It seems to me that, while the dataset focuses on the UAV scenario, the direct and long-range temporal relationships focused by the proposed method is not closely related to the UAV scenario. I appreciate if the connection (if any) can be more clearly explained. (2) Besides comparing with those existing UAV datasets, I suggest the authors to also include a statistical discussion (in a table format maybe) between AeroEye and those existing VidSGG datasets. (3) In line 43, the authors claim that "They [5, 19] usually struggle with long-term dependencies due to the diminishing influence of inputs over time." This claim should be made with better support. (4) Moreover, I believe that the connectivity between the proposed CYCLO method and scene graph needs to be better discussed. This is important since the usage of "cyclic attention" solely in the video context seems to be not a new stuff already (e.g., Transformer Tracking with Cyclic Shifting Window Attention CVPR 2022). Thus, for authors to clearly indicate the novelty of their CYCLO method, from my perspective, it is necessary to (a) discuss how CYCLO is designed for scene graph more clearly and (b) discuss the difference between CYCLO and existing cyclic attention methods in the video context. Confidence: 3 Soundness: 2 Presentation: 3 Contribution: 3 Limitations: The authors have discussed their limitations. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We are grateful to Reviewer 5Gaf for the constructive feedback. Your suggestions on clarifying our method's UAV context, dataset comparisons, and CYCLO's scene graph relation have greatly improved this paper. Q1: It seems to me that, while the dataset focuses on the UAV scenario, the direct and long-range temporal relationships focused by the proposed method is not closely related to the UAV scenario. Our intention developing CYCLO does not limit to UAV scenario, but demonstrates effectiveness across in-the-wild datasets like OpenPVSG and ASPIRe as in experiments. The long-range temporal relationships crucial in UAV footage, such as tracking object movements over large areas and extended timeframes, are equally important in ASPIRe's street-level scenes. Here, understanding prolonged interactions between people and vehicles requires similar temporal analysis. Q2: Comparison between AeroEye and existing VidSGG datasets. We've included a statistical comparison of AeroEye with both UAV and non-UAV VidSGG datasets in Table A.11 of the Appendix. This comparison will be moved to the main paper in the revision. Q3: In line 43, the authors claim that "They [5, 19] usually struggle with long-term dependencies due to the diminishing influence of inputs over time." This claim should be made with better support. [5] employed Transformers with self-attention for modeling long-term dependencies in videos. However, Transformers lack inherent temporal order [A], and their attention mechanism struggles with distant elements in long sequences [B]. [9] utilized a hierarchical graph-based approach to model long-term dependencies by representing the video as a sequence of graphs, each capturing the evolving relationships among objects at different temporal and spatial scales. This method integrates temporal and spatial information by constructing and updating node and edge features at multiple hierarchical levels. However, this approach requires observing the entire video to build comprehensive hierarchical representations, which poses significant challenges for real-time or online processing. Q4: Discuss how CYCLO is designed for scene graph more clearly. CYCLO is specifically designed for video scene graph generation, building evolving graphs where nodes represent objects and edges represent relationships. The construction process involves: 1. CYCLO first identifies objects in each video frame, creating nodes for each detected object. 2. It then infers relationships between objects, establishing edges between nodes to represent these relationships. 3. CYCLO employs a temporal graph transformer with cyclic attention across the video sequence. It processes the graph structure over time, updates node and edge features based on spatial and temporal context, and uses cyclic attention to connect information from the start to the end of the video. 4. CYCLO cycles the attention mechanism between relationships over time. This process allows it to maintain continuity in object relationships across frames and enhance understanding of long-term dependencies. It also helps to recur patterns in object interactions and connect information from distant parts of the video. 5. CYCLO integrates spatial information, such as object locations and current interactions, with temporal data, including past interactions and object trajectories, to preserve directional context. It also maintains historical context and learns how initial interactions influence subsequent actions. 6. As the video progresses, CYCLO continuously updates the scene graph, refining object states, relationships, and the overall structure based on new information from each frame. Q5: Discuss the difference between CYCLO and existing cyclic attention methods in the video context. Thanks for this suggestion. We will include this MS-CSWA [C] and its description in our final version. CYCLO differs from MS-CSWA [C] in several important ways: 1. Spatio-temporal integration: - CYCLO combines spatial and temporal dependencies in a graph-based framework, allowing dynamic refinement of spatial relationships over time. - MS-CSWA focuses on maintaining spatial consistency within individual frames for object tracking but lacks temporal depth across frames. 2. Operation: - CYCLO uses cyclical indexing and shifting to ensure inter-frame temporal continuity, modeling how past interactions influence present and future relationships. - MS-CSWA enhances spatial attention through only cyclic shifts but does not address temporal depth or graph-based updates across frames. 3. Long-term dependencies: - CYCLO captures long-term dependencies and evolving interactions across frames, preserving directional and historical information. - MS-CSWA is limited to intra-frame consistency and is unable to model long-term dependencies across the video. References [A] Truong, T. D., Bui, Q. H., Duong, C. N., Seo, H. S., Phung, S. L., Li, X., & Luu, K. (2022). Direcformer: A directed attention in transformer approach to robust action recognition. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition (pp. 20030-20040). [B] Dai, Z., Yang, Z., Yang, Y., Carbonell, J., Le, Q. V., & Salakhutdinov, R. (2019). Transformer-xl: Attentive language models beyond a fixed-length context. In Proceedings of the 57th Annual Meeting of the Association for Computational Linguistics. [C] Song, Z., Yu, J., Chen, Y. P. P., & Yang, W. (2022). Transformer tracking with cyclic shifting window attention. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition (pp. 8791-8800). --- Rebuttal Comment 1.1: Comment: Thank you for your response. I believe that most of my concerns have been well-solved and I thus increase from 5 to 6. --- Rebuttal 2: Comment: Dear Reviewer 5Gaf, We want to express our gratitude for your valuable time and constructive feedback. Best regards, Authors	Summary: This paper tackles an interesting task for understanding video scenes that focuses on modeling object relationships in aerial videos. Specifically, it introduces a new dataset, the AeroEye dataset, and proposes a novel approach, CYCLO, to better model the video object relationships. Experimental results demonstrate the effectiveness of CYCLO. CYCLO also achieves state-of-the-art performance on two scene graph generation benchmarks. Strengths: - The paper is well-written, easy to follow, and presents many key points clearly. - Introducing the AeroEye dataset is a valuable contribution, as it fills an important gap in video scene graph generation datasets by providing a drone perspective relation dataset. - The design of CYCLO is both interesting and inspiring. The paper also demonstrates its superior performance compared to prior solutions. Weaknesses: - It would be great to report the inference cost of the proposed approach. - It is unclear how the proposed solution works in live (online) mode, e.g., video streaming. Technical Quality: 3 Clarity: 4 Questions for Authors: - In the ablation study (line 265), when a frame is discarded, is it something like that the frame is set to some random noise? Confidence: 3 Soundness: 3 Presentation: 4 Contribution: 4 Limitations: I don't have concerns about the potential negative societal impact of this work. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We sincerely thank Reviewer QFfh for the positive feedback and constructive suggestions. We appreciate your recognition of the AeroEye dataset and CYCLO approach. We will carefully address your suggestions regarding inference cost and live video streaming applications. Q1: It would be great to report the inference cost of the proposed approach. In the table below, we report FPS for models discussed in Section 2.2. CYCLO significantly outperform these models in both recall and mean recall with a slight trade-off in FPS. \| Method \| R/mR@20 \| R/mR@50 \| R/mR@100 \| FPS \| \|------------------\|-------------------\|-------------------\|-------------------\|----------\| \| Vanilla \| 31.04 / 11.20 \| 34.28 / 11.27 \| 34.62 / 12.43 \| 19.5 \| \| Transformer \| 41.09 / 11.88 \| 46.52 / 12.31 \| 47.15 / 12.91 \| 17.8 \| \| HIG \| 37.28 / 11.98 \| 38.59 / 13.12 \| 39.27 / 13.29 \| 15.3 \| \| CYCLO \| 59.59 / 13.29 \| 60.37 / 13.69 \| 43.53 / 13.86 \| 14.2 \| Q2: It is unclear how the proposed solution works in live (online) mode, e.g., video streaming. CYCLO online processes video streams frame-by-frame, continuously updating the scene graph to reflect the latest object relationships. As new frames arrive, CYCLO dynamically adjusts object relationships and refines the scene graph based on the most recent data while leveraging historical context. Q3: In the ablation study (line 265), when a frame is discarded, is it something like that the frame is set to some random noise? No, we discard one frame out of every two successive frames rather than replacing them with random noise. --- Rebuttal Comment 1.1: Comment: Dear Reviewer QFfh, The reviewer-author discussion deadline is nearing. We have yet to receive your final responses to our rebuttal. If you have any further questions, please let us know. We appreciate your invaluable input. Best regards, Authors	Summary: This paper presents a new problem: modeling multi-object relationships from a drone's perspective. To address this, the authors propose the AeroEye dataset and introduce the Cyclic Graph Transformer (CYCLO) method. This method captures both direct and long-range temporal dependencies by continuously updating the history of interactions in a circular manner. The authors not only validate the CYCLO approach on the AeroEye dataset but also test it on the PVSG and ASPIRe datasets, demonstrating the effectiveness of their method. Strengths: 1. The authors have introduced the problem of multi-object relationship modeling from a drone's perspective for the first time and constructed the AeroEye dataset, which effectively fills a gap in the field of multi-object relationship modeling and has significant application value. 2. The CYCLO method proposed by the authors is not only useful for the dataset introduced in this paper, AeroEye, but is also a versatile method that can be applied to general Video SGG tasks. It has been tested on datasets like PVSG and achieved good performance. 3. The structure of the paper is clear, the writing is standard and fluent, making it easy to understand. Weaknesses: 1. The method proposed in this paper could benefit from a clearer network architecture figure, which would allow everyone to better understand the method presented. 2. Is there an issue with non-differentiability in the Cyclic Attention described in Eq. 3? It would be helpful if the authors could provide further explanation of the Cyclic Attention mechanism. 3. It is suggested to include some analysis of bad cases, which would help future researchers understand from which directions further optimizations can be made. Technical Quality: 3 Clarity: 3 Questions for Authors: 1. The current model proposed by the authors shows low mR@K scores on the AeroEye dataset. However, from the figures in the supplementary material, the long-tail distribution of relations in this dataset does not appear to be very severe. What could be causing the low mR@K scores? If possible, I would like to see some typical bad cases. Confidence: 5 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: It is recommended that the authors consider the limitations of this paper not only from a technical perspective but also from a societal standpoint. Given that relationship modeling from a drone's perspective may lead to widespread applications in surveillance and potentially significant impacts, this aspect requires special consideration. Flag For Ethics Review: ['Ethics review needed: Data quality and representativeness', 'Ethics review needed: Safety and security'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We express our gratitude to Reviewer nRfD for your recognition of the AeroEye dataset and the CYCLO method. We will enhance our paper by improving the architecture figure, addressing Cyclic Attention issues, expanding the failure case analysis, and elaborating on the suggested limitations. Q1: The method proposed in this paper could benefit from a clearer network architecture figure, which would allow everyone to better understand the method presented. We have included a detailed network architecture figure in the attached file. Q2: Is there an issue with non-differentiability in the Cyclic Attention described in Eq. 3? It would be helpful if the authors could provide further explanation of the Cyclic Attention mechanism. Eqn. 3 has no non-differentiability issues. The modulo operation (mod T) is used only for key matrix indexing and does not affect gradient computation. Gradients flow through differentiable components (dot product, softmax, summation), while the modulo operation implemented by a for-loop for indexing does not interfere with continuous gradient computations. Q3: The current model proposed by the authors shows low mR@K scores on the AeroEye dataset. However, from the figures in the supplementary material, the long-tail distribution of relations in this dataset does not appear to be very severe. What could be causing the low mR@K scores? If possible, I would like to see some typical bad cases. While the AeroEye dataset does not show a severe long-tail distribution of relationships, the low mR@K scores stem from the model's challenges in adapting to rapidly changing relationships within dynamic scenes in videos. In fast-paced environments like sport events or emergency responses, which were not well-investigated in OpenPVSG or ASPIRe, the model needs to work on keeping pace with swift changes in actions and interactions. An instance of bad cases is in the attached rebuttal file, the model need to quickly update its prediction of player interactions in soccer. Ethics Review In line 124, we mentioned that we use videos from the ERA [A] and MAVREC [B] datasets, without including new videos. Videos are compliant with the European Union’s drone regulations [B]. It is always possible that some individual or an organization can use this annotation to devise a technique that can appear harmful to society. However, as authors, we are absolutely against any detrimental usage of our annotation and pledge not to support any detrimental endeavors concerning our data or the idea therein. References [A] Mou, L., Hua, Y., Jin, P., & Zhu, X. X. (2020). Era: A data set and deep learning benchmark for event recognition in aerial videos. IEEE Geoscience and Remote Sensing Magazine, 8(4), 125-133. [B] Dutta, A., Das, S., Nielsen, J., Chakraborty, R., & Shah, M. (2024). Multiview Aerial Visual Recognition (MAVREC): Can Multi-view Improve Aerial Visual Perception?. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (pp. 22678-22690). --- Rebuttal Comment 1.1: Comment: The author's response has addressed my concerns, I will maintain my original score.	Summary: This paper proposes a video scene graph generation dataset called AeroEye on aerial videos and a framework called cyclic graph transformer to tackle the problem of video scene graph generation. The authors annotated the ERA and MAVREC dataset with keyframes at 5FPS. They manually annotated the frames for bounding box localization for each frames along with the tracking. The relationship annotations were done using a GPT4RoI model. The proposed cyclic graph transformer uses a cyclic attention mechanism which the author claims, are able to capture the direct and long-term temporal dependencies. Strengths: 1. The proposed video scene graph dataset for aerial videos with a diverse set of predicates can offer more granular and nuanced understanding of dynamic interactions and relationships within aerial footage 2. The dataset will be publicly available 3. The proposed approach for circular attention for dynamic online scene graph generation seems promising Weaknesses: 1. the paper is very difficult to follow. There are separate discussion sections which somewhat disrupts the flow. 2. line 82 seems incomplete 3.Line 118: 'no temporal edge is treated a boundary' can it not be a disadvantage as well since it does not takes into account for an event boundary? 4. A very brief discussion of annotation procedure should be in the main paper such as manual annotation of bounding boxes and relationship annotations done by GPT4RoI model. 5. For loss function section, it would be better to include the overall loss equation. Does the object distribution refers to the object detection loss using the DETR? 6. For table 2, you can refer to the shift value term from equation 3. It will be easy to follow. Table 2 refers to the ablation studies 'Semantic Dynamics in Cyclic Attention'. I think this section and the section followed by it should have a detailed explanation. Technical Quality: 2 Clarity: 2 Questions for Authors: 1. Did you do evaluation on the 5 keyframes for each videos? 2. point 5 in weakness section Confidence: 4 Soundness: 2 Presentation: 2 Contribution: 2 Limitations: yes, the limitations are addressed. Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We sincerely thank Reviewer Zf4k for your thoughtful review. We appreciate the recognition of our novel dataset and approach. We acknowledge the need to provide clearer explanations. Q1: The paper is very difficult to follow. There are separate discussion sections which somewhat disrupts the flow. We appreciate your feedback on the paper's readability. We are encouraged that multiple reviewers found our paper clear (Reviewer nRfD), well-written, and easy to follow (Reviewers QFfh and 5Gaf). Nevertheless, we value all the feedback and will further enhance our paper's organization in the revision. Q2: Line 82 seems incomplete 3.Line 118: 'no temporal edge is treated a boundary' can it not be a disadvantage as well since it does not takes into account for an event boundary? We have updated line 82. Regarding line 118, 'no temporal edge is treated as a boundary' is advantageous. CYCLO's continuous temporal information flow allows it to capture gradual changes and complex dynamics, such as the slow formation of traffic jams. This would be missed by models that frequently reset at event boundaries. Q3: A very brief discussion of annotation procedure should be in the main paper such as manual annotation of bounding boxes and relationship annotations done by GPT4RoI model. Thank you for your suggestion. We will include a brief overview of the annotation procedure, with full details provided in Appendix A.2. Q4: For loss function section, it would be better to include the overall loss equation. Does the object distribution refers to the object detection loss using the DETR? We will add the combined loss equation in line 242, where we mention that the total loss combines these two losses. 'Object distribution' is not the detection loss which refers to predicted class probabilities for DETR-detected objects. Q5: Did you do evaluation on the 5 keyframes for each videos? As mentioned in Section 3.2, we annotated keyframes at 5 FPS and thus evaluate the model's performance on these keyframes. Q6: For table 2, you can refer to the shift value term from equation 3. It will be easy to follow. Table 2 refers to the ablation studies 'Semantic Dynamics in Cyclic Attention'. I think this section and the section followed by it should have a detailed explanation. We appreciate your suggestion and will incorporate it into the revision. The shift term shift term ($\eta$) in Eqn. 3 plays a crucial role in our model's temporal coherence and resolution. Our analysis reveals several key insights: 1. Optimal temporal coherence: At $\eta = 1$, the model achieves peak performance by effectively capturing transitions between adjacent frames. 2. Information loss with increasing $\eta$: Larger $\eta$ values cause the model to skip intermediate frames, resulting in loss of crucial temporal information and consequently degraded performance. 3. Maximized temporal resolution: $\eta = 1$ allows the capture of fine-grained dynamics, which is essential for accurately predicting object interactions. 4. Impact on sequence modeling: Higher $\eta$ values impede the model's ability to capture long-range dependencies, affecting the integration of detailed temporal features. 5. Frame order sensitivity: The model's non-permutation equivariance ensures sensitivity to frame order. For instance, the sequence of a person approaching a car, entering it, and then driving away must be captured correctly for the scene graph to represent the event accurately. --- Rebuttal Comment 1.1: Comment: Dear Reviewer Zf4k, The reviewer-author discussion deadline is nearing. We have yet to receive your final responses to our rebuttal. If you have any further questions, please let us know. We appreciate your invaluable input. Best regards, Authors	Rebuttal 1: Rebuttal: We sincerely thank all reviewers for their valuable feedback. Reviewers nRfD and QFfh recommend acceptance, praising our CYCLO approach to multi-object relationship modeling, the AeroEye dataset, and the versatility of our approach. Reviewer 5Gaf leans towards acceptance with a Borderline Accept. Reviewer Zf4k suggests a Borderline Reject, noting to explain more details. We have updated the typos in our paper. We will clarify how our CYCLO approach applies to video scene graph generation with an illustration of the overall framework in the rebuttal PDF file. Individual responses for each reviewer are included below for specific concerns. Pdf: /pdf/b195ea47b6a72bdfc4b17bd520af1ce32c2d745a.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
IRCAN: Mitigating Knowledge Conflicts in LLM Generation via Identifying and Reweighting Context-Aware Neurons	Accept (poster)	Summary: This work presented a framework IRCAN to locate key neurons for processing contextual cues, thereby mitigating conflicts between knowledge obtained from pre-training and knowledge within the context. Experiments on completion and multi-choice tasks showed that the IRCAN benefits the base model in knowledge conflict tasks. Strengths: 1. This paper is well-written and easy to read, and the authors present their methods and experiments very clearly. 2. The paper innovatively addresses the knowledge conflict issues by manipulating neurons. Experimental results validate the effectiveness of the method. Particularly, the improvement in results on knowledge completion tasks is quite significant. 3. Ablation analysis is sufficient for understanding the proposed method in depth. Weaknesses: 1. While the paper has demonstrated the effectiveness of the proposed IRCAN on 3 datasets, its performance on additional datasets remains unexplored. It would be beneficial for the authors to include more knowledge-related datasets in future versions of the paper to further validate the generalizability of the model. 2. In the completion task, the experiments compared the accuracy of the proposed IRCAN and baselines, and the IRCAN improved the performance by a large margin. However, the experiments are conducted on merely one dataset, weakening the generalization of the IRCAN, and there is no computing comparison, for example, GPU time-consuming. Technical Quality: 3 Clarity: 4 Questions for Authors: 1. This paper assumed that contextual knowledge was more reliable than parametric knowledge, and what if the context itself was fake or misleading? 2. How did the authors construct knowledge datasets along with the context? 3. The paper mentioned: “To calculate the attribution score Attr(n^{l}_{i}), we gradually change the activation value of a neuron n^{l}_{i} from v^{l}_{q_{i}} to v^{l}_{(c,q)_{i}}…”, what are the details of the activation value’s change process? 4. In section 3.3, what is the object W(n^{l}_{i}) for the reweighting? Activation value or the attention matrix? 5. For the evaluation of general abilities, results in Table 3 show that IRCAN can cause other knowledge-related tasks like MMLU and Winograd to fluctuate. What could be the cause of this fluctuation? Does that demonstrate that emphasizing the context may bring knowledge degradation? Confidence: 4 Soundness: 3 Presentation: 4 Contribution: 3 Limitations: Various LLMs were employed in this paper, however, most of the models were 7B/8B. The authors could validate the proposed IRCAN in larger LLMs to complete the work in the future. Flag For Ethics Review: ['No ethics review needed.'] Rating: 8 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We are deeply grateful for your positive assessment of our work and the recognition of the value in our work. Your feedback is highly encouraging and valuable to us. We will address each of your concerns and questions in detail: Re to W1: IRCAN’s performance on additional knowledge-related datasets remains unexplored. Thank you for your insightful comments. We highly agree with your suggestion that incorporating more knowledge-related datasets would be beneficial for further validating the generalizability of our model. Indeed, in the ongoing process of our research, we have been actively investigating the existence of such datasets that include new correct knowledge in context, while the corresponding knowledge encoded in the LLM is outdated or incorrect. For example, an LLM trained by December 19, 2022 (the date of the Qatar World Cup final) would only have knowledge that Argentina has won the World Cup twice. If we present the results of the 2022 World Cup in the context and construct question-answering tasks, such a dataset would provide an excellent means to further validate the effectiveness and generalization of our model. However, to the best of our knowledge, such datasets are currently unavailable, which hinders the further validation of our IRCAN. We look forward to the emergence of such datasets and would like to collect more suitable datasets for our framework in the future. Re to W2 (1): The experiments are conducted on merely one completion dataset. Thank you for your valuable feedback. To the best of our knowledge, other datasets involving knowledge conflicts for completion tasks are not available. We are willing to validate IRCAN on more completion datasets if they are available in the future. Re to W2 (2): There is no computing comparison. We are grateful for your suggestion. Although we have stated and discussed the computational resources and time consumption required for our method in Appendix F, we will also include a time-consumption comparison with other methods in the next version of the paper as Section 5.1. Re to Q1: This paper assumed that contextual knowledge was more reliable than parametric knowledge, and what if the context itself was fake or misleading? Thank you for your insightful comments. The issue you mentioned is precisely what we have considered during the course of this work. In our future work, we plan to delve deeper into this research. Specifically, we intend to propose a framework that first incorporates a judgment mechanism to determine whether to focus more on contextual knowledge or adhere to the internal knowledge of the LLM, and then enhances the fidelity to the chosen aspect during generation. Re to Q2: How did the authors construct knowledge datasets along with the context? As described in Section 4.1 of our paper, we used publicly available datasets, MemoTrap, COSE_KRE and ECARE_KRE, in our experiments. The MemoTrap [1] dataset is created by replacing the ending words of common proverbs with other words, and then prompting the model with the context instruction: "Write a quote that ends with the word '{the replaced word}'". It evaluates the models’ ability to adhere to the given context to complete an unfamiliar phrase, rather than defaulting to a well-known phrase that has been encoded in its parameters during training. The COSE_KRE and ECARE_KRE [2] datasets are respectively derived from the ECQA and e-CARE datasets. The derivation process involves selecting one of the incorrect answer choices and prompting ChatGPT to generate explanations supporting this incorrect answer. Specifically, the selected incorrect answer is treated as the correct answer, and the generated explanation is used as the context for the multiple-choice question. [1] Liu et al. The MemoTrap Dataset, 2023. https://github.com/inverse-scaling/prize/tree/main/data-release. [2] Ying et al. Intuitive or Dependent? Investigating LLMs' Behavior Style to Conflicting Prompts. CoRR, abs/2309.17415, 2023. Re to Q3: What are the details of the activation value's change process? For simplicity, let us denote the difference of {v}_{(c,q)}_{i}^{l} minus {v}_{q}_{i}^{l} as z. We divide z into m = 20 equal parts. The activation value’s change process involves performing 20 forward propagations, each time replacing the model activation with ${\boldsymbol{v}_{q}}_i^l + \frac{1}{20}z$, ${\boldsymbol{v}_{q}}_i^l + \frac{2}{20}z$, … ${\boldsymbol{v}_{q}}_i^l + z$ respectively. Finally, we compute the cumulative sum according to Equation (3) in our paper to obtain the attribution score. However, in practical implementation, we repeat each example 20 times to form a batch, and also use the 20 activation values mentioned above as a batch to replace to the model. This allows us to complete the process with a single forward pass. Re to Q4: In section 3.3, what is the object W(n^{l}_{i}) for the reweighting? Activation value or the attention matrix? The object we reweight is the weights of the MLP layer. Re to Q5: Cause of the fluctuation in experimental results in Table 3. As we have enhanced certain neurons, it is expected and normal for the model's outputs to change. As demonstrated in Table 3 in our paper, the fluctuation amplitude of the results is very small, which is entirely acceptable. Even minor modifications to the model's decoding hyperparameters or the use of different decoding methods can cause significant variations in the generated results. However, these variations do not indicate an increase or decrease in the model's inherent capabilities. Re to Limitations: Validation on larger LLMs. Thank you for your great suggestion. We must emphasize that the experiments in our paper have been conducted on 13B models for both the completion task and the multiple choice task, in addition to the 7B/8B scale model. In the future, we will validate the proposed IRCAN on LLMs with larger scales, e.g., 70B. --- Rebuttal Comment 1.1: Comment: Thank you for the detailed responses, my concerns were addressed, and I will change my previous score. --- Reply to Comment 1.1.1: Comment: We sincerely thank you for your constructive feedback and for the revised score. Your insightful comments and suggestions have been instrumental in refining the quality of our paper.	Summary: The paper addresses the valuable problem of mitigating parametric and contextual knowledge conflicts in LLM generation with a novel and reasonable method. It is well-written, with a comprehensive experimental design showing significant improvements in completion and multi-choice tasks. However, the evaluation is limited to short contexts, raising concerns about scalability to longer contexts. The assumption that contexts are contradictory to parametric knowledge may not always hold, and the method's performance on RAG tasks and its impact on inference speed needs further exploration. Additionally, unexpected performance results between llama3-8b and llama2-7b require explanation. Strengths: - S1: The studied problem of mitigating parametric and contextual knowledge conflicts is of great value - S2: The paper is well-written and easy to follow - S3: Though simple, the proposed method is novel and reasonable for mitigating knowledge conflicts - S4: The experimental design is comprehensive and rigorous, and the results show significant improvement in completion and multi-choice tasks - S5: The discussion and results on preserving performances on other tasks are highly appreciated Weaknesses: - W1: The evaluation is limited to datasets with relatively short contexts, it is questionable whether the proposed method can scale to long contexts. - W2: The paper assumes that the contexts are contradictory to the parametric knowledge. However, in many cases, only a tiny fraction of the context is inconsistent with the parametric knowledge, while the others are consistent or unknown. Is the proposed method still valid under these situations? - W3: The (partly) contradiction may frequently occur in RAG, it would be great to know how this method performs on RAG tasks. - W4: It seems the proposed method has to select neurons first before answering and this involves forward passes once with and once without contexts, will this process make the inference significantly slower? Some results and discussions on time complexity would be highly appreciated. - W5: As shown in Table 1, llama3-8b performs worse than llama2-7b, which is not as expected. Is there any explanation for this? - W6: Are the salient neurons selected specifically for each question (with or without context), or are shared across data points like this: https://arxiv.org/abs/2311.15983, why or why not? Technical Quality: 3 Clarity: 3 Questions for Authors: Please refer to W1-W6. 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: Thank you so much for your valuable feedback and insightful comments. We will address each of your concerns and questions in detail: Re to W1 & W3: Evaluations on datasets with long contexts and RAG tasks. Thank you for this valuable feedback. We understand the prevalence of long-context inputs in real-world applications. In future work, we will continue to look for knowledge conflict datasets with long context and explore the effectiveness of our proposed method on such datasets. As discussed in Section 6 of our paper, we also acknowledge that applying our method on RAG tasks is a promising and practical direction. Specifically, by enhancing the model’s sensitivity and fidelity to retrieved documents in context, IRCAN is expected to significantly improve the performance of generation models in RAG systems, enabling more accurate and contextually relevant text generation. In subsequent work, we will explore IRCAN’s effectiveness in application scenarios such as long-context tasks and RAG. Re to W2: Is the proposed method still valid in situations where the contextual knowledge is inconsistent with the parametric knowledge? Thank you for your insightful comment. We believe our proposed method remains valid when the knowledge in the context does not conflict with the internal knowledge of LLMs. Our IRCAN enhances specific neurons crucial for processing contextual cues, ensuring LLMs generate outputs more faithful to the knowledge in the context. Moreover, the experiments in Section 5.4 demonstrate that IRCAN does not compromise other general capabilities. Therefore, when there is no conflict between the knowledge in the context and the knowledge inherent to the LLMs, enhancing these neurons solely improves the fidelity of the models to the contextual knowledge (i.e., internal knowledge), without other effects. Re to W4 (1): Will the process of selecting neurons make the inference significantly slower? Thank you for your valuable comments. The neuron selection process in our IRCAN does not lead to more inference time costs. 1. First, we utilize some examples to identify context-aware neurons offline. Specifically, for each example, we first calculate the attribution scores of neurons. Then, we select the top z neurons with the highest attribution scores as the candidate set for each example. Ultimately, we count the number of co-occurrences of neurons in all candidate sets, and we select the top h neurons with the highest number of co-occurrences as identified context-aware neurons. Therefore, identified context-aware neurons are shared across all data instances. 2. Then, we reweight these context-aware neurons of the LLM. 3. During online testing, we take the modified model for inference, without adding any inference time cost. We suspect that such misunderstanding may be caused by the lack of clarity of the expression in Section 3.2: "Ultimately, we allow each example to vote for the candidate neurons based on their attribution scores, and we select the top h neurons that receive the most votes.". We will revise this sentence to "Ultimately, we count the number of co-occurrences of neurons in all candidate sets, and we select the top h neurons with the highest number of co-occurrences as identified context-aware neurons." in the next version of our paper. Moreover, at the end of Section 3.2, we will add "These context-aware neurons are shared across all data instances." to enhance the clarity of the paper. Re to W4 (2): Some results and discussions on time complexity would be highly appreciated. Due to page limitations, we have stated and discussed the computational resources and time consumption required for our method in Appendix F. In the revised version of our paper, we will move this content to the main body of the paper as Section 5.5. Re to W5: Explanation for why llama3-8b performs worse than llama2-7b in Table 1. Thank you for bringing this to our attention. As shown in Table 1, LLaMA-3-8B achieved lower accuracy (ACC) on the completion task, along with a higher stubbornness rate (SR). The SR measures how often the model's output matches common ending words of well-known proverbs. These results suggest that LLaMA-3-8B, trained on extensive, high-quality multi-source data, has acquired more extensive world knowledge and relies more on its pre-stored intrinsic knowledge when generating responses. We will incorporate this discussion into Section 4.4 in the next paper version. Re to W6: Are the salient neurons selected specifically for each question (with or without context), or are shared across data points, why or why not? Thank you for your insightful comments. We have thoroughly read the paper you mentioned, which employs a linear probing method to select salient neurons and then integrates them to serve as curated multi-layer features for text classification, effectively improving text classification accuracy, efficiency, and interpretability. The neurons we selected are the same as those in this work, which are shared across data points. Our rationale for adopting this neuron selection method is twofold: Firstly, we utilize some data to find the neurons responsible for processing the context in an offline setting, and then augment their weights in LLMs. During online inference, we can improve the model's attention to contextual knowledge in the input data without increasing inference time. Secondly, if for each example, the neurons are individually identified by the attribution scores computed through two forward propagations (once with and once without context), the identified neurons may be not all responsible for processing contexts, and may have poorer generalizability to other examples. --- Rebuttal Comment 1.1: Comment: Thanks for the rebuttal and I will keep my evaluation. --- Reply to Comment 1.1.1: Comment: We sincerely appreciate the time and effort you have dedicated to reviewing our paper and our rebuttal. We are grateful for your constructive comments and valuable insights.	Summary: The paper proposed a new framework, IRCAN, to enable LLMs to pay more attention to new knowledge in context and generate context-sensitive outputs. The framework first identifies neurons that significantly contribute to context processing by utilizing a context-aware attribution score derived from integrated gradients and then reweighting these neurons. Experiments show the framework can effectively mitigate knowledge conflicts while not harming the general abilities of LLMs. Strengths: 1. The proposed framework is novel and effective. 2. The analysis of the framework is comprehensive. 3. The paper is well written and easy to follow. Weaknesses: 1. The authors state they have discussed the limitations in the checklist, but no limitation section is found. Technical Quality: 3 Clarity: 3 Questions for Authors: 1. Why the paper does not compare the proposed framework with fine-tuning? How will instruction-tuning the model to be more sensitive to new knowledge in context help? While the proposed framework and fine-tuning both involve updating parameters and the proposed framework costs many hours that might not be much more efficient than fine-tuning, it seems natural to consider fine-tuning as a baseline. 2. What is the performance of instructing the LLM to pay more attention to the knowledge in context in the prompt? For the multi-choice task, it seems that simply instructing the model to adopt the knowledge in the context will be effective enough, which will cost much less compared to the framework. Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The authors state they have discussed the limitations in the checklist, but no limitation section is found. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you very much for your insightful comments and valuable suggestions! We greatly appreciate you taking the time to review our work and provide constructive feedback to improve the quality of our paper. We will address each of your concerns and questions in detail: Re to Weaknesses #1 & Limitations: No limitation section. Thank you for this valuable feedback. We have discussed the limitation of our paper in Section 6, that is, the effectiveness of the proposed method on the retrieval-augmented generation (RAG) tasks was not verified, but it was not explicitly written as a limitation section. We are very sorry for the confusion. We will remove the second paragraph regarding RAG in Section 6 and add a limitation section as Section 7. We have drafted a preliminary version of the Limitation section below and would greatly appreciate your feedback: Our current study has only experimented on a few synthetic datasets, however, exploring the effectiveness of IRCAN in application scenarios such as long-context tasks and RAG is also necessary and valuable. For instance, by enhancing the model’s sensitivity and fidelity to retrieved documents in context, IRCAN is expected to significantly improve the performance of generation models in RAG systems, enabling more accurate and contextually relevant text generation. We will explore this in the future. Re to Questions #1: Comparisons with instruction-tuning. Thank you for bringing this to our attention. We fine-tune Gemma-2B and LLaMA-2-7B on the Conifer dataset proposed by Sun et al. [1] to improve the model's ability to follow complex instructions. To ensure data diversity, we mixed this dataset with the general SFT dataset ShareGPT [2] for training, following Sun et al. The original ShareGPT dataset comprises 93,336 examples, and after filtering out unavailable or low-quality data instances, the dataset size remains at 92,585. The data size of the Conifer dataset is 13606. We utilized 8 A100 GPUs to train each model for 3 epochs, with a maximum sequence length of 4,096 tokens during training. The training time is 3.25 hours for Gemma-2B and 11.75 hours for LLaMA-7B. Experiment results are reported in Table 4 in the attached PDF. During testing, we used two settings: one using the same prompt as our method (indicated as IT in Table 4) and the other adding the template used in training to the prompt (indicated as IT-template in Table 4). The experimental results show that the instruction-tuned LLMs struggle to handle the knowledge conflict task. Furthermore, compared to our method (which requires only one A100 GPU, taking 1.1 hours for Gemma-2B and 2.5 hours for LLaMA-7B), the instruction-tuning method requires a significantly larger training dataset and greater resource consumption, which is a substantial drawback. In addition, we must emphasize that, IRCAN, functioning as a post-processing neuron editing method, holds a unique advantage of offering remediation for already trained models. [1] Conifer: Improving Complex Constrained Instruction-Following Ability of Large Language Models. https://arxiv.org/abs/2404.02823. [2] The ShareGPT dataset. https://huggingface.co/datasets/anon8231489123/ShareGPT_Vicuna_unfiltered Re to Questions #2: Comparisons with the experiment that instruct LLMs to pay more attention to the knowledge in context in the prompt. We greatly appreciate your feedback. We curated three types of prompts to explicitly instruct LLMs to pay more attention to the knowledge in the context, and experimented on the multiple-choice task. Below are these prompts (the changes are highlighted in bold) and the original prompt used in our paper: Original Prompt: Choose the correct option to answer the following question: {context} {question} {choices} …… Prompt 1: Choose the correct option to answer the following question based on the context: {context} {question} {choices} …… Prompt 2: Choose the correct option to answer the following question based on the context: Context: {context} Question: {question} Choices: {choices} …… Prompt 3: Choose the correct option to answer the following question utilizing the knowledge in the context: Context: {context} Question: {question} Choices: {choices} …… Experimental results are shown in Table 3 in the attached PDF. We can observe that our method achieves the best performance overall. There remains a large gap between the performance achieved by these prompt engineering based methods and that obtained by IRCAN-CAD. This indicates that only instructing LLMs to pay more attention to the knowledge in the context is not sufficient to enhance the model's utilization of contextual knowledge. Moreover, the prompts with the best performance differs for different datasets and different models. Therefore, the requirement of meticulous prompt engineering damages their generalizability. We will add these results and further analyses to the next version of our paper. --- Rebuttal 2: Title: Thanks for your reply Comment: Thanks for your reply. The new experiments address my concerns well. I have one more question about your limitation section. > For instance, by enhancing the model’s sensitivity and fidelity to retrieved documents in context, IRCAN is expected to significantly improve the performance of generation models in RAG systems In RAG systems, the retrieved text can sometimes be noisy. Would enhancing the model’s sensitivity and fidelity to retrieved documents help in these scenarios? --- Rebuttal 3: Comment: Thank you for your prompt and insightful response. We appreciate the time and effort you've taken to review our rebuttal. The RAG technology supplements models by fetching external data in response to queries, thus ensuring more accurate and current outputs. In fact, in the field of RAG, researchers have recognized that noise in retrieved external data can adversely affect the quality of generated content. To address this, they often employ post-retrieval processing techniques to remove noise from the retrieved documents. For instance, some researchers incorporate a re-ranking stage subsequent to the initial retrieval process, where the retrieved documents are reassessed, scored, and reorganized to more effectively emphasize those most relevant to the query while diminishing the influence of less relevant ones. Methods such as sequence pair classification and re-scoring are introduced to re-rank documents [1-5], thereby improving the relevance between the retrieved content and the query. Additionally, some approaches involve filtering phase to remove documents that fail to meet specified quality or relevance standards. For example, FiD-TF [6] and RECOMP [7] focus on removing irrelevant or redundant tokens and information from retrieved documents. Self-RAG [8] introduces a self-reflection mechanism to efficiently filter out irrelevant content. Therefore, we believe that addressing the noise problem in retrieved text is a critical issue that the RAG field is actively tackling and one that the RAG community should indeed resolve. Our IRCAN method can complement these efforts by enhancing the model’s sensitivity and fidelity to re-ranked or filtered text, thereby further improving the effectiveness of RAG and its ability to deliver more accurate and current outputs. [1] Glass et al. Re2g: Retrieve, Rerank, Generate. NAACL 2022. [2] Dai et al. Promptagator: Few-shot Dense Retrieval From 8 Examples. ICLR 2023. [3] Ram et al. In-Context Retrieval-Augmented Language Models. TACL 2023. [4] Shao et al. Enhancing Retrieval-Augmented Large Language Models with Iterative Retrieval-Generation Synergy. EMNLP 2023. [5] Hofstätter et al. Fid-light: Efficient and effective retrieval-augmented text generation. SIGIR 2023. [6] Berchansky et al. Optimizing Retrieval-augmented Reader Models via Token Elimination. EMNLP 2023. [7] Xu et al. RECOMP: Improving Retrieval-Augmented LMs with Compression and Selective Augmentation. arXiv, abs/2310.04408. [8] Asai et al. Self-RAG: Learning to Retrieve, Generate, and Critique through Self-Reflection. arXiv, abs/2310.11511. --- Rebuttal 4: Comment: Thanks for your response. I will improve the score from 5 to 6. Please make sure these new experiments are appropriately included in the revised version. I would recommend the authors discuss the application scenarios of the proposed method in the limitation or discussion section. --- Rebuttal 5: Comment: Thank you very much for your positive feedback and for improving the score of our paper. We sincerely appreciate your valuable comments and suggestions, which have greatly contributed to enhancing the quality of our work.	Summary: The paper introduces a novel framework, IRCAN, aimed at addressing knowledge conflicts in Large Language Models (LLMs). By identifying and enhancing neurons that are crucial for processing contextual cues using an attribution score derived from integrated gradients, the framework significantly improves the generation of context-sensitive outputs. Tested across various models and tasks, IRCAN not only enhances model performance notably but also integrates seamlessly as a plug-and-play solution with existing models, establishing new performance benchmarks in handling knowledge conflicts. Strengths: 1. The proposed method is plug-and-play and does not need additional training. 2. The authors conduct comprehensive experiments. 3. Steering the context-aware neurons seems effective on many large language models and many down-stream tasks. Weaknesses: 1. Lack comparisons between other steering methods, like steering probed directions or steering SAE's features. 2. The propose methods will cost more inference time. 3. I think knowledge conflict also has its benefits. It may help LLMs defend some jailbreaking or harmful uses. So increase the model's faithfulness to its context may introduce some safety problems. Technical Quality: 3 Clarity: 3 Questions for Authors: Who you choose neurons? How do neurons compare with probed directions (https://arxiv.org/abs/2306.03341) or features from SAEs (https://transformer-circuits.pub/2024/scaling-monosemanticity/index.html#assessing-interp/) ? Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: As mentioned in weaknesses. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We are deeply grateful for your positive assessment of our work and the recognition of the value in our work. Your feedback is highly encouraging and valuable to us. Below, we provide detailed answers to each of your concerns. Re to Weaknesses #1 & Questions: Lack of comparisons with other steering methods, like steering probed directions or steering SAE's features. Thank you for bringing this to our attention. The Inference-Time Intervention (ITI) method you mentioned identifies a direction in the activation space associated with factually correct statements and shifts activations along this direction during inference, thereby enhancing the truthfulness of LLMs. Analogous to their experimental setup, we conducted experiments on the completion and multiple-choice tasks to explore whether it is possible to find a direction related to perceiving and processing context, and whether it is possible to enhance LLMs' attention to contextual knowledge during generation by shifting activations along this direction. Similarly, for each sample in the MemoTrap or COSE_KRE dataset, we concatenate the question/answer, extract head activations at the last token to collect a probing dataset. Then we use the ITI to identify the direction and intervene activations. We implemented both intervention directions, i.e., Probe Weight Direction and Mass Mean Shift, and reported the results in Table 1 and Table 2 in the attached PDF. Experimental results show that intervening along the Mass Mean Shift direction significantly degrades the performance of most LLMs on both datasets, even more, causing models like Gemma-2B and LLaMA-3-8B to completely fail to respond normally. Improvements along the Probe Weight Direction are also limited, and our IRCAN still achieves the best performance. We will continue to complete experiments on the ECARE_KRE dataset. These experimental results and further analyses will be integrated into the revised version of our paper. As for the method of steering SAE's features as you suggested, we don't think it can be applied to our task. The SAE series of works aims to extract interpretable specific features from LLMs, such as features for famous people, features related to bias, etc. Furthermore, through feature steering, where they clamp specific features of interest to artificially high or low values during the forward pass, the output of the model can be specifically modified, and the specific behavior of the model can be controlled. For example, clamping the Transit infrastructure feature "1M/3" to 5× its maximum activation value causes the model to mention a bridge when it otherwise would not. Similarly, steering features related to bias can alter the model’s biases. However, in our work, the context may encompass a wide variety of knowledge (equivalent to a wide variety of features). Despite the varied nature of this contextual knowledge, our IRCAN approach successfully achieves the manipulation behavior of "enabling LLMs to generate outputs that are more faithful to the context". However, it would not be feasible to manipulate LLMs to produce outputs related to a broad spectrum of contextual knowledge by adjusting one or several SAE's features. Consequently, the SAE approach cannot be implemented on our task and is not suitable for comparison with our approach. Re to Weaknesses #2: More inference time costs. Thank you for your valuable feedback, but we have to emphasize that our IRCAN does not lead to more inference time costs. 1. First, we utilize some examples to identify context-aware neurons offline. Specifically, for each example, we first calculate the attribution scores of neurons. Then, we select the top z neurons with the highest attribution scores as the candidate set for each example. Ultimately, we count the number of co-occurrences of neurons in all candidate sets, and we select the top h neurons with the highest number of co-occurrences as identified context-aware neurons. Therefore, identified context-aware neurons are shared across all data instances. 2. Then, we reweight these context-aware neurons of the LLM. 3. During online testing, we take the modified model for inference, without adding any inference time cost. We suspect that such misunderstanding may be caused by the lack of clarity of the expression in Section 3.2: "Ultimately, we allow each example to vote for the candidate neurons based on their attribution scores, and we select the top h neurons that receive the most votes.". We will revise this sentence to "Ultimately, we count the number of co-occurrences of neurons in all candidate sets, and we select the top h neurons with the highest number of co-occurrences as identified context-aware neurons." in the next version of our paper. Moreover, at the end of Section 3.2, we will add "These context-aware neurons are shared across all data instances." to enhance the clarity of the paper. Re to Weaknesses #3: Safety issues raised by increasing faithfulness to the context. Thank you for your insightful comments. Our research aims to address the scenario where the internal knowledge of LLMs is outdated or wrong, by enhancing the LLMs’ ability to process and capture the correct or domain-specific knowledge incorporated in the context. This capability is crucial in practical applications such as retrieval-augmented generation (RAG) and LLMs as agents. We acknowledge the existence of the scenario you mentioned. In this scenario, we can completely select to not adopt the proposed method and let the LLM use its own knowledge and ability to generate responses, by using a filter to identify jailbroken context. However, we firmly believe that effectively utilizing contextual knowledge and incorporating it into the generation process is an essential capability for LLMs. While not needed in every scenario, this ability is indispensable when required. --- Rebuttal Comment 1.1: Title: Thanks for the rebuttal! Comment: Thanks for the responses, which addressed my questions. I will retain my positive scores. --- Reply to Comment 1.1.1: Comment: Thank you for your supportive comments and positive evaluations. We sincerely appreciate the time and effort you have dedicated to reviewing our responses.	Rebuttal 1: Rebuttal: Many thanks to all the reviewers for providing insightful comments and suggestions! We greatly appreciate you taking the time to review our work and provide constructive feedback to improve the quality of our paper. The attached PDF shows all the comparison experiments we have done, including comparative experiments with Inference-Time Intervention (ITI) (Tables 1 and 2), with prompt engineering-based methods (Table 3), and with instruction-tuning (Table 4). We will incorporate your comments and suggestions into the revised version of our paper. Pdf: /pdf/d25f166428d6672ae12400be81d632ecc57d0602.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
TripletCLIP: Improving Compositional Reasoning of CLIP via Synthetic Vision-Language Negatives	Accept (poster)	Summary: The paper proposes enhancing CLIP's compositional reasoning by generating high-quality negative image-text pairs using LLMs and text-to-image models. This approach improves beyond previous works that considered unrealistic, rule-based captions and unexplored negative images. Experiments show consistent improvements across different tasks. Strengths: - Dataset: The paper proposes using LLMs and text-to-image models to generate hard negative captions and images, respectively. The generation and filtering methodology is effective. I find that releasing TripletData alone is already valuable for the community. - Comprehensive experiments: The paper shows extensive evaluation and consistent improvements over baselines on compositional and downstream tasks like SugarCrepe, zero-shot classification, and image-text retrieval. - Clear presentation: The paper is well-structured and clearly written, explaining the methodology and results effectively. Weaknesses: - Limited scaling: The authors acknowledged the lack of experiments on increasing data and model size due to academic budget constraints. - Limited study on the selection of LLM and image-to-text model: The authors acknowledged the limited study on how the selection of the models could affect the quality of the TripletData. - Nit: Consider using \log and \exp in the equations. Technical Quality: 4 Clarity: 3 Questions for Authors: - Have you considered splitting the test set and evaluating the models on the TripletData? - Could you clarify how the total of 13M image-text pairs is calculated? The numbers provided (2.6M for CC3M and 8.6M for CC12M) in Section 4.1 add up to 11.2M. - Since the negative images are generated from a text-to-image model, there's likely a distribution mismatch from the real positive images. Have you inspected this potential discrepancy? - Can you elaborate on the relatively poor performance on the Winoground benchmark compared to other compositional tasks? Are there specific aspects of Winoground that TripletCLIP struggles with? - There's a mention of "MiraData" in the Appendix - is this a typo for TripletData, or is it referring to something else? Confidence: 3 Soundness: 4 Presentation: 3 Contribution: 4 Limitations: The authors have clearly addressed limitations in their paper. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We are encouraged by your review! We thank you for your comprehensive evaluation of our paper. We are grateful that you found TripletData alone to be of significant value and that our experiments are comprehensive. Please find the requested clarifications below. > ## Response to Weaknesses [W1] Limited Scaling: We acknowledge that scaling our experiments further in academic settings is challenging. However, to approximate this, we experimented with increasing the data (i.e., WordNet synsets), as shown in Figure 3. Our findings indicate a consistent upward trend, with TripletCLIP outperforming the baseline CLIP in terms of compositionality while maintaining zero-shot classification performance. [W2] Selection of LLMs and T2I Models: Grounding the selection procedure of LLM to generate negative captions is indeed essential. We performed additional experiments with three LLMs and trained NegCLIP++ to evaluate their behaviors. The results show that Phi-3 is the best overall. However, at the time of submission, Phi-3 wasn’t released, so we selected the current second-best option, Mistral. The selection of T2I models is straightforward, as their goal is to generate images that truthfully align with the text. Therefore, selecting the best open-source T2I model is a logical choice. \| Models \| SugarCrepe \| Retrieval (R@5) \| ImageNet1k (top-5) \| \|-----------------------------\|:----------------:\|:---------------------:\|:-----------------------:\| \| Gemma-2b-it \| 56.00 \| _0.1260_ \| 12.09% \| \| Phi-3-mini-4k-instruct \| _61.22_ \| 0.1302 \| _10.94%_ \| \| Mistral-7b-instruct-v0.2 \| 61.69 \| 0.1072 \| 10.52% \| [W3] We will update the equations in the final draft (if accepted). Thank you! > ## Response to Questions [Q1] Evaluations on valdiation subset of TripletData: Thank you for suggesting this interesting analysis. We evaluated the CC12M pre-trained models on a 50,000 random subset of the CC3M dataset and reported the scores below. As expected, TripletCLIP significantly boosts the performance of the baselines. However, we also partially attribute this to the spurious correlation learned from the data (related to Q3). At the same time, we note that models are not fully converged, so there is very little chance of overfitting on this spurious correlation. \| Model \| Text Score \| Image Score \| Group Score \| \|-----------------\|:----------------:\|:-----------------:\|:-----------------:\| \| CLIP \| 52.69 \| 29.66 \| 24.64 \| \| NegCLIP \| _54.84_ \| 30.42 \| _25.82_ \| \| NegCLIP++ \| 36.50 \| _30.67_ \| 20.11 \| \| TripletCLIP (ours) \| 92.25 \| 66.82 \| 64.30 \| [Q2] Clarification on TripletData size: We created TripletData on top of LaCLIP, which provides a ~2.9M subset of captions for CC3M and a ~10M subset for CC12M, totaling ~12.9M. However, we observed failures in downloading several images during training, leading to a further decrease in image-text pairs during the training phase. We will clarify this in the final draft (if accepted). [Q3] Potential real vs. synthetic distribution mismatch: Yes, a distribution mismatch exists between real and synthetic images. The generated images are of higher quality than CC3M/12M, potentially adding spurious correlations (partially observed in the Q1 table). However, other generated images represent similar objects with different semantics/relations that are not present in the real data. Despite TripletCLIP learning these biases, it still improves compositionality. [Q4] Winoground clarification: Winoground data contains only 400 instances, which may not be statistically significant for evaluating models trained with lower resources. Even with finetuning on top of the pretrained models, we observed a decrease in performance. Ideally, TripletData should replace the Winoground. We will plan to release the high-quality subset of TripletData as an evaluation set for the community to rely on. Thank you for inspiring this idea. \| Models \| Text-score \| Image-score \| Group-score \| \|---------------------\|:----------------:\|:-----------------:\|:-----------------:\| \| CLIP (org) \| 0.3125 \| _0.1100_ \| 0.0875 \| \| CLIP (finetuned) \| _0.2975_ \| 0.0875 \| 0.0625 \| \| NegCLIP \| 0.2700 \| 0.0875 \| _0.0700_ \| \| TripletCLIP \| 0.2700 \| 0.1125 \| _0.0700_ \| [Q5] Yes, this is a typo. We meant TripletData. Thank you for pointing this out. We hope this clarifies all the remaining questions. Additionally, we offer a summary of responses to other reviews for your reference in the global response. --- Rebuttal Comment 1.1: Comment: Thank you for the detailed response. I appreciate additional experiments that you provided. I have no further concerns. Overall, I’m looking forward to the dataset that you will provide. --- Reply to Comment 1.1.1: Title: Reply to Reviewer m3ja Comment: Thank you for all your time and attention given to our work. We are pleased to see that all concerns have been effectively addressed. Yes, we are planning to release the all versions of the TripletData (CC3M, CC12M, and High-quality filtered version -- 2.8M).	Summary: This paper proposes a TripletCLIP, a pre-training framework aimed at enhancing compositional reasoning task. It computes the NegCLIP objective separately for each, with the image serving as the anchor in each instance. For training TripletCLIP, such triplet data is constructed as follows: Hard negative captions are generated from the original LaCLIP captions using a large language model (LLM) through in-context learning mechanism. Hard negative images are created from text-to-image diffusion models. The experiment section compared various hard negative (HN) based objectives and demonstrated the superior performance of the proposed TripletCLIP mechanism across a wide range of benchmarks: compositionality, zero-shot retrieval, and classification. Strengths: [Originality and Significance] This paper addresses both model and data aspects in the context of pre-training CLIP. Given the challenges of synthesizing hard negative texts and particularly images at scale, the proposed work for constructing triplet data is likely to be valuable to the research community. On the model side, the proposed hard negative objective in pre-training, though simple, consistently enhances performance across a variety of tasks, including compositionality, retrieval, and classification. [Quality and Clarity] The experiments are well-designed and meticulously verify the claims made in the paper, demonstrating the necessity of such design choices. Some additional baselines, beyond the default LaCLIP, are included to demonstrate the effectiveness of TripletCLIP. The overall presentation was clear. Weaknesses: - [W1] The effectiveness of the TripletCLIP objective is less convincing. Although the paper considered some hard negative (HN)-based baselines such as NegImage and NegCLIP++, it did not compare with HN baselines that jointly consider both HN text and image in the loss calculation, such as [1, 2, 3, 4, 5]. I understand that some works are concurrent, but it would be more comprehensive to see whether the design of the TripletCLIP objective is optimal, either quantitatively or conceptually. In addition, it is necessary to note the 'previous' work that generates hard negative images to enhance compositional reasoning tasks [2, 3]. Accordingly, the sentence from [L136-137] needs to be adjusted. - [W2] Though there are consistent improvements, the absolute level of performance is relatively weak compared to the 'default' CLIP models from the CyCLIP [1] and ALIP [6] papers (in terms of zero-shot imagenet and retrieval tasks). This may be due to the reduced computational resources during pre-training, which limits the significance of the results in the context of pre-training. The only possibility left, and neither the triplet data nor the pre-trained model shows the evidence of benefiting further downstream tasks in applications such as advanced VLMs like LLaVA, or text-to-image generation, as noted in [L70-72]. - [W3] Connected to [W2], if only a single GPU is used for pre-training, it would be an attractive alternative to fine-tune the pre-trained CLIP model with the (subset of) triplet data. It's clear that the proposed methodology remains valid, and it would be interesting to see whether employing triplet data with the proposed hard negative objectives proves superior compared to other compositional reasoning methodologies in the context of fine-tuning [7, 8], specifically on both compositional reasoning and retrieval/classification tasks. If the authors wish to focus solely on the pre-training context, referencing other previous work discussing both pre-training, as well as fine-tuning is missed [9]. - [W4] It is suggested to consider including additional compositional benchmarks for evaluation that consist of counterfactual image-text pairs, similar to the Winoground style: EqBen [2], COCO-Counterfactuals [10], MMVP-VLM [11], and SPEC [4], for comprehensiveness. In summary, the main concerns are the missing comparisons with hard negative (HN) objectives that incorporate both image and text, and the limited significance due to small-scale pre-training. Fine-tuning could be considered as an alternative approach to address these issues. Superiority over previous fine-tuning methodologies can further increase the significance. Meanwhile, I believe the large-scale triplet data constructed in the paper is valuable and could promote further studies in various aspects. --- References [1] Goel et al., CYCLIP: Cyclic Contrastive Language-Image Pretraining, in NIPS 2022. [2] Wang et al., Equivariant Similarity for Vision-Language Foundation Models, in ICCV 2023. [3] Sahin et al., Enhancing Multimodal Compositional Reasoning of Visual Language Models with Generative Negative Mining, in WACV 2024. [4] Peng et al., Synthesize, Diagnose, and Optimize: Towards Fine-Grained Vision-Language Understanding, in CVPR 2024. [5] Singh et al., Learn “No” to Say “Yes” Better: Improving Vision-Language Models via Negations, in arXiv preprint 2024. [6] Yang et al., ALIP: Adaptive Language-Image Pre-training with Synthetic Caption, in ICCV 2023. [7] Doveh et al., Teaching Structured Vision&Language Concepts to Vision&Language Models, in CVPR 2023. [8] Doveh et al., Dense and Aligned Captions (DAC) Promote Compositional Reasoning in VL Models, NIPS 2023. [9] Singh et al., Coarse-to-Fine Contrastive Learning in Image-Text-Graph Space for Improved Vision-Language Compositionality, in EMNLP 2023. [10] Le et al., COCO-Counterfactuals: Automatically Constructed Counterfactual Examples for Image-Text Pairs, in NIPS Dataset and Benchmark Track, 2023. [11] Tong et al., Eyes Wide Shut? Exploring the Visual Shortcomings of Multimodal LLMs, in CVPR 2024. Technical Quality: 2 Clarity: 3 Questions for Authors: - Missing citations [L17-19]; image classification [CITATION], segmentation [CITATION], and image-text retrieval [CITATION] - From [L180], it needs referring to the proper section in the appendix - From [L227], what is the meaning of the 'real' hard negatives? Confidence: 4 Soundness: 2 Presentation: 3 Contribution: 2 Limitations: Limitations are adequately and honestly addressed in the appendix. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We appreciate your review of TripletCLIP and the time you've dedicated to it. Thank you for the detailed and holistic review of our work. We are delighted that you found it valuable to the research community. > ## Comparison with Related Works [W1] Firstly, we want to clarify the key baselines selected in the main paper, reflecting the current state of research at the pretraining stage: - NegCLIP: SOTA baseline for negative captions based on the latest CVPR’24 work [12]. - NegCLIP++: LLM-enhanced negative caption similar to [6,7]. - CLIP + HN: Real-world hard negatives filtered from existing datasets. We further divided the related works into two categories: ### Orthogonal Works [1,6-9] Our contributions are orthogonal, meaning our findings can be combined with theirs for further improvements. For instance, CyCLIP [1] introduces a novel regularizer but does not include hard negatives. [6,7] introduce synthetic captions similar to NegCLIP++. [8] focuses on detailed caption-based NegCLIP fine-tuning. [9] introduces scene graph-based negative captions. We retrained CLIP and CyCLIP models with and without TripletLoss using the CC3M training dataset and a batch size of 512. Adding TripletLoss consistently improved performance over baseline CLIP and CyCLIP: \| Models \| SugarCrepe \| Retrieval (R@5) \| ImageNet1k (top-5) \| \|--------\|:-----:\|:------:\|:--------:\| \| CLIP \| 55.11\| 0.1280\| 12.58% \| \| TripletCLIP\| 65.71\| 0.2462\| 19.95% \| \| CyCLIP \| 54.62\| 0.1177\| 13.01% \| \| CyCLIP+TripletLoss \| 58.64\| 0.2029\| 19.05% \| ### Negative Captions and Images [2-5] These works are closer to TripletCLIP. Specifically, [2] utilizes the video dataset to perform hard negative mining and [3] focuses on object-centric caption and image editing for hard negatives, while we focus on free-form captions and image editing that modifies semantics globally. [4] introduces a synthetic data pipeline for benchmarking and proposes a simple extension to NegCLIP pretraining, aligning with our analysis in Table 3, which shows TripletCLIP’s significance. [5] focuses on a "negation" and utilizes a method similar to [4]. Although we could incorporate these negative captions [6-9] along with the TripletCLIP procedure for further improvements, due to time constraints, we perform direct comparisons with finetuning-based experiments and leave the joint optimization as future work. We will include this detailed comparisons in the related work to make it more comprehensive in the final draft. > ## Finetuning Based Experiments [W2 + W3] Our paper focuses on pre-training, as fine-tuning focuses on post-training solutions, which may not be generalizable. That said, we performed additional finetuning experiments with hyper-parameters similar to [3,5,7] (w/o LoRA) and compared against various baselines [3,5,7,8], _whose public checkpoints are available_. Our results show that TripletCLIP improves compositionality and outperforms the almost all baselines. Additionally, the drop in retrieval and zero-shot classification is attributed to the vision encoder (Table 7), indicating the limitations of existing pre-trained vision encoders to represent semantics. This another reason to conduct the pretraining based experiments for comprehensive evaluations. \| Models \| SugarCrepe \| Retrieval (R@5) \| ImageNet1k (top-5) \| \|------\|:-----:\|:----:\|:-------:\| \| CLIP (org) \| 73.06 \| 0.8899\| 88.82% \| \| CLIP (finetuned) \| 74.73\| 0.8475\| 79.16% \| \| NegCLIP\| 80.59\| 0.8486\| 78.34% \| \| Baseline [3] \| 77.84\| 0.9292\| 88.10% \| \| CoN-CLIP [5] \| 75.58\| -\| -\| \| TSVLC (RB) [7]\| 77.84\| 0.9006\| 85.97% \| \| TSVLC (LLM + RB) [7] \| 73.61 \| 0.8998\| 87.02% \| \| DAC [8]\| 86.41\| 0.8372\| 81.22% \| \| TripletCLIP (ours)\| 82.46\| 0.8174\| 75.54% \| Here, DAC [8] introduces detailed human-annotated captions with additional loss functions to incorporate multiple sentences of the captions, which is crucial this performance. Our work focuses on synthetic data with short captions. Future work could explore combining both approaches together. > ## Additional Clarifications on W2 Lines 70-72 convey that CLIP models are key components behind VLMs and T2I models. Our method can potentially improve CLIP models, directly impacting downstream tasks. TripletData could inspire future improvements (noted by ZTUH), possibly requiring different pretraining like DPO. We leave this as future work. However, we will make it clear in the camera-ready draft. > ## Additional Benchmark Evaluations We have already provided additional comparisons on three widely adopted benchmarks in Table 9. Importantly, the newly suggested benchmarks [2,4,10,11] are not well-adopted by the community. But below are the additional evaluations on COCO-counterfactuals [10] that is very similar to [2]. Interestingly, all models perform consistently with no significant improvements over the baseline, possibly due to the evaluation data's difficulty or noise. Having said that, due to the time constraints associated with rebuttal phase, we could not extend large-scale evaluations on another two benchmarks. \| Model \| Text-Score \| Image-Score \| Group-Score \| \|------\|:-----:\|:-----:\|:----:\| \| CLIP\| 26.1 \| 24.77 \| 16.73 \| \| NegCLIP\| 26.06\| 25.55 \| 17.56 \| \| NegCLIP++\| 27.21\| 25.6 \| 16.82 \| \| TripletCLIP \| 26.47\| 25.37 \| 17.92 \| > ## Response to Remaining Minor Questions - [Q1] We will add the suggested citations in the final draft (if accepted). - [Q2] We will clarify the section we are referring to, specifically Figure 2 (main paper) and Figure 6 (appendix). - [Q3] By “real” hard negatives, we mean the hard negative image-text mining within the training datasets instead of synthesizing them. We trust that our response adequately addresses your concerns and encourages you to reevaluate our submission. We look forward to the discussion. --- [12] Zhang et. al., “Contrasting Intra-Modal and Ranking Cross-Modal Hard Negatives to Enhance Visio-Linguistic Compositional Understanding,” CVPR 2024. --- Rebuttal 2: Comment: Thank you for the detailed response. I have no remaining concerns and will adjust the score to 6. I believe that including additional experiments with CyCLIP and fine-tuning comparisons will provide valuable references for future research. It would be great if that part of the codebase were released. --- Rebuttal Comment 2.1: Title: Reply to Reviewer f4Gf Comment: Thank you for raising the score! We are pleased to see that all concerns have been effectively addressed. Yes, we will add all the new experiments in the camera-ready version as they will make our work more impactful. We are also planning to release the code, data, and checkpoints.	Summary: To enhance the compositional capabilities of CLIP, authors propose to generate “hard” negative captions via in-context learning and synthesizing corresponding negative images with text-to-image generators offers a solution. Strengths: 1. Authors introduce a novel CLIP pre-training strategy that employs hard negative images in conjunction with triplet contrastive learning to enhance compositionality. 2. TripletCLIP consistently improves across downstream tasks. 3. A new dataset TripletData is proposed. Weaknesses: The novelty and contribution are limited. While [1] builds negative samples from the text perspective, similar to [1], authors primarily build additional negative samples from the image perspective with LLM and generated images. Given the existing observations (bag-of-words phenomenon, etc.) and soulutions presented in [1], I think the contribution of the current version is marginal. ### Reference [1] When and why vision-language models behave like bags-of-words, and what to do about it? ICLR 2023 Technical Quality: 2 Clarity: 2 Questions for Authors: see weakness Confidence: 4 Soundness: 2 Presentation: 2 Contribution: 2 Limitations: n/a Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your review. We respectfully disagree with the claims regarding our work's limited novelty and contributions. Other reviewers have unanimously recognized numerous strengths in our work despite its straightforward nature. Therefore, we would like to reiterate our research's key strengths and contributions. > ## Novelty and Contributions Importance: CLIP models have demonstrated limited performance in terms of compositionality and tend to behave as bags-of-words, as observed by [1]. This work suggested introducing negative mining, particularly negative captions, could enhance model performance. Following this, several studies have focused on improving synthetic hard negative captions [2,3,4,5], while others have aimed at enhancing data quality [6,7,8]. However, with recent advances in image generative models, it remains unclear whether such tools can improve compositionality. Another recent study introduced training CLIP on a fully synthetic dataset [9], but it required three times more data to achieve performance comparable to real data. Novelty/Contributions: To address these limitations and improve image-text understanding, we propose TripletCLIP. TripletCLIP leverages LLMs to generate hard negative captions (similar to [3,4]) and introduces hard negative images focusing on various image semantics. Additionally, we introduce a novel contrastive pretraining loss, TripletLoss, which enhances the usability of our synthetic data generation pipeline. To be specific, our contributions are as follows: - TripletCLIP significantly improves baseline performance by an absolute 6-10% across benchmarks and shows absolute 4-7% improvements over the baseline proposed by [1]. - We have released approximately 13M synthetic image-text pairs, complementing real-world datasets like CC3M and CC12M. - Additional experiments (Table 7) indicate that vision encoders are the primary source of compositionality limitations in pretrained CLIP models, which were previously unknown. TripletCLIP offers a promising solution to overcome this through careful training on hard negative images, specifically using TripletLoss. - Experiments with increasing concept diversity (Figure 3) further validate our approach, demonstrating that TripletCLIP consistently improves performance with larger dataset sizes. We trust that our response adequately addresses your concerns regarding novelty and encourages you to reevaluate our submission. We also kindly request you to consider the feedback from other reviewers and our responses, contributing to a comprehensive assessment of our work. --- [1] When and why vision-language models behave like bags-of-words, and what to do about it? ICLR 2023. [2] Contrasting Intra-Modal and Ranking Cross-Modal Hard Negatives to Enhance Visio-Linguistic Fine-grained Understanding, CVPR 2024. [3] Dense and Aligned Captions (DAC) Promote Compositional Reasoning in VL Models, NeurIPS 2023. [4] Teaching Structured Vision&Language Concepts to Vision&Language Models, CVPR 2023. [5] Coarse-to-Fine Contrastive Learning in Image-Text-Graph Space for Improved Vision-Language Compositionality, EMNLP 2023. [6] DataComp: In search of the next generation of multimodal datasets, NeurIPS 2023. [7] Demystifying CLIP Data, ICLR 2024. [8] DreamLIP: Language-Image Pre-training with Long Captions, ArXiv 2024. [9] SynthCLIP: Are We Ready for a Fully Synthetic CLIP Training?, ArXiv 2024. --- Rebuttal Comment 1.1: Comment: Thanks for authors' explanation. Although the methodology is simple and the results are actually not surprising to me as it is pretty intuitive that constructing such “hard” negative would lead to improvements, the additional analytical experiments and analysis could be interesting. I would raise my score to 5. --- Reply to Comment 1.1.1: Title: Reply to Reviewer U1Yz Comment: Thank you for raising the score. While incorporating hard negative scores might seem obvious, much of the existing literature overlooks the significance of negative images and how to utilize them effectively. Through this work, we aim to offer a more comprehensive perspective on compositionality and demonstrate how recent generative models can aid in this, even in their simplest forms.	Summary: The paper introduces a novel pre-training strategy aimed at enhancing the compositional reasoning capabilities of CLIP models. The authors identify the limitation in current image-text datasets that restricts the compositional understanding of CLIP models and propose a solution that involves generating "hard" negative captions and corresponding images. This is achieved through a two-step process: leveraging in-context learning for negative caption generation and utilizing text-to-image generators to create matching negative images. The improvement in modeling effectiveness is more significant with the manufactured negative sample dataset. Strengths: [S1] This paper is well-written, making it easy for readers to follow. [S2] The method of the paper is concise and easy to implement, and the experimental results demonstrate its effectiveness, which could encourage more people to apply this method to their own tasks. [S3] For multimodal contrastive learning pre-training, incorporating both image negative samples and text negative samples is comprehensive. Weaknesses: This research primarily involves leveraging LLMs to generate negative samples of similar image descriptions based on the original descriptions, followed by synthesizing the corresponding images using text-to-image models. It is well-known that using synthetic data can easily lead to model overfitting. Consequently, various techniques are typically employed to enhance data diversity, such as data augmentation. It would be intuitive to explore whether utilizing multiple models (multiple LLMs and text-to-image models) during the synthesis process might yield better results. I would be interested in seeing an analysis related to this issue, which could make this paper comprehensive. Technical Quality: 3 Clarity: 3 Questions for Authors: See Weaknesses. 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: Thank you for your time and consideration given to our paper. We are delighted that our work is recognized as well-written, easily reproducible, and effective. We appreciate your belief in our approach and its potential to inspire similar strategies in downstream tasks. In response to your inquiries, please find our clarifications below: > ## Ablation on Generative Model Choices While we acknowledge that exploring multiple LLMs and T2I models could be beneficial, our focus in the paper was shaped by three primary considerations: - The semantic manipulation of text by an LLM is paramount, regardless of the specific LLM used. For better comprehensiveness, we have performed an additional ablation study, which is detailed below. - T2I models must precisely synthesize images from hard negative captions. Hence, we selected SDXL-Turbo, a state-of-the-art and efficient open-source model, thus not necessitating further ablation on T2I model choices. - Synthesizing negative captions and images at scale demands significant resources, making holistic evaluations challenging. For better comprehensiveness, we conducted experiments with different LLMs to generate negative captions, which is a crucial component. The table below presents results from using three LLMs to generate 3M negative captions each for the CC3M dataset. We then trained NegCLIP++ models to assess the effectiveness of these synthetic captions. Notably, Gemma-2 significantly reduces compositionality, while Phi-3 performs best overall. The Phi-3 model was released after the NeurIPS deadline; hence, we use Mistral (second-best choice) in this case. \| Models \| SugarCrepe \| Retrieval (R@5) \| ImageNet1k (top-5) \| \|-----------------------------\|:------------:\|:------------------:\|:--------------------:\| \| Gemma-2b-it \| 56.00 \| 0.1260 \| 12.09% \| \| Phi-3-mini-4k-instruct \| 61.22 \| 0.1302 \| 10.94% \| \| Mistral-7b-instruct-v0.2 \| 61.69 \| 0.1072 \| 10.52% \| > ## Overfitting Due to Synthetic Data We agree that synthetic data can lead to overfitting. As noted in our paper and supported by recent work on fully synthetic CLIP models like SynthCLIP [1], three times more synthetic data is required to match the performance of real data due to limited diversity. Our research was motivated by the question: “What kind of synthetic data can enhance performance?” We found that generating hard negative captions and images is the optimal solution. Preliminary analyses on data scaling trends, shown in Figure 3, demonstrate consistent performance improvements with our approach as we scale the synsets. While our experiments did not observe overfitting (Figure 3), it remains a potential issue if scaled to billions of hard negative image-text pairs. This topic extends beyond the scope of our current work, and we suggest further exploration by the community in future research. We hope these clarifications address all your questions and enhance the comprehensiveness of our work. Additionally, we provide a summary of responses to other reviews in our global response for your reference. --- [1] Hammoud, Hasan Abed Al Kader, Hani Itani, Fabio Pizzati, Philip Torr, Adel Bibi, and Bernard Ghanem. "SynthCLIP: Are We Ready for a Fully Synthetic CLIP Training?." arXiv preprint arXiv:2402.01832 (2024). --- Rebuttal Comment 1.1: Comment: Thanks for the response. I have no more concerns. --- Reply to Comment 1.1.1: Title: Reply to Reviewer ZTUH Comment: We are pleased to see that all concerns have been effectively addressed.	Rebuttal 1: Rebuttal: We sincerely appreciate the constructive feedback provided by the reviewers. It is gratifying to observe the positive evaluations across various dimensions of our work, as highlighted by the reviewers unanimously. - The reviewers unanimously recognize our paper as "well-written and easy to follow" (Reviewers ZTUH, U1Yz, f4Gf, m3ja). - Reviewers f4Gf and m3ja highlight our work's originality and significance in addressing model and data aspects in pre-training CLIP. - The thoroughly designed experiments, which verify our claims and demonstrate the effectiveness of TripletCLIP compared to baselines, are acknowledged by Reviewers f4Gf and m3ja. - Reviewer ZTUH finds the paper concise, reproducible, and effective enough to encourage wide adoption of similar strategies across the tasks. - The extensive evaluation and consistent improvements over baselines in compositional and downstream tasks, such as SugarCrepe, zero-shot classification, and image-text retrieval, are noted by Reviewers f4Gf and m3ja. - Reviewers f4Gf and m3ja value the contribution of releasing large-scale TripletData to the community. We have provided detailed responses to each reviewer individually. Below, we summarize responses to two key questions. Additionally, we have attached the pdf containing detailed benchmark performance for all the experiments conducted during the rebuttal. > ## Summarized Responses to Key Questions - Choice of LLMs and T2I models: We provide additional information on the choice of LLMs for generating hard negative captions. We trained NegCLIP++ on 3M generated negative captions for CC3M using three different LLMs and reported the results. We find that Phi-3 performs the best on average, and Gemma-2b surprisingly affects the compositionality significantly. Moreover, unlike LLMs, whose goal is to follow instructions (which is complicated to evaluate), the T2I model's straightforward goal is to synthesize images faithfully. Therefore, we use SDXL Turbo (SOTA fast model) as the default choice without requiring any ablation. \| Models \| SugarCrepe \| Retrieval (R@5) \| ImageNet1k (top-5) \| \|-----------------------------\|:----------------:\|:---------------------:\|:-----------------------:\| \| Gemma-2b-it \| 56.00 \| _0.1260_ \| 12.09% \| \| Phi-3-mini-4k-instruct \| _61.22_ \| 0.1302 \| _10.94%_ \| \| Mistral-7b-instruct-v0.2 \| 61.69 \| 0.1072 \| 10.52% \| - Comparison with related works: Reviewer f4Gf kindly pointed out several related works for comparison. We categorize these related works into two categories: 1) Orthogonal works: Our paper makes orthogonal contributions to methods like CyCLIP, meaning our work can be jointly utilized with these works, advocating independent contributions that do not necessitate comparisons. 2) Relevant works focusing on hard negatives: Most of the existing works are orthogonal and focus on various ways to improve hard negative captions with minor perturbations in loss functions. While two relevant works focus on generating negative images. - In response to Reviewer f4Gf, we have performed additional finetuning-related experiments and reported the detailed comparisons. We find that additional baselines struggle even to match the compositionality performance of NegCLIP. While TripletCLIP retains the competitive compositionality performance. Again, we thank the reviewers and AC for their time reviewing our paper and providing detailed feedback. We hope that we have addressed all remaining concerns and questions. We look forward to the rebuttal discussion period. Pdf: /pdf/31fd740e563464da8668c9b365cfd49a37dce8ca.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
$\beta$-DPO: Direct Preference Optimization with Dynamic $\beta$	Accept (poster)	Summary: This paper proposes a dynamic method to tune the hyperparameter $\beta$ in DPO according to the data in each batch. The proposed method is tested on Pythia-410M, 1.4B, and 2.8B base models. Compared to vanilla DPO, it performs better on Anthropic HH and Reddit TL;DR summarization datasets. Strengths: 1. The topic is meaningful. The method of tuning hyperparameter $\beta$ potentially influences the RLHF or alignment research if the work is solid. 2. The presentation is excellent. The paper is easy to read. Weaknesses: The proposed method is not sound, neither in theory nor experiments. 1. The experiences are only based on small models, Pythia-410M, 1.4B, and 2.8B. It is hard to evaluate the performances on SOTA (relatively large) models, e.g., 7B or 8B models. 2. In theory, this paper fails to show how the dynamic terms are derived. It gives the dynamic terms directly with more hyperparameters. 3. In practice, the vanilla DPO only has one hyperparameter $\beta$. This paper aims to solve the hyperparameter tuning problem. However, it solves this problem by introducing two hyperparameters $\beta_{0}$ and $\alpha$. With more hyperparameters and space to tune, it is not surprising to fit better, especially on small models. Technical Quality: 1 Clarity: 4 Questions for Authors: 1. $\beta$ is not a simple learning rate. $\beta$ is derived from the KL-divergence penalty term. It ensures that the tuned policy is not "far away" from the original policy. Thus, it should be based on global information, which is the whole training data in offline RLHF. However, in this paper, the dynamic $\beta$ is only based on batch-level information. How does the algorithm capture the global information through batch-level data? 2. The proposed algorithm has two hyperparameters $\beta_{0}$ and $\alpha$. Is it harder to tune compared to the vanilla DPO with only one hyperparameter $\beta$? Confidence: 5 Soundness: 1 Presentation: 4 Contribution: 2 Limitations: The authors addressed the limitations of the paper. Here are some additions. 1. The proposed method is only tested on small models, Pythia-410M, 1.4B, and 2.8B. It is hard to evaluate the performances on SOTA (relatively large) models, e.g., 7B or 8B models. 2. The winning rates are only evaluated by GPT-4 instead of real human groups. But this is a common issue in most LLM studies, and may be acceptable for research. Flag For Ethics Review: ['No ethics review needed.'] Rating: 3 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Dear Reviewer, Thanks for your kind review. We are glad that you found our paper meaningful and easy to follow. We provide detailed answers to your comments below. Q1: It is hard to evaluate the performances on SOTA (relatively large) models, e.g., 7B or 8B models. > A1: Thank you for raising this concern. To expand our approach to more diverse datasets and model sizes, we follow the current state-of-the-art models SimPO[3]. We perform $\beta$-DPO with two families of models, Llama3-8B-Instruct and Mistral-7B-Instruct, on UltraChat-200k UltraFeedback. For comparison with baselines, we assess our models using one of the most popular open-ended instruction-following benchmarks: AlpacaEval 2. All settings are consistent with SimPO [1]. Please refer to Table below: \| Method \| Mistral-Instruct (7B) \| Mistral-Instruct (7B) \| Llama3-Instruct (8B) \| Llama3-Instruct (8B) \| \|--------\|----------------------\|-----------------------\|---------------------\|---------------------\| \| \| LC (%) \| WR (%) \| LC (%) \| WR (%) \| \| DPO \| 20.98 \| 21.60 \| 40.44 \| 37.38 \| \| $\beta$-DPO \| 23.56 \| 20.42 \| 43.38 \| 38.21 \| \| SimPO \| 28.50 \| 30.56 \| 44.38 \| 38.97 \| \| $\beta$-SimPO \| 30.48 \| 32.13 \| 46.03 \| 40.18 \| > Table: AlpacaEval 2 results under the Mistral-Instruct (7B) and Llama3-Instruct (8B). LC and WR denote length-controlled and raw win rate, respectively. Regardless of whether we use Llama3-8B or Mistral-7B, and whether the loss function is DPO or SimPO, our $\beta$-{D, Sim}PO strategy consistently demonstrates significant performance improvements. This thoroughly showcases the method's strong generalization ability and excellent scalability. Q2: This paper fails to show how the dynamic terms are derived. > A2: Thank you for your suggestion. Our work primarily identifies an empirical relationship between $\beta$ and data quality, validated across various datasets and model architectures. While we recognize that the theoretical foundations warrant further exploration, the proposed dynamic strategy is nonetheless notable, providing a new and effective paradigm for fine-tuning large models and studying data quality. Q3: Is it harder to tune compared to the vanilla DPO with only one hyperparameter? > A3: Our proposed $\beta$-DPO is a straightforward, efficient, and easily transferable strategy. Firstly, the selection of $\beta\_0$ in all instances of $\beta$-DPO is consistent with the $\beta$ used in DPO, with a default choice of 0.1 (0.01 for UltraChat-200k), eliminating the need for extensive hyperparameter tuning for $\beta$. As for the uniquely introduced $\alpha$, we find: > In most scenarios, setting $\alpha = \frac{2}{M_0}$ yields stable performance improvements, where $M_0$ can be estimated using a moving average updating scheme (refer to Equation 7). This is informed by the formula $\beta\_{\text{batch}} = [1 + \alpha(\mathbb{E}\_{i \sim \text{batch}}[M\_i] - M\_0)]\beta\_0$, resulting in an overall change range of $[\frac{2\mathbb{E}\_{i \sim \text{batch}}[M\_i] - M\_0}{M\_0}]\beta\_0$, which normalizes based on $M\_0$ over the foundation of $\beta\_0$. \| \| HH \| TLDR \| \|-------------------\|-------------------\|-------------\| \| DPO \| 51.01 \| 32.45 \| \| $\beta$-DPO \| 57.68 \| 51.67\| \| $\beta$-DPO ($\frac{2}{M\_0}$) \| 58.02 \| 51.32 \| > To substantiate this perspective, we present performance in the above table, demonstrating that our setting achieves significant enhancements across various datasets and models compared to DPO, without imposing additional pressure for hyperparameter searches. We appreciate your concern; while we believe that further theoretical consolidation is a meaningful future endeavor, we maintain that the $\beta$-DPO approach remains valuable, offering a straightforward (not overly reliant on hyperparameter tuning) and effective (stable performance enhancements) new paradigm for fine-tuning large models and studying data quality. Q4: How does the algorithm capture the global information through batch-level data? > A4: We employed a moving average estimator to estimate the global reward margin, as referenced in Equation 7. This technique has been commonly used in deep learning [1, 2]. Q5: The winning rates are only evaluated by GPT-4 instead of real human groups. > A5: Thank you for your suggestion. As it stands, the current research landscape indicates that GPT-4 provides the most common strategy for validation. Moreover, the alignment between GPT-4 assessments and human evaluations has been sufficiently established in existing benchmarks (AlpacaEval 2). [1] Yuan et. al. Provable stochastic optimization for global contrastive learning: Small batch does not harm performance. ICML2022. [2] ADAM: A METHOD FOR STOCHASTIC OPTIMIZATION. ICLR 2015. [3] SimPO: Simple Preference Optimization with a Reference-Free Reward. Yu Meng, Mengzhou Xia, and Danqi Chen. --- Rebuttal Comment 1.1: Comment: Thank the authors for the response. 1. As the calibration is better at the batch level than the instance level, do you have an ablation on batch size $b$? (Sorry to bring up this concern late.) 2. Is it equivalent to calibrating the learning rate instead of $\beta$? --- Reply to Comment 1.1.1: Title: Follow-up Discussion Comment: Thank you for your valuable comments and suggestions on our submission. Your suggestions to 1) assess the performance on SOTA models with relatively large scale, such as 7B or 8B models; 2) compare the performance with the vanilla DPO using only one hyperparameter through automated parameter tuning; 3) conduct an ablation study on batch size; and 4) explore the calibration of learning rate and dynamic $\beta$ have significantly contributed to enhancing the coherence and impact of our work. We hope that these improvements will be taken into account during the evaluation process. If our response has resolved your concerns on our paper, we will greatly appreciate it if you could re-evaluate our paper. Should you have any further questions or need additional clarification, please know that we are eager and prepared to continue our discussions. --- Rebuttal 2: Comment: Thank you for your response. Regarding the question about batch size and calibrating the learning rate, we provide the following elaboration: Q1: As the calibration is better at the batch level than the instance level, do you have an ablation on batch size? > A1: We have experimented with different batch sizes for $\beta\_{\text{Batch}}$ on the Pythia-410M model, and the results are as follows: > \| Batch Size \| WR (%) \| > \|------------\|--------\| > \| 128 \| 30.18 \| > \| 64 \| 29.35 \| > \| 32 \| 28.78 \| > The above results demonstrate that larger batch sizes lead to better model performance on Pythia-410M model. Our intuitive understanding of this observation is: > - Larger batch sizes enable more accurate estimation of $\beta$. > - In the extreme case where batch size = 1, batch-level calibration degrades to instance-level, resulting in high instability in the estimation of $\beta\_{\text{Batch}}$. > > We appreciate your suggestion. Due to the limited time for discussion, we will further investigate this conclusion's reliability by experimenting with other model sizes (Pythia 2.8B, Mistral-Instruct (7B) \| Llama3-Instruct (8B)). Q2: Is it equivalent to calibrating the learning rate instead of $\beta$? > A2: Dynamic $\beta$ is not equivalent to calibrating the learning rate. We can further analyze this issue from the perspective of gradients. > $$\nabla\_\theta \mathcal{L}\_\text{DPO}(\pi\_\theta;\pi\_{\text{ref}}) = -\beta\mathbb{E}\_{(x, y\_w, y\_l) \sim \mathcal{O}}[\sigma(\hat{r}\_\theta(x, y\_l) - \hat{r}\_\theta (x, y\_w)) (\nabla\_{\theta, y\_w} - \nabla\_{\theta, y\_l})]$$ > where $\sigma(\hat{r}\_\theta(x, y\_l) - \hat{r}\_\theta (x, y\_w)) =\sigma(\beta \log \frac{\pi\_{\theta}(y\_l\|x)}{\pi\_{\text{ref}}(y\_l\|x)} - \beta \log \frac{\pi\_{\theta}(y\_w\|x)}{\pi\_{\text{ref}}(y\_w\|x)})$. > Therefore, the gradients are correlated with $\beta \sigma(\beta [\log \frac{\pi\_{\theta}(y\_l\|x)}{\pi\_{\text{ref}}(y\_l\|x)} - \log \frac{\pi\_{\theta}(y\_w\|x)}{\pi\_{\text{ref}}(y\_w\|x)}] )$, but non-linearly correlated with $\beta$. Here, $[\log \frac{\pi\_{\theta}(y\_l\|x)}{\pi\_{\text{ref}}(y\_l\|x)} - \log \frac{\pi\_{\theta}(y\_w\|x)}{\pi\_{\text{ref}}(y\_w\|x)}] < 0$. Consequently, as $\beta$ increases, $\sigma(\beta [\log \frac{\pi\_{\theta}(y\_l\|x)}{\pi\_{\text{ref}}(y\_l\|x)} - \log \frac{\pi\_{\theta}(y\_w\|x)}{\pi\_{\text{ref}}(y\_w\|x)}] )$ approaches 0, and the entire gradient also approaches 0. > Considering the gradient update: `params = old_params - lr * grad` Directly calibrating the learning rate cannot achieve the same effect as calibrating $\beta$. However, if an appropriate construction of `lr` can be found (high gap --> small learning rate), the experience from $\beta$-DPO suggests that there may be some improvements. We sincerely appreciate your valuable feedback and eagerly anticipate integrating these improvements into our manuscript. Please let us know if you have any further concerns, and we are encouraged to have a discussion.	Summary: This paper studies the relation between the best $beta$ parameter of DPO and the data quality. Motivated from the observation, the authors propose a way to dynamically choose the $beta$ at the batch level. The evaluation shows the proposed method improves DPO and its variants' (IPO, KTO, SPPO) performance on Antrhopic-HH dataset. Strengths: * The proposed method is motivated from empirical finding that the optimal beta tends to be positively correlated with the reward discrepancy. * The proposed method is based on highly principled ideas such as batch average, exponential moving average, gaussian pdf. * Experiments demonstrate the effectiveness of the proposed method over DPO, IPO, KTO, SPPO Weaknesses: * The experiment mainly relies on Anthropic HH dataset, containing 170000 dialogues. It would be nice if the author can verify the results on another dataset with different domains. Technical Quality: 3 Clarity: 3 Questions for Authors: * $\beta_{batch}$ is defined in Eq. (6). What is a usual range of $\beta_{batch}$ in experiment? Is it possible that $\beta_{batch}$ goes to negative? * In section 4.2.2 data filtering, the authors adopt a sampling without replacement with weights defined in Eq. (8). This cannot completely remove the outlier (i.e., there are still small chance for the outliers to be selected). What if you sort the data in an increasing order according to $\|M_i-M_0\|$ and select the top $\|data\|\times \rho$ instances? (this can completely remove the outliers) How do you compare your method with this? Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: No potential negative societal impact. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Dear Reviewer, Thanks for your kind review. We are glad that you found our paper meaningful and easy to follow. We provide detailed answers to your comments below. Q1: It would be nice if the author can verify the results on another dataset with different domains. > A1: Thank you for raising this concern. To expand our approach to more diverse datasets and model sizes, we follow the current state-of-the-art models SimPO[1]. We perform $\beta$-DPO with two families of models, Llama3-8B-Instruct and Mistral-7B-Instruct, on UltraChat-200k UltraFeedback. For comparison with baselines, we assess our models using one of the most popular open-ended instruction-following benchmarks: AlpacaEval 2. All settings are consistent with SimPO [1]. Please refer to Table below: \| Method \| Mistral-Instruct (7B) \| Mistral-Instruct (7B) \| Llama3-Instruct (8B) \| Llama3-Instruct (8B) \| \|--------\|----------------------\|-----------------------\|---------------------\|---------------------\| \| \| LC (%) \| WR (%) \| LC (%) \| WR (%) \| \| DPO \| 20.98 \| 21.60 \| 40.44 \| 37.38 \| \| $\beta$-DPO \| 23.56 \| 20.42 \| 43.38 \| 38.21 \| \| SimPO \| 28.50 \| 30.56 \| 44.38 \| 38.97 \| \| $\beta$-SimPO \| 30.48 \| 32.13 \| 46.03 \| 40.18 \| > Table: AlpacaEval 2 results under the Mistral-Instruct (7B) and Llama3-Instruct (8B). LC and WR denote length-controlled and raw win rate, respectively. Regardless of whether we use Llama3-8B or Mistral-7B, and whether the loss function is DPO or SimPO, our $\beta$-{D, Sim}PO strategy consistently demonstrates significant performance improvements. This thoroughly showcases the method's strong generalization ability and excellent scalability. Q2: What is a usual range of beta in experiment? Is it possible that goes to negative? > A2: Our initial $\beta\_0$ is set to 0.1, and the range of beta in experiments falls within [0.0, 0.4]. The specific range of variation is detailed in `REBUTTAL Figure 2 Middle`. Experimentally, $\beta\_{\text{batch}}$ can become negative. According to Equation 6, a negative value implies that the reward discrepancy is negative or $\mathbb{E}\_{i \sim \text{batch}}[M\_i]$ is significantly lower than the global mean of $M\_i$, indicating a high likelihood of outliers. Therefore, we apply a cutoff at 0 to ensure training stability, $\beta\_{\text{batch}} = \max(0.0, \beta\_{\text{batch}})$. Q3: What if you sort the data in an increasing order and select top instances? > A3: Thank you for pointing this out. This method represents a hard selection approach, whereas our method utilizes soft selection. The hard selection concept aligns with what we have shown in Figure 5 Left (Filter Head & Tail), and we believe both are effective filtering methods. Both approaches validate that extreme $M\_i$ values are likely outliers that need filtering. > It is important to highlight that this work does not propose a novel filtering method, but we find that filtering enhances stability. As shown in Figure 5 Left, dynamic scheduling could also improve other filtering methods. We are confident that our dynamic schedule will continue to provide stable performance improvements as better LLM data filtering techniques emerge in the future. [1] SimPO: Simple Preference Optimization with a Reference-Free Reward. Yu Meng, Mengzhou Xia, and Danqi Chen. --- Rebuttal Comment 1.1: Title: Post-rebuttal update Comment: This is to confirm that I have reviewed the author's response and the materials given by the authors during the rebuttal. These responses have answered my questions. However, after reading other reviewers' questions, I feel there are some other works to do. So I decided to keep my initial rating.	Summary: This work proposes two techniques to improve the performance of the popular DPO alignment algorithm. The first technique proposes a strategy to dynamically adapt the $\beta$ coefficient of DPO, which controls the strength of the KL penalty with respect to the reference policy. The second technique proposes a filtering mechanism that uses reward margins (the difference between the rewards of the preferred and dispreferred response) to filter the data being sampled for DPO training. Results show that the two techniques complement each other and lead to increased win rates in a range of settings. Strengths: 1. The paper is well-organized and technically sound. The general flow of the paper is smooth. The paper has an appropriate number of citations and properly details existing work in the related work section. 2. The method presented is simple to understand and easy to integrate into any DPO implementation. 3. The results are promising and are giving consistent improvements in a range of scenarios. Weaknesses: 1) Technical and experimental details need to be clearly clarified (refer to questions). Currently, I am unable to see how the techniques presented are related, they seem to be independent. 2) Writing can be improved. In particular, there are very few details about the reward models used in the paper and no acknowledgment of the fact that in contrast to vanilla DPO, the proposed method is reliant on access to a reward model. Technical Quality: 3 Clarity: 2 Questions for Authors: 1. The paper makes an implicit assumption that low-gap examples are high-quality. However, I do not think this is generally true. For example, if both the preferred and dispreferred response are rated very poorly by the reward model, they will also have low-gap. Having clearer writing in this regard and a general explanation of this would be useful. 2. On what criteria does the paper make the claim that Anthropic HH is a low-gap dataset? In my experience, the dataset contains numerous pairs that are easily separable as well. Is any dataset where both $y_w$ and $y_l$ are sampled from the same policy considered low-gap? 3. In contrast to DPO, this method necessitates learning/using an off-the-shelf reward model. There are very few details about this reward model in the paper. Currently, the paper assumes that the reward gaps are generally available, however this is often not the case. It would also be good to have a few sentences acknowledging this difference between DPO and the proposed method. 4. How is beta being used in data filtering? $\beta$ is not mentioned anywhere in Section 4.2.2. The data filter seems like a normal reward margin-based filter. 5. How is the selective filtering ablation run? What does arranging the gradients mean? Is gradient referring to the reward margin? 6. Is m (the momentum coefficient) also a hyper parameter? The claim of the paper is that $\alpha$ is the only hyperparameter. 7. Current results are only on the Pythia class of models and it would be interesting to see the same improvements on a different class of models. I think that is necessary to substantiate the claim of model agnosticity. Confidence: 3 Soundness: 3 Presentation: 2 Contribution: 2 Limitations: N/A Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Dear Reviewer, Thanks for your kind review. We are glad that you found our paper meaningful and easy to follow. We provide detailed answers to your comments below. Q1: There are very few details about the reward models used in the paper > A1: Thank you for pointing this out. We directly use the implicit reward model induced by the policy trained by DPO, where the reward discrepancy in DPO is expressed as: $ \beta \log (\frac{\pi\_\theta (y\_w \mid x) }{\pi\_{\text{ref}}(y\_w \mid x)}) - \beta \log (\frac{\pi\_\theta (y\_l \mid x) }{\pi\_{\text{ref}}(y\_l \mid x)})$. Q2: Why are low-gap examples considered high-quality? > A2: We appreciate your concern regarding this matter. First, it is crucial to clarify that both the low-gap and high-gap examples are derived from data of a certain quality, rather than from extremely poor quality sources characterized by meaningless chatter. We posit that datasets of extremely poor quality would not be utilized for training at this stage. Furthermore, we can categorize the cases of $y\_w$ and $y\_l$ into the following four types: \| Quality of $y\_w$ \| Quality of $y\_l$ \| Description \| Behavior of $\beta$-DPO \| \|-------------------\|-------------------\|-------------\|-------------------------\| \| Low \| Low \| High-quality, hard discriminated pairs \| Lower $\beta$ → Assertive updates \| \| Low \| High \| Label flipping, noise \| Larger $\beta$ → Cautious updates \| \| High \| Low \| Easily discriminated pairs \| Larger $\beta$ → Cautious updates \| \| High \| High \| High-quality, closely matched pairs \| Lower $\beta$ → Assertive updates \| > To further elucidate, both preferred and dispreferred responses are low-quality, yet they serve a beneficial purpose. We follow the settings of controlled sentiment generation in DPO. With access to the ground-truth reward function (a sentiment classifier), we control the quality of $y\_w$ and $y\_l$, where high-quality response is derived from a fine-tuned GPT-2 large model and low-quality response from an unrefined GPT-2 large model. The following table, derived from the IMDB test dataset, illustrates the KL-divergence and the associated rewards: \| KL-divergence \| 2 \| 4 \| 6 \| 8 \| 10 \| 12 \| 14 \| \|---------------------\|----\|----\|----\|----\|----\|----\|----\| \| Both High-quality \| 65.68 \| 89.16 \| 94.26 \| 96.24 \| 97.74 \| 98.91 \| 98.58 \| \| Both Low-quality \| 63.72 \| 80.42 \| 84.00 \| 85.00 \| 81.80 \| 82.20 \| 81.75 \| \| High-quality $y\_w$, Low-quality $y\_l$ \| 45.93 \| 39.55 \| 39.46 \| 36.59 \| 29.98 \| 30.71 \| 31.27 \| > The results indicate that low-quality responses can be even more meaningful for model improvement than high-gap examples. Q3: Why is the Anthropic HH dataset considered low-gap? Are there better datasets available? > A3: The terms "low-gap" and "high-gap" are employed in a relative context. In comparison to the negative samples generated by SFT, the overall distribution of Anthropic HH exhibits smaller differences. To support this assertion, please refer to Appendix Figure 6, where positive samples originate solely from the HH dataset, while negative samples consist of a mix from SFT-generated and original negative samples from Anthropic HH. As the proportion of original Anthropic HH samples increases (i.e., the mixture ratio decreases), the distribution of reward margins becomes more concentrated. Q4: How is beta utilized in data filtering? > A4: In this work, the reward margin informs both the choice of $\beta$ and the framework for data filtering, establishing a bridge between $\beta$ and data filtering. The specific expression is: $p(\beta\_i)= \frac{1}{\sqrt{2\pi}\sigma}\exp(-\frac{(\beta\_i/\beta\_0-1)^2}{2\sigma^2\alpha^2})$ Q5: How is the selective filtering ablation conducted? > A5: We apologize for any misunderstanding in our expression. Your interpretation is correct; we operate based on the reward margin. We will revise this section for clarity. In the DPO formulation, the sample gradients are strictly negatively correlated with the reward margin, implying that a larger reward margin corresponds to a smaller gradient. Therefore, during loss computation for each batch, we sort samples based on their reward margins and conduct selection accordingly. In the experiment corresponding to Figure 5 (Left), "Filter Tail 20%" refers to the filtering of the 20% of samples with the largest gradients, which corresponds to those with the smallest 20% reward margins, and vice versa. Q6: Is m (the momentum coefficient) also a hyperparameter? > A6: m (the momentum coefficient) is indeed a hyperparameter. However, in all our experiments, we consistently set it to 0.9 without any hyperparameter search. To further illustrate, we present additional comparisons in `REBUTTAL Table 2`, showing that this parameter has a minimal effect on model performance. Q7: Current results are only on the Pythia class of models > A7: Thank you for raising this concern. To expand our approach to more diverse datasets and model sizes, we follow the current state-of-the-art models [1]. We perform beta-DPO with two families of models, Llama3-8B-Instruct and Mistral-7B-Instruct, on UltraChat-200k UltraFeedback. For baseline comparisons, we assess our models using one of the most popular open-ended instruction-following benchmarks: AlpacaEval 2. All settings are consistent with SimPO [1]. > Please refer to `REBUTTAL Table 1`. Regardless of whether we use Llama3-8B or Mistral-7B, and whether the loss function is DPO or SimPO, our $\beta$-{D, Sim}PO strategy consistently demonstrates significant performance improvements. This thoroughly showcases the method's strong generalization ability and excellent scalability. [1] SimPO: Simple Preference Optimization with a Reference-Free Reward. Yu Meng and Mengzhou Xia and Danqi Chen. --- Rebuttal Comment 1.1: Title: Reply to rebuttal Comment: I thank the authors for the efforts they have put in the paper and rebuttal. When writing my original review, I was almost certain that an external reward model is being used. The paper never mentioned the use of DPO as an implicit reward model and was generally unclear on this very important detail. Section 3 has no mention of DPO as an implicit reward model and instead introduces the standard external RM, which led me to believe that an external RM is being used. This ambiguity was the main concern of reviewer fXTA as well. Upon learning that the model is in fact an implicit reward model, I believe that many more clarification/experiments are necessary - 1. How does this method perform with an external reward model? 2. I think the method presented is preventing overfitting using margin-based regularization. The open-source community has noted that margins in DPO explode if it is trained for multiple epochs. By increasing the KL penalty for higher margins, this method might be regularizing against such overfitting. This is definitely worth exploring more. 3. At the start of training, all margins should theoretically be $0$ as $\pi = \pi_{ref}$. One of the implications of this is that data points sampled early during training will increase in margin (as they are being trained on). I am unsure of the implications but the data ordering introduces some bias. 4. The non-stationarity is particularly concerning. Moreover, the intermediate states during DPO training all correspond to different reward models. The reward margin for any given datapoint is thus changing at each tilmestep. I think more analysis of how these margin trajectories look like for different datapoints will be very interesting and improve the quality of the paper. I do note that the results for the current method are promising, but I believe that this paper has potential to be a much better one. I will maintain my current score for now, but will follow the discussion and possibly revise based on more discussion with reviewers and authors. --- Reply to Comment 1.1.1: Comment: Thank you for your response. We apologize for not explicitly mentioning that the model is an implicit reward model in the initial draft. We will promptly revise this in the next version. Regarding your question about implicit rewards, we respond as follows: 1. How does this method perform with an external reward model? > Thank you for highlighting this point. Computing the external reward for the training set of 160k samples would 1) significantly increase computational complexity and 2) make the reward highly sensitive to the external reward model used for annotation. Such an approach is difficult to generalize to arbitrary data scenarios and DPO-like methods. Previous studies have raised concerns about the computational complexity to external reward models [1], and it has been suggested that employing implicit rewards could potentially lead to better alignment [2]. We appreciate your suggestion and agree that this is indeed an aspect that could be refined. 2. I think the method presented is preventing overfitting using margin-based regularization. > Thank you for your suggestion. We believe this is one of the advantages and motivations behind $\beta$-DPO. As stated in lines 151-152 of the original text: "Conversely, for high gap pairwise data, maintaining a low $\beta$ may lead to overfitting, which significantly undermines the alignment process." 3. I am unsure of the implications but the data ordering introduces some bias. > We suggest that data ordering has minimal impact. Please refer to `REBUTTAL Figure 2 Middle` (The value of $\beta_{\text{Batch}}$ and preference accuracy along the training steps.). The overall distribution of $\beta_{\text{Batch}}$ does not tend to disperse, indicating that the corresponding margin distribution is relatively stable. In the early stages of training (< 10k / 160k steps), the performance of $\beta$-DPO is similar to DPO; as the model's discriminative power improves, $\beta_{\text{Batch}}$ varies dynamically within the range of [0, 0.4] without further continuous amplification of its value range. 4. The non-stationarity is particularly concerning. The reward margin for any given datapoint is thus changing at each timestep. > The moving average updating scheme on $M_0$ (ref to Equation 7) helps mitigate the potential instability. Although the reward margin increases further ($M_i$ increases) as the model's capability improves, $\beta_{\text{Batch}}$ is positively correlated with $M_i - M_0$. As a result, $\beta$-DPO focuses more on the dynamic reward of different datapoints relative to global datapoints, rather than their absolute values. This approach may help reduce the impact of the changing reward margins on the overall stability of the system. The evolution of $\beta_{\text{Batch}}$ over the course of training steps, as illustrated in `REBUTTAL Figure 2 Middle`, corroborates this perspective. We sincerely appreciate your valuable feedback and eagerly anticipate integrating these improvements into our manuscript. Please let us know if you have any further concerns, and we are encouraged to have a discussion. [1] Filtered Direct Preference Optimization. https://arxiv.org/pdf/2404.13846. [2] Bootstrapping Language Models with DPO Implicit Rewards. https://arxiv.org/pdf/2406.09760	Summary: The paper presents an improvement in Direct Preference Optimization (DPO), a method for aligning and fine-tuning large language models (LLMs) based on human preferences. The authors identify two critical factors affecting DPO performance: the parameter $\beta$ and the quality of preference data. The existing literature has largely neglected the joint impact of these factors. This study investigates how varying $\beta$ and preference data quality influence DPO outcomes. It finds that optimal $\beta$ values depend on the informativeness of pairwise data. Based on this insight, the authors propose enhancements to DPO that involve batch-level dynamic $\beta$ calibration and $\beta$-guided data filtering. The efficacy of these improvements is empirically validated across two NLP tasks (dialogue and text summarization) using models of different sizes. Strengths: Overall, the paper is well-written and easy to follow. The authors make an interesting empirical observation about DPO dynamics: an increase in $\beta$ improves performance when the gap in pairwise preference data is large but degrades performance when the gap is small. The authors perform a thorough empirical analysis, including ablation and compatibility studies, to validate their proposed improvements. The merits of the proposed enhancements to DPO are: (1) Easy to implement, with no additional computational overhead. (2) Compatible with other preference data filtering strategies and DPO variants like IPO and KTO. (3) Utilizes the "running" reward discrepancy instead of relying on teacher/gold rewards. Weaknesses: Despite the comprehensive empirical analysis, the experiments are limited to specific datasets and model size ranges. Given the potential impact on the DPO literature, broader verification across diverse datasets and model sizes would strengthen the claims. The dynamic $\beta$ approach could introduce instability by using the "running" reward discrepancy instead of teacher/gold rewards. A comparative analysis with methods that utilize teacher/gold rewards would be beneficial. Technical Quality: 3 Clarity: 3 Questions for Authors: In Figure 5a, including the $\beta$-guided filtering strategy on the x-axis alongside various gradient-based filtering strategies would be valuable. This addition would help assess its effectiveness compared to existing gradient-based approaches. Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The authors acknowledge the limitations of their work in the conclusion. While the focus is on the technical improvement of preference alignment techniques for LLMs, a detailed discussion on the potential societal impact of these advancements would be a worthwhile addition. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thanks for your kind review. We are glad that you found our paper meaningful and easy to follow. We provide detailed answers to your comments below. Q1: The experiments are limited to specific datasets and model size ranges. > A1: Thank you for raising this concern. To expand our approach to more diverse datasets and model sizes, we follow the current state-of-the-art models SimPO[1]. We perform $\beta$-DPO with two families of models, Llama3-8B-Instruct and Mistral-7B-Instruct, on UltraChat-200k UltraFeedback. For comparison with baselines, we assess our models using one of the most popular open-ended instruction-following benchmarks: AlpacaEval 2. All settings are consistent with SimPO [1]. > Please refer to Table below: \| Method \| Mistral-Instruct (7B) \| Mistral-Instruct (7B) \| Llama3-Instruct (8B) \| Llama3-Instruct (8B) \| \|--------\|----------------------\|-----------------------\|---------------------\|---------------------\| \| \| LC (%) \| WR (%) \| LC (%) \| WR (%) \| \| DPO \| 20.98 \| 21.60 \| 40.44 \| 37.38 \| \| $\beta$-DPO \| 23.56 \| 20.42 \| 43.38 \| 38.21 \| \| SimPO \| 28.50 \| 30.56 \| 44.38 \| 38.97 \| \| $\beta$-SimPO \| 30.48 \| 32.13 \| 46.03 \| 40.18 \| > Table: AlpacaEval 2 results under the Mistral-Instruct (7B) and Llama3-Instruct (8B). LC and WR denote length-controlled and raw win rate, respectively. Regardless of whether we use Llama3-8B or Mistral-7B, and whether the loss function is DPO or SimPO, our $\beta$-{D, Sim}PO strategy consistently demonstrates significant performance improvements. This thoroughly showcases the method's strong generalization ability and excellent scalability. Q2: Comparison with gold reward. > A2: Thank you for pointing this out. In fact, computing the gold reward for the training set of 160k samples 1) greatly increases computational complexity and 2) makes the gold reward highly sensitive to the particular model used for annotation. Such an approach is difficult to generalize to arbitrary data scenarios. Additionally, to reduce the instability of "running" reward discrepancies, $\beta$-DPO utilizes batch-level calibration. Figure 5 (right) and Table 2 clearly demonstrate its superiority. This aligns with our original intent for this work: to develop a simple-to-implement, highly scalable dynamic $\beta$ strategy. Q3: Including the $\beta$-guided filtering strategy. > A3: Thank you for this suggestion. We have included the complete comparison chart in `REBUTTAL Figure 2 Left`. It can be clearly observed that: 1) the dynamic $\beta$ strategy can adapt to various data filtering methods, and 2) the $\beta$-guided filtering proposed in this paper remains optimal. [1] SimPO: Simple Preference Optimization with a Reference-Free Reward. Yu Meng and Mengzhou Xia and Danqi Chen. --- Rebuttal Comment 1.1: Comment: Thank you for the clarifications and additional experiments! I will increase my score.	Rebuttal 1: Rebuttal: We thank all reviewers for their valuable and insightful feedback. - We are encouraged that the reviewers found our paper meaningful (Reviewers $\color{red}{\text{fXTA}}$, $\color{green}{\text{UzDb}}$, $\color{black}{\text{4RgK}}$). - Moreover, we are grateful that the reviewers found our proposed $\beta$-DPO algorithm simple and effective (Reviewers $\color{blue}{\text{3526}}$, $\color{green}{\text{UzDb}}$, $\color{orange}{\text{uGzu}}$). - We also appreciate that the reviewers found our paper easy to follow and well-written (Reviewers $\color{red}{\text{fXTA}}$, $\color{blue}{\text{3526}}$, $\color{black}{\text{4RgK}}$). We also appreciate reviewers pointing out our weaknesses. We address their comments point by point and try our best to respond to them. We hope our response addresses the reviewers' concerns. The additional experiments in the Rebuttal PDF are summarised as follows: - In `Rebuttal Figure 1`, we compare the different dynamic schedules on HH and TLDR. - In `Rebuttal Figure 2 (Left)`, we introduce the $\beta$-guided filtering strategy. - In `Rebuttal Figure 2 (Middle)`, we visualize the range of beta in experiments and the corresponding preference accuracy across training steps. - In `Rebuttal Figure 2 (Right)`, we compare the different dynamic schedules on AlpacaEval. - In `Rebuttal Table 1`, we extend our approach to include a more diverse set of datasets and model sizes. - In `Rebuttal Table 2`, we conduct a parameter sensitivity analysis on $m$. We have carefully considered the comments and suggestions provided by the reviewers, and we have addressed them point by point in our rebuttal. We believe that our responses adequately address the concerns raised. Once again, we sincerely thank the reviewers for their valuable feedback, which has significantly contributed to the improvement of our work. Pdf: /pdf/0a4aeabc0936972a746f6e45c84670b43ef625d0.pdf	NeurIPS_2024_submissions_huggingface	2,024	Summary: The authors's goal is to introduce adaptive schedules for the KL regularization $\beta$ in RLHF. This is a useful quality of life improvement with high potential impact on the final performance of an RLHF algorithm (similarly to how adaptive learning rate schedules are crucial in optimization). As a guiding principle for the adaptive schedule the authors propose to adjust $\beta$ according to the "quality" of the data used in the update. This decision is driven by preliminary experiments that show that: - when RLHF is performed on low gap data (i.e. a human rater barely prefers a completion $y$ over $y'$ and there is no strong quality difference or preference towards $y$ or $y'$) the authors deem the data as high quality, and show that lowering the $\beta$ is beneficial as less regularization allows the model to fit the subtle difference between close pairs of examples - when RLHF is performed on high gap data (i.e. a human rater strognly prefers a completion $y$ over $y'$) the authors deem the data as low quality, and show that increasing the $\beta$ is beneficial as more regularization prevents the model from overfitting only to the preferred sample at the detriment of pre-trained knowledge already stored in the weigths Based on this quality principle, the author propose to measure the gap using a reward model to compute a reward discrepancy, and try to adjust $\beta$ as a function of the sample's reward discrepancy. This turns out to be too unstable and sensitive to outliers, so the authors propose a number of strategies to stabilize the learning while retaining an adaptive $\beta$ - adding a baseline reward discrepancy to "center" the $\beta$ updates - moving from a per-sample reward discrepancy to batch statistics to smoothen the effect of outliers while retaining some adaptivity - leveraging the reward discrepancy as a filtering measure, and simply skipping the updates on high-discrepancy (i.e. lowest quality) samples to reduce variance in the updates - various combinations and ablations of the above The authors show the usefulness of their approach on small to medium scale experiments using helpfulness and summarization text tasks, showing that an LLM judge prefers sentences from a policy fine-tuned with $\beta$-DPO to those from a DPO-finetuned policy, and in some cases even over the golden ground truth. Strengths: Adaptive schedules have always been pretty impactful in practice (although hard to tune), so I would consider the significance of this paper above average. The principle used to quantify "quality" is both a strength and a weakness. The strength are: - conceptually simple, and quite related to existing concept in the literature (e.g. class margins in regression as a similar quantity was used in SLiC [1r] ) which means there is literature and past insights that can guide both usage and future development - computationally reasonable to compute (when using an implicit or explicit reward model) and in some cases even free (DPO implicit reward model, when the reward is part of the dataset) - task-and-data-specific, so avoids a lot of common pitfalls that happen with e.g. schedules that depend only on features (e.g. maximum data norm) or not even that (e.g. linear warm-ups) The paper is very clear and easy to follow. Experiments include useful ablations, and in general are detailed and show improvement over baseline. A few aspects could be improved (more details in weaknesses) Weaknesses: The main (and critical weakness) of the paper is that while it extensively relies on a reward model (e.g. for computing reward discrepancies used in scheduling $\beta$ and filtering), I could not find details on how the authors recommend this reward model is implemented in practice. The two ways I can imagine. The first is to pre-train a reward model as described in section 3 (e.g. by fitting the model in Eq. 2). If this is the case there are a bunch of disconnects in the paper: - this disconnects the approach from DPO (which builds its own implicit reward model), resulting in different reward estimates for the tuning of $\beta$ and for the PO procedure - if the reward model is trained on the same offline data used in the $\beta$-DPO run, then negative reward discrepancies should be treated differently than positive discrepancies, since r(y_w) < r(y_l) indicates either an outlier but possibly also inaccuracy of the reward model (and in general should not happen as often as described by the experiments) The second is to use directly the implicit reward model induced by the policy trained by DPO: - this solves the disconnect between DPO and discrepancy rewards, but note that the accuracy of the intermediate implicit models is bound to be poor, as the goal of DPO is to start with a poor policy (poor reward model) and improve it over time, relying on the supervised signal of offline winners and losers (which does not depend on neither policy or reward model) to drive this improvements. as a consequence using the intermediate rewards for additional online choices (tuning $\beta$, filtering) might be not very sound in theory (but maybe works in practice?) - an implicit DPO reward model makes the whole process even more non-stationary At an empirical level, while the combination of dynamic schedule and filtering proves effective, it is unclear when only one or both techniques are necessary. This weakens the contribution as $\beta$-DPO is not only DPO+a dynamic schedule but DPO+dynamic schedule + filtering. As such, in the natural attempt to transfer the schedule to other PO methods (e.g. KTO, IPO, c-DPO, RPO, etc..) one must also find a way to transfer the filtering technique, making the contribution less general. The principle used to quantify "quality" is both a strength and a weakness. The weaknesses are: - the guidelines proposed that connect $\beta$ schedule to reward gap (high gap -> high $\beta$, low gap -> low $\beta$) seem entirely driven by empirical observations in Figure 1, and are not supported by any further insight or justifications for why this might be the one correct choice when moving away from a constant schedule. More insight would be valuable, where for example DPO gradients are rescaled by a $(1 + e^{M_i})^{-1}$ which means that $\beta$ is somewhat rescaled according to the gradient norm, although in a non-monotonic way. While the proposed dynamic schedule might sound reasonable (or at least I found it so), the exact opposite (high gap -> low $\beta$ since the high margin gives us confidence to fit fully, low gap -> high $\beta$ to avoid overfitting random perturbations on the reward) also sounds reasonable. The soundness of this "quality" measure and its role in tuning $\beta$ should be either evaluated on ablations against other dynamic schedules/principles as baslines, or supported theoretically before it can be fully considered a strong contribution. - according to the authors introduction, the "quality" has a (at least) bimodal distribution in the dataset (high gap data and low gap data), however outlier filtering is performed using only an unimodal 3sigma principle, which looks counterintuitive to me (e.g., aren't all high gaps pairs technically outliers from the low gap sample point of view and vice-versa?) Experiments are good, but without better explainations on how the reward is computed they are hard to evaluate. Technical Quality: 3 Clarity: 3 Questions for Authors: How is the reward model constructed and used? (this is my main question and I am open to revise my score based on the answer) Can you strengthen your support for the gap principle beyond the empirical observation of Figure 1? It seems pretty convincing that a dynamic schedule outperforms a fixed one. There is a missing ablation showing that the one you proposed is strongly preferrable over others (e.g., high gap -> low $\beta$, low gap -> high $\beta$). Can you show that different schedule do not work in your experiments (adapting the filtering if necessary)? Alternatively, can you show which schedules work for which datasets (while keeping that in general dynamic schedules are better than a fixed schedule)? Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The main limitations as I see now are the lack of clarity on the reward model, and the limited support on why this specific schedule is to be preferred over other dynamic schedules. Beyond those, the authors correctly identify important other open questions in the limitation settings. I'd like to highlight among those two that I think would be very relevant in increasing the impact of the paper and make it jump several levels in my evaluation: - Testing the approach beyond DPO. Just like learning rate schedules generalize across optimizers, it's crucial for a good $\beta$ dynamic schedule to generalize across PO methods like c-DPO/IPO/SPO/RPO etc... - Automated parameter tuning. The authors make a good effort on this aspect (automatic choice for $\beta$ and variance estimation) with only one hyperparameter left ($M_0$) to tune despite moving from a simple constant schedule to a dynamic one. However, a true hyperparameter-free method would be much more valuable. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Dear Reviewer, Thanks for your kind review. We are glad that you found our paper clear and easy to follow. We provide detailed answers to your comments below. Q1: How is the reward model constructed and used? > A1: Thank you for pointing this out. We directly use the implicit reward model induced by the policy trained by DPO, where the reward discrepancy in DPO is expressed as: $ \beta \log (\frac{\pi\_\theta (y\_w \mid x) }{\pi\_{\text{ref}}(y\_w \mid x)}) - \beta \log (\frac{\pi\_\theta (y\_l \mid x) }{\pi\_{\text{ref}}(y\_l \mid x)})$. Q1.1: As a consequence, using intermediate rewards for additional online choices (such as tuning and filtering) may lack theoretical soundness. > A1.1: In the early stages of training, $\beta$-DPO behaves similarly to DPO (see `REBUTTAL Figure 2 Middle`). Due to the low accuracy of the intermediate implicit models, the margin between winners and losers is minor, resulting in $\beta\_{\text{batch}} \approx \beta\_0$. However, in the later stages of training, as the margin begins to exhibit significant differences, the advantages of a dynamic $\beta$ become apparent. Q1.2: An implicit DPO reward model introduces greater non-stationarity into the process. > A1.2: This question raises a pertinent point. An implicit DPO reward model can lead to instability in the estimation of dynamic $\beta$, thus making the entire training process more non-stationary. To address this issue, we propose that batch-level calibration is essential. As demonstrated in Table 2 of the initial manuscript, instance-level calibration on dynamic $\beta$ results in a substantial performance drop. In contrast, batch-level calibration enhances stationarity and accentuates the effects of dynamic $\beta$. Additionally, Figure 5 (Right) illustrates that instance-level calibration exacerbates the influence of outliers. Q2: It is unclear when only one or both techniques are necessary. > A2: As demonstrated in Table 1 of the original manuscript, we observe that in a smaller model (410M), the improvement of data filtering is more significant, while in a larger model (2.8B), the improvement of dynamic $\beta$ is more significant. Additionally, the dynamic schedule can also improve other filtering methods (Figure 5 Left). Since our filtering method relies only on implicit reward discrepancy, it also works with other PO methods (Figure 5 Middle). Q3: Can you strengthen your support for the gap principle beyond the empirical observation of Figure 1? > A3: We also attempt the exact opposite (high gap -> low $\beta$; low gap -> high $\beta$). Refer to `REBUTTAL Figure 1, REBUTTAL Figure 2 Right` for the experimental results. We find that across multiple datasets and models, the current strategy remains optimal. Q4: Outlier filtering is performed using only an unimodal 3-sigma principle > A4: Utilizing the 3-sigma principle is primarily to reduce the bias in $\beta$ estimation and thus enhance training stability. Intuitively, high-gap samples often carry low information content, whereas low-gap samples might still be noisy, indicating that winners and losers may not be well distinguished (label flipping). We hope this helps you gain an intuitive understanding. A more detailed analysis can be found in the original manuscript, Section 4.1 (lines 157-170). Q5: Testing the approach beyond DPO >A5: Thank you for pointing this out. First, we demonstrate Dynamic $\beta$ Enhancement across IPO, KTO, and SPPO in Figure 5 (Middle) of the original paper. To expand our approach to more diverse datasets and model sizes, we follow the current state-of-the-art models SimPO[1], which surpass c-DPO/RPO etc. We perform $\beta$-DPO with two families of models, Llama3-8B-Instruct and Mistral-7B-Instruct, on UltraChat-200k UltraFeedback. For comparison with baselines, we assess our models using one of the most popular open-ended instruction-following benchmarks: AlpacaEval 2. All settings are consistent with SimPO [1]. > Please refer to `REBUTTAL Table 1`. Regardless of whether we use Llama3-8B or Mistral-7B, and whether the loss function is DPO or SimPO, our $\beta$-{D, Sim}PO strategy consistently demonstrates significant performance improvements. This thoroughly showcases the method's strong generalization ability and excellent scalability. Q6: Automated parameter tuning. > A6: In most scenarios, setting $\alpha = \frac{2}{M_0}$ yields stable performance improvements, where $M_0$ can be estimated using a moving average updating scheme (refer to Equation 7). This is informed by the formula $\beta\_{\text{batch}} = [1 + \alpha(\mathbb{E}\_{i \sim \text{batch}}[M\_i] - M\_0)]\beta\_0$, resulting in an overall change range of $[\frac{2\mathbb{E}\_{i \sim \text{batch}}[M\_i] - M\_0}{M\_0}]\beta\_0$, which normalizes based on $M\_0$ over the foundation of $\beta\_0$. \| \| HH \| TLDR \| \|-------------------\|-------------------\|-------------\| \| DPO \| 51.01 \| 32.45 \| \| $\beta$-DPO \| 57.68 \| 51.67\| \| $\beta$-DPO ($\frac{2}{M\_0}$) \| 58.02 \| 51.32 \| > To substantiate this perspective, we present performance in the above table, demonstrating that our setting achieves significant enhancements across various datasets and models compared to DPO, without imposing additional pressure for hyperparameter searches. We appreciate your concern; while we believe that further theoretical consolidation is a meaningful future endeavor, we maintain that the $\beta$-DPO approach remains valuable, offering a straightforward (not overly reliant on hyperparameter tuning) and effective (stable performance enhancements) new paradigm for fine-tuning large models and studying data quality. [1] SimPO: Simple Preference Optimization with a Reference-Free Reward. Yu Meng and Mengzhou Xia and Danqi Chen. --- Rebuttal 2: Title: Thank you for your time and consideration. We look forward to hearing back from you. Comment: Dear reviewer, We greatly appreciate your invaluable feedback. We now aim to provide a concise summary that carefully addresses your main concerns. We hope that this effort will be worthy of your support. Q1: How is the reward model constructed and used? > A1: As you mentioned in your second point, we directly utilize the implicit reward model induced by the policy trained with DPO, where the reward discrepancy in DPO is expressed as: $ \beta \log (\frac{\pi_\theta (y_w \mid x) }{\pi_{\text{ref}}(y_w \mid x)}) - \beta \log (\frac{\pi_\theta (y_l \mid x) }{\pi_{\text{ref}}(y_l \mid x)})$. Q1.1: As a consequence, using intermediate rewards for additional online choices (such as tuning and filtering) may lack theoretical soundness. > A1.1: In the early stages of training, $\beta$-DPO exhibits similar behavior to DPO (`REBUTTAL Figure 2 Middle`). Due to the low accuracy of the intermediate implicit models, the margin between winners and losers is small, resulting in $\beta_{\text{batch}} \approx \beta_0$. However, as training progresses and the margin starts to show significant differences, the benefits of a dynamic beta become evident. Q1.2: An implicit DPO reward model introduces greater non-stationarity into the process. > A1.2: An implicit DPO reward model can indeed lead to instability in the estimation of dynamic $\beta$, making the entire training process more non-stationary. To mitigate this issue, we propose that batch-level calibration is crucial. As shown in Table 2 of the original manuscript, instance-level calibration on dynamic $\beta$ leads to a significant performance drop. In contrast, batch-level calibration improves stationarity and emphasizes the effects of dynamic $\beta$. Furthermore, the moving average updating scheme on $M_0$ (ref to Equation 7) helps alleviate the impact of （`Q1.1`） the poor reward model and （`Q1.2`） potential instability. Although the reward margin increases further ($M_i$ increases) as the model's capability improves, $\beta_{\text{Batch}}$ is positively correlated with $M_i - M_0$. Consequently, $\beta$-DPO focuses more on the dynamic reward of different datapoints relative to global datapoints, rather than their absolute values. This approach may help reduce the impact of the changing reward margins on the overall stability of the system. The evolution of $\beta_{\text{Batch}}$ over the course of training steps, as illustrated in `REBUTTAL Figure 2 Middle`, supports this perspective. We were wondering if our responses have addressed your concerns since the discussion phase is coming to a close. We are also eager to know if you have any other concerns or suggestions. Thank you for your time and consideration! --- Rebuttal Comment 2.1: Title: Inquiry on Additional Feedback Comment: Thanks for your constructive feedback on our paper. We kindly inquire whether there may exist any additional concerns or unresolved questions that might be impeding the paper's attainment of a higher rating. We are available for any further clarifications or discussions!	null	null	null	null	null	null
PureGen: Universal Data Purification for Train-Time Poison Defense via Generative Model Dynamics	Accept (poster)	Summary: The paper presents a novel approach to securing model's performance (robust and natural accuracy) against train-time data poisoning attacks by introducing a set of data purification transformations during training, specifically employing Energy-Based Models (EBM) and Denoising Diffusion Probabilistic Models (DDPM). The effectiveness of the proposed method is demonstrated through evaluations on CIFAR-10, Tiny-ImageNet, and CINIC-10 datasets. Strengths: 1. The paper is generally well-written and structured. However, certain sections could benefit from additional clarity and elaboration to enhance the overall presentation quality. 2. The elucidation of the L2 Distance in Section 3.4 is commendable, offering a lucid explanation of the method's underlying mechanism for aligning poisoned data with the benign data distribution. 3. The exploration of different variants of the proposed method in Section 4.4 is a valuable addition to the paper. 4. The method achieves state-of-the-art performance in the conducted experiments, with a comprehensive exploration of its capabilities across various scenarios. Weaknesses: 1. Section 3.1 could be improved by providing a more in-depth discussion on the application of EBM models within the context of the proposed method, rather than focusing predominantly on foundational concepts. 2. The relevance of Section 3.3 is questionable, as the equations introduced (e.g., Eq. 6) do not appear to be integral to the subsequent discussion. 3. The paper may benefit from a clearer articulation of its novelty within the field. Technical Quality: 3 Clarity: 3 Questions for Authors: 1. The application of EBM and DDPM for adversarial purification is gaining traction, particularly in defense against inference attacks [1]. Is this the first application of these models for training-time data poisoning defense? How does this work distinguish itself within the existing body of literature regarding its novelty? 2. The claim on Page 2, Line 45, that purification models require training with a POOD dataset may not present a significant challenge. Pre-trained DDPM models are readily available in open-source repositories and can be employed for data purification, as demonstrated in [1]. Could the authors conduct a comparative analysis between the performance of publicly available DDPM models and those trained in-house? [1] "(Certified!!) Adversarial Robustness for Free!." Carlini, Nicholas, et al. The Eleventh International Conference on Learning Representations. 2022. Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: See weakness and questions. 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 directly respond to the stated questions and weaknesses. --- ### Weaknesses 1. The reviewer suggests that Section 3.1 could be improved by providing a more in-depth discussion on the application of EBM models within the context of the proposed method. We appreciate this feedback and are open to modifying Section 3.1. As this is the first application of an EBM in the poison setting, we believe it was useful background information. That being said, we can condense the fundamental concepts more in the camera-ready version and move more details to the appendix. 2. The reviewer questions the relevance of Section 3.3, as the equations introduced do not appear integral to the subsequent discussion. While these sections provide a theoretical basis for a stochastic transformation defense, we can further condense this section down and move some details to the appendix. We will revise the paper to ensure a clearer connection between these theoretical concepts and their practical application in our method. 3. The reviewer states that the paper may benefit from a clearer articulation of its novelty within the field. We agree and have articulated the novelty in more detail in the general rebuttal Novelty of Work section. We will similarly update the camera-ready version of the paper. --- ### Questions 1. Is this the first application of EBM and DDPM for training-time data poisoning defense? How does this work distinguish itself within the existing body of literature regarding its novelty? Yes, this is the first application of EBM and DDPM models for training-time data poisoning defense to the best of our knowledge. We address the main novelty points of our paper in our general rebuttal Novelty of Work section and clarify the difference between train-time and test-time poisons. 2. The claim on Page 2, Line 45, that purification models require training with a POOD dataset may not present a significant challenge. Could the authors conduct a comparative analysis between the performance of publicly available DDPM models and those trained in-house? We have included an additional experiment using two pre-trained diffusion models from HuggingFace. The results show that these models can achieve defense performance similar to that of some of our POOD in-house trained models. The table below includes 4 baseline PureGen models and the two Hugging Face models trained on butterflies and anime datasets [5,6], showing both are comparable for poison defense and natural accuracy to some POOD datasets in performance. We will include these results and make clear that when available, a pre-trained diffusion model is quite capable of providing poison defense. Our primary insight was in reducing training and improving performance for a given architecture and dataset if one needs to train a diffusion model and if purification is the known use-case. \| \| Model \| Poison Success (%) \| Nat Acc (%) \| Max Poison (%) \| \|---:\|:-----------------------\|:------------------:\|:------------:\|:--------------:\| \| 0 \|PureGen-EBM CINIC-10_IN \| 1.39 ± 0.80 \| 92.92 ± 0.20 \| 2.50 \| \| 1 \|PureGen-DDPM CINIC-10_IN\| 1.64 ± 0.82 \| 90.99 ± 0.22 \| 3.83 \| \| 2 \|PureGen-DDPM Food-101 \| 1.71 ± 0.74 \| 88.35 ± 0.21 \| 2.72 \| \| 3 \|PureGen-DDPM Office-Home\| 1.80 ± 0.83 \| 87.32 ± 0.22 \| 3.16 \| \| 4 \|HuggingFace Butterflies \| 1.65 ± 0.83 \| 87.79 ± 0.18 \| 3.01 \| \| 5 \|HuggingFace Anime \| 1.47 ± 0.75 \| 90.91 ± 0.13 \| 2.95 \| --- We hope these responses clarify any stated weaknesses and answer the reviewer’s questions. References are in general rebuttal. We look forward to any additional discussion. --- Rebuttal Comment 1.1: Comment: Dear Authors, Thank you for the efforts you have made to address the concerns raised in my previous review. Upon careful consideration of your response, I would like to offer the following feedback: - Concern Regarding Novelty: The concept of adversarial purification is indeed established within the literature. While its application during the training phase is an interesting direction, I am not entirely convinced that this alone constitutes a substantial contribution or presents a significant advancement to warrant a recommendation for acceptance in its current form. - Concern Regarding Performance: The effectiveness of pre-trained models, as demonstrated in your work, raises important questions. Specifically, it prompts an inquiry into whether the natural image distribution encompasses the test dataset used in your evaluation. In light of these concerns, I believe that the manuscript would benefit from a major revision, particularly in the following area: Rather than focusing solely on the application of adversarial purification during the training phase as the primary novelty, I encourage you to delve deeper into the effects of data distribution. A thorough analysis and discussion on how data distribution influences the outcomes could significantly enhance the paper's contribution and elevate its importance within the field. I hope that these suggestions will assist you in refining your manuscript. Regrettably, I must maintain my current score, as the contribution does not yet meet the threshold for acceptance. Warm regards, --- Reply to Comment 1.1.1: Comment: Dear Reviewer, Thank you for responding to our rebuttal, and we are glad to respond to the feedback and concerns: * Concern Regarding Novelty: We disagree with this characterization since our novel contributions include extensive distributional analysis and impact of poisoning on defense generative models (Section 4.4), combinations of generative models and energy-based filtering (Section 4.5), extensive analysis on purification and poisons in the energy space (Section 3.4), and the decreased DDPM training pipeline. Train-time poisons have unique enough considerations and have been separated in the literature for a few years. Considering the growth of poisons and defenses within train-time poison literature alone since then, the fact that we comprehensively address SoTA, and the added novelties above, we believe the paper is a strong contribution to the field in its current form. * Concern Regarding Performance and Data Distribution Analysis: This experiment was done as per the reviewer's request, and these were the pre-trained models with the right resolution we could find. All models in the paper have clearly defined train distributions that do not contain the test dataset (unless explicitly called out as a baseline as in the POOD analysis). *Further, Section 4.4 is entirely focused on the impact of data distribution on purification performance for both EBMs and DDPMs.* We believe we thoroughly explore this topic on data distribution impact on purification (far beyond any paper that uses generative models in any adversarial setting). We hope you can further clarify what additional analysis would look like. We thank you again for the discussion and for giving us the added feedback. We believe your concerns are adequately addressed in the paper and in our clarifications. We hope you can reconsider your assessment with these comments. Kindly, Authors	Summary: This paper studies the generative purification methods, i.e., EBM and DDPM-based purifications, as defenses against a set of data poisoning attacks. Strengths: 1. They suggest that a proper range of implementation steps in the EBM and DDPM-based purification methods matters for defense performance. 2. They conduct comprehensive experiments to evaluate the effectiveness of PureGen methods. Experimental results show that proposed defenses perform better than the baselines in the paper. 3. They study some considerations in practical scenarios including (a) training distribution shift in the generative model training; (b) training the generative model on poisoned data; (c) network architecture transferability 4. They explore some PureGen variants. Weaknesses: 1. The idea of employing generative methods to purify imperceptive noises has been explored, i.e. EBM [1] and DDPM [2]. As for training-time poisoning attacks, [3, 4] propose to use diffusion process to defend against availability attacks. Though this paper studies different data poisoning attacks such as Bullseye Polytope, Gradient Matching, and Narcissus, I don't think there is any essential difference in the defense mechanism. 2. Since the technical modification in DDPM lies in the truncation of training steps, it's beneficial to move Figure 4 to the main paper which illustrates how the the selection of steps influences the defense performance. [1] Yoon J, Hwang S J, Lee J. Adversarial purification with score-based generative models [2] Nie W, Guo B, Huang Y, et al. Diffusion Models for Adversarial Purification [3] Jiang W, Diao Y, Wang H, et al. Unlearnable examples give a false sense of security: Piercing through unexploitable data with learnable examples [4] Dolatabadi H M, Erfani S, Leckie C. The devil’s advocate: Shattering the illusion of unexploitable data using diffusion models Technical Quality: 3 Clarity: 3 Questions for Authors: 1. Can you provide more intuition about why sacrificing generative capabilities can improve poison defense? 2. Can AVATAR[1] work as a defense baseline against Bullseye Polytope, Gradient Matching, and Narcissus? 3. In Table 1, why are there no gradient matching results on CINIC-10 and no Narcissus results on Tiny-ImageNet? 4. Why do some Poison Success cells show no standard deviations in Table 1,2? And is the bold font abused in these tables? [1] Dolatabadi H M, Erfani S, Leckie C. The devil’s advocate: Shattering the illusion of unexploitable data using diffusion models Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: See weaknesses and questions. 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 directly respond to the stated questions and weaknesses. --- ### Weaknesses 1. The idea of employing generative methods to purify imperceptible noises has been explored before and the defense mechanism is not different from other attack paradigms such as the availability/unlearnable attack. In the general rebuttal (Train-Time vs. Inference-Time Attacks), we detail the differences between train and inference-time attacks and availability attacks. Our initial EBM work is based on the 2020 paper Stochastic Security [1]. We adapted a similar setup in PureGen-EBM for the poison setting, showing it defends against poisons much better than SoTA. We found poisons are separable as high-energy, which is specific to train-time poison settings. We scaled up the EBM and optimized the number of steps. Given the popularity of diffusion models related to EBMs via Langevin sampling, we found they also reach near SoTA performance. Unlearnable examples (availability attacks) are recent, and so is the Devil's Advocate paper [4]. AVATAR is related to diffusion-style purification, which is why we compared PureGen-DDPM on availability examples in Table 2. We see that out-of-the-box PureGen performs nearly as well as AVATAR. Using AVATAR would be "cheating" since it has seen clean versions of poisoned images as it was designed for inference-time attacks. Additionally, the augmentations used in their method (Cut-Mix, Cut-Out, etc.) are not used in our method to isolate PureGen's impact. Unlearnability and clean-label train-time poisons pose different problems; unlearnability produces detectable results counter to neural network goals, while poisoning is harder to detect post-training, posing significant security risks. Our technique provides universal defense against the strongest poisoning techniques. Finally, we conducted numerous additional experiments for intuition, exploring POOD distribution shifts, poisoning generative model training data, and combining EBM+DDPM and EBM filtering, pushing the boundaries of generative model defense work. We believe these differences and extensive experiments make PureGen a valuable contribution to the community. 2. The reviewer suggests moving Figure 4 to the main paper to illustrate how the selection of steps influences the defense performance. We appreciate this suggestion and will move Figure 4 to the main paper for the camera-ready version to clarify the justification for our pipeline modification. --- ### Questions 1. Can you provide more intuition about why sacrificing generative capabilities can improve poison defense? The empirical results in Figure 4 support that for a given architecture, dataset, and training pipeline, sacrificing some generative capabilities improves poison defense. We utilize Langevin dynamics as a "restoration" of the conditional information in the corrupted image, akin to EBM dynamics moving a sample to a lower-energy, more realistic image. Since the model is not trained to generate from the prior, no model capacity is needed for this initial high-energy, random noise sample. All model capacity is dedicated to restoring the corrupted image, which retains significant low-energy information, similar to conditional generative diffusion processes like in-fill or super-resolution, rather than standard unconditional DDPMs. We will include more discussion around this in a camera-ready version. 2. Can AVATAR work as a defense baseline against Bullseye Polytope, Gradient Matching, and Narcissus? AVATAR is primarily designed for unlearnable examples, which differ from train-time poisoning attacks. The released AVATAR checkpoints are trained on CIFAR-10, making it unfair to use them for purifying unpoisoned images as they have memorized the clean images. However, diffusion methods trained on the correct subsets or POODs likely work, as shown by our results with pre-trained diffusion models in the general rebuttal (Usage of Pre-Trained Diffusion Models). While PureGen-DDPM training offers computational advantages and some performance improvements, it is not necessary to achieve reasonable defense performance when pre-trained models are available. 3. Why are there no gradient matching results on CINIC-10 and no Narcissus results on Tiny-ImageNet? We focused our experiments on the most relevant and challenging scenarios for each dataset, leveraging available poisons from crafting papers. Crafting new poisons is computationally expensive, highly hyper-parameter dependent, and not typically done by defense paper authors. We will clarify this in the appendix. We crafted “new” poisons for analysis in the “defense-aware Narcissus poison” in the general rebuttals, going beyond the scope of typical defense papers. 4. Why do some Poison Success cells show no standard deviations in Table 1,2? And is the bold font abused in these tables? Standard deviations are not shown for un-triggered poison scenarios (Gradient Matching and Bullseye Polytope) for Poison Success. For these experiments, the poison success is based on training 100 classifiers (as each classifier has a single target image for which it is poisoned or not). It would be possible to obtain a standard deviation using different initialization seeds, such repetitions are quite costly (core table results alone took over 7k TPU V3 hours). We can obtain these results for a camera-ready version. We use bold fonts to highlight the highest performing method for each category within reason (highest natural accuracy might be ignored if there is poor poison defense). The exception is Table 3 where we try to highlight all the poisoned model scenarios that would still be SoTA. We will modify Table 3 to use bold font for the highest performing methods as well. --- We hope these responses clarify any weaknesses and answer the reviewer’s questions. References are in the general rebuttal. We look forward to any additional discussion. --- Rebuttal 2: Comment: Thanks for your responses and clarifications; they have indeed addressed some of my concerns. However, I will maintain my score due to the remaining major concerns: - There is no fundamental difference between training-time purification and test-time purification. Before retraining, the poisoned samples have already been purified and fixed. In other words, purification is not truly integrated into the training process; purification and retraining are completely separate. I am not convinced by the story which applies existing diffusion purification to a new perturbation type and makes it the first work addressing this problem. - Main comparisons in the paper, including Tables 1 and 2, adopt no diffusion purification methods as baselines. However, additional results in rebuttal show that pre-trained diffusion models also work in purifying poisoning attacks. Considering the authors' claim that their methods provide SOTA defense, I have concerns about whether the advantages of specially designed techniques are still solid under more comprehensive comparisons, especially with more pre-trained diffusion models. I indeed appreciate the studies regarding practical scenarios, as I stated in Strength 3, 4. Therefore, I agree with other review's suggestions that it might be better to shift the focus of this paper. --- Rebuttal Comment 2.1: Comment: Respectfully, we feel the reviewer has a miss understanding of the point of the paper. In this paper we set-out to show users should purify their datasets with an EBM or diffusion model to get SoTA defense against training poisons with little degradation in natural accuracy. We consider how diffusion models that have been trained on out of distribution data perform in the purification task. We conclude that; 1) EBMs and diffusion models perform SoTA for defense while retraining nat acc, 2) OOD EBM/diffusion works so people should be purifying all image data with whatever EBM/diffusion model they have access to. Now we will go through the latest concerns of the reviewer. The reviewer says: "Before retraining, the poisoned samples have already been purified and fixed. In other words, purification is not truly integrated into the training process; purification and retraining are completely separate. " - That is the entire point. Other defense methods that prevent training poisons slow down training and or reduce performance. Our method protects against training poisons by purifying the entire dataset. We compare to two other SoTA training defense methods; EPIC and FRIENDs. EPIC does not adjust the poisoned training images but instead rejects some, FRIENDS uses the classifier's state during training to calculate a perturbation to the image. Both of these methods require modification to the training loop and FRINDS is very computationally expensive. - Our method as we stated thought the paper and should not be a shock to the reviewer at this point in the review cycle "fixes" or "purifies" the entire dataset before training begins. The class of poisons we are protecting against are named train time poisons. The defense does not require one to augment to training pipeline to be considered a defense. "I am not convinced by the story which applies existing diffusion purification to a new perturbation type and makes it the first work addressing this problem. " - What does the reviewer need to be convinced of? We show that the perturbations intact defend, we show that when we are OOD we might degrade the natural accuracy and increase poison success but we simply share the empirical findings... If you do not believe us feel free to use our posed code to verify. "Main comparisons in the paper, including Tables 1 and 2, adopt no diffusion purification methods as baselines. However, additional results in rebuttal show that pre-trained diffusion models also work in purifying poisoning attacks." - Yes, we are the first to apply EBMs and Diffusion models to purify train time poisons for classifier backdoors. In the paper, so as to not add extra complications (as we don't know how many of the diffusion models are trained on HuggingFace, if they use score matching etc) we trained our own simple DDPM diffusion model ourselves. In the original submitted paper we showed out of distribution(OOD) datasets work. Once you suggested to show numbers from per-trained HF models we simply ran the experiments you requested. But the results remained the same. OOD dataset trained diffusion/EMB models still work for purification. We are certainly the first to show this. "Considering the authors' claim that their methods provide SOTA defense, I have concerns about whether the advantages of specially designed techniques are still solid under more comprehensive comparisons, especially with more pre-trained diffusion models." - We show a clear trade off between using in distribution and out of distribution data. We show that the user can choose to either train their own model or use a per-trained one. This gives the user freedom and confidence that even if they cannot muster up their own diffusion model, they should certainly purify their data with an EBM or diffusion model (in the schedule we suggest) to secure their dataset to SoTA levels.	Summary: This work introduces PureGen, a method to purify a potentially poisoned dataset before the dataset is used to train a classifier. The work explores using Langevin MCMC with both EBMs and diffusion models to remove potential adversarial artifacts from data, with the justification that MCMC sampling should move a sample away from the adversarial artifacts and towards the data distribution. The number of Langevin steps is chosen to be enough to remove adversarial artifacts while preserving the original image. Experimental comparison shows strong performance of the proposed method for training robust classifier with a variety of data poisons compared to existing approaches. Strengths: * The presentation of the method is clear and straightforward, and the paper is easy to follow. * The work proposes interesting adaptions of Langevin purification for white-box adversarial defense to the domain of data poisons. * Empirical results show that the proposed defense can outperform existing defense. There is a thorough examination of different poisons and comparison with existing methods. Weaknesses: * The defense requires costly Langevin iterations and has a higher computational burden compared to existing methods. I appreciate that this is acknowledged clearly and discussed by the authors in the limitations section. * My main concern about this work involves the situation where the data poisoner is aware of the defense method that will be applied to the dataset. Developing attacks that can adapt to different defense strategies is standard in the white-box attack literature, although I am not as familiar with such procedures in the poison literature. Will the defense remain robust if the attacker is aware of the defense strategy? See, for example, [a]. [a] https://arxiv.org/abs/1802.00420 Technical Quality: 3 Clarity: 3 Questions for Authors: Could the authors discuss the situation where the attacker is aware of the defense? I am willing to raise my score if this concern can be addressed. Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: Limitations are adequately discussed. 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 directly respond to the stated questions and weaknesses. --- ### Weaknesses 1. The defense requires costly Langevin iterations and has a higher computational burden compared to existing methods. The Langevin sampling is not as costly as it may seem. With modern GPUs, the cost is comparable to gradient descent. Our timings show that MCMC is actually much faster than the SoTA defense FRIENDS [3], as demonstrated in Table 5. This table also illustrates that PureGen's cost becomes negligible when the purified dataset is reused. 2. Concern about the situation where the data poisoner is aware of the defense method that will be applied to the dataset and white-box scenarios. In the context of train-time poisons (see general rebuttal Train-Time vs. Inference-Time Attacks for detailed differences), the poisoner must stealthily insert poisoned samples into the training dataset to create a backdoor in the NN. A central assumption is that the poisoner has no access to the training pipeline after impacting the train dataset, and the impact of those poisons remains undetected (minimal impact on standard train/test losses). Thus, in this context, a white-box attack refers to the poisoner having the exact architecture, initialization, and weights (for transfer learning scenarios) of a pre-trained or from-scratch model, but they still lack access to the training pipeline and the model after training. This scenario is addressed in Table 1, bottom right (Bullseye Polytope Linear Transfer White-Box Scenario), representing the strongest possible poison scenario. Although crafting poisons is outside the scope of defense papers, *we did craft an EBM dynamics-aware Narcissus trigger and found that it was unable to poison against PureGen. The stochastic nature of PureGen ensures that almost any effective poison perturbation will be high-energy and thus "purified" by PureGen dynamics, with the main concern being a tradeoff in natural accuracy. \| Poison Craft Method \| Defense \| Poison Success \| \|:----------------------------------------\|:-----------:\|:-----------------:\| \| Narcissus Label 2 Baseline (In-Paper) \| No Defense \| 70.95 % \| \| Narcissus Label 2 Baseline (In-Paper) \| PureGen-EBM \| 2.70% \| \| Narcissus Label 2 PureGen-EBM Aware \| No Defense \| 3.63% \| \| Narcissus Label 2 PureGen-EBM Aware \| PureGen-EBM \| 2.37 % \| Additional analysis of these results can be found in the general rebuttal Defense-Aware Poison. We encourage poison researchers to utilize our code and attempt to break the defense, but we already include results with the strongest scenarios available per the train-time poison literature along with this additional defense-aware experiment. Note, crafting this single trigger took over 20+ hours of A100 GPU time. While we could not get more results for this rebuttal, we will include results and analysis in an appendix for the camera-ready version for all classes and for “PureGen-DDPM aware” Narcissus. --- ### Questions 1. The reviewer asks if we could discuss defense-aware poisons.* See the Weakness 2 above and the Defense-Aware Poison section in the general rebuttal where we discuss this at length and include an additional experiment showing PureGen’s robustness to a custom defense-aware poison for PureGen-EBM. --- We hope these responses clarify any stated weaknesses and answer the reviewer’s questions. References are in general rebuttal. We look forward to any additional discussion. --- Rebuttal Comment 1.1: Title: Thanks for the response. I will raise my score. Comment: I appreciate the efforts to investigate the defense-aware data poison, and it is reassuring to see the defense retains security. This addresses my main concern. While the EBM and diffusion purification methods fall within established practice, there appears to be a consensus among reviewers that this work does cover an area that has not yet been directly investigated in published work, namely purification-type defense applied for train-time data poisoning/purification. It does seem like there should be a work like this as a reference point for the community and the authors performed a wide array of experiments to investigate this scenario. I understand the concerns of other reviewers regarding novelty, but I nonetheless feel this work makes an expected but useful contribution. I will increase my score since my main concerns have been addressed.	Summary: This paper proposes a stochastic preprocessing defense technique, named PureGen, against train-time poisoning attacks, with EBM-Guided and Diffusion-Guided sampling processes. First, with EBM-based purification, called PureGen-EBM, the purifier first evaluates the (unnormalized) energy function of the images. Then, this considers the high-energy images as the 'posioned' images, and purifies with the stochastic preprocessor $\Psi_T$. On the other hand, with Diffusion-based purification, called PureGen-DDPM, the purifier first add Gaussian noises to the inputs and run the reverse diffusion process using DDPM. Strengths: * This paper demonstrates purification results with respect to diverse poisoning attacks and data availability attacks, which provides a new benchmarks on the adversarial learning communities. * To the best of my knowledge, this is the first result to implement adversarial purification to poisoning attacks, achieving superior performances compared to other existing methods. Weaknesses: * The idea of using adversarial purification to adversarial attacks is already well-known, and this is an increment of the adversarial purification to other kinds of attacks. * There are still scenarios that also breaks the adversarial robustness of the purification models such as BPDA+EOT [Athalye et al, 2018]. To mitigate this, additional consideration like fine-tuning on the adversarial perturbation models is required. [Lin et al., 2024]. Without this, the purified images will be easily poisoned with stronger poisoning attacks, which also involves with the purifier in the poisoning steps. * Some additional validation on using the diffusion models on adversarial purification should be addressed: see __Questions__. * In my opinion, with improved sampling methods using a higher-order solver of consistency-based distillation models, the purification can be drastically faster compared to both the proposed methods and the existing method. I presume that this can be easily improved: See __Questions__. [Athalye et al, 2018] Obfuscated Gradients Give a False Sense of Security, ICML 2018 \ [Lin et al., 2024] Adversarial Training on Purification (AToP): Advancing Both Robustness and Generalization, ICLR 2024 Technical Quality: 3 Clarity: 3 Questions for Authors: * In the PureGen-DDPM process, the dataset is trained with DDPM fewer steps, (250 steps rather than the conventional 1000 steps). Nevertheless, training DDPM with fewer discrete steps yields heavier posterior mismatch between the DDPM posterior covariance and the optimal covariance, according to [Bao et al, 2022]. I doubt that the purification gain from less timesteps from Figure 4 (bottom right) is just a side-effect of this posterior mismatch, which is not rigorously intended. I will be more convinced if some explanation on setting the fewer steps in PureGen-DDPM for training. * Even though the time complexity of the proposed purification method is comparable to the existing methods, this can be easily improved with some higher-order solvers without any additional training. The paper will be much stronger if more results with some solvers are addressed. [Bao et al, 2022] Analytic-DPM: an Analytic Estimate of the Optimal Reverse Variance in Diffusion Probabilistic Models, ICLR 2022 --- Minor typos * (Appendix C) Intition $\to$ Intuition Confidence: 5 Soundness: 3 Presentation: 3 Contribution: 1 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 time and directly respond to the stated questions and weaknesses. --- ### Weaknesses 1. Contributions are limited and adversarial purification is a known technique. We respectfully disagree that our contribution is incremental and believe that conflating inference and train-time attacks contributes to this impression. In the general rebuttal (Train-Time vs. Inference-Time Attacks), we detail the differences between train and inference-time attacks. Train-time attacks require preventing the creation of "latent" backdoors during training, where defenders have no knowledge of poison presence in the data, and *the attacker no longer has access to the training or inference pipeline after poisoning. We demonstrate significant improvements across diverse train-time poisoning scenarios, establishing a new benchmark in this domain. Our extensive experiments provide practical applications beyond the norm in defense literature. We hope clarifying this distinction allows the reviewer to see the novelty of this work. 2. There are still scenarios that break the adversarial robustness of the purification models such as BPDA+EOT [Athalye et al, 2018]. To mitigate this, additional consideration like fine-tuning on the adversarial perturbation models is required. [Lin et al., 2024].* BPDA+EOT is an inference-time attack, which is out of scope for our paper. PureGen is focused on train-time attacks, where attackers poison a dataset but lack access to the training pipeline afterwards. This central assumption in train-time attack and defense literature makes BPDA+EOT irrelevant here. As a side note, the SoTA defense against PGD+EOT(the full gradient version of BPDA+EOT) uses an EBM [1]. The published SoTAs for train-time poisons are EPIC [2] and FRIENDS [3], which do not defend against PGD/BPDA+EOT. DiffPure claims SoTA against BPDA+EOT but fails when true gradients, which is memory intensive and requires gradient checkpointing, are calculated i.e. PGD+EOT. Fine-tuning in this way is not applicable in the train-time attack setting. The train-time poisons in this paper are SoTA in strength, and our EBM and Diffusion models defend against them better than any other defense while maintaining natural accuracy. Even if future train-time poisons are stronger, the goals differ from PGD/BPDA+EOT and a comparison is not possible. For this rebuttal, *we collected results crafting a defense-aware Narcissus patch (see Defense-Aware Poison in the general rebuttal), showing PureGen-EBM dynamics make crafting itself no longer possible in the standard budget* (8/255) . Note, we are a defense paper, and not a poison paper, and coming up with a defense aware train time poison is not our burden, but we did so to answer these questions raised directly and indirectly by multiple reviewers. We provide concrete evidence that our PureGen method is SoTA under from-scratch, fine-tune, and linear transfer modes across various architectures, poison types, and attacker knowledge levels of gray and white-box scenarios covering all attacks relevant to train-time attack literature. --- ### Questions 1. The reviewer asks about fewer DDPM steps in training and resulting heavier posterior mismatch Our choice balances the fidelity of the original image with the need to effectively remove the poison perturbation and improve diffusion model training time. While a posterior mismatch is theoretically possible, Figure 4 in Appendix B.3 shows empirical evidence that the truncated DDPM training schedule results in better poison defense and natural accuracy for a given architecture and dataset. We will move this figure to the main paper due to its importance. We also include results with pre-trained Diffusion models (see Usage of Pre-Trained Diffusion Models in the general rebuttal), showing they can achieve reasonable defense success. However, for specific purification use-cases, the truncated PureGen-DDPM method offers improved performance and decreased training burden. 2. The reviewer states even though the time complexity of the proposed purification method is comparable to the existing methods, this can be easily improved with some higher-order solvers without any additional training. The time complexity of PureGen is significantly faster than SoTA defense FRIENDS as shown in Table 5, and is quickly marginalized over usage of the data as we only need to purify once. Using higher-order solvers can potentially give marginal speedups to diffusion, but as the reviewer mentioned, can be used on our diffusion models without re-training. Since we only need to purify one time, the delta between standard DDMP and using a higher-order solver is negligible. In the context of adversarial inference attacks where one must defend against every incoming image with gradients needing to be propagated through every step of diffusion, this may make a difference, but not in our train-time poison context. --- We hope these responses clarify any stated weaknesses and answer the reviewer’s questions. References are in general rebuttal. We look forward to any additional discussion. --- Rebuttal 2: Title: Response Comment: Thank you for the detailed response and additional experiments. I agree with the following point, and would not reflect the following point for deducting the rating of the paper. __Purification on training-time attacks__ I still consider that the novelty of this work is incremental, as directly applying diffusion/EBM (for adversarial purification) to mitigate poisoning attack. This would be the primary reason of my rating of this paper, unless having ample experiments. --- On the other hand, I address further questions below. __Defense-aware Poisoning__ The authors mentioned that "_cannot hypothesize new poison techniques to bypass PureGen._" However, there is a simple and efficient poisoning method that can bypass the purification method. For example, we know from the literature that the ODE and SDE that runs through the diffusion model (and also the EBM) have the same density function, according to the _Fokker-Planck equation_. Then, for example, there can be a full pipeline that starts from the _purified image_ to the classifier: 1. begin with the noisy image, and run the purifier to obtain the clean(-ized) image. 2. Then, run the "poisoned" network for prediction. According to the authors' response, the authors presumed that the poisoning method for the purifier is beyond the scope. However, we can raise some issues: - The ODE solver is effectively a series of deterministic forward neural network run. This means that, if we run 10 steps of ODE solver, the purifier-classifier pipeline can consist of __"10 steps of deterministic run"-"classifier"-"prediction"__, which is just a larger neural network. In this case, train-time poisoning is obviously available without complex methods bypassing the obfuscated gradients proposed in [Athalye et al., 2018] or so. Can the authors manage this issues that the attacker threatens not only the classifier but the generative models? ``` [Athalye et al, 2018] Obfuscated Gradients Give a False Sense of Security, ICML 2018 ``` --- __Posterior Mismatch Issues__ Firstly, we agree with the authors that this is not the primary issue of this paper, and __we do not deduct rating__ with respect to this following part. Nevertheless, there is still not enough relevance between [_Truncation of DDPM posterior_] and [_Better performance of train-time derense_] without any generic analysis. Hence, I do not agree with the authors to move this part into the main part of the paper. --- Rebuttal Comment 2.1: Comment: We respectfully but firmly disagree with the reviewer's opinions. The reviewer states "This would be the primary reason of my rating of this paper, unless having ample experiments." How many experiments would be ample? We have trained over 3k classifiers throughout this paper showing that PureEBM and PureGen outperform all current defense methods which were published 2021/2022 at top conferences. In this we also trained 10s of 100s of EBMs and Diffusion models. The point of training poisons is that they are stealthy, as such the point of the reviewer that we could do SDEs to try to create a stronger attack is moot. To do this the attacker would need access to significantly more information than any of the poisoning papers are assuming. The reviewer also describes a scenario where one begins with a noisy image and then purifies and "Then, run the "poisoned" network for prediction." The reviewer is mistaken on the setup of poisons. This setup is for the adversarial attack and not poisons. The setup for from scratch poisons is this. No more no less. 1 . A poisoner adds small perturbations $\epsilon$ of their choosing to a small subset of images which will be used to train a classifier in step 2. - The poisoner can have access to at most the initialization of the classifier that will be trained in step 2. 2 . The train dataset that has been tampered with by the poisoner is used to train a classifier. 3 . If the poison is successful, the poisoner can pass a specific image of a cat through the classifier and have it be classified as a dog as they wanted. There is absolutely no other information given to either side. PGD attacks to augment step 3 are not allowed. The reviewer states: "According to the authors' response, the authors presumed that the poisoning method for the purifier is beyond the scope." We feel this is a miss-characterization of what we have said. In fact trained the EBM/Diffusion models with 100% poisoned images. These poisons did not significantly affect our purification performance as seen in Table 3, where we considered fully poisoned (all classes at once). The reviewer cites "Obfuscated Gradients Give a False Sense of Security, ICML 2018," again this paper is only on test time active attacks where the attacker has significantly more access to the classification problem, namely fully trained model. Again, this is a totally different problem and it not relevant to the setup of our paper. Still in the full PGD+EOT attack setup which is certainly outside of the cope of this paper, EBMs are still SOTA.	Rebuttal 1: Rebuttal: We thank the reviewers for their thoughtful feedback and the opportunity to address their concerns. Below, we provide a concise response to the main points raised by the reviewers and outline main revisions we will make to improve our paper. --- ### Responses to General Points 1. Train-Time vs. Inference-Time Attacks *PureGen is the first method to use EBMs and DDPMs for defending against train-time data poisoning attacks.* Our work focuses on train-time poisoning attacks, which aim to manipulate training data to cause misclassification during inference. This is distinct from inference-time attacks (PGD/BPDA+EOT), which aim to fool a trained model with perturbed test samples. Clean-label train-time attackers manipulate a small portion of training data to introduce undetected backdoors, without further access to the model once training begins. In practice, attackers may disseminate poisoned images on public platforms like social media, hoping they are used for training. The goal is to avoid human detection, have images classified as intended in training, and not significantly alter training or validation metrics to avoid suspicion. We acknowledge works on generative models for inference-time attacks (e.g. Avatar [4], Stochastic Security [1]) but focus on the unique risk of train-time attacks, where an attacker creates a latent backdoor that can be exploited later without alerting the model trainer or deployer. 2. List of Novel Contributions: - We are the first to bring generative model defense to train-time poisons and provide a comprehensive set of experiments showing SoTA performance over the strongest poisons and scenarios. - We demonstrate that poisoned samples are separable as high-energy using EBMs, showing why generative model dynamics purify and lower the energy of such samples. - We find generative models effective even when trained with distributionally shifted or poisoned data. - We introduce a truncated DDPM training cycle to reduce computational costs and improve purification performance. - We explore a combination of EBMs and DDPMs for better purification. 3. Defense-Aware Poison To address concerns about “defense-aware” attackers, we conduct experiments using "defense-aware" Narcissus poisons crafted with knowledge of the EBM defense (using EBM dynamics in the crafting process directly). The results show PureGen's robustness, even against attacks designed with defense knowledge. \| Poison Craft Method \| Defense \| Poison Success \| \|:----------------------------------------\|:-----------:\|:-----------------:\| \| Narcissus Label 2 Baseline (In-Paper) \| No Defense \| 70.95 % \| \| Narcissus Label 2 Baseline (In-Paper) \| PureGen-EBM \| 2.70% \| \| Narcissus Label 2 PureGen-EBM Aware \| No Defense \| 3.63% \| \| Narcissus Label 2 PureGen-EBM Aware \| PureGen-EBM \| 2.37 % \| Our “defense-aware” Narcissus experiments suggest two possible results: finding a hole in the EBM defense or failing to craft effective poisons due to stochastic purification. Our success against various poisons makes the first scenario unlikely. While not theoretically guaranteed, the new results further support that finding an effective poison with EBM knowledge is improbable. We can expand on this table for the camera-ready version but emphasize that we are not a poison paper and cannot hypothesize new poison techniques to bypass PureGen. We could not get more results for this rebuttal (crafting this single trigger took over 20+ hours of A100 GPU time), we will include results and analysis for the camera-ready version for all classes. 4. Usage of Pre-Trained Diffusion Models We include an experiment using two pre-trained diffusion models from HuggingFace, showing similar results to our POOD DDPM results on Narcissus From-Scratch attack. PureGen-DDPM training is beneficial but not required for good defense performance; pre-trained models are often adequate when available. \| \| Model \| Poison Success (%) \| Nat Acc (%) \| Max Poison (%) \| \|---:\|:-----------------------\|:------------------:\|:------------:\|:--------------:\| \| 0 \|PureGen-EBM CINIC-10_IN \| 1.39 ± 0.80 \| 92.92 ± 0.20 \| 2.50 \| \| 1 \|PureGen-DDPM CINIC-10_IN\| 1.64 ± 0.82 \| 90.99 ± 0.22 \| 3.83 \| \| 2 \|PureGen-DDPM Food-101 \| 1.71 ± 0.74 \| 88.35 ± 0.21 \| 2.72 \| \| 3 \|PureGen-DDPM Office-Home\| 1.80 ± 0.83 \| 87.32 ± 0.22 \| 3.16 \| \| 4 \|HuggingFace Butterflies [5] \| 1.65 ± 0.83 \| 87.79 ± 0.18 \| 3.01 \| \| 5 \|HuggingFace Anime [6] \| 1.47 ± 0.75 \| 90.91 ± 0.13 \| 2.95 \| --- ### Revision and Improvements - We will include the results from both our additional experiments: “Defense-aware” Narcissus showing PureGen is still effective when attackers can utilize the PureGen-EBM dynamics Use of pre-trained Diffusion models that can obtain comparable defense performance to PureGen-DDPM - We will clarify that the PureGen-DDPM training process shows gains empirically over standard diffusion but it not necessary to obtain reasonable defense performance - We will add more detail to Section 1 to clearly enumerate our novel contributions. - We will move Figure 4 into main paper --- ### References [1] Hill M, Mitchell J, Zhu S. Stochastic Security: Adversarial Defense Using Long-Run Dynamics of Energy-based Models. [2] Yang Y, Liu T Y, Mirzasoleiman B. Not All Poisons are Created Equal: Robust Training against Data Poisoning. (EPIc). [3] Liu T Y, Yang Y, Mirzasoleiman B. Friendly Noise against Adversarial Noise: A Powerful Defense against Data Poisoning Attacks. [4] Dolatabadi H M, Erfani S, Leckie C. The devil’s advocate: Shattering the illusion of unexploitable data using diffusion models. [5] https://huggingface.co/johnowhitaker/ddpm-butterflies-32px [6] https://huggingface.co/onragi/anime-ddpm-32-res2-v3	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Wasserstein convergence of Cech persistence diagrams for samplings of submanifolds	Accept (poster)	Summary: The paper provides a more fine-grained analysis of stability results for persistent homology for data sampled from manifolds, proving new theoretical guarantees for methods in topological data analysis. Strengths: The results of the paper are in this reviewers opinion strong and interesting. Topological methods, in particular persistent homology, has become a widely used and powerful tool for the analysis of data, in particular data zhat is sampled from an underlying manifold. In many cases, the use of persistent homology can add an additional layer of explainability. For this, mathematical guarantees are fundamental. The new guarantees proven in this paper are significantly stronger than previous ones. In this reviewers opinion the proofs are correct and the precise arguments as well as the underlying ideas are nicely presented. Weaknesses: As the authors note, the proofs require some assumptions, which are not always guaranteed: they assume the manifold hypothesis and that the points are sampled without noise. Also, their analysis is based on Cech persistence and not Vietoris-Rips persistence, which is used more often in practice. In this reviewers opinion it is however still reasonable to make these assumptions, as they provide the necessary structure to thoroughly mathematically analyze the used tool (in this case persistent homology) in an „ideal world setting“, as is often done for mathematical guarantees. Technical Quality: 4 Clarity: 4 Questions for Authors: -Did you perform any experiments on data with noise or with Vietoris-Rips persistence? If so, how did the results compare to the ones you present in the paper? Confidence: 4 Soundness: 4 Presentation: 4 Contribution: 3 Limitations: The limitations (that are also mentioned above) are addressed and explained at multiple points in the paper: -in line 169 the authors argue why some assumptions are always needed. -in line 216 they explain why the genericity assumption is needed for their Theorem 3.3. - in line 353 they again mention the assumptions as the main limitation of their work. Flag For Ethics Review: ['No ethics review needed.'] Rating: 9 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Dear reviewer, Thank you very much for your interest in our work. We address the issue of noisy data in our response to all reviewers, and we agree that similar guarantees for the Vietoris-Rips complex would be valuable; in fact, we are already working towards proving such results. Regarding experiments in particular, preliminary investigations suggest that comparable results should hold for the Vietoris-Rips persistence, and also seem to support what we explain regarding noisy data in our general response. --- Rebuttal Comment 1.1: Comment: I would like to thank the authors for their convincing rebuttal.	Summary: The paper describes three new theorems on the stability of persistence diagrams with respect to Bottleneck and Wasserstein distance under certain additional assumptions. Strengths: All three results are interesting fundamental contributions to the field of topological data analysis Weaknesses: I am not sure about how much the results are in scope for a machine learning conference. I do agree that a solid foundational layer is important but my feeling is that the connection could be described in more length (Sec 4.4 seems to serve this purpose partially). The authors also admit themselves in the conclusion that the results rely on the manifold hypothesis and the absence of noise. I guess one could argue in length about the manifold hypothesis and how realistic it is in practice. But my hunch is that not allowing any noise is a more serious limitation. Technical Quality: 4 Clarity: 4 Questions for Authors: Why do you think that the paper is an adequate fit for Neurips, as opposed to, say, a journal specialized on TDA? Confidence: 3 Soundness: 4 Presentation: 4 Contribution: 4 Limitations: As mentioned, they address the limitations of their results adequately Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Dear reviewer, Thank you for your appreciation of the overall quality of our work.\ We discuss the soundness and importance of our noiseless data hypothesis, as well as the relevance of our work for the ML community, in our response to all reviewers.\ Regarding specifically the question Why NeurIPS rather than a journal specialized in TDA?, our understanding is that any high-quality contribution to a subfield of Machine Learning (e.g. TDA, bandits, causality, fairness, etc.) is welcome at NeurIPS, though such a contribution could also be submitted to a more specialized journal or conference. --- Rebuttal Comment 1.1: Comment: Thanks for the answer. I guess it is up to the area chair, or somebody higher up to decide whether a theory TDA paper is suitable for the conference. My low score reflects my expectations that a Neurips paper should have a more direct connection to machine learning, not because I find the paper weak. In that sense, I am satisfied with the author's response that clarifies that the paper's contribution is on the theory side.	Summary: The $p$-optimal transport convergence of the Cech persistence diagram of a sample of a closed embedded manifold is studied, both in a deterministic and a probabilistic setting. The paper has three main results: 1. An improvement of the classical Cech bottleneck stability result for sufficiently good samples of closed embedded manifolds. 2. A bound for the total $p$-persistence, and a $p$-optimal transport-convergence result, for the Cech persistence diagram of sufficiently good (deterministic) samples of generically embedded closed manifolds; in the case $p$ is strictly larger than the dimension of the manifold. 3. A probabilistic convergence result for the Cech persistence diagram, and a law of large numbers for its total persistence. The probabilistic convergence result says in particular that $p$-optimal transport convergence of the Cech persistence diagram occurs if and only if $p$ is strictly larger than the manifold dimension. Strengths: - The paper is very well written: it is clear and easy to follow, it contains many useful and relevant references, and the results are clear and well abstracted. - The results are (to the best of my understanding) novel, as well as relevant for both theoretical and applied purposes. The results are connected to a lot of previous literature, so they should be of great interest to researchers in stochastic topology as well as the Topological Data Analysis public in general. - The probabilistic result identifies precisely the choices of $p$ that lead to convergence. Weaknesses: - The intersection of Topological Data Analysis and Machine Learning is non-trivial but not huge, restricting the audience of the paper to some extent. - The results have several restrictive hypothesis: strict manifold hypothesis (data lies exactly on a manifold), genericity of the manifold, no noise of any kind. Technical Quality: 4 Clarity: 4 Questions for Authors: 1. Is there any hope that (at least part of) the main probabilistic result (Corollary 4.3) still holds for non-generic manifolds? Could the genericity assumption be removed if we instead assume that the data is sampled from a manifold plus noise? 2. Theorem 3.3 fails for non-generic manifolds. Is it possible to quantify (say, with a number or function) how generic a manifold is, in such a way that the constants of Theorem 3.3 only depend on the level of genericity of the manifold? 3. In your summary of Corollary 4.3, in the introduction, why don't you say that optimal transport convergence occurs if and only if $p > m$? Confidence: 4 Soundness: 4 Presentation: 4 Contribution: 3 Limitations: The manifold being generic also seems like a limitation to me. It seems genericity could fail in highly structured scenarios (data sampled from a configuration space or a simulation of a dynamical system). Please correct me if I am wrong. Flag For Ethics Review: ['No ethics review needed.'] Rating: 8 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Dear reviewer, Thank you for your appreciation of our work and your interesting questions. We discuss noisy data in general in our response to all reviewers. To answer your questions more specifically: Is there any hope that (at least part of) the main probabilistic result (Corollary 4.3) still holds for non-generic manifolds? : No, one can build strong counter-examples (e.g. with a well-chosen union of circles in a high-dimensional space). In fact, such configurations will be studied at length in our next work on persistent homology dimension. Could the genericity assumption be removed if we instead assume that the data is sampled from a manifold plus noise? This is a very interesting question, whose answer seems to depend on the kind of noise considered. See also our discussion of noisy data in our answer to all reviewers. Theorem 3.3 fails for non-generic manifolds. Is it possible to quantify (say, with a number or function) how generic a manifold is, in such a way that the constants of Theorem 3.3 only depend on the level of genericity of the manifold? It might be doable, but it would require a lot of additional (and somewhat tedious) work. Indeed, the proofs of [ACSD 23] rely on nonquantitative compactness arguments; quantitative versions of these arguments would need to be developed to achieve such a result. In your summary of Corollary 4.3, in the introduction, why don't you say that optimal transport convergence occurs if and only if $p>m$? Convergence also occurs if $i\geq m$ and $p=m$. Furthermore, we do not know under which precise conditions it occurs when $p<m$ and $i\geq m$. The manifold being generic also seems like a limitation to me. It seems genericity could fail in highly structured scenarios (data sampled from a configuration space or a simulation of a dynamical system). Please correct me if I am wrong. You are right to point out that we cannot expect all submanifolds to be generic. However, one can easily build counter-examples to most of our results if the genericity assumption is dropped - as such, the need for genericity is not really a limitation of our work in itself, but rather an unavoidable constraint. Note also that not all highly structured scenarios are hopeless: in particular, it has been shown that among real algebraic submanifolds (a highly non-generic and structured subset of all submanifolds), a generic subset satisfies conditions similar to ours (see e.g. https://arxiv.org/abs/2402.08639). --- Rebuttal Comment 1.1: Comment: I am satisfied with the authors' responses.	Summary: The authors study the behaviour of persistent homology under subsampling of compact sets. They have provided new convergence guarantees with respect to the p-Wasserstein distance and asymptotic results for their $\alpha$-persistence. Strengths: (S1) The paper addresses a relevant problem in TDA, and proves a number of significant results (S2) The paper is comprehensive and well-written Weaknesses: (W1) While the main results of this paper are theoretically solid and of strong interest to the TDA community, I do not see direct applications of this work to AI/ML. The authors have referenced a few works where their work might be applied (persistent homology dimension), but they have not elaborated enough on how exactly their method can be used, what kind of significant questions it can answer, and how successful that will be. (W2) The experiments are very limited and do not demonstrate the implications of the proved results in ML Technical Quality: 3 Clarity: 3 Questions for Authors: (Q1) Are there any results about real-world applications of the theory? Confidence: 2 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: Yes, all limitations are addressed adequately by the authors. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Dear reviewer, Thank you for your feedback. We address your concerns and your question in our response to all reviewers. --- Rebuttal Comment 1.1: Comment: I thank the authors for their response. I have read the response and would like to stick with my score.	Rebuttal 1: Rebuttal: We thank all reviewers for their time, effort, and valuable feedback. We are grateful for the overall positive reception of our work. The most common questions pertained 1) to the practical applications of our results, and 2) to our assumption that the data is noiseless. We address these two points below, and respond to each reviewer individually regarding their more specific questions. * Applications and relevance to the ML community: (particularly in response to reviewers G8s6 and xmoJ) Though our paper does provide some new heuristics regarding the optimal choice of parameter for the Wasserstein distance (see Section 5), its main goal is to offer strong theoretical guarantees and a better understanding of techniques and objects routinely used by the TDA community, which is part of the wider ML community. As such, it is a study of existing ML methods rather than the description of a new method, similar e.g. to http://proceedings.mlr.press/v139/carriere21a.html (for an example within the field of TDA). Hence the main real world applications of our results are to be found in more experimental papers that apply the techniques that we examine, and for which we provide new guarantees. Of course, we also hope that a deeper understanding of those methods will in turn result in new methods, but those are beyond the scope of this (already rather long) article. This explains the relatively small number of experiments as well (which was commented upon by reviewer G8s6); those are not meant to showcase the power of some new method, nor to prove that our results are correct (as the mathematical proof is enough), but rather to illustrate them and to show that our asymptotic results are already observable with a reasonably small number of points. * Noise: (particularly in response to reviewers rgww, xmoJ and hrBD): \ Being limited by space constraints, we chose to focus on the noiseless case, but we agree that statements that allow for some noise would be a welcome addition to our results. \ Depending on the nature of the noise considered, some of our results extend seamlessly to the noisy case, while others would require additional work: for example, if we let the maximum amplitude of the noise be small compared to the density $\epsilon = d_H(A,M)$ of the sampling $A$ in the manifold (before the addition of the noise), i.e. of order $\epsilon^2$, then Theorem 2.2 still holds (with modified constants) thanks to the Bottleneck stability theorem, and Region 3 of the diagram still has a finite number of points in expectation, as in Proposition 4.2. \ If we assume that the noise is normal to the submanifold and uniform (or at least that its density is lower and upper bounded) and that its amplitude $l$ is fixed and independent from the point cloud, then the situation is equivalent to sampling from an upper and lower bounded distribution on the open set $M^l$ (the offset of the submanifold by the amplitude of the noise). Its boundary is smooth or at least very regular, depending on the amplitude of the noise. Regarding the small cycles (i.e. the points in Region 1 of the diagram), everything should work roughly as in the case of the $d$-dimensional cube, i.e. the limit distribution of $\mu_{n,i}$ should be some integral of $\mu_{\infty,i,d}$ over the open set. The behavior of the large cycles, i.e. of the points in Regions 2 and 3, should be dictated by the shape of the boundary of $M^l$. In particular, $\partial M^l$ should be generic enough for a generic choice of $M$ and $l$ that slightly modified of most of our results still hold, in particular the finite expected number of points in Region and the Wasserstein convergence of the diagrams (except that $p$ needs to be greater than the ambient dimension $d$, rather than the intrinsic dimension $m$). These questions might be explored in detail in future work.	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Stochastic Amortization: A Unified Approach to Accelerate Feature and Data Attribution	Accept (poster)	Summary: The paper proposes using stochastic amortization to speed up feature attribution and data attribution. This is applicable when the attribution technique is expensive to compute exactly (e.g. LIME), and when unbiased estimators of the attributions exist. Specifically, the paper proposes to, for a given machine learning model (e.g. Resnet) and a dataset of inputs (e.g. cifar) on which we want to compute attribution (e.g. Shapley feature values), obtain noisy estimates of the attributions (e.g. by sampling permutations), and then train a least square regression model to predict these noisy estimates from the input. The paper evaluates this method against the ground-truth attribution values for Shapley values on Imagenette, data valuation shapley on adult census and MiniBooNE datasets, and Distributional data valuation on the CIFAR-10 dataset. Strengths: - The paper clearly explains its motivations and approach - Using the amortized model improves performance over the initial noisy labels used for training, clearly showing the benefits of using an amortized method - The paper provides some theoretical arguments for using unbiased estimators. Weaknesses: - The related work section could benefit with a more direct and concrete comparison with prior work. For example, the paper says that "while there are works that accelerate data attribution with datamodels, we are not aware of any that use amortization". It is not clear to me in what "amortization" mean here exactly --- in what way does your work perform amortization that datamodels do not? - In addition, the experimental results lack baselines that compare with prior amortization work. The related work section describes a number of prior works (citations 50, 86, 18, 14) that all seem to be about computing Shapley values with amortization. - Figures are missing error bars Technical Quality: 3 Clarity: 3 Questions for Authors: - S5.1: would be interested to look at fig 3 right with a log scale on the y axis. Amortization seems to benefit with increasing dataset size, and I wonder what the scaling looks like - Related to that, a key hyperparameter in your amortization set up is to choose between spending compute to get fewer but more accurate labels vs more noisy labels. Is there a way of determining an optimal trade-off? - How does the paper's method compare with prior works? This is a crux for me. Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The authors adequately discussed technical limitations of their amortization approach in the appendix. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you very much for your review, we've responded to your points below. > The related work section could benefit with a more direct and concrete comparison with prior work. For example, the paper says that "while there are works that accelerate data attribution with datamodels, we are not aware of any that use amortization". It is not clear to me in what "amortization" mean here exactly --- in what way does your work perform amortization that datamodels do not? We can clarify this in the paper, but datamodels isn’t a form of amortization because it doesn’t learn a neural network that takes two data points as input and predicts the attribution score. It instead learns a linear model that takes a one-hot representation of the training dataset as the input, and predicts the loss for an inference example. The attribution scores are the learned coefficients of that model, not its predictions. Crucially, you can’t use the datamodels linear model to estimate attributions for new data points. Appendix B contains a brief discussion on how amortization would be implemented for datamodels, including a neural network $\zeta(z, x; \theta)$ whose output is the estimated attribution score. > In addition, the experimental results lack baselines that compare with prior amortization work. The related work section describes a number of prior works (citations 50, 86, 18, 14) that all seem to be about computing Shapley values with amortization. [...] How does the paper's method compare with prior works? This is a crux for me Thanks for this request, you raise a good point. There are fewer relevant comparisons than it might seem, but you’re correct that we missed the comparison with FastSHAP. We’ve now fixed this, as we describe below, and we can also clarify why certain other papers aren’t useful comparisons. First, we’ll address [86] and [14]. Setting aside some minor details, these are basically versions of stochastic amortization with much less noisy labels. They train explainer models to predict SVs using a supervised objective and targets computed with relatively high accuracy: [86] uses 10$\times$ the number of samples we do, and [14] claims to use either exact labels or orders of magnitude more than us depending on the experiment. (Besides these details, [86] also includes an unnecessary normalization step and regularization term, and [14] suggests a custom pre-training approach, which is an orthogonal contribution.) Given that these are basically much less noisy versions of stochastic amortization, a direct comparison wouldn’t be very interesting: using more accurate labels will yield a more accurate explainer, but at the cost of much more computation. This type of comparison is already shown in our work (e.g., Figure 3 left), only we don’t use as many samples as those works even in our most compute-intensive settings. Our goal here was to explore the other direction and demonstrate the ability to use noisier supervision. Next, [50, 18] both explore SV amortization using a custom weighted least squares objective, which we’ll refer to as “FastSHAP.” The main differences from our approach are that FastSHAP uses new samples for every gradient step and requires a complex training procedure, whereas we use pre-computed noisy labels from any unbiased estimator and train with MSE loss. Notably, the FastSHAP explainer model can’t make predictions without access to the original model’s predictions due to an output transformation required by its objective (“additive efficient normalization” [18]). Our approach is simpler to train, more flexible in the supervision, and the explainer can operate as a standalone model. Still, it’s worth including the comparison. To provide a compute-matched comparison, we implemented FastSHAP and measured the error from each approach as a function of the total FLOPs (including the cost of querying the original model, plus the cost of training the amortized model), using 32 subset samples/step for FastSHAP as in [18]. We found that the error and correlation with the ground truth is very similar between FastSHAP and our approach, with both significantly more accurate than KernelSHAP, but that FastSHAP is marginally more accurate ([plot link](https://imgur.com/a/5oGOjTK)). The result doesn’t seem conclusive, however, because our approach can be implemented with any noisy oracle, including more advanced ones that we didn’t test here; future work testing other unbiased estimators could find that stochastic amortization is more accurate. Overall, we believe our work is still valuable in presenting a simpler/more flexible alternative that reaches basically the same accuracy, and which can be easily applied to other XML methods like data valuation. > Figures are missing error bars Thanks for noticing this. We didn’t perform multiple trials due to the high computational cost, specifically the time required to run the Monte Carlo estimators for a small-to-moderate number of samples for all training data points. Given the wide margin of improvement we saw in the experiments (often an order of magnitude lower error), we didn’t think it would add much value to repeat the experiments multiple times. But we’ll try to fix this and prepare error bars in time for the final version of the paper. > S5.1: would be interested to look at fig 3 right with a log scale on the y axis. Amortization seems to benefit with increasing dataset size, and I wonder what the scaling looks like That’s a good idea, we made a version of the plot with both axes shown in log-scale ([plot link](https://imgur.com/a/lWC1YPR)). We hoped to see a log-linear trendline, because this is similar to a Kaplan et al. (2020)-style scaling curve, and it’s close but not quite linear. The error for the smallest dataset size is a bit too high, perhaps because it’s the least reliable point. If it’s helpful, we can change the plot in the final version to use log-scale on both axes. --- Rebuttal Comment 1.1: Title: Rebuttal by Authors (cont.) Comment: > Related to that, a key hyperparameter in your amortization set up is to choose between spending compute to get fewer but more accurate labels vs more noisy labels. Is there a way of determining an optimal trade-off? That’s a good question, and one that we didn’t try to answer conclusively here. Our goal was to show that training with noisy labels works, that it tolerates surprisingly high noise levels, and that it’s applicable to many XML tasks (including both feature attribution and data valuation). Investigating the quality-quantity tradeoff in noisy labels is an interesting question and a natural subject for future work, but addressing it thoroughly would be a bit too much work for our current paper. We are happy to mention this in the conclusion and provide some preliminary thoughts on how one should approach it. Intuitively, the optimal point can’t be at either extreme: a very small number of exact labels would be unlearnable, as would a large number of extremely noisy labels. Finding the optimal point requires reasoning about how well neural networks learn as a function of the dataset size and label noise, which is dataset- and model-dependent and likely best to approach empirically. One idea is to 1) measure the estimation error as a function of dataset size and number of Monte Carlo samples (i.e., run stochastic amortization under a range of settings), 2) fit the observed errors using a simple analytic function (in the style of recent scaling laws), and 3) use this to estimate the optimal trade-off (sort of like Chinchilla’s compute-optimal training). This approach seems reasonable and straightforward, but it would require many training runs and is beyond the scope of our current paper. --- Rebuttal 2: Comment: Thank you for the detailed response. Just an additional clarification about the comparison with prior work - would you agree that the technique you use is a simplification of previous techniques, which is enabled by the observation that stochastic amortization can tolerate more noise than previous methods assumed? --- Rebuttal Comment 2.1: Title: Author response Comment: Thanks for your response, we hope we resolved the concerns mentioned in your review. As for whether our technique is a simplification of prior works – you could describe it that way, that's basically correct regarding [86, 14]: the fact that amortization tolerates high noise levels enables our more practical approach, although the mathematical justification makes it perhaps less conceptually simple than training with exact targets. As for FastSHAP, our approach is simpler, but it’s not exactly a simplification of [50, 18] in the sense that the objective is derived differently. (FastSHAP is based on a weighted least squares view of SVs, whereas our approach is based on SVs being the expectation of a Monte Carlo estimator.)	Summary: This paper presents a fast prediction explanation approach for machine unlearning models that approximates traditional explanation approaches by using an neural network. The network is trained with noisy labels (so called stochastic amortization) such that it learns to approximate the prediction explanations of various approaches, including Shaply, LIME, and others. Experiments covers multiple explanation approaches from feature explanation to data instance explanation, showing effectiveness of the approximation. Strengths: Using network to approximate prediction explanation of various explanation methods seem an interesting idea. Using noisy labels to train the approximation model is also well justified with corresponding proofs. Experiments covers the various scenarios from feature to instance based explanation approaches. Weaknesses: It is concerning to use neural networks to explaining the predictive behaviour of another machine learning model. In fact, how do we know whether the explanation itself is trustworthy? If the prediction explanation is given to an stakeholders, is it possible to distinguish the potential concern between target machine learning model's trustworthiness and the approximative explainer? This concern needs to be addressed further to let the proposed approach practically useful. Partial experimental results show the proposed model may not be a good approximation approach; the results can be interpreted as the approximation fails to provide correct explanation to feature importance (Section 5.1). It causes me wonder if there is a practical value for the proposed approach if it is fast but not accurate. Technical Quality: 3 Clarity: 2 Questions for Authors: How do you prove the proposed approximation is, in general, faithful to the ground-truth explanation results from the actual explanation models? Why would the proposed approach to be useful if the explanation is off from the ground-truth? Confidence: 3 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: I don't see limitations. But, as the proposed approach is about XAI, it should be sound in terms of improving the trustworthiness of prediction instead of introducing another layer of uncertainty. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you very much for your review, we've responded to your points below. > It is concerning to use neural networks to explaining the predictive behaviour of another machine learning model. In fact, how do we know whether the explanation itself is trustworthy? Thanks for raising this question—by “trustworthy”, we assume you’re asking how we know that the amortized estimates are accurate. Ensuring high accuracy is very important, and our theory and experiments are all about showing that the error from amortization is small despite training with noisy labels. You can see that across all our experiments, amortization is always more accurate than Monte Carlo estimation for an equal computational budget, in most cases by a wide margin. For example, Figure 3 shows that the error from amortization is 1-2 orders of magnitude smaller than the standard KernelSHAP approach. This high accuracy (low error) is what makes the explanations trustworthy. We aren’t sure if this is what you meant, but you may be getting at the fact that our analysis focuses on average error across data points rather than worst-case error. Minimizing average-case error is useful in many scenarios, e.g., identifying mislabeled data points with data valuation scores, understanding a classifier by visually checking many feature attributions, and identifying common shortcuts/confounders. There’s an established literature on this type of approach, but there may be cases where Monte Carlo estimation with a large computational budget is preferable to provide guarantees for each data point's explanation. > Partial experimental results show the proposed model may not be a good approximation approach; the results can be interpreted as the approximation fails to provide correct explanation to feature importance (Section 5.1). We aren’t sure what you mean and which of these results reflect that the approximation is inaccurate. The examples in Figure 2 are qualitatively quite accurate, and the metrics in Figure 3 show that amortization achieves significantly lower error than the non-amortized estimates. Note that some of the metrics are shown in log-scale, which may make the error appear far from zero when it’s actually quite small. If you’re expecting to see zero error, note that these XML methods are never used with zero error due to the high computational cost – the only option is to use approximations, that’s why there’s so much work on efficient approximation algorithms. > How do you prove the proposed approximation is, in general, faithful to the ground-truth explanation results from the actual explanation models? Why would the proposed approach to be useful if the explanation is off from the ground-truth? Thanks for bringing this up. We establish the faithfulness of the approximation empirically: the estimation error is often small in our experiments, where we substitute the ground truth for estimates obtained using a large number of samples (e.g., 1M samples for KernelSHAP, see details in Appendix F). The error from amortization is always smaller than the Monte Carlo error given an equal computational budget, so our approach seems strictly preferable. The proposed approach wouldn’t be useful if the explanation was significantly off from the ground truth. However, a small degree of error is generally tolerable in practice, as evidenced by the fact that the community relies entirely on approximation algorithms, which are rarely run long enough to reach exact convergence (see for example the number of samples in KernelSHAP https://github.com/shap/shap/blob/master/shap/explainers/_kernel.py#L192). Our focus on fast/accurate approximation is not unusual, it’s an established line of work in the literature. --- Rebuttal Comment 1.1: Comment: Thanks for your answers. While my concerns of faithfulness of the NN approximation are not fully address, I think the paper may add value to the literature. Hence, I bumped my rating.	Summary: In this paper, the authors introduce a framework termed stochastic amortization that can accelerate computationally expensive explainable machine learning (XML) tasks by training models with noisy but unbiased labels. They provide theoretical analysis that shows that unbiased noisy labels allow learning the correct function. Empirically, the authors demonstrate the effectiveness of this approach on several XML tasks, including Shapley value feature attributions, Banzhaf values, LIME, and data valuation, achieving speedups over traditional per-example computation and improvements over simply using noisy labels. Strengths: - The paper is well-written, with clear motivations and a thorough discussion of related work. The technical details appear sound and well-presented. - The proposed approach offers a simple yet effective framework for accelerating computationally expensive XML methods, potentially enabling their application to large-scale datasets. - The authors provide code (with good documentation) and detailed experimental information in the Appendix for reproducability. - Limitations of the proposed approach are well discussed, demonstrating a balanced perspective. - Comprehensive experiments across multiple XML tasks (Shapley values, Banzhaf values, LIME, and data valuation) consistently demonstrate the benefits of stochastic amortization over per-example computation. Weaknesses: While the concept of amortization for Shapley value prediction is not entirely new, this paper makes a good contribution through its use of noisy labels and the accompanying theoretical analysis. I don't find any major weaknesses that would significantly detract from the paper's value, and I recommend acceptance. Reflecting my limited familiarity with some aspects of the relevant literature, I set my confidence to 3. Technical Quality: 3 Clarity: 4 Questions for Authors: - For applying stochastic amortization to a new XML task, how should practitioners determine an appropriate error level from a practical perspective? - Regarding line 99, "while there are works that accelerate data attribution with datamodels, we are not aware of any that use amortization". Could datamodels themselves be considered a form of amortized optimization (linear regression model)? - What guidelines can you provide for defining the architecture for amortization (e.g., ResNet) in practice? Did you observe significant differences with various architectures? Should the architecture be similar to the base model? - In Figure 4 (right), why does the correlation decrease for MC as the number of data points increases (intuitively, I expected correlation to remain relatively flat for both MC and amortized approaches, assuming a constant number of samples per point)? Confidence: 3 Soundness: 3 Presentation: 4 Contribution: 3 Limitations: The authors adequately addressed the limitations of the proposed approach. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you very much for your review, we've responded to your points below. > For applying stochastic amortization to a new XML task, how should practitioners determine an appropriate error level from a practical perspective? Thanks for asking this question. Our recommendation is to create a small validation set with near-exact estimates, for example by running a standard Monte Carlo estimate for many iterations, and then use this to determine what level of label noise achieves low enough error. This is how we evaluated estimation accuracy in our experiments. As for how to define “low enough error”, this depends on the task and its error tolerance, e.g., feature attribution can tolerate some error if its goal is to visually show humans the important part of an image. > Regarding line 99, "while there are works that accelerate data attribution with datamodels, we are not aware of any that use amortization". Could datamodels themselves be considered a form of amortized optimization (linear regression model)? That’s a good question and one that we get a lot. Datamodels isn’t a form of amortization because it doesn’t learn a neural network that takes two data points as input and predicts the attribution score. It instead learns a linear model that takes a one-hot representation of the training dataset as the input, and predicts the loss for an inference example. The attribution scores are the learned coefficients of that model, not its predictions. Crucially, you can’t use the datamodels linear model to estimate attributions for new data points. Appendix B contains a brief discussion on how amortization would be implemented for datamodels, including a neural network $\zeta(z, x; \theta)$ whose output is the estimated attribution score. > What guidelines can you provide for defining the architecture for amortization (e.g., ResNet) in practice? Did you observe significant differences with various architectures? Should the architecture be similar to the base model? That’s an interesting question. The best architecture for each problem is likely a function of how much expressive power you need and how much training data is available, similar to any setting where you use deep learning. Using the pre-trained base model is natural because it already extracts many relevant features, which can help with efficient fine-tuning, but it’s possible that in some cases you could benefit from a larger architecture or that you could get sufficient accuracy with a smaller one. In our experiments, we only tried training the base model architecture. > In Figure 4 (right), why does the correlation decrease for MC as the number of data points increases (intuitively, I expected correlation to remain relatively flat for both MC and amortized approaches, assuming a constant number of samples per point)? This was somewhat surprising to us as well. We believe it’s because as you increase the size of the dataset, the variance of each data point’s marginal contributions becomes larger relative to the expectation (reflecting a lower signal-to-noise ratio), and this leads to decreasing correlation even with a fixed number of samples. This observation is related to, but not exactly the same as one in the Beta Shapley paper (see Figure 1 in https://arxiv.org/abs/2110.14049). --- Rebuttal Comment 1.1: Title: Response Comment: Thank you for the comments. I read the author's response and other reviewers' comments. The clarification on the datamodels was helpful, and it would be great if you could add this explicit answer somewhere (I have read Appendix B but was still unsure). Overall, I am satisfied that the authors addressed all my questions. --- Reply to Comment 1.1.1: Title: Author response Comment: Thanks very much for reading our rebuttal and for your response. We'll make sure to add that clarification about datamodels to the paper, especially since hGpm had the same question.	Summary: This paper proposes a stochastic amortization framework for efficiently estimating feature attribution and data attribution values. The idea is to learn a parameterized model from noisy while unbiased samples of the value to be estimated. In comparison to naive Monte Carlo sampling, this amortized estimation is empirically more efficient when achieving similar estimation accuracy. The authors conducted experiments on a diverse set of feature attribution and data attribution problems. Strengths: - This paper tackles the computational efficiency issue in a set of feature attribution and data attribution problems, which is an important problem that could have significant impact to the area of explainable machine learning (XML). - This paper abstracts the paradigm of learning a parameterized function to estimate the attribution values in some XML methods with a more general amortized estimation framework, making it possible to extend this approach to more XML methods that conventionally rely on naive Monte Carlo estimators. - The authors conducted comprehensive experiments in diverse settings to demonstrate the effectiveness of the stochastic amortization. Weaknesses: - The theoretical analysis, especially Theorem 1, is not directly relevant to the main argument of this paper, i.e., stochastic amortization is more efficient than naive Monte Carlo. IMO this Theorem 1 is a bit distracting than being helpful for this paper. Furthermore, the theoretical result about the unbiasedness in lines 128 - 132 only concerns the expected loss, $\tilde{\mathcal{L}}_{reg}$, which doesn't directly imply the property of the empirically learned parameterized model. Overall, the advantage of stochastic amortization over Monte Carlo estimation is established empirically instead of theoretically, while the current presentation reads a bit misleading on this point. - In most of the experiments, only relatively naive Monte Carlo estimators compared as baselines. However, for certain specific problems, more efficient estimators may be available. For example, in the context of Data Shapley, how does the stochastic amortization compare with Gradient Shapley proposed in Ghorbani and Zou [33], or the compressive-sensing-based method proposed in Jia et al. (2019). References - Jia et al. (2019) Towards Efficient Data Valuation Based on the Shapley Value. AISTATS 2019. Technical Quality: 3 Clarity: 3 Questions for Authors: See Weaknesses. Confidence: 5 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: None. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you very much for your review, we've responded to your points below. > The theoretical analysis, especially Theorem 1, is not directly relevant to the main argument of this paper, i.e., stochastic amortization is more efficient than naive Monte Carlo. Thanks for bringing up this concern. To clarify, Theorem 1 shows that when training the amortized model $a(b; \theta)$ with SGD and noisy labels $\tilde a(b)$, the convergence rate is affected by label noise via $\text{N}_q(\tilde a)$. This means that noisier labels make training slower, which is an important theoretical point to understand about stochastic amortization: label noise is the key difference between stochastic amortization and the noiseless version, so it seems important to include Theorem 1 and highlight its role in slowing optimization. However, you’re correct that Theorem 1 doesn’t consider the stochastic amortization vs. Monte Carlo comparison. We found that harder to characterize in a satisfactory way and therefore relied on empirical results. But just to show that it’s possible, here’s a result that follows from Theorem 1 and demonstrates the advantage of sharing information across data points (as compared to Monte Carlo estimation, which treats each point independently): When we take $T$ SGD steps to update the amortized model, Theorem 1 shows that the estimation error shrinks at a rate of $\mathcal{O}(1/T)$. If we instead used the exact same training labels $\tilde a(b)$ as one-sample Monte Carlo estimates for each training data point $b$, our expected error across those would be $\text{N}_p(\tilde a)$ (this is a quick result to show). Crucially, this error does not shrink with $T$, as we just obtain (bad) estimates for more data points. So, we can see that for a sufficient number of gradient steps $T$, which depends on the label noise and data distribution, our error from the amortized model will eventually become lower than the error from the single-sample Monte Carlo estimates. And notably, the model can be used to generate estimates for any data point $b$ rather than only the fixed set of training data points. Hopefully this helps clarify the advantage of amortization over per-example Monte Carlo estimation. We’re happy to add the result to the paper, but we think the empirical results are most convincing for this point. > Furthermore, the theoretical result about the unbiasedness in lines 128 - 132 only concerns the expected loss, $\tilde{\mathcal{L}}_{\text{reg}}(\theta)$, which doesn't directly imply the property of the empirically learned parameterized model. Thanks for pointing this out. Your concern seems to be that our theoretical results don’t address the generalization gap between the empirical and population version of $\tilde{\mathcal{L}}_{\text{reg}}(\theta)$. That’s correct, but if you’re concerned about a large generalization gap in practice, generalization is famously not much of an issue with deep learning (https://arxiv.org/abs/1611.03530). We use standard approaches like a validation set to avoid overfitting, and some existing theoretical results also apply here (https://arxiv.org/abs/1901.08584). We can mention these points in the paper, but extending our theory to include the generalization gap doesn’t seem helpful given the technical complexity of the topic. > In most of the experiments, only relatively naive Monte Carlo estimators compared as baselines. [...] For example, in the context of Data Shapley, how does the stochastic amortization compare with Gradient Shapley proposed in Ghorbani and Zou [33], or the compressive-sensing-based method proposed in Jia et al. (2019). Thanks for raising this point. We prioritized breadth of experiments across XML techniques rather than depth in a single one, and as a result we can’t explore the full range of Monte Carlo estimators. There are numerous choices for both data valuation and feature attribution, several of which are discussed in Section 4 and Appendix E; since our theory applies to any unbiased estimator, we can’t see a reason why other options wouldn’t work. However, the two techniques you mentioned are different because they’re both biased estimators (Gradient Shapley because it uses a cheap proxy for the marginal contribution, and Compressive Permutation because it relies on sparsity assumptions). Our work is focused primarily on unbiased estimators, so adding these doesn’t seem like a priority, but it could be an interesting topic for other work to explore. One immediate intuition for such work is that with these approaches, stochastic amortization would learn to predict the expectation of those biased estimators, which may or may not be close to the true Data Shapley values. --- Rebuttal 2: Title: Thanks for the response Comment: I appreciate the authors' response. I would encourage the authors to at least add a remark after Theorem 1 clarifying the gap between Theorem 1 and the main claims of the advantage of the proposed method (which are evaluated empirically). This will help avoid potential confusions by readers like myself. PS: Part of the confusion comes from the paper abstract: "Through theoretical analysis of the label noise and experiments with various models and datasets, we show that this approach significantly accelerates several feature attribution and data valuation methods", which sets up an expectation that Theorem 1 is directly about the advantage of the proposed method. Overall I think this is a solid paper worth publication at NeurIPS. And this assessment has already been reflected by my previous rating. --- Rebuttal Comment 2.1: Title: Author response Comment: Thanks very much for reading our rebuttal and for your response. We understand the confusion about Theorem 1, thanks for pointing out that sentence in the abstract. We'll make sure to clarify that and add a remark after Theorem 1 to avoid confusion for other readers.	Rebuttal 1: Rebuttal: Thank you to all reviewers for your detailed feedback. We have addressed your points in individual responses below. If you find that we have resolved your concerns, we would greatly appreciate it if you would consider revising your score.	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Normalization and effective learning rates in reinforcement learning	Accept (poster)	Summary: This work attempts to improve the optimization for deep reinforcement learning by inserting additional layer norms into the architecture and performing weight projection steps that constrain the magnitude of the matrix weights. The paper discusses how the implicit effective learning rate schedule resulting from the growth of weight norms in standard optimization (without weight decay) affects reinforcement learning. The authors perform experiments across several domains, including non-stationary learning and standard deep reinforcement learning, generally obtaining improvements with their method. Strengths: + The paper is well written overall with relatively clear figures and sufficient details (hyperparameters etc) to allow reproduction + The topic and proposed method are of relevance to the community + The proposed NaP method demonstrates good performance across varied experiments + The method is seemingly novel to the reinforcement field (but this not my background) + Variance quantification for at least some experiments Weaknesses: - The NaP method seems to be closely related to various deep learning optimization methods that are not discussed in the paper (see details in question section). There should ideally be a comparison or at the very least a discussion of similar methods. - The experimental procedure could be slightly more rigorous / complete in some places (see details in question section) - Some parts of the paper are a bit unclear (details below) Technical Quality: 3 Clarity: 3 Questions for Authors: ### Related work Controlling some notion of an effective learning rate is not new to the broader field of deep learning. There are various optimizers that attempt to do this including LARS [1], LAMB [2], Nero [3], RVs [4]. Over time weight decay has also been shown to modulate the effective learning rate, bringing it towards a specific value, especially for SGD [5] and AdamW [4] (which should result in a very similar effect to projecting the weights, see discussion in [4]). It would be interesting to see a comparison or at least a discussion of these related works and techniques. Nero, RVs and the forced weight normalization of [6] use weight projections that should work very similarly to the proposed method (although on a finer granularity). These optimizers and weight decay in general would probably also need a learning rate schedule similar to NaP. I find it weird that this is supposedly not standard practice in DeepRL. Even for a stationary distribution the learning rate needs to be decreased with a schedule to obtain good results when weight decay is used on top of stochastic optimization. This can be seen e.g. in the original AdamW work [7], where the optimal weight decay for standard CIFAR ResNet training is zero when a fixed learning rate is used but not with a cosine schedule. * [1]: You, Yang, Igor Gitman, and Boris Ginsburg. "Large batch training of convolutional networks." arXiv preprint arXiv:1708.03888 (2017). * [2]: You, Yang, et al. "Large batch optimization for deep learning: Training bert in 76 minutes." arXiv preprint arXiv:1904.00962 (2019). * [3]: Liu, Yang, Jeremy Bernstein, Markus Meister, and Yisong Yue. "Learning by turning: Neural architecture aware optimisation." In International Conference on Machine Learning, pp. 6748-6758. PMLR, 2021. * [4]: Kosson, Atli, Bettina Messmer, and Martin Jaggi. "Rotational equilibrium: How weight decay balances learning across neural networks." arXiv preprint arXiv:2305.17212 (2023). * [5]: Wan, Ruosi, Zhanxing Zhu, Xiangyu Zhang, and Jian Sun. "Spherical motion dynamics: Learning dynamics of neural network with normalization, weight decay, and sgd." arXiv preprint arXiv:2006.08419 (2020). * [6]: Karras, Tero, Miika Aittala, Jaakko Lehtinen, Janne Hellsten, Timo Aila, and Samuli Laine. "Analyzing and improving the training dynamics of diffusion models." In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 24174-24184. 2024. * [7]: Loshchilov, Ilya, and Frank Hutter. "Decoupled weight decay regularization." arXiv preprint arXiv:1711.05101 (2017). ### Experimental Procedure The paper proposes two tricks, additional normalization and the weight projection. However the effects of each one individually are not evaluated very well, only their combination. For example in Figure 1, the effects of only weight projections without the additional normalization layers is not shown. There is little comparison with simpler baselines. For example, if preventing dead ReLUs are the main advantage of layernorm, why not consider leaky ReLUs as a baseline? The hyperparameter tuning is not very clear. In general the weight projection change is quite significant and should have the learning rate etc tuned separately from the baseline for a fair comparison. ### Clarity Algorithm 1: This is quite unclear in the main body. Why are rho, mu, sigma not defined? Should these be arguments to the function along with W? Why is rho an argument but no value is provided when it is called? How do theta and theta prime relate to W? Is the semicolon subscript used to denote all layers or a subset of the matrix? The whole description of the bias and gain handling is a bit unclear. I find it somewhat surprising that the “drift” causes problems in some of your settings. I wonder if this is due to the learning rate being too high for these parameters. One important property of weight decay is that it effectively defines a second learning rate for the bias and gain parameters by scaling the effective learning rate of the other weights (as shown / discussed in [4]). I wonder if this aspect is missing from NaP leading to some of these issues with gains and biases. Scaling the norm of the sphere you project onto might give you a similar effect. Minor suggestions and notes: L196: Algorithm reference is undefined L224: This forward reference to Figure 2 is unclear since the relevant information for it has not been included and the figure caption only states “as described in text”. L273: I disagree that the benefits of better conditioning should be independent of the effective learning rate in general. It is quite clear that if you set the effective learning rate sufficiently high or low you won’t learn anything, regardless of conditioning. L278: This corresponds nicely with standard training, see e.g. example for ResNet AdamW mentioned above. EQ14: This seems wrong. Is it supposed to be an inner product and a scalar zero? L637: I don’t think this is correct, linear growth would result in something more like 1/x decay in the effective learning rate schedule, not something like 1-x which is typically meant by linear decay. Figure 10: The caption is unclear or cut off. EQ33: You don’t use the d term here like you do in the algorithm Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: Yes, no concerns here Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for their extremely helpful comments, in particular introducing us to a number of work on optimization dynamics in scale-invariant networks of which we were not aware. We address individual concerns below. W1: We thank the reviewer for the recommended citations, and will be sure to include them in our related work. Implementing these methods as baselines was unfortunately outside of the scope of the rebuttal period, but we have read the papers with great interest and plan on including them in our revisions. As the reviewer mentions they do not come from a reinforcement learning background, we want to emphasize that there is an extensive “graveyard” of tried-and-true supervised learning methods which have been unable to provide analogous benefits in reinforcement learning, including such basic methods as weight decay [3] and batch normalization [2]. We emphasize that translating an insight or technique from supervised learning to RL is often a highly nontrivial task (see e.g. [1] on the challenges of using momentum-based optimizers in RL), and hope that the reviewer takes this into account when assessing the significance of the contribution. ### Questions Related work. We thank the reviewer for the references, and will be sure to discuss them in the context of related work to the paper in our revisions. While it is an interesting direction for further work to explore these methods in RL, doing so was outside of scope for the rebuttal period. We reiterate that it is common for techniques standard in deep learning to fail to yield benefits in deep RL, and while it is likely possible that methods which are similar to our approach . Ablating WP and LN: We agree with the reviewer that the paper would benefit from including baselines where WP and LN are studied in isolation. An important point to emphasize is that without normalization layers, weight projection no longer carries th esemantics of constraining the effective learning rate. In our preliminary evaluations, we found weight projection alone without normalization to be a weak baseline and did not include it in our final results, however we will be sure to include this data in our revisions. Why not leaky ReLUs: We evaluate against a number of dead-unit-mitigating baselines in the experiments in Figure 4, including leaky ReLUs. While leaky ReLUs in particular provide some benefits, they do not typically completely mitigate plasticity loss (see e.g. [4] ). Further, while preventing dead ReLUs is one advantage of layernorm, many other advantages have been noted as well [5], which we wished to benefit from. Hyperparameter tuning: For standard baselines (CIFAR/Imagenet, Rainbow) we use the default LR from the baseline method we compare against and set the LR schedule to end ~2 OOMs below this value (rounding to the nearest power of 10). We found that optimal LRs and schedules for NaP often involve slightly smaller initial learning rates and more aggressive decay than their counterparts (especially if no or weak weight decay or L2 regularization is used) but that it is typically more robust to the particular starting/ending values of the learning rate when using a schedule compared to a fixed value. Algorithm 1 notation: We thank the reviewer for highlighting this, and will clarify the notation for Algorithm 1 in our revisions to the paper. Specifically: - $\rho_l$ is the weight scale for a specific layer. We set this to be equal to its norm at initialization - $\mu_l$ and $\sigma_l$ are the (possibly vacuous) layernorm offset and scale terms respectively, which are learned parameters in the network. To make this clearer and to address another reviewer’s concern about the absence of an explicit definition of LayerNorm, we will include these terms in our LayerNorm expression which will be added to Section 3. description of the bias and gain handling: In most settings involving fewer than O(10^8) optimizer steps (i.e. all of the supervised learning benchmarks and single-task RL), we did not notice a significant effect from the choice of strategy for dealing with the bias and gain, and found even in the sequential ALE that the obvious solution of mild weight decay worked out of the box. We therefore did not devote much space in the paper to discuss how best to deal with these parameters as this choice does not appear to be practically significant. We will be sure to emphasize this more in our revisions. Learning rate for the bias and gain parameters We thank the reviewer for the pointer to the reference. We agree that in principle a similar phenomenon should be at play here, with NaP behaving similarly to the RV-AdamW method in [4 (Reviewer’s reference)]. While we unfortunately did not log the relative values of the scale and offset parameters in our continual atari experiments, we do observe that the total norm of these parameters does noticeably increase over the course of training if they are allowed to evolve unimpeded (the total parameter norm grows from ~135 to ~330, and all of this growth is attributable solely to the scale/offset terms). [1] Correcting Momentum in Temporal Difference Learning. Emmanuel Bengio, Joelle Pineau, Doina Precup. https://arxiv.org/abs/2106.03955 [2] Liu, Zhuang, et al. "Regularization Matters in Policy Optimization-An Empirical Study on Continuous Control." International Conference on Learning Representations. [3] Salimans, Tim, and Durk P. Kingma. "Weight normalization: A simple reparameterization to accelerate training of deep neural networks." Advances in neural information processing systems 29 (2016). [4] Lyle, Clare, et al. "Disentangling the causes of plasticity loss in neural networks." Third Conference on Lifelong Learning Agents (2024). [5] Nauman, Michal, et al. "Overestimation, Overfitting, and Plasticity in Actor-Critic: the Bitter Lesson of Reinforcement Learning." Forty-first International Conference on Machine Learning. --- Rebuttal Comment 1.1: Comment: I thank the authors for their detailed response and clarifications. I agree that the core contribution of demonstrating these methods in DRL is valuable and non-trivial. I will raise my review score to 6. A few minor notes on the rebuttal: > An important point to emphasize is that without normalization layers, weight projection no longer carries the semantics of constraining the effective learning rate. I am not sure this actually matters that much, especially with normalized optimizers like Adam. Aside from the magnitude on the forward pass (assuming normalization of the activations and not the weights), the only aspect that changes is the removal of the component of the gradient parallel to the weights. Unless this component is very large, the resulting optimization dynamics (measured via relative or angular updates) will remain very similar. > In our preliminary evaluations, we found weight projection alone without normalization to be a weak baseline and did not include it in our final results, however we will be sure to include this data in our revisions. Just in case you are not familiar with this, there is a line of work that shows that normalization layers serve an important role in the signal propagation of networks with residual connections, see e.g. https://arxiv.org/abs/2002.10444. When removing activation normalization layers it is important to preserve these signal propagation dynamics with methods like those described in e.g. https://arxiv.org/abs/2102.06171 (the initialization / downweighting of the residual branches mostly, the weight standardization is unlikely to matter with Adam + projection in my opinion). I hope you account for this in your baselines, but including the results would be interesting either way. --- Reply to Comment 1.1.1: Comment: We thank the reviewer for their consideration of our rebuttal and for the additional references. Regarding the first point: we now realize that we misunderstood the original point in the review, as in many of the architectures we evaluated (particularly those used in value-based deep reinforcement learning) no normalization layers are included by default, and so removing the normalization introduced by the method would destroy the network's scale-invariance. However, we agree that isolating the effect of the additional layers on e.g. transformers or ResNets would be a useful baseline to include and plan to do so in our revisions. Regarding the second point: while exploring the interaction between residual connections, layer normalization, signal propagation and effective learning rates was outside the scope of our submission, we are keen to explore it in future work and agree that the two papers mentioned are very relevant to this direction.	Summary: This paper explores the use of normalization layers in deep reinforcement learning and continual learning, as well as their impact on the effective learning rate. Although normalization layers offer a variety of benefits in stabilizing optimization and improving the loss landscape, they also introduce a significant side effect: the growth of the network parameter norm is equivalent to the decay of the effective learning rate. In continual learning environments, the implicit decay of the learning rate due to the increase in parameter norm may drop too quickly relative to the timescale of the learning problem, which is detrimental. Therefore, this paper proposes a new method called Normalize-and-Project (NaP). The NaP method consists of two main steps: inserting normalization layers in the network architecture before non-linear activation functions; and regularly projecting the network's weights onto a fixed norm radius during the training process, along with corresponding updates to the learning rates for each layer in the optimization process. This approach ensures that the effective learning rate remains constant throughout the training. Furthermore, this paper validates the effectiveness of the NaP method through a series of experiments, demonstrating its potential to enhance performance and robustness across different learning environments and settings. Strengths: Firstly, this paper addresses a significant issue within the machine learning community, namely, the plasticity of neural network learning. It offers novel and intriguing insights into the widely-used layer normalization technique, revealing its advantages in controlling the growth of parameter norms and its disadvantages in continual learning settings. Thus, the paper provides innovative insights. Secondly, the paper presents a concise and effective method that builds upon the commonly used layer normalization by incorporating a parameter norm projection step, making it more suitable for continual learning scenarios. Consequently, the method proposed in this paper has universality and practicality. Lastly, through a series of experiments, the paper demonstrates that the NaP method does not affect learning in static tasks and has distinct advantages in continual supervised learning and reinforcement learning tasks. Additionally, the paper is supported by theoretical analysis and ablation study evidence, which solidify and complete the arguments presented in the paper. Weaknesses: 1. This paper lacks a unified mathematical expression framework; the mathematical notation for many theoretical conclusions is disjointed and abrupt, increasing the cognitive cost for readers. For instance, throughout the paper, the specific definition of layer normalization is not explicitly provided, which leaves me somewhat confused about whether normalization is applied to the parameters of each layer itself or to the inputs of the layer. Moreover, in Definition 1, parameters are denoted by $\theta_t$, but in Proposition 1, a new symbol $h$ is introduced without clarifying its relationship to $\theta_t$; furthermore, in Algorithm 1, the left column only uses WeightProject($W_l$), while the right column defines WeightProject($W_l$, $\rho_l$) and employs an undefined function $len$. Therefore, I suggest the authors carefully review the mathematical language they have used. 2. Although the title of this paper indicates a focus on reinforcement learning, more than half of the experiments in the paper are based on supervised learning or artificial experiments, and the discussion and theory in this paper do not seem to be specific to reinforcement learning. Therefore, the authors need to discuss the strong coupling relationship of this scheme with reinforcement learning. In addition, there are some logically inconsistent aspects in this paper. On one hand, the paper argues that the decay of the learning rate is inappropriate in the supervised learning setting, which supports the design concept of NaP; on the other hand, in the reinforcement learning setting, learning rate decay is needed, but NaP cannot provide an independent solution, that is, it still requires some learning rate scheduling strategies. Therefore, I am more skeptical about the universality of the NaP method for the RL field. Technical Quality: 3 Clarity: 2 Questions for Authors: 1. Please clarify the standard mathematical definition of layer normalization and its relationship with the notation used in the various mathematical theories presented in this paper. Specifically, it would be helpful to understand how the notation for layer normalization relates to the symbols used in Definition 1， Proposition 1 and Algorithm 1, and to have a clear explanation of the transition from $\theta_t$ to $h$ in the context of the paper's mathematical framework. 2. Elucidate the strong coupling relationship between NaP and reinforcement learning. Particularly, please supplement the performance of NaP on typical continuous tasks such as Gym Mujoco, because on these types of tasks, a decaying learning rate schedule design is often not required. This could potentially better demonstrate the advantages of NaP, as it may allow for a more consistent learning rate that could be beneficial in environments where the learning problem does not necessitate a reduction in learning rate over time. Confidence: 3 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: The authors have not discussed the potential negative impacts of this paper, but I believe this work indeed has no significant negative societal impacts. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for their careful engagement with the manuscript and for their helpful comments. We will ensure to take these into account in our revisions. Mathematical notation. We thank the reviewer for highlighting this. We will be sure to review the mathematical notation and improve it in our updates based on these suggestions. We had left out a formal definition of layer normalization because of its widespread use, but can include LN explicitly in the same section where we define RMS-norm, and will also include the following clarifications: - h refers to a hidden unit’s pre-activation - $\rho_l$ refers to the reference norm to which layer l is projected. - Len is standard length function which returns the length of a tuple/vector as in python. Strong coupling relationship of this scheme with reinforcement learning. While we agree with the reviewer that NaP can be applied outside of reinforcement learning problems, we do not view the generality of our approach as a weakness but rather as a strength: NaP is not only a highly effective tool for understanding and improving reinforcement learning algorithms, but also more broadly applicable to other nonstationary learning problems. We emphasize RL in the title because it is both the regime where NaP is most beneficial, and also the regime where NaP offers the most insight as a diagnostic tool. In particular, NaP yields significant performance improvements in both single- and multi-task variants of Atari, and further demonstrates the surprising and previously unknown importance of ELR decay in this regime when used as a diagnostic tool. Figure 6 in the Appendix offers particularly intriguing hints at the possibility that learning certain components of a value function require dropping the learning rate below some critical threshold. We will be sure to emphasize this point in our revisions to make the relationship between NaP and reinforcement learning clearer. ... the paper argues that the decay of the learning rate is inappropriate in the supervised learning setting, which supports the design concept of NaP. We emphasize that we do not claim that learning rate decay is always bad for network training dynamics – rather, we argue that unintended ELR decay due to parameter norm growth can slow down learning in some cases, particularly in long training runs such as those used in continual learning benchmarks. Some learning rate decay can be appropriate for supervised learning, and is indeed a standard part of neural network training. Our emphasis is that for long and/or nonstationary training problems, parameter norm growth can induce excessive decay that slows down learning if it is not controlled for in some way. We will endeavour to make this point clearer in our revisions, and thank the reviewer for highlighting this ambiguity in our original text. on the other hand, in the reinforcement learning setting, learning rate decay is needed, but NaP cannot provide an independent solution, that is, it still requires some learning rate scheduling strategies. As our previous point has hopefully clarified, the main message of this paper is not that ELR decay is bad, but that depending on growth in the parameter norm to decay the ELR is sub-optimal compared to tuning the schedule explicitly. The strength of NaP is that it allows the learning rate schedule to be set based on prior knowledge of the problem, rather than depending on incidental growth in the parameter norm. In the case of single-task RL, for example, the natural parameter norm growth is too mild, and we find that a more aggressive schedule is beneficial. By contrast, in the sequential atari benchmark, the natural decay is too extreme and a cyclic schedule that periodically re-warms the learning rate is preferrable instead, an intuitive solution given the cyclic nature of the problem. “Skeptical … universality of the NaP method for the RL field.” We find that the basic principle of “start at the default learning rate used by the baseline, then decay by 2 orders of magnitude” is a relatively robust recipe for not just Atari but also the continuous control tasks “Ant” and “Humanoid” with PPO agents (see our “General Comment” for numerical details from these experiments). We believe that even better LR schedules which depend on properties like the signal-to-noise ratio in the gradients and the local curvature of the loss landscape can likely provide further benefits, and are an exciting direction for future work.	Summary: Normalization layers improve various aspects of deep RL and continual learning, such as loss landscape conditioning and reducing overestimation bias. However, normalization can inadvertently decrease the effective learning rate as network parameters grow. This effect is problematic in continual learning where the learning rate can decay too quickly. This work proposes a re-parameterization method called Normalize-and-Project (NaP) to maintain a consistent effective learning rate throughout training, improving performance in both stationary and nonstationary environments. - Normalization layers stabilize optimization by conditioning the loss landscape and mitigating overestimation bias. They create a scale-invariance in the network parameters, leading to a decline in the effective learning rate as the parameter norm increases. Normalize-and-Project (NaP) - NaP is a protocol combining normalization layers with weight projection to keep the effective learning rate constant. It involves inserting normalization layers before nonlinearities and periodically rescaling the network’s weights to maintain a fixed norm. -The paper explores how normalization layers affect a network’s plasticity and introduce the concept of effective learning rates. It shows that normalization can lead to implicit learning rate decay, which can be beneficial or harmful depending on the learning context. -The paper evaluates NaP on various architectures and datasets, including RL tasks and benchmarks like CIFAR-10 and ImageNet. NaP demonstrates improved robustness to nonstationarity and maintains performance in stationary settings. -Loss of plasticity is a major barrier in RL and continual learning.Normalization layers help maintain plasticity by reducing parameter norm growth and stabilizing gradients. -NaP can be easily integrated into existing architectures like ResNets and transformers.It provides a framework for better understanding and managing learning rate schedules in nonstationary problems. The paper validates NaP through experiments on synthetic tasks and large-scale benchmarks, showing consistent improvements in performance and stability.It highlights the importance of controlling parameter norms and maintaining effective learning rates to mitigate plasticity loss. Strengths: Originality Innovative Method: The introduction of Normalize-and-Project (NaP) is a novel approach that addresses the challenge of effective learning rate decay in deep reinforcement learning and continual learning. Creative Combinations: Combining normalization with weight projection to maintain a consistent learning rate is both original and practical. New Application: Applying these concepts to nonstationary reinforcement learning settings is a novel contribution. Quality Theoretical Rigor: The paper provides some theoretical insights into the relationship between parameter norms, learning rates, and network plasticity. Empirical Validation: Robust experiments across various architectures and datasets convincingly demonstrate NaP's effectiveness. Reproducibility: Clear methodology and detailed descriptions ensure that the work can be reproduced and built upon. Clarity Clear Writing: The paper is well-written and logically structured, making it easy to follow the arguments and results. Good Coverage: Background and related work sections provide context and help readers of all levels grasp the contributions. Significance Broad Impact: NaP has the potential to significantly impact deep reinforcement learning and continual learning by addressing a fundamental challenge. Practical Applicability: The method can be easily integrated into existing architectures, enhancing its real-world relevance. Advancing Understanding: Theoretical insights advance the field's understanding of learning rates and network plasticity, suggesting new research directions. Overall Assessment The paper combines originality with practical impact, offering a novel solution to a key challenge in reinforcement learning and continual learning. Its good theoretical and empirical work, clear exposition, and significant contributions make it a valuable addition to the field. Weaknesses: Lack of Theoretical RL Analysis: The paper primarily focuses on the impact of normalization on network parameters and effective learning rates without delving into the theoretical implications from a reinforcement learning (RL) perspective, particularly regarding policy learning. Potentially include a section discussing how the NaP method affects the learning of policies in RL. Explain how the steps in network parameter space translate to changes in policy space and the potential impact on policy optimization. This addition would provide a more comprehensive theoretical foundation and align the method's analysis with RL-specific objectives. Experiments Add a continuous control tasks or more complex environments, as in environment with more actions, beyond the Atari suite, to add evidence to the generality and robustness of NaP across different RL scenarios. Technical Quality: 3 Clarity: 3 Questions for Authors: No questions. Confidence: 3 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: We thank the reviewer for their engagement with the paper, and for their constructive comments. We address individual concerns below. Lack of theoretical RL analysis: We agree with the reviewer that translating insights on the optimization and trainability of neural networks to policy optimization is an interesting area for future work. Given the relatively nascent state of the field’s understanding of the relationship between optimization dynamics and policy learning, particularly in actor-critic settings (see e.g.[1]), we are not currently aware of an existing framework in which we could insert our method to study its impact on policy learning and would be interested in hearing if the reviewer had a particular flavour of result in mind. One result from our paper which could provide an interesting foundation for future investigation in this direction is Figure 6 in Appendix C, which shows that inflection points in the agent’s learning curve across different schedules tend to occur when the schedules reach a particular learning rate, suggesting that some environments require decaying the learning rate to a particular value for the network to be expressive enough for an optimization step to translate to an improved policy. Additionally, we are interested in exploring whether the optimal ELR for the actor and critic may differ in policy gradient algorithms. Experiments. We have evaluated NaP on PPO agents trained with the Brax framework on Mujoco and have included these results in our general comment. [1] Ilyas, Andrew, et al. "A Closer Look at Deep Policy Gradients." International Conference on Learning Representations.	Summary: When training a neural network with layer normalization, an increase in the norm of the parameters can lead to a lower effective learning rate. This paper makes the observation that, when layer normalization is used, periodic projection is enough to overcome this vanishing step-size. The idea is verified empirically, and involves essentially no tuning due to the norm being set to initialization and the periodicity of the projection does not significantly impact the performance. Decision: This paper provides a clear articulation of a relatively straightforward observation. However, the implications of the observation seem wide ranging: from non-stationary problems to reinforcement learning and even supervised learning. Although the method is relatively simple and lacks "novelty", I think this paper merits acceptance. It could be further improved by providing a more nuanced investigation of the interplay between layer normalization and normalize-and-project. After rebuttal: I have updated my score to reflect the additional results in the shared reply and the discussion with authors (6 -> 7) Strengths: - The problem of reduced effective learning rate is clearly articulated. The solution is simple and straightforward, translating to improved performance across a wide range of problems: non-stationary supervised learning, reinforcement learning and even stationary learning tasks. - The toy experiments presented before the main experiments are convincing. I particularly like the result with the coupled networks, Weaknesses: - Some of the arguments are ad-hoc, and rely on "folk knowledge" specific to deep learning. Layer normalization is indeed commonly used, and it is a good starting point, but understanding the interplay of layer-normalization and the normalize-and-project (in particular, to what degree it affects capacity) would provide more insight. - The empirical results, while comprehensive, provide little further insight in addition to the toy examples presented earlier. Technical Quality: 3 Clarity: 3 Questions for Authors: - Section 1: "We first show that when coupled with adaptive optimizers [..] saturated units still receive sufficient gradient signal to make non-trivial changes to their parameters" Is this claim at odds with the growing empirical evidence that loss of plasticity often occurs (without normalization layers)? - Section 2.1: "learning dynamics can be well-characterized in the infinite-width limit [...], although in practice optimization dynamics diverge significantly from the infinite-width limit" What is the distinction between learning dynamics in the infinite-width limit and the optimization dynamics in the infinite width limit? I am not sure what the takeaway of this discussion should be. - Section 2.1: "Plasticity loss can be further decomposed into two distinct components [Lee et al., 2023]" While I agree that loss of plasticity can be thought of as loss of trainability and loss of generalization, the provided reference discusses input and label plasticity. I do not see the distinction between trainability and generalization discussed in the paper. - Section 2.2: "$\nabla f(c\theta) = \frac{1}{c} \nabla f(\theta)$" There is some ambiguity here in what the gradient operator is with respect to. For example, $\nabla_\theta f(c\theta) = c \nabla_{c\theta} f(c\theta)$. If the parameter norm is large, then the parameter is not defined as the effectively normalized parameter but the "raw" parameter $c \theta$. The intuition provided is not quite as simple as the authors make it seem: it assumes that the perturbations are independent of the scale. - Section 4.2: The schedule proposed seems completely ad-hoc and the Appendix does not describe this in sufficient detail. Could the authors comment on how "schedule misspecification" may impact performance? For example, does this Atari-based schedule harm performance on other RL tasks? If so, then the use of the schedule seems to use relatively priviledged knowledge for a continual learning algorithms (it requires running an algorithm on the entire continual learning problem to track the parameter growth) - Section 5.1: "Further, we observe constant or increasing slopes in the online accuracy, suggesting that the difference between methods has more to do with their effect on within-task performance " Can you clarify how the slope of the online accuracy has to do within-task performance rather than loss of plasticity? It could be that the effect of NAP is redundant in conjunction with some of these methods. Regenerative regularization, for example, likely keeps the norm close to that of NAP. - Section 5.2: The results on language tasks is interesting, because some degree of weight decay is usually used to train transformers (AdamW is a common choice, which your experiments also use). What effect does NAP have in conjuction with weight deacy? This is obviously related to my previous question, but NAP+AdamW seems redundant. - Section 5.3: I find the use of knowledge of the game switch to be against the spirit of sequential ALE. The results are interesting, and impressive with this caveat. But the results would be much more impressive if evaluated without this type of human intervention. ### Minor: - Section 3.3: There is a reference to an Algorithm -1 which does not point to anything. Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: See above Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Comment: We thank the reviewer for their detailed and helpful comments, and for their deep engagement with the paper. We address specific comments and questions individually as follows. W1: “folk knowledge” … “interplay between layer normalization and NaP”: We agree that further theoretical analysis into the dynamics of NaP is an exciting direction for further research. However, we emphasize that the theory explaining much of the “folk knowledge” referred to by the reviewer has been extensively developed in recent years, giving NaP a more rigorous grounding (see e.g. Martens et al. (2021)). Further, the study of optimization in scale-invariant networks and the resulting tying of the parameter norm and learning rate has been extensively developed by the works highlighted in Section 2.2, among others. These works show that the interaction between layer normalization and the parameter norm is precisely the effective learning rate. The interplay between the normalization and projection steps of NaP is therefore to keep the ELR exactly equal to the explicit learning rate schedule. Indeed, we motivate the weight projection step as a means of ensuring that the ELR does not unexpectedly shrink or grow over the course of training as a result of unintended changes in the parameter norm. We hope that future work may yield further insights into the implications of these works in the reinforcement learning context. Regarding capacity, we show in Proposition 2 (Appendix A.7) shows that NaP does not change a particular notion of network expressivity studied extensively by Poole et al. W2: "The empirical results [...] little further insight." While we agree with the reviewer that the primary function of our supervised learning evaluations is to simply verify that NaP does not harm performance on standard benchmarks, we note that our experiments in the deep reinforcement learning settings do provide additional nuance to our understanding of NaP. In particular, we find that contrary to folk wisdom, decay in the effective learning rate can indeed be beneficial in reinforcement learning. Further, our detailed learning curves in Figure 6 illustrate how upticks in performance frequently occur when the network passes through a specific range of learning rates, suggesting that different learning rates are needed to learn different skills within a task. These insights could not have been deduced from the toy experiments, and demonstrate that NaP can be used to gain new insights into well-studied problem settings. [Q1] There are a variety of reasons for loss of plasticity in neural networks. Some of these involve saturated units, while others are more complex and involve collapse of the features or starvation dynamics. Proposition 1 notes a new mechanism by which layer normalization helps to protect against plasticity loss, but does not claim that this implies LN completely mitigates the plasticity loss phenomenon. [Q2-4] We thank the reviewer for highlighting these sources of ambiguity. We will rewrite [Q2] to clarify that we mean that infinite-width dynamics (optimization/training are equivalent in this sentence) are well-characterized theoretically but don’t accurately capture empirically-observed dynamics in finite-width settings. The “input plasticity” referred to by Lee et al. in [Q3] subsumes the “warm-starting effect”, where networks generalize worse after being trained on nonstationary inputs. We will clarify this in our revisions. We can confirm that the gradient is w.r.t. the inputs of f in [Q4]. We will rewrite this statement to clarify that we are interested in computing the gradient of f w.r.t. Inputs $\theta$ evaluated at two particular values of $\theta$. I.e. $\nabla_\theta f(\theta) $ evaluated at $\theta_1$ vs $\nabla_\theta f(\theta)$ evaluated at ${\theta_2}$ where $\theta_1 = c \theta_2$ for some $c$. [Q5] please see “general comment” (choice of learning rate schedules/schedule misspecification). [Q6] We understand the reviewer’s confusion, as we did not have space in the paper to include per-task learning curves in Figure 4. Our comment refers to the fact that even in the first task, some strategies, in particular those which add noise to the training process, result in slower learning and `shallower’ learning curves. We will be sure to add these results to the supplementary material in our revisions and refer to them in this section of the paper. [Q7] On projected parameters, adamw has no effect because its parameter scaling step is immediately undone by the projection step (though we might see slightly more complex behaviour with L2 regularization). However, because transformers have a number of nonlinear layers (in particular positional encodings) which are not invariant under parameter projection, some form of weight decay is likely helpful to improve stability in these layers where we can’t project. [Q8] please see "general comment" (continual atari schedule). --- Rebuttal 2: Comment: The shared reply addresses many of my concerns, and I will be increasing my score. However, I have a few followups: - Re Q2-Q4: "The “input plasticity” referred to by Lee et al. in [Q3] subsumes the “warm-starting effect”, where networks generalize worse after being trained on nonstationary inputs." It is true that the warm-starting paper (Ash and Adams, 2019) investigates loss of generalization. It is also true that the problem studied in that paper has changes in the input distribution. But I am struggling to see how input plasticity would "subsume" warm-starting. I think this would require further explanation to make this connection clear. One alternative is to separately reference papers that individually investigate loss of trainability and loss of generalization. - Re Q5/Q8 and general reply: I am pleased to see that the specifics of the learning rate schedule does not necessarily require knowledge of the parameter norm growth. I am also generally surprised by the Mujoco results you presented, especially the effectiveness of learning rate schedules. I understand LR schedules are somewhat common in supervised learning, I do not know how common they are in RL. I hope that the future revision of this paper reflect the surprising effectiveness of learning rate schedules in addition to the proposed method (or otherwise points to previous work that investigates LR schedules in RL). - Re Q7: Thanks, I did not realize that the positional encoding layers would be trainable. The standard transformer architecture introduced by Vaswani et al. (2017) used non-trainable positional encodings. Could you comment on the specifics of the positional encoding used? --- Rebuttal Comment 2.1: Comment: We thank the reviewer for their consideration of our rebuttal. We appreciate the additional suggestions, which we believe will further improve the paper. Concretely: - [Q2-Q4]: We will take this point into account in our revisions and plan to clarify the sentence per the reviewer's suggestion by citing separate papers describing input plasticity and loss of generalization ability. - [Q5/Q8]: We are glad the reviewer is satisfied by our response. While it is likely that some RL papers have used non-constant learning rate schedules, a quick survey of papers which proposed popular RL methods (e.g. [PPO](https://arxiv.org/pdf/1707.06347), [DQN](https://arxiv.org/pdf/1312.5602), [SAC](https://arxiv.org/pdf/1801.01290), and [CURL](https://arxiv.org/pdf/2004.04136)) suggests that their use is quite rare, and has to the best of our knowledge not been studied systematically. The reviewer is correct that this lack of analysis starkly contrasts to the deep study of learning rate schedules in supervised learning problems. In this context, our findings on the benefits of learning rate schedules in deep RL are quite surprising and suggest that the learning rate schedule has been overlooked relative to other hyperparameters to the detriment of performance on benchmarks. We will be sure to emphasize this point in our revisions. - [Q7]: We use relative positional encodings as described in [1], which involves learnable weights, and will be sure to make this point clearer in our architecture description in our revisions. [1] Self-Attention with Relative Position Representations. Shaw et al., ACL 2018. https://arxiv.org/pdf/1803.02155	Rebuttal 1: Rebuttal: We thank the reviewers for their careful engagement with the work and thoughtful reviews. Reviewers generally agreed on the “wide ranging” implications of our findings [6ZG9], along with the “good theoretical and empirical work”[KJMZ], and “novel and intriguing insights”[vdAM], agreeing that while developing on a strong body of existing work in deep learning theory, our findings were “novel to the reinforcement [learning] field” and our method “demonstrates good performance across varied experiments”[AEQp]. We have addressed specific comments in individual rebuttals, and respond to shared concerns in this general note. Notation: we clarify the following notation for Algorithm 1, which we will incorporate in our revisions: Choice of learning rate schedules: While any particular learning rate schedule may seem arbitrary, we emphasize that we chose each task's schedule with relatively little tuning -- in the case of supervised benchmarks we swept over number of training steps and initial learning rate and used the benchmark's default schedule. Our choices for RL were inspired by parameter norm growth curves, but the principles underlying them can be applied more broadly (and indeed, were applied to our Mujoco experiments that follow with relative ease without any prior knowledge of the baseline parameter norm growth). Sensitivity to schedule mis-specification: Just as using a too-large or too-small learning rate can result in poor performance in deep RL, we find analogously that using a schedule that decays too quickly, or which starts at too high of a value and decays too slowly, can hurt performance. In general, we find that schedule misspecification is slightly more forgiving than standard learning rate misspecification where the learning rate is held fixed throughout training. By letting training pass through a wider range of learning rates, we increase the probability that the network will spend at least some time in the optimal range for the given problem. Continual atari schedule: The purpose of this experiment was to show that there exists a learning rate schedule under which we do not see loss of plasticity on the sequential ALE. We think further work exploring how to adaptively set the learning rate in response to environment nonstationarity is a particularly exciting direction to eliminate the need for this human intervention. In this particular setting, we expect that using a sufficiently good changepoint detection algorithm as a trigger for schedule resets would be sufficient to recover the performance of the handcrafted schedule. Mujoco experiments: Multiple reviewers have requested evaluations on continuous control domains such as mujoco to complement our results in Atari. While we did not have sufficient time during the rebuttal period to conduct and hyperparameter-tune long-running experiments, we found that using the highly parallel brax library enabled sufficiently speedy iteration time that we could get reasonable baselines running fairly quickly, and provided a reasonable set of default hyperparameters. We have included results from training PPO a handful of popular continuous control benchmarks in the following table, in order to highlight the versatility of our method, based on the hyperparameters outlined in [this iPython notebook](https://github.com/google/brax/blob/main/notebooks/training.ipynb), using a 4-layer, 1024 width MLP as the network architecture for both actor and critic networks. The results here suggest that while different design choices contribute more or less significantly to performance depending on the environment (for example, the ant environment benefits most from a learning rate schedule, whereas humanoid-stand benefits most from layer normalization), the general recipe of normalization + LR schedule consistently outperforms the standard baseline, and is more robust to varying the learning rate. We do not observe significant parameter norm growth in any of these environments due to the comparatively short training times relative to Atari (even in the longest-running task humanoid-stand, parameters increased by less than an order of magnitude). We also note that due to the large scale of the value function in these environments, using layer norm and weight projection can make it difficult for the critic network to accurately predict the value. We therefore found it beneficial in these domains to omit the normalization in the final layer of the critic network to allow it to scale its outputs to the target magnitude. \| PPO \| ant \| hopper \| humanoid \| humanoid-standup \| \|------------------------------------------------\|----------\|----------\|----------\|------------------\| \| Baseline \| 4286 \| 2527 \| 6182 \| 33093 \| \| + LR Schedule \| 7154 \| 3400 \| 8366 \| 33810 \| \| + LR Schedule + LayerNorm \| 7336 \| 2574 \| 8473 \| 45793 \| \| + LR Schedule + Layer Norm + Weight Projection \| 7186 \| 2232 \| 8677 \| 50563 \| \| + LR Schedule + Weight Projection \| 6843 \| 1276 \| 7315 \| 33982 \| \| + LayerNorm \| 2764 \| 2652 \| 7080 \| 39224 \| \| + LayerNorm + Weight Projection \| 3379 \| 2458 \| 6911 \| 31367 \| \| + Weight Projection \| 4629 \| 922 \| 4470 \| 34256 \| \| \| \| \| \| \|	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
ClavaDDPM: Multi-relational Data Synthesis with Cluster-guided Diffusion Models	Accept (poster)	Summary: The paper tackles the problem of synthetic data generation in tabular formats and particularly focuses on data generation in multi-relational (multi-table) setups like relational databases. Whereas existing tabular diffusion models work only on single tables, the proposed ClavaDDPM extends the DDPM framework to support many relational tables linked via primary-foreign keys. In the hierarchy of parent-child tables, child tables contain keys from parent tables, and ClavDDPM conditions the generative process of child entries on their parent entries (grouped by the foreign key). To enable this, the model learns latent variables (expressed as GMMs) corresponding to the groups of foreign keys. Capturing the hierarchy of parent-child relations enables learning quite deep, long-range dependencies between k-hop neighbors in the relational schema. Experimentally, ClavaDDPM outperforms existing non-diffusion baselines both in terms of effectiveness and efficiency. Strengths: S1. The problem of synthetic data generation is of growing importance in the era of large, data-hungry models whose quality depends on the quality of training data. Besides, synthetic generation enables upsampling of a small custom dataset (with possible private and sensitive data) for fine-tuning backbone models. In the world of relational databases, most databases consist of multiple linked tables that have to be modeled jointly to capture data dependencies. ClavaDDPM is the first tabular DDPM that supports generation conditioned on multiple tables (organized in several hierarchy levels) and can be used on real-world datasets. S2. The idea of learning latent variables with classifier guidance for grouped keys is rather clever. In addition, the model supports both numerical and categorical data as well as attempts to model the generative process for tables with several parents. Conditioning on several parent tables, the authors propose soft matching of latents (conditioned on each parent separately) via approximate nearest neighbor search. S3. Compelling experimental results - ClavaDDPM was compared against existing non-diffusion multi-table models (PrivLava and Synthetic Dava Vault), the authors also adapted single-table baselines CTGAN and TabDDPM in several versions as baselines. Ablation studies are informative. S4. The paper is well-written and structured, I enjoyed reading the manuscript. Weaknesses: W1. The idea of long-range dependencies in relational tables has been introduced in the beginning and highlighted in the experiments, but the main part (Section 4) does not go into the details. Perhaps Section 4.2 could expand on long-range modeling mapping to the example hierarchy from Figure 1. W2. No discussion of the limitations, e.g., how long the training took; inference on the datasets takes several days. The checklist mentions “the second paragraph of the Conclusion” but this section in the manuscript has only one paragraph. Technical Quality: 3 Clarity: 4 Questions for Authors: Q1. Most of the reported numbers (total variation distance between synthetic and real data) are in the higher 95%+ range which makes it hard to distinguish the quality of new models. Are there any other metrics close to real-world tasks that could be of use? For instance, TabDDPM and others report the quality of CatBoost/XGBoost and other standard tabular ML algorithms trained on the synthetic data. Comments: * Line 206: Typo in LavaDDPM * Captions of Tables 1 and 2 could also mention what the reported metrics are. Confidence: 3 Soundness: 3 Presentation: 4 Contribution: 3 Limitations: There is no discussion of the limitations. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: A-W1 Metric Details: Thank you for your suggestion. We agree that expanding on the details about long-range dependencies in Section 4.2 and mapping them to the example hierarchy from Figure 1 would greatly enhance the clarity. We will make this change in the revised version. $\quad$ A-W2 Limitations and Future Works: Thank you for identifying this issue, and we apologize for the confusion.To respect NeurIPS page limit, we submitted a shortened version of our paper. However, after the submission deadline, we realized that the limitations and future work that we referred to were unfortunately part of what was cut . Here is the original second paragraph of the conclusion, we will make sure to add this to the main paper in the revised version: >"We focused on foreign key constraints in this work, and made the assumption that child rows are conditionally independent given corresponding parent rows. This brings three natural follow-up research directions: i) extension to the scenarios where this prior information is not available and these relationships need to be discovered first[3], ii) further relaxing the assumptions, and iii) inspecting multi-relational data synthesis with other integrity constraints (e.g, denial constraints[4], general assertions for business rules). >Furthermore, we evaluated ClavaDDPM's privacy with the common (in tabular data literature) DCR metric. Nonetheless, we think it is worthwhile to: i) evaluate the resiliency of ClavaDDPM against stronger privacy attacks[5], and ii) investigate the efficacy of boosting ClavaDDPM with privacy guarantees such as differential privacy. Similarly, the impacts of our design on fairness and bias removal, as another motivating pillar in synthetic data generation, is well worth exploring as future work. We believe the thorough multi-relational modeling formulation we presented in this work, can serve as a strong foundation to build private and fair solutions upon. " $\quad$ A-Q1 Real-world Metrics: Yes, there are other metrics being used for evaluation. We conducted single-table machine learning efficacy (MLE) experiments using the same settings as in TabSyn, which employs an XGBoost model to predict one column given the remaining columns. The results of these experiments are presented in the appendix (section D.2). These results demonstrate that, in terms of high-order or real-world metrics, ClavaDDPM achieves state-of-the-art performance, even though it was designed for multi-table synthesis. In the revised version of our paper, we will include comments about the MLE results in the main paper. Additionally, our primary focus in this work is on multi-table quality. As shown in Table 1, ClavaDDPM exhibits significant advantages over other baselines regarding long-range dependencies. This advantage becomes more pronounced as the number of hops increases, making the quality of ClavaDDPM more distinguishable. For multi-table MLE, this remains an unexplored area, and we plan to address it in our future work. $\quad$ Reply to comments: Thank you for pointing out the typo, and suggestions about captions. We will make these changes in the revised version. --- Rebuttal Comment 1.1: Comment: Thank you, after reading the responses to this and other reviews my concerns are resolved and I remain positive about the work. --- Reply to Comment 1.1.1: Comment: Thank you for your time and effort in reviewing our work as well as the rebuttal. We greatly appreciate your constructive feedback and the positive score you've given, which encourages us to further refine the research.	Summary: This paper proposes the new ClavaDDPM approach to address the scalability and long-range dependency challenges in tabular data synthesis. ClavaDDPM uses clustering labels to model inter-table relationships, particularly focusing on foreign key constraints, and employs diffusion models' robust generation capabilities along with efficient algorithms to propagate learned latent variables across tables. Evaluations demonstrate ClavaDDPM's superior performance in capturing long-range dependencies and competitive utility metrics for single-table data. Strengths: $\bullet$ The manuscript is commendably well-structured, with a logical flow that effectively guides the reader through the paper. The clarity in writing and the organization of content significantly enhance the reader's comprehension and the overall quality of the presentation. $\bullet$ The authors have conducted a thorough experimental validation, which is a significant strength of the paper. The meticulous detailing of experimental procedures, including data handling, model training, and evaluation metrics, greatly contributes to the reproducibility and credibility of the study. $\bullet$ The topic of the paper addresses a highly relevant issue in the field, which is a strong point. The research aligns well with current trends and challenges in the domain, ensuring that the findings will be of interest to a broad audience and have potential applications in real-world scenarios. Weaknesses: $\bullet$ The manuscript exhibits a lack of punctuality and standardization in the presentation of mathematical formulas, leading to potential ambiguity in interpretation. Key terms are not consistently defined upon first use, and there is a misuse of symbols that may confuse readers. Additionally, the placement of table names appears to be incorrect in some instances, further detracting from the paper's clarity. It is essential to standardize the notation and ensure consistent definitions and proper placement of table names for better readability. $\bullet$ The assumptions made in the model section require more rigorous justification. The authors should provide a more detailed explanation of why these assumptions are reasonable and how they contribute to the validity of the model. This will strengthen the theoretical foundation of the work and enhance the credibility of the proposed approach. $\bullet$ The paper would benefit from an analysis of the model's complexity, particularly in the context of large-scale databases. Given the increasing size and complexity of real-world databases, understanding how the proposed model scales and performs under such conditions is crucial. Including a complexity analysis will provide insights into the model's practicality and efficiency. $\bullet$ The ablation study regarding the cluster number 'k' lacks necessary granularity. A more fine-grained investigation is needed to understand the impact of varying 'k' on the model's performance and to identify the optimal settings for different scenarios. This will provide a clearer understanding of the model's behavior and its adaptability to various contexts. $\bullet$ The section on the multi-relational synthesis problem, currently placed in the appendix, should be relocated to the main body of the paper. This will improve the flow of the paper and make it easier for readers to follow the synthesis process and understand its relevance to the overall work. Integrating this section into the main text will enhance the coherence and comprehensiveness of the paper. Technical Quality: 2 Clarity: 3 Questions for Authors: See the above weaknesses. Confidence: 3 Soundness: 2 Presentation: 3 Contribution: 2 Limitations: No. Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: A1: Presentation improvements Thank you for your valuable feedback. We will take steps to improve the writing and overall presentation of the paper, and have fixed the table names issue, and will have a better written revised version. To further enhance our manuscript, we would greatly appreciate it if you could point out any specific issues with the mathematical formulations or inconsistency in definitions, so we can address them in detail. $\quad$ A2: Justification of assumptions Thank you for highlighting the need for more rigorous justification of our assumptions. We appreciate your feedback and would like to provide a detailed explanation: We understand the importance of validating assumptions in tabular data synthesis. When reviewing the literature, such as TabSyn and TabDDPM, we observed that they implicitly rely on the naive row-wise i.i.d. assumptions, which lack validity when extended to multi-table scenarios. To address this, we reexamined the problem and adopted a weaker and more realistic assumption: that child rows are conditioned on foreign key constraints. We provided a mathematical deduction to strengthen the theoretical foundation of our approach, aiming to address tabular data synthesis more rigorously than simply applying generative models as done in previous works. While it is challenging to justify these assumptions perfectly in alignment with real-world scenarios, we designed experiments to empirically validate them. In section 5.1, Table 1, we compared ST-ClavaDDPM with ClavaDDPM. ST-ClavaDDPM utilizes the same model backbone as ClavaDDPM but makes the i.i.d. assumption on all child table rows. In contrast, ClavaDDPM assumes that child rows are conditioned on parent rows. The experimental results in Table 1 indicate that ClavaDDPM significantly outperforms ST-ClavaDDPM, empirically demonstrating that our assumption is more effective on real-world datasets compared to the naive row-wise i.i.d. assumption. Although our assumptions may not be perfect, our empirical results show that the theoretical analysis in our paper is robust and surpasses the assumptions made in previous works. Additionally, we consider exploring even weaker and more realistic assumptions as a direction for future work. $\quad$ A3: Complexity analysis Thank you for your suggestion. We agree that a complexity analysis is essential for understanding the scalability and efficiency of our model, especially for large-scale databases. Here is a preliminary analysis, which we will expand upon with detailed results in the revised version. Given a multi-relational database $G = (R, E)$ with $m$ tables, $n$ foreign key constraints, and $p$ rows per table. Given a p-row table, we denote the time complexity of performing GMM clustering $c_{GMM}(p)$, training a diffusion model as $c_{diff}(p)$, training a classifier as $c_{class}(p)$, synthesizing as $c_{syn}(p)$, ANN searching complexity as $c_{ann}(p)$. Phase 1: Latent Learning and Table Augmentation: - Runtime: $n \cdot c_{GMM}(p)$. Phase 2: Training: - Runtime: $n \cdot c_{class}(p) + m \cdot c_{diff}(p)$. - This phase is dominated by diffusion training, primarily influenced by $m$. Phase 3: Synthesis: - Runtime: $n \cdot c_{syn}(p)$. Additional Step: Matching: - Runtime: $n \cdot c_{ann}(p)$. - Negligible runtime with FAISS implementation. Summary: - Dominated by Phase 2 (training) and Phase 3 (synthesis). - Critical factors: $m, n$, and $p$. - Robust against the number of clusters $k$ in Phase 1 due to the dominance of later phases. Our model shows significant scalability and practicality compared to existing methods like SDV, which is limited to synthesizing at most 5 tables with a depth of 2 (section 5.2). We will provide empirical runtime measurements and baseline comparisons in the revised version. $\quad$ A4: Fine-grained investigation of $k$ Thank you for your valuable suggestion. We agree that a more fine-grained analysis of the cluster number $k$ is essential for understanding its impact on the model's performance and identifying optimal settings for different scenarios. Our preliminary results show an interesting trend: the model quality initially performs lower when $k$ is small, peaks at $k=25$, and then decreases. When $k$ is very large, the model performance converges to a local optimum. This suggests that a technique similar to binary search could be applied empirically to find the optimal $k$. $\quad$ $\textbf{Table 1: Model Performance for Different k}$ \|Berka\|$k=1$\|$k=10$\|$k=25$\|$k=50$\|$k=100$\|$k=500$\|$k=1000$\|$k=\infty$\| \|-\|-\|-\|-\|-\|-\|-\|-\|-\| \|AVG 2-way\|81.64 $\pm$ 1.09\|86.87 $\pm$ 3.51\|89.21 $\pm$ 1.95\|87.43 $\pm$ 1.34\|84.7 $\pm$ 2.27\|86.4 $\pm$ 1.56\|87.77 $\pm$ 0.83\|87.81 $\pm$ 1.70\| The results of these experiments will be included in the revised paper. This will provide a clearer understanding of the model's behavior and its adaptability to various contexts. $\quad$ A5: Relocation of research problem Thank you for pointing this out. We agree that moving the section on the multi-relational synthesis problem to the main body of the paper would improve the flow and make it easier for readers to follow the synthesis process and understand its relevance to the overall work. However, due to the NeurIPS page limit, we had to place the definition in the appendix. We will integrate this section into the main text in the revised version to enhance the coherence and comprehensiveness of the paper. --- Rebuttal Comment 1.1: Comment: Dear reviewer, Please respond to the rebuttal and provide substantive arguments and, in particular, more concrete strengths and weaknesses of the paper. Unless you update your line of argument, I will not be able to take your review into account in the decision making process. --- Rebuttal Comment 1.2: Comment: Thank you for your detailed responses and efforts to address my concerns. I appreciate the clarifications provided, particularly regarding the assumptions in your approach. However, after careful consideration, I have decided to maintain my original score. I believe there are still several areas that require further attention: Reference to Appendix A Notation Summary: I suggest adding explicit references to the notation summary provided in Appendix A within the main text. This will help readers navigate the mathematical formulations more effectively and avoid potential confusion. Issues with Equations 5-9: I noticed that there are some missing symbols in Equations 5 through 9, which result in these equations not being properly formatted. Addressing these inconsistencies is crucial for the clarity and accuracy of your mathematical presentation. Visualization of Label Clustering and Table Relationships: It would be beneficial to include some visualizations that illustrate the relationship between label clustering and table structures. Such visual results would provide additional empirical evidence and enhance the understanding of your approach. Clarification on Mathematical Deduction: You mentioned that you provided a mathematical deduction to strengthen the theoretical foundation of your approach. Could you clarify where and how this deduction is presented in the paper? A clearer explanation or more detailed description would be helpful in understanding the rigor of your theoretical contributions. I hope these suggestions help further refine your work. Thank you again for your dedication and for considering my feedback. I look forward to seeing the final version of your paper. --- Reply to Comment 1.2.1: Comment: Thank you for your response and we appreciate your comments that help refine our paper. $\quad$ > Reference to Appendix A Notation Summary Thank you for your feedback. To ensure clarity and consistency, we have included a paragraph at the beginning of Section 4.1 that introduces the relevant notations, such as parent/child tables, the entire database, and the distinctions between data and random variables. This section is complemented by a running example using a subset of the Berka dataset. We appreciate your suggestion and will add a reference to Appendix A for further clarification. $\quad$ > Issues with Equations 5-9 We would greatly appreciate it if you could point out any specific missing symbols or inconsistencies in Equations 5-9. This would help us further improve the clarity and accuracy of our work. $\quad$ >Visualization of Label Clustering and Table Relationships Thank you for your suggestions. We will consider adding some visualizations in the appendix to enhance understanding in the revised version. $\quad$ >Clarification on Mathematical Deduction The mathematical derivation spans from Equation 5 to Equation 10, where we derive a probability expression for the parent-child scenario under the assumptions we have applied. The final expression (Equation 10) illustrates the distribution modeled by each component in the ClavaDDPM framework. We believe this strengthens the theoretical foundations of our work, as previous approaches in tabular data synthesis, such as TabDDPM and TabSyn, do not explicitly provide the probability assumptions they rely on or clarify the distributions they model, instead solving the problem in a purely end-to-end manner. - Equation 5 is a direct result of the i.i.d. assumption on $(g_j, y_j)$. - Equation 6 is based on conditional probability. - Equation 7 introduces an independence assumption we are making. - Equation 8 is a series of conditional probability expansions of Equation 6, given Equation 7. - Equation 9 expands the conditional foreign key group distribution by introducing the group size variable, which directly extends a part of Equation 8. - Equation 10 presents the final expression of the parent-child distribution we are modeling, incorporating the independence assumptions introduced in our work. This final expression involves three probability distributions, each representing a learnable component of the ClavaDDPM framework: - $p(y, c)$ is the augmented parent distribution, modeled by training a parent diffusion model. - $p(s\|c)$ is the conditional group size distribution, calculated through frequency counting. - $p(x\|c)$ is the conditional child distribution, modeled using classifier-guided diffusion. We are happy to provide further details and welcome any specific recommendations to improve clarity.	Summary: This paper proposes ClavaDDPM to address two key deficiencies in multi-table data generation: scalability for larger datasets and capturing long-range dependencies, such as correlations between attributes across different tables. This approach utilizes cluster labels as intermediaries to model relationships between tables, paying special attention to foreign key constraints. The authors elaborated on the proposed method, made some assumptions, conducted some experiments for evaluation, and performed some analysis about the results. Strengths: 1. The paper proposes an efficient framework to generate multi-relational data that preserves long-range dependencies between tables, and proposes relation-aware clustering for modeling parent-child constraints. 2. The paper applies a matching technique based on approximate nearest neighbor search as a general solution to the problem of multi-parent relation synthesis for a child table with multiple parents. Weaknesses: 1. I have some concerns about the assumptions made in the paper, which seem to be somewhat inconsistent with the scenarios in real world settings. Please refer to Questions 1 and 2 for details. 2. There may be some clarifications needed in the experimental section. Meanwhile, the analysis of the experimental results does not cover some key points. Please refer to Questions 3-6 for details. 3. There are some problems with the writing and formatting of this paper. Please refer to Questions 7-8 for details. Also, there are some confusing statements in the paper, which hinder the readability of the paper. Please refer to Questions 9-10 for details. Technical Quality: 2 Clarity: 2 Questions for Authors: 1. The paper assumes that there are parent-child relationships between different tables and the relationships are known. I However, in real life, the relationships may be very complex and may not be known in advance. In this case, how can ClavaDDPM handle it? 2. The i.i.d. assumption in Section 4.1 seems too strong, because the child rows corresponding to different primary keys may not be independent in real-world scenarios. If this is the case, does the theoretical analysis in the paper still hold? 3. Please clarify why you selected CTGAN over newer or state-of-the-art models like CTAB-GAN, TabSyn, and CoDi mentioned in the related work for your experiments. 4. The reason for the absence of average agree rate in the last two columns of Table 2 remains unclear. Additionally, it is not specified what NA represents. Moreover, there is a lack of clarity regarding the calculation method and formula used to determine the agree rate in this experiment. 5. I feel a bit confused about why TabDDPM converges so slowly on the Instacart05 and Movie Lens datasets. The authors of TabDDPM stated in their work that TabDDPM can converge quickly with a 2080Ti GPU. In addition, I noticed that the Berka dataset seems to be larger than those two datasets. Could you kindly provide an explanation as to why TabDDPM exhibits convergence on this larger dataset, while failing to do so on the two smaller datasets? 6. Are the evaluation metrics used in the experiment widely used in the field or are they proposed by the authors? I haven't seen similar metrics in related works. If they are proposed by the authors, why don't you use metrics from other papers, such as the relative error used in PrivLava [1] or more comprehensive metrics used in TabSyn [2]? 7. There are some typos in the paper: “LavaDDPM” in line 206, “Dnorm” in the caption of Table 1, “The experiment result show…” in line 355. 8. Page 18's experimental results table lacks a caption. 9. In Section 5.2, you referred to additional results in Appendix 5.3, which is missing from the paper. Please provide the mentioned experimental results. 10. In the checklist, you said that you discussed the limitations and future work in the second paragraph of the conclusion section, but there is no relevant discussion in the conclusion of the paper, not even the second paragraph, which is confusing. Reference: [1] K. Cai, X. Xiao, and G. Cormode. Privlava: synthesizing relational data with foreign keys under differential privacy. Proceedings of the ACM on Management of Data, 1(2):1–25, 2023. [2] H. Zhang, J. Zhang, B. Srinivasan, Z. Shen, X. Qin, C. Faloutsos, H. Rangwala, and G. Karypis. Mixed-type tabular data synthesis with score-based diffusion in latent space. arXiv preprint arXiv:2310.09656, 2023. Confidence: 3 Soundness: 2 Presentation: 2 Contribution: 2 Limitations: n/a Flag For Ethics Review: ['No ethics review needed.'] Rating: 3 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: A1: Known relationships We fully agree on the importance of realistic assumptions. This work tackles a prevalent challenge in the finance industry [in collaboration with them] on tabular synthesis. Synthesizing data for multiple interconnected tables, even with known foreign keys, has been entirely overlooked in the literature, with only two notable exceptions offering inefficient solutions [1,2]. Our work presents a practical approach that surpasses the state of the art (SOTA) with known foreign keys. We will discuss addressing unknown constraints in future work in the revision. $\quad$ A2: I.i.d assumptions We appreciate your perspective and agree that the assumption in Sec 4.1 is strong. While previous works TabSyn and TabDDPM [6,7] made even stronger assumptions (each row is i.i.d), we introduced a weaker assumption: in a parent-child two-table scenario (in Sec 4.1), each parent row is i.i.d., while the child rows are dependent on its corresponding parent row. In fact, we are making a Bayesian modeling assumption that each child row, although not independent by itself, is conditionally independent of other child rows given its parent. Our evaluation in Sec 5.1 demonstrates the effectiveness of our weaker assumption (ClavaDDPM) on real-world datasets compared to that of prior works (ST-ClavaDDM with strong i.i.d assumptions for child rows). While our assumption may not be perfect (modeling all dependencies with perfect accuracy is hard), our empirical results support our theoretical analysis and outperform previous works' assumptions. We will clarify these and discuss weaker and more realistic assumptions as future work. $\quad$ A3: Choice of baselines (CTGAN and TabDDPM over CTABGAN, TabSyn, and CoDi) Our work focuses on a multi-table synthesis with a new paradigm. Thus, the strength of single-table baseline models was not our only consideration. Our goal was to pick one diffusion model and one GAN-based model, each being SOTA and representative in their domain for a diverse comparison. Firstly, we excluded CTABGAN(+) or CoDi because they were shown inferior to TabDDPM and TabSyn [6,7]. Since both TabDDPM and TabSyn are SOTA, we chose between them. Given our ClavaDDPM employs a similar model to TabDDPM, comparing against baselines using TabDDPM offers a fair evaluation, highlighting the effect of our Clava framework while disregarding the inherent advantages of TabSyn over TabDDPM. Additionally, our preliminary results (with slightly different metrics) at Clava’s early development indicated TabDDPM’s superior performance over TabSyn as the backbone on real-world datasets. (Table 2 in comments) Thus, we chose TabDDPM as the backbone for both our model and the two baselines, ST- and Dnorm-. Even with other baselines, ClavaDDPM's advantage would remain evident. Though CTGAN is weaker than TabDDPM, we included it because it is a representative GAN-based tabular synthesis model, aligning with the TabSyn paper’s inclusion of CTGAN over CTABGAN. We will add the clarification and include experiments on other baseline models, as you suggested in the revised version. $\quad$ A4: Clarification on agree rate Thanks for the suggestion. We will detail the agree rate formulation in the appendix. The agree rate is only influenced by k and lambda, but not eta or “no matching” (the last two columns that are not involved in the clustering process). We will include the agree rates in those columns for completeness and clarity. $\quad$ A5: Clarification on convergence We will add a complexity analysis in the revised paper. Convergence depends on both the data size and the domain size. Even though TabDDPM can handle all datasets on a 2080Ti GPU (A6000 is overkill), its multinomial diffusion for categorical features is a bottleneck with large domain sizes, as exemplified by Instacart05 and Movie Lens datasets. For instance, Instacart05 has a categorical column with 49,688 values, requiring one-hot encoding and expensive multinomial diffusion. In TabDDPM's single-table datasets, categorical columns have relatively few values(e.g., the largest category count in the adult dataset is 42). The Berka dataset, despite having more tables, has the largest categorical domain size of 77, allowing faster convergence for TabDDPM. Real-world data often contain categorical columns with numerous distinct values. ClavaDDPM accelerates training by applying a unified Gaussian diffusion to both categorical and numerical columns, leading to faster convergence. Additionally, for fair comparison, we aligned TabDDPM's hyperparameters with ClavaDDPM's, which are larger than the original TabDDPM settings, and thus will be slower than the original TabDDPM (e.g., diffusion timesteps = 2000 vs. 1000). Our TabDDPM experiments used the TabDDPM library within the Synthcity framework. We will release the baseline code for reproducibility. $\quad$ A6: The choice of evaluation metrics We used single-table data quality metrics from TabSyn and reported KS/TV metrics in the main paper, and the rest (alpha precision, beta recall, classifier detection, machine learning efficacy) in the appendix (section D.2) due to space constraints. We did not use the multi-table metric like relative error from PrivLava for - It relies on human-designed queries, not applicable to all datasets. - No open-source evaluation code, hard to replicate. - No theoretical validation for these hand-designed queries. These limitations highlighted a gap in multi-table synthesis evaluation. Therefore, we proposed the long-range dependency metric, a statistical measure applicable to all multi-table datasets without needing hand-designed queries. $\quad$ A 7,8,9: Formatting issues Thank you for your feedback. We will address them in our revision. $\quad$ A10: Conclusion We apologize for the omission of limitations and future work due to page constraints. These sections will be included in the revision. --- Rebuttal Comment 1.1: Comment: Dear reviewer, Please respond to the rebuttal as is expected of you as a NeurIPS reviewer asap! Thanks --- Rebuttal Comment 1.2: Title: Additional comment on question 9 Comment: We would like to additionally address question 9, where the mentioned experiment results are actually located in Appendix D.1. It was a typo for reference and we will fix it in the revision.	Summary: This work addresses the challenges inherent in generating multi-relation tabular data and proposes a novel generation method based on hidden random variables. The approach analysis correlations between primary and foreign keys between tables by predicting hidden variables associated with these keys within simultaneous tables. These hidden random variables are inferred using Denoising Diffusion Probabilistic Models (DDPM) grounded in stochastic processes. The method is elaborated from two-table linkage generation to multi-table linkage generation, with a step-by-step explanation of the approach. Comprehensive experiments are conducted to demonstrate the practical effectiveness of the proposed method. Strengths: This paper highlights the extensive dependencies between different tables in the process of multi-relation tabular data synthesis and introduces an innovative approach by analyzing the relationships between primary keys and foreign keys using hidden variables. The proposed ClavaDDPM process is well-articulated and has demonstrated promising results across several datasets. Additionally, the subsequent analysis of hidden variables enhances the credibility of this work. Weaknesses: Although this work attempts to elaborate on its theoretical framework with substantial content, the notation system and descriptive symbols used do not conform to standard academic mathematics conventions (see sections 3. Background and 4.1 Notations). The marks in equation are not uniform (Eq.2). Furthermore, several key formulas lack thorough proofs (for example, Formula 8). The proof of this key formula would be best placed in the appendix. Additionally, Formula 3 from a previous study lacks supporting evidence; a brief explanation of its proof process or an indication of its rationale is necessary. The validity of the method “we introduce latent random variables c such that g is independent of y conditioned on c” also requires theoretical verification. Technical Quality: 3 Clarity: 2 Questions for Authors: Question 1: In line 79 to 85, the author mention table with R and relation with R. Is this means that a relation in Relational Database is a table in this paper? Since the relations are model as edges of graph. Question 2: According to the paper content, the author mention that “the primary key of table serves as the unique identifier for each row in the table”. And in section 4.1 the rows in parent table can suitable i.i.d assumption. If every row is unique, how rows can be suitable independent and identification distributions? Question 3: From the perspective of learning latent variable method alone, what are the advantages of CLavaDDPM proposed in this paper compared with other studies? Confidence: 3 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: The authors adequately addressed the limitations. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Title: Rebuttal to the Questions Comment: A1: Terminologies of table Yes, a relation is a table. In this paper, we primarily adhere to the terminology used in relational database literature, where a “table” is formally referred to as a “relation”, and multi-relational synthesis corresponds to multi-table synthesis. Consequently, our notation slightly differs from previous works that only consider single tables, such as TabDDPM[2] and TabSyn[3]. To be clear, we used “tables” and “relations” interchangeably in the paper. Specifically, we model “relations” or “tables” as nodes and “foreign key constraints” as edges, consistent with relational database terminology. We apologize for any confusion and will clarify this further in the revised version. $\quad$ A2:I.i.d. assumptions We fully understand your concern. In our work, the term “unique identifier” refers to a unique ID for a row and is not related to the data distribution itself. Below is an example table: \|Primary key(id)\|Gender\|Country\| \|-\|-\|-\| \|2\|M\|US\| \|3\|F\|UK\| In this table, the primary key (unique identifier) is simply an ID, while the actual data distribution involves attributes like (gender, country). By i.i.d., we mean that the distribution of $(gender, country)$ is independent. When modeling, the primary key is not included as part of the data but is used solely for enforcing foreign key constraints. For example, if a child table row has a foreign key value of $3$, it refers to the row $(F, UK)$ in the parent table. The value $3$ is not passed into the diffusion model and is assigned additionally. Similarly, previous works in tabular data synthesis, such as SDV, PrivLava, and TabDDPM, treat keys as identifiers rather than data, with key values not being passed into the model. We will clarify this in our revised version to prevent further confusion. $\quad$ A3: Latent variable learning In the context of tabular data synthesis, PrivLava[4] is the only prior work that has learned latent variables (excluding the works that directly adopt latent generative models, which do not explicitly learn latent variables). Compared to PrivLava, our approach is agnostic to data domain size and has faster convergence. PrivLava's latent learning is marginal-based, making it applicable only to predefined fixed domains (they primarily support integers). Additionally, their use of the EM algorithm is slow and prone to convergence issues in practice. Our experiments in Section 5, Table 1, demonstrate that their method fails to converge on many real-world datasets. Importantly, our method (diagonal covariance GMM) enforces our independence assumption and aligns with our theoretical analysis. In Section 4.1, Equation 7, we assume that child table groups $g$ are independent of parent row $y$, conditioned on latent variable $c$. Thus, we learn latent variable $c$ such that its distribution supports this assumption. As mentioned in Section 4.3.1, we use a GMM with diagonal covariances in the joint space of $(X, Y)$. This ensures that, when the GMM is properly trained, the covariance between $X$ and $Y$ is zero in each Gaussian cluster with centroid $c$. Consequently, conditioned on $c$, $g$ and $y$ will tend to be independent, as $g$ is a collection of $X$. While more advanced latent learning methods, such as VQVAE[5], could perform latent learning and quantization simultaneously, we considered them during development but identified potential trade-offs in terms of runtime. Currently, the runtime of the latent learning phase is negligible compared to other phases, and VQVAE lacks synergy with our theoretical assumptions. Nevertheless, as noted at the end of Section 4.3.1, we are open to exploring the impact of other latent learning methods in future work. --- Rebuttal 2: Title: Rebuttal to the Weakness Comment: >Although this work attempts to elaborate on its theoretical framework with substantial content, the notation system and descriptive symbols used do not conform to standard academic mathematics conventions (see sections 3. Background and 4.1 Notations). R: Non-standard notations Thank you for pointing this out. We acknowledge that our notation differs slightly from the standard. In probability theory, capital letters typically denote random variables, while lower case letters represent their actual values. We modified this convention to distinguish between row data and table data. For example, we use $x$ to denote a row of a child table and $X$ to denote the entire child table. To avoid conflicts, we use bold letters $\mathbf{x}$ and $\mathbf{X}$ to represent the corresponding random variables. To clarify this further, we will describe our design choices in detail and ensure consistency throughout the manuscript in the revised version. $\quad$ >The marks in equation are not uniform (Eq.2) R: Non-uniform marks We obtained Equation 2 from the Background section of TabDDPM[2]. We would greatly appreciate it if you could point out the specific issues with the notation or formality, and we are more than happy to make any necessary improvements. $\quad$ >Furthermore, several key formulas lack thorough proofs (for example, Formula 8). The proof of this key formula would be best placed in the appendix. R: Proofs for formula We agree with your observation that this is a key formula in our work. The derivation is based on Equation 7. Due to space constraints, we provided only a brief one-line expansion in the main paper. We appreciate your suggestion and will include a detailed proof in the appendix. $\quad$ >Formula 3 from a previous study lacks supporting evidence; a brief explanation of its proof process or an indication of its rationale is necessary. R: Formula 3 Formula 3 is directly adopted from previous work [1], which was derived using Bayes' theorem. Due to space limitations, we were unable to provide a more detailed explanation in the main paper and included only the result. However, we appreciate your point and will add a more detailed background section in the appendix of the revised version. Additionally, we will briefly mention the Bayesian modeling rationale in the main paper. $\quad$ >The validity of the method “we introduce latent random variables c such that g is independent of y conditioned on c” also requires theoretical verification. R: Validity of assumption This is a valid concern. In fact, ClavaDDPM adopts a Bayesian modeling paradigm, where we make certain Bayesian assumptions and let the trained models enforce those assumptions. Therefore, we chose GMM with diagonal covariance, which by design learns latent variables $c$ that enforce conditional independence between $g$ and $y$ (with covariance being zero). We will include a more detailed demonstration of this aspect in the appendix to better address the theoretical foundations. --- Rebuttal 3: Title: References Comment: [1] P. Dhariwal and A. Nichol. Diffusion models beat gans on image synthesis. Advances in neural information processing systems, 34:8780–8794, 2021. [2] A. Kotelnikov, D. Baranchuk, I. Rubachev, and A. Babenko. Tabddpm: Modelling tabular data with diffusion models. In International Conference on Machine Learning, pages 17564–17579. PMLR, 2023. [3] H. Zhang, J. Zhang, B. Srinivasan, Z. Shen, X. Qin, C. Faloutsos, H. Rangwala, and G. Karypis. Mixed-type tabular data synthesis with score-based diffusion in latent space. arXiv preprint arXiv:2310.09656, 2023. [4] K. Cai, X. Xiao, and G. Cormode. Privlava: synthesizing relational data with foreign keys under differential privacy. Proceedings of the ACM on Management of Data, 1(2):1–25, 2023. [5] Razavi, Ali, Aaron Van den Oord, and Oriol Vinyals. "Generating diverse high-fidelity images with vq-vae-2." Advances in neural information processing systems 32 (2019).	Rebuttal 1: Rebuttal: We greatly appreciate the reviewers' efforts and constructive feedback. We humbly accept their suggestions and will make improvements accordingly. These insights will help make the paper more solid and better organized. Here, we address some general questions and misunderstandings and outline the steps we will take to address the issues in each aspect. $\quad$ ## Assumptions and Theoretical Foundations >Previous works like TabDDPM and TabSyn on tabular data synthesis for single tables have implicitly assumed that each row in the table is i.i.d. (independently and identically distributed). This assumption: (1) has not been specifically analyzed or validated, and (2) is unsuitable for multi-table synthesis. Therefore, our work aims to address this by extending the problem to multi-table synthesis. Our improvements include: >1. Explicitly stating the assumptions and deriving mathematical deductions based on them. >2. Introducing a weaker, more realistic assumption for multi-table synthesis: > - In a multi-table database forming a DAG, each row in a root table (i.e., tables without parent tables) is i.i.d. > - Each child table row is dependent on its corresponding parent row. > >We acknowledge that misunderstandings occurred, and we will enhance clarity and organization in the revision. $\quad$ ## General Writing and Formatting >Reviewers identified several typos and incorrect table references. Additionally, we received valuable suggestions to move some sections from the appendix to the main paper and to add discussions of limitations and future work. These issues arose primarily due to NeurIPS page limits, and we appreciate the feedback. All these points will be addressed in the revision. $\quad$ ## Complexity analysis >We appreciate reviewer bZ6q’s constructive suggestion about having a complexity analysis. We summarize the analysis here and will add it in the revised version. Given a multi-relational database $G = (R, E)$ with $m$ tables, $n$ foreign key constraints, and $p$ rows per table. Given a p-row table, we denote the time complexity of performing GMM clustering $c_{GMM}(p)$, training a diffusion model as $c_{diff}(p)$, training a classifier as $c_{class}(p)$, synthesizing as $c_{syn}(p)$, ANN searching complexity as $c_{ann}(p)$. >Phase 1: Latent Learning and Table Augmentation: >- Runtime: $n \cdot c_{GMM}(p)$. >Phase 2: Training: >- Runtime: $n \cdot c_{class}(p) + m \cdot c_{diff}(p)$. >- This phase is dominated by diffusion training, primarily influenced by $m$. >Phase 3: Synthesis: >- Runtime: $n \cdot c_{syn}(p)$. >Additional Step: Matching: >- Runtime: $n \cdot c_{ann}(p)$. >- Negligible runtime with FAISS implementation. >Summary: >- Dominated by Phase 2 (training) and Phase 3 (synthesis). >- Critical factors: $m, n$, and $p$. >- Robust against the number of clusters $k$ in Phase 1 due to the dominance of later phases. Our model shows significant scalability and practicality compared to existing methods like SDV, which is limited to synthesizing at most 5 tables with a depth of 2 (section 5.2). We will provide empirical runtime measurements and baseline comparisons in the revised version. $\quad$ ## Experiments >Multi-table synthesis, as a superset of single-table synthesis, necessitates more comprehensive evaluations, especially to assess how well the synthetic dataset captures inter-table correlations. Current metrics (e.g., machine learning efficacy, statistical metrics used in TabSyn and TabDDPM) are insufficient. In addition to including experiment results for the previous metrics, we have proposed a novel multi-table quality measure: long-term dependency, which evaluates the capture of long-range correlations in a multi-table database. Reviewers noted the lack of clear demonstration and formulation of this metric. We agree and will include an additional section detailing this metric. >Furthermore, reviewers suggested adding a finer-grained ablation study on the number of clusters k. We conducted these experiments and discovered meaningful trends that can guide practical hyperparameter searches. We appreciate this suggestion and will incorporate the findings in the revised version. $\quad$ ## Limitation and future work >As pointed out by reviewers, we are missing a discussion about limitations and future works. This is because of the page limit. We are going to add the following discussion in the revised version: >“We focused on foreign key constraints in this work, and made the assumption that child rows are conditionally independent given corresponding parent rows. This brings three natural follow-up research directions: i) extension to the scenarios where this prior information is not available and these relationships need to be discovered first[3], ii) further relaxing the assumptions, and iii) inspecting multi-relational data synthesis with other integrity constraints (e.g, denial constraints[4], general assertions for business rules). Furthermore, we evaluated ClavaDDPM's privacy with the common (in tabular data literature) DCR metric. Nonetheless, we think it is worthwhile to: i) evaluate the resiliency of ClavaDDPM against stronger privacy attacks[5], and ii) investigate the efficacy of boosting ClavaDDPM with privacy guarantees such as differential privacy. Similarly, the impacts of our design on fairness and bias removal, as another motivating pillar in synthetic data generation, is well worth exploring as future work. We believe the thorough multi-relational modeling formulation we presented in this work, can serve as a strong foundation to build private and fair solutions upon. ”	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
DiGRAF: Diffeomorphic Graph-Adaptive Activation Function	Accept (poster)	Summary: Inspired by the continuous piecewise-affine based transformation, this paper argued that the activation function should not be an uniform selection for different nodes, and developed a learning activation function method, that can take the graph structure into account to activate node-specific features. The experimental results support their proposed model's effectiveness through comparing with existing activation functions in several datasets. Strengths: This paper provides a new method to learn the activation function, where instead of activating every nodes (representations) uniformly, this method helps generate a node-specific function. The experimental results prove that this method can significantly increase the model performance. Weaknesses: Many formula seem to be repeated, such as equations in 3.2 and 4.1. The complexity is a bit high compared with an existing activation function. Technical Quality: 3 Clarity: 2 Questions for Authors: 1. How will you ensure the parameter \theta you learn from the training can return you a diffeomorphism activation function? It is not clearly stated in your experimental settings, such as how you define transformation T and space \Omega. 2. The method used a GNN to learn the activation function, is there an activation function in the GNN_act? 3. In the node classification experiments, there are some significant improvement in some tasks, while some of them have a minor improvement. Have you tried to figure out the reasons? Confidence: 3 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: There is no potential negative societal impact of this work. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We appreciate the reviewer's thoughtful evaluation and are happy to see that the reviewer recognized the performance increase yielded by our method. We now proceed by addressing the questions and comments, and hope you find them satisfactory to consider revising your score. Q1: Many formulas seem to be repeated, such as in 3.2 and 4.1. The complexity is a bit high compared with an existing activation function. A1: Thank you for the feedback. Section 3.2 serves as the blueprint of the framework, where notations, GNN layers, and a general parameterized activation function are defined. Please note that each Equations (3),(4), and (5) each describe a different tensor, and are essential to define the notations that are used throughout the paper .Section 4.1 specializes in this blueprint to diffeomorphisms, in which we explain how DiGRAF transforms the node features using the CPAB framework and how this differs from traditional activation functions. We agree that some equations in Section 4.1 can be incorporated in the text instead of having a unique Equation. One example is Equation (8) that introduces the element-wise application of DiGRAF to the input node feature tensor. We followed your guidance in our revised paper. Regarding the complexity of the method, please note that we discuss this aspect in the limitations paragraph in our paper. Also, we emphasize that DiGRAF exhibits linear computational complexity with respect to the input size, and can achieve sub-linear running times through parallelization, as discussed in Section 4.3. Although DiGRAF includes an additional component compared to standard activation functions, such as ReLU and Tanh, it delivers significantly better performance, as evident from our diverse experiments in Section 5. Furthermore, compared with other graph activation functions such as GReLU we note that our DiGRAF maintains faster runtimes and superior performance. We have detailed the time complexity and measured runtimes in Table 13 at Appendix H, and compared it with other methods as well. We revised the paper to better highlight this discussion. Thank you. Q2: How will you ensure the parameter $\theta$ you learn from the training can return you a diffeomorphism activation function? It is not clearly stated in your experimental settings, such as how you define transformation $T$ and space $\Omega$. A2: Thank you for the question. Please allow us to start by stating that by construction, DiGRAF yields a diffeomorphic activation function within the domain $\Omega$, because of the utilization of the CPAB framework, which yields a diffeomorphic transformation based on velocity field weights $\theta$. In the case of DiGRAF, we show that the velocity field weights can be learned to be both (i) task-aware, and (ii) graph-aware. In particular, using $\text{GNN}\_{act}$, we learn the velocity field weights $\theta$, which serves as the parameter for the diffeomorphism transformation built on the CPAB framework. Following the construction in the work of CPAB (Freifeld et al. 2017), the velocity field, computed using the parameter $\theta$ and the predefined tessellation setup, is always continuous piecewise affine (CPA). To be precise, by definition, the integral of a CPA velocity field is guaranteed to be a diffeomorphic function. Therefore, the DiGRAF learned is inherently a diffeomorphic activation function. We would like to kindly note that the mathematical background for this discussion is provided in Section 3.1, and we show how to use it to learn our graph activation function DiGRAF in Section 4. In addition, we provided an overview of CPAB transformations in Appendix B. Regarding the definition of $T$, as defined in Equation (1) and (6), the CPAB transformation $T$ in DiGRAF at layer $l$ is $T^{(l)}(\bar{h}^{(l)}\_{u, c}; \theta^{(l)}) \triangleq f^{\theta^{(l)}}(\bar{h}^{(l)}_{u, c}) = \phi^\theta(\bar{h}^{(l)}\_{u, c}, t=1)$, where $\bar{h}^{(l)}\_{u, c}$, defined by Equation (4), represents the intermediate value of a node between the GNN layer and the activation function layer. Regarding the domain $\Omega = [a, b]$, it is defined by hyperparameters $a$ and $b$ where $a < b$, as discussed in detail in Section 4. In practice, we set $a = -b$ to ensure that the activation function is symmetric and centered around 0. We thank you for the questions, and we revised our text to better highlight these aspects, discussed in our paper. Freifeld et al. 2017. Transformations based on continuous piecewise-affine velocity fields. Q3: The method used a GNN to learn the activation function, is there an activation in the $\text{GNN}_{\text{act}}$? A3: We use the ReLU activation function within $\text{GNN}\_{act}$, as it is widely used in GNNs, in order to make it non-linear. The important part is that $\text{GNN}\_{act}$ predicts the velocity field that defines our learned activation function. We added these details to our paper. Q4: In the node classification experiments, there are some significant improvements in some tasks, while some of them have a minor improvement. Have you tried to figure out the reasons? A4: We thank the reviewer for their insightful question. Following the reviewer’s suggestion, we have conducted an investigation on the differences between the datasets. Interestingly, our findings reveal that the datasets where DiGRAF showcases the largest performance improvements (9.5% on Blog Catalog and 18.9% on Flickr) over baselines (ReLU), have more balanced label distributions, while this is not the case for the other datasets (Cora and CiteSeer, where DiGRAF nonetheless still improves by 3.6% and 1.8%). We present the distribution of these labels as Figure 1 in the additional PDF file. We believe that further understanding the impact of the activation function and in particular of DiGRAF on imbalanced data represents an interesting future direction, which we are eager to conduct in future work.	Summary: This paper introduces a new activation function, DIGRAF, specifically tailored for graph data in Graph Neural Networks (GNNs). The approach is based on Continuous Piecewise-Affine Based transformation (CPAB). The authors demonstrate that DIGRAF possesses the desired properties highlighted in existing literature and provide a thorough analysis of these properties. Extensive experiments conducted on diverse datasets across various tasks show that DIGRAF outperforms three different types of baselines in downstream performance. Strengths: 1. This paper devise an activation function based on CPAB, which possess many desirable properties of activation functions (e.g. zero-centered, permutation equivariant, etc.) and has solid theoretical guarantees. It's an ingenious idea and seems that this method has never been adopted before in the activation function of GNN. 2. The variables and equations are well-defined and thoroughly explained. The experiments are extensive and robust, effectively supporting the corresponding claims with comprehensive data. 3. The paper addresses the most critical questions about the effectiveness of the proposed method. Each question is answered with extensive experiments and explicit explanations, providing clear evidence for the method’s efficacy. The figures are well-designed, enhancing understanding and readability. Overall, the paper is smoothly written and easy to follow. Weaknesses: 1. Apart from the adoption of the CPAB approach, the primary contribution appears to be the introduction of GNN_act. However, the discussion on why GNN_act is effective is relatively brief. Including more detailed discussions or theoretical justifications would help in understanding its advantages. 2. How do the properties of DIGRAF influence the convergence? It would be nice if it could be discussed which property the gain comes from. 3. As I mentioned above, more ablation studies should be done to reveal how each property and design contribute to the performance gain. Otherwise, DIGRAF (w/o adap.) is good and simple enough. Maybe we can save the budget of GNN_act for a larger GNN_layer. Technical Quality: 3 Clarity: 3 Questions for Authors: 1. The size of GNN_act seems to have a minor influence (non-monotonic) on performance according to Appendix F.2. What if you increase the size of GNN_layer a little bit (add the parameter of GNN_act to GNN_layer) and compare DIGRAF (w/o adap. & larger GNN_layer) with the current DIGRAF? I believe this could provide a better justification for the effectiveness of GNN_act. 2. What are the properties that DIGRAF has but general-purpose activation functions or existing graph activation functions do not have? Can you put up a table to clarify it? 3. How do the properties of DIGRAF influence the convergence and performance? 4. The tessellation size decides the degree of freedom of DIGRAF, right? Why does increasing the tessellation size result in marginal changes (non-monotonic)? Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The authors have discussed the limitations. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We greatly appreciate the reviewer’s constructive and positive feedback. We are delighted to see the reviewer has valued our experimental analysis. We proceed by answering the questions in the following. Q1: The discussion on why $\text{GNN}_\text{act}$ is effective is relatively brief. Including more detailed discussions or theoretical justifications would help in understanding its advantages. A1: We thank you for your suggestion, and mention that $\text{GNN}\_\text{act}$ boosts performance by adapting the activation function to the input graph, specifically by returning the parameter $\theta$, which governs the CPAB diffeomorphism used as an activation function. This graph adaptivity represents the critical factor of the performance boost, as evident by DiGRAF consistently outperforming DiGRAF (w/o ADAP), where $\text{GNN}\_\text{act}$ is replaced by a learnable $\theta$ which is the same for all graphs. To make this point clearer, in Figure 2 in the additional PDF, we plot the learned activation functions for two distinct randomly sampled graphs from the ZINC dataset, which differ in the number of nodes, features, and the connectivity. While using the non-adaptive variant DiGRAF (w/o ADAP) yields a (learned) fixed activation function for all inputs, $\text{GNN}_\text{act}$ can account for the variables discussed above, and learn distinct activation functions for different graphs. Q2: The size of $\text{GNN}\_\text{act}$ seems to have a minor influence (non-monotonic) on performance according to Appendix F.2. What if you increase the size of $\text{GNN}\_{\text{layer}}$ a little bit (add the parameter of $\text{GNN}\_\text{act}$ to $\text{GNN}\_{\text{layer}}$) and compare DiGRAF(w/o ADAP. \& larger $\text{GNN}\_{\text{layer}}$ ) with the current DiGRAF? A2: As shown in Table 5 in Appendix E, for ZINC and MOLHIV datasets the difference in the number of parameters between DiGRAF and DiGRAF (w/o ADAP) is relatively small, with DiGRAF having 10% and 30% more parameters than DiGRAF (w/o ADAP), respectively. However, we welcome the reviewer’s suggestion and we have now conducted an additional experiment, where we increase the number of parameters of DiGRAF (w/o ADAP) to match the one of DiGRAF by increasing the size of $\text{GNN}_\text{layer}$. We denote this variant by DiGRAF(w/o ADAP. \& larger $\text{GNN}\_{\text{layer}}$ ). In the Table below, we report the performance on the ZINC-12k and OGBG-MOLHIV datasets. The results show that the improvement of DiGRAF cannot be attributed to the (small) increase in the number of parameters. On the contrary, it is the way these parameters are allocated, namely for $\text{GNN}_\text{act}$, which adapts the activation function to the graph, that yields significant improvements. \| Method \| ZINC (MAE) $\downarrow$ \| MOLHIV (ROC AUC) $\uparrow$\| \|:--\|:--\|:--:\| \| DiGRAF (w/o ADAP.) with larger $\text{GNN}_\text{Layer}$ \| 0.1388 $\pm$ 0.0071 (337K) \| 79.22 $\pm$ 1.40 (85K) \| \| DiGRAF (w/o ADAP.) (Original) \| 0.1382 $\pm$ 0.0086 (308K) \| 79.19 $\pm$ 1.36 (63K) \| \| DiGRAF \| 0.1302 $\pm$ 0.0094 (333K) \| 80.28 $\pm$ 1.44 (83K) \| Furthermore, we would like to kindly refer you to a similar experiment in our submission. In Table 5, we show that the contribution of DiGRAF (for all variants) stems from the learning of the activation function, rather than adding more parameters to a baseline model. Q3: What are the properties that DiGRAF has but general-purpose activation functions or existing graph activation functions do not have? Can you put up a table to clarify it? A3: We appreciate the reviewer's suggestion. We have identified the desirable properties of activation functions and examined various activation functions in the following table. \| Properties \ Act \| ReLU \| Tanh \| PReLU \| Swish \| Max \| Median \| GReLU \| DiGRAF \| \|-\|-\|-\|-\|-\|-\|-\|-\|-\| \| Boundness \| N \| Y \| N \| N \| N \| N \| N \| Y (within $\Omega)$ \| \| Differentiability Everywhere \| N \| Y \| N \| Y \| N \| N \| N \| Y \| \| Linear Complexity \| Y \| Y \| Y \| Y \| Y \| Y* \| Y \| Y \| \| Permutation Equivariance \| Y \| Y \| Y \| Y \| Y \| Y \| Y \| Y \| \| Lipschitz Continuity \| Y \| Y \| Y \| Y \| Y \| NA in their paper \| NA in their paper \| Y \| \| Graph Adaptivity \| N \| N \| N \| N \| Y \| Y \| Y \| Y \| In practice, the Median-of-medians Algorithm can achieve linear time complexity on average. We discuss these properties in Section 4.3, with proofs of Lipschitz continuity and permutation equivariance provided in Appendix D. We added the Table and a discussion in our revised paper. Q4: How do the properties of DIGRAF influence the convergence and performance?* A4: DiGRAF possesses the key properties typically associated with faster convergence: differentiability everywhere, boundedness within the input-output domain $\Omega$, zero-centrality (Szandala, 2021, Dubey et al., 2022). In our revised paper, we improved the connection between these properties and the faster convergence and performance offered by DiGRAF. Q5: The tessellation size decides the degree of freedom of DiGRAF right? Why does increasing the tessellation size result in marginal changes (non-monotonic)? A5: The reviewer is correct in that the tessellation size determines the degree of freedom of the velocity field. However, our ablation studies (Appendix F) demonstrate that even a small size suffices for the considered tasks. This result suggests that CPAB is highly flexible, and aligns with the conclusions in previous studies on different applications of CPAB (Martinez et al., 2022), which have shown that small sizes are sufficient in most cases. We added this discussion to our revised paper. Martinez et al., 2022. Closed-form diffeomorphic transformations for time series alignment Dubey et al., 2022. Activation functions in deep learning: A comprehensive survey and benchmark Szandala, 2021. Review and comparison of commonly used activation functions for deep neural networks	Summary: This paper introduces DIGRAF, Diffeomorphic Graph-Adaptive Activation Function, which is a novel activation function adaptive to graph data. DIGRAF leverages Continuous Piecewise-Affine Based transformations, possesses several necessary properties of a good activation function, such as differentiability, zero-centering and permutation equivariance. The author allows DIGRAF adapt to graph data by using an additional GNN to learn the final activation function formula. Adequate experiments which take use of DIGRAF in GNNs proved the high efficiency of this activation function. Strengths: 1. The activation function DIGRAF is a good choice for GNN model design, more effective than the common activation function such as ReLU. 2. The soundness of this paper is wonderful. The theoretical proof of DIGRAF’s properties is detailed and experiments in this paper is convictive, which contain node classification, graph classification and graph regression in task level. Weaknesses: There should be an ablation study (can be set in the supplementary part) about the hyper-parameters and training strategy in the process of leaning DIGRAF. Technical Quality: 3 Clarity: 3 Questions for Authors: 1. In the experiments, why was the sigmoid function not used as an activation function? 2. Are there any differences in the DIGRAF learning process for GCN and GIN? Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: 1. As the author mentioned, the current DIGRAF may not be optimal since it was learned only for simple tasks, but it can be improved in future work. 2. The application of DIGRAF has not been discussed or implemented in this research. However, using DIGRAF as a novel activation function in some current models might improve their efficiency. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We are glad to see the reviewer has particularly appreciated the soundness of our paper, while finding the theoretical analysis detailed and the experiments convincing. We proceed by answering the questions raised by the reviewer in the following. We hope that you find our responses satisfactory to consider revising your score. We are welcoming any question, comment, or suggestion. Q1: There should be an ablation study (can be set in the supplementary part) about the hyper-parameters and training strategy in the process of learning DiGRAF. A1: We would like to kindly note that Appendix F contains an ablation study on the effect of the hyper-parameters added by DiGRAF. We found that a small tessellation size is sufficient for good performance, and increasing its size results in only marginal changes (Figure 7). Moreover, increasing the depth of $\text{GNN}_\text{act}$ improves the performance of DiGRAF marginally (Table 6). For regularization, the results (Table 7) reveal that the optimal value of the coefficient depends on the dataset of interest, with small positive values generally yielding good results across all datasets. Also, we discuss the training loss, protocols and hyperparameter tuning in Appendices B and G, respectively. In our revised paper, we improved the link between the relevant parts in the main paper and the appendices. Thank you. Q2: In the experiments, why was the Sigmoid function not used as an activation function? A2: We appreciate the reviewer's observation. We have conducted additional experiments using the Sigmoid function, and added them to our revised paper. As can be seen from the table below, DiGRAF consistently outperforms Sigmoid with a large margin across various datasets: \|Activation\Dataset\| Blog Catalog $\uparrow$ \| Flickr $\uparrow$ \| CiteSeer $\uparrow$ \| Cora $\uparrow$ \| PubMed $\uparrow$ \| \|-\|-\|-\|-\|-\|-\| \| Sigmoid \|39.7 $\pm$ 4.5\| 18.3 $\pm$ 1.2\| 27.9 $\pm$ 2.1 \| 32.1 $\pm$ 2.3 \| 52.8 $\pm$ 6.6 \| \| DiGRAF (w/o ADAP.) \| 80.8 $\pm$ 0.6 \| 68.6 $\pm$ 1.8 \| 69.2 $\pm$ 2.1 \| 81.5 $\pm$ 1.1 \| 78.3 $\pm$ 1.6 \| \| DiGRAF \| 81.6 $\pm$ 0.8 \| 69.6 $\pm$ 0.6 \| 69.5 $\pm$ 1.4 \| 82.8 $\pm$ 1.1 \| 79.3 $\pm$ 1.4\| \|Activation\Dataset\| MUTAG $\uparrow$ \| PTC $\uparrow$ \| PROTEINS $\uparrow$ \| NCI1 $\uparrow$ \| NCI109 $\uparrow$ \| \|-\|-\|-\|-\|-\|-\| \| Sigmoid \| 90.9 $\pm$ 5.5 \| 65.3 $\pm$ 4.8 \| 75.0 $\pm$ 5.0 \| 82.6 $\pm$ 1.4 \| 81.2 $\pm$ 1.6 \| \| DiGRAF (w/o ADAP.) \| 92.0 $\pm$ 5.6 \| 68.9 $\pm$ 7.5 \| 77.2 $\pm$ 3.6 \| 83.0 $\pm$ 1.3 \| 82.9 $\pm$ 2.2 \| \| DiGRAF \| 92.1 $\pm$ 7.9 \| 68.6 $\pm$ 7.4 \| 77.9 $\pm$ 3.4 \| 83.4 $\pm$ 1.2 \| 83.3 $\pm$ 1.9 \| \|Activation\Dataset\| MOLESOL (RMSE) $\downarrow$\| MOLTOX21 (ROC AUC) $\uparrow$ \| MOLBACE (ROC AUC) $\uparrow$ \| MOLHIV (ROC AUC) $\uparrow$ \| \|-\|-\|-\|-\|-\| \| Sigmoid \| $0.8836 \pm 0.043$ \| $69.15 \pm 0.52$ \| $68.70 \pm 3.68$ \| $73.87 \pm 0.80$ \| \| DiGRAF (w/o ADAP.) \| $0.9011 \pm 0.047$ \| $76.37 \pm 0.49$ \| $78.90 \pm 1.41$ \| $79.19 \pm 1.36$ \| \| DiGRAF \| $0.8196 \pm 0.051$ \| $77.03 \pm 0.59$ \| $80.37 \pm 1.37$ \| $80.28 \pm 1.44$ \| \|Activation\Dataset\| ZINC (MAE) $\downarrow$ \| \|-\|-\| \| Sigmoid \| $0.3839 \pm 0.0058$ \| \| DiGRAF (w/o ADAP) \| $0.1382 \pm 0.0080$ \| \| DiGRAF \| $0.1302 \pm 0.0090$ \| Q3: Are there any differences in the DiGRAF learning process for GCN and GIN? A3: There are no differences in the learning process for DiGRAF in GCN and GIN. Specifically, although the GNN layer in $\text{GNN}\_{act}$ aligns with the primary GNN model, $\text{GNN}\_{act}$ still takes in the input graph data and returns the parameter $\theta$ that is used in the activation DiGRAF. In terms of training, we did not change the training procedure for different backbones. We added this important discussion to the revised paper. Thank you. Q4: As the author mentioned, the current DIGRAF may not be optimal since it was learned only for simple tasks, but it can be improved in future work. A4: We thank the reviewer for their comments. While we evaluated DiGRAF on a wide variety of available real-world datasets and tasks, which are widely utilized by the GNN community, it would be interesting to see DiGRAF performance on additional real-world tasks, and we are eager to explore this in future work. Our motivation in demonstrating DiGRAF on such a variety of datasets and benchmarks is to show its general effectiveness, and its ability to cater different communities that utilize GNNs to solve hard problems like drug discovery and weather prediction. Overall, we found that DiGRAF consistently offers better performance than other activation functions, thereby motivating its application in additional tasks. We thank you for the insightful comment, and we added this discussion to our revised paper. Q5: The application of DiGRAF has not been discussed or implemented in this research. However, using DiGRAF as a novel activation function in some current models might improve their efficiency. A5: We believe the reviewer is referring to applying an adaptive activation function, such as DiGRAF, to other domains. While this represents an intriguing avenue of research, it falls outside the scope of the current work, which specifically focuses on graph inputs, as discussed throughout our paper. DiGRAF leverages graph information, making it particularly well-suited for graph-related tasks. We believe however specialization to other domains is possible and we are happy to try in future work. It is also important for us to note that to comprehensively demonstrate the effectiveness of DiGRAF, our experimental section was carefully designed to include different tasks, from node to graph level, inductive and transductive, spanning across various domains, from citation networks to molecular datasets. We further highlighted these aspects in our revised paper - thank you.	Summary: The paper “DiGRAF: Diffeomorphic Graph Activation Functions” introduces DiGRAF, a novel graph neural network (GNN) activation function based on diffeomorphisms. DiGRAF adapts to graph structures and tasks by learning transformation parameters, enhancing performance across various GNN scenarios. The method demonstrates its effectiveness through extensive experiments on node classification, graph classification, and regression tasks, showing significant improvements over standard and graph-specific activation functions. Strengths: 1. Power of DiGRAF: The paper effectively demonstrates the superiority of DiGRAF in various GNN scenarios, showcasing its adaptability and performance improvements. 2. Extensive Experiment Analysis: The experiments are comprehensive, covering multiple datasets and comparing them with various baseline activation functions. 3. Learnable Activation Function: DiGRAF uses a flexible, learnable activation function that is differentiable and bounded, providing desirable characteristics for machine learning applications. Weaknesses: 1. Limited Contribution: The paper appears to be more of an application of CPAB. The primary contribution of the analysis of the connection between CPAB and GNNs is not thoroughly explored. 2. Performance and Gradient Optimization: The paper lacks a detailed analysis of performance and gradient optimization aspects. 3. Clarification on GNN_act: It needs to be clearer how GNN_act helps boost performance. Is there a way to analyze the new source of information it brings? 4. Proofs for GNN: Most analyses focus on the boundedness of the activation function without specifics tailored to GNNs, making it unclear why this approach is particularly suited for GNNs. 5. Edge Classification Performance: The report on edge classification performance is missing. 6. Hyper-Parameter Effects: It is not clear what the effect of each hyper-parameter is on the performance of the activation function. 7. Source Code: The source code is not available. Technical Quality: 3 Clarity: 3 Questions for Authors: How are the parameters {b_j} (orthonormal basis of the space of velocity fields V) calculated? 2. What would be the activation function of GNN_act if the method’s purpose was to design a new activation function? 3. Are there results for other GNN structures beyond GCN? For instance, GReLU reports results for different GNN structures. 4. Since DiGRAF is also applicable to non-graph datasets, would it be beneficial to see its results on other machine learning methods? 5. What is the closed-form solution of the integral in Equation (2) for 1-dimensional vectors? 6. Is there any information on the learned \theta parameters in terms of sparsity or graph structure? Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: Inductive Learning: Since the method is task-dependent, it loses its inductive capabilities and cannot be used for cases it did not see. 2. Hyperparameter Choice: There is a dependency on hyperparameter tuning, which may affect generalizability. 3. Time Complexity: DiGRAF has higher time complexity compared to standard activation functions. 4. Decentralized Tasks: The approach is not ideal for decentralized tasks where there is no central data. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We sincerely thank the reviewer for the insightful comments, and appreciation of our experiment analysis. We now address them. New results and discussions were added to our paper. 1. On Contribution: We distinguish between CPAB's original purpose (signal alignment via diffeomorphism) and our novel use for learning an activation function (Section 4.1 and Figure 4). Additionally, we made several key contributions: (i) Sections 4.2 and 5 demonstrate the importance of correctly parameterizing the velocity field for graph adaptivity, (ii) Section 4.3 discusses DiGRAF's properties, justifying its design and effectiveness as a graph activation function. 2.On Optimization: DiGRAF's behavior is analyzed by its Lipschitz constant (Proposition D.2), related to its optimization[5,6]. Figure 5 and Appendix E.1 show DiGRAF's faster convergence and lower loss compared to other activation functions. 3.On $\text{GNN}_\text{act}$: $\text{GNN}_\text{act}$ adapts the activation function to the graph, by returning the parameter $\theta$ for the learned diffeomorphism. This graph adaptivity is crucial, as shown by DiGRAF consistently outperforming its non-adaptive counterpart (DiGRAF w/o ADAP). Figure 2 in the additional PDF shows learned activation functions for two graphs from ZINC, differing in number of nodes, features, and connectivity. $\text{GNN}_\text{act}$ enables DiGRAF to capture these differences and learn distinct activation functions for them. 4.On DiGRAF Analyses: DiGRAF is well-suited for GNNs because $\theta$, determining the activation function (Equation 7), is learned by $\text{GNN}_{\text{act}}$ (Equation 9), making it adaptive to different input graphs. Our experiments and response 3 highlight that adaptivity enhances performance. 5.On Edge Classification: Following your suggestion, we performed experiments on link prediction using GCN+DiGRAF on the OGBL-Collab dataset (Table 2, Additional PDF), showing that DiGRAF improves ReLU and surpasses DiGRAF (w/o ADAP) on this additional task, supporting our claims of consistent improvements. 6.On Hyper-parameters: We provide experiments on key hyper-parameters (Appendix F). A small tessellation size suffices for good performance (Figure 7). Increasing $\text{GNN}_\text{act}$ depth marginally improves DiGRAF's performance (Table 6). Regularization coefficient $\lambda$ varies by dataset, with small positive values yielding good results (Table 7). 7. On Code: As promised in our submission, we will publicly release the code upon acceptance. 8. On $b_j$:The orthonormal basis $\mathbf{B}$ for the velocity field is obtained via SVD of $\mathbf{L}$, which constrains velocity function coefficients by ensuring consistent values at shared endpoints [4]. 9. On Activation in $\text{GNN}_\text{act}$: We use ReLU within $\text{GNN}_\text{act}$, as it is widely used in GNNs, to make it non-linear. 10. On GNN Structures: Our experiments include GCN and GIN. With your suggestion, we additionally tested GAT [1] and SAGE [2]. Table 1 in the additional PDF shows that DiGRAF continues to consistently offer superior results. 11. On Non-graph data: Graphs are more diverse than other data due to their unstructured nature, making adaptativity more crucial. Still, DiGRAF can potentially be specialized to other domains, like vision, by using a CNN instead of $\text{GNN}_\text{act}$ or our non-adaptive variant. We are eager to explore this in future work. 12. On Closed-form solution: Eq. (2) has an equivalent ODE [4]. By varying $x$ and fixing $t$ the solution to this ODE can be written as a composition of a finite number of solutions: $\\phi^{\theta} (x, t) = (\psi^{t_m}\_{\theta, c_m} \circ \psi^{t_{m-1}}\_{\theta, c_{m-1}} \circ \cdots \circ \psi^{t_2}\_{\theta, c_2} \circ \psi^{t_1}_{\theta, c_1})(x)$ Here $m$ is the number of cells visited. Given $x, \theta$, time $t$, and the smallest cell index containing $x$, $c$, we can compute each $\psi^{t_i}\_{\theta, c_i}(x), i \in \{1, …, m\}$ from $\psi^{t_1}\_{\theta,c_1}(x)$ to $\psi^{t_m}_{\theta,c_m}(x)$. This iterations continue until convergence, with an upper bound for $m$ being $max(c_1, N_P-c_1+1)$, where $c_1$ is to the first visited cell index, and $N_P$ is the number of closed intervals in $\Omega$. Unrolling these steps, we obtain the closed form solution for Eq. (2). 13. On $\theta$: $\theta$ governs the learned velocity field for the activation function. While CPAB transformations don’t require $\theta$ to be sparse, the sparsest vector (zeros) results in an identity activation function. Predicted by $\text{GNN}_\text{act}$, $\theta$ reflects the graph structure and can produce different functions for different graphs, as discussed in response 3. 14. On Inductive Learning: DiGRAF is inductive in the sense of graph learning, it is capable of handling new graphs in tests. By design, it is task and data-driven, which may limit generalization to entirely new tasks. This is common to almost all GNN models, and not specific to DiGRAF. Recent Graph Foundation Models study generalization to new tasks, and it would be interesting to adapt DiGRAF to such models. 15. On Hyperparameter Tuning: Tuning is common in GNNs [3]. Our experiments show DiGRAF's effectiveness across diverse tasks and datasets. The ablation study (Appendix F) demonstrates that DiGRAF performs consistently in different hyperparameters. 16. On Complexity: While DiGRAF requires more computations than ReLU, its asymptotic complexity is still linear (Section 4.3). Table 13 shows DiGRAF is ~3.5x slower than ReLU but offers significantly better performance. Additionally, DiGRAF is 1.35x faster than other graph activation functions and achieves better performance. 17. On Decentralized Tasks: This limitation is common to most GNNs, similar to the discussion in 14. While it is an interesting research direction, addressing it is beyond the scope of our work. --- Rebuttal Comment 1.1: Comment: Thanks for your response. I read it carefully.	Rebuttal 1: Rebuttal: # General Response We would like to express our gratitude to all reviewers for their valuable feedback. Overall, the reviewers appreciated the breadth and depth of our experimental analysis, defined ``extensive`` (mZzm, SUte) and ``comprehensive`` (mZzm). They found our experimental design to be ``robust`` (SUte), and ``adequate and convincing`` (LFcv). They recognized the ``significant improvements`` (mZzm) over standard and graph-specific activation functions, acknowledging our method ``can significantly increase`` (AwEg ) the performance of GNNs. We are also pleased to see that reviewer LFcv highlighted the soundness of our contributions, describing our theoretical proof as ``detailed``. Furthermore, reviewer SUte commented on the clarity of our presentation, noting that our notations and equations are ``well-defined and thoroughly explained`` with ``well-designed figures``, and emphasized that our method addresses the ``most critical questions`` effectively (SUte). Your thoughtful comments and suggestions allowed us to improve our paper, and we provided individual responses to each reviewer. We hope that you will find them satisfactory, and that you will consider revising your score. We are happy to discuss existing or additional questions and suggestions you may have. New Experiments. Several additional experiments were conducted following the reviewers’ comments, as follows: 1. A visualization of the learned activation functions for two randomly chosen graphs from the ZINC dataset, showing how $\text{GNN}_\text{act}$ adapts to different graph structures and results in different activation functions (mZzm, SUte); 2. An experiment on an additional task, namely link prediction, using GCN and comparing ReLU, DiGRAF (w/o ADAP) and DiGRAF, further demonstrating DiGRAF’s consistent improvements (mZzm); 3. Additional experiments using different GNN backbones beyond GCN and GINE, such as GAT and SAGE, showing DiGRAF consistently yields performance improvements, regardless of the base GNN architecture (mZzm), further highlighting the effectiveness of DiGRAF across multiple benchmarks and its applicability to multiple GNN backbones; 4. Additional baselines using Sigmoid as the activation function on all tasks and datasets (LFcv), which we show to be consistently outperformed by our DiGRAF; 5. A comparison of the performance between DiGRAF (w/o ADAP) and DiGRAF using the same number of parameters (SUte). Our results in this experiment further support our findings in the paper, and in particular in Table 5, showing that the performance improvement of DiGRAF cannot be attributed to the (small) increase in the number of parameters, but rather in the way in which they are allocated to obtain graph-adaptivity. All new experiments were discussed in their respective responses, as well as in the added rebuttal PDF. We also added all discussions and results to our revised paper. *** References: [1] Veličković et al., 2018. Graph Attention Networks [2] Hamilton et al., 2017. Inductive Representation Learning on Large Graphs [3] Tönshoff et al., 2023. Where did the gap go? reassessing the long-range graph benchmark [4] Martinez et al., 2022. Closed-form diffeomorphic transformations for time series alignment [5] Scaman and Virmaux, 2018. Lipschitz regularity of deep neural networks: analysis and efficient estimation [6] Xu and Zhang, 2023. Uniform Convergence of Deep Neural Networks with Lipschitz Continuous Activation Functions and Variable Widths Pdf: /pdf/9016a082bed663557dc7f7f0da2dd287d49bb588.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Recurrent neural network dynamical systems for biological vision	Accept (spotlight)	Summary: The paper proposes a hybrid architecture that integrates continuous-time recurrent neural networks (RNNs) with convolutional neural networks (CNNs), named CordsNet, to improve biological realism in vision models. The authors claim that CordsNet matches CNN performance on benchmarks like ImageNet while showing increased robustness to noise. They also present a toolkit for analyzing these models and demonstrate the model's ability to capture time-dependent neural activity. Strengths: 1. The proposed model demonstrates connections to neural behavior and shows effectiveness in dealing with continuous-time modeling. It might inspire future biologically feasible network design. 2. The sharing of weights for convolutional and recurrent operations is novel since these are typically done sequentially in a backbone. 3. The introduction of tools for analyzing convolutional structures in dynamical systems is potentially helpful for future research, but more details are needed. Weaknesses: 1. The comparative result can be conducted more comprehensively. Some comparative results are not conducted on models with the same temporal processing power (Figure 3 only CNN shown). Comparison to similar temporal models such as convolutional RNN and vanilla RNN are lacking. These models can likely exhibit similar behaviors while requiring a less complex training scheme. 2. The choice of image datasets is questionable. The dataset is in discrete-time space, and continuous-time training might not provide any advantages over traditional CNN. The proposed model enables intra-batch information flow between images, which can provide certain robustness to discrete data. Still, the advantages should be more prominent when images in a batch are naturally sequential and have dense temporal information. Technical Quality: 3 Clarity: 3 Questions for Authors: What’s your model’s advantage over a simple sequential design of convolutional preprocessing followed by a dynamical RNN? Confidence: 2 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: 1. The use case of the proposed model is limited and the advantage over discrete-time models is not clear. I believe continuous-time vision tasks are needed to fully demonstrate the effectiveness of this method. Tasks such as video prediction, and video feature extraction might be good candidates. Small-scale experiments can be also conducted on augmented image datasets with more temporal information. 2. The proposed model is novel, but if it provides advantages over existing hybrid models remains questionable. It shares similar design intuitions to convolutional RNN, effectively mimicking the visual preprocessing of visual information followed by temporal processing in a later stage in the brain. Such designs are widely used in the form of CNN + vision Transformer in video processing (XMem, Cheng & Schwing, 2022) and video generation (Video Diffusion Model, Ho et al., 2022) domain where both spatial and temporal processing are conducted concurrently. However, a comparison with such an existing design is not provided. The provided CNN baseline is relatively weak compared to the above-mentioned recent architecture. 3. Intuitively the spontaneous activity attraction is functionally similar to weight decay, whether this regularization term provides advantages remains questionable. Ablation studies can be conducted to provide more rationales behind your design choice since multiple design options are present in your model. 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 suggestions. For the sake of consistency across reviews, we would first like to clarify a few definitions used in our response: - We think that the reviewer is referring to "convolutional RNN" as a CNN connected to an RNN (typically LSTM in literature but could be any type of RNN). This is most likely the widely-adopted definition that the reviewer is using. However, in our response, we will refer to these models as CNN-RNN models. - In contrast, we will refer to convolutional RNNs as RNNs whose recurrence is represented by a convolution, just like in this work. This is also consistent with the terminology used by other reviewers. Advantages over CNN-RNN In the first point raised in the weaknesses section, as well as in the question section, the reviewer made a sharp observation that simply using CNN-RNN architectures would be sufficient to reproduce the results in Figure 3, and therefore questioned the advantage of our proposed model. We raise several orthogonal points below that we hope would help the reviewer see our work in a better light. - Not all results can be reproduced by CNN-RNN. We agree that the results in Figures 3 and (quite likely but we cannot confirm) Figure 5 can be obtained by the CNN-RNN architecture, but the results in Figures 4B and 6 remain exclusive to our continuous-time model. The phenomenon in Figure 4B is attributed to the temporal lag that arises due to every layer being continuous in time and require time to ramp up. Figure 6 compares neural trajectories across time in CNN layers with neural activity in the macaque ventral stream (their biological visual system), but the CNN in a CNN-RNN architecture is static in time. - Applying results from CNN and RNN neuroscience. CNNs and RNNs have both been proposed as models of the brain (or parts of it). By building a hybrid model, we may integrate results from both fields which may lead to unified results and potentially generate new hypotheses about how the brain works. - Redefining expectations for this work. If the end goal of this work is to find a model that can perform the feats that we show in the paper, then CNN-RNNs would probably have an edge over our model. But our goal here is to build models of the brain and help improve our understanding of how continuous-time dynamics work in a competent model of vision. This means that we incorporate biological constraints in our models, even if they are detrimental to final performance. Just like how the brain operates in continuous-time, including its visual system, we build a model that also runs continuous in time. - CNN-RNNs requiring less complex training. We absolutely agree that the computational resources required to train a model with a static CNN is considerably less than the resources required to train CordsNet. We like to view this as a positive aspect of our work, rather than a negative one. We are knowingly building a model that is harder to train, with constraints that are likely to impede training and testing performance (short inference time, continuous-time and recurrent properties offering nothing to image classification performance), so that we can obtain a model that can be used to study the dynamics underlying visual processing in a continuous-time dynamical system. In fact, we consider the success of our training, using our proposed algorithm, to be a key result of this work. Suitability of ImageNet and other use cases The reviewer has raised concern that ImageNet, being a static dataset that does not change in time, may not be the most suitable task for showcasing how our model works. We agree with this viewpoint and are impressed by their pursuit for engineering optimality. Fundamentally, the theoretical and experimental sides of neuroscience work closely with each other. New experiments are conducted from proposed theories, and in turn new models are built from experimental results. Similarly, this work is designed based on influences from a variety of past works in neuroscience. There has been decades of results on dynamical models of the brain, which are still being worked on today. In recent years, CNNs have gained traction in vision neuroscience, and one of the main driving forces of this is the BrainScore platform [(link here)](https://www.brain-score.org/vision/), where CNNs are trained on ImageNet, and their neural activities are then compared to neural data. This also comes with years of results reported by various neuroscience groups. Our goal here is to bridge the gap between results from dynamical system models and results from CNN models for vision. To that end, training and evaluating our model on ImageNet would best facilitate this. Spontaneous activity penalty We thank the reviewer for the suggestion. We have performed ablation studies in the general response that would help clarify your doubts on the impact of this term. We would also like to specifically comment on the reviewer's intuition, which is largely in the correct direction. We cannot make strong claims for non-linear models, but in the linear case of our model, it would be the largest eigenvalue of the recurrent weight matrix that would determine whether the model is monostable or not. This is definitely related to the magnitude of the weights to some extent, just as the reviewer has suggested. --- Rebuttal Comment 1.1: Comment: Thanks for the clarification and the additional file. I'm not very familiar with the related works in the neuroscience community, but based on the explanation and the reviews from other reviewers, I believe this work has a moderate amount of contribution in its field and will adjust my score up by a point. I have some personal questions from a deep-learning perspective, that might or might not related to this work: 1. The goal of this work is to close the gap between artificial neural networks to neural activities(?), is the backpropagation-based optimization inherently unsuitable for this goal? 2. It looks like transformer variants (CVT) have great performance on BrainScore, is your method potentially extendable from recurrence dynamics to self-attention dynamics? --- Reply to Comment 1.1.1: Title: Thank you Comment: We thank the reviewer for their revised score and we are very happy to see that the reviewer is curious about potential future directions of this work. (For meta-reviewing purposes, we would like to state that everything below is not related to the rebuttal and is simply an out-of-scope discussion with the reviewer.) Backpropagation is generally understood to be biologically not realistic, and the reviewer is right to doubt whether models trained with backprop are appropriate for the pursuit of uncovering the mysteries of the brain. Plasticity (the neuroscience term for learning by changing connection weights) is a big field in neuroscience, and our line of work would greatly benefit from implementing a biologically realistic learning mechanism. Right now, backprop remains superior not just for its simplicity but also due to its optimization in hardware by NVIDIA. As such, for now we can argue that we are just interested in the end goal (a trained model that can do some task), and how we get there (backprop) is not too important. See [Table S1](https://proceedings.neurips.cc/paper_files/paper/2023/file/65ccdfe02045fa0b823c5fa7ffd56b66-Supplemental-Conference.pdf) here for a list of influential RNN models in neuroscience, trained by backprop. The reviewer also aptly raised an interesting point that transformer architectures are also doing well on BrainScore. From a neuroscience point of view, visual information processing typically happens in the visual areas of the brain. Biological attention, maintaining fixation, and general interpretation of the visual signal is done brain-wide, and commonly studied in the prefrontal cortex (which includes the frontal eye fields) along with their top-down feedback loops with the visual pathway [(example)](https://www.nature.com/articles/s41586-021-03390-w). We speculate that it would be more appropriate for self-attention mechanisms in vision to be implemented as another brain area, and the interesting way forward would be to understand the interactions between the two models of the two different areas.	Summary: Biological neural networks are continuous-time dynamical systems. However, the previous models that are carefully designed to explain biological networks are discrete-time systems or even non-dynamical ones like convolutional neural networks (CNNs). However, the model that best explains biological vision and achieves high performance on downstream tasks is CNNs. This work fills the gap by creating novel networks that combine CNNs and continuous-time recurrent neural networks called CordsNet. CordsNet is evaluated on a standard ImageNet classification task and also across several standard cognitive neuroscience tasks. Strengths: 1. Biological realism during inference: CordsNet might be one of the most biomimetic deep learning models, as its dynamics are more realistic than other state-of-the-art models like CORnet-RT and CORnet-S. It is motivated by neural dynamics models. 2. A broad range of cognitive tasks are studied: Beyond the ImageNet classification task, this work investigates the responses of CordsNet on several standard cognitive tasks that neuroscientists use to study humans and animals. 3. Benefit of recurrence dynamics over CNN: CordsNet demonstrates the advantage of classification with noisy images over CNN. This suggests the missing piece to make computer vision models more robust, like humans. 4. Great visualization: The visualization is very insightful and provides intuition on how CordsNet works. Weaknesses: 1. Other methods like CORnet-RT and CORnet-S are not evaluated on the cognitive tasks that plug RNN. Therefore, we cannot see if CordsNet is better than others on this benchmark. I believe they can perform the same tasks but they may have different characteristics or different representations than CordsNet 2. CordsNet is trained to predict stimuli at a certain duration, but it cannot accurately predict other durations. 3. The task is supervised image classification where the models learn from rich human labels. Moreover, brains perform with minimal or no strong supervision from others. Instead, brains may learn in a self-supervised manner. It is possible to explore self-supervised learning tasks that are more like what brains do. 4. Embodied tasks are not included: To study the benefits and characteristics of neural dynamics, embodied tasks may be more interesting. Technical Quality: 4 Clarity: 4 Questions for Authors: 1. Citation [36] is wrong. That one is CORnet-S, not CORnet-RT [1]. 2. Why are brain scores low compared to the leader board on the same public datasets? Is the score a neural predictivity score defined in the Brain Score paper [2] or a different metric? 3. How are brain-scores of the proposed method compared to CORnet-S and CORnet-RT? How many total parameters of the CordsNet compared to those models? Reference [1] Kubilius, Jonas, Martin Schrimpf, Aran Nayebi, Daniel Bear, Daniel LK Yamins, and James J. DiCarlo. "Cornet: Modeling the neural mechanisms of core object recognition." BioRxiv (2018): 408385. [2] Schrimpf, Martin, Jonas Kubilius, Ha Hong, Najib J. Majaj, Rishi Rajalingham, Elias B. Issa, Kohitij Kar et al. "Brain-score: Which artificial neural network for object recognition is most brain-like?." BioRxiv (2018): 407007. Confidence: 4 Soundness: 4 Presentation: 4 Contribution: 4 Limitations: A lot if memory is required during training. Flag For Ethics Review: ['No ethics review needed.'] Rating: 9 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We are heartened by the extremely positive review and high regard the reviewer has for our work. We thank the reviewer for their time and encouragement. Comparison of CORNet on tasks in Figure 5 We agree with the reviewer that CORNets could potentially arrive at different solutions compared to CordsNets. This would be in line with our efforts to bring analyses that are commonly found in dynamical systems (such as the cognitive tasks in Figure 5, where a dynamical RNN would have to be plugged) to the CNN vision neuroscience community. It is exactly our hope that our analysis of CordsNet as a dynamical system would spark such applications for CORNets and other models in vision neuroscience. Performance across time of CordsNet We note that since CordsNet arrives at a steady-state at time of inference, it can indefinitely maintain the accurate classification for as long as the image is still presented, even far beyond the trained duration. In addition, CordsNet is also able to reset back to baseline when an image is removed, and correctly classify another new image when it is presented at a later time. These results can be found in Figure 3. Self-supervised learning and embodied tasks We fully agree with the reviewer that the literature of CNNs in neuroscience have progressed far beyond straightforward supervised learning. As a starting point for incorporating dynamical system, we believe that our work will motivate future endeavors on these ideas (including for ourselves). Citation error We thank the reviewer for the clarification. BrainScore clarification In order to evaluate our models' ability to capture temporal signatures in neural data, we had to extend the BrainScore similarity metric to account for time. The original formulation performs a partial-least-squares fit between CNN activations, with shape [number of images, number of nodes] with neural data, with shape [number of images, number of neurons]. This is done with time-averaged neural activity. Here, we make the most minimal extension, so that we are now fitting CNN activations, with shape [timesteps $\times$ number of images, number of nodes] with neural data, with shape [timesteps $\times$ number of images, number of neurons], which means that the time-averaging step is omitted. Without the time averaging step, the BrainScore drops. --- Rebuttal Comment 1.1: Title: Thank you Comment: As the discussion period is coming to an end, we would like to once again thank the reviewer for the positive endorsement of this work, and for taking part in the rebuttal with other reviewers.	Summary: The paper proposes a recurrent convolutional neural network architecture and training algorithm that simulates the biological visual system of mammals. The technical novelty is mostly in the training algorithm which is meant to mimic biological systems, with a first stage of spontaneous activities followed by learning and then again spontaneous activities. Since this process is too computational intensive, the authors introduce approximations, such as initializing from a supervised trained network. The empirical analysis shows that the method is not too far from standard supervised learning while being robust to noise and while exhibiting a behavior that better matches biological systems. Also, the approach is used to predict brain activity data as an application. Disclaimer: My background is machine learning rather than comp. neuroscience. I am not qualified to assess the impact that this work can have in that community and my assessment is mostly limited to the ML side of this contribution. Strengths: + simple and intuitive architecture + generally well written and fluent paper + the loss definition (in its original formulation of eq. 2) is very interesting and novel + nice analysis of how this work relates and contributes to the field of comp. neuroscience + overall motivation and research topic Weaknesses: - important technical details are missing. For instance, in sec. 2 only few lines are used to give a high level description of the architecture. Too much material that should be in the main paper is placed in the appendix (e.g., comparison to supervised CNNs mentioned in the abstract) . Overall the paper is not self-contained and misses critical details. - there is a big approximation between the original loss function and what actually is minimized in practice. If the goal is to simulate a biological system, it is unclear to me how the approximation made fit in the context of that goal. - overall, claims are not entirely supported. For instance, it is not true that on ImageNet the performance is "comparable" to a standard CNN. A difference of 5% is big in that context. Some accomplishments of this work should be toned down a bit. - missing references: There is prior work on recurrent CNNs that is not cited. For instance, Recurrent Convolutional Neural Network for Object Recognition by Liang et al. CVPR 2015 uses the same architecture as far as I can tell. - missing ablations: The authors well ablated the contribution of the recurrent and convolutional part of their model. However, their approach makes lots of design choices which are not very well justified empirically. For instance, what happens if fewer recurrent iterations are used? or what happens if only the top-most fully connected layer are made recurrent? what happens if some terms of the loss are removed? etc. Technical Quality: 2 Clarity: 2 Questions for Authors: I am curious whether the model oscillates when there are multiple interpretation of the input. In the simplest setting, the input could be linearly "mixed-up". I am also curious whether "easy" examples require less iterations to converge. Confidence: 2 Soundness: 2 Presentation: 2 Contribution: 2 Limitations: No concern. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for the helpful suggestions. In response to these points, we have performed additional analyses and made several changes to our submission, as explained below (or referred to general response). Important information in appendix We thank the reviewer for raising this important point. We would like to direct the reviewer to our general response, which provides a detailed plan on how we plan to rebalance the results in the main text and the appendix. Issue of unsupported claims We agree with the reviewer that the performance of CordsNets fine-tuned on ImageNet is lower than their CNN counterparts with the same convolutional layers, and that this discrepancy may possibly be large enough to challenge our claim. We have made the necessary changes to the submission to account for this, as detailed below. - Line 163 updated to read, "We also find that our fine-tuned models perform only slightly poorer than their initial feedforward CNN counterparts, which nonetheless represents a significant improvement over existing continuous-time dynamical models in visual processing." - Line 387 updated to read, "Our fine-tuned CordsNets are able to attain accuracies that are only slightly poorer than their feedforward CNN counterparts." We feel that the term "comparable" is modestly subjective. We initially chose this word because of the current inability of continous-time dynamical systems to process visual information, as seen in the third column of Table S5. Dynamical RNNs are barely beating chance level in a classification task with 1000 classes, which is rightfully "incomparable" to CNNs. By being in a very broad performance range (50% to 80%), we feel that we may use the term "comparable" in this very specific context. However, we will still make the changes above for clarity. At the same time, we wish to also review and defend the other claims that we have made about this work, which we hope that the reviewer would agree with. - Dynamical expressivity analysis. We claimed that we have rigorously explored the possible dynamical regimes that our model can express, and also made comparisons to other model architectures. We provided instances of different dynamical regimes in Figure 1B. In addition to CordsNet, we also trained low-rank, dense and sparse RNNs (Section B.3, which is in the appendix in the initial submission) on five different cognitive tasks in neuroscience (Section B.4), for three different network sizes (Section B.5). We then compared the activity trajectories of all these trained models (results from Figures S2 and S3). - New training algorithm. We have provided full details of our training algorithm in Section 3 in the main text. In addition, we explain certain design choices and perform ablation studies for the loss function in the general response. - Autonomous and robust inference. We show in Figure 3B that our model is able to reset to baseline levels after stimulus presentation, and can then accurately classify a new input image. This supports our claim on autonomous inference. We also provide evidence that our model is robust to noise, due to the "evidence integration" mechanism that is present in dynamical systems. This is explained in lines 190-196, and equation (7). - Analytical toolkit. We claim to provide a toolkit consisting of Arnoldi and power iteration algorithms and partial SVD specifically for convolutional architectures (i.e. our model). We demonstrate the effectiveness of our implementation of Arnoldi iteration in Figure 4A, and applied partial SVD to a particular scenario in Figure 4C. - Image-computable models. We have trained CordsNet appended to a fully-connected RNN on four actual tasks in neuroscience literature (Figure 5, left), and provided evidence of our trained models (Figure 5, right). At the same time, we acknowledge that this analysis is brief, which is why we make no predictions or neuroscientific claims based off our results here. An in-depth investigation on this topic would be outside the scope of this work. The intention is to show the potential applications of CordsNet as a multi-area, image-computable model, which we have delivered. - Prediction of neural activity. We leveraged on a robust and popular benchmark platform known as BrainScore to compute similarity metrics between model activations in CordsNet to actual neural activity recorded in the visual system of the macaque monkey (Figure 6). We show statistical significance in our results. We hope that with this overview, the reviewer would agree with the stated accomplishments of this work. Missing references We thank the reviewer for the citation. and thoroughly comb through relevant literature in our final version. Motivation for loss function and ablation studies We thank the reviewer for this suggestion. We have done an extensive ablation study for our proposed loss function, as detailed in the general response. Model behavior subjected to ambiguous input The concept of multistable perception has been extensively studied in neuroscience, with many theories proposed based on dynamical systems. Coincidentally, we have shown preliminary results on this phenomenon in Figure 4C, where the activity just goes to some interpolated activity space between the two interpretations, which is currently still a steady-state response. --- Rebuttal Comment 1.1: Title: thank you Comment: I'd like to thank the authors for their rebuttal which I found useful to address my concerns. I feel that the revision required to account for including the ablations, moving parts of the appendix to the main paper and address all the other comments will be substantial. Because of this I've only slightly increased my score. --- Reply to Comment 1.1.1: Title: Thank you Comment: We thank the reviewer for their time and reply. We are glad that we are able to improve their impression of this work.	Summary: In this work, the authors proposed CordsNet (Convolutional RNN dynamical system), which provides incorporates a conventional neuroscientific model of RNN incorporating the convolutional layer. Strengths: 1. The authors analyzed the proposed dynamic convolutional RNN from different aspects. 2. Derived batch normalization for the case of linear dynamic RNN Weaknesses: 1. The authors failed to compare it with a series of works named Deep Equilibrium Models (DEQs), which model a layer or a block of layers including the non-linearities as a fixed-point problem. CordsNet is limited to the linear part of the layer while DEQs are not. And DEQs achieved SoTA performance on many large-scale tasks. 2. In the comparison seems Convolutional LSTM/GRU is missing, which is an important family of RNN with Conv layers. Could the authors explain why they are not necessary to be included in the benchmarks? 3. The contribution points are really scattered and don’t feel elaborated enough. Maybe it’s more suitable as a journal paper with more elaborated experimental details for each section. Technical Quality: 3 Clarity: 2 Questions for Authors: 1. Is the analytical formulation of CordNets limited to only linear layer? Confidence: 3 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: The authors discussed the limitations. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Comment: This reviewer (8dkQ) seems to not understand the field of "modelling the primate visual cortex". I suggest you to read this paper: https://www.nature.com/articles/s41593-019-0520-2 before making a new judgement. The proposed method is definitely novel because there is no dynamical model of CNN that can model visual cortex before. The proposed method definitely contributes to computational neuroscience. The proposed method also shows some interesting properties, e.g., in Fig. 5. --- Rebuttal 2: Rebuttal: We thank the reviewer for raising these important points in their review. Our general interpretation of the reviewer's concern is that this work failed to provide what seems to be minimally-required benchmarks, which in turn translates to lack of evidence for any performance improvements. The reviewer is also well-read in the field of convolutional, recurrent and fixed-point architectures, and thus was able to pinpoint key literature that overlap with our proposed work. From this point of view, it can be hard to find significance in this work. As such, we would like to provide a personalized summary of this work that brings the reviewer's aptly-raised concerns into perspective and explains why we believe our work is still a significant contribution despite those concerns. - Dynamical systems in neuroscience study how neural activity evolves over time and how these changes relate to brain functions. They are prevalent in neuroscience, recently in the form of continuous-time RNN dynamical systems with biological constraints such as realistic neuron time constants. - Training with a handicap. Such dynamical RNNs are harder to train than vanilla RNNs in machine learning, because of the continuous-time property that inflates the number of time steps when coupled with the fast time constants present in biological neurons. Since vanilla RNNs are already ill-suited for image processing, this makes dynamical RNNs even harder to train on ImageNet, and for this reason no such model has been proposed to date. - Motivation and potential. Yet, there is a strong need for such a model to be built, so that decades of dynamical systems theory can be applied to a model that can actually process natural images. Such a model would be studied by the theoretical neuroscience community to understand continuous-time dynamics underlying biological visual information processing, which we hope will give rise to new ideas and theories to be tested. - Defining expectations. To that end, our objective is to train the first dynamical system to classify ImageNet at an accuracy that would be deemed as “comparable to CNNs”. We approach this goal with the understanding that the constraints we impose on our model are likely to be detrimental to performance, and we will most likely not be achieving anything SoTA outside the field of neuroscience at this stage; we therefore omit benchmarks typically found in machine learning literature. - Significance of our architecture. CNNs and convolutional RNNs have already been proposed and extensively analyzed in vision neuroscience as candidate models of the visual system. The logical approach would therefore be to build a continuous-time dynamical extension of these models. Such a model would not only build on the work on convolutional architectures by the vision neuroscience community, but also incorporate the legacy of dynamical systems from the wider neuroscience community. - Evaluating our success. The best top-1 accuracy achieved by our models on ImageNet (<60%) is modest compared to what vision models today can do. Understandably, as a result of the aforementioned biological constraints, our models fail to outperform basic CNNs with the same convolutional layers (but we are close). But ultimately, we can reasonably say that the models that we trained are indeed performing some meaningful processing of visual information, and that we have successfully built a dynamical system that can classify natural images. - Focusing on the objective. Finally, we dedicated the majority of the main text, including figures 3,4,5 and 6, to show how our trained model can be studied as a continuous-time dynamical system in various fields of neuroscience, thereby highlighting its potential applications and how it opens up new avenues of research in these areas. We hope that this summary is able to help the author gain a different (and hopefully more optimistic) perspective of our work. We now address specific points raised by the reviewer below. Issue on DEQs We thank the reviewer for bringing DEQs into the discussion. Due to the character limit, we refer the reviewer to our discussion on DEQs in the general response. Issue on linearity CordsNet is nonlinear in the exact same way that RNNs or DEQs are nonlinear. The evolution of activity across time in CordsNet is described by equation (1) in the main text, which includes a ReLU activation function. While training the nonlinear model, we split training into several stages (Figure 2B), and one of the stages involves linear models (lines 142-152), which may be the source of this misunderstanding. Comparison with convolutional LSTM/GRU There are two key reasons why comparison with gated RNNs is not necessary. - Artificial gating mechanisms are not biologically-realistic and do not fall within our objectives. - We are trying to model the biological visual system, which is (generally) not the part of the brain that stores memories or makes decisions based on long-term dependencies. Our task is classifying ImageNet, where gating mechanisms may not offer much advantage. Issue on scattered points We thank the reviewer for the suggestion. Overall, we feel that this work lies comfortably in the intersection of machine learning and neuroscience, and that there would be an audience for this work in this conference. We also acknowledge the reviewer’s concern that the work presents too many points that have not been sufficiently covered. CordsNet is both a dynamical RNN and a CNN, where each architecture, on their own, has been studied by the neuroscience community for years. As such, the narrative of our paper is focused on introducing the model, how it compares with past RNN or CNN models in neuroscience, and briefly demonstrating the many ways in which new research directions can be explored using this hybrid model. It is also why we developed tools to help analyze our model (lines 214-216). --- Rebuttal Comment 2.1: Comment: I thank the authors for the detailed rebuttal which convinced me comparison with sota computer vision models is not necessary in this work. The work is more related to the CORNet works and in that context I can better appreciate the contributions. Thus I am raising the ratings. I am also curious about whether such modelled architectures have advantages over artificial neural networks such as in (adversarial) robustness. But this is out side the scope of this work I understand. --- Reply to Comment 2.1.1: Title: Thank you Comment: We thank the reviewer for taking the time to better understand our work and appreciating our results from a different angle. (For meta-reviewing purposes, we would like to state that everything below is not related to the rebuttal and is simply an out-of-scope discussion with the reviewer.) The reviewer made a sharp observation by considering the advantages of biological visual perception (which is essentially immune to the kind of adversarial images that plague artificial models), there might be some potential to exploit this and improve artificial models. In general, biological perception differs from machine perception in the following ways: - context awareness, where the entire image is interpreted as a whole and the subject can predict what might happen next or relate what they are seeing with past experience - biological attention mechanisms, in which subjects can focus on certain stimuli by adjusting their brightness sensitivity and maintaining fixation - 3D perception, where a 2D input image is understood as a 3D scene in the mind of a subject - multisensory integration, where hearing and smell can influence a visual percept among many others. These factors contribute to biological holistic scene understanding, leading to robustness. The reviewer is right that there is potential for biologically-motivated models that incorporate any of these effects to be a contribution for the machine learning community. As a pure speculation, we think early implementations of these effects would make training harder, and may result in a robust model but with lower classification performance, just like in our work. The common theme of all the aforementioned mechanisms is that they all need time to process in a biological brain, which is why we hope that our work can inspire these types of research directions in the future.	Rebuttal 1: Rebuttal: We thank all reviewers for their time and effort in reviewing our submission. We will address common issues here. Important details in Appendix Reviewers A7p2 and 7DkU raised the issue that important results are reported in the appendix, and recommended for their (minimally) brief inclusion in the main text. We agree with this point, and provide a summary of all the changes to our submission below. This summary includes additional changes requested from other reviewers as well. 1. Introduction (additional 3-4 lines) - mention existing works on recurrent CNNs in machine learning literature - briefly mention DEQs and their relevance to this work (complete review in the appendix) 2. Model architecture (additional 15-20 lines) - introduce the model architecture in a more complete way - include details of the analysis from Appendix B 3. Training and results (additional 5-10 lines) - move the technical derivations to the appendix (lines 139-156) and briefly describe them in the main text - include brief descriptions and state results from the ablation studies in the appendix - move parts of Table S5 into the main text and interpret the results 4. Model analysis (reduced by 15-20 lines) - remove Figure 3A as Figure 3B illustrates a similar point - remove explanations about Figure 3A 5. Applications (reduced by 5-10 lines) - remove the methodology for BrainScore in the main text (lines 236-242) and instead elaborate in detail as a section in the appendix These changes are expected to stay within the 9-page limit. However, if our work is accepted, we would also make full use of the additional page to remedy the information load in the appendix. Comparison to DEQs Reviewer 8dkQ commented that comparing our model to DEQs is necessary and important. DEQs are inherently similar to RNNs, and therefore CordsNets by transitivity. To address this point, we will mention DEQs in the introduction in the main text, as well as a more in-depth review of the differences between CordsNets and DEQs as a subsection in Appendix A. Fundamentally, DEQs are focused on arriving at a fixed point required for the completion of some task. In contrast, we proposed CordsNet as a model of the biological visual system, and we are concerned with the model activations before, during, and after steady-state inference has been achieved, so that we may compare them with experimental data and generate new hypotheses on how the brain works. - CordsNet expresses a range of dynamical behaviors depending on the required task, including oscillatory, chaotic and stable dynamical regimes (Figure 1B). Even within the stable regime, which results in fixed points, they manifest in different patterns, such as point, line and ring attractors (Figures 1C, 1D and S3). Evidence of these temporal behaviors have been found in the brain, which is the focus of this work, even though they may not be ideal for tasks. On the other hand, DEQs prefer fixed points only, in the true spirit of machine learning that seeks optimal performance. - When DEQs complete a task, the simulation ends. They are run again from scratch for the next task. In contrast, a biological brain runs perpetually, even when there are no tasks. CordsNet follows the same principles, and returns to some baseline activity by itself without external interference after the input image is removed (Figure 3B). Another image can then be presented for future inference. Ablation studies Reviewers 7DkU and UEUJ have requested for certain ablation studies to be performed in order to justify several design choices in our models. We carefully disect each term in our loss function, as shown in equation (1) of the rebuttal PDF. Firstly, we note that the goal of our model is to bring together the results from CNN vision neuroscience and RNN cognitive neuroscience communities. To that end, we have to select a suitable objective that is guided by experimental literature (Figure R1 in rebuttal PDF). This influences the inference window in which we aim to minimize the cross-entropy classification loss, and also determines the neuron time constant of 10ms, as well as the way stimuli is presented to the model. We next look at the effects of introducing the spontaneous penalty term (Figure R2). In order to do so, we train 20 CordsNet-R2s on the CIFAR-10 dataset for 6 different values of penalty coefficients, for a total of 120 models in this analysis. Without the spontaneous penalty term, we find that the solutions can fall in three broad dynamical regimes: unstable, multistable and monostable (Figure R2A). In the unstable regime (top row), neural activity explodes after stimulus presentation, and never recovers, which is undesirable. In the multistable regime (middle row), the model remains stable throughout the first stimulus presentation, but is also unable to return to baseline due to the presence of additional attractors in its activity space. As such, when a second image is presented, it is unable to make the correct classification, despite being stable. The only solution that we want is the monostable case. Figure R2B presents the effects of different penalty coefficients on the types of solutions obtained. We find that our choice of $10^{-3}$ is ideal for only allowing monostable solutions. We also performed an ablation study on the log-weights that we have introduced to our cross-entropy term. Here, we trained 10 CordsNet-R2s for 5 different log-weighing scales. We find that without this term, there is a small chance that a transient solution is obtained (Figure R3B), where the model does not arrive at a fixed point, but is instead optimized to only classify for the particular inference window. As such, it is unable to exhibit most of the other properties that our models in the main text have. By introducing this weighing scheme, we have eliminated this class of solutions. Pdf: /pdf/2fe16d9b6063fd26efe292e5c42d0567d4ec837d.pdf	NeurIPS_2024_submissions_huggingface	2,024	Summary: Inspired by neuroscience, the authors propose to introduce recurrent connections in conventional convolutional neural networks (CNNs). The resulting model shows comparable performance with regular CNNs, but exhibits higher noise robustness. The authors also developed a toolkit to analyze the resulting architecture, using iterative and dimensionality reduction methods. The architecture is used to model complex cognitive tasks, mimicking the higher order visual areas in the monkey. Strengths: - This paper seamlessly weaves inspiration from neuroscience, dynamical systems theory, learning algorithms, analysis methods, performance, and modeling and replicating results from neuroscience experiments. - Introducing continuous dynamics into CNN+RNN seems to exhibit really interesting properties. - Analysis of the dynamical behavior by finding the eigenvalues directly from the recurrent weight matrices is interesting. This has been used to uncover some really interesting dynamical patterns dependent on the time of classification (fater or slower inference). - The use of the model in various visual cognitive tasks (in V4 and IT) is also quite impressive. Weaknesses: - Too much technical details are hidden in the appendix. Please at least provide a brief sketch in the main text. Technical Quality: 4 Clarity: 3 Questions for Authors: Questions - Isn't the task in Fig 5D handled by area MT? Have you considered computing the BrainScore for this? In general, can results in Fig 5 be compared to the experimental literature? Comments - There is an earlier recurrent CNN than the one cited: Ming Liang and Xiaolin Hu. Recurrent convolutional neural network for object recognition. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 3367–3375, 2015. Confidence: 3 Soundness: 4 Presentation: 3 Contribution: 4 Limitations: The discussion/conclusion provides adequate assessment. Flag For Ethics Review: ['No ethics review needed.'] Rating: 8 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We truly appreciate the reviewer for the encouraging and positive review. Technical details in the appendix The reviewer has expressed concern that important technical details that are in the appendix should briefly be mentioned in the main text. We agree with this point and refer the reviewer to the general rebuttal for all the changes we plan to make to our submission. Random dot motion task and area MT The reviewer has correctly mentioned experimental literature pertaining to evidence of neural activity tuned to random dot direction and coherence in area MT in the dorsal stream. In general, the RNN that we append to the back of our model represents either a decision-making part of the brain, such as the prefrontal cortex, or a motor region such as the frontal eye fields (which is still prefrontal). While MT contains direction-tuned cells, the eventual motor response (in the form of eye saccades) would likely be similarly tuned. However, this is ultimately an (unsubstantiated) interpretation on our end. A more rigorous analysis is required for any conclusions to be drawn. Interpretation of results in Figure 5 The main goal of the results in Figure 5 is to illustrate the point that we can now build completely continuous-time models that accept real images as an input, rather than abstract one-hot vectors as found in many past works. We do provide some interpretation of the solutions we found, but to draw any conclusions about the brain from this would require a much more in-depth analysis that is currently outside the scope of this work. We do not have the neural data to compute BrainScore, and we foresee that the dataset would not be big enough (small number of coherence levels) for strong statistical significance. Missing citation We thank the reviewer for pointing out this missing citation, we will add this citation into our introduction. We will also thoroughly find and include other relevant literature in our final version. --- Rebuttal Comment 1.1: Title: Detailed comments appreciated Comment: Thank you for the detailed response. The proposed revision plan also looks reasonable. --- Reply to Comment 1.1.1: Title: Thank you Comment: We thank the reviewer for the acknowledgement and once again would like to express our appreciation for the positive review.	null	null	null	null	null	null
Voila-A: Aligning Vision-Language Models with User's Gaze Attention	Accept (spotlight)	Summary: This work proposes an approach to align Vision-Language Models (VLMs) with users' gaze. To develop such a method, the project first creates a mock dataset of human gaze from image captions, known as Voila-coco. It then develops a model to integrate gaze data into VLMs. Additionally, a new dataset called Viola-gaze has been introduced. Strengths: This paper proposes an interesting idea of aligning the attention of vision-language models to human attention indicated by fixation locations. It contains several components ranging from data collection to model development. Weaknesses: - Motivation: The motivation for aligning VLMs to gaze attention is to enhance the models' interpretability and effectiveness (L8). However, if I didn't miss anything, the experiments do not evaluate interpretability. More importantly, it is not clear to me why textual descriptions are not enough in the provided application scenarios and what the benefits of incorporating gaze are. - Clarity: I find it difficult to follow and understand what exactly has been done in the project. For example, Sec. 2 explains that this project uses BubbleView to collect gaze-like data. However, the motivation to do so is not clear. It is also not clear how good the transformation of trace data to pseudo gaze sequences is. Overall, the write-up and general presentation can be improved. - Limited technical contribution: I understand the challenge when training with limited data, however, this also limits the design of the model. The encoding of heatmap generated from gaze sequences seems to have limited technical contribution. - Evaluation: first of all, it is not clear what Otter and Kosmos2 refer to and why they are chosen for comparison. It is also not clear what the GPT-4 ranking results mean. Similarly, why not just directly use human preference to evaluate the performance of VOILA? What's the performance of the reward-scoring network? It seems to me that both evaluation methods need to be evaluated first. Technical Quality: 2 Clarity: 1 Questions for Authors: - Why textual descriptions are not enough in the provided application scenarios, for example directly include orange in the question instead of using it with gaze point? - What are the benefits of incorporating gaze? - Why not use an eye tracker to directly collect gaze instead of using BubbleView? - What do Otter and Kosmos2 refer to? Why are they chosen for comparison? - Why not just directly use human preference to evaluate the performance of VOILA? What's the performance of the reward-scoring network? - Similarly, what would be GPT-ranking results compared to human preference? Confidence: 4 Soundness: 2 Presentation: 1 Contribution: 1 Limitations: The authors have addressed the limitations to a very limited extent. There is no discussion related to the gaze modality and the limited amount of data for example. Flag For Ethics Review: ['No ethics review needed.', 'Ethics review needed: Research involving human subjects'] Rating: 3 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We sincerely appreciate your critique of our work and will take your comments into consideration for future revisions. We would like to clarify a few points that may have been misunderstood, hoping this will enable you to re-evaluate our work more accurately. W1 & Q1, Q2 on Motivation We envision that gaze-facilitated visual question answering may take place on future wearable head devices, such as VR/AR and smart glasses. During such an interaction process, users may ask contextual questions that have proven to be ambiguous by many human-computer interaction (HCI) researches, such as using pronouns to refer to surrounding objects. Therefore, using "it" instead of the object name, which is the indirect question in our case, is very likely to happen in real-life scenarios. Furthermore, with advanced devices like the Apple Vision Pro utilizing gaze as a crucial interface for spatial computing, the integration of gaze tracking into Vision-Language Models (VLMs) presents an important yet unexplored challenge. Another important use case of incorporating gaze is visual question answering for visually impaired people. The VizWiz-VQA-Grounding, which we also evaluated VOILA on in Appendix I, presents questions collected with blind people and the majority of these questions have at least one pronoun in them. W2 & Q3 on the process of gaze collection The main experiment in this paper is the gaze-incorporated VLM, which refers to Voila. To train Voila, one challenge lies in the training data, where it is hard to collect a large-scale gaze VQA dataset. Alternatively, we used a mouse trace dataset called Localize Narrative as a substitution and constructed visual questions using GPT-4, thus we derived a trace-augmented VQA dataset, which we refer to as VOILA-COCO in this paper. The above is the main workflow of our project. However, we need to prove that mouse trace can be an approximation for gaze trace, even though this approximation has been used for many HCI research already. This is the reason why BubbleView is used in Section 2: we want to illustrate one basic belief of our work before we dive into it. To illustrate this, the VOILA-GAZE dataset we collected already contains gaze trace data because it is collected by gaze-sensing smart glasses, then we use BubbleView to derive mouse trace annotation on the same dataset. By comparing the two trace modalities, we provide strong evidence for using VOILA-COCO as the training dataset for a gaze-incorporated VLM. W4 & Q4, Q5 on Evaluation We choose Otter and kosmos-2 for several reasons: 1. these two models each represents a typical VLM architecture. Current dominat VLM architectures are either cross attention based where visual feature is injected to each layer of language backbone, or token based where visual tokens were treated similarly to language tokens in an autoregressive manner. For the baselines we've chosen, Otter and Kosmos-2 are both fully open-sourced and received hundreds of citations, representing each type of VLM architecture mentioned above. 2. Compared to other Open-flamingo based VLMs, Otter is tuned on a Multi-modal in-context instruction tuning dataset (MIMIC-IT), which we believe that building upon Otter should be the best choice for a user-centered QA manner like Voila, because Voila's use case also involved in-context querying and need to follow user's instruction. 3. Compared to other VLMs that have similar architecture to Llava, Kosmos-2 has grounding ability by inputing bounding-boxes, which is the most common strategy of incorporation location information currently, thus forms a comparable baseline against our location injection strategy. There are 2 major concerns about using human preference: 1. For the majority of questions in VOILA-COCO, the correctness of an answer can be judged with a reference answer and ground truth description given, while human preference is necessary for tasks that can not be judged objectively such as writing or image generation. 2. The goal of this paper is to establish a groundwork for gaze-facilitated VLMs, therefore reproducibility is very important. This yields the demand for an autonomous evaluation pipeline instead of human preference, which results may vary depending on multiple factors, such as region/religion/education/gender/etc. However, as a user intention incorporated VLM, reflecting user preference during the evaluation process is indeed a matter. We believe the GPT-4 ranking metric can reflect user preference since it is trained with tons of user preference data through RLHF, further, we believe that the user preference data used in GPT-4 should generally be more unbiased. This has also been demonstrated in many other works such as GPTScore[1], GPTRank[2]. [1] Fu, Jinlan, See-Kiong Ng, Zhengbao Jiang and Pengfei Liu. “GPTScore: Evaluate as You Desire.” ArXiv abs/2302.04166 (2023): n. pag. [2] Liu, Yixin, Alexander R. Fabbri, Pengfei Liu, Dragomir R. Radev and Arman Cohan. “On Learning to Summarize with Large Language Models as References.” ArXiv abs/2305.14239 (2023): n. pag. --- Rebuttal 2: Comment: I thank the authors for providing the detailed clarification and appreciate the effort. Regarding motivations: the current statement doesn't mention anything related to "interpretability and effectiveness" which was originally mentioned in L8, instead it focuses on using gaze in applied settings to refer to objects. What are the relevant HCI works that show languages are ambiguous? Gaze is also ambiguous as people naturally move their eyes and identifying the right fiction that is intent-relevant is also not trivial. I might miss something here, how is gaze going to help visually impaired people? Could you please comment on this? Thanks! --- Rebuttal Comment 2.1: Comment: We would like to clarify the points raised and ensure the intended message of our work is conveyed effectively. Regarding interpretability, it is indeed referenced once in the abstract to conceptually emphasize that a VLM that is well-aligned with the user's gaze intention can yield responses that are more comprehensible and practical for human users. This concept is central to our research and our contributions in this area are clearly stated in the introduction for your convenience. Concerning the role of gaze in assistive technology, we acknowledge in the introduction the comprehensive review by Zhang et al. [58], as well as recent human-computer interaction (HCI) research, such as GazeGPT [1], which examines similar trends. Our argument is not that gaze is the sole determinant of a model's response but rather that it is a significant signal that, when integrated with language, can enhance the user experience. Our empirical work demonstrates that current VLMs often struggle with ambiguous language, which is prevalent in everyday communication. By incorporating gaze data, our model aims to interpret user intent more effectively, a finding supported by both qualitative and quantitative evidence in our study. It is also crucial to highlight that a substantial demographic of visually impaired individuals, including those with Amblyopia, myopia, and astigmatism, can provide accurate gaze signals despite their visual limitations. For these users, a VLM that can accurately align with their intentions can serve as an invaluable aid, a point that our research addresses and substantiates. We appreciate your attention to these details and are happy to provide further information if required. [58] R. Zhang, A. Saran, B. Liu, Y. Zhu, S. Guo, S. Niekum, D. H. Ballard, and M. M. Hayhoe.556 Human gaze assisted artificial intelligence: A review. IJCAI : proceedings of the conference,557 2020:4951–4958, 2020. [1] GazeGPT: Augmenting Human Capabilities using Gaze-contingent Contextual AI for Smart Eyewear	Summary: In their paper, Voila-A: Aligning Vision-Language Models with User’s Gaze Attention, the authors introduce a dataset, a new model architecture Voila-A, which is a cognitively-enhanced VLM. After motivating the research and introducing both the datasets and model design, the authors cover a lot of experiments on the new open-source benchmark dataset. After evaluating their model and some baselines, they perform an ablation study and conlude the paper. Strengths: New open-source dataset in a low-resource modality (gaze, trace). New open-source benchmark constructed from the dataset mentioned above. New open-source VLM model (including training procedure etc.), based on OpenFlamingo that integrates both gaze and trace. In detail description of the model and each layer as well as experimental details. Mostly nicely written. Extensive ablation study. Weaknesses: Missing comparison to previous VQA/VLM models, e.g. Sood et al. [43], only one baseline mdel (Otter-Base). Unclear how hyperparameter were tuned. Presentation needs some work e.g. 223, 249, 276, replace \cite{ by ~\cite{ for more readability. Technical Quality: 3 Clarity: 3 Questions for Authors: What does Voila-A stand for? Why didn't you compare to more baseline models? Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: Yes Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We sincerely thank you for your support of our work and for your attentive reading and thoughtful suggestions. Baseline models Note that except for Otter, we also have Kosmos-2 as baseline, as shown in Figure 5 and 6. For reference [43], this is a paper published in 2020 and in their experiment description, they stated that all the models they used were published before 2019, which VLMs haven't emerged back then, therefore comparing our Voila to their models may be unfair and liekly to have obvious outcome. We choose Otter and kosmos-2 for several reasons: (1) these two models each represents a typical VLM architecture. Current dominat VLM architectures are either cross attention based where visual feature is injected to each layer of language backbone, or token based where visual tokens were treated similarly to language tokens in an autoregressive manner. For the baselines we've chosen, Otter and Kosmos-2 are both fully open-sourced and received hundreds of citations, representing each type of VLM architecture mentioned above. (2) Compared to other Open-flamingo based VLMs, Otter is tuned on a Multi-modal in-context instruction tuning dataset (MIMIC-IT), which we believe that building upon Otter should be the best choice for a user-centered QA manner like Voila, because Voila's use case also involved in-context querying and need to follow user's instruction. (3) Compared to other VLMs that have similar architecture to Llava, Kosmos-2 has grounding ability by inputing bounding-boxes, which is the most common strategy of incorporation location information currently, thus forms a comparable baseline against our location injection strategy. Presentation Issue 1. Hyperparameter settings can be find in Appendix F. 2. We will proof read again and fix format issues.	Summary: This paper proposes Voila-A, an instruction-tuned VLM that integrates “gaze” information. The instruction data is constructed using tracing data from “Localized Narratives” and GPT-4 assistance, then converted to gaze-like data using the Bubbleview method. The overall approach is evaluated on newly collected datasets: Voila-COCO with 1900 questions (in the test set) and Voila-GAZE with 200 questions. A GPT-4 aided ranking of Q&A is employed to compare Voila-A against Otter (image input only) and Kosmos-2 (also takes bbox inputs), where Voila-A is shown to out-perform the baselines on both the synthetic and real-world evaluation datasets. Strengths: The authors motivate their case for a gaze-guided instruction-tuned VLM well. Understandably, collecting sufficient real-world gaze data can be challenging, so the authors propose to convert trace data from the Localized Narratives dataset to pseudo-scanpaths using Bubbleview - this is a creative and realistic solution to their problem. In addition, the authors collect real-world data using the Pupil Labs Invisible eye tracker from 21 participants and show that their proposed Voila-A out-performs contextual (Otter) and bbox-guided (Kosmos-2) approaches as assessed by GPT-4. Weaknesses: The proposed method in terms of the Voila Perceiver Resampler and Block (VPR and VPB) generally make sense. However, the decision on how to define the K, Q, and V are insufficiently motivated. Ideally, it would be good to see at least a simple ablation study to justify the design decisions that depart from the original Flamingo architecture. The main results are easy to understand, especially when viewed with the Appendix in mind. However, it is a purely GPT-based evaluation and while it is a good effort, one wonders whether there could be a more objective and quantitatively distill-able way of measuring performance. For example, one could evaluate referring tasks or use a user survey to evaluate the methods against each other. A user study could be particularly helpful, as it would evaluate the quality of the VOILA-GAZE dataset simultaneously (and it only consists of 200 questions). Technical Quality: 3 Clarity: 3 Questions for Authors: - What is “1k gaze” (mentioned on page 3)? - It is mentioned in Sec. 3.4 that “the g in each VPB are initialized as 0”. How do these gating values look post-training? Does the value increase in later layers, or earlier layers? Why not initialize to random or non-zero-constant values? - Would Voila-A perform well in referring expression comprehension tasks such as RefCOCO, in comparison to Kosmos-2? Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The authors briefly discuss the limitations of their work in Appendix A. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Dear reviewr 3dvo, we sincerely thank you for your support of our work and appreciate your thoughtful suggestions that have helped us improve. W1 Regarding the Perceiver's choices for Key (K), Query (Q), and Value (V), we can delve into a clearer explanation here. The primary function of this component is to condense visual information into compact latent representations, which can subsequently be utilized for cross-attention with language models. In this setup, the Q are derived from the latent representations, while the K and V originate from the visual inputs. However, calculating K and V from the latents as well allows for an efficient self-attention mechanism within the latents themselves. In section 4.3.2 and Figure 16, we compare more design choices beyond Flamingo structure. W2 Thank you for your kind suggestion. Our primary goal is to establish a reproducible automated benchmark, and as such, most of our evaluations are conducted without the inclusion of supplementary user surveys. To guarantee that the question-answer pairs are amenable to automatic evaluation, each reference answer has undergone meticulous review by our dedicated annotator and has been subject to a rigorous double-checking process during the selection of the final test cases. We acknowledge the potential benefits of a user study on the voila-gaze results and will take into consideration the incorporation of such a study to further validate the dependability of our automated metrics. Q1 Note that Section 2's motivation is to demonstrate the similarity between gaze trace and mouse trace so that training with VOILA-COCO can make sense. Therefore, we collected some mouse trace data on the VOILA-GAZE dataset to compare with its gaze trace. For this comparison, the gaze trace contains 1k sample of gaze points. Q2 We observe that the value of 'g' is larger in the median layers, whereas it is relatively smaller in both the later and the earlier layers. We initialize 'g' to zero to guarantee that the output matches that of the original model at the start of training. Q3 RefCOCO's referring expression comprehension task requires models to predict a bounding box with a given referring phrase, however, our VOILA model does not possess the ability to generate bounding boxes as it is not trained on such data. Instead, we were able to test VOILA's overall referring expression comprehension ability using VizWiz-VQA-Grounding dataset (as shown in Appendix I). VizWiz dataset is specially collected for answering visual question for blind people and the majority of VizWiz-VQA-Grounding dataset contains pronoun usage in the questions. Therefore, to accurately answer VizWiz's question, the model should understand what the pronoun refers to in the image. --- Rebuttal Comment 1.1: Comment: Thank you very much for your explanations and clarifications. It helps me understand the paper better. While I like the work very much, the purely synthetic nature of the evaluation is somewhat concerning. I see that in your response to Reviewer qe53, you mention the GPTRank paper which was recently accepted at NAACL 2024. In that paper, the authors show that LLM-based evaluation and human-based evaluation can have differences. Though we are looking at different tasks (summarization vs VQA), I wonder if it is essential to include some human evaluation in a work such as Voila-A. I understand that the GPT-4 ranking method was introduced to allow your evaluations to be reproduced. However, would you say that in your work, sufficient evaluations were done to demonstrate the necessity of integrating gaze information into VLMs? --- Reply to Comment 1.1.1: Comment: Thank you for your insightful comments. We acknowledge the importance of a comprehensive user evaluation and appreciate your concern in this regard. Due to the constraints of time, we were able to conduct a preliminary user survey involving five participants. Each participant was asked to evaluate 50 queries using both Voila and Otter. The outcomes of this survey indicated that Voila had a winning rate of 52%, a tie rate of 36%, and a loss rate of 12%. These results are in close agreement with the GPT-rank findings presented in our main results, suggesting a consistent performance trend. We recognize the value of a more extensive user study and are committed to conducting a thorough evaluation on the entire Voila-Gaze test set. We intend to include this expanded analysis in the camera-ready version of our paper, which we believe will provide a more robust validation of our findings.	Summary: The paper aims to improve the integration of VLMs in real-world applications such as AR/VR by making the interaction seamless and user-centric. This is achieved by incorporating users’ gaze information into the VLM for a more natural conversation and a frictionless experience. First, the LN-COCO dataset is proposed as a benchmark to train models for this task, after experimentally validating that mouse traces can be used as a proxy for gaze behavior. Furthermore, the authors collect and annotate VOILA-GAZE with real gaze data to be used as another test set. Second, the authors introduce the VOILA architecture which takes an image, a gaze heatmap, and a related question as input, and provides an answer as output. This model is compared against two popular VLMs on the two benchmarks using two newly introduced performance metrics. Ablation studies are also conducted to validate model design choices and training schedules. Strengths: - The paper is really well-written, easy to read and sufficiently illustrated. The motivation is thoughtfully outlined, and the contribution is clearly stated and properly contextualized relative to prior works. - The paper addresses an important and original research topic that is severely underexplored despite being very relevant and holding significance for certain applications. - The introduced benchmarks VOILA-COCO and VOILA-GAZE are novel, and will be useful to the broader community working on this topic. - Overall, the proposed Voila model seems to outperform other baselines (Otter and Kosmos-2) on both datasets according to the chosen metrics. Weaknesses: - The biggest problem I have with the paper concerns the main experiments. The authors compare Voila to Otter and Kosmos-2, however important information about the evaluation is missing or unclear, which makes the interpretation of the results difficult: - It is not clear whether the baseline models are trained on VOILA-COCO or simply evaluated. - It is not explained how the authors deal with direct vs indirect questions during training and evaluation. In figures 5 and 6, are they counted as two separate instances? Or is only one of them selected? In this case, which one? - Voila takes the gaze information as input, but it is not clear whether Otter and Kosmos-2 are fed that information as well. The comparison would be unfair in the latter case, especially since we have coreference queries with pronouns like “it” and no location information to disambiguate the intent. In L393-394, it is mentioned that Kosmos-2 can take bounding boxes as input, but does this mean it is used this way during evaluation to consider gaze input? Also, even for Otter which is not specifically designed to include location information, it would be possible to inject it in the text prompt (similar to the design in Figure 16 top-right and bottom-right) - Some quantitative results are suspiciously surprising. In table 2, the winning rate, which I assume is based on the GPT4 Ranking metric, is only 1% better for Otter with direct queries (51%) compared to indirect ones. How is this possible if Otter doesn’t have access to gaze information to disambiguate the question? I would expect many answers to be completely incorrect for any question that is not focused on an obviously salient part of the image. Also, all variants of Voila (including in-context prompt) underperform the base otter on indirect queries according to the same metric, even though Voila explicitly uses gaze. The numbers for the reward score, on the other hand, are more reasonable. - There is limited novelty in the architecture itself, since all the components are exactly like the Flamingo model. The contribution of the paper is in the introduction of the gated gaze heatmap tokens as an additive soft bias to the keys K computed from the image tokens within the Perceiver module. However, as far as I’m concerned, the value of the paper lies more in investigating and establishing the groundwork for an important research direction by proposing benchmarks, protocols and baselines for more works to follow. Technical Quality: 2 Clarity: 4 Questions for Authors: - L25-27: needs a reference or experiment to back it up. How is the limited alignment with human gaze detrimental for VLMs? - The resolution of the word clouds in Figures 10, 11, and 12 should be increased - Why is the (key of the) gated gaze feature added to (key of the) image features instead of multiplication? - Why is the VPR using an attention between latent embeddings, and a concatenation of latent embeddings and image tokens (+gaze tokens) instead of the more natural cross-attention from the latent embeddings to the image+ gaze tokens? - Is the learnable gating parameter $g$ a scalar or vector? - L274: What is meant by “the input and output embeddings of the language encoder”? - Is the model trained for 2 (L272-274) or 3 (L737) epochs? - Related to the previous point, the color of the Voila Perceiver Resampler module in figure 4 is inconsistent with the text. The figure says that the Perceiver is fine-tuned in the first stage, but the text says otherwise (L273-274 and L379-381). Which one is it? - Is the learnable $g$ part of the “gaze-related weights” that are fine-tuned in the first step? - What are the “linear layers” used to encode the gaze heatmap? Is it a linear projection on each patch token? or an MLP? - Can you elaborate more on the role of [fixation] token? Confidence: 4 Soundness: 2 Presentation: 4 Contribution: 3 Limitations: The authors properly address the limitations of their work together with useful discussions, an impact section, and a reproducibility statement. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We sincerely thank you for your support of our work, for your meticulous review, and for your thoughtful suggestions that have helped us improve. W1 - Both Kosmos-2 and Otter are finetuned on the same training set of VOILA-COCO. - During the data generation process, we generate one direct question and one indirect question for each query content. During the training process, we randomly select one question from each question pair, i.e., the direct questions and indirect questions are expected to be balanced during the training stage. This training question composition remains unchanged for all tables and figures in the Experiment session. During the validation process, by default, we use only indirect questions (Figures 5 and 6, Tables 3 and 4). The only exception is Table 2, which shows the ablation results on query types, row 1/3/5 use indirect questions and row 2/4/6 use direct questions as validation set. - During evaluation, kosmos-2 takes bounding boxes as input, following the same format as in their paper and code repo. The way we preprocess bounding boxes for kosmos-2 is consistent with VOILA's variant in Table 3 (row 3 and 4). Specifically, we calculate the minimum bounding box that includes the gaze trace of each question. For Otter evaluation, we do not directly inject gaze traces or bounding box data because Otter hasn't seen such kind of data during training. As shown in Figure 16 you've mentioned, the top-right and bottom-right setting maintains the same model architecture as Otter. These settings add special trainable tokens for the gaze trace/fixation bounding box, which can be considered as a location information-injected version of Otter. As shown in Table 3, our VOILA also surpasses these Otter variants. In Figures 5 and 6, although we compared VOILA to no location information-injected version of Otter, it is because the main goal of our paper is to (1) examine the necessity of additional signals for generating appropriate responses in everyday scenarios, and (2) evaluate whether gaze signals offer a superior representation of user intent compared to other modalities such as bounding boxes, instead of establishing a traditional benchmark for competitive model architectures based on specific metrics. W2 The GPT-4 ranking has 3 outcomes, that is, win, tie, or lose. As shown in Figure 5 "Voila vs Kosmos-2" Grounding column, approximately 40% winning rate already surpass its competitor. Therefore, in Table2, comparing row 1/3/5, VOILA surpasses Otter in indirect questions, and comparing row 2/4/6, VOILA surpasses Otter in direct questions. Also, comparing row 1/2, 3/4, 5/6, both model variants and prompt strategy performs better on direct questions compared to indirect ones. We will update tie/loss rate into the table in later revision. W3 As you kindly point out, instead of chasing technical novelty, our paper aims to implement modifications and prove them to be necessary and beneficial, establishing the groundwork for gaze-incorporated VLMs. In developing VOILA, a critical consideration is the adherence to the established architecture of current VLMs, making it easy to follow and generally applicable. It is essential to avoid introducing a significant number of new parameters or making extensive structural modifications. This constraint is due to the limitations of the current gaze dataset, which does not support large-scale pretraining. Additionally, we must be vigilant in preventing catastrophic forgetting during the fine-tuning process. Q1 Thanks for pointing out and we will update our statement accordingly: Our study on Otter demonstrate that current VLMs fails on various daily usecases because of disalignment with users' intention. Also, recent HCI research like GazeGPT[1] incorporates only one gaze point as location information to GPT-4v in the form of bounding boxes, illustrating the improved alignment and user preference after the incorporation of gaze. [1] GazeGPT: Augmenting Human Capabilities using Gaze-contingent Contextual AI for Smart Eyewear Q2 Will update high resolution illustrations. Q3 For better numerical stability, we choose addition instead of multiplication. Q4 This architecture, drawing inspiration from Perceiver and Flamingo, seamlessly integrates self-attention within latent features and cross-attention between latent and visual features in a unified step. Q5 The vector $g$ is a trainable multi-channel variable with dimensions corresponding to (Number of Heads, Dimensionality). Q6 That means word embedding and final projection after the last layer of language model. Q7,8,9,10 Sorry for the mismatch and we will revise it. Here is the fact: In the first stage colored in pink, we train the MLPs and gate $g$ of gaze inputs for 1 epoch, then tune together with Perceiver resampler module for 1 epoch. In the second stage colored in orange, we finetune MLPs, $g$, Perceiver, Cross attention, word embeddings together for 1 epoch. In total, that's three epoch as stated in L737. Q11 To maintain the model's versatility in handling scenarios without trace input, the inclusion of a special token like 'fixation' is crucial for ensuring the model's robustness across diverse situations. --- Rebuttal 2: Title: Clarification Comment: Thank you for taking the time to write a rebuttal. I will be taking it under advisement. That being said, could you elaborate more on W2? I'm still not sure I'm interpreting the results properly. My understanding from your response is that Table 2 is missing the tie and loss rates, which means the win rate alone is not enough to actually determine which method is winning. For example, comparing row 3 to row 1, VOILA is achieving a win rate of 41% compared to Otter-base on coreference queries, if the tie rate is 19% or higher, this would mean that VOILA is better, otherwise, Otter-base would be better. Is my reasoning correct? If the answer is yes, then how are we supposed to interpret those results based on the win rate alone? The scenario you describe in Figure 5 where Voila has around 40% win rate against Kosmos and is winning overall may not be happening in Table 2 if the tie rate is smaller. Thank you. --- Rebuttal Comment 2.1: Comment: You are correct in your understanding. As replied in W2, we acknowledge that presenting only the winning rate for each table does not sufficiently substantiate our claims in the ablation studies. To address this, we will incorporate the loss rate alongside the winning rate in each table. As the following table shows, when comparing both winning and loss rates, our observations remain consistent and valid. ### Table 2 \| Methods \| Question types \| WR \| LR \| Reward Score \| \|------------\|-----------------------------------------\|------\|------\|--------------\| \| Otter-base \| coreference query \| - \| - \| -1.91 \| \| Otter-base \| direct query \| 0.51 \| 0.10 \| 0.02 \| \| Voila \| coreference query \| 0.41 \| 0.18 \| -0.79 \| \| Voila \| direct query \| 0.62 \| 0.15 \| 0.14 \| \| Voila \| in-context prompt + coreference query \| 0.46 \| 0.16 \| -0.02 \| \| Voila \| in-context prompt + direct query \| 0.77 \| 0.12 \| 0.20 \| ### Table 3 \| Methods \| WR \| LR \| Reward Score \| \| --------------------------------------------- \| ---- \| ---- \| ------------ \| \| Otter-base \| - \| - \| -1.91 \| \| Gaze as discrete position tokens \| 0.19 \| 0.25 \| -2.44 \| \| Gaze bounding box as image patch \| 0.36 \| 0.20 \| -1.26 \| \| Gaze bounding box as discrete position tokens \| 0.21 \| 0.22 \| -1.72 \| \| Voila (Gaze as heatmap) \| 0.41 \| 0.18 \| -0.79 \| ### Table 4 \| Layers fine-tuned \| WR \| LR \| Reward Score \| \|--------------------------------------------------------\|------\|------\|--------------\| \| Otter-base \| - \| - \| -1.91 \| \| Otter-base vision perceiver+cross attention \| 0.25 \| 0.24 \| -1.78 \| \| Voila gaze weight \| 0.24 \| 0.20 \| -1.52 \| \| Voila gaze weight+LORA \| 0.23 \| 0.21 \| -1.02 \| \| Voila gaze weight ->perciever+cross attention \| 0.41 \| 0.18 \| -0.79 \|	null	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Towards Next-Generation Logic Synthesis: A Scalable Neural Circuit Generation Framework	Accept (poster)	Summary: The paper studies the application of differentiable neural architecture search (DNAS) to the problem of logic synthesis from input-output examples. The authors first analyze several challenges when directly applying existing DNAS methods to the problem. Based on those findings three modifications are proposed: (1) A transformation of the input-output examples that decreases the number of input and increases the number of output variabels. (2) Changing the network search space from rectangular to triangular shaped to be more aligned with typical network shapes. (3) Adding a regularization to avoid overfitting to shallow circuits and adding weights to the loss of positive and negative examples. In addition to adapting DNAS methods, the authors present a neural circuit optimization postprocess which learns a sequence of circuit operations to optimize the size of the circuit. The sequence is learned with reinforcement learning and an evolutionary algorithm. In an experimental evaluation, the authors demonstrate that both the modification of the DNAS method and the circuit optimization postprocess yield large gains in terms of correctness and circuit size. Strengths: - Recent International Workshop on Logic & Synthesis (IWLS) contest results sparked interest in the application of neural architecture search (NAS) to logic synthesis. To the best of my knowledge, this paper is the first to extensively study this promising combination. The paper first presents valuable insights into the challenges of applying the NAS methods as is. Derived from those challenges the authors propose well-motivated changes to the standard methods. In the experimental evaluation, it is shown that each change either contributes to improving the accuracy or decreasing the size of the resulting circuit. - As part of the framework, the authors introduce a novel circuit optimization based on learning a sequence of circuit operations with reinforcement learning and an evolutionary algorithm. This optimization step does not only seem valuable in combination with the introduced T-Net but also as an independent postprocess on top of other logic synthesis techniques. - The size of the circuits is evaluated in comparison with the top teams from recent IWLS contests. The winners of IWLS can be considered state-of-the-art methods and the experimental evaluation demonstrates substantial improvements over them. To perform this comparison the authors re-implemented some of the approaches which have not been open-sourced. If the authors were to make their code publicly available this would also be a valuable contribution to the research community. Weaknesses: - Large parts of the paper rely on previous work for the background of the problem and the method itself. For example, the paper does not formally introduce the logic synthesis problem from input-output examples, nor does the paper introduce the notion of differentiable neural architecture search. The exact method of relaxing a logic neural network for training and discretizing for evaluation only becomes evident in the second half of the paper (Section 5.2), making it difficult to understand the first half on motivating challenges. Another difficulty in following the paper is that the authors refer to the appendix for many aspects of the approach. For example, experiments on the motivating challenges, the implementation of the newly introduced regularization and weighted loss, and details on the circuit optimization in general can only be found in the appendix. - Since the authors already compare with the top winners from the IWLS contests, it is not clear to me why they do not evaluate the IWLS benchmarks. Instead, the authors choose a smaller (potentially less challenging) set of benchmarks without providing insights into how the benchmarks were selected. Technical Quality: 3 Clarity: 2 Questions for Authors: Is the circuit optimization evaluated on top of T-Net or is the input circuit obtained in a different way? Confidence: 3 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: The authors only discuss the GPU requirement as a limitation such that important aspects are missing from the discussion. For example, even though T-Net largely improves on accuracy compared to previous methods, it is not guaranteed to reach perfect accuracy. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: # Response to Reviewer qf83 We thank the reviewer for the insightful and valuable comments. We respond to each comment as follows and sincerely hope that our rebuttal could properly address your concerns. If so, we would deeply appreciate it if you could raise your score. If not, please let us know your further concerns, and we will continue actively responding to your comments and improving our submission. ## Weakness 1. > 1. The paper does not formally introduce the logic synthesis problem from input-output examples and the notion of differentiable neural architecture search. Thanks for the valuable suggestions. We have revised the Background Section as follows. Formulation of LS from IO examples In recent years, synthesizing circuits from IO examples has gained increasing attention [1][2][3]. Specifically, researchers aim to use machine learning to generate a circuit based on a truth table that describes the circuit's functionality. Each line in the truth table represents an input-output pair, indicating the output produced by the circuit for a given input. In the machine learning domain, researchers formulate the truth table as a training dataset comprising many input-output pairs and use an ML model to generate circuits that accurately fit the dataset. DNAS for LS from IO Examples Recent works [1][2] propose leveraging traditional DNAS methods for generating circuit graphs from IO examples, showing a promising direction for next-generation logic synthesis. Specifically, they formulate a neural network as a circuit graph, where each neuron represents a logic gate and connections between neurons represent wires connecting these logic gates. For a parameterized neural network, the neurons are fixed as logic gates, and the connections between neurons are parameterized as learnable parameters. To enable differentiable training via gradient descent, continuous relaxation is introduced into discrete components of the neural network. First, the logical operations of logic gates (neurons) are translated into their differentiable counterparts. For example, $a \ \textit{AND} \ b$ is relaxed to $a\cdot b$ [4]. Second, discrete network connections are parameterized using Gumbel-softmax [5]. > 2. Another difficulty in following the paper is that the authors refer to the appendix for many aspects of the approach. Thanks for the valuable suggestion. We will revise our manuscript by retaining the key content in the main text and moving the minor content to the appendix. Specifically, we will update the "Background," "Motivation," and "Method" Sections as follows. For Background, we present the problem formulation of logic synthesis (LS) from input-output examples, and details of the traditional DNAS approach for LS. For Motivation, we first present the main challenge of the traditional DNAS for LS that the method struggles to generate circuits accurately, especially for large circuits. We then present two major reasons for this challenge: the curse of skip-connection and the structure bias of circuits. For Method, we first present the three key modules for neural circuit generation. 1) To reduce the learning complexity of large circuits, we present the multi-label transformation module to decompose a large truth-table (dataset) into several small sub-truth-tables (sub-datasets). 2) To address the curse of skip-connection challenge, we present details of the regularized skip-connections module. 3) To leverage the structure bias of circuits, we present details of the triangle-shaped network architecture. We then present details of our circuit optimization approach and provide the pseudocode of the algorithm. ## Weakness 2. > 3. Since the authors already compare with the top winners from the IWLS contests, it is not clear to me why they do not evaluate the IWLS benchmarks. Thanks for the valuable suggestion. We have compared our method with Google DeepMind's contest results on 30 more circuits from the IWLS benchmark as shown in Table 2 in the attached pdf in Global Response. The results show that our method achieves 3.03% node reduction compared with Google DeepMind's contest results. In addition, the 18 circuits used in the main text are indeed sourced from the IWLS benchmark as well, and we compared our method with Google DeepMind's contest results on these circuits in the main text (achieving 5.36% node reduction). ## Question 1: > 4. Is the circuit optimization evaluated on top of T-Net or is the input circuit obtained in a different way? Yes, the results of our method are obtained by optimizing circuits generated using T-Net. ## Limitation 1. > 5. T-Net is not guaranteed to reach perfect accuracy. To ensure perfect accuracy in our circuit generation, we applied a legalization method to our final generated circuits as detailed in Appendix D.6. ## Open-source code. > 6. If the authors were to make their code publicly available this would also be a valuable contribution to the research community. Yes, we will make our code publicly available once our paper is accepted. [1] Designing better computer chips. Google DeepMind, 2023, https://deepmind.google/impact/optimizing-computer-systems-with-more-generalized-ai-tools/. [2] Peter Belcak, et al. Neural combinatorial logic circuit synthesis from input-output examples. NeurIPS Workshop, 2022. [3] IWLS Programming Contest Series Machine Learning + Logic Synthesis. IWLS, 2024, https://www.iwls.org/contest/. [4] Petersen, et al. Deep differentiable logic gate networks. NeurIPS, 2018. [5] Jang, et al. Categorical Reparametrization with Gumble-Softmax. ICLR, 2017. --- Rebuttal 2: Title: Response to Reviewer qf83--Looking forward to your further feedback Comment: Dear Reviewer qf83, We are writing as the authors of the paper "Towards Next-Generation Logic Synthesis: A Scalable Neural Circuit Generation Framework" (ID: 17130). We sincerely thank you once more for your insightful comments and kind support! We are writing to gently remind you that the deadline for the author-reviewer discussion period is approaching (due on Aug 13). We eagerly await your feedback to understand if our responses have adequately addressed all your concerns. If so, we would deeply appreciate it if you could raise your score. If not, we are eager to address any additional queries you might have, which will enable us to enhance our work further. Once again, thank you for your guidance and support. Best, Authors --- Rebuttal 3: Comment: I would like to thank the authors for their text revisions and the evaluation of the additional IWLS benchmarks. I believe the proposed revisions will improve the presentation of the paper. The evaluation of the additional benchmark further strengthens the experimental results. However, the additional benchmarks are again a subset of the IWLS competition benchmarks. I am still concerned that the method is not compared on the full benchmark set. --- Rebuttal Comment 3.1: Title: Evaluation on the full IWLS benchmark set (1/3) Comment: Dear Reviewer qf83 We would like to extend our sincere gratitude for the time and effort you have devoted to reviewing our submission. Your insightful comments and constructive suggestions have been invaluable to us, guiding us in improving the quality of our work! > Remark: Since the rebuttal phase, we have been actively expanding our experiments to include the entire IWLS benchmark. However, due to limited time and computational resources, we have to manage to keep the optimization time for each circuit within a week. In contrast, the SOTA method from Google, which we are comparing against, is reported to take 3 weeks per circuit to optimize. We have presented the results of our method on the full benchmark compared to the top IWLS winners in Tables 1 and 2 as follows. As shown in Table 1, our method significantly outperforms the top IWLS winners, including the IWLS 2022 first-place team (EPFL), the IWLS 2023 first-place team (Google), and the IWLS 2023 second-place team (TUW), in terms of the number of Wins (smaller circuit sizes). Moreover, Table 2 provides a detailed comparison for each circuit, demonstrating that our method reduces circuit sizes by an average of 8.78% compared to SOP, 17.02% compared to the IWLS 2022 first-place team (EPFL), and 10.7% compared to the IWLS 2023 second-place team (TUW). Our method does not fully outperform the IWLS 2023 first-place team (Google) due to limited optimization time (1 week versus 3 weeks). Nevertheless, it's important to note that when excluding just five corner cases, our method achieves comparable circuit sizes to the IWLS 2023 first-place team while using only one-third of the optimization time, highlighting the strong performance of our approach. We sincerely hope that our results on the full IWLS benchmark has adequately addressed your concerns. If so, we would deeply appreciate it if you could raise your score. If there are any further questions or concerns, we would be more than willing to address them in order to further enhance the quality of our submission. Table 1. We report the number of Wins of our method (smaller circuit sizes) compared to the IWLS 2022 first-place team (EPFL), the IWLS 2023 first-place (Google) and second-place (TUW) teams, on the full IWLS benchmark set. \| \| Generation \| Optimization \| \| \| \|:---:\|:---:\|:---:\|:---:\|:---:\| \| \| SOP \| EPFL \| TUW \| Google \| \| Ours Wins \| 75/100 \| 80/100 \| 60/100 \| 43/100 \| \| Ours Ties \| 3/100 \| 17/100 \| 27/100 \| 29/100 \| \| Ours Loses \| 22/100 \| 3/100 \| 13/100 \| 28/100 \| Due to limited space, please refer to the next two pages for Table 2. --- Reply to Comment 3.1.1: Title: Evaluation on the full IWLS benchmark set (2/3) Comment: Table 2. Our method reduces circuit sizes by an average of 8.78% compared to SOP, 17.02% compared to the IWLS 2022 first-place team (EPFL), and 10.7% compared to the IWLS 2023 second-place team (TUW). Our method does not fully outperform the IWLS 2023 first-place team (Google) due to limited optimization time of our method (1 week versus 3 weeks). Nevertheless, it's important to note that when excluding just five corner cases, our method achieves comparable circuit sizes to the IWLS 2023 first-place team while using only one-third of the optimization time, highlighting the strong performance of our approach. \| \| Generation \| \| \| Optimization \| \| \| \| Improvement(%) \| \| \| \| \|:---:\|:---:\|:---:\|:---:\|:---:\|:---:\|:---:\|:---:\|:---:\|:---:\|:---:\|:---:\| \| IWLS \| SOP \| T-Net \| Impr.(%)↑ \| EPFL \| TUW \| Google \| Ours \| v.s. EPFL \| v.s. TUW \| v.s. Google \| Google-5 Corner Cases \| \| ex00 \| 39 \| 34 \| 12.82 \| 26 \| 22 \| 23 \| 21 \| 19.23 \| 4.55 \| 8.70 \| 8.70 \| \| ex01 \| 44 \| 41 \| 6.82 \| 32 \| 25 \| 24 \| 24 \| 25.00 \| 4.00 \| 0.00 \| 0.00 \| \| ex02 \| 149 \| 143 \| 4.03 \| 97 \| 78 \| 69 \| 69 \| 28.87 \| 11.54 \| 0.00 \| 0.00 \| \| ex03 \| 75 \| 75 \| 0.00 \| 24 \| 24 \| 24 \| 24 \| 0.00 \| 0.00 \| 0.00 \| 0.00 \| \| ex04 \| 586 \| 494 \| 15.70 \| 312 \| 343 \| 287 \| 367 \| -17.63 \| -7.00 \| -27.87 \| -27.87 \| \| ex05 \| 168 \| 117 \| 30.36 \| 44 \| 40 \| 38 \| 37 \| 15.91 \| 7.50 \| 2.63 \| 2.63 \| \| ex06 \| 2267 \| 2065 \| 8.91 \| 1056 \| 1269 \| 1075 \| 961 \| 9.00 \| 24.27 \| 10.60 \| 10.60 \| \| ex07 \| 1327 \| 1256 \| 5.35 \| 183 \| 129 \| 112 \| 107 \| 41.53 \| 17.05 \| 4.46 \| 4.46 \| \| ex08 \| 1074 \| 842 \| 21.60 \| 564 \| 558 \| 567 \| 501 \| 11.17 \| 10.22 \| 11.64 \| 11.64 \| \| ex09 \| 1095 \| 819 \| 25.21 \| 561 \| 570 \| 538 \| 504 \| 10.16 \| 11.58 \| 6.32 \| 6.32 \| \| ex10 \| 12 \| 13 \| -8.33 \| 10 \| 10 \| 10 \| 10 \| 0.00 \| 0.00 \| 0.00 \| 0.00 \| \| ex11 \| 26 \| 30 \| -15.38 \| 20 \| 20 \| 20 \| 20 \| 0.00 \| 0.00 \| 0.00 \| 0.00 \| \| ex12 \| 44 \| 53 \| -20.45 \| 32 \| 30 \| 30 \| 30 \| 6.25 \| 0.00 \| 0.00 \| 0.00 \| \| ex13 \| 66 \| 106 \| -60.61 \| 48 \| 40 \| 42 \| 42 \| 12.50 \| -5.00 \| 0.00 \| 0.00 \| \| ex14 \| 94 \| 144 \| -53.19 \| 68 \| 52 \| 52 \| 56 \| 17.65 \| -7.69 \| -7.69 \| -7.69 \| \| ex15 \| 126 \| 226 \| -79.37 \| 92 \| 68 \| 72 \| 74 \| 19.57 \| -8.82 \| -2.78 \| -2.78 \| \| ex16 \| 32 \| 34 \| -6.25 \| 18 \| 18 \| 18 \| 18 \| 0.00 \| 0.00 \| 0.00 \| 0.00 \| \| ex17 \| 59 \| 61 \| -3.39 \| 24 \| 24 \| 24 \| 24 \| 0.00 \| 0.00 \| 0.00 \| 0.00 \| \| ex18 \| 99 \| 75 \| 24.24 \| 32 \| 32 \| 32 \| 32 \| 0.00 \| 0.00 \| 0.00 \| 0.00 \| \| ex19 \| 131 \| 166 \| -26.72 \| 38 \| 38 \| 38 \| 38 \| 0.00 \| 0.00 \| 0.00 \| 0.00 \| \| ex20 \| 195 \| 217 \| -11.28 \| 60 \| 50 \| 46 \| 52 \| 13.33 \| -4.00 \| -13.04 \| -13.04 \| \| ex21 \| 240 \| 206 \| 14.17 \| 70 \| 58 \| 56 \| 60 \| 14.29 \| -3.45 \| -7.14 \| -7.14 \| \| ex22 \| 336 \| 382 \| -13.69 \| 86 \| 70 \| 63 \| 68 \| 20.93 \| 2.86 \| -7.94 \| -7.94 \| \| ex23 \| 386 \| 463 \| -19.95 \| 104 \| 78 \| 72 \| 94 \| 9.62 \| -20.51 \| -30.56 \| -30.56 \| \| ex24 \| 440 \| 626 \| -42.27 \| 116 \| 90 \| 106 \| 102 \| 12.07 \| -13.33 \| 3.77 \| 3.77 \| \| ex25 \| 587 \| 877 \| -49.40 \| 146 \| 102 \| 90 \| 124 \| 15.07 \| -21.57 \| -37.78 \| -37.78 \| \| ex26 \| 741 \| 944 \| -27.40 \| 163 \| 114 \| 122 \| 159 \| 2.45 \| -39.47 \| -30.33 \| -30.33 \| \| ex27 \| 841 \| 1242 \| -47.68 \| 183 \| 178 \| 138 \| 174 \| 4.92 \| 2.25 \| -26.09 \| -26.09 \| \| ex28 \| 141 \| 123 \| 12.77 \| 39 \| 39 \| 39 \| 39 \| 0.00 \| 0.00 \| 0.00 \| 0.00 \| \| ex29 \| 71 \| 85 \| -19.72 \| 39 \| 35 \| 35 \| 35 \| 10.26 \| 0.00 \| 0.00 \| 0.00 \| \| ex30 \| 1159 \| 207 \| 82.14 \| 68 \| 68 \| 68 \| 68 \| 0.00 \| 0.00 \| 0.00 \| 0.00 \| \| ex31 \| 2858 \| 2604 \| 8.89 \| 1372 \| 1364 \| 1280 \| 1293 \| 5.76 \| 5.21 \| -1.02 \| -1.02 \| \| ex32 \| 65 \| 90 \| -38.46 \| 46 \| 44 \| 45 \| 44 \| 4.35 \| 0.00 \| 2.22 \| 2.22 \| \| ex33 \| 205 \| 155 \| 24.39 \| 79 \| 70 \| 72 \| 69 \| 12.66 \| 1.43 \| 4.17 \| 4.17 \| \| ex34 \| 187 \| 140 \| 25.13 \| 48 \| 46 \| 44 \| 46 \| 4.17 \| 0.00 \| -4.55 \| -4.55 \| \| ex35 \| 17 \| 18 \| -5.88 \| 16 \| 15 \| 16 \| 15 \| 6.25 \| 0.00 \| 6.25 \| 6.25 \| \| ex36 \| 3220 \| 2954 \| 8.26 \| 1345 \| 1501 \| 1590 \| 1519 \| -12.94 \| -1.20 \| 4.47 \| 4.47 \| \| ex37 \| 482 \| 334 \| 30.71 \| 152 \| 138 \| 141 \| 139 \| 8.55 \| -0.72 \| 1.42 \| 1.42 \| \| ex38 \| 72 \| 60 \| 16.67 \| 29 \| 27 \| 27 \| 27 \| 6.90 \| 0.00 \| 0.00 \| 0.00 \| \| ex39 \| 1224 \| 544 \| 55.56 \| 220 \| 191 \| 181 \| 153 \| 30.45 \| 19.90 \| 15.47 \| 15.47 \| \| ex40 \| 960 \| 853 \| 11.15 \| 197 \| 180 \| 183 \| 175 \| 11.17 \| 2.78 \| 4.37 \| 4.37 \| \| ex41 \| 43 \| 34 \| 20.93 \| 17 \| 17 \| 17 \| 17 \| 0.00 \| 0.00 \| 0.00 \| 0.00 \| \| ex42 \| 116 \| 90 \| 22.41 \| 28 \| 28 \| 28 \| 28 \| 0.00 \| 0.00 \| 0.00 \| 0.00 \| \| ex43 \| 172 \| 105 \| 38.95 \| 37 \| 37 \| 37 \| 37 \| 0.00 \| 0.00 \| 0.00 \| 0.00 \| \| ex44 \| 172 \| 139 \| 19.19 \| 59 \| 52 \| 51 \| 47 \| 20.34 \| 9.62 \| 7.84 \| 7.84 \| \| ex45 \| 944 \| 809 \| 14.30 \| 196 \| 179 \| 186 \| 175 \| 10.71 \| 2.23 \| 5.91 \| 5.91 \| \| ex46 \| 55 \| 50 \| 9.09 \| 32 \| 31 \| 31 \| 31 \| 3.13 \| 0.00 \| 0.00 \| 0.00 \| \| ex47 \| 129 \| 37 \| 71.32 \| 25 \| 25 \| 25 \| 25 \| 0.00 \| 0.00 \| 0.00 \| 0.00 \| \| ex48 \| 2135 \| 1913 \| 10.40 \| 598 \| 406 \| 482 \| 459 \| 23.24 \| -13.05 \| 4.77 \| 4.77 \| \| ex49 \| 133 \| 123 \| 7.52 \| 39 \| 39 \| 39 \| 39 \| 0.00 \| 0.00 \| 0.00 \| 0.00 \| --- Rebuttal 4: Comment: I would like to thank the authors for the additional experiments. They provide a full and transparent evaluation of the method. I will raise my score accordingly and encourage the authors to include the results on all IWLS benchmarks into the paper. --- Rebuttal Comment 4.1: Comment: Dear Reviewer qf83 Thank you for your kind support and valuable feedback on our paper! Your invaluable comments and constructive suggestions have not only strengthened our work but have also greatly enhanced the clarity and depth of our manuscript.	Summary: The manuscript describes a method to synthesize logic circuits using neural architecture search (NAS). The authors first evaluate some short-comings of earlier approaches and develop a generation method that adds regularization of skip connections, a prior on the shape of the circuit (triangle shape), transforms truth tables, and adapts a loss function. They also propose a circuit optimization step which utilizes reinforcement learning and evolutionary optimization. They use a number of benchmarks to show that the circuit generation performs very well compared to earlier NAS methods, in particular for larger circuit sizes. For the circuit optimization, the proposed method is similar or slightly better to the state-of-the-art. Strengths: - Good results compared to the earlier methods, in particular for the generation of large circuits, slightly improving on the state-of-the-art for circuit optimization. - The authors investigate both generation and optimization of logic circuits. Weaknesses: - The paper is poorly written in a sense that all relevant methods and many essential details and text sections are pushed into the appendix (that is almost 10 pages long). The main text reads just like a long introduction and discussion. It is not possible to follow what exactly was done when reading only the main text. This is not in line with the 9 page requirement. The appendix should be reserved for truly supplementary data and proofs. - The paper motivates with saying that differential neural architecture search (DNAS) has weaknesses such as producing excessive skip-connections. However, it turns out that this is (1) not a problem of DNAS per se, but just an inadequate way to setup up and perform the DNAS. In fact, the authors' method also employs DNAS but just adds some additional constraints and modifies the loss and adds regularization. Thus the motivation is misleading. Moreover, (2), as the authors acknowledge, this "curse of skip connection" is actually a known issue and already has been addressed by others (e.g. Darts). So there is little novelty in this section. - The math description e.g. in general is very poor, for instance in section 5.2 (Eq 2) proper math symbols should be used instead of "in", "out", "unit" etc. It is also not clear what the indeces mean, for instance "unit^{l, k, p}" is a tensor with dimension l x K ? So it is just a matrix? What is the third index (p) then? Also there is no equation in the main text for the loss and other details, such as the evolutionary and RL approaches, making it impossible to follow what actually was done exactly. - Prior approaches to the problem are not well explained in the main text (only a section in the appendix). - From the ablation study it seems that regularizing the skip connections has by far the most impact, while the loss adaption and the triangle shape prior improves only relatively little. Given, that the skip-connection issues was already addressed by others, it seems that the contribution of the study is somewhat incremental. Technical Quality: 3 Clarity: 1 Questions for Authors: See above Confidence: 3 Soundness: 3 Presentation: 1 Contribution: 2 Limitations: Limitations are addressed. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: # Response to Reviewer Qczw We thank the reviewer for the insightful and valuable comments. We respond to each comment as follows and sincerely hope that our rebuttal could properly address your concerns. If so, we would deeply appreciate it if you could raise your score. If not, please let us know your further concerns, and we will continue actively responding to your comments and improving our submission. ## Weakness 1. > 1. Relevant methods and essential details are pushed into the appendix. Please see Global Response 1. ## Weaknesses 2 and 5. > 2. The motivation that "DNAS has weaknesses such as producing excessive skip-connections" is misleading. Recent works [1,2] have applied traditional DNAS methods, such as DARTS [3], to circuit generation, revealing a promising direction. Our motivating insight revisits the direct application of traditional DNAS methods to circuit generation and identifies several specific challenges for circuit generation, including the curse of skip-connections. Note that the skip-connection problem in circuit generation is significantly different from that in traditional DNAS (see the next response). > 3. This "curse of skip connection" is already addressed by methods like Darts. Differences in the Skip-Connection Challenge In traditional DNAS, the skip-connection problem arises as the skip-connection operation often dominates other operations, such as convolution and zero operations. In contrast, when applying DNAS to circuit generation, a neural network is formulated as a circuit graph, where each neuron represents a logic gate and connections between neurons represent wires connecting these logic gates. The neurons are fixed as logic gates, and the connections between neurons are learnable. Most learnable connections skip layers, called skip-connections in circuit neural networks. In this paper, we found that the traditional DNAS method tends to overfit to skip-connections that bypass a large number of layers, a phenomenon we call the curse of skip-connections in circuit generation. (1) The definitions of skip-connections in DNAS and circuit generation are different. (2) In traditional DNAS, it is required to encourgae balance between skip-connection operation and other operations. In contrast, it is required to balance between numerous skip-connections that span different layers in circuit generation. Inapplicability of Existing DNAS Methods to Circuit Generation We have compared our method with DNAS-based methods for addressing the skip-connection challenge, including P-DARTS [4], PR-DARTS [5], and DARTS-ES [6]. As shown in Table 1 in attached pdf in Global Response, the results demonstrate that our method significantly outperforms these approaches. The primary reason is that these methods struggles to balance between numerous skip-connections in circuit generation tasks. In contrast, our method proposes a novel layer-aware regularized skip-connection module, which effectively balances skip-connections that span different layers. > 4. The loss adaption and the triangle shape prior improves only relatively little. We have conducted detailed ablation experiments to show that each of our proposed modules is significant. The results in Tables 3, 4, and 5 in attached pdf in Global Response show that the proposed loss enhances accuracy to 99%, and the T-architecture achieves an average node reduction of 16.9% and a training time reduction of 40.8%. ## Weakness 3. > 5. The math description is poor. It is also not clear what the indexes p mean. Thanks for the valuable suggestion. We have revised our math description accordingly. Note that each neuron (And gate) in the circuit neural network has two input signals. The $unit^{l, k, p}$ is a tensor with dimension $l \times K \times 2$. The index $p$ represents the $p^{th}$ input signal of current neuron. Details are as follows. (Revision) We denote the output of the $k^{th}$ neuron in the $l^{th}$ layer by $\textbf{o}^{l,k}$. We denote the $p$-th input of the neuron (NAND gate) $\textbf{o}^{l,k}$ by $\textbf{i}\_{p}^{l,k}$, where $p \in \{0,1\}$. Note that each neuron $o^{l,k}$ has two inputs $i^{l,k}\_{0}$ and $i^{l,k}\_{1}$, and can be connected to any neuron with layer number smaller than $l$ as its input neuron. We parameterize the connections of each neuron $o^{l,k}$ by a tensor of learnable parameters $\mathbf{\theta}^{l,k} \in \mathbb{R}^{2 \times (l-1) \times K}.$ Each parameter in the tensor $\mathbf{\theta}^{l,k}\_{p,i,j}$ represents the probability of connecting the $j^{th}$ neuron in the $i^{th}$ layer to the $p^{th}$ input of current neuron $o^{l,k}$. The computation of the $p^{th}$ input value for the neuron $o^{l,k}$ takes the form of $$i_p^{l, k} :=\sum_{i=0}^{l-1} \sum_{j=1}^{K} o^{i,j} \left[\operatorname{softmax}\left(\mathbf{\theta}^{l, k}\right)\right]_{p,i,j}, p=0,1;\ \ o^{l,k} := 1 - \Pi\_{p=0}^{1} i_p^{l, k}$$ > 5. There is no equation in the main text for the loss and other details. Thanks for the suggestion. We will provide these equations in the main text. ## Weakness 4. > 6. Prior approaches to the problem are not well explained in the main text. Please see Global Response 2. [1] Designing better computer chips. Google DeepMind, 2023, https://deepmind.google/impact/optimizing-computer-systems-with-more-generalized-ai-tools. [2] Peter Belcak, et al. Neural combinatorial logic circuit synthesis from input-output examples. NeurIPS Workshop, 2022. [3] Hanxiao Liu, et al. Darts: Differentiable architecture search. ICLR 2019. [4] Xin Chen, et al. Progressive differentiable architecture search: Bridging the depth gap between search and evaluation. ICCV 2019. [5] Pan Zhou, et al. Theory-inspired path-regularized differential network architecture search. NeurIPS 2020. [6] Zela, et al. Understanding and Robustifying Differentiable Architecture Search. ICLR 2020. --- Rebuttal Comment 1.1: Comment: Many thanks for the detailed responses. I don't have any further questions. I will keep my original score, as it seems that the level of contribution, novelty, and improvements of state of the art would fit better a more targeted conference or journal. --- Reply to Comment 1.1.1: Title: Further Response to Reviewer Qczw (1/2) Comment: We would like to express our sincere gratitude once again for your valuable feedback and constructive suggestions. We have made detailed clarifications regarding our contributions, novelty, and the improvements over the state-of-the-art. We sincerely hope that our additional response has adequately addressed your concerns. If so, we would greatly appreciate your consideration in raising the score. If there are any remaining concerns, please let us know, and we will continue to actively address your comments and work on improving our submission. ## Contributions - To the best of our knowledge, we are the first to conduct an extensive study on the application of differentiable neural architecture search (DNAS) to circuit generation, which provides valuable insights for both hardware design researchers and AI researchers in the field of neural architecture search. (Reviewer qf83 commented in Strengths that "Recent International Workshop on Logic & Synthesis (IWLS) contest results sparked interest in the application of neural architecture search (NAS) to logic synthesis. To the best of my knowledge, this paper is the first to extensively study this promising combination.") - Through detailed analysis, we present several insightful observations regarding the specific challenges of directly applying classical DNAS methods (e.g., DARTS) to circuit generation, including the curse of skip connections, structural biases in circuits, and the varying learning difficulties of different input-output examples. (Reviewer PMQo commented in Strengths that "Through a detailed analysis, the paper presents insightful observations that underpin current challenges". Reviewer qf83 commented in Strengths that "The paper first presents valuable insights into the challenges of applying the NAS methods as is." Reviewer gSL5 commented in Strengths that "The paper provides a detailed sensitivity analysis of using DNAS for logic synthesis, which gives valuable insights into overfitting, structure bias, and learning difficulties, etc.") - We propose a novel regularized triangle-shaped circuit network generation framework, called T-Net, which significantly enhances generation accuracy and scales effectively to large circuits. (Reviewer PMQo commented in Strengths that "The proposed T-Net highlights its capability to generate exact circuits and precisely generate large bit-width circuits." Reviewer gSL5 commented in Strengths that "The introduction of T-Net, a regularized triangle-shaped network architecture, addresses significant limitations in existing DNAS methods, improving the accuracy and scalability of neural circuit generation.") - Extensive experiments demonstrate our method significantly outperforms state-of-the-art methods in terms of both generation accuracy and circuit size. (Reviewer qf83 commented in Strengths that "The size of the circuits is evaluated in comparison with the top teams from recent IWLS contests. The winners of IWLS can be considered state-of-the-art methods and the experimental evaluation demonstrates substantial improvements over them." Reviewer gSL5 commented in Strengths that "Extensive experiments on multiple benchmarks show that T-Net significantly outperforms state-of-the-art methods, with improvements in both circuit accuracy and size.")	Summary: Existing DNAS methods face challenges in accurately generating circuits, particularly with large-scale circuits, and exhibit high sensitivity to random initialization. To address these challenges, this paper proposes a framework named T-Net. The experiments demonstrate that T-Net can precisely generate large bit-width circuits and that the generated circuits show a significant improvement in circuit area compared to traditional methods. Strengths: Through a detailed analysis, the paper presents insightful observations that underpin current challenges, showcasing a strong logical progression in its argument. The proposed T-Net highlights its capability to generate exact circuits and precisely generate large bit-width circuits. Weaknesses: The experimental section raises some concerns. 1. The paper evaluates T-Net using circuits from four benchmarks: Espresso, LogicNets, Random, and Arithmetic. However, the results seem curated, as the paper does not provide results for specific cases such as Espresso 1, Espresso 2, Espresso 5, and Espresso 6. 2. The paper claims that T-Net is a state-of-the-art approach based on 72 competitive winners in the IWLS 2022 and 2023 competitions. Additionally, the paper mentions re-implementing DNAS Skip by Google DeepMind for the IWLS 2023 competition. However, the authors should compare T-Net with DNAS Skip on the IWLS benchmark using Google DeepMind's results for a more robust comparison. Technical Quality: 2 Clarity: 3 Questions for Authors: 1. Please include more cases from the four benchmarks (Espresso, LogicNets, Random, and Arithmetic) to make the experiment more convincing. 2. Please provide a comparison with Google DeepMind's DNAS Skip on the IWLS benchmark, given the claim that T-Net is state-of-the-art in IWLS 2022 and 2023. Confidence: 4 Soundness: 2 Presentation: 3 Contribution: 2 Limitations: Yes, the authors have stated the limitations of their work. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: # Response to Reviewer PMQo We thank the reviewer for the insightful and valuable comments. We respond to each comment as follows and sincerely hope that our rebuttal could properly address your concerns. If so, we would deeply appreciate it if you could raise your score. If not, please let us know your further concerns, and we will continue actively responding to your comments and improving our submission. ## Weakness 1 & Question 1. > 1. The paper does not provide results for specific cases such as Espresso 1, Espresso 2, Espresso 5, and Espresso 6. Please include more cases from the four benchmarks (Espresso, LogicNets, Random, and Arithmetic) to make the experiment more convincing Thanks for the valuable suggestion. We indeed conducted experiments on circuits such as Espresso 1, Espresso 2, Espresso 5, and Espresso 6 as shown in Appendix E.2 (Tables 8, 9, and 10) in the main text. The results demonstrate that our method improves the average generation accuracy by 17.5%, reduces the number of generated nodes by 33.4%, and reduces the optimized circuit size by 68.7% on these cases compared to traditional baselines. In addition, we have conducted experiments on 30 more circuits from the IWLS benchmark. Please see the next response for details. ## Weakness 2 & Question 2. > 2. Please provide a comparison with Google DeepMind's DNAS Skip on the IWLS benchmark. Thanks for the valuable suggestion. We have compared our method with Google DeepMind's contest results on 30 more circuits from the IWLS benchmark as shown in Table 2 in the attached pdf in Global Response. The results show that our method achieves 3.03% node reduction compared with Google DeepMind's contest results. For your convenience, we quote Table 2 as follows. In addition, the 18 circuits used in the main text are indeed sourced from the IWLS benchmark as well, and we compared our method with Google DeepMind's contest results on these circuits in Tables 3 and 10 in the main text (achieving 5.36% node reduction). Table 2. We evaluate our approach on 30 other circuits in the IWLS benchmark. Our T-Net surpasses the traditional method by 10.64\%, and surpasses the IWLS 2023 champion, Google DeepMind, by 3.03\% after optimization. \| \| \| \| \| Generation \| \| \| Optimization \| \| \| \|---\|---\|:---:\|:---:\|:---:\|:---:\|:---:\|:---:\|:---:\|:---:\| \| Benchmark \| IWLS \| PI \| PO \| SOP \| T-Net(ours) \| Impr.(%)↑ \| Google \| Ours \| Impr.(%)↑ \| \| Espresso \| ex49 \| 8 \| 16 \| 133 \| 123 \| 7.52 \| 39 \| 39 \| 0.00 \| \| Espresso \| ex38 \| 10 \| 11 \| 72 \| 60 \| 16.67 \| 27 \| 27 \| 0.00 \| \| Espresso \| ex28 \| 8 \| 16 \| 141 \| 123 \| 12.77 \| 39 \| 39 \| 0.00 \| \| Espresso \| ex46 \| 6 \| 13 \| 55 \| 50 \| 9.09 \| 31 \| 31 \| 0.00 \| \| Espresso \| ex16 \| 6 \| 4 \| 39 \| 34 \| 12.82 \| 17 \| 17 \| 0.00 \| \| Espresso \| ex35 \| 8 \| 3 \| 17 \| 18 \| -5.88 \| 16 \| 15 \| 6.25 \| \| Espresso \| ex48 \| 16 \| 23 \| 2135 \| 1913 \| 10.40 \| 482 \| 490 \| -1.66 \| \| LogicNets \| ex94 \| 13 \| 6 \| 100 \| 86 \| 14.00 \| 33 \| 33 \| 0.00 \| \| LogicNets \| ex86 \| 15 \| 7 \| 406 \| 399 \| 1.72 \| 146 \| 125 \| 14.38 \| \| LogicNets \| ex77 \| 15 \| 7 \| 967 \| 828 \| 14.37 \| 224 \| 203 \| 9.38 \| \| LogicNets \| ex88 \| 15 \| 7 \| 949 \| 724 \| 23.71 \| 261 \| 254 \| 2.68 \| \| LogicNets \| ex68 \| 15 \| 7 \| 925 \| 584 \| 36.86 \| 118 \| 111 \| 5.93 \| \| LogicNets \| ex87 \| 15 \| 7 \| 992 \| 741 \| 25.30 \| 322 \| 318 \| 1.24 \| \| LogicNets \| ex91 \| 15 \| 7 \| 838 \| 746 \| 10.98 \| 200 \| 198 \| 1.00 \| \| LogicNets \| ex93 \| 15 \| 7 \| 73 \| 69 \| 5.48 \| 41 \| 39 \| 4.88 \| \| LogicNets \| ex95 \| 13 \| 6 \| 152 \| 140 \| 7.89 \| 62 \| 56 \| 9.68 \| \| LogicNets \| ex90 \| 15 \| 7 \| 1965 \| 1714 \| 12.77 \| 413 \| 432 \| -4.60 \| \| LogicNets \| ex95 \| 13 \| 6 \| 152 \| 164 \| -7.89 \| 62 \| 56 \| 9.68 \| \| LogicNets \| ex99 \| 15 \| 7 \| 228 \| 257 \| -12.72 \| 79 \| 72 \| 8.86 \| \| Arithmetic \| ex53 \| 10 \| 5 \| 82 \| 81 \| 1.22 \| 35 \| 34 \| 2.86 \| \| Arithmetic \| ex56 \| 15 \| 7 \| 70 \| 61 \| 12.86 \| 29 \| 29 \| 0.00 \| \| Arithmetic \| ex51 \| 10 \| 5 \| 97 \| 91 \| 6.19 \| 26 \| 26 \| 0.00 \| \| Arithmetic \| ex54 \| 10 \| 7 \| 14 \| 14 \| 0.00 \| 12 \| 12 \| 0.00 \| \| Arithmetic \| ex50 \| 10 \| 5 \| 35 \| 25 \| 28.57 \| 18 \| 18 \| 0.00 \| \| Arithmetic \| ex58 \| 15 \| 7 \| 209 \| 218 \| -4.31 \| 77 \| 71 \| 7.79 \| \| Arithmetic \| ex57 \| 15 \| 7 \| 1342 \| 531 \| 60.43 \| 81 \| 83 \| -2.47 \| \| Random \| ex06 \| 15 \| 4 \| 2267 \| 2065 \| 8.91 \| 1075 \| 961 \| 10.60 \| \| Random \| ex07 \| 15 \| 4 \| 1327 \| 1256 \| 5.35 \| 112 \| 107 \| 4.46 \| \| Random \| ex03 \| 10 \| 3 \| 75 \| 75 \| 0.00 \| 24 \| 24 \| 0.00 \| \| Random \| ex02 \| 10 \| 3 \| 149 \| 143 \| 4.03 \| 69 \| 69 \| 0.00 \| \| \| Average \| \| \| 533.53 \| 444.43 \| 10.64 \| 139.00 \| 132.97 \| 3.03 \| --- Rebuttal Comment 1.1: Comment: Thank you for adding additional experiments, which further validate the performance of the proposed solution. I'll raise my score accordingly. --- Reply to Comment 1.1.1: Title: Response to Reviewer PMQo Comment: Dear Reviewer PMQo, Thank you again for your insightful comments and constructive suggestions. We deeply appreciate your decision to raise your evaluation score.	Summary: The paper tackles the challenges in logic synthesis (LS) for integrated circuit design by proposing a novel neural circuit generation framework. Traditional LS methods rely on heuristics, which can be suboptimal and inefficient. The authors revisit differentiable neural architecture search (DNAS) methods and identify key limitations: overfitting to skip-connections, structure bias, and imbalanced learning difficulties. To overcome these, they introduce T-Net, a regularized triangle-shaped network architecture with a multi-label transformation of training data and a regularized training loss function. Additionally, the paper propose an evolutionary algorithm assisted by reinforcement learning for neural circuit optimization. Extensive experiments demonstrate that T-Net outperforms state-of-the-art methods in generating precise and scalable circuits. Strengths: 1. The introduction of T-Net, a regularized triangle-shaped network architecture, addresses significant limitations in existing DNAS methods, improving the accuracy and scalability of neural circuit generation. 2. The paper provides a detailed sensitivity analysis of using DNAS for logic synthesis, which gives valuable insights into overfitting, structure bias, and learning difficulties, etc.. 3. Extensive experiments on multiple benchmarks show that T-Net significantly outperforms state-of-the-art methods, with improvements in both circuit accuracy and size Weaknesses: 1. The multi-label transformation and regularized loss functions added additional complexity and reduces the efficiency of the model. 2. More justifications are required for the evolutionary algorithm + reinforcement learning method for the circuit optimization process. minor: extra space after line 384 "T" Technical Quality: 3 Clarity: 3 Questions for Authors: 1. How the proposed T-Net compare to previous SOTA in terms of model size, latency, energy efficiency etc? 2. Why no parameter for Appendix Table 7 &st? Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: No significant negative societal impact Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: # Response to Reviewer gSL5 We thank the reviewer for the insightful and valuable comments. We respond to each comment as follows and sincerely hope that our rebuttal could properly address your concerns. If so, we would deeply appreciate it if you could raise your score. If not, please let us know your further concerns, and we will continue actively responding to your comments and improving our submission. ## Weakness 1. > 1. The multi-label transformation and regularized loss functions added additional complexity and reduces the efficiency of the model. We have conducted experiments to demonstrate that our proposed modules not only enhance accuracy significantly but also substantially reduce training time. - The multi-label transformation module can significantly reduce input complexity by decomposing the entire truth-table (dataset) into several small sub-truth-tables (sub-datasets). As shown in Table 4 (in the main text), experiments show that using multi-label transformation reduces the wrong bits by 90%, and reduces the training time by roughly 40%. - Our proposed boolean hardness-aware loss also significantly enhanced the efficiency of our circuit generation. As shown in Table 5 in the attached pdf in Global Response, this loss function reduces training time by 20% while preserving accuracy. For your convenience, we quote Table 5 as follows. Table 5. The ablation study demonstrates that the boolean hardness-aware loss significantly reduces training time by 19.9\%. The reported time is the training time required to achieve 99\% accuracy. \| Circuit \| Training Time(h) \| \| Impr.(%) \| \|:---:\|:---:\|:---:\|:---:\| \| \| w/o. Loss \| w. Loss \| \| \| Espresso5 \| 10.4 \| 9.9 \| 4.8% \| \| LogicNets2 \| 14.5 \| 11.3 \| 22.1% \| \| Arithmetic2 \| 10.7 \| 7.6 \| 29.0% \| \| Random1 \| 7.3 \| 5.6 \| 23.6% \| \| Average \| 10.7 \| 8.6 \| 19.9% \| ## Weakness 2. > 2. More justifications are required for the evolutionary algorithm + reinforcement learning method for the circuit optimization process. Circuit optimization is recognized as an NP-hard problem, where traditional methods, often greedy and local, struggle to achieve optimal solutions. Reinforcement learning (RL) has demonstrated robust capabilities in navigating extensive search spaces, prompting the exploration of RL-based strategies to identify optimal sequences of circuit optimization operations. Nevertheless, due to the expansive and irregular nature of the search space, RL can suffer from limited exploratory capabilities, often resulting in convergence to local optima. To address this challenge, we incorporate evolutionary algorithms (EA), which preserve a population of diverse circuit solutions, thereby enhancing the exploration of the search space and leading to the discovery of superior circuits. Additionally, as shown in Table 3 in the main text, our novel circuit optimization approach outperforms previous state-of-the-art optimization methods. > 3. minor: extra space after line 384 "T" Thanks for pointing out this typo. We will correct it accordingly. ## Question 1. > 4. How the proposed T-Net compare to previous SOTA in terms of model size, latency, energy efficiency etc? Table 6 in the attached pdf in Global Response presents a comparison between T-Net and the SOTA DNAS (PR-DARTS [1]) in terms of model size, latency, and training time. The table shows that our method achieves perfect accuracy with 29% shorter training time. Additionally, our parameters, model size, and latency are comparable to the SOTA. For your convenience, we quote Table 6 as follows. Table 6. Comparation of T-Net and the SOTA DNAS baseline in terms of model efficiency. The table shows that our method achieves perfect accuracy with 29\% shorter training time. Additionally, our parameters, model size, and latency are comparable to the SOTA. \| \| Acc(%) \| \| Parameter (K) \| \| Model size(KB) \| \| Latency(s) \| \| Training Time(h) \| \| \|:---:\|:---:\|:---:\|---:\|:---:\|:---:\|:---:\|:---:\|:---:\|:---:\|:---:\| \| \| PR-DARTS \| T-Net \| PR-DARTS \| T-Net \| PR-DARTS \| T-Net \| PR-DARTS \| T-Net \| PR-DARTS \| T-Net \| \| Espresso5 \| 98.53 \| 100 \| 298 \| 287 \| 1182 \| 1138 \| 0.114 \| 0.113 \| 12.6 \| 10.1 \| \| Logicnets2 \| 97.64 \| 100 \| 751 \| 733 \| 2952 \| 2882 \| 0.246 \| 0.190 \| 15.4 \| 11.7 \| \| Arithmetic2 \| 96.15 \| 100 \| 733 \| 718 \| 2880 \| 2819 \| 0.155 \| 0.180 \| 16.9 \| 7.8 \| \| Random1 \| 91.89 \| 100 \| 266 \| 224 \| 1061 \| 898 \| 0.103 \| 0.084 \| 7.2 \| 5.8 \| [1] Pan Zhou, et al. Theory-inspired path-regularized differential network architecture search. NeurIPS, 2020. ## Question 2. > 5. Why no parameter for Appendix Table 7 &st? Thanks for the question. Indeed, the &st operator does not possess tunable hyperparameters. We will update the table to indicate 'N/A' for this operator's parameter in the revised manuscript. --- Rebuttal 2: Title: Response to Reviewer gSL5--Looking forward to your further feedback Comment: Dear Reviewer gSL5, We are writing as the authors of the paper "Towards Next-Generation Logic Synthesis: A Scalable Neural Circuit Generation Framework" (ID: 17130). We sincerely thank you once more for your insightful comments and kind support! We are writing to gently remind you that the deadline for the author-reviewer discussion period is approaching (due on Aug 13). We eagerly await your feedback to understand if our responses have adequately addressed all your concerns. If so, we would deeply appreciate it if you could raise your score. If not, we are eager to address any additional queries you might have, which will enable us to enhance our work further. Once again, thank you for your guidance and support. Best, Authors --- Rebuttal Comment 2.1: Title: Eagerly await your valuable feedback Comment: Dear Reviewer gSL5, We would like to extend our sincere gratitude for the time and effort you have devoted to reviewing our submission. Your positive feedback, insightful comments, and constructive suggestions have been invaluable to us, guiding us in improving the quality of our work! We are writing to gently remind you that the author-reviewer discussion period will end in less than 36 hours. We eagerly await your feedback to understand if our responses have adequately addressed all your concerns. If so, we would deeply appreciate it if you could raise your score. If not, we are eager to address any additional queries you might have, which will enable us to enhance our work further. Once again, thank you for your guidance and support. Best, Authors --- Reply to Comment 2.1.1: Title: Eagerly await your valuable feedback Comment: Dear Reviewer gSL5, We would like to express our sincere gratitude once again for your positive feedback, insightful comments, and constructive suggestions. Your guidance has been invaluable in helping us improve the quality of our work! We are writing to gently remind you that the author-reviewer discussion period will end in less than 24 hours. We eagerly await your feedback to understand if our responses have adequately addressed your concerns. If so, we would deeply appreciate it if you could raise your score. If not, we are eager to address any additional queries you might have, which will enable us to further enhance our work. Once again, thank you for your kind support and constructive suggestions! Best, Authors	Rebuttal 1: Rebuttal: # Global Response We would like to extend our sincere gratitude for your valuable feedback and constructive suggestions. For your convenience, we have prepared a summary of our responses and outlined how we have addressed the reviewers' concerns as follows. We sincerely hope that this summary will facilitate your review and lighten your workload. Our paper has received encouraging positive feedbacks from the reviewers, such as "addresses significant limitations (Reviewer gSL5)", "valuable insights (Reviewers gSL5 and qf83)", "significantly outperforms/substantial improvements (Reviewers gSL5 and qf83)", "insightful observations (Reviewer PMQo)", "strong logical progression" (Reviewer PMQo), "the first to extensively study" (Reviewer qf83), "well-motivated" (Reviewer qf83). We outline how we have addressed the concerns raised by each reviewer as follows. ## Common Concerns > (Reviewers Qczw and qf83) 1. All relevant methods and many essential details are pushed into the appendix. Thanks for the valuable suggestion. We will revise our manuscript by retaining the key content in the main text and moving the minor content to the appendix. Specifically, we will revise the "Background," "Motivation," and "Method" Sections as follows. For Background, we present the problem formulation of logic synthesis (LS) from input-output examples, and details of the traditional DNAS approach for LS. For Motivation, we first present the main challenge of the traditional DNAS for LS that the method struggles to generate circuits accurately, especially for large circuits. We then present two major reasons for this challenge: the curse of skip-connection and the structure bias of circuits. For Method, we first present the three key modules for neural circuit generation. 1) To reduce the learning complexity of large circuits, we present the multi-label transformation module to decompose a large truth-table (dataset) into several small sub-truth-tables (sub-datasets). 2) To address the curse of skip-connection challenge, we present details of the regularized skip-connections module. 3) To leverage the structure bias of circuits, we present details of the triangle-shaped network architecture. We then present details of our circuit optimization approach and provide the pseudocode of the algorithm. > (Reviewers Qczw and qf83) 2. Background on prior approaches to the problem are not well explained in the main text. Thanks for the valuable suggestions. We have revised the Background Section as follows. Formulation of LS from IO examples In recent years, synthesizing circuits from IO examples has gained increasing attention. Specifically, researchers aim to use machine learning to generate a circuit based on a truth table that describes the circuit's functionality. Each line in the truth table represents an input-output pair, indicating the output produced by the circuit for a given input. In the machine learning domain, researchers formulate the truth table as a training dataset comprising many input-output pairs and use an ML model to generate circuits that accurately fit the dataset. DNAS for LS from IO Examples Recent works propose leveraging traditional DNAS methods for generating circuit graphs from IO examples, showing a promising direction for next-generation logic synthesis. Specifically, they formulate a neural network as a circuit graph, where each neuron represents a logic gate and connections between neurons represent wires connecting these logic gates. For a parameterized neural network, the neurons are fixed as logic gates, and the connections between neurons are parameterized as learnable parameters. To enable differentiable training via gradient descent, continuous relaxation is introduced into discrete components of the neural network. First, the logical operations of logic gates (neurons) are translated into their differentiable counterparts. For example, $a \ \textit{AND} \ b$ is relaxed to $a\cdot b$. Second, discrete network connections are parameterized using Gumbel-softmax. > (Reviewers PMQo and qf83) 3. Evaluation on IWLS benchmark. We have compared our method with Google DeepMind's contest results on 30 more circuits from IWLS benchmark. The results show that our method still outperforms Google DeepMind's contest results. ## Reviewer gSL5 > 4. Module efficiency. We have conducted an ablation study to demonstrate that multi-label transformation and our loss function reduce the training time by roughly 40%. > 5. Justification for mombining RL and EA. We have provided detailed reasons for integrating RL and EA in circuit optimization, specifically to enhance the exploration of search space. > 6. Model metrics. We have conducted experiments to compare the size, latency, and training time of our model against the state-of-the-art method, demonstrating our model's high efficiency. > 7. Other details. We have provided these details accordingly. ## Reviewer PMQo > 8. More cases from the 4 benchmarks. We indeed conducted experiments on circuits such as Espresso 1, 2, 5, and 6 as shown in Appendix E.2 in the main text. ## Reviewer Qczw > 9. The "curse of skip connection" is already addressed by methods like Darts. We have explained that skip-connections pose unique challenges in circuit generation. We have evaluated three methods tailored for the challenge in DNAS and our approach significantly outperforms them. > 10. The loss adaption and the triangle shape prior improves only relatively little. We have conducted experiments to demonstrate that each of our modules are significant for improving generation accuracy, reducing training time and circuit sizes. > 11. The math description is poor. We have revised our math description accordingly. ## Reviewer qf83 > 12. Other details. We have provided these details accordingly. Pdf: /pdf/62f37c79a84020f939b68ea1c539ade7c4b94a78.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Latent Diffusion for Neural Spiking Data	Accept (spotlight)	Summary: In their study "Latent Diffusion for Neural Spiking Data", the authors introduce the titular LDNS model for generating realistic neural population activity, and apply it to three datasets: a synthetic dataset with true latents generated from the three-dimensional Lorenz system, and two previously published neuroscientific datasets. The LDNS model is an instance of the latent diffusion model (LDM) introduced by Rombach et al. (2022), which is adapted here by the authors to support generation of variable-length discrete-valued time series. The autoencoder of the LDM in this case is trained with a Poisson loss to account for the discrete nature of neural spiking data. The diffusion model of the LDM operating in latent space here is constructed with layers of structured state space sequence (S4) models of Gu et al. (2021). The diffusion model can be trained to generate samples conditional on certain external covariates by conditioning the reverse mode on the covariates. The split of LDMs between the autoencoder stage and the diffusion stage is particularly convenient for the task of generating spike trains, as it avoids any adjustment to the diffusion model for generating discrete variables. A variant of the LDNS model has additional parameters trained post-hoc to incorporate the spike-time history of individual output neurons to account for refractoriness and other single-cell auto-regressive features. According to the considered neural population statistics, the LDNS model gives an excellent fit to the synthetic data generated from the three-dimensional Lorenz system. For the two neuroscientific datasets, the LDNS performs solid in terms of matching the considered neural population statistics, outperforming the important reference model LFADS (Sussillo, 2016) in one case. On the first neuroscientific dataset comprised of human neural population data sampled during attempted speech, the LDNS is shown to handle variable sequence lengths in the training data and during sampling. The second neuroscientific dataset consists of monkey neural population data recorded during a maze reach task. Here, the LDNS variant with additional spike-history parameters fitted post-hoc is shown to also capture the temporal auto-correlation structure of neural subpopulations. The authors furthermore showcase the ability to generate samples conditionally on experimental covariates, by conditioning sampling on the initial reach angle, respectively the full velocity trajectory. Strengths: The submitted work is original, in that latent diffusion models (LDMs) to my knowledge have not yet been used to (conditionally) generate neural population activity. I agree that LDMs are indeed a nice idea here, since the separation into autoencoder stage and diffusion model stage means we can try to use denoising diffusion models without much changes. The work seems technically solid to me. The authors make sensible changes to the LDM for the task of generating neural population activity. The adaptations for discreteness (Poisson loss, spike-history terms) show a good understanding of best practices in neural data analysis. The inclusion of S4 layers into autoencoder and diffusion models to handle and generate variable-length sequences is interesting, and could further spread usage of these tools in the computational neuroscience community. The manuscript is well written, explaining not only the key ideas and experiments, but also summarizing the important model parts (autoencoders, denoising diffusion models) next to the non-standard adaptations (Poisson loss, S4 layers, spike-history terms) done by the authors for this study. The figures are high quality and way above what I would expect from a conference paper. This study follows and expands a (small) recent trend of using modern machine learning algorithms for generation of neural population activity. LDNS models / LDMs clearly have some advantages over previously suggested models, in that they combine the low-dimensional representation of autoencoders with the generative fidelity of diffusion models. Weaknesses: The authors have adapted the latent diffusion model to the task of generating neural population activity. While I believe they did good work on that, I am less convinced of the evaluation and comparison of their model, which is important to judge its overall usefulness. For a generative model of multivariate time-series, I find the evaluation somewhat lacking. I understand that judging spike train generation is still a much harder task than judging image generation, and that one could argue that to date we don't understand all the relevant aspects of neural population activity. But firing rates, pairwise correlations and population spike counts are features that don't take dynamics into account. Average interspike interval and standard deviations of interspike intervals are still very local temporal features. Computational neuroscience has come up with a host of methods for analysing neural population dynamics -- in particular those with low-dimensional structure as assumed by the LDNS model -- which could be used here for comparing the sampled spike trains against the data. The authors already cited both LFADS and Gaussian Process Factor Analysis, but did not compare e.g. the low-dimensional trajectories extracted from their sampled data against the low-dim. trajectories extracted from the neural recordings. If nothing else, a supplementary figure or two with a handful of additional sampled spike trains against real recordings could help readers judge if the model captures the overall neural dynamics of the data. Another aspect that makes it difficult to evaluate the quality of their suggested model is the lack of comparison against direct competitors. The authors do an excellent job of explaining LFADS and its relevance as a comparison, but from what I understand only compare against LFADS on one of the three numerical experiments (I take that figure A4 which isn't mentioned in the text is also about the monkey data?). I understand that autoLFADS is significantly more computationally expensive to run than the LDNS model, (which I would encourage the authors to state more prominently also in the main text!) but especially for the second experiment with human data, the LDNS model seems to perform the worst of the three experiments, and I could find no alternative model for comparison. Technical Quality: 3 Clarity: 4 Questions for Authors: As explained above, analysis of the full population dynamics of their sampled neural population data would be very interesting. The authors could, but do not have to follow my suggestion of analysing the sampled neural population with one of the more commonly used dynamical dimensionality reduction methods. Can we get some comments or additional analysis of the LDNS model in cases where it doesn't work perfectly? There are several interesting supplementary figures for the Lorenz synthetic data, but for the other two experiments I am left wondering whether the non-negligible model errors arise primarily from the autoencoder or from the diffusion model. Those are the cases where I would most appreciate a comparison of the pairwise correlations from autoencoder against those of the full LDNS model, as in Fig A7 for the Lorenz data. Confidence: 4 Soundness: 3 Presentation: 4 Contribution: 2 Limitations: I think the authors have adequately addressed limitations and possible negative societal impacts of their work. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for their detailed summary and evaluation and suggestions that will significantly improve our work, e.g. recommending to further assess the dynamics of the generated samples. We are also thankful for the generally positive response and describing our work as original. Analyzing population dynamics to assess sample quality beyond spike statistics We agree with the reviewer’s point that an evaluation of LDNS-generated samples in terms of dynamics would be valuable. We addressed this in two different ways: 1\. Principal Component Analysis (PCA) on smoothed spikes: We followed a common approach in neuroscience of performing dimensionality reduction using PCA on smoothed spikes and then visualizing the resulting first n principal components over time (Fig. R7; please see attached PDF, here, n=2). Overall, we see that PCs of unconditional LDNS samples closely match that of the real held-out data samples. This approach allowed us to clearly see inconsistencies in the dynamics, e.g. for an added baseline model pi-VAE (see Reviewer AuW4) that does not model dynamics, leading to flat PCs (Fig. R7, left, yellow) and higher MSE between the median power spectral density of pi-VAE samples to true data as compared to all other methods (Fig. R7, right). 2\. Comparing inferred latent dynamics of sampled spikes using LFADS: As a more sophisticated dynamics analysis, we followed the reviewer’s suggestion and embedded both the true data and the unconditionally generated sampled spiking data from LDNS using LFADS (used here as an analysis tool). This allows us to compare latent dynamics by comparing the distributions of inferred initial states of the LFADS generator RNN (Fig. R8, visualized as PCs of $g\_0$) across true data and generated spikes. This analysis revealed that LDNS spikes more closely capture the broad true data distributions than, e.g., spikes sampled from LFADS (as a generative model) (Fig. R8). Such analyses, however, require a well-fit state-space model, which in of itself poses a challenge for many datasets. We agree on the value of visualizing more spike raster plots and extracted principal components, and will add them in the Appendix for all models and tasks. Similar to Appendix A6, we will also add and quantify power spectral densities of the principal components (Fig. R7) for the different methods against the real data. Fitting the LFADS baseline to the human data and the Lorenz dataset Following the reviewer’s suggestion, we now also trained LFADS on the human dataset and the Lorenz dataset. Human: The human dataset is challenging as the trials are highly heterogeneous with different lengths. LDNS can handle these challenges due to our architectural choices and our masking training scheme even if, as pointed out, LDNS does not work as perfectly (see discussion below) as in the other datasets. Please note that this is a new dataset (released less than a year ago), and to date, no readily available generative modeling baseline exists for this data. To allow for a fair comparison, we now attempted to modify LFADS so that it can be fit to this data. To be able to fit LFADS on this dataset, we had to cut the data into equal length segments of 140 time steps (2.8s), since without major modifications LFADS (with its bidirectional encoder architecture) is not well-suited to handling variable length inputs. Despite capturing the spiking statistics on the 2.8s length it was trained on \-- LFADS failed to capture any realistic dynamics beyond the 2.8s cut-off during sampling (Fig. R3). The latents of LFADS decay to a fixed point when the RNN is run forward beyond 2.8s, indicating that it is ill-suited to variable-length generation of such heterogeneous data (Fig. R3), highlighting the need for flexible methods such as LDNS. We acknowledge that there may be variants of LFADS that can handle this case better, however, our point is that “vanilla” LFADS is unable to handle this task without significant modifications. Lorenz: While it is well established that LFADS fits the Lorenz dataset well (Sussillo et al. 2015, Pandarinath et al. 2018), LFADS struggles with length generalization: Running the LFADS generator on 16 times the original length results in inconsistent latent trajectories (Fig. R2) compared to LDNS (Fig. 2c). We will additionally point out in the main text, not just in the Computational Resources Appendix, that LFADS is significantly more computationally expensive to run than LDNS, and we thank the reviewer for this suggestion. Comparison against additional baselines on the monkey reach task In addition, as also suggested by other reviewers, we include two additional baselines for comparison on the monkey dataset: TNDM (Hurwitz et. al, 2021\) and pi-VAE (Zhou et al. 2020), are VAE-based models that were proposed as analysis tools to jointly study neural and behavioral data. We find that LDNS and its spike-history based extension outperforms these baselines on the monkey dataset (see Fig. R1 and response to reviewers AuW4 and pMhd for implementation details). Contribution of autoencoder vs. diffusion for correlations We agree that disentangling the contribution of the S4 autoencoder and diffusion is useful, particularly in cases when LDNS does not work perfectly. The model errors arise primarily from the autoencoder, not from the diffusion model: The values of pairwise correlations both in monkey reach data and human are very similar for the autoencoder reconstructions and LDNS samples (Fig. R9), i.e. mismatches arose at the autoencoder and not the diffusion stage. Analogous to the Lorenz experiment (Fig. A7), we will add the analyses comparing the autoencoder performance and the diffusion performance in the Supplementary Material for the two other datasets (monkey, human). --- Rebuttal Comment 1.1: Comment: I thank the authors for their in-depth response and the additional analyses they added to address my concerns. I am happy to raise my rating by a point. --- Reply to Comment 1.1.1: Comment: Thank you for the positive response, detailed engagement with our work, and further increasing the score.	Summary: This paper introduces the Latent Diffusion Model for Neural Spiking data (LDNS). LDNS combines the capacity of autoencoders to extract low-dimensional representations of discrete neural population activity with the capability of denoising diffusion probabilistic models to generate realistic neural spiking data. It achieves this by modeling the inferred low-dimensional continuous representations. Through experiments on three different datasets, LDNS has been proven to achieve low-dimensional latent variable inference and realistic conditional generation of neural spiking datasets, providing possibilities for simulating experimentally testable hypotheses. Strengths: 1. Quality: The paper is comprehensive, with detailed explanations of the model's characteristics and corresponding experimental designs. 2. Clarity: The paper is logically clear and well-structured. 3. Importance: The paper significantly contributes to addressing the modeling challenges of complex datasets in neuroscience. Weaknesses: 1. There is only one comparison method in this paper. Technical Quality: 2 Clarity: 3 Questions for Authors: 1. What is the significance of studying the generation of spiking data? Is this generated data of practical value? 2. Have you tried to compare it with other VAE-based methods? Despite the claim of the authors that LFADS is the most successful VAE-based method available, it is clear that no method performs best in all tasks, especially in more cutting-edge tasks like this paper. 3. Can you explain how the stochastic operations in Figure 1 are performed? 4. In the conditional generation experiment of neural activity given the reach direction, the experiment is conducted under conditions of only two directions. Is it possible to conduct the experiment under conditions of three directions? Confidence: 3 Soundness: 2 Presentation: 3 Contribution: 3 Limitations: This paper still has certain limitations. Firstly, the exploration of LDNS in simulating neural activity is currently confined to the abdominal cortex during speech, which leaves the simulation of neural activities under more complex behavioral patterns in other parts of the body unexplored. Secondly, the processing of human-related data in the research raises concerns about privacy protection. In response to these limitations, the following suggestions are offered: 1. This paper has initiated an investigation into the effects of LDNS in simulating neural activities in the abdominal cortex during human speech. To further verify its potential, future research could expand to simulate cortical neural activities in other parts of the body under more complex behavioral patterns, aiming for a comprehensive evaluation of LDNS's applicability and efficacy in the field of neuroscience. 2. Regarding the use of human-related data in the paper, it is suggested that in subsequent research, greater emphasis should be placed on protecting data privacy to avoid negative social impacts. Flag For Ethics Review: ['Ethics review needed: Research involving human subjects'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for finding our work comprehensive and our writing and presentation clear and well-structured. We also appreciate that the reviewer finds our contributions of addressing the modeling challenges of complex neuroscientific datasets significant. Additional comparison with other VAE-based methods Following reviewer suggestions (as well as that of AuW4), we have now included two additional proposed VAE-based models as baselines: Poisson-identifiable VAE (pi-VAE, Zhou et. al, 2020\) and Targeted Neural Dynamical Modeling (TNDM, Hurwitz et. al, 2021\) on the unconditional monkey reach task. We emphasize that while these LVMs have successfully been used for analyzing neural and behavioral data, they were not intended for realistic spike generation. New figures (Fig. Rx) are in the PDF. Compared to these additional baselines, as well as an extended LFADS model augmented with spike history, we found that LDNS remains superior in realistic spike generation (Fig. R1), and recovers structured latents informative of behavior (Fig. R6). Implementation details of these baselines are provided below, and will be included in the revised paper. We also now trained LFADS on the Lorenz and human BCI tasks, in particular to evaluate its ability to length-generalize and handle variable length input data compared to LDNS. We find that LFADS had difficulties in extending the learned dynamics correctly (e.g., Fig. R2,3) – in contrast to LDNS, which can accurately generalize to 16 times the training length in the Lorenz task and can naturally deal with variable length trials in the human task. TNDM: We trained TNDM on the monkey dataset using the original proposed architecture and model hyperparameters. We used 5+5 latent factors, the maximum shown in the original paper. We used the prior N(0,1) to sample the initial generator states for unconditional sampling of spikes (Fig. R1, blue). pi-VAE: We trained pi-VAE on the monkey dataset using the original proposed architecture and model hyperparameters. pi-VAE’s architecture does not consider temporal dynamics, and treats each time point as an independent sample. Furthermore, while Zhou et al. 2020 evaluated pi-VAE on 50ms time bins and straight reaches only, we here use 5ms bins and condition on angles of all reaches in the middle and end of the trajectory. Sampled spiking data shows poor statistics mainly due to the lack of temporal dependence in the model (Fig. R1, R7, yellow). Significance and practical value of realistic spiking data generation Accurate modeling and generation of neural spiking data has scientific, clinical, and practical value. If generated data were used for augmenting training for a downstream task, for example, introducing obvious artifacts (such as not capturing refractory periods) can introduce bias. Furthermore, when studying relations between variables in neuroscience with such emulator models, subtle changes such as spike times or phases when spikes occur in oscillations are known to make a difference. Modeling activities from other brain regions Our work proposes a general methodology for modeling and generating spiking data, and is agnostic to the particular brain region where it may be recorded from. In our evaluation, we have considered the motor cortex of monkeys and the speech cortex of humans, but it can be straightforwardly applied to other datasets as well. We will discuss these possibilities in the revised paper. Clarification on ethics concern and suggestions on data privacy The human BCI dataset we used is publicly available under a CC0 1.0 Universal Public Domain Dedication license. It is from a peer-reviewed paper that was previously published in Nature (Willett et al. (2023). A high-performance speech neuroprosthesis. Nature.), and according to this paper, was cleared in ethical reviews by the Institutional Review Board at Stanford University (protocol \#20804). Our paper did not provide new sensitive data, nor does it provide a methodology to obtain such data. We will make this information clear in the appendix of the revised paper. We agree that protecting data privacy is very important, especially when using sensitive data involving human participants, and will further acknowledge this in the Discussion section. Other clarifications Stochastic operation in Figure 1: Unless specified otherwise, we use the Poisson observation model as the stochastic operation, going from inferred Poisson rates to spike counts. In specific scenarios (e.g., Fig. 4e), we extend this observation model to include spike history dependence in the LDNSsh model. This dependence allows us to capture e.g. refractory periods of neuron firing behavior by reducing the probability of a spike occurring directly after a previous spike, enabling LDNSsh to accurately capture biologically plausible spiking statistics. 3-axis reach conditioning: Our architecture is agnostic to the number of reach axes. The dataset we consider involves monkeys performing 2-dimensional reach tasks, which we pass to the diffusion model as two additional channels or as a scalar reach angle (see Fig. 5 and A1). This can be extended straightforwardly to condition on higher-dimensional behavioral variables, allowing to also model reaches in 3-dimensions. We hope these additions, in particular the inclusion of additional comparison methods, and clarifications, address the reviewer’s concerns and enable them to raise their score.	Summary: This paper proposes a new generative model for neural spiking datasets. The model consists of a deterministic, deep SSM (S4) autoencoder paired with a diffusion model of the learned autoencoder latent sequences. This enables generating accurate neural time series traces across variable length trials lasting up to 10ms and conditional generation given behavioral covariates. The approach is applied to a synthetic dataset and two different neural datasets, where the authors investigate a variety of uses of the model. Strengths: The proposed generative model of neural activity appears powerful and generally useful of fitting neural responses across a large variety of conditions. Both the unconditional and conditional generative performance of the model is impressive. Many components of the model and training process are well-motivated and clearly described. For these reasons, I find this to be a significant contribution. Weaknesses: While much of the modeling approach is well-motivated, I do not find that to be the case for the specific implementation of the spike-history component. Additionally, it appears that the spike-history component is responsible for much of the improvement over LFADS, and not the alternative underlying generative model that is the primary novel contribution of this paper (one could imagine also training LFADS with a spike history filter). In particular, it is not well-motivated why the filters are trained post-hoc and why the softplus approximation is preferred over using the exponential function. Technical Quality: 2 Clarity: 3 Questions for Authors: - Why is the spike-history filter trained posthoc instead of during the autoencoder training? Additionally, can the authors provide more details about why they choice the softplus approximation? I do not necessarily agree that the approximation is accurate, and its not clear why this approximation is even necessary during training or why it is used over a numerically stable exponential function. Is this primarily an issue when the model is run in generative mode? - The LDNS overestimates some of the pairwise neural correlations in the attempted speech dataset. Is it typical for LDNS to overestimate pairwise correlations? Could this be improved by increasing the latent dimensionality of the model, to allow for more uncorrelated latent dimensions? - Could the authors comment on the use of S4 as compared to other deep state space models like Mamba? Does one appear to work better than the other? - Have the authors considered using the approach to do conditional generation of the attempted speech neural recordings given the cued sentence? This seems like a challenging but direct application of the proposed method. Confidence: 4 Soundness: 2 Presentation: 3 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 finding the contributions presented in our work significant, and for noting the flexibility and performance of our model in generating unconditional and conditional neural spiking data in a wide variety of conditions. The reviewer had questions and concerns over training and architectural details of the model, and the role of the spike history dependence model in the superior performance of LDNSsh. To disentangle the contribution of this observation model from the architectural contributions of our work, as suggested by the reviewer, we now trained an extended LFADS model by equipping it with the same spike history observation and found that it is still matched or outperformed by the equivalent LDNSsh model. We also discuss our reasoning for fitting these terms post-hoc, and why we used a softplus approximation. Finally, we address the reviewer’s questions on architectural choices, and on the attempted speech dataset. New figures (Fig. Rx) are in the PDF. Equipping LFADS with spike history We agree that a better characterization of the contribution of spike history, relative to S4 and diffusion, would be beneficial. We have now extended LFADS with spike history dependence (LFADSsh) using the approach we introduced for LDNS, and found it to improve its performance (Fig. R1,4). However, LDNS with spike history (LDNSsh) is still superior or on par on spike generation metrics. Furthermore, even without spike history, LDNS was already on par or better compared to its counterpart in LFADS in our original evaluation, and we will emphasize the corresponding comparisons more prominently in Table 1 (LDNS vs. LFADS, with and without sh). Thus, while spike history couplings are needed for realistic spike train generation (as neural data contains dynamics that are not shared across the population, and thus cannot be captured by a low-d latent state), the performance benefits of LDNS are not due to spike history couplings alone. Your suggestion also allowed us to show that our post-hoc fitting of spike-history couplings provides a way to increase the realism of generated spike data not just for LDNS but for a class of VAE-based methods. Table 1 \|Method\|$\mathbf{D_{KL},\text{psch}}$\|RMSE pairwise corr\|RMSE mean isi\|RMSE std isi\| \|--\|--\|--\|--\|--\| \|AutoLFADS\|$0.0040\pm2.2\times10^{-4}$\|$0.0026\pm1.25\times10^{-5}$\|$0.039\pm0.003$\|$0.029\pm0.001$\| \|LDNS\|$0.0039\pm3.9\times 10^{-4}$\|$\mathbf{0.0025\pm1.1\times10^{-5}}$\|$0.037\pm0.001$\|$\mathbf{0.023\pm0.001}$\| \| \| \| \| \| \| \|AutoLFADSsh\|$0.0036\pm2.1\times10^{-4} $\|$0.0026\pm1.8\times10^{-5}$\|$0.034\pm0.002$\|$\mathbf{0.023\pm0.0001}$\| \|LDNSsh\|$\mathbf{0.0016\pm6.2\times10^{-4}}$\|$\mathbf{0.0025\pm1.07\times10^{-5}}$\|$\mathbf{0.024\pm0.002}$\|$\mathbf{0.023\pm0.001}$\| Post-hoc training for spike history, and choice of softplus vs. exponential Taking rate predictions from LDNS (or any model, see previous paragraph), we optimize the spike history parameters with respect to the ground-truth spiking data. As a result, this alternative observation model does not impact the latents inferred by the S4-autoencoder. It allows us to independently improve generated spike trains, in particular to capture realistic autocorrelations, an important component towards accurate modeling of spiking data that is missing in the deep LVM literature as a whole. Furthermore, this opens the possibility for replacing our current version of spike history dependence with more sophisticated observation models without re-incorporating it into autoencoder or diffusion model training. We fit spike history dependence post-hoc since jointly optimizing with the autoencoder would likely interfere with the coordinated dropout regularization (Keshtkaran et al. 2019, see methods), which has been shown to be critical for other LVMs for neural dynamics. As we show in the above experiment, this post-hoc fitting process can be straightforwardly adapted to improve other models as well. Empirically, we found that using the exponential function was less numerically stable and resulted in higher loss values and poorer data fit than using the softplus-approximation. Softplus resulted in faster training convergence and a lower final loss (Fig. R5). Furthermore, we believe that in the low spike count regime this is a fair approximation, as 99.8% of the inferred rates (across time bins) were less than 0.2 (per bin). Other questions S4 vs. Mamba as an architectural choice: S4 is parameterized as a time-invariant (stationary/autonomous dynamics) system, while Mamba and other context-selective models are parameterized as (and may be better suited for) non-stationary, input-driven dynamics, such as the human speech data. Both S4 and Mamba allow for time-parallelized training and length generalization. Exploring Mamba and other non-stationary linear recurrence models is an interesting idea of future work, but would go beyond the scope of this project. Overestimation of correlation in attempted speech data: Based on the reviewer’s suggestion, we increased the dimensionality of the latent space in LDNS from 32 to 48 and observed that the overestimation remains. We also analyzed the autoencoder and diffusion model separately and find that the inflated correlations are a result of the AE, not the diffusion part (Fig. R9). We do not yet fully understand the exact source of this overestimation, which we only observed for this particular dataset, and agree that further characterization would be beneficial. Conditional generation of speech data: While this application would be a natural extension for conditional generative modeling on complex behavioral data, in this work we focus on developing the methodology to enable such exciting applications in the future. Decoding speech from spiking data is an active research area, and consequently, evaluating the correctness of sampled data and decoded speech would be beyond the scope. --- Rebuttal Comment 1.1: Comment: Thank you for your thorough response and for running the additional experiments. I especially appreciate the new comparisons of the spike history filter with LFADS, and for the additional baselines and visualizations. Overall, I have decided to increase my score and recommend accepting this paper. Nonetheless, I still remain unconvinced that the spike-history filter should be fit post-hoc and find the need for the softplus approximation unsatisfactory. Perhaps this implies the model should use a softplus nonlinearity rather than exponential during the initial training phase. Alternatively, joint training may alleviate the stability issues. To fit the model jointly with the spike history filter, I suggest using alternative masking schemes -- see e.g. a very recent paper [1] with alternative options that should work with the spike history filter. [1] Towards a "universal translator" for neural dynamics at single-cell, single-spike resolution. Zhang et al., arXiv:2407.14668 --- Reply to Comment 1.1.1: Comment: Thank you for the positive response, detailed engagement with our work, and further increasing the score. We really appreciate the thorough questions about the spike history term and agree it would be interesting to see the effect of different nonlinearities in future work and how joint training would interact with coordinated dropout and alternative regularization schemes. Thank you for pointing us toward this paper; combining such approaches is indeed very promising.	Summary: The authors here propose a new autoencoder style latent variable model for neuroscience which flexibly adapts to variable time-series using S4 encoders and decoders. They then train diffusion based models with option behavioral covariates to generate realistic neural spiking data. Additionally, they use a more flexible spiking likelihood with history-filters which more accurately capture within neuron statistics. They evaluate their model on a synthetic lorenz-attractor example as well as multiple real-work datasets. Strengths: I see three separate contributions of this paper -- 1) The ability to handle time-varying inputs in VAE based neural models is rare, as the authors point out, yet important in many practical neuroscience applications. 2) Using diffusion-based methods to generate samples from the auto-encoder inferred latents, allowing for the generation of variable length, realistic spiking data on unseen behaviors. I think the results of figure 5 are particularly interesting in this regard. 3) the addition of a history-based poisson likelihood, which better captures individual spiking statistics. This is a somewhat superficial contribution, but is nonetheless important to many of the authors' reported improvements. Weaknesses: I think the authors could do a better job communicating the disparate contributions and capabilities of this model more clearly to the reader, especially in contrast to existing approaches. For example, I am having a hard time understanding to what extent the spike-history likelihood is important for this model. Many of the reported results in figures 2 and 3 are on the statistics of the spiking. Are these figures using the likelihood with the spike-history filter? I am assuming they are not, as the spike-history filter is explicitly specified as the likelihood used for figure 4, but not in figures 2 and 3. If they are not used here, why not? Further, can the authors demonstrate that this spike-history filter leads to a different scientific result? I.e. are the conditioned latents any more accurate or do they provide any more insight if one likelihood is used compared to another. The evaluations in the supplement demonstrate that the spiking statistics is better captured with this more sophisticated likelihood, but further discussion as to why this is important for scientific insight would be appreciated. Overall, the authors primarily use spiking statistics as their measure of accuracy in this model throughout the paper. While the ability of a model to capture single-level neural statistics is important, it seems to me that the core use this model would have to an experimental practitioner is to visualize latents in an informative way in trial-varying data, potentially conditioned on behavior. Because of this, it would be nice to see more evaluations of the latent space, and not focus as much on the spiking statistics. Similar to the point above, it would be interesting to take a couple existing autoencoding LVMs used in neuroscience (like LFADs and others) and augment them with the same history-based Poisson likelihood. Then we would be able to see more clearly the contributions of the other features of the model such as S4 and diffusion, which I think are quite interesting, and their roles in identifying interpretable scientific latents where other models fail or cannot do so, such as in the trial-varying case or conditioned on behavioral covariates. Lastly, there are many models that use autoencoder based approaches other than LFADS that could be compared to here but are not. It is of course not possible to compare to all of them, but some more thorough evaluation and discussion alongside existing approaches I think would significantly improve the paper. See for example, Poisson Interpretable VAE, Targeted neural dynamical modeling, *PSID and Duncker and Sahani 2018. LFADs alone, especially one without the same history-dependent observation likelihood, does not provide a complete picture of the capabilities of latent identification of this model in relationship to other other approaches. ) "Learning identifiable and interpretable latent models of high-dimensional neural activity using pi-VAE" ) "Targeted Neural Dynamical Modeling" *) "Modeling behaviorally relevant neural dynamics enabled by preferential subspace identification" Technical Quality: 4 Clarity: 2 Questions for Authors: Are the results reported in figures 2 and 3 using the spike history filter or just Poisson likelihoods? What is the 'kde' in figure 3d? Confidence: 4 Soundness: 4 Presentation: 2 Contribution: 3 Limitations: See above. Further discussion and potential evaluation of this model alongside other approaches, and the dissociating the particular role of the likelihood as compared to the other model features, especially concerning scientific purposes, would be helpful for this paper. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for finding our work relevant, and our approach sound. Based on your suggestions, we have now performed new baseline experiments with additional VAE-based models. We also performed latent space analyses of sampled spikes from all models (using PCA and LFADS embeddings) to supplement the spike statistics. We additionally inspected the quality and interpretability of LDNS-derived latents as suggested. Lastly, we augmented LFADS with spike history dependence for a more clear comparison, and clarify how and why we account for it post-hoc. In summary, LDNS remains the most performant model overall for spike generation, and its single-trial latents are informative of behavior. We detail the experiments and analyses below, and clarify the disparate contributions and capabilities of LDNS more clearly, especially in contrast to existing approaches. We hope these additions address the reviewer’s concerns and enable them to raise their score. New figures (Fig. Rx) are in the PDF. New VAE-based baseline experiments We implemented two new VAE-based models suggested by the reviewer, TNDM (Hurwitz et. al. 2021\) and pi-VAE (Zhou et al, 2020), on the unconditional monkey reach task, and find that LDNS is superior in realistic spike generation (Fig. R1, see PDF). TNDM: We trained TNDM on the monkey dataset using the original proposed architecture and hyperparameters. We used 5+5 latent factors, the maximum in the original paper, and used the prior N(0,1) to sample the RNN initial states for unconditional generation. pi-VAE: We trained pi-VAE using the original architecture (and model hyperparameters), which does not consider temporal dynamics and treats each time point as an independent sample. Thus, pi-VAE samples exhibit poor spiking statistics and no temporal structure (Fig. R1, R7, yellow). Evaluation of LDNS latents We agree that, while generation of realistic spike trains in terms of spike statistics is important, many neuroscientists are interested in the extracted latents. Thus, we analyzed LDNS-extracted latents of unseen test samples from the monkey reach dataset and colored them by reach angle (Fig. R6, straight reaches only for visualization). Note that behaviorally relevant information is clearly reflected in single-trial latents of LDNS (Fig. R6, bottom row). Furthermore, this latent structure is preserved when sampling from LDNS conditioned on unseen velocity trajectories (Fig. R6, top row). We will add this result to Fig. 5, highlighting the ability of LDNS to extract meaningful latents. Contribution of spike history and extension to LFADS Spike trains exhibit autoregressive temporal dependencies not shared across the population, and therefore spike-history coupling is needed for any low-dimensional model to achieve realistic spike train generation. The spike history model in LDNS is fit post-hoc after autoencoder training, and therefore does not impact the inferred latents. This allows us to independently improve LDNS-generated spike trains and their autocorrelations, an important component towards accurate modeling of spiking data. Directly optimizing the spike history features during autoencoder training might interfere with the coordinated dropout regularization (Keshtkaran et al. 2019, see methods), which has been shown to be critical for other LVMs of neural dynamics. Lastly, we view the post-hoc augmentation of the observation model with spike history as a key modular contribution, which can be flexibly applied to other generative models. Based on the reviewer’s suggestion, we have additionally extended LFADS with spike history dependence, which improves its performance (Fig. R1,4). However, LDNS with spike history is still superior or on par on spike metrics against this extended version of LFADS. We also emphasize that, both with and without spike history, LDNS outperforms its LFADS counterpart, and we highlight the corresponding comparisons in Table 1 (see Reviewer y7Q4). We will include these results and clarifications in the revised paper. Contributions of LDNS (in contrast to other approaches): - LDNS combines S4 and diffusion models for the purpose of accurately modeling and generating neural spiking data—a task often ignored by other LVMs designed for neural data analysis (such as LFADS, pi-VAE, and TNDM). - The S4 autoencoder and diffusion model are trained in separate stages, offering modularity and easier debugging, while both components naturally account for temporal dependencies (unlike pi-VAE). - Furthermore, S4 is autoregressive, similar to other RNN-based models, but empirically we found it to perform better when extending past the training trial length and more readily handle variable length data (compared to LFADS), due to the masked training procedure we propose here. - Finally, the spike history-dependent observation model is modular and can be optimized post-hoc using rate predictions of any model, offering flexibility while improving spike generation quality. - One feature provided by other neural-behavioral analysis models (such as pi-VAE and TNDM) is an explicit disentangling of neural vs. behavior-relevant latents, which we did not consider but is a possible future extension for LNDS. Are the results reported in figures 2 and 3 using the spike history filter or just Poisson likelihoods? For the results in Figs. 2, 3, 4(b,c,d), 5, we only use the Poisson likelihood with no history terms. In the Lorenz experiment, we know the ground-truth generative model uses Poisson emission, and for the human BCI dataset we omitted them due to the large bin size (20ms) used here. What is the 'kde' in figure 3d? A Kernel Density Estimate (KDE) with a Gaussian kernel to estimate the population spike count distribution. We will clarify both points in the revision. --- Rebuttal 2: Comment: This is a very thorough and impressive response. I think these additional figures paint a much more complete picture of the model's capabilities in a way that now clarifies it's disparate contributions compared to competing approaches. I believe these will substantially increase the work's impact. Particularly, R2 and R3 clearly demonstrate the LDNS addresses something that is lacking in modern generative LVMs for neural data, and I believe they should be highlighted in the main manuscript. R1 also adds important baselines that would be nice to prominently highlight as well (particularly including the LFADS sh). The additional latent space characterizations (R6-R8) helps future model practitioners get an idea of the model's scientific utility. It would be nice if possible to include some of this in the main body of the paper, but I don't believe it is necessary. I have updated my score accordingly and am excited to hopefully see this work at this year's NeurIPs. --- Rebuttal Comment 2.1: Comment: Thank you so much for the prompt and kind response, and now recommending acceptance. We appreciate your thorough engagement with our work and detailed comments, which allowed us to clarify our contributions. We agree that adding these analyses will strengthen the paper.	Rebuttal 1: Rebuttal: We thank all the reviewers for their constructive and detailed engagement with our work, resulting in many helpful comments and opportunities for clarification. We are especially grateful for several reviewers’ assessments that the work is “original” (mYEj), well written and clearly motivated (y7Q4, mYEj, pMhd), technically sound (mYEj, AuW4) with “impressive performance” (y7Q4), and represents a significant contribution to the field (pMhd, y7Q4). We agree with many of the suggestions and questions raised, and respond individually to each review in detail. We summarize here the main points and new experiments. We hope that our response addresses their questions and concerns, allowing all reviewers to recommend our work for acceptance. Summary of original contribution LDNS combines S4-based autoencoders and diffusion models for both extracting low-dimensional latent dynamics from neural population spiking data and generating realistic spike trains, an aspect of evaluation often ignored by other works in the literature. On a commonly used monkey reach task, LDNS outperforms or matches LFADS in all metrics. By equipping LDNS with a modular spike history-dependent observation model, it surpasses LFADS on all metrics and accurately captures spike autocorrelation. Moreover, LDNS works well with variable trial lengths and shows length generalization abilities. Finally, LDNS can conditionally generate realistic spiking data based on behavioral covariates for the monkey reach task. Summary of new results In response to the reviewers, we substantially expanded our evaluation with new experiments: On the monkey reach task, LDNS outperforms two newly suggested baseline models (Fig. R1, see PDF). We also augment LFADS with spike history and report increased performance, but it is still surpassed or matched by LDNS-sh on the same task (Fig. R4, Table 1 in response to pMhd). In addition, we evaluate LFADS on the other two datasets and find that unlike LDNS, LFADS failed at length generalization (Fig. R2,3). Moreover, we show that on the monkey task, LDNS latents contain behaviorally relevant information, suggesting their utility in analyzing and visualizing neural data (Fig. R6). Finally, we evaluate the dynamics of generated spikes sampled from LDNS (and other models) via PCA and LFADS embedding, and find that LDNS accurately captures the dynamics of real data (Fig. R7,8). 1\. New baseline experiments (AuW4, pMhd, mYEj) We conducted numerous additional baseline experiments to demonstrate the contributions of LDNS relative to existing (VAE-based) methods: We implemented and fit two other methods, pi-VAE (Zhou and Wei, 2020\) and TNDM (Hurwitz et al. 2021), to the monkey dataset (Fig. R1), and find that LDNS still consistently outperforms the others on spike generation. Details in individual responses to AuW4 and PMhd. We added our proposed spike history observation model (see point 3 below) to the LFADS baseline on the same task, which increases performance but still not to the level of LDNS with spike history. We note that LDNS without spike history is still superior or on par compared to all baselines, highlighting the contribution from the latent diffusion model. 2\. Evaluating LFADS on the other datasets (mYEj) We further applied LFADS on the Lorenz and human dataset, in particular, to assess the length-generalization ability of LDNS relative to existing models of neural dynamics. It is well established that LFADS fits the Lorenz dataset well (Pandarinath et al. 2018). However, LFADS struggles with length generalization (Fig. R2), while LDNS samples can be generated at 16x the training trial length (Fig. 2c), a key feature made possible by S4. We also fit LFADS to spike recordings from the human brain, a challenging task due to highly heterogeneous trials with variable length, which LDNS can handle thanks to its architecture and masking scheme. To fit LFADS, we cut the data into equal length segments. Despite successful training, LFADS failed to capture dynamics beyond the cut-off during sampling (Fig. R3 vs. Fig. 3). This highlights the capability of LDNS to deal with variable-length data, which is highly relevant for many neuroscience datasets (as pointed out by AuW4). Further discussion in response to reviewer mYEj. 3\. Contribution of, and clarifications on, spike-history coupling (AuW4, y7Q4) We clarify that the spike-history observation model is applied after first training the autoencoder model with standard Poisson likelihood. The history model increases the quality of the sampled spikes, and can be flexibly applied to other models. Addressing questions raised by reviewers, we ran a new experiment augmenting LFADS with spike history, which increases the realism of generated samples from this baseline model (Fig. R4), though it still underperforms LDNS with spike history. 4\. Analysis of LDNS latents (AuW4, mYEj) We agree that single-trial latent analysis is of interest to the neuroscience community, and have therefore evaluated the quality of LDNS latents (Fig. R6). On the monkey reach dataset, we plot PCs of the inferred latents and show that behaviorally relevant information (colored by reach angle) is reflected in the latent space of LDNS, a desirable property for neuroscientists aiming to visualize their data. 5\. Evaluating dynamics of LDNS samples (mYEj) We evaluated the realism of LDNS samples in terms of underlying low dimensional dynamics using PCA (applied to smoothed, generated spikes vs. true data, Fig. R7). This suggestion clearly distinguished failure cases (e.g., no temporal dependencies in samples generated using pi-VAE). As suggested by reviewer mYEj, we also embedded the generated spikes using LFADS, and show that LFADS latents extracted from LDNS spikes more closely capture the broad distributions of the true data than, e.g., spikes sampled from LFADS (Fig. R8). Pdf: /pdf/08e7274d1e2416c4e329c9478f8d0069f57fc398.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
NeoRL: Efficient Exploration for Nonepisodic RL	Accept (spotlight)	Summary: This paper proposes a model-based RL algorithm NeoRL for continuous state-action spaces in the nonepisodic setting, where the agent learns from a single trajectory without resets. Strengths: 1. The paper provides the first regret bound for nonepisodic RL in general nonlinear systems, addressing a gap in the literature. 2. NeoRL is grounded in the optimism principle and leverages well-calibrated probabilistic models, providing a theoretically justified exploration strategy. 3. The experiments demonstrate the practical effectiveness of NEORL, achieving sublinear regret and converging to the optimal average cost in various environments. Weaknesses: 1. The optimization problem in Equation (6) for policy selection may be computationally expensive, especially for high-dimensional systems. 2. While the experiments demonstrate the efficacy of NEORL, a more comprehensive evaluation across a diverse set of environments and comparisons with state-of-the-art methods would strengthen the empirical results. 3. The authors can discuss some data-driven MPC framework, like [1,2]. [1] Berberich J, Köhler J, Müller M A, et al. Data-driven model predictive control with stability and robustness guarantees[J]. IEEE Transactions on Automatic Control, 2020, 66(4): 1702-1717. [2] Berberich J, Allgöwer F. An overview of systems-theoretic guarantees in data-driven model predictive control[J]. arXiv preprint arXiv:2406.04130, 2024. Technical Quality: 4 Clarity: 3 Questions for Authors: 1. How sensitive is the performance of NeoRL to the choice of kernel and the maximum information gain? What guidance can be provided for selecting appropriate kernels in practice? 2. Can the bounded energy assumption be relaxed or replaced with alternative assumptions to broaden the applicability of NEORL? Confidence: 2 Soundness: 4 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 for their feedback and are happy to see the reviewer acknowledge how our work bridges a significant gap in RL theory. In the following, we respond to the weaknesses and questions raised by the reviewer. W1: Expensive computation. A1: Thanks for raising this concern. Indeed the optimization problem in (6) may fair infavourably for high-dimensional systems. However, there are heuristic approximations that can be made that favor much better for the high dimensional case (c.f., [1, 2] or our response to reviewer zoj1’s second question). W2: Comparisons with state-of-the-art methods. A2: In our experimental evaluation, we focus only on model-based methods due to their sample efficiency. As we highlight in section 4, MBRL methods vary mostly in how the model is represented (GPs, BNNs, world models, etc), the choice of policy optimizer, and how the dynamics are propagated to facilitate exploration. Our contribution is for the third axis of differentiation, i.e., we show that the celebrated principle of optimism works for many cases in the nonepisodic setting. Thereby we compare our method to other approaches of dynamics propagation such as mean (which is most widely used), trajectory sampling (PETS [3]), and Thompson sampling. To the best of our knowledge, these are the only approaches (along the third axis) typically considered in MBRL. W3: Discuss some data-driven MPC framework. A3: Thanks for pointing us to these references, we have added them to our related work. Q1: Sensitivity to the choice of kernel. A1: In theory, the choice of the kernel has an effect on the convergence guarantees/max info gain (c.f., Table 1 in Appendix A). Practically, we used the most common kernel, the Gaussian kernel, in our experiments which worked completely fine. However, according to the theory, choosing the right kernel can affect the performance/convergence of the underlying algorithm. One way to make this choice is to use some offline/pre-recorded data on the system for kernel selection or meta-learn the kernel parameters from other data sources (c.f., Rothfuss, Jonas, et al. "Meta-learning priors for safe Bayesian optimization." Conference on Robot Learning. PMLR, 2023) Q2: Bounded energy assumption. A2: Thanks for this very interesting question. The bounded energy assumption stems from the classical results on Markov chains (Meyn, Sean P., and Richard L. Tweedie. Markov chains and stochastic stability. Springer Science & Business Media, 2012.), therefore we are unsure if this can be further relaxed. Nonetheless, we are currently looking into possible ways to relax this assumption. However, as highlighted in Corollary 2.5., for many practical problems, where the control input is bounded and we have at least 1 policy with bounded energy, this assumption is satisfied. If the system is linear, having a stabilizing controller is enough [4], so perhaps something like this could be enough also for our case. References 1. Kakade, Sham, et al. "Information theoretic regret bounds for online nonlinear control." Advances in Neural Information Processing Systems 33 (2020) 2. Sukhija, Bhavya, et al. "Optimistic active exploration of dynamical systems." Advances in Neural Information Processing Systems 36 (2023) 3. Chua, K., et al. (2018) Deep reinforcement learning in a handful of trials using probabilistic dynamics models. Advances in neural information processing systems. 4. Simchowitz, Max, and Dylan Foster. "Naive exploration is optimal for online lqr." International Conference on Machine Learning. PMLR, 2020. --- Rebuttal Comment 1.1: Title: Follow up on the rebuttal Comment: Dear Reviewer, We hope this message finds you well. We have noticed that our detailed rebuttal, addressing each of the concerns raised in your review, has not yet received any feedback. Please let us know if our responses address your concerns or if you have any other concerns. We hope with our response we could further reinforce your confidence and positive evaluation of our work. Thank you, Authors	Summary: This work introduces a novel model-based RL algorithm, named NeoRL, for nonepisodic RL problems with unknown system dynamics and known costs. A cumulative regret bound is provided for NeoRL with well-calibrated dynamic models. The proposed method achieved lower accumulative regret and average cost compared with baselines in several continuous control tasks. In the end, NeoRL shows it needs less reset before convergence in a reverted pendulum task with automatic reset. Strengths: 1. the research question this paper tries to address is important and interesting, as the difficulty of resetting the environment is a notorious blocker for deploying RL agents in the real world. 2. A bound for cumulative regret is provided for the proposed algorithm when certain conditions are satisfied. 3. The proposed algorithms show lower average cost and cumulative regret than baselines in the empirical evaluation. Weaknesses: 1. The paper is difficult to follow for readers without much control theory background (such as me), and it is difficult to distinguish the algorithmic contributions of this work. Could the author provide a more intuitive explanation about how NeoRL is connected and different from [1,2] and which part of the algorithm actually improves performance in a non-episodic setting? 2. Another major concern of mine is the selection of baseline algorithms, which are not compared to other recent model-based RL algorithms, such as [3-5] and RL algorithms designed to deal with non-episodic problems [6, 7]. 3. No analyses were presented to understand how critical design choices influence the proposed methods' performance, such as the choice of planning horizon H_0 and whether to double the planning horizon. [1] Treven, L., Hübotter, J., Dorfler, F. and Krause, A., 2024. Efficient exploration in continuous-time model-based reinforcement learning. Advances in Neural Information Processing Systems, 36. [2]Curi S, Berkenkamp F, Krause A. Efficient model-based reinforcement learning through optimistic policy search and planning. Advances in Neural Information Processing Systems. 2020;33:14156-70. [3]Hafner D, Pasukonis J, Ba J, Lillicrap T. Mastering diverse domains through world models. arXiv preprint arXiv:2301.04104. 2023 Jan 10. [4] Hansen N, Wang X, Su H. Temporal difference learning for model predictive control. arXiv preprint arXiv:2203.04955. 2022 Mar 9. [5] Hansen N, Su H, Wang X. Td-mpc2: Scalable, robust world models for continuous control. arXiv preprint arXiv:2310.16828. 2023 Oct 25. [6] Sharma A, Ahmad R, Finn C. A state-distribution matching approach to non-episodic reinforcement learning. arXiv preprint arXiv:2205.05212. 2022 May 11. [7] Chen A, Sharma A, Levine S, Finn C. You only live once: Single-life reinforcement learning. Advances in Neural Information Processing Systems. 2022 Dec 6;35:14784-97. Technical Quality: 3 Clarity: 3 Questions for Authors: 1. Could the author provide a more intuitive explanation about which part of the algorithm improves performance in non-episodic settings? 2. Could the author explain why the planning horizon needs to be doubled after each “artificial episode”? 3. Is NeoRL extendable to problems with unknown rewards (cost functions)? Confidence: 2 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The limitations and assumptions for the theory results are discussed in section 2 Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your feedback. In the following, we respond to the weaknesses and questions raised by the reviewer. W1: Difficult to follow for people with limited knowledge of control theory and connection to other prior work on optimistic exploration. A1: While control theory plays a crucial role in our analysis, we understand that it can be tough to follow with limited prior knowledge. We’d be happy to address any specific questions on the manuscript regarding this or provide additional explanations in the parts of the papers if the reviewer believes they might help the reader. On the comparison to [1, 2], both algorithms leverage the concept of optimism but consider very different settings. [1] studies the episodic setting in discrete time, whereas [2] for continuous time. As the reviewer zoj1 also highlights, we are not the first to propose optimistic exploration for model-based RL, but, to the best of our knowledge, we are the first to study it in the context of nonlinear systems and nonepisodic RL/average cost criterion. Algorithmically, a key difference is that [1] optimizes the policy for a finite horizon, [2] for continuous-time and finite horizon, and both reset the environment after every episode. In both cases, the horizon $H$ is fixed. We optimize for the average cost criterion, where there is no notion of a horizon. Since the settings/problems are very different, we cannot quantify the difference in performance among the different methods. NeoRL in essence leverages the same idea of optimism as [1,2] but studies the much more challenging non-episodic setting. W2: Baselines A2: In our experimental evaluation, we focus only on model-based methods due to their sample efficiency. As we highlight in section 4, MBRL methods vary mostly in how the model is represented (GPs, BNNs, world models etc), the choice of policy optimizer, and how the dynamics are propagated to facilitate exploration. Methods [3-5] study the first two axes (representation, e.g., RSSMs or policy optimization TDMPC). Furthermore, they are developed for the episodic/discounted reward setting with POMDPs, we study (theoretically and practically) the average cost criterion with MDPs, therefore these methods significantly diverge from our setting. Crucially, our contribution is for the third axis of differentiation, i.e., we show that the celebrated principle of optimism works for many cases in the nonepisodic setting. To this end, we study different dynamics propagation approaches such as mean sampling (this is also used in [3-5] where no epistemic uncertainty is considered), trajectory sampling (PETS), and Thompson sampling. To the best of our knowledge, these are the only approaches (along the third axis) typically considered in MBRL. Lastly, note that [6, 7] both assume access to prior data, which we do not. Furthermore, they are model-free methods whereas we focus on model-based approaches. Q1: Intuitive explanation about which part of the algorithm improves performance in non-episodic settings A1: We are unsure about what the reviewer means by “which part of the algorithm improves performance in non-episodic settings”. We would appreciate it if the reviewer could elaborate on the question further. However, we also provide a tentative response; The key contribution of our work is to show that optimism, which is often used in bandit optimization and episodic RL, also yields theoretical guarantees and good empirical performance for the non-episodic case. Hence, akin to the episodic setting [1, 2, 8] optimism is crucial for NeoRL's theoretical guarantees. We also refer the reviewer to our response to W1. W3/Q2: Doubling of the planning horizon. A2: Note that it is not the planning horizon, but the model update horizon that is doubled, i.e., the frequency of our model update is reduced as we run the algorithm for longer. The intuitive explanation for this is that the longer we run the algorithm, the more data we collect and our model gets more accurate. Thus it requires less regular updates. Also, by doubling the horizon, we also improve the quality of the data by reducing transient effects in the collected trajectories. In practice, we observe that having a fixed horizon also works very well. In this case, the choice of the horizon depends on the available compute, the shorter the horizon, the more often you update your model. Furthermore, note that also other algorithms for the non-episodic setting increase the “artificial horizon/episode length” [9, 10]. This is also common for bandit optimization (see [11]). Q3: Extension to unknown rewards (costs). A3: Yes, NeoRL can in principle be extended to this setting. This can be simply done by including the cost “as part of your dynamics”. Moreover, given $x_t, a_t$ our model predicts the augmented $x_{t+1}, c_{t}$ and the last elemented of the augmented is used in our cost function. Under similar continuity assumptions on the cost as for the dynamics, we can extend our analysis to this setting. Having addressed the reviewer’s questions, we would appreciate it if the reviewer would increase their score for our paper. For any remaining questions, we are happy to provide further clarification. References [1] -- [7] as listed by the reviewer. [8] Kakade, Sham, et al. "Information theoretic regret bounds for online nonlinear control." Advances in Neural Information Processing Systems 33 (2020) [9] Simchowitz, Max, and Dylan Foster. "Naive exploration is optimal for online lqr." International Conference on Machine Learning. PMLR, 2020. [10] Auer, Peter, Thomas Jaksch, and Ronald Ortner. "Near-optimal regret bounds for reinforcement learning." Advances in neural information processing systems 21 (2008). [11] Besson, Lilian, and Emilie Kaufmann. "What doubling tricks can and can't do for multi-armed bandits." arXiv preprint arXiv:1803.06971 (2018). --- Rebuttal Comment 1.1: Comment: I thank the authors for their very detailed response, which addressed most of my concerns and made the contribution of this work clear. I raised my score from 4 to 6. --- Reply to Comment 1.1.1: Title: Response to reviewer Comment: Thanks a lot for the active engagement in the review process and for increasing our score. We are glad we could adeptly address your concerns. If there are any other questions, that we can address to to further improve your score or confidence in our work, please let us know.	Summary: The paper proposes NeoRL for non-episodic RL with nonlinear dynamical systems. NeoRL has a first-of-its-kind regret bound for general nonlinear systems with Gaussian process dynamics. The paper also proposes a practical implementation of NeoRL with MPC, which significantly outperforms baseline algorithms. Strengths: The paper paper proposes NeoRL, which has a first-of-its-kind regret bound for general nonlinear systems with Gaussian process dynamics. The paper also proposes a practical implementation of NeoRL with MPC, which significantly outperforms baseline algorithms. The paper is very well-written and easy to follow. While the basic idea of the algorithm is not novel, the paper considers a very important topic of average RL and has a large impact on the theory of average RL, I think. Weaknesses: I do not see any particular weakness in this paper. Maybe one weakness is that the tightness of the derived bound is unclear because there is no lower bound for the considered setting, as the authors also mentioned in Conclusion. Technical Quality: 4 Clarity: 4 Questions for Authors: - Is there any comment on the tightness of the regret? - How well does NeoRL scale to high-dimensional environments such as Humanoid? Confidence: 3 Soundness: 4 Presentation: 4 Contribution: 4 Limitations: The paper discuss the limitation of the theoretical results. I do not see any potential negative societal impact. Flag For Ethics Review: ['No ethics review needed.'] Rating: 8 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for their invaluable feedback. We are happy to hear that they also appreciate the significance of our work. Below, we have our responses to the questions. Q1: Is there any comment on the tightness of the regret? A1: We would have loved to give a lower bound, but as acknowledged by the reviewer, lower bounds do not exist for this and in fact even for the simpler episodic setting (c.f, [1, 2] for example). However, we are actively working towards bridging this gap. Particularly, there is some hope that the upper bound is tight. This is motivated from results on Gaussian process bandit optimization [3], where the tightness of the regret is shown by providing similar order lower bounds. Since our upper bounds are of similar order, and motivated through a similar analysis, as the ones derived in GP bandits, we have some hope that they are also tight (with respect to T). However, overall, this is still an open problem. Q2: How well does NeoRL scale to high-dimensional environments such as Humanoid? A2: NeoRL has the same limitations as any model-based RL algorithm such as planning in high-dimensional input spaces. Particularly, NeoRL has to, in addition to the control inputs, optimize over the hallucinated controls $\eta$. There are heuristics to replace a direct optimization over $\eta$ with a sampling-based approach (c.f., [1, 4]), which scales much better (e.g., [4] evaluate it on a 58D system). Lastly, we use the iCEM [5] optimizer for planning, which has demonstrated scalability on the humanoid task. References 1. Kakade, Sham, et al. "Information theoretic regret bounds for online nonlinear control." Advances in Neural Information Processing Systems 33 (2020) 2. Curi, Sebastian, Felix Berkenkamp, and Andreas Krause. "Efficient model-based reinforcement learning through optimistic policy search and planning." Advances in Neural Information Processing Systems 33 (2020) 3. Scarlett, Jonathan, Ilija Bogunovic, and Volkan Cevher. "Lower bounds on regret for noisy gaussian process bandit optimization." Conference on Learning Theory. PMLR, 2017. 4. Sukhija, Bhavya, et al. "Optimistic active exploration of dynamical systems." Advances in Neural Information Processing Systems 36 (2023) 5. Pinneri, Cristina, et al. "Sample-efficient cross-entropy method for real-time planning." Conference on Robot Learning. PMLR, 2021. --- Rebuttal Comment 1.1: Comment: Thank you very much for the rebuttal! I acknowledge that I read it. --- Reply to Comment 1.1.1: Title: Official Comment Comment: Thank you also for your engagement in the review process and the constructive feedback!	null	null	null	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
A Simple Remedy for Dataset Bias via Self-Influence: A Mislabeled Sample Perspective	Accept (poster)	Summary: The paper proposes a method for debiasing biased models through fine-tuning on a specific subset with a high portion of unbiased ("bias-conflicting") samples. The paper uses self-influence in the early training epochs to identify this specific subset, where high self-influence is an indicator of a bias-conflicting sample. The intuition behind this approach is that models tend to learn biases early in training, so that samples without the bias feature will have high self-influence scores. Strengths: - The paper is well-written. - The hypothesis of fine-tuning on a subset of bias-conflicting samples is grounded on a thorough analysis. Weaknesses: - There are some unclarities in the method. Please see questions. - As "bias-aligned" and "bias-conflicting" is new terminology, it is slightly hard to follow as a reader. Adding an example image instead of the description in section 3.2 would help this. - Formatting: - Figure 2: Please add the error bars from your 3 runs. - Figure 3: For easier comparability of (b) and (c) please use the same y-axis., same for the histogram’s x-axis of (d). - Figure 4: Please use the same x-axis across the subplots. Using your 3 runs, it would be interesting to add error bars to the plot, too. - “Figure x” and “Table x” font sizes are larger than the caption font size. - Table 1 caption: space between the cross symbol and “denotes” missing - Minor: - Line 33: It’s unclear what “it” refers to. - Line 79: Please also include the citation Hampel 1974 that introduced Influence Functions from Robust statistics. Technical Quality: 2 Clarity: 3 Questions for Authors: - Self-influence is often used in mislabeled sample detection as a way to evaluate training data attribution methods. Still, SI mainly indicates that a sample is OOD (which could be a case of mislabeling). Does your approach generalize to OOD cases, then, too? - What is the difference between IF and SI is? SI has been used in IF and data attribution work commonly as an evaluation protocol to find mislabeled samples. - Equation 2: It makes sense to detect bias-conflicting samples early in training. Yet, at this stage the model has yet to converge and I can imagine that the estimation quality of the inverse Hessian vector product for self-influence is rather low and uses a large damping factor. What is the damping factor used? - How does the estimation quality influence your method and results? Would a dynamic training data attribution approach like e.g. TracIn (computing influence as a sum of gradient dot products across training) be an alternative? - How do you compute self-influence/what kind of HVP estimation algorithm do you use? - Lines 203-205: How many samples are in the intersection? Is there high variance in the self-influence? - Line 330 Broader impact: If only biased data is available, how can bias-conflicting samples be found? Confidence: 3 Soundness: 2 Presentation: 3 Contribution: 2 Limitations: Limitations and broader impact are discussed in the conclusion. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank you for your constructive comments. --- ### [Q1] Self-influence is often used in mislabeled sample detection as a way to evaluate training data attribution methods. Still, SI mainly indicates that a sample is OOD (which could be a case of mislabeling). Does your approach generalize to OOD cases, then, too? Yes, our approach generalizes to OOD cases. The core idea of using Self-Influence in mislabeled sample detection is to identify minority samples that contradict the dominant features learned by the model. Since OOD samples, including mislabeled ones, also exhibit a contradiction due to their incorrect labels or the absence of the dominant features learned by the model, our approach is applicable to them as well. In terms of the degree of contradiction, although we have not thoroughly validated this, it is reasonable to predict the following order: mislabeled samples > non-mislabeled OOD samples > bias-conflicting samples. Since bias-conflicting samples share task-related features with the majority, the degree of contradiction is weaker than that of OOD samples, making their detection a significant challenge. --- ### [Q2] What is the difference between IF and SI is? In Figures 2 and 3, the notation $IF$ refers to the Influence Function on the training set, as specified in the captions. Please note that IF on the training set is the baseline in our experiments, substituting for IF on the unbiased validation set, which is unavailable in our target problem. To avoid any misunderstanding, we will modify the notation to $IF_{train}$. To elaborate, typically, if a validation set that resembles the distribution of the test set is available, it is used as $z'$ in Influence Function $I(z, z′)$. However, in challenging situations where an unbiased validation set is not available, Self-Influence $I(z,z)$ is used by setting $z’$ as the training sample $z$ itself instead of the validation set. SI measures how the prediction of $z$ changes when $z$ is excluded from the training set. This means that the higher contradiction the sample $z$ exhibits, the more difficult it becomes for the model to make accurate predictions based on features learned from other samples. --- ### [Q3] Equation 2: It makes sense to detect bias-conflicting samples early in training. Yet, at this stage, the model has yet to converge and I can imagine that the estimation quality of the inverse Hessian vector product for self-influence is rather low and uses a large damping factor. What is the damping factor used? As the reviewer mentioned, since we use an early-stage model, the estimation quality of the inverse Hessian vector product is to some extent insufficient. To compensate for this, we follow a widely used convention by adding the absolute value of the smallest negative eigenvalue plus 0.0001 to avoid negative eigenvalues. Without additional tuning of the damping factor, this setting has empirically shown good performance across various benchmark datasets in our experiments. However, resolving the issue of insufficient estimation quality due to using an early-stage model is crucial for further performance improvements, making it a primary objective in future work. --- ### [Q4] How does the estimation quality influence your method and results? Would a dynamic training data attribution approach like e.g. TracIn (computing influence as a sum of gradient dot products across training) be an alternative? We leveraged the fundamental form of Influence Functions to demonstrate the generalizability of our approach. Of course, other forms of Influence function, such as dynamic training data attribution methods like TracIn[1], can also be viable alternatives. To further demonstrate this, we have conducted additional experiments on BFFHQ and Waterbird using TracIn and MoSo [2], a recent method that leverages gradients from the training process. As shown in the table below, using TracIn results in better performance compared to the basic form of IF, and MoSo demonstrates comparable performance. \| \| BFFHQ \| Waterbird \| \|----------------\|-----------------\|----------------\| \| SelecMix \| 63.07 ± 2.32 \| 74.72 ± 1.14 \| \| SelecMix + Ours \| 65.80 ± 3.12 \| 89.67 ± 0.38 \| \| SelecMix + Ours_MoSo \| 63.13 ± 3.27 \| 89.72 ± 1.12 \| \| SelecMix + Ours_TracIn \| 69.20 ± 0.50 \| 90.39 ± 0.70 \| [1] Pruthi et al. "Estimating training data influence by tracing gradient descent." NeurIPS, 2020. [2] Tan et al. "Data pruning via moving-one-sample-out." NeurIPS, 2023. --- ### [Q5] How do you compute self-influence/what kind of HVP estimation algorithm do you use? For both efficiency and bias-focused computations, we calculate self-influence using only the last layer (classification layer), with the Hessian inverse computed exactly. By following [3], we limit the Hessian computation to the parameters of the last layer to reduce computational cost. Additionally, considering [4]'s discovery that retraining only the classification layer can achieve debiasing, focusing on the last layer allows for more bias-focused computations. In the table below, we present experiments with Arnoldi [5], which estimates self-influence utilizing all the parameters in the model. The results show that Arnoldi performs comparably or worse, underscoring the effectiveness of using only the last layer. \| \| BFFHQ \| Waterbird \| \|----------------\|-----------------\|----------------\| \| SelecMix \| 63.07 ± 2.32 \| 74.72 ± 1.14 \| \| SelecMix + Ours \| 65.80 ± 3.12 \| 89.67 ± 0.38 \| \| SelecMix + Ours_Arnoldi \| 66.40 ± 3.12 \| 71.08 ± 3.12 \| [3] Daxberger et al. "Laplace redux-effortless bayesian deep learning." NeurIPS, 2021. [4] Kirichenko et al. "Last layer re-training is sufficient for robustness to spurious correlations." arXiv, 2022. [5] Schioppa et al. "Scaling up influence functions." AAAI, 2022. --- --- Rebuttal 2: Comment: ### [Q6] Lines 203-205: How many samples are in the intersection? Is there high variance in the self-influence? The variance of self-influence is to some extent high due to the usage of the early-stage model. However, the intersection process substantially mitigates this issue and enhances the ratio of bias-conflicting samples in the resulting pivotal set. We provided an ablation study on the intersection in Appendix G. The study shows that as the ratio of bias-conflicting samples increases up to 20%, the number of samples after the intersection also increases. This indicates that the intersection adaptively adjusts the size of the pivotal set based on the bias-conflicting ratio, as we intended. --- ### [Q7] Line 330 Broader impact: If only biased data is available, how can bias-conflicting samples be found? We apologize for the confusion. We intended to refer to scenarios where both bias labels and an unbiased validation set are unavailable. We will revise the statement to clarify this point. --- ### [Q8] As "bias-aligned" and "bias-conflicting" is new terminology, it is slightly hard to follow as a reader. Adding an example image instead of the description in section 3.2 would help this. The terms "bias-aligned" and "bias-conflicting" were first proposed by LfF [6] and are widely used in research on spurious correlations. However, to aid readers who may not be familiar with this terminology, as the reviewer suggested, we will provide additional explanations and include example images in Section 3.2. [6] Nam et al. "Learning from failure: De-biasing classifier from biased classifier." NeurIPS, 2020. --- ### [formatting issues and an additional citation] As the reviewer suggested, we will revise formatting issues, and include the citation Hampel 1974 in the revision. Title: Rebuttal by Authors (2/2) --- Rebuttal Comment 2.1: Comment: Thank you for your answers to the many questions I posed. I am optimistic about this work and find the research direction of finding bias-conflicting samples important as this is probably a widespread contributor to spurious correlations in learned models. However, some concerns remain: I agree with reviewers BCqo and yem8 that the current evaluation and experiments presented do not test for debiasing per se. I believe that expanding on the Grad-Cam experiments for qualitative analysis and adding a quantitative analysis with e.g. error-parity experiments or spurious Imagenet/waterbirds will improve the paper for a future version. Due to these concerns, I will keep the current score of 4. --- Rebuttal 3: Comment: We sincerely appreciate the reviewer’s time and effort in carefully considering our response. --- The reviewer expressed concerns that the current quantitative evaluation and experiments do not test for debiasing per se. However, the quantitative evaluation approach we have presented aligns with the primary and standard evaluation convention in the spurious correlation (debiasing) domain, which assesses the degree of debiasing using an unbiased test set or by measuring average group accuracy and worst-group accuracy [1-11]. Evaluating on an unbiased test set effectively tests for debiasing per se, as it determines whether the model's predictions are driven by genuine task-related features rather than a specific malignant bias. For example, if a model is biased towards a particular attribute, it will likely perform well only on subgroups with that attribute, resulting in lower accuracy on the unbiased test set. As mentioned in the evaluation protocols in Sec 5.1, we also adhered to the convention by using worst-group accuracy in Waterbird and bias-conflicting accuracy in BFFHQ as the evaluation metrics, further reinforcing the test for debiasing per se. To the best of our knowledge, there is currently no qualitative evaluation method in the spurious correlation community that is considered more reliable than these quantitative evaluations. While methods like Grad-CAM to visualize activation map changes or t-SNE to examine how class instances cluster in latent space post-debiasing are sometimes used, these techniques are typically employed as supplements to quantitative results and are not considered more accurate than the quantitative evaluations that we, along with most previous works, have presented using an unbiased test set. Additionally, we conducted experiments on five benchmark datasets and further tested on CIFAR-10C by adjusting the severity of bias to levels closer to unbiased conditions. This extensive evaluation not only covers a broader range of datasets and scenarios but also provides a more rigorous and comprehensive validation of our method compared to other existing works. We once again sincerely thank the reviewer for the thoughtful feedback and the time dedicated to reviewing our work. We hope our responses have addressed the additional concern raised and welcome any further questions. [1] Nam et al. "Learning from failure: De-biasing classifier from biased classifier." NeurIPS, 2020. [2] Sagawa et al. "Distributionally robust neural networks.", ICLR, 2020. [3] Lee et al. "Learning debiased representation via disentangled feature augmentation." NeurIPS, 2021. [4] Liu et al. "Just Train Twice: Improving Group Robustness without Training Group Information." ICML, 2021. [5] Seo et al. "Unsupervised learning of debiased representations with pseudo-attributes." CVPR, 2022. [6] Hwang et al. "Selecmix: Debiased learning by contradicting-pair sampling." NeurIPS, 2022. [7] Park et al. "Training debiased subnetworks with contrastive weight pruning." CVPR, 2023. [8] Lim et al., "Biasadv: Bias-adversarial augmentation for model debiasing." CVPR, 2023. [9] Deng et al. "Robust Learning with Progressive Data Expansion Against Spurious Correlation." NeurIPS, 2023. [10] Ahn et al. "Mitigating dataset bias by using per-sample gradient." ICLR, 2023. [11] Jung et al. "Fighting fire with fire: Contrastive debiasing without bias-free data via generative bias-transformation", ICML, 2023. --- Rebuttal Comment 3.1: Comment: I apologize for the late reply and thank the authors for their explanations and additional experiments posted during the discussion period. I think that they show the promise of this direction, and I raise my score accordingly from 4->6. --- Reply to Comment 3.1.1: Comment: Thank you for taking the time to review our paper and provide valuable feedback. We are grateful for your decision to raise the score to 6.	Summary: This paper tackles the problem of learning generalized models from biased data by detecting mislabeled samples. The authors use BCSI (SI estimated on a trained model with GCE) to detect bias-conflicting samples and construct a pivotal subset based on the BCSI scores of these samples for correcting the biased model without access to a clean validation set. Strengths: - Originality and Significance: Rather than computing influence scores on a clean validation set (which is usually not feasible to obtain in practice), this paper uses self-influence estimated by the model trained with GCE to detect bias-conflicting samples. - Quality and Clarity: Since the proposed method heavily relies on the assumption that if the loss increases when a sample is removed from the training set, that sample is likely to be mislabeled, the empirical analysis of self-influence (SI) in detecting bias-conflicting samples is sufficient across four different tasks. The experiments, including ablation studies, are comprehensive. Weaknesses: - The concept of bias-conflicting samples is not equivalent to unbiased samples, so in the introduction, “by first identifying bias-conflicting (unbiased) samples” should be rephrased. - Some grammar errors: - Section 3: “A analysis” => “An analysis”. - “trainset” => “training set”. - The bias issue introduced in this paper is more about robustness rather than fairness since no sensitive attributes (such as gender or race) are included in the problem formulation, and no fairness evaluation (demographic parity or equalized odds) is conducted in the experiment. I recommend the authors change the terminology from fairness to robustness for a more precise expression. - In Section 3.2, I strongly recommend introducing the concepts of “mislabeled samples,” “bias-conflicting samples,” and “bias-aligned samples” in Section 2.1 for better readability. - In “Note that since an unbiased validation set is unavailable in our target problem, we additionally estimate the influence score on the training set, indicated as IF in Figure 2.” The measure of IF is problematic since it should be obtained via a clean validation set, which is not equivalent to the training set. The authors could conduct the experiment in a noisy label setting, for example, treating a subset as a clean validation set and flipping the others with a noise rate. - “GCE emphasizes samples that are easier to learn, amplifying the model’s bias by giving more weight to bias-aligned samples in the training set.” GCE does prioritize samples that are easier to learn, but this does not necessarily mean that these samples are all bias-aligned. - The proposed method BCSI in Equation 2 is just SI, it appears to have limited novelty. Technical Quality: 2 Clarity: 2 Questions for Authors: From my understanding, the pivotal subset is used to correct and mitigate bias in the model. So why do the authors mention “use pivotal set (bias-conflicting samples) to recover a biased model”? What the paper actually does is use bias-conflicting samples to correct the biased model. This is very confusing. Is this a typo? Or should it be rephrased to “recover an unbiased model from a biased one” for better clarity? Confidence: 5 Soundness: 2 Presentation: 2 Contribution: 2 Limitations: The authors have adequately addressed the limitations. Since this work is mainly about dataset bias, so I do not see any negative societal impact. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We appreciate your valuable feedback. --- ### [Q1] The bias issue introduced in this paper is more about robustness rather than fairness since no sensitive attributes (such as gender or race) are included in the problem formulation, and no fairness evaluation (demographic parity or equalized odds) is conducted in the experiment. I recommend the authors change the terminology from fairness to robustness for a more precise expression. As the reviewer mentioned, the term robustness is more precise since our target problem is addressing malignant biases (spurious correlations) in the dataset that prevent the model from learning task-related features. However, there is also an intersection with fairness, especially when considering cases where the malignant bias involves sensitive attributes such as gender or race. Numerous related studies addressing spurious correlations [1,2,3,4,5,6] have shown that mitigating these correlations aids in achieving fairness. For example, in the Biased FFHQ (BFFHQ) dataset, which is one of the benchmark datasets consisting of images of human faces, the designated task label is age {young, old} while the bias attribute is gender {man, woman}. In addition, we conduct experiments on CelebA, a more widely used benchmark dataset in the fairness domain. As shown in the table below, our method also demonstrated effective performance on this dataset. \| CelebA \| Averaged Acc. \| Worst Group Acc. \| \|----------------\|-----------------\|----------------\| \| ERM\| 95.32 ± 0.34 \| 45.19 ± 0.67 \| \| JTT \| 90.14 ± 0.61 \| 72.22 ± 2.51 \| \| JTT + Ours \| 86.19 ± 1.32 \| 80.17 ± 1.29 \| [1] Nam et al. "Learning from failure: De-biasing classifier from biased classifier." NeurIPS, 2020. [2] Lee et al. "Learning debiased representation via disentangled feature augmentation." NeurIPS, 2021. [3] Seo et al. "Unsupervised learning of debiased representations with pseudo-attributes." CVPR, 2022. [4] Hwang et al. "Selecmix: Debiased learning by contradicting-pair sampling." NeurIPS, 2022. [5] Park et al. "Training debiased subnetworks with contrastive weight pruning." CVPR, 2023. [6] Deng et al. "Robust Learning with Progressive Data Expansion Against Spurious Correlation", NeurIPS, 2023. --- ### [Q2] In Section 3.2, I strongly recommend introducing the concepts of “mislabeled samples,” “bias-conflicting samples,” and “bias-aligned samples” in Section 2.1 for better readability. To aid readers who may not be familiar with this terminology, as the reviewer suggested, we will introduce these concepts in Sec 2.1 for better readability. --- ### [Q3] In “Note that since an unbiased validation set is unavailable in our target problem, we additionally estimate the influence score on the training set, indicated as IF in Figure 2.” The measure of IF is problematic since it should be obtained via a clean validation set, which is not equivalent to the training set. The authors could conduct the experiment in a noisy label setting, for example, treating a subset as a clean validation set and flipping the others with a noise rate. In Figures 2 and 3, the notation $IF$ refers to the Influence Function on the training set, as specified in the captions. Please note that IF on the training set is the naive baseline in our experiments, substituting for IF on the unbiased validation set. While IF on the unbiased validation set would be a stronger baseline, it is not available in our target problem. To avoid any misunderstanding, we will modify the notation to $IF_{train}$. --- ### [Q4] “GCE emphasizes samples that are easier to learn, amplifying the model’s bias by giving more weight to bias-aligned samples in the training set.” GCE does prioritize samples that are easier to learn, but this does not necessarily mean that these samples are all bias-aligned. We apologize for any confusion. We agree that GCE does not necessarily imply that all these samples are bias-aligned, and our intention was to highlight this tendency. We will revise the statement to: "GCE emphasizes samples that are easier to learn, thereby amplifying the model’s bias by tending to give more weight to bias-aligned samples in the training set.” --- ### [Q5] So why do the authors mention “use pivotal set (bias-conflicting samples) to recover a biased model”? We apologize for the confusion. Our intention was to convey the meaning of "rectify a biased model." We will revise it. --- ### [Minor issues] As the reviewer suggested, we will revise grammar errors, and rephrase “by first identifying bias-conflicting (unbiased) samples” in the revision. --- Rebuttal Comment 1.1: Comment: To further address the reviewer's concerns about fairness, we conduct experiments on the text dataset MultiNLI (experiments on the CivilComments dataset are currently running due to time constraints), which is an widely used benchmark dataset in the fairness domain. Specifically, MultiNLI involves classifying the relationship between two sentences, with the bias label being the presence of negation words in the second sentence, often linked to the contradiction label. As shown in the table below, our method effectively works on a text dataset as well. We will include the complete table in the revision. \| MultiNLI \| Avg Acc. \| Worst-group Acc. \| \|---\|---\|---\| \| JTT \| 80.0 \| 70.2 \| \| JTT+Ours \| 79.8 \| 73.6 \| --- Rebuttal 2: Comment: Thank you for your comments, and we would like to provide a response to the reviewer's remaining concerns. --- ### [The clarity of definitions] ### We carefully defined the terms in Sec. 3 using formulas following the conventions. However, if any definitions remain unclear, we would be more than willing to clarify them further (e.g., by including additional images for bias-aligned and conflicting samples [3]) to improve readability. We would be grateful if you could specify which definitions are unclear, as your feedback will help us to further enhance the clarity and quality of our paper. --- ### [Explicit addressing of fairness metrics] ### The primary goal of our paper is to address spurious correlations in training datasets. Therefore, our primary evaluation focus is on assessing how well the trained model predicts on test datasets that are free from the spurious correlations present in the training set, using task-related features. We have employed the standard and widely accepted benchmark datasets and evaluation metrics in spurious correlation studies [1-20]. It is important to note that the vast majority of spurious correlation studies[1-20] used evaluation methods the same as ours, such as unbiased accuracy and worst(or minority)-group accuracy, rather than the fairness metrics commonly used in the fairness domain. However, we agree that incorporating fairness metrics would further enhance the evaluation section. Accordingly, we share experimental results evaluated using demographic parity (DP) and ~~equalized odds~~ equal opportunity (EOP) metrics on the Waterbird dataset. As shown in the table below, our approach demonstrates clear performance improvements, even when evaluated using fairness metrics. \| Waterbird \| DP \| EOP \| \|:---:\|:---:\|:---:\| \| ERM \| 0.1826 ± 0.0044 \| 0.2731 ± 0.0187 \| \| SelecMix \| 0.1146 ± 0.0004 \| 0.1885 ± 0.0100 \| \| SelecMix+Ours \| 0.0242 ± 0.0053 \| 0.0099 ± 0.0064 \| --- We appreciate the reviewer’s valuable feedback and the time spent reviewing our work. We hope that our responses have addressed the remaining concerns raised. --- [1] Wang et al. "Learning robust representations by projecting superficial statistics out." ICLR, 2019. [2] Bahng et al. "Learning de-biased representations with biased representations." ICML, 2020. [3] Nam et al. "Learning from failure: De-biasing classifier from biased classifier." NeurIPS, 2020. [4] Sagawa et al. "Distributionally robust neural networks.", ICLR, 2020. [5] Liu et al. "Just Train Twice: Improving Group Robustness without Training Group Information." ICML, 2021. [6] Kim et al. "Biaswap: Removing dataset bias with bias-tailored swapping augmentation." ICCV, 2021. [7] Lee et al. "Learning debiased representation via disentangled feature augmentation." NeurIPS, 2021. [8] Hong et al. "Unbiased classification through bias-contrastive and bias-balanced learning." NeurIPS, 2021. [9] Nam et al. "Spread spurious attribute: Improving worst-group accuracy with spurious attribute estimation." ICLR, 2022. [10] Seo et al. "Unsupervised learning of debiased representations with pseudo-attributes." CVPR, 2022. [11] Idrissi et al. "Simple data balancing achieves competitive worst-group-accuracy." CLeaR, 2022. [12] Hwang et al. "Selecmix: Debiased learning by contradicting-pair sampling." NeurIPS, 2022. [13] Kim et al. "Learning debiased classifier with biased committee." NeurIPS, 2022. [14] Park et al. "Training debiased subnetworks with contrastive weight pruning." CVPR, 2023. [15] Lim et al., "Biasadv: Bias-adversarial augmentation for model debiasing." CVPR, 2023. [16] Deng et al. "Robust Learning with Progressive Data Expansion Against Spurious Correlation." NeurIPS, 2023. [17] Ahn et al. "Mitigating dataset bias by using per-sample gradient." ICLR, 2023. [18] Kirichenko et al.. "Last layer re-training is sufficient for robustness to spurious correlations." ICLR, 2023. [19] Liu et al. "Avoiding spurious correlations via logit correction." ICLR, 2023. [20] Jung et al. "Fighting fire with fire: Contrastive debiasing without bias-free data via generative bias-transformation", ICML, 2023. --- --- Rebuttal Comment 2.1: Comment: I greatly appreciate the authors’ response in providing supplementary experimental results and explanations to address my remaining concerns with such a short time. As I mentioned, I really like the idea of this paper, so if the authors can guarantee improvements to the manuscript, I will raise my score. --- Reply to Comment 2.1.1: Comment: We sincerely appreciate the reviewer for the time and effort dedicated to reviewing our paper. We guarantee that all the discussions and improvements made during the rebuttal period will be incorporated into the manuscript. We are deeply grateful for the valuable feedback, which has significantly strengthened our paper. --- Rebuttal 3: Comment: By the way, I think Reviewer BCqo meant Equal Opportunity (EOP), not Equalized Odds (EO). These two metrics are slightly different. Please ensure the authors are using the correct metric for evaluation.	Summary: The authors focus on detecting bias-conflicting samples to recover biased models. They propose a Bias-Conditioned Self-Influence to help identify bias-conflicting samples in the early stage of model training. Experiments on public datasets are conducted to demonstrate the effectiveness of the proposed method. Strengths: 1. The introduced perspective of using a bias-conditioned self-influence for bias-conflicting sample detection is interesting; 2. The experimental results look promising. Weaknesses: Majors: 1. The paper aims to rectify bias within a model. However, only the accuracy of models and distribution of BCSI scores are provided. Additional experiments are needed to demonstrate that the bias within a model could be reduced by the proposed method. 2. The authors employ Generalized Cross Entropy to get a more biased model. What about the performance with other losses? 3. Why does ERM perform better than the proposed method in Table 2? An insightful analysis is needed. 4. I suggest the authors to reorganize the paper to make it easier to follow. See minors for details. Minors: 1. Table 2 is mentioned before Table 1; 2. Figure 2 mentioned before Figure 1; 3. Experimental settings are mentioned in the technical part ($\lambda=0.1$). 5. There are some typos. For example, on Page 3, Line 102: A analysis of ... Technical Quality: 3 Clarity: 2 Questions for Authors: Please see the Weaknesses part and kindly correct me if there are any misunderstandings. Confidence: 4 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: N/A Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank you for the constructive comments. --- ### [Q1] The paper aims to rectify bias within a model. However, only the accuracy of models and distribution of BCSI scores are provided. Additional experiments are needed to demonstrate that the bias within a model could be reduced by the proposed method. To further demonstrate the effectiveness of our framework in reducing model bias, we have conducted Grad-CAM [1] analysis on the BFFHQ and Waterbird datasets. In the BFFHQ dataset, the target attribute set is {young, old} and the bias attribute set is {man, woman}. For the Waterbird dataset, the target attribute set is {waterbird, landbird} and the bias attribute set is {water, land}. As shown in Figure 1 of the attached PDF in the global response, the biased models (a) and (c) tend to focus on biased attributes such as gender and background. However, when applying our method, as illustrated in (b) and (d), the model's attention shifts to more task-related features, such as age in faces and bird species. This indicates that our method effectively redirects the model’s focus away from biased attributes and toward the target attributes. [1] Selvaraju et al. "Grad-cam: Visual explanations from deep networks via gradient-based localization." CVPR, 2017. --- ### [Q2] The authors employ Generalized Cross Entropy to get a more biased model. What about the performance with other losses? We utilize Generalized Cross Entropy (GCE) since it is commonly used in the debiasing domain to obtain a biased model. However, other loss functions can also be viable alternatives. To demonstrate this, we conducted additional experiments on the BFFHQ and Waterbird datasets, employing other loss functions that are follow-ups to GCE, such as SCE [2] and NCE+RCE [3], which are designed for noisy label settings. As shown in the table below, we present the performance of our method with each applied loss function. Both SCE and NCE+RCE exhibit performance comparable to or slightly better than GCE in our method. These loss functions encourage the model to focus more on the majority of normal samples rather than the minority noisy ones, which also results in a more biased model in the given bias setting. \| \| BFFHQ \| Waterbird \| \|----------------\|-----------------\|----------------\| \| SelecMix \| 63.07± 2.32 \| 74.72 ± 1.14 \| \| SelecMix + Ours_CE \| 62.73 ± 3.71 \| 88.73 ± 0.45 \| \| SelecMix + Ours_GCE \| 65.80 ± 3.12 \| 89.67 ± 0.38 \| \| SelecMix + Ours_SCE \| 66.20 ± 0.53 \| 89.46 ± 0.36 \| \| SelecMix + Ours_NCE+RCE \| 67.73 ± 1.99 \| 89.72 ± 0.41 \| [2] Wang et al. "Symmetric cross entropy for robust learning with noisy labels." ICCV, 2019. [3] Ma et al. "Normalized loss functions for deep learning with noisy labels." ICML, 2020. --- ### [Q3] Why does ERM perform better than the proposed method in Table 2? An insightful analysis is needed. Recent debiasing methods are typically designed under the assumption that the bias is malignant enough to mislead a model into extensively relying on the bias to produce a biased predictor. Consequently, in the cases of 70% and 90% in Table 2, the dataset is nearly an unbiased set, breaking this assumption. This leads to the opposite effect, where important samples for learning are disregarded. Ensuring robust performance even when given such unbiased datasets remains an important future goal for the debiasing community. --- ### [Minor issues] As the reviewer suggested, we will revise the organization of the paper and correct any typos to make it easier to follow. --- Rebuttal Comment 1.1: Comment: Thanks for conducting additional experiments and providing the response. However, I still have concerns as follows: For Q1: What about fairness metrics (DP, EOP)? For Q3: The response only discussed the cases of 70% and 90%. However, in Table 2, ERM performs better than the proposed method in most settings (30%, 50%, 70%, and 90%). --- Rebuttal 2: Comment: We thank you for the detailed review of our work and for your help in improving it further. --- ### [Q1.] What about fairness metrics (DP, EOP)? ### As the reviewer recommended, we additionally evaluate our method on Waterbird using fairness metrics such as DP and EOP. Note that we evaluate ours solely on Waterbird since CMNIST, CIFAR10-C, and NICO have more than two classes, and that BFFHQ's test set contains only bias-conflicting samples. As shown in the table below, our approach demonstrates clear performance improvements, even when evaluated using fairness metrics. \| Waterbird \| DP \| EOP \| \|:---:\|:---:\|:---:\| \| ERM \| 0.1826 ± 0.0044 \| 0.2731 ± 0.0187 \| \| SelecMix \| 0.1146 ± 0.0004 \| 0.1885 ± 0.0100 \| \| SelecMix+Ours \| 0.0242 ± 0.0053 \| 0.0099 ± 0.0064 \| --- ### [Q3.] The response only discussed the cases of 70% and 90%. However, in Table 2, ERM performs better than the proposed method in most settings (30%, 50%, 70%, and 90%). ### We apologize for the insufficient response. In the case of CIFAR-10C, as the bias severity decreases from 30% to 90%, the dataset gradually transitions into the low-bias domain, ultimately approaching an unbiased state at 90%. As mentioned in our previous response, this reduction in bias severity undermines the assumption that the bias is sufficiently malignant, resulting in reduced effectiveness of previous debiasing methods and allowing ERM to achieve better performance. In this context, to improve the performance of our method when applied to ERM—which leverages a large number of conflicting samples—it is necessary to increase the size of the pivotal set, thereby expanding the number of conflicting samples that our method can utilize. As demonstrated in the table below, expanding the pivotal set can lead to performance improvements even in low-bias settings, achieving state-of-the-art (SOTA) performance. Furthermore, if we had access to information regarding bias severity (i.e., the proportion of bias-conflicting samples), we could further optimize performance by adjusting the top-k value. \| \| CIFAR10C-30% \| CIFAR10C-50% \| CIFAR10C-70% \| CIFAR10C-90% \| \|---\|---\|---\|---\|---\| \| ERM \| 65.64 ± 0.51 \| 71.33 ± 0.09 \| 74.90 ± 0.25 \| 76.03 ± 0.26 \| \| ERM+Ours (topk=100) \| 65.61 ± 0.77 \| 70.61 ± 0.62 \| 73.20 ± 0.35 \| 73.57 ± 0.16 \| \| ERM+Ours (topk=2000) \| 71.25 ± 0.34 \| 74.46 ± 0.34 \| 75.84 ± 0.33 \| 76.14 ± 0.23 \| We appreciate the reviewer for highlighting this point, which has contributed to enhancing the rigor of our paper. We will include a discussion of these findings in the revision. --- --- Rebuttal Comment 2.1: Comment: I appreciate the authors' efforts in providing a detailed response addressing most of my concerns. I will raise my rating from 4 to 5. --- Reply to Comment 2.1.1: Comment: We sincerely appreciate the reviewer’s insightful suggestions and the decision to raise the score.	Summary: The authors propose a method to tackle spurious correlations by using influence functions. Specifically, they compute the self-influence on the training set -- the amount that a particular sample's loss changes when it is removed from the training set. Samples with the highest self-influence are then assumed to be in the bias-conflicting (minority group). Then, models can be finetuned, up-weighting this set of identified samples, to obtain a debiased model. The authors benchmark their method on typical spurious correlation benchmarks, finding that they outperform the baselines. Strengths: - The paper is well-written and easy to follow. - The proposed method is intuitive, and - The method outperforms the baselines on typical benchmark datasets. Weaknesses: 1. The proposed method has no theoretical justifications, and so it is unclear under what circumstances it would fail. 2. The authors should evaluate on a few more datasets from the spurious correlation domain, such as CelebA, MultiNLI, and CivilComments. It would be particularly important to demonstrate that the method can work on text datasets. The authors should also add JTT [1] as a baseline. 3. If compute allows, the authors should compute the ablations (Figure 6) for all other datasets. In addition, it would be interesting to show particular samples in the top-k set. Do the samples differ visually as their ranking decreases? How do the samples which are in the top-k set but are not bias-conflicting look? 4. Once the candidate set of bias conflicting samples is identified, there are many other approaches that could be taken. The authors use a simple upweighting approach, but one could e.g. apply GroupDRO to the dataset, with two groups, as well. The authors should benchmark a few of these alternatives. 5. In Table 1, the proposed method only outperforms the baselines when it is used to finetune a model which has had another debiasing approach applied to it, i.e. Ours_ERM underperforms the baselines. Thus, the method requires a decent starting point to work well. 6. The authors should discuss some of the failure modes of the method. One potential failure mode seems to be when the dataset actually contains mislabeled samples, and so the identified set consists of mislabeled samples instead of bias-conflicting samples. The authors should benchmark their method in these settings, potentially with synthetic noise. [1] https://arxiv.org/pdf/2107.09044 Technical Quality: 2 Clarity: 3 Questions for Authors: 1. Was there any model selection required in the experiments? If so, how was it done? 2. Why were some baselines omitted from Tables 2 and 3? 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: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We sincerely appreciate your time and effort to review our paper. --- ### [Q1] The proposed method has no theoretical justifications, and so it is unclear under what circumstances it would fail. Although we did not provide theoretical justification, we demonstrated the effectiveness of our method across various settings and datasets. For the circumstances where our method would fail, our method might fail when there is a significant number of mislabeled samples. Specifically, the intuition behind our method is that generic features for bias-conflicting samples are learned later in the training process, and by using the model in its early stage, we can identify these samples through self-influence. If mislabeled samples are present in the dataset, these samples would also exhibit high self-influence, making bias-conflicting samples difficult to distinguish. --- ### [Q2] The authors should evaluate on a few more datasets from the spurious correlation domain. The authors should also add JTT as a baseline. We conduct an additional experiment on CelebA, including JTT as a baseline. As shown in the table below, our method significantly improves the performance of JTT, exhibiting the effectiveness of our method on datasets with spurious correlations. We are currently running experiments on the MultiNLI and CivilComments and will report the results during the remaining discussion period. \|CelebA\|Avg Acc.\|Worst-group Acc.\| \|---\|---\|---\| \|ERM\|95.32$\pm$0.34\|45.19$\pm$0.67\| \|JTT\|90.14$\pm$0.61\|72.22$\pm$2.51\| \|JTT+Ours\|86.19$\pm$1.32\|80.17$\pm$1.29\| --- ### [Q3] If compute allows, the authors should compute the ablations (Figure 6) for all other datasets. For the ablation study, we will report the results for other datasets during the remaining discussion period. --- ### [Q4] In addition, it would be interesting to show particular samples in the top-k set. Do the samples differ visually as their ranking decreases? How do the samples that are in the top-k set but are not bias-conflicting look? In Figure 2 of the global response, we provide examples of bias-conflicting and bias-aligned samples from BFFHQ, based on their BCSI scores. All images belong to the top 100 samples according to BCSI. Specifically, (a) shows bias-conflicting samples with high BCSI. (b) indicates bias-conflicting samples with low BCSI. (c) denotes bias-aligned samples with high BCSI. Note that, in BFFHQ, the target attribute set is {young, old} and the bias attribute is {man, woman}. There is a spurious correlation as young women and old men. First, we will analyze only the first row of Figure 2. In (a), the bias-conflicting sample with high BCSI depicts old women, who appear younger compared to the woman in (b). Additionally, bias-aligned samples with high BCSI in (c), depict older men who appear more like women due to makeup, thus having higher BCSI. --- ### [Q5] Once the candidate set of bias-conflicting samples is identified, there are many other approaches that could be taken. The authors use a simple upweighting approach, but one could e.g. apply GroupDRO to the dataset, with two groups, as well. Thank you for your constructive suggestion. To demonstrate the generalizability of our method, we leverage the most fundamental approach of upweighting. As the reviewer mentioned, various methods to leverage the candidate set are certainly applicable. (However, since bias labels are still not provided, employing other methods like GroupDRO would require additional modules.) --- ### [Q6] In Table 1, the proposed method only outperforms the baselines when it is used to finetune a model which has had another debiasing approach applied to it, i.e. Ours_ERM underperforms the baselines. Thus, the method requires a decent starting point to work well. As we consistently fine-tune models for only a few iterations across all models due to the unknown severity of bias, this approach may be insufficient for heavily biased models like ERM. We have empirically observed that additional iterations lead to further performance improvements in such cases. Furthermore, a key advantage of our method is that it is complementary to existing methods and can further rectify models that have already undergone recent debiasing techniques. --- ### [Q7] The authors should discuss some of the failure modes of the method. One potential failure mode seems to be when the dataset actually contains mislabeled samples, and so the identified set consists of mislabeled samples instead of bias-conflicting samples. As the reviewer mentioned, when the dataset contains mislabeled samples, our method might fail to detect bias-conflicting samples because both bias-conflicting samples and mislabeled samples possess high self-influence values. We will discuss this in our revision. However, this issue is not unique to our method; many recent debiasing methods also fail in the presence of mislabeled samples, as they amplify the learning signal of samples based on loss or gradient values, which can mislead models under these conditions. --- ### [Q8] Was there any model selection required in the experiments? If so, how was it done? We used the same hyperparameters across all datasets and settings in the main experiments and consistently selected the model from the last epoch (The hyperparameters are provided in Appendix H.3). If an unbiased validation set were available, hyperparameters could be tuned, potentially leading to further performance improvements. --- ### [Q9] Why were some baselines omitted from Tables 2 and 3? These baselines were omitted from Tables 2 and 3 because they did not conduct experiments on these benchmark datasets, requiring us to perform the hyperparameter search to obtain reasonable performance. Additionally, these methods exhibit a significant performance gap compared to the state-of-the-art method. To further demonstrate the effectiveness of our method, we will report the results in the remaining discussion phase. --- Rebuttal 2: Comment: We appreciate the reviewer for the valuable feedback. We have provided the requested experiments below and hope our responses address the concerns raised. We welcome any further questions. --- ### [Q2.] The authors should evaluate on a few more datasets from the spurious correlation domain. ### As the reviewer requested, we conduct experiments on the MultiNLI dataset, and experiments on the CivilComments dataset are currently running due to time constraints. As shown in the table below, our method effectively works on a text dataset as well. We will include the complete table in the revision. \| MultiNLI \| Avg Acc. \| Worst-group Acc. \| \|---\|---\|---\| \| JTT \| 80.0 \| 70.2 \| \| JTT+Ours \| 79.8 \| 73.6 \| --- ### [Q3.] If compute allows, the authors should compute the ablations (Figure 6) for all other datasets. ### As the reviewer recommended, we conduct additional ablation studies on the Waterbird, BFFHQ, and CIFAR-10C (1%) datasets. The overall results are consistent with those presented in the main paper. Specifically, in the additional results, unbiased accuracy across varying $k$ values showed that performance was not sensitive to changes in $k$. Although $k$ = 100 was used in all our experiments, it was not always the optimal choice, as we lacked prior knowledge such as bias severity, and some other $k$ values yielded slightly better performance. \| SelecMix+Ours \| k=50 \| k=100 \| k=150 \| k=200 \| \|---\|---\|---\|---\|---\| \| BFFHQ \| 68.73 $\pm$ 0.79 \| 65.80 $\pm$ 3.12 \| 68.53 $\pm$ 1.16 \| 67.87 $\pm$ 1.16 \| \| Waterbird \| 88.37 $\pm$ 0.70 \| 89.67 $\pm$ 0.38 \| 89.72 $\pm$ 0.45 \| 89.25 $\pm$ 0.32 \| For$\lambda$, using $\lambda$ > 0 has shown to yield robust performance across both low-bias and high-bias datasets; however, setting $lambda$ too high can result in performance degradation. For the $\lambda$, on the highly biased dataset, increasing $\lambda$ results in performance degradation, while on the low-bias dataset, $\lambda=0$ causes a significant performance drop. \| SelecMix+Ours \| lambda=0 \| lambda=0.1 \| lambda=0.2 \| lambda=0.5 \| \|---\|---\|---\|---\|---\| \| BFFHQ \| 68.67 $\pm$ 1.00 \| 65.80 $\pm$ 3.12 \| 68.53 $\pm$ 1.23 \| 67.47 $\pm$ 1.23 \| \| Waterbird \| 78.92 $\pm$ 4.16 \| 89.67 $\pm$ 0.38 \| 88.01 $\pm$ 0.48 \| 85.72 $\pm$ 0.49 \| For epochs, aside from the extremely short training with epoch = 1, we observe that performance is not sensitive to the number of epochs. \| SelecMix+Ours \| epoch=1 \| epoch=3 \| epoch=5 \| epoch=7 \| epoch=9 \| epoch=11 \| \|---\|---\|---\|---\|---\|---\|---\| \| CIFAR10C-1% \| 43.76 $\pm$ 0.67 \| 44.79 $\pm$ 0.40 \| 46.18 $\pm$ 0.33 \| 45.43 $\pm$ 0.61 \| 45.20 $\pm$ 0.61 \| 45.69 $\pm$ 0.08 \| \| Waterbird \| 87.90 $\pm$ 0.32 \| 89.56 $\pm$ 0.09 \| 89.67 $\pm$ 0.38 \| 89.98 $\pm$ 0.21 \| 90.03 $\pm$ 0.39 \| 89.15 $\pm$ 0.63 \| --- ### [Q9.] Why were some baselines omitted from Tables 2 and 3? ### We conduct evaluations of DCWP on the benchmark datasets presented in Tables 2 and 3. As shown in the table below, our method still outperforms DCWP. (Please note that "Ours (best)" refers to the highest performance achieved in Tables 2 and 3.) \| \| CIFAR10C-20% \| CIFAR10C-30% \| CIFAR10C-50% \| CIFAR10C-70% \| CIFAF10C-90% \| Waterbird \| NICO \| \|---\|---\|---\|---\|---\|---\|---\|---\| \| DCWP \| 63.37 $\pm$ 1.01 \| 67.31 $\pm$ 0.54 \| 69.61 $\pm$ 0.21 \| 71.54 $\pm$ 0.10 \| 71.85 $\pm$ 0.08 \| 73.31 $\pm$ 1.78 \| 44.98 $\pm$ 1.59 \| \| Ours (best) \| 66.67 $\pm$ 0.43 \| 68.13 $\pm$ 0.45 \| 72.79 $\pm$ 0.38 \| 73.56 $\pm$ 0.15 \| 73.57 $\pm$ 0.16 \| 89.67 $\pm$ 0.38 \| 45.69 $\pm$ 1.12 \| --- --- Rebuttal Comment 2.1: Comment: Thank you for the detailed response. I would encourage the authors to characterize (either theoretically, or empirically with synthetic noise) the behavior of their method under mislabeling, which is an important potential failure mode. The authors have addressed most of my other concerns, and I would like to keep my score. --- Rebuttal 3: Comment: We are grateful for your insightful feedback and the thoughtful suggestions that have significantly enhanced our work. --- ### [Q2.] The authors should evaluate on a few more datasets from the spurious correlation domain. ### We carried out further experiments on the CivilComments-WILDS dataset. As presented in the table below, the results demonstrate that our method performs well on CivilComments-WILDS. Consequently, our method has shown effective performance across CelebA, MultiNLI, and CivilComments, highlighting its effectiveness on text datasets. We will ensure that the complete table is included in the revision. \| CivilComments \| Avg Acc. \| Worst-group Acc. \| \|---\|---\|---\| \| JTT \| 92.6 \| 63.7 \| \| JTT+Ours \| 86.9 \| 78.5 \| --- --- Rebuttal 4: Comment: ### I would encourage the authors to characterize (either theoretically, or empirically with synthetic noise) the behavior of their method under mislabeling, which is an important potential failure mode ### We sincerely appreciate the reviewer’s valuable suggestion regarding mislabeled samples, which is indeed an important issue in real-world scenarios. However, we would like to emphasize that the primary focus of our paper, as well as prior studies on spurious correlations, is to address spurious correlations within training datasets. While considering mislabeled samples in conjunction with spurious correlations is an important future direction, please note that the debiasing community is still facing significant challenges in effectively addressing spurious correlations alone. In fact, addressing both problems together introduces a new and complex challenge in this field. Therefore, we respectfully ask that if the reviewer’s last concern involves addressing the mislabeling problem simultaneously, we would greatly appreciate reconsideration of this given context. Once again, we sincerely thank you for your thorough review of our paper and for the valuable feedback provided. ---	Rebuttal 1: Rebuttal: We provide Grad-CAM visualizations [1] for both ERM and ERM+Ours on BFFHQ and Waterbird in Figure 1. We also include example images from the top 100 samples, as ranked by BCSI, in Figure 2. [1] Selvaraju, Ramprasaath R., et al. "Grad-cam: Visual explanations from deep networks via gradient-based localization." CVPR, 2017. Pdf: /pdf/2acb8d59dd79feede5b5bc7591d36772904a7c3c.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Reconstructing the Image Stitching Pipeline: Integrating Fusion and Rectangling into a Unified Inpainting Model	Accept (poster)	Summary: This work proposes to integrate the fusion and rectangling of image stitching into a unified inpainting model. In particular, the weighted masks are designed to guide the reverse process in a pre-trained large-scale diffusion model, which implements this integrated inpainting task in a single inference. Extensive experiments demonstrate the interpretability and generalization capabilities of the proposed unified model. Strengths: + The motivation for reconstructing the image stitching pipeline into a unified model is sound and clear. + Some discussions on image stitching are insightful. For example, in the Introduction, the authors claimed that "To address the error propagation problem, we identify image fusion as the key point for improvement". I agree it is an accurate point to inspire this work. + The reviews of previous methods are detailed and comprehensive (in Tab. 1 and Section B in the Appendix), which clearly shows their limitations and potential improvements. Weaknesses: - While this work is well-motivated, the proposed contributions seem to be weak for me. For instance, the authors proposed a weighted mask to guide the reverse process in the diffusion model. However, the current presentation regarding this contribution looks like an experimental trick rather than a technical proposal. - The contribution of the proposed unified inpainting model (Section 3.1) is also expected to be highlighted. It is still ambiguous how the fusion part and rectangling part are merged into a unified model. I believe this module is much more important than applying cutting-edge generative models. - This work leverages a generation view to address the reconstruction problem. Such an interesting trend can be noticed in the recent works from other research regions as well. However, how to balance the generation and reconstruction in the image stitching problem remains unclear. I believe the users may prefer accurate reconstruction instead of introducing novel content (sometimes artifacts). Moreover, some previous works also proposed to fill the irregular boundaries of images or holes by warping with generative models, such as "Free View Synthesis (ECCV'2020)", "Towards complete scene and regular shape for distortion rectification by curve-aware extrapolation (ICCV'2021)", "iNVS: Repurposing Diffusion Inpainters for Novel View Synthesis (SIGGRAPH Asia)", etc. More discussions are expected to be provided. - There are some typos in the paper: Line 49: "Therefore, We question". The authors are suggested to further polish this work. Technical Quality: 3 Clarity: 3 Questions for Authors: - Can the proposed unified model be extended into other research areas? Confidence: 5 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: - The proposed unified inpainting model seems to be impractical compared to previous reconstruction-based solutions. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We greatly appreciate your careful assessment of our work. Please see our responses below. ## Weaknesses We start with weakness 3, and then discuss weaknesses 1, 2 and 4. W3: The reconstruction-based image fusion model has significant limitations and has fallen into the development bottleneck. Users may prefer accurate reconstruction, but only if the reconstruction is truly accurate. First reconstruction-based image fusion model is a UNet-like model proposed by VFISnet [A] in 2020. The subsequent classical learning-based image stitching works [B, C, D] generally follow this model structure, and there are few structural breakthrough innovations. Now, the SOTA reconstruction-based model is UDIS [C]. However, it is mentioned in UDIS++ that UDIS has significant defects, and UDIS may introduce blurred parallax regions in the fusion image with large parallax. Therefore, UDIS++[D] focused on finding a suitable soft seam and ultimately gave up improving the reconstruction-based fusion model. Based on the above discussion, in image stitching, the reconstruction-based image fusion model research has not been a fundamental breakthrough for many years, and its SOTA method UDIS still has apparent defects. Therefore, we propose another idea to explore a new direction of image fusion based on the generative model. A single research perspective limits the breadth of the development of a research field. We believe our method provides a new research perspective for the fusion problem in image stitching. Related work of irregular boundaries Thank you for reminding us of the work related to irregular boundaries. We will add the discussion about these works in the related work. W1: The construction of the weighted mask has the theoretical basis. Due to the space limitation of the main paper, we put the detailed theoretical basis and design principle in Appendix A "More Details of SRStitcher". To address this weakness, we thoroughly rewrote and supplemented Weighted masks parts in Section 3.2 Weighted mask guided reverse process in the new manuscript, as shown in the gray box. Weighted inpainting mask is inspired by the suffix principle [E]. This principle allows for the customization of the variation for each pixel or image region during the reverse process. We extend this concept by applying it to the diffusion-based Inpainting model and incorporating the requirements of image stitching task to construct weighted masks. > The weighted inpainting mask, as described in Eq. 11, is inspired by the suffix principle [E]. During the reverse process, weighted inpainting mask is mapped into multiple sub-masks to define the modified regions at each step $t$. ....This gradual modification method facilitates a more seamless blending of the inpainting content with the original image content. However, the suffix principle is a scheme to smooth the transition between the inpainting and non-inpainting areas, which cannot perceive the original content. Inspired by the attention map, we design the weighted initial mask, which assigns different fidelity to each pixel in the original image. > The weighted initial mask assigns different fidelity levels to each pixel of the fusion image, determining how much to modify each pixel based on its fidelity during the reverse process. The formula of weighted initial mask is given by Eq. 10, which is composed of two parts. The left part determines the fidelity levels of pixels in $M_{seam}(x,y)$ region, and the right part determines the fidelity levels of pixels in $M_{content}(x,y)$ region. Weighted masks are a further extension of the suffix principle, which discusses how to achieve more fine-grained and content-fidelity inpainting control and provides some technical contributions to image stitching and the control of diffusion-based inpainting process. W2: We believe that the challenge of unified models is not in definition but in implementation. Our unified model definition is straightforward and intuitive (Eq. 8). The real difficulty lies in finding a suitable model to implement this unified problem efficiently. The image stitching is a field where data is extremely scarce. All datasets used in this paper are unlabeled, which makes it difficult to train the model. So, our first task is not to design a theoretically elegant model, but to design a practically feasible model. Without prior knowledge provided by large-scale generative model, corrected registration errors and unsupervised rectangling are a struggle to succeed. Therefore, in the description of the main paper, we emphasize how to be compatible with the structure of existing large-scale generative models in the unified problem definition. In doing so, our method can introduce large-scale models into image stitching, which opens a new research direction for image stitching with extreme data shortage. W4: Thank you for your careful check. We have re-checked the paper and revised all typos. ## Questions Our unified model is specifically designed for image stitching pipelines. Given that we have yet to conduct a systematic study of the application of the model to other domains, we are careful to avoid asserting its universality in other domains. The core of our technique lies in its fine processing ability of image content to correct abnormal content while preserving the original content, which is potentially valuable for applications in multiple low-level vision domains, such as image restoration, artifact removal, and low-light enhancement. ## Limitations Answered, see W3. references [A] A view-free image stitching network based on global homography, 2020. [B] Learning edge-preserved image stitching from multi-scale deep homography, 2022. [C] Unsupervised deep image stitching: Reconstructing stitched features to images, 2021. [D] Parallax-tolerant unsupervised deep image stitching, 2023. [E] Differential diffusion: Giving each pixel its strength, 2023. --- Rebuttal Comment 1.1: Comment: Thanks for the detailed rebuttal, which addressed most of my concerns. I would like to increase my rating. The updated clarifications and experiments are expected to be presented in the final version.	Summary: This paper proposes an image stitching algorithm that unifies fusion and rectanguling stages of a conventional pipeline with an image inpainting diffusion model applied with a progressive reverse process guided by weighted masks. Their reverse algorithm progressively inpaints seam regions by gradually increasing the size of soft mask holes, while keep outpainting rectanguling regions with the same hard mask holes. The proposed work is compared with previous works by keeping the registration and fusion stages with UDIS/UDIS++ while altering with various models for a rectangling stage. Strengths: In their setup of experiments, theirs generally showed higher quality quantitatively and quantitatively than compared methods. The proposed reverse process results in a high quality generation, suitable to inpaint and outpaint the seam and rectangling regions naturally. Weaknesses: It is unclear if the repeated reverse process with gradually dilating mask holes is really beneficial than a single reverse process guided by a fixed mask. The repeated application of the re-noising + de-noising step makes the algorithm much slower. Considering the seam regions are usually narrow while the rectanguling regions could be quite wide, the progressive soft mask dilation during the progressive reverse process may be more useful with the rectanguling masks than the seam masks. Technical Quality: 3 Clarity: 3 Questions for Authors: Comparing with a case of a single reverse process guided by a fixed mask would make the paper more convincing. Comparing with a case that applies progressive mask dilation of the rectanguling mask holes would be useful. Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: Technical limitations are properly addressed. No serious potential negative societal impact is expected. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for the thoughtful review of our work. Please see below for the responses. ## Weaknesses Please see the newly added PDF in Global Response. We have provided the Rebuttal Fig. 3 and Rebuttal Fig. 4 to explain your confusion. W1: Gradually dilating mask holes in seam regions are based on content preservation consideration. Imagine that there is a painter, and this painter has an unfinished painting(Coarse fusion image). There are two things the painter needs to finish on this painting: 1. The painter is not satisfied with the finished part of the painting and needs to modify it (seam regions). 2. There are still parts of the painting that are not painted (rectanguling regions). Let us do the first thing: if this painter smears out everything in the seam region at once (fixed mask), the modified image differs significantly from the original content, see Rebuttal Fig. 3(a) red box. So this painter needs to modify it slowly, a little at each time (step $t$), so that the painter can refer to what is still in the seam regions to ensure that the modified content still has the original content, see Rebuttal Fig. 3(b) red box. This is why we use Gradually dilating mask holes in seam regions. W2: Using gradually dilating mask holes in rectangling regions is disappointing. Let us do the second thing: the painter wants to paint the rectangling regions using the same strategy as seam regions. However, there is nothing in this region. When the painter starts drawing from a small mask, the painter finds the information near the mask is insufficient. One side of the mask has the content, and the other has no content (Rebuttal Fig. 4(b)). Alternatively, one side of the mask has no content, and the other is directly out of the image (Rebuttal Fig. 4(a)). The painter must smooth the contents of both sides of the mask with each step, and smoothing the image without content introduces blurring noise. If the painter were a human, he would know that he only needed to consider the pixels with content. Unfortunately, the painter is a robot whose execution program is inflexible. Therefore, in rectangling regions, we use fixed mask. One side of the mask has content, and the other is directly out of the image. Our smart robot painter knows that there is no need for smoothing the content beyond the image. Speed: Our method does not increase the inference time. Our design does not increase the computational complexity of the model, and the re-noising + de-noising step is the standard process of the diffusion model. The original diffusion model still needs multi-step sampling without our method [A]. We achieve fine-grained control for local adjustment of different image regions by using weighted masks in the reverse process. This approach keeps the basic computational structure of the model the same. Thus, the inference time of the model with our method remains relatively consistent compared to the original model. ## Questions Q1: We provide a case of the reverse process guided by a fixed mask in the new pdf. It is shown in Rebuttal Figure 3. There is no single reverse process. The reverse process of the diffusion model is multi-step [A]. Q2: We provide a case that applies progressive mask dilation of the rectanguling mask holes in the new pdf. It is shown in Rebuttal Figure 4. references [A] Denoising diffusion probabilistic models, 2020. --- Rebuttal 2: Comment: Thank you for your rebuttal. It clarifies the need of different masking strateges for the seam and rectangling regions, and the preservation of computational complexity for the inference. Therefore, my major concerns have been resolved. I find that the proposed scheme, which converts conventional multiple stages for a stiching problem into unified one by adapting diffusion based inpainting models, holds certain values suitable for the venue. Existing inpatining models would not be able to achieve this goal without applying the proposed algorithm. I would like to update the final rating from from BA to WA.	Summary: The paper introduces SRStitcher, a novel method that integrates the fusion and rectangling stages of the image stitching pipeline into a unified inpainting model using a pre-trained large-scale diffusion model, eliminating the need for additional training. This approach addresses the issue of error propagation in traditional pipelines, offering a streamlined and robust solution. Strengths of the method include improved performance in image quality and content consistency, as well as robustness to registration errors. The experimental results are extensive, providing both quantitative and qualitative evidence of SRStitcher's superiority over existing state-of-the-art methods. Strengths: SRStitcher's primary strength lies in its innovative integration of the fusion and rectangling stages into a unified inpainting model, which addresses the long-standing issue of error propagation in traditional image stitching pipelines. By leveraging a pre-trained large-scale diffusion model, SRStitcher eliminates the need for stage-specific training, thereby simplifying the pipeline and enhancing its robustness. This approach ensures superior performance in handling registration errors, which are typically propagated and amplified in multi-stage pipelines. Additionally, the use of weighted masks to guide the inpainting process allows for precise control over inpainting intensity, significantly improving image quality and content consistency. These advancements address the limitations of existing methods, which often struggle with the independent optimization of each stage and the associated parameter tuning challenges. The extensive experimental results, including both quantitative metrics and qualitative assessments, robustly demonstrate SRStitcher's superiority over state-of-the-art methods, showcasing its ability to produce high-quality stitched images with greater stability and fewer artifacts. Weaknesses: While SRStitcher simplifies the image stitching pipeline by integrating the fusion and rectangling stages into a unified inpainting model, its technical novelty is questionable. The approach primarily combines existing technologies—pre-trained diffusion models and weighted masks—rather than introducing fundamentally new methodologies. The integration, while effective, does not inherently surpass the capabilities of current state-of-the-art techniques used separately for fusion and rectangling. For SRStitcher to be considered truly novel, it should achieve technical goals that were unattainable with the two processes handled independently. As it stands, the method appears to be more of a consolidation of existing practices rather than a groundbreaking innovation, merely reorganizing the workflow without providing substantial new capabilities or overcoming significant limitations of the previous approaches. Technical Quality: 3 Clarity: 3 Questions for Authors: - Technical Novelty: How does SRStitcher fundamentally advance the field of image stitching beyond merely integrating existing fusion and rectangling processes into a unified model? Can the authors provide more evidence of novel technical contributions? - Performance Comparison: While the paper claims superior performance, how does SRStitcher specifically outperform existing state-of-the-art methods in scenarios with extreme registration errors(large parallax)? Are there any edge cases where SRStitcher struggles compared to traditional methods? Confidence: 4 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: The authors have adequately addressed the limitations of their work and there appear to be no significant issues with the broader societal impacts. They have demonstrated transparency and responsibility in discussing the constraints and potential improvements of SRStitcher. Overall, their approach seems robust and well-considered, with no apparent concerns regarding its application or societal implications. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank the reviewer for the comments and careful reading. Please see our responses below. ## Weaknesses We would like to clarify that SRStitcher achieves technical goals that were unattainable with the two processes handled independently, especially in image rectangling. 1. SRStitcher improves the robustness of the fusion technique The image fusion method can be broadly categorized into two types: reconstruction-based method and seam-based fusion method. The SOTA reconstruction-based model is UDIS[A], which has been observed to introduce blurring parallax regions, particularly in scenes with large parallax. This issue is thoroughly documented in UDIS++[B]. To address this, the SOTA seam-based model UDIS++ attempts to improve the fusion image quality by the soft seam. However, in scenarios with registration errors between images, a perfect seam does not exist. In such scenarios, UDIS++ forces the image distortion to "create" a perfect seam, which results in the distortion of the pillar as illustrated in Figure 1② of our paper. To address the aforementioned issues, we propose a new solution for image fusion that uses the inpainting-based method to smooth the image. In contrast to reconstruction-based methods, SRStitcher does not introduce blurred regions when handling large parallax scenes. Furthermore, in comparison to seam-based methods, SRStitcher does not depend on the existence of perfect seams in the image. Consequently, SRStitcher exhibits greater robustness in dealing with registration errors compared to previous methods. 2. SRStitcher is the first rectangling solution that does not require supervised data and has higher generalization performance SRStitcher represents a major breakthrough for the rectangling problem. Existing rectangling methods [C, D, E] are all supervised learning methods and require labeled datasets. And the only labeled dataset for image rectangling is DIR-D[C]. DIR-D is an ideal dataset that excluded some challenging scenes during its production process, and its scale is relatively small. Models trained on DIR-D have limited generalization ability, as evidenced by zero-shot experimental results of DeepRectangling. Our solution is the first rectangling method that does not require supervised data. It generalizes much better than the SOTA rectangling model DeepRectangling, due to the prior knowledge from large-scale pre-trained models. We appreciate the reviewer's comments, which helped us identify the areas for improvement in the writing of our contributions section. We modify the contributions in the Introduction section as follows: > The main contributions of this paper are: (1) We propose SRStitcher, which reformulates the problem definitions of the fusion and rectangling stages to construct a more streamlined and robust image stitching pipeline. (2) SRStitcher is the first to introduce the concept of inpainting to address the image fusion problem. It incorporates prior knowledge from large-scale pre-trained models into the image stitching pipeline, enhancing the robustness of image fusion against registration errors. (3) Without additional fine-tuning or supervision, SRStitcher improves the generalization of the rectangling method in the zero-shot scenario, opening up new possibilities for unsupervised image rectangling research. (4) We conduct extensive experiments to verify the interpretability and generalization of the proposed unified model. The results show that SRStitcher significantly outperforms the state-of-the-art methods in both quantitative and qualitative evaluations. ## Questions Q1: SRStitcher has three novel technical contributions 1. SRStitcher first proposed the inpainting-based fusion method, a new thinking direction. 2. SRStitcher first incorporates prior knowledge from large-scale pre-trained models into the image stitching pipeline. 3. Weighted masks are not existing techniques, we design them to get a more refined inpainting control. Thanks to the reviewer' suggestions, we have revised the description in the Introduction section to emphasize the significant contributions of our method in both fusion and rectangling techniques. Q2: We provide a case for an extreme registration error scenario in the Rebuttal Fig. 2 Please see the newly added PDF in Global Response for Rebuttal Fig. 2. In this scene, due to the large parallax and complex floor tile texture, other comparison fusion methods exhibit noticeable misalignment and artifacts. SRStitcher addresses these issues using an inpainting-based method. Although SRStitcher cannot guarantee perfect results in the presence of such significant registration errors, it markedly outperforms previous methods in terms of tile continuity. According to the definition of $K_s$ (Lines 187), our method adaptively increases the width of $M_{seam}(x,y)$ in large parallax scenarios. Therefore, our method performs effectively in large parallax. Edge cases exist. Specifically, in "small parallax scenes with substantial color differences between the stitched images", our method may exhibit more pronounced stitching seams compared to existing methods such as UDIS and UDIS++. Because, the current hyper-parameter settings are relatively conservative, resulting in a relatively small value of $K_s$ in small parallax scenes. The width of $M_{seam}(x,y)$ is insufficient to provide enough space for color difference smoothing. We think that this issue can be mitigated by pre-calculating the color differences and design a more flexible hyper-parameter setting method. references [A] Unsupervised deep image stitching: Reconstructing stitched features to images, 2021. [B] Parallax-tolerant unsupervised deep image stitching, 2023. [C] Deep rectangling for image stitching: A learning baseline, 2022. [D] Recdiffusion: Rectangling for image stitching with diffusion models, 2024. [E] RectanglingGAN: Deep rectangling for stitched image via image inpainting, 2024.	Summary: This paper tried to integrate the fusion and rectangling stages in image stitching into a unified model. More concretely, a special fusion, a rectanlging step, and a mask-guided diffusion model are gathered to implement stitching-customized image inpainting, especially for the irregular boundaries. It is worth mentioning that, the inpainting model uses the pre-trained model and requires no more fine-tuning. To evaluate the proposed method, the authors designed a quantitative metric named CCS and conducted extensive experiments. Strengths: 1. The concept of integrating multiple stages of image stitching into a single stage is novel and promising. 2. The experiments are abundant and convincing. 3. The authors leverage a pre-trained model to implement stitching-customized inpainting without any extra training. Weaknesses: 1. The so-called unified model consists of several steps including a specially-designed fusion step, a rectangling step, and a inpainting step. I don’t think this multi-step design can be regarded as a unified model. 2. I am skeptical of whether the inpainting model is meaningful to image stitching. As claimed in the DeepRectangling paper, they abandoned the inpainting model because they think it may introduce some contents that are far from the reality. The manuscript seems to ignore the problem. And I do not think the proposed method can address this issue in the so-called unified inpainting model. 3. The inpainting results are still not perfect, as illustrated in the image boundaries of Fig. 14. 4. The fusion step of Eq. 4 is special. What’s the motivation for that? Technical Quality: 2 Clarity: 2 Questions for Authors: My concern lies in my second weakness. Will this inpainting model for irregular boundaries be meaningful? I have another idea for the inpainting model of image stitching. The inpainting model should not concentrate on the boundaries but on the regions where the artifacts and distortion are produced. Let’s put it in this way. The registration stage may introduce artifacts or distortion. So can we eliminate these issues through an inpainting model? It may be more meaningful to locate these regions, mask them, and then inpaint them. The inpainting process can be implemented with the guidance of original contents, thus contributing to a reliable completion model. This is just a simple discussion. But from my perspective, I cannot figure out the meaning of the proposed inpainting model. Confidence: 4 Soundness: 2 Presentation: 2 Contribution: 2 Limitations: No limitation is mentioned in the manuscript. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We thank you for raising these issues and your comments. Please see below for the responses. ## Weaknesses We start with weakness 2, which is most concerned by the reviewer, and then discuss weaknesses 1, 3 and 4. W2: DeepRectangling's experimental results of inpainting models are outdated. The DeepRectangling paper claimed that: > Nevertheless, there is currently no work to design a mask for irregular boundaries in image stitching, and even SOTA completion works [26, 28] show unsatisfying performance (Fig.1d) when processing the stitched images. However, it is important to note that DeepRectangling paper was published in 2022, and its references 26[A] and 28[B], were completed in 2021 and 2019, respectively. Notably, since 2022, there has been substantial progress in diffusion-based inpainting methods[C, D, E], which demonstrate far superior performance in terms of image quality and semantic coherence. Therefore, [A, B] in DeepRectangling paper are not SOTA now. Also, a recent work[F], published in June 2024 (and therefore not cited in this paper), has begun exploring inpainting-based methods to address the rectangling problem, yielding promising results. Thus, the potential and value of the inpainting-based method for rectangling problem should not be denied based only on the results in DeepRectangling paper. To address the unrealistic content problem mentioned in the DeepRectangling paper, we propose an innovative solution, based on the weighted initial mask and coarse rectangling, that effectively controls abnormal content. The unrealistic content problem has been successfully resolved in our method. W1: The unified model is clearly defined in the paper by Eq. 8. In Section 3.1 Unified inpainting model, we first define the image fusion problem(Eq. 4), and then define the image rectangling problem(Eq. 6). Finally, we explain how these two originally separate problems can be abstracted into one unified problem that can be solved by one single learning-based model (Eq. 8). This is not a "multi-step design", but rather a conceptual process of integrating two individual problems into a unified framework. W3: No method can perfectly stitch the images in Fig. 14. In the newly added PDF in Global Response, we provide the Rebuttal Fig. 1 to show the performance comparison of our method with UDISplus+DR, UDISplus+SD1.5, and UDISplus+SD2 under the scenes in Fig. 14. The results show that DeepRectangling causes distortion in the overall structure of the image, while both SD1.5 and SD2 introduce content in the upper-left corner of the image that is not present in the original. In contrast, our method exhibits only minor issues with edge clarity. Local blurring is a limitation of our method, which is discussed in the 5 Discussion and conclusion of the main paper (Lines 249-254). This blurring results from a trade-off to reduce the likelihood of generating abnormal content. The presented limitations provide directions and possibilities for future research. So, we do not shy away from our imperfections in Fig. 14, they do not imply that our method is inferior to other methods. W4: The motivations of Eq. 4 are in the text directly above this equation and Introduction section. The text directly above Eq. 4 (Lines 90-93) : "Precisely, as shown in Eq. 2, the distortion degree of $I_{wl}(x, y)$ is relatively low because it involves only minor warping based on $\texttt{I}$. This means that even in the presence of registration errors, $I_{wl}(x, y)$ does not introduce large-scale distortions. Therefore, we propose to construct a coarse fusion image $I_{CF} (x, y)$ via Eq. 4." Also, in the Introduction section (Lines 44-46) : "We propose to reformulate the fusion problem by overlaying the less distorted aligned image over the more distorted one, and inpainting the seam area between the images to correct the inappropriate image content." ## Questions The "another idea" is the core idea of our paper. In the Questions, the reviewer proposes an "another idea". We believe it is a super excellent idea, because this "another idea" is highly consistent with the core idea of our paper introduced in the Introduction section (Lines 41-44) : "Therefore, we reconsider the problem definition of the fusion challenge and hypothesize that: By determining the appropriate modification region and introducing an inpainting model with strong generalization ability, the abnormal image content caused by registration error can be effectively corrected." We have detailed how our core idea is implemented in the paper. Therefore, this so-called "another idea" proposed by the reviewer has been realized in our paper. Overall, our unified inpainting model is meaningful. 1. Our response to "weakness2" has proved that the results from DeepRectangling do not indicate that inpainting-based methods are ineffective for rectangling problem. 2. The so-called "another idea" proposed by the reviewer has been implemented in our paper. 3. Experiments (Fig. 2 and Rebuttal Fig. 1) show that our method significantly outperforms DeepRectangling in the ability to preserve the original structure of the fusion image. Based on the aforementioned arguments, we are confident that the unified inpainting model is effective and has a solid theoretical foundation and significant experimental results. ## Limitations We mentioned the limitations in section "5 Discussion and conclusion" of the manuscript. references [A] Resolution-robust large mask inpainting with fourier convolutions, 2021. [B] Boundless: Generative adversarial networks for image extension, 2019. [C] Repaint: Inpainting using denoising diffusion probabilistic models, 2022. [D] Palette: Image-to-image diffusion models, 2022. [E] Smartbrush: Text and shape guided object inpainting with diffusion model, 2023. [F] RectanglingGAN: Deep rectangling for stitched image via image inpainting, 2024. --- Rebuttal Comment 1.1: Comment: My concerns are addressed in the rebuttal and I would like to raise my evaluation.	Rebuttal 1: Rebuttal: We thank all the reviewers for their careful comments and agreement with our motivation. Here, We address some of the concerns shared by multiple reviewers and upload a PDF with rebuttal figures. 1. We clarified key contributions Due to the previous manuscript's limited space, our contributions are not clear enough, leading reviewers to underestimate our work's technical contributions to the image stitching. Here, we revised the contributions at the end of Introduction section as follows: >The main contributions of this paper are: > >1. We propose SRStitcher, which reformulates the problem definitions of the fusion and rectangling stages to construct a more streamlined and robust image stitching pipeline. > >2. SRStitcher is the first to introduce the concept of inpainting to address the image fusion problem. It incorporates prior knowledge from large-scale pre-trained models into the image stitching pipeline, enhancing the robustness of image fusion against registration errors. > >3. Without additional fine-tuning or supervision, SRStitcher improves the generalization of the rectangling method in the zero-shot scenario, opening up new possibilities for unsupervised image rectangling research. > >4. We conduct extensive experiments to verify the interpretability and generalization of the proposed unified model. The results show that SRStitcher significantly outperforms the state-of-the-art methods in both quantitative and qualitative evaluations. 2. Feasibility of the unified inpainting model 1. Feasibility of applying the Inpainting model to the fusion problem At present, image fusion models are mainly divided into two categories: reconstruction-based and seam-based. SOTA reconstruction-based model UDIS [A] has been shown to introduce blurring parallax regions when dealing with large parallax inevitably. When there are registration errors between images, SOTA seam-based method UDIS++ [B] forcibly searches for seams, which leads to severe image distortion, as shown in Fig.1 ② in our paper. To solve the above problems, we propose a new solution to the image fusion problem based on inpainting model. Compared with reconstruction-based methods, our method does not introduce blurred regions when dealing with large parallax scenes. In contrast to seam-based methods, our method does not rely on the assumption that perfect seams exist in the fusion image. Therefore, our inpainting-based method improves the fusion robustness for registration errors. Our method needs to paint some image pixels, and we use the seam mask to limit the scope of modification strictly. Secondly, we introduce weighted masks to control the intensity of modification, ensuring the image's semantic consistency before and after modification. Extensive experiments confirm the effectiveness of our method. Therefore, we firmly believe that the proposed method is practical for the fusion problem. 2. Feasibility of applying the Inpainting model to the rectangling problem One reviewer questioned the feasibility of applying the inpainting model to the rectangling problem based on the DeepRectangling paper. However, the DeepRectangling [C] paper was published in 2022, and diffusion-based inpainting methods have substantially progressed after 2022. Therefore, the possibility of applying the current diffusion-based Inpainting model in the image rectangling problem can not be denied based only on the conclusion of DeepRectangling. Also, RectanglingGAN [D], a paper published in June 2024, verifies the feasibility of the inpainting model for the rectangling problem. Our method adopts the inpainting-based model to solve the rectangling problem. To deal with abnormal content generation, we design a combination strategy of coarse rectangling and weighted initial mask, which has solved the concern proposed by DeepRectangling. Experiments (Fig. 2 and Rebuttal Fig. 1) show that our method significantly outperforms DeepRectangling in the ability to preserve the original structure of the fusion image. Therefore, we firmly believe that the proposed method is practical for the rectangling problem. Improvement introduction: Due to the space limitation, the Introduction section of the previous paper does not discuss in detail the inherent limitations of the existing fusion and rectangling methods and the breakthrough contribution of our method to them. We realize that it may lead to the reviewers underestimating the contribution of our method. Therefore, we have integrated the above discussion into our Introduction section in the revised paper. 3. Controllability of generative model Some reviewers expressed concern that generative models might introduce uncontrollable content. We believe that the controllability of generative models is an optimistic research direction. In recent years, the study of controllability of generative models has made remarkable progress and produced many widely influential works. For us, an important insight is provided by the work of Diff-Plugin[E], which verifies that large-scale pre-trained diffusion models and lightweight plugin networks can effectively handle low-level tasks in various visual domains, including de-rain, de-fog, and low-light enhancement while maintaining high-fidelity content consistency. Diff-Plugin confirms the ability of generative models in terms of content fidelity, giving us confidence to SRStitcher. Therefore, we hold a positive attitude toward the controllability of generative models and believe that the research prospects in this area are up and coming. references [A] Unsupervised deep image stitching: Reconstructing stitched features to images, 2021. [B] Parallax-tolerant unsupervised deep image stitching, 2023. [C] Deep rectangling for image stitching: A learning baseline, 2022. [D] RectanglingGAN: Deep rectangling for stitched image via image inpainting, 2024. [E] Diff-Plugin: Revitalizing Details for Diffusion-based Low-level Tasks, 2024. Pdf: /pdf/3a26b1b59aa6973d4de2f191b56b8109a1ae6334.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Learning to compute Gröbner bases	Accept (poster)	Summary: This paper provides a machine learning algorithm to compute Gröbner bases of 0-dimensional ideals in shape position. To address the backward Gröbner problem, the authors propose an algorithm based on 1) random generation of Gröbner bases by sampling univariate polynomials related to the shape position, then on 2) random generation of a polynomial matrix to generate non-Gröbner sets. The associated algorithm running time is derived in Theorem 4.8. After generating tuples with the two above-mentioned steps, the authors rely on Transformers for learning to compute Gröbner bases. Strengths: - The benchmarks show that computing Gröbner bases with the proposed backward approach can be substantially more efficient than with the usual "forward" algorithms. Weaknesses: - The paper contains many typos, grammatical mistakes and missing articles. The authors are invited to carefully rewrite the paper to increase the overall quality. Two examples (among many) are in p6, l255: "Consider polynomial ring", "Given dataset size". - The training approach, via Transformers, does not come with any theoretical guarantees related to global/local convergence, running time, error bounds. No explanation is provided regarding the cases where the method works or fails. The ML algorithms related to transformers are mostly described in the appendix and only vaguely in the main text. - The paper does not address concrete benchmarks of target applications (e.g. in cryptography or biological systems) where computing Gröbner bases is out of reach or very time consuming. Providing such experiments would definitely make the approach credible. - Many important aspects (theorem proofs, limitations) are postponed to the appendix. Overall I believe that this work, possibly sound and surely interesting, would be worth publishing but the current conference format (coming together with a short allocated review time) and focus are certainly not the best fit. Technical Quality: 2 Clarity: 1 Questions for Authors: - The framework is limited to 0-dimensional ideals in shape position. It is well known that the shape position assumption is not so strong but the 0-dimensional ideal one is very strong. Random search applied to higher-dimensional ideals would be more challenging and interesting. Could the authors provide more insights to address such problems? - Could the authors derive a killer application for which their framework would provide new results or results obtained in a more efficient way than with the forward approach? Confidence: 4 Soundness: 2 Presentation: 1 Contribution: 2 Limitations: - There is no section dedicated about the limitations of this work in the main text. Section H is not part of the main text. Flag For Ethics Review: ['No ethics review needed.'] Rating: 3 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: # NeurIPS 2024 Rebuttal (Reviewer q3D1) We appreciate your thorough review and valuable feedback. Below, we answer the weaknesses and questions. ## On Weaknesses Theoretical guarantees on training. Providing theoretical guarantees on global/local convergence, running time, and error bounds for the training of Transformers (or deep neural networks) is generally difficult. To our knowledge, such guarantees have been (partially) given only for simple models, e.g., two-layer networks or infinitely wide networks. Hence, this should be beyond the scope of our study. The tight page limitation forced us to send the description of Transformers and its training to the appendix, but as mentioned around [l.335], they follow a standard one. The exception is when hybrid embedding is used, where we have a small MLP at the input embedding, a regression head for predicting coefficients, and MSE loss. These are described in Section 5 and Appendix D, but we will review the manuscript to give further details. Benchmarks and applications. Showing the superiority of using Transformers for large-scale problems in benchmarks and applications is indeed important. However, to achieve this, we need a few more fundamental steps, e.g., 1. Designing dataset generation algorithms tailored for target applications. 2. Discovering an efficient tokenization of large polynomial systems. On 1), since the characteristics of polynomial systems vary across applications, one needs to design a special way of generating them. Our work did this for zero-dimensional radical ideals as a first step because 0-dimensionality is common in several applications (cf. Global Response). On 2), we need an efficient representation of polynomial systems for scale-up. The scope of this study is to establish the problem of learning to compute Gröbner bases, and thus, we tested its learnability based on a standard model and training. The tokenization of polynomials also follows a standard one; for example, $\{x^2-10, y\}$ is tokenized as $\texttt{[x, , 2, +, -10, <sep>, y]}$, (cf. Section 5). Eventually, a single $n$-variate term requires $O(n)$ tokens, leading to a long input sequence for large $n$. As well known in Transformer literature, the space complexity of the attention mechanism scales as $O(L^2)$ with input length $L$. A potential approach to shorten the input is to embed a term by its coefficient and inject the exponent part as position vectors because this is literally a position in the term space. We are currently working on it in our follow-up paper. It is worth noting that the current study already observed that Gröbner basis computation is computationally costly for $n=5$ in Table 1, where about 24% of the instances encountered timeout for two standard algorithms. Further, Table 22 shows that for all the algorithms, there are several instances for which Transformers run accurately and significantly faster. Thus, we have already partially observed the Transformer's supremacy. Writing and format. We will carefully clean up our manuscript manually and systematically (e.g., using LLM). A grammar checker applied before submission does not seem to work well for sentences with latex codes. As for the placement of the proofs and limitations, in my limited experience, it is common for the NeurIPS papers to have them in Appendix. The paper checklist justifies this; see [l.947], > The proofs can either appear in the main paper or the supplemental material, but if they appear in the supplemental material, the authors are encouraged to provide a short proof sketch to provide intuition. In our manuscript, the intuition is provided below each theorem. About the limitations, because this study tackles a new problem, we needed a thorough discussion of open questions, which led us to send it to Appendix. The checklist does not clarify whether the limitation section should be included in the main text. According to the submission instructions, accepted papers will get another content page, so we may be able to include the proofs and/or limitations in the main text in such a case. ## On Questions 0-dimensional ideals. If an ideal is in shape position, it is also 0-dimensional. Thus, the assumption of shape-positioned ideals cannot be weaker than that of 0-dimensionality. We assume that you intend to mean "assuming 0-dim is strong; further assuming shape position is OK." As several reviewers ask about the assumption, we provide the Global Response to address it. Please kindly refer to it. Killer applications.** One of the potential killer applications is cryptanalysis. The security of cryptography is often reduced to the difficulty of solving certain mathematical problems. Recently, the SALSA project [1] has shown that a Transformer-based approach can solve the LWE (Learning With Errors) problem, which is the basis for the security of lattice-based cryptographies. The overview of their approach is as follows: 1. From the cryptosystem to be analyzed, generate samples of LWE and their solutions as training data and perform training. 2. Input the LWE corresponding to the ciphertext to be attacked into the model constructed in Step 1. If the output gives the secret, the cryptosystem is vulnerable. The computational difficulty of the Gröbner basis problem for 0-dimensional ideals is the basis for the security of AES [2], which is currently the mainstream symmetric key encryption, and multivariate polynomial encryption [3], which provided candidates in the NIST Post-Quantum Cryptography Standardization process. Our future target is to make our proposed efficient data set generation and machine learning the basis for some security analysis in cryptography. [1] E. Wenger, et al., SALSA: Attacking lattice cryptography with transformers, 2022. [2] J. Buchmann, et al., Block ciphers sensitive to Gröbner basis attacks. 2005 [3] A. Kipnis, et al., Unbalanced oil and vinegar signature schemes, 1999 --- Rebuttal Comment 1.1: Title: Answer to authors' rebuttal Comment: Thanks for your comments, I will maintain my score. --- Reply to Comment 1.1.1: Comment: Thank you for reading our rebuttal and responding promptly. We again clarify that your comments/questions are very critical to improving the current work and also directing future work. We believe that we've addressed your comments/questions. Particularly, it is important for us that you kindly comprehend the scope of this study and its value within this scope, with which your evaluation of our work hopefully increases. We'd be happy to engage further.	Summary: This article investigates the use of machine learning techniques to compute Gröbner basis of polynomial systems. This problem consists in, given a term order and a finite set of polynomials $f_1, \cdots, f_m$, to compute another set of polynomials $g_1, \cdots, g_m$ that have the following desirable properties $(P)$: $(P)$ the $g_i$'s all belong the ideal generated by $f_1, \cdots, f_m$, and such that any leading term in the ideal generated by the $f_i$'s is generated by the $g_i$'s. To do so, the authors propose a method to first sample training data, which was previously problematic. Then, after embedding the set of polynomials $f_i$'s and $g_i$'s that they embed (after tokenization and a hybrid embedding technique that they detail in the appendix), they make use of a transformer to output the $g_i$'s given the $f_i$'s. Strengths: - The article proposes a serious study, is well-written and very comprehensible for non-experts in computational algebra and Gröbner basis. - The introduction and comparison to existing work is clear. - The articles presents interesting ideas to generate training datasets, using a backward approach. Instead of first sampling the $f_i$'s (non-Gröbner set) and then an associated Gröbner basis, they first generate a set of polynomials formed by some gi's and then generate an associated system of polynomials fi's that thave property (P) (in other words, first generate the solutions, then the problem). - The authors included example of success for, but also examples of failure, which can be of use for future improvements. - The authors share in details the results and conclusion of their study, in particular their experiments. Therefore, this article may be of great interest beyond the computational algebra community, including those who have to solve polynomial systems of questions for various applications. Weaknesses: I do not see a major weakness of this article. It constitutes a serious study of the use of machine learning advancements for computational algebra. One comment (not a weakness): Section D, there is a reference to a Table that is missing (line 728). Technical Quality: 4 Clarity: 4 Questions for Authors: - Line 115, the authors mention the notion of reduced Gröbner basis. Do they mean normalized and in shape position? The authors may want to clarify this. - The authors may want (if they think this is relevant) to introduce some short additional comment for non-experts about the Gröbner basis definition line 109. This would help to understand the motivation of the definition. Namely: Understanding and finding solutions of a polynomial system can be adressed via studying the ideal generated by the fi's. For example, if one is able to find if the constant 1 is in the ideal generated by the fi's, then there is no solution for the system. It turns out the condition on the leading terms in the defintion are equivalent to, given a polynomial h, that the remainder after multivariate division of h by the gi's to be zero if and only if the h is in the ideal generated by the fi's (see for instance Definition 1 in [70]). Hence one can answer the above question (if 1 is in the ideal) -- as well as others-- by performing a multivariate division algorithm taking on 1 and the Gröbner basis. It the output is 0, then 1 belong to the ideal and there is no solution. Confidence: 5 Soundness: 4 Presentation: 4 Contribution: 4 Limitations: The authors clearly explain the apparent limitation of their work, in particular to which extent the experiments they conducted are successful. They report extensive experimental results in the appendix, in particular failed examples. Flag For Ethics Review: ['No ethics review needed.'] Rating: 8 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We sincerely appreciate your thorough review and strongly positive assessment of our work. We are grateful that you listed many strengths of our work. Reduced Gröbner basis. The reduced Gröbner basis is defined independently from shape position. A Gröbner basis $G$ is called reduced when i) the leading term coefficients are all one and ii) there is no redundancy (see. Definition A.13.) in that any terms of $g \in G$ is not divisible by the leading term of other polynomials in $G$. We will include a few follow-up lines to make it more friendly to readers unfamiliar with Grönber bases. Gröbner basis definition for non-experts. It is indeed very important to broaden the scope of readers by introducing some intuition on the definition of a Gröbner basis. We prepare the paragraph at [l.118] to give such an intuition of Gröbner bases, but it is true that this does not give an intuition of Definition 3.2. The suggested explanation elegantly presents the point of the definition, and we will integrate it into our explanation. Once our paper gets accepted, there will be an additional content page. We will exploit it. We will clean up our manuscript by taking into account your comments on missing table references and providing a more friendly introduction to Gröbner bases. Again, we thank you for your strong support of our work. --- Rebuttal Comment 1.1: Comment: Thanks for your reply. I will maintain my score and will argue in favor of this work if needed. --- Reply to Comment 1.1.1: Comment: Thank you for your reading and support!	Summary: The paper proposes to learn to compute Gröbner bases (as the title says). This includes two important problems. 1) Generating the dataset and 3) Finding an appropriate encoding of the problem to feed into a transformer architecture. That is finding an encoding for a system of polynomials to be solved. The paper gives adequate solution for both of these issues and implements it, Strengths: The paper tackles a really tough and important problem with a novel approach. This is done while also placing the work nicely in the existing literature. I enjoyed reading the open questions section in the Appendix. Weaknesses: The method does not provide any guarantees. In this regard it is then not entirely clear what the benefit would be of having "hints at the right solution". Technical Quality: 3 Clarity: 3 Questions for Authors: 1) Could the authors comment on my point raised in the "weakness". Specifically, how do you envisage to use learned Gröbner basis to be useful for any downstream tasks? Would you use them as a heuristic to exactly solve polynomial systems? 2) Why did you limit the rings to Q,R F_p. Why not N or p-adic numbers? Confidence: 2 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: Exemplary! Flag For Ethics Review: ['No ethics review needed.'] Rating: 8 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your strongly positive evaluation of our work! Benefits. In general, if the terms of the input polynomial system $f_1,\ldots,f_m$ are fixed and the coefficients $\{c_{i,\alpha}\}$, where $f_i = \sum_{\alpha} c_{i,\alpha} x^{\alpha}$, are considered as parameters, it is known that by using the comprehensive Gröbner basis theory, i.e., the parameterized Gröbner basis theory, the terms appearing in the reduced Gröbner basis $G$ of the ideal $\langle f_1,\ldots,f_m \rangle$ are identical for general coefficient values of $\{c_{i,\alpha}\}$. In other words, this means that in most cases, the combinations of terms on a reduced Gröbner basis are determined only by the combinations of terms in the input polynomial system. This can also be observed from the relatively high support accuracy in our experiments. From the above, there is still no concrete guarantee that our method will give a correct model, including the coefficients, but it is believed that there is some guarantee that the terms will be guessed correctly. In algebra, guessing the terms of the Gröbner basis gives a global invariant of the ideal, such as the initial ideal or the Hilbert polynomial. Therefore, we can consider using our model as an oracle or heuristic to provide global invariants of ideals (initial ideals, Hilbert polynomials) for downstream tasks. Indeed, there is an accelerated Gröbner basis computation algorithm using Hilbert polynomials [1]. In future work, we can construct efficient polynomial solving and Gröbner basis computation theory by assuming further information (e.g., entire supports) given by Transformers. Other fields. The proposed dataset generation works for other coefficient fields, including $\mathbb{Q}_p$. However, as $\mathbb{N}$ is not a field (or even a ring), the set $\mathbb{N}[x_1,\ldots, x_n]$ is beyond the scope of Gröbner basis theory. The ring $\mathbb{Q}_p[x_1, \ldots, x_n]$ is associated with a non-Archimedean geometry, so it should be interesting to see how the learning goes. In our experiments, the learning was more successful with $\mathbb{Q}$, which equips a canonical metric, than with $\mathbb{F}_p$, which has no non-trivial metrics. An experiment on $\mathbb{Q}_p[x_1, \ldots, x_n]$ may serve as the midpoint between them. [1] C. Traverso, Hilbert functions and the Buchberger algorithm, Journal of Symbolic Computation, 1997. --- Rebuttal Comment 1.1: Comment: I thank the reviewer for their detailed overall rebuttal and intend to maintain my score. (and yes N is not a field, apologies)	Summary: Gröbner bases are a tool of fundamental importance in the field of computational algebra. Unfortunately known algorithms for computing Gröbner bases are very ineficient, having a running time that is double-exponential on the number of variables. In this work, the authors propose a machine-learning based approach for the computation problem. Instead of devising an algorithm that is always guaranteed to correctly output a Gröbner basis, the authors propose a learning algorithm based on transformers. To address this learning problem, the authors address other interesting problems such as random generation of Gröbner bases and the Backward Gröbner problem. Strengths: The paper provide an interesting experimental evaluation on how transformers can be used to learn Gröbner bases. The random generation of Gröbner bases is also interesting. Weaknesses: The main weakness, in my opinion, is that the paper does not attempt to provide a characterization of a subclass of polynomial systems that can be efficiently solved using the transformed-based approach. Therefore it is difficult to have an idea of what properties the input polynomial system must satisfy in order for the approach to give reasonable results. The number of variables considered in the experiments (n=2,3,4,5) is way to low to give an idea about the complexity of the problem. For this number of variables it is not clear whether the machine learning method provides any advantage at all with respect to traditional computational algebraic approaches. The theoretical part of the paper is much more concentrated on the issue of random generation of Gröbner bases than on the learning part. For this reason, it is my impression that the authors are putting too much emphasis on the part of the paper where results are not very satisfactory (the learning theory part). The paper would be more solid if concentrated on random generation of Gröbner bases with the learning part as an interesting application. Technical Quality: 2 Clarity: 3 Questions for Authors: 1) What is the largest number of variables for which the machine learning method gave interesting results? 2) How does the accuracy of the model decay with the number of variables? 3) What is the relation between the number of variables and the time necessary to train the model? Confidence: 3 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: We sincerely appreciate your thorough review and insightful comments. You raise the characterization of a subclass of polynomial systems as the main concern, and our rebuttal mostly focuses on this point. We would like you to refer to the Global Response as well. ### On Weaknesses Characterization of a subclass of polynomial systems. We appreciate your fundamental remark. We acknowledge that our paper does not provide a comprehensive characterization of the subclass of polynomial systems that can be efficiently solved using our transformer-based approach. Generally speaking, it is difficult to answer what problems can be solved by Transformers or what sample distributions are learnable by Transformers. Instead, our study currently approaches the question: for what class of polynomial systems can we prepare a dataset efficiently for Transformer training? The trainablity in this sense should come before the learnability from a practical point of view. As an initial work, we break down the trainability question into two components: Gröbner basis sampling and backward Gröbner problem. These can be answered affirmatively through the design of algorithms. For the former, we suggest ideals in shape position, Cauchy module, and potentially, ideals of points (cf. Appendix~G). For the latter, we suggest 0-dimensional ideals (Theorem 4.7). Number of variables This is also an important point. Ultimately, we envision that Transformers will be used for large-scale problems (i.e., problems with many variables and equations) that mathematical algorithms cannot address. However, the number of variables that Transformer can handle is currently restrictive. The restriction comes from the current simple tokenization of polynomial systems: for example, {$x^2-10, y$} is tokenized as $\texttt{[x, , 2, +, -10, <sep>, y]}$, (cf. Section 5). Eventually, a single $n$-variate term requires $O(n)$ tokens, leading to a long input sequence for large $n$. As well known in Transformer literature, the space complexity of the attention mechanism scales in $O(L^2)$, where $L$ denotes the input length. The scope of this study is to establish the problem of learning to compute Gröbner bases, and thus, we tested its learnability based on a standard model, including tokenization. For scale-up, one may be able to embed a term by its coefficient (i.e., single token) and inject the exponent part as a position vector because this is literally a position in the term space. We are currently working on it in our follow-up paper. It is also worth noting that even for $n=5$, we have observed a potential advantage of using machine learning. Table 22 shows that there are several instances in which Transformer models successfully compute Gröbner bases in less than a second, whereas algebraic methods take much longer (100 seconds and timeout for most cases). Balance between theoretical and learning parts. Thank you for your fair evaluation and great writing suggestions. We indeed have a great algebraic interest in random generation of (non-Gröbner basis, Gröbner basis pair). We adopted the current structure by taking into account the potential readers (i.e., NeurIPS readers), who may be more interested in the learning part. We will reconsider the presentation. Thank you very much. ### On Questions We appreciate your insightful questions. We believe the learning approach of Gröbner bases has an advantage over algebraic algorithms for large-scale problems. However, as described above, the training on large $n$ requires an efficient input embedding of polynomial systems. We could also try larger $n$ by using a few more GPUs, but we considered this to be very interesting. It should be more reasonable to design an efficient input embedding for polynomial systems first and then see the impact of the increase in $n$ on the learning complexity. Here, we only provide quick answers to your questions below. Largest number of variables with interesting results: We have only tested up to $n=5$. Even at this point, we have already observed interesting results, such as the contrast between infinite and finite fields (Table 2) and Transformer supremacy (Table 22). Accuracy decay with the number of variables: The accuracy change with respect to the number of variables is given in Table 2, but the results would also change the density parameter $\sigma$. This is also a consequence of the input length restriction. Relation between the number of variables and training time.** We collected the training time from our experiment log and summarized it below. Note that the training time here can have been affected by the other processes running in parallel, so these numbers can be regarded as upper bounds. The table shows that we generally need longer training time for larger $n$. Not shown here, but we also tried longer training but we only observed a subtle improvement. \| \| $n=2$ \| $n=3$ \| $n=4$ \| $n=5$ \| \| -------- \| -------- \| -------- \| -------- \|-------- \| \| $\mathbb{Q}[x_1,\ldots, x_n]$ \| 5.8 \| 8.4 \| 9.8 \| 12.5 \| \| $\mathbb{F}_7[x_1,\ldots, x_n]$ \| 6.2 \| 12.6 \| 8.6 \| 9.5 \| \| $\mathbb{F}_{31}[x_1,\ldots, x_n]$\| 7.3 \| 10.4 \| 10.6 \| 11.8 \| *The training time in hours. Thanks to the questions, we realize that there are two interleaving factors that affect the complexity of learning. For larger $n$, the Gröbner basis computation becomes algebraically more difficult. At the same time, dataset generation algorithms generate larger systems (i.e., longer input/target sequences), making learning more difficult from a machine learning perspective. We have to find a way to separate these factors for future discussion. --- Rebuttal Comment 1.1: Comment: Thanks for the clarifications. I will keep my current recommendation.	Rebuttal 1: Rebuttal: # Global Response We sincerely appreciate the reviewers' time and efforts in reviewing our manuscript. We have received many insightful comments and questions, which have been carefully considered in this rebuttal and the next manuscript update. While we will answer most of the comments and questions from each reviewer individually, here we would like to elaborate on our assumption of 0-dimensional ideals, as this topic appears to be of interest to several reviewers (particularly Reviewers BQDD and q3D1). ### On 0-dimensional ideal settings This study focuses on 0-dimensional ideals, and several reviewers asked about its motivation and generalization to positive-dimensional ideals. A short answer is that the choice of 0-dimensional ideals is reasonable from both computational algebra and application standpoints, and generalization to the positive-dimensional case is challenging but interesting future work. ### Motivation Our study is the first to approach Gröbner basis computation via end-to-end learning. We found that dataset generation poses unexplored algebraic tasks, i.e., sampling of Gröbner bases and their back-transformation to non-Gröbner sets. It is very difficult to resolve this in the most general case in a single work, so we naturally had to restrict ourselves to a particular case. We chose 0-dimensional ideals for two reasons: i) From a computer algebraic perspective, 0-dimensional ideals are the most popular class of ideals to study. This is partly because of the ease of analysis. As Definition A.5 shows, 0-dimensional ideals relate to finite-dimensional vector spaces, and thus, analysis and algorithm design can be essentially addressed by matrices and linear algebra. As a consequence, we have more useful statements and algorithms for this case. As such, we focused on the 0-dimensional case as a reasonable starting point, where many facts and tools are accessible. It is also worth noting that on a finite field, any ideal becomes 0-dimensional by including the field equations (i.e., polynomials restricting the solutions to the finite field; e.g., $x(x-1)$ for $\mathbb{F}_2[x]$) to the generators. Such extensions of generators are perfectly acceptable when we are interested in the solutions, not the Gröbner bases themselves. ii) From an application perspective, 0-dimensional ideals are again popular objects to study. Namely, many applications share a motivation of finding solutions for polynomial systems with an implicit assumption of finitely many solutions. If a system (or its associated ideal) is 0-dimensional, it has finitely many solutions (and the reverse is also true if the coefficient field is algebraically closed). For example, the multivariate cryptosystem, a promising candidate for signature-based post-quantum cryptosystem standardization by NIST, is based on 0-dimensional ideals [1]. In control theory, finding equilibria of rational dynamical systems is reduced to polynomial system solving with an assumption that there are finite equilibria. The estimation of the domain of attraction around an equilibrium is also reduced to polynomial system solving [2]. In machine learning, the computation of generators of 0-dimensional ideals has been studied as a feature extraction method [3, 4, 5] (see Appendix G for more), including an ICML'13 best paper. ### Generalization Generalization to positive-dimensional ideals is non-trivial, and we leave it to future work. One of our contributions to the community is posing this new open problem with motivation from machine learning. We currently have no particular idea to address this. Perhaps we might be able to design some constructive algorithms for binomials, which appear in applications to combinatorics and algebraic statistics. [1] T. Yasuda, X. Dahan, Y.-J. Huang, T. Takagi, and K. Sakurai. MQ challenge: hardness evaluation of solving multivariate quadratic problems. Cryptology ePrint Archive, 2015. [2] D. Nešić, I.M.Y. Mareels, T. Glad, M. Jirstrand, The Gröbner Basis Method in Control Design: an Overview, IFAC, 2002, [3] R. Livni, D. Lehavi, S. Schein, H. Nachliely, S. Shalev-Shwartz, and A. Globerson. Vanishing component analysis. ICML, 2013. (Best Paper Award) [4] H. Kera and Y. Hasegawa. Gradient boosts the approximate vanishing ideal. AAAI, 2020 [5] E. S. Wirth and S. Pokutta. Conditional gradients for the approximately vanishing ideal. AISTATS, 2022	NeurIPS_2024_submissions_huggingface	2,024	Summary: This paper presents a Transformer based method to compute Gröbner basis, a known NP-hard problem. The authors focus on polynomials with 0-dimensional radical ideals and propose efficient algorithms to generate training samples of polynomial systems and their corresponding Gröbner basis. The main novelties include (1) an efficient backward transformation algorithm from a Gröbner basis to an associated non-Gröbner set; (2) a hybrid input embedding for both discrete and continuous-value tokens. The transformer, which was trained on millions of Gröbner basis pairs generated by the authors, performed well on some types of rings. Strengths: The paper introduced a novel method to compute a significant problem in computational algebra, demonstrating high accuracy for certain types of rings. The efficient backward sampling methods are less explored and may facilitate further ML studies in this field. Additionally, this backward approach helps restrict the Gröbner basis to applications of interest. The paper is well-written and easy to follow. Weaknesses: * I have serval questions about the choice of the 0-dimensional ideal as the scope of the study : (1) the authors first mentioned “…, and thus, we should focus on a particular class of ideals and pursue in-distribution accuracy” and then claimed “… and thus, we focus on the generic case and leave the specialization to future work”. Do you regard this choice as a “particular” or “general” case of the Gröbner basis computation? (2) What is motivation of focusing on 0-dimensional ideals (since it is already mentioned that this work is meant to be general)? Is it purely because of the sampling easiness? Also, what are the difficulties of working on the more general Gröbner basis computation problem? (3) The discussion of, whether Transformers, or more generally, ML methods, can help NP-hard problems generally or only in-distribution, is interesting. There are some results from the SAT field that end-to-end ML models may be able to generalize to out-of-distribution problems [1]. As you claim here “in-distribution accuracy” is what we are after, it is important to include some experiments across different applications, to support this claim. * The hybrid input embedding for both discrete and continuous-value tokens is claimed to be one of the paper’s contributions. However, this idea is not new, as other research has explored similar problems (e.g., [2, 3, 4]). The authors do not provide a review of existing methods or distinguish their approach from these works. It is interesting to note that many incorrect results are reasonable. This suggests that incorporating the Transformer method with planning (5) or RL (6) may help the performance through feedbacks. Reference [1] Cameron, Chris, et al. "Predicting propositional satisfiability via end-to-end learning." Proceedings of the AAAI Conference on Artificial Intelligence. Vol. 34. No. 04. 2020. [2] Charton, François. "Linear algebra with transformers." arXiv preprint arXiv:2112.01898 (2021). [3] Golkar, Siavash, et al. "xval: A continuous number encoding for large language models." arXiv preprint arXiv:2310.02989 (2023). [4] McLeish, Sean, et al. "Transformers Can Do Arithmetic with the Right Embeddings." arXiv preprint arXiv:2405.17399 (2024). [5] Kamienny, Pierre-Alexandre, et al. "Deep generative symbolic regression with Monte-Carlo-tree-search." International Conference on Machine Learning. PMLR, 2023. [6] Jha, Piyush, et al. "RLSF: Reinforcement Learning via Symbolic Feedback." arXiv preprint arXiv:2405.16661 (2024). Technical Quality: 3 Clarity: 3 Questions for Authors: * With the proposed sampling methods based on shape position and Cauchy module, how diverse is this generated set? Does these generating methods further restrict the scope less than the 0-dimensional radical ideals? Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: It is not clear whether this work can be generalized to beyond 0-dimensional ideals. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: We appreciate your insightful and constructive comments and thorough review, as well as many pointers to related papers. ### On Weaknesses Choice of 0-dimensional ideals. We received several comments/questions about this assumption from several reviewers; please refer to the Global Response for the motivation for the choice. Particular v.s. generic. You seem to find contradictive policies from our claims: > [l.178] > ... focus on a particular class of ideals..." > > [l.183] > ..., the form of non-Gröbner sets varies across applications, and thus, we focus on the generic case and leave the specialization to future work. The former claims the need to focus on a particular class of ideals as it is difficult to cover all the cases in a single work. The latter says that our way of particularization is more driven by a computer-algebraic viewpoint and not biased toward a single application. We will update our manuscript to avoid such confusion. Hybrid input embedding. Thank you for completing our literature survey! In our reading, [2,4] rely on traditional discrete embedding based on mantissa (between 0 and 9999) and exponent, which requires keeping a large vocabulary and learning the numbers' relation from scratch. We found [3; Golkar+, Oct. 2023] to be close to our idea. The difference is that in their work, a real value is represented as the length of the embedding vector of the number token, while we use an MLP to find an embedding directly and have more degree of freedom (i.e., length and direction). Interestingly, Figure 1 shows that our embedding also encodes the values by the scale. We need experiments of Gröbner basis computation learning to check if their method outperforms ours and also discrete embedding. We will review and include them in our references. In-distribution accuracy. We appreciate your pointer to an interesting work. It seems that the paper (particularly Table 2) indicates a potential generalization even for NP-hard problems. It is also very surprising to me that models trained on a 100-variable dataset perform better in a 600-variable dataset than in a 100-variable dataset. We are not sure if this is called generalization (although it is great). > As you claim here "in-distribution accuracy" is what we are after, it is important to include some experiments across different applications, to support this claim. We don't claim that a generalization of learning is unachievable for NP-hard problems; we only present our picture of using Transformer for Gröbner basis computation. The learning approach may provide faster computation than classical algorithms, but the problem itself has been proven NP-hard, so machine learning models cannot break this. ### On Questions Dataset diversity. Table 6 provides several statistics of the datasets (we will make it cleaner in the update). The degrees and the number of terms have certain variances, which empirically shows diversity. Tables 4 and 22 also present the existence of hard samples for mathematical algorithms, which supports a certain diversity of the generated samples. Theoretically, defining and measuring the diversity of generators is not very clear. For Gröbner basis sampling, we performed uniform sampling for degree, the number of terms, and so on, so the Gröbner bases were sampled uniformly randomly in a sense. For non-Gröbner sets computed from the Gröbner bases, a reasonable starting point would be the question on the reachability: can we sample all possible generating set $F$ such that $\langle F \rangle = \langle G \rangle$ from a Gröbner basis $G$? As of now, we suspect the answer is negative because we are based on Theorem 4.2 (2), a sufficient condition. We are now tackling designing an efficient algorithm based on Theorem 4.2 (3), a necessary and sufficient condition, but this requires a deeply algebraic discussion. Generalization to the positive-dimensional case. Please kindly refer to the Global Response.	null	null	null	null	null	null
Learning the Expected Core of Strictly Convex Stochastic Cooperative Games	Accept (poster)	Summary: The paper tries to find an expected core under the assumption that a characteristic function is $\varsigma$-strictly convex cooperation game. The authors provide a bandit-based sampling algorithm called Common-Points-Picking, which allows us to compute the expected core in a polynomial number of samples. They prove that strictly convex is a sufficient condition to find an expected core with the polynomial number of samples. Strengths: s1. The paper discusses the learnability of the expected core and shows that strict convexity is a sufficient condition to guarantee thelearnability. s2. The paper also provides a novel algorithm based on convex geometry and the proposed algorithm outputs an expected core with probability 1 - $\delta$. s3. The sample complexity of the proposed algorithm is polynomial in the size of the players. Weaknesses: w1. My main concern is that the assumption of strict convexity is not very natural while providing the hardness of learnability in a non-strict convexity situation is good. It would be more better to show the validity of the assumption by showing that some known application of cooperative games satisfies it. For example, it is better to provide a discussion that in some known convex games, such as induced subgraph games with positive weights[1], airport games[2], and some others[3-6], which parameters of these convex games are related to the parameter \varsigma. w2. Providing the upper bound of sampling complexity is good, but I cannot measure how tight the bound is. Since the paper provides a discussion of the hardness of calculating the lower bound, providing the tight lower bound of sample complexity is ideal. w3. It would be better to discuss other sampling-based algorithms for computing core. For example, [7] provides an FPRAS algorithm for the convex(supermodular) cooperative game, and [8] provides a PAC-learning-based algorithm for finding the core. While they each have different assumptions and problem settings, the discussion about them is useful for readers to clarify where the paper stands. [1] Deng, X., & Papadimitriou, C. H. (1994). On the complexity of cooperative solution concepts. Mathematics of operations research, 19(2), 257-266. [2] Littlechild, S. C., and Owen, G. 1973. A simple expression for the shapley value in a special case. Management Science 20(3):370–372. [3] Oishi, T., & Nakayama, M. (2009). Anti-dual of economic coalitional TU games. The Japanese Economic Review, 60, 560-566. [4] Graham, D. A., Marshall, R. C., & Richard, J. F. (1990). Differential payments within a bidder coalition and the Shapley value. The American Economic Review, 493-510. [5] Feigenbaum, J.; Papadimitriou, C. H.; and Shenker, S. 2001. Sharing the cost of multicast transmissions. Journal of computer and system sciences 63(1):21–41. [6] O'Neill, B. (1982). A problem of rights arbitration from the Talmud. Mathematical social sciences, 2(4), 345-371. [7] Liben-Nowell, David, et al. "Computing shapley value in supermodular coalitional games." Computing and Combinatorics: 18th Annual International Conference, COCOON 2012, 2012. [8] Igarashi, A., Sliwinski, J., & Zick, Y. (2019). Forming probably stable communities with limited interactions. In Proceedings of the AAAI Conference on Artificial Intelligence (Vol. 33, No. 01, pp. 2053-2060). Technical Quality: 3 Clarity: 3 Questions for Authors: Could you please comment about the weakness comments if I have misunderstood something? The following is a comment rather than a question. q1. Is there any relationship between totally balanced games [9]? Totally balanced condition is a necessary and sufficient condition for guaranteeing the existence of the core. It may be useful for generalizing the proposed problem setting. [9] Shapley, L. S., & Shubik, M. (1969). On the core of an economic system with externalities. The American Economic Review, 59(4), 678-684. Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: Yes, they adequately address the limitations. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: # Response to reviewer f4nV We thank the reviewer for the insightful comments. Below are our responses/clarifications to your questions: ## Comment 1: Practical example is needed. ### Response: Consider a facility-sharing game (a generalisation of cost-sharing games [1, 2]) where joining a coalition $S$ would provide each player of that coalition a utility value $v(k)$ where $\|S\| = k$, and they have to pay an average maintenance cost $c(k)$. The expected reward of $S$ is defined as $\mu(S) = v(k) - c(k)$, representing the average utility of its coalitional members. This setting represents many real-world scenarios, such as: - University departments together plan to set up and maintain a shared computing lab. The value of using the lab is the same $v(k) = v$ for each department (e.g., their students can have access computing facilities), but the maintenance cost $c(k)$ is monotone decreasing and strictly concave (e.g., the more participate the less the average maintenance cost becomes). An example to such maintenance cost function is, e.g., $c(k) = C_1 - C_2k^\alpha$, where $\alpha > 1$ and $C_1, C_2$ are appropriately set constants such that the total maintenance cost $kc(k) = C_1k - C_2k^{(\alpha +1)}$ is non-negative and monotone increasing in the $[0,n]$ range ($n$ is the total number of departments). - (An alternative version of airport games) Airlines decide whether they launch a flight from a particular airport. The more airlines decide to do so, the higher value $v(k) $ (e.g., more connection options), and the lower average buy-in cost $c(k)$ (e.g., runway maintenance, staff cost etc.) each airlines can have. It's reasonable to assume that $v(k)$ is strictly convex and monotone increasing (e.g., the number of connecting combinations grows exponentially) and $c(k)$ is monotone decreasing and strictly concave. An example for strictly convex and monotone increasing benefit function is, e.g., $v(k) = k^\alpha$ with $\alpha > 1$. For each of the scenarios above, we can see that the expected reward function $\mu(S) = v(\|S\|) - c(\|S\|)$ is indeed strictly supermodular. In addition, due to the fact that $v(k)$ and $c(k)$ are discrete and finite on $[0,n]$, we can easily find $\varsigma > 0$ for which these games also admit $\varsigma$-strict convexity. ## Comment 2: Discussion on parameters of practical convex games and the conditions for strict convexity. ### Response: It is indeed challenging to determine the conditions under which the core of popular games, such as induced subgraph games and airport games, is full-dimensional, let alone strictly convex. We conjecture that additional conditions on the parameters of the game would be needed to guarantee either strict convexity or full-dimensionality of the core, which would enable the learnability of the problem. While the primary goal of this paper is to identify a general sufficient condition to achieve polynomial sample complexity, it is indeed interesting to investigate the conditions for particular games. Therefore, we leave this to future work. Note that in our response to your Comment 1 (see above), we have demonstrated how strict convexity can occur in other types of popular games such as cost/facility sharing games, when additional structures of the reward functions are included. ## Comment 3: It would be better to discuss other sampling-based algorithms for computing core. ### Response: We thank the reviewer for the suggestion of comparing our result to the literature on Shapley value approximation and learning PAC-stable allocations from samples. Compared to [3] and other works on Shapley approximation, their key limitation is that they can only return a value that is within a bounded distance of the Shapley value, which may not necessarily be in the core. Our algorithm is designed to directly return a point in the core instead. Regarding the literature on learning PAC-stable allocations from given samples [4, 5], the goal is to find an $(\delta, \epsilon)$-PAC stable allocation $x$, that is, an allocation that satisfies $$ \mathrm{Pr}[(1-\epsilon) x(S) \leq f(S)] \geq 1-\delta. $$ In some sense, our result can be understood as $(\delta, 0)$-PAC. However, to achieve $\epsilon = 0$, we require active sampling, not just from a given set of data, and also assumptions on the strict convexity of the game. As such, existing PAC-stable allocations would not work well in our setting. ## Comment 4: Relation to balanced game. ### Response: We thank the reviewer for the suggestion. Although a totally balanced game is both a necessary and sufficient condition for guaranteeing the non-emptiness of the core, it is unclear how to strengthen the condition of a totally balanced game to guarantee the full-dimensionality of the core, which enables the learnability of the problem. The setting of totally balanced games and its further conditions is indeed an interesting area that we wish to explore in future work. ## Comment 5: on the lower bound. ### Response: We agree that having a matching lower bound would be ideal. As currently we do not have it, we have conducted some additional experiments to compare the sample complexity our algorithm needs in practice with the derived theoretical upper bound from Theorem 19. Due to space constraints, we refer to the discussion with Reviewer 1Z68 (Comment 1) for the simulation details. The simulation results can be found in the attached PDF and they show that our theoretical upper bound is comparable with the empirical numbers (Figure 1); that is, the order of the polynomial in $n$ more or less matches the experimental results. ### References: [1]Aadland\&Kolpin. Shared irrigation costs: an empirical and axiomatic analysis. 1998. [2]Ambec\&Ehlers. Sharing a river among satiable agents. 2008. [3]Liben-Nowell et al. Computing shapley value in supermodular coalitional games. 2012. [4]Balcan et al. Learning cooperative games, 2015. [5]Balkanski et al. Statistical cost sharing. 2017. --- Rebuttal Comment 1.1: Comment: Dear Reviewer, Thank you for your time and effort in reviewing our paper. We hope our responses have addressed your concerns and questions. If you have any further questions, please don’t hesitate to let us know. Best regards, The Authors	Summary: This paper studies the problem of learning the expected core when only bandit feedback is available, under the assumption that the problem is strictly convex. They proposed Common-Point-Picking (CPP) algorithm that returns a point in the expected core given an oracle that provides noisy samples of the unknown (full-dimensional) simplex's vertices. Sample complexity analysis is provided. Strengths: The paper is in general well-written and smooth to follow. The technical proofs seem to be rigorous. The proposed CPP algorithm is novel to me and has a sound theoretical guarantee. Weaknesses: Although the paper is basically theoretical, I would appreciate it if simulation results could be provided. For example, the authors could plot the actual number of samples used to reach the given precision to validate the sample complexity results. Also, as this paper is motivating CPP using geometric intuitions, some illustrations about this would be helpful. Currently, the only simulation result is providing empirical evidence of the conjecture that $C_W$ is relatively small. Moreover, although full-dimensionality is used as an intuition for assuming strict convexity, the latter seems too strong. Technical Quality: 3 Clarity: 3 Questions for Authors: - Figure 2 shows that $C_W$ tends to be long-tailed, which makes the empirical validation relatively weak. Could the authors comment more on this? - If the strict convexity assumption is replaced with purely the full dimensionality assumption, do the authors expect CPP to work? Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: I don't see any limitations or potential negative societal impact of this work. Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: # Responses to Reviewer oJVQ We thank the reviewer for the insightful comments. Below are our responses/clarifications to your questions: ## Comment 1 - Simulation results for sample complexity ### Response: To illustrate the sample complexity of our algorithm in practice and how it is compared to our theoretical upper bound, we have conducted a simulation as described below. Simulation setting: We generate convex game of $n$ players with the expected reward function $f$ defined recursively as follows: For each $S \subset N$, $$ f(S \cup \{i\}) = f(S) + \|S\| + 1 + 0.9\omega, $$ for some $\omega$ sampled i.i.d. from the uniform distribution $\mathrm{Unif}([0,1])$. We then normalize the value of the reward function within the range $[0,1]$. The strict convexity constant is $\varsigma \approx 0.1/n$. We plot the samples required by the algorithm to find a point in the true core in the attached PDF file (Figure 1). From the simulation results, we can see that the growth pattern nearly matches that of the theoretical bound given in Theorem 19 in our paper, indicating that our theoretical bound is highly informative. ## Question 1: If the strict convexity assumption is replaced with purely the full dimensionality assumption, do the authors expect CPP to work? ### Response: Our algorithm exploits the property of convex games where each vertex corresponds to some marginal vectors. Hence, convexity is necessary. However, we expect that the CPP algorithm can work well even when the strict convexity assumption is violated and replaced by convexity and full-dimensionality. In fact, our algorithm operates quite independently of the strict convexity assumption, as it does not require the knowledge of the strict convexity constant $\varsigma$ neither the width constant $c_W$ of the function. In more detail, from a theoretical perspective, strict convexity allows us to provide a provable approach to find an input for the algorithm easily, which is the set of any permutation and its adjacent permutations. However, in practice, the algorithm works independently of the strict convexity assumption by using the collection of cyclic permutations $\mathfrak{C}_n$ as the input. To demonstrate that our algorithm is indeed still robust even when the strict convexity assumption is violated, we ran a simulation where the characteristic function is only convex, or the strict convexity constant is arbitrarily small as follows: Simulation setting: We generate convex game of $n$ player with the expected reward function $f$ defined recursively as follows: For each $S \subset N$, $$ f(S \cup \{i\}) = f(S) + \|S\| + 1 + \omega. $$ for some $\omega$ sampled i.i.d. from the uniform distribution $\mathrm{Unif}([0,1])$. We then normalize the value of the reward function within the range $[0,1]$. To see that the strict convexity constant $\varsigma$ can be $0$, consider the example: Let $S = \\{1\\}$, and $T=\\{1,2\\}$, and suppose that $$ f(S\cup \{3\}) = f(S) + 3, \text{suppose that $\omega = 1$}; \quad \quad f(T\cup \{3\}) = f(T) + 3, \text{suppose that $\omega = 0$}. $$ Therefore, the marginal contribution of player $3$ to both $S$ and $T$ is $3$, hence the game is only convex, not strictly convex. We then generate stochastic rewards following the Bernoulli distribution $r_t(S) \sim \mathrm{Ber}(f(S))$. For each $n \in \\{2,...,10\\}$ we ran $100$ game samples. We use the cyclic permutations $\mathfrak{C}_n$ as the input for the algorithm. We plot the samples required by the algorithm to find a point in the true core in the attached PDF file (Figure 2). On the log scale, one can see that the number of samples required as $n$ grows is sub-exponential, indicating that our algorithm is robust when the strict convexity assumption is violated. ## Question 2: Figure 2 shows that tends to be long-tailed, which makes the empirical validation relatively weak. Could the authors comment more on this? ### Response: From our simulation, we can observe that with significantly high probability (i.e., 99.6 percent), the constant $c_W$ falls into the $[0,30]$ interval, independently from other parameter settings. This indicates that this constant is relatively small for the majority of strictly convex game instances. --- Rebuttal Comment 1.1: Comment: Dear Reviewer, Thank you for your time and effort in reviewing our paper. We hope our responses have addressed your concerns and questions. If you have any further questions, please don’t hesitate to let us know. Best regards, The Authors	Summary: The paper studies the problem of finding the core for Reward allocation when the information about reward functions is incomplete. Specifically, previous works either study deterministic games and assume that the reward function is known, or study stochastic games and assume that the reward distribution is known. In contrast, this paper assumes that we have access to an oracle that takes as input a coalition and outputs a stochastic reward for that coalition. The paper obtains an algorithm for the special case of strictly convex games which outputs a point in the expected core and with high probability uses as most a polynomial number of samples. The main idea behind the algorithm is as follows. If there was no issue with the noise, then one could simply take the marginal vector of an arbitrary distribution as done by [21]. The noise prohibits us from estimating this vector exactly however and one can form only a confidence set. The main idea is to form multiple confidence sets around multiple marginal vectors. Next, we look for common points which are points $p$ with the following property: if we choose one arbitrary point from each of the confidence sets, and calculate the convex combination of these points, then this will contain $p$. Perhaps surprisingly, this set is non-empty. Strengths: - The paper studies an interesting problem, and provides an elegant solution for it. - The paper is well-written; the algorithm in particular is explained very well and is easy to understand. Weaknesses: - It would be good to obtain a lower bound. As is, the sample complexity is a (large) polynomial in $n$. Not clear to what extent this can be improved. While the authors discuss this briefly, it is an important drawback of the work. Technical Quality: 3 Clarity: 4 Questions for Authors: Questions: - Are there any works that are similar to yours in terms of techniques? Seems to me like similar ideas should appear in the bandits literature but the only citation I can find is [14]. Typo: Equation 2 should require $C \ne S$. Confidence: 3 Soundness: 3 Presentation: 4 Contribution: 3 Limitations: N/A Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: # Response to reviewer 1Z68 We thank the reviewer for the insightful comments. Below are our responses/clarifications to your questions: ## Question 1: Are there any works that are similar to yours in terms of techniques? ### Response: Learning the core via sampling is typically considered to be a difficult problem within both the algorithmic game theory and learning theory communities, and thus, not many results have been published to date. Nevertheless, you are correct that our technique borrow some ideas from the bandit and learning theory literature: Our problem formulation can be viewed as finding a point within an unknown feasible set, defined by $f: 2^N\rightarrow [0,\;1]$. From this perspective, it is somewhat related to the literature on linear bandits with constraints [1, 2]. However, existing techniques require the number of samples to scale with the number of free parameters that define the feasible set, which is not desirable in our problem as it leads to $\Omega(2^n)$ number of samples required. In contrast, we exploit the property of supermodular functions, where each marginal vector corresponds to a vertex of the feasible set, i.e., the core. Hence, we only need to estimate $n$ vertices. Moreover, we believe our CPP framework and the development of an extension of the separating hyperplane is the first of its kind, and we hope that it can find its application in other domains such as stochastic optimization and bandit theory. Regarding the impossibility results on sample complexity, the information-theoretic framework is typically used to derive lower bounds for bandit algorithms. While this framework is general, the main challenge and novelty of new lower bounds often lie in finding a collection of hard problem instances that satisfy the assumptions of the particular setting, which has led to various lower bounds in the literature [3, 4, 5]. Our impossibility result follows this approach as the key challenge in deriving our Theorem 7 lies in constructing hard game instances such that their cores do not intersect, while the KL distance between the games is arbitrarily small, making it difficult to distinguish them with a finite number of samples. While existing techniques in the online learning literature are typically not suitable to derive lower bounds for our setting, we found that face-game problem instances [6] perfectly strike that balance, allowing us to derive the impossibility result through the information-theoretic framework. ## Comment 1: It would be good to obtain a lower bound. As is, the sample complexity is a (large) polynomial in $n$. Not clear to what extent this can be improved. While the authors discuss this briefly, it is an important drawback of the work. ### Response: We agree that having a matching lower bound would be ideal. As currently we do not have it, we have conducted some additional experiments to compare the sample complexity our algorithm needs in practice with the derived theoretical upper bound from Theorem 19. Simulation setting: We generate convex game of $n$ players with the expected reward function $f$ defined recursively as follows: For each $S \subset N$, $$ f(S \cup \{i\}) = f(S) + \|S\| + 1 + 0.9\omega, $$ for some $\omega$ sampled i.i.d. from the uniform distribution $\mathrm{Unif}([0,1])$. We then normalize the value of the reward function within the range $[0,1]$. The strict convexity constant is $\varsigma \approx 0.1/n$. We plot the samples required by the algorithm to find a point in the true core in the attached PDF file (Figure 1). From the simulation results, we can see that the growth pattern nearly matches that of the theoretical bound given in Theorem 19 in our paper, indicating that our theoretical bound is highly informative. ## References: [1] Shipra Agrawal and Nikhil R. Devanur. Bandits with concave rewards and convex knapsacks. Proceedings of the 15th ACM Conference on Economics and Computation, 2014. [2] Sanae Amani, Mahnoosh Alizadeh, and Christos Thrampoulidis. Linear stochastic bandits under safety constraints. In Advances in Neural Information Processing Systems, 2019. [3] Peter Auer, Nicolo Cesa-Bianchi, Yoav Freund, and Robert E. Schapire. The non-stochastic multi-armed bandit problem. SIAM journal on computing 32(1), 2002. [4] Paat Rusmevichientong and John N. Tsitsiklis. Linearly parameterized bandits. Mathematics of Operations Research, 35, 2010. [5] Robert Kleinberg, Aleksandrs Slivkins, and Eli Upfal. Bandits and experts in metric spaces. Journal of the ACM, 66, 2019. [6] Miguel Ángel Mirás Calvo, Carmen Quinteiro Sandomingo, and Estela Sánchez Rodríguez. The boundary of the core of a balanced game: face games. International Journal of Game Theory, 49, 2020 --- Rebuttal Comment 1.1: Comment: Thank you for the response. I have no further questions at this time.	null	null	Rebuttal 1: Rebuttal: Thank you for your valuable and constructive feedbacks. We have performed the additional simulations as requested by the reviewers and have provided the results in this pdf file. Pdf: /pdf/c9b32f01b71b6c768e84cc9ae6427ef968a21a94.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
User-item fairness tradeoffs in recommendations	Accept (poster)	Summary: In this paper, the authors studied the tradeoff between user and item fairness in a recommendation setting. They proposed a constrained optimization problem that imposes user fairness as its objective and incorporates item fairness as its constraints. The authors also identified that (1) when user preferences are diverse, item fairness can be easily achieved; (2) when there is mis-estimation of user preference, imposing item constraint can lead to further cost for the users. Finally, the authors illustrated their findings using arXiv data. Strengths: - The problem of multi-sided fairness is an important problem, but most existing literature focus on studying single-sided fairness. Understanding the price of fairness is a meaningful problem for decision-makers in practice. Weaknesses: 1. The model and framework used in this paper would require significantly more justification. More specifically, - It is unclear why the authors choose to consider an optimization problem which maximizes normalized user preference as the objective subject to item fairness constraints. To me this is a rather counterintuitive choice and requires more motivation. Why not solving a dual-objective problem and treating user/item fairness in the same fashion? Alternatively, why not maximizing online platform's recommendation quality? - The assumption that user and item share the same utility $w_{i,j}$ is too strong and can hardly hold in practice. In recommendation systems, a number of factors such as pricing, rankings, utility models, etc., could impact the item/user utilities in different ways. (See prior works such as [10, 11, 32], all of which use different definitions of user/item utilities.) - The fairness notion that the authors adopt for users/items resemble a min-max type of fairness notion. This is again quite restrictive and requires more justification. Does your framework and results hold under alternative notions? 2. The theoretical results of this paper do not have sufficient technical contributions. For example, - Proposition 2 basically uses the properties of BFS in LPs. - Theorems 3 and 4 are only shown on a restrictive example (where there are only 2-3 types of users with opposing preferences in a pre-defined form). This raises the question of whether the theoretical results/insights can be extended to more general setups. Due to the restrictive setup and assumptions, the insights might also not have much practical relevance. 3. The price of fairness of multi-sided recommendations is a topic already studied in prior works. The insights provided in this work are not particularly surprising, nor distinguishable from prior works. - For example, in [11] the authors also studied price of fairness and show that the price relates to the misalignment of platform/item/user objectives and designed an algorithm that resolves the issue of having unknown user/item data. - The phenomena described in this work, such as more diverse user preferences naturally inducing item fairness, is also rather natural especially when min-max fairness is imposed, which encourages uniform item exposure. I'd expect such statement would fail to work if a different type of item fairness is considered. 4. No algorithm has been studied or introduced in this work. The empirical study of arXiv data merely serves to evaluate Problem (1) on arXiv data, but the model and framework itself already raises questions and requires extensive justification. Overall, I think this work would require significantly more work in both its model and results and would recommend rejection. Technical Quality: 2 Clarity: 2 Questions for Authors: See weaknesses. Confidence: 4 Soundness: 2 Presentation: 2 Contribution: 1 Limitations: See weaknesses. Flag For Ethics Review: ['No ethics review needed.'] Rating: 3 Code Of Conduct: Yes	Rebuttal 1: Comment: Dear reviewer: I am another reviewer and an engineer who work in industrial RS. I would like to answer your question. "Why not solving a dual-objective problem and treating user/item fairness in the same fashion? Alternatively, why not maximizing online platform's recommendation quality?" In recommendation system, the key goal is to serve most user the item she want. The "platform's recommendation quality" could be evaluated in two perspectives: 1) is the users as a whole group satisfied? namely the "user utilities" defined in line 135. 2) is every individual satisfied? In other world, maximize the user utilities of the least satisfied user, ie, "minimum user utilities" defined in this paper. In industrial system, we care about both the overall recommendation quality (point 1) and the recommendation quality for each user (point 2). Actually, if the least satisfied user is satisfied, the overall recommendation quality should be ok, although not optimal. While whether an item get enough chance to be seen, is not the key concern of commercial RS. Bad item should naturally be less shown to users. Thus, "treating user/item fairness in the same fashion" does not make sense. A reasonable formulation is to treat recommendation quality as objective, while item fairness as constrain. --- Rebuttal 2: Rebuttal: Thank you for your valuable feedback! We hope that the additional experiments we describe in the main rebuttal as well as the justification provided below address your concerns. ### Constrained optimization justification We agree that we could have modeled this as a dual objective problem – constraints at varying strength versus objectives with different weights are often interchangeable. We believe that our choice is reasonable, and using fairness constraints rather than objectives is consistent with related work [11]. We agree with reviewer yH5N that user and item fairness are not necessarily equally important in practice, and note that this could be captured by the dual-objective framework suggested by reviewer t7QC by using different weights on each objective. We will update our text to clarify this justification. ### Symmetric utility assumption Thank you for this feedback! - In the main response we provide experiments showing the robustness of our diversity result to alternative item utility models. - We also provide additional justification for why it is reasonable to restrict our analysis to this model: it is necessary and common in related work [10,32] to assume a specific utility model, and we believe a symmetric utility model captures a fundamental characteristic of producer preferences in many recommendation settings better than alternative models. We give more detail for these positions in the main response. We hope this addresses your concerns! ### Alternative notions of fairness We agree that other notions of fairness are also interesting, and re-ran our experiment in Figure 1(a) with Nash welfare as our definition of fairness for users and items, and see qualitatively the same results. We include an additional discussion of these points in the main response. We believe extending our theoretical results to additional definitions of fairness is an interesting question for future work. ### Insufficient technical contributions - We agree that Proposition 2 is mainly a result of using BFS properties: we included it as a separate result because it has an interesting qualitative interpretation. - However, we respectfully disagree that our work is not sufficiently technical – one challenge is to transform our problem into a setting where Proposition 2 can be applied, and then using the result for our conceptual findings. Proposition 1 provides a framework to transform the complicated program into a much simpler program. The proof involved manipulating the problem in a sequence of non-obvious ways. We then found closed form solutions to the transformed problem in Proposition 1, which was also non-trivial. We agree that the question of whether our results extend to populations with arbitrary preferences is crucial, and this was the intention of the experiments with arXiv data in Section 6. We hope that these experiments address your concerns, and agree that finding more general theoretical results is an interesting question for future work. ### Prior work Thank you for pointing this out! - [11] indeed defines the price of fairness, but in a different way from us: they examine the price of imposing fairness constraints on the revenue, thus capturing the impact of item/user fairness on revenue, while we examine the price of imposing item fairness constraints on user fairness, thus capturing the interplay between user and item fairness. - Moreover, their concept of objective misalignment (the difference in fairness between the {item, user} utility required by the constraints, and the {item, user} utility in a revenue-optimal solution) is not the same as our concept of user preference diversity (agreement between users' utilities). User preference diversity may cause objective alignment, but it is a different concept. - Their algorithm focuses on the algorithmic question of how to impose fairness constraints when preferences are unknown, but their analysis does not answer our question of whether fairness constraints disproportionately harm users with unknown preferences. We will update our related work section to make these points clearer. ### The diversity phenomenon is natural, and will fail with a different fairness definition. We agree that this phenomenon is natural, but disagree that it only would hold in a max-min fairness definition. Moreover, as mentioned above, we re-ran our arXiv experiment that demonstrated this result in the setting of Nash welfare fairness and saw the same effect (see Figure 3 in the PDF) ### No algorithm has been introduced Several algorithms have been developed to ensure multi-sided fairness in the existing literature [4,10,11]. The aim of this project is to understand factors affecting the trade-off between user fairness and item fairness. For example, in the algorithm in [11] the platform must choose the strength of the user- and item- fairness constraints. What constitutes a reasonable choice for the relative strength of the constraints depends heavily on how user and item fairness trade off, and is an important question independent from the development of the algorithm. Thank you for your consideration of our response!	Summary: The paper works on the relationship between user fairness and item fairness in recommender system settings. A theoretical framework is proposed and some theoretical results and intuitions are provided based on the framework. The main results are the tradeoffs between fairness and 1) uncertainty and 2) diversity where theorems are proved together with some discussions. --- I have read the rebuttal and other reviews. My rating is unchanged. Strengths: I like this paper. The theoretical framework is clear and useful. I expect more results can be derived out of this framework in the future e.g. assuming the utility w_{ij} is an estimator with certain bias and variance, or in practice one may not achieve the global optimal \rho^* but with a gap. The main results lie in theorem 3 and 4. Both results seem valid and intuitive. They illustrate how the price of fairness is changed when other factors like diversity/uncertainty are part of the consideration. Weaknesses: The empirical part on arxiv is quite light. I see more details in the appendix but the main body part needs more information to make it self-contained. In the theoretical framework part, I would make the setting more comprehensive but put additional assumptions in later sections in order to support those theorems e.g. I think the current setting is for a single-item recommendation problem and all users are independent. There will be correlation terms for different items when multiple items are shown to users together. In addition, the paper focuses on individual utility. Technical Quality: 3 Clarity: 3 Questions for Authors: I think the platform-level utility is missing from the discussion? In practice the platform controls the recommendation algorithm and therefore they may favor their utility as the primary objective. The default for cold start user may not be the average of existing users, but selecting top-performing items. Suggest to consider this aspect in the revision process. 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 your thoughtful feedback and suggestions; we are glad you like our theoretical framework! We agree that there are likely to be other applications of the framework, and we are currently looking at ways to further draw out and interpret the sparsity result in the writing. ### Empirical details We will move more details from the appendix into the main body as you suggest for a more self-contained description. ### Theoretical framework generality Thank you for your comments regarding the theory writing. We agree that one possible writing approach is to introduce a general model and then later introduce the necessary assumptions. We will consider such a rewrite, though also would like to make our assumptions clear early. ### Platform-level utility Our main goal was to understand the interplay between user and item fairness. We agree that platform utility is a key follow-up question and include this in our list of suggested future work; this question is partially explored in [11], where they look at how the platform’s revenue trades off with fairness. We expect our diversity and mis-estimation results to extend to this setting. For example, with diverse users, giving every user their favorite item is optimal for users, items, and likely platform revenue as well. ### Cold start user default This is an interesting suggestion. We will try to model this and see what insights our framework gives for this case. We note that this choice partially occurs with our current framework without fairness constraints, since items that are generally popular will have high expected utility. Thank you for your consideration of our response! --- Rebuttal Comment 1.1: Title: Thanks Comment: I have read the rebuttal and other reviews. Still, I think this is a solid work and will leave my rating (7-accept) unchanged	Summary: This paper investigates the trade-off between user fairness and item fairness in recommender systems. The authors develop a theoretical framework to characterize the user-item fairness trade-off by analyzing the recommendation strategy optimization problem. The following phenomena are found: 1. The more diversified the user preferences are, the smaller the user-item fairness trade-off is. 2. Inaccurate estimation of user preferences exacerbates the fairness trade-off, especially for new users. 3. In real data, moderate item fairness constraints have a small effect on user fairness but very strong constraints can significantly reduce user fairness. Overall, the theoretical derivation part of this study is brilliant and provides theoretical assurance for the framework. It is a worthy study to explore the fairness problem of recommender systems in depth. Strengths: 1. The trade-off relationship between user fairness and item fairness is systematically analyzed for the first time. 2. A new theoretical framework is proposed to simplify complex optimization problems. 3. the theoretical analysis is rigorous and provides in-depth mathematical proofs. Weaknesses: 1. Limitations of the definition of fairness: the paper focuses mainly on minimized fairness indicators. Have other indicators of fairness been considered? 2 No specific methodology is given for actually achieving the three balances 3. The thesis assumes that the utility of users and items is symmetric, which may not always hold in reality. Technical Quality: 3 Clarity: 2 Questions for Authors: 1. The paper assumes that the utility of users and items is symmetric, which may not always hold in reality. How does this assumption affect the generalisability of the results? 2. In this paper, fairness is quantified as the minimum normalized utility. This definition is supposed to follow Rawlsian fairness. it is not based on group fairness? fairness in this paper is measured using individuals. I am concerned about this because there are a large number of users in a recommender system and individual users may not be representative. I would like the authors to explain my concerns. 3. The selection of scenarios in the experimental section is limited, and the experiment on arXiv recommender systems, while meaningful, may not be sufficiently representative of all types of recommender systems. The generalisability of the results of this experiment could be discussed, or additional experiments in other domains could be considered. Confidence: 3 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: 1. Simplification of model assumptions: It assumes symmetric user and item utilities, which may not always hold in reality. It only considers the case of a single-item recommendation, whereas real systems usually recommend multiple items. 2. Limitations of the fairness definition: it focuses mainly on minimized fairness metrics and does not consider other possible fairness measures (e.g. group fairness). Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for your helpful feedback; we believe addressing them makes for a stronger paper. ### Fairness definitions We agree that it is important to study how our results extend to other definitions of fairness. In the main response, we give further justification for our choice, and show experiments demonstrating that our diversity result generalizes to Nash welfare fairness, $\sum_i \log(U_i(\rho))$. While still being an individual fairness measure (in considering fairness to users as individuals rather than as members of a certain group, which is outside the scope of our paper), Nash welfare incorporates a term from each user in the sum, resulting in a more holistic measure of user fairness. We hope this new experiment addresses your concern about representation and generalizability. We think that extending our results theoretically for additional definitions of fairness is an interesting question for future work. ### Achieving the three balances It is true that our paper does not provide a novel efficient algorithm for achieving multi-sided fairness (besides our reduced optimization problem); this is an interesting technical problem that has been explored in related work [4,10,11]. Our work complements these papers: we provide conceptual insights into the tradeoffs between user and item fairness. This is especially important for work like [11], whose algorithm needs to set hyper-parameters for the strength of user and item fairness constraints; setting these values appropriately requires understanding how and whether the two objectives trade off in the deployment setting. ### Symmetric utility In the main response, we provide experiments showing that the diversity phenomenon extends to settings where user and item utility are not symmetric, and further explain our reasoning for choosing this simplification. ### Single-item recommendation We agree that this is a limitation of our framework, and discuss this in the limitations section. Our intuition is that since in our framework the platform selects probabilistic policies, increasing the number of items will not affect the solutions qualitatively as much as a discrete policy would. We believe this is an important but difficult question for future work; one challenge with considering multiple items is modeling a tractable choice model that allows users to choose multiple items from the set of recommended items. ### ArXiv experiment generalizability Thank you for this suggestion; we will add a discussion of the generalizability of the experiment to other domains. Thank you for your consideration of this response! --- Rebuttal Comment 1.1: Comment: Thanks to the authors for the response. I keep my positive score.	Summary: This paper develop a theoretical framework to analysis the trade-off between user fairness and item fairness. From the theoretically analysis, we understand that diverse user population benefits the recommendation, and users whose preferences are misestimated can be disadvantaged by the constraints on item fairness. The conclusion makes sense and is useful. Strengths: Clear definition on user fairness, item fairness, item utility constrained user utility, price etc. Good analysis on the two conclusion. Weaknesses: Relatively easy setting, e.g., only one item is recommended to a user. While the author honestly pointed out these weaknesses in the last paragraph, these weaknesses are acceptable. Technical Quality: 3 Clarity: 4 Questions for Authors: . Confidence: 3 Soundness: 3 Presentation: 4 Contribution: 4 Limitations: . Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for reading our work! We agree that only recommending one item is an aspect of our current theoretical model. We note that recommendations being probabilistic (e.g., one can think of an item being sampled each time period) somewhat mitigates this aspect, though agree that more explicitly modeling recommending multiple items (and how users select between them) is an important consideration for future work. --- Rebuttal Comment 1.1: Comment: I have read the rebuttal	Rebuttal 1: Rebuttal: We thank the reviewers for their helpful feedback, and are glad that you found the paper “clear and useful” and the results to be both “rigorous” and “intuitive”. Multiple reviewers sought more justification for our symmetry assumption and fairness definition, so we discuss these issues here. Overall, we appreciate the reviewer’s questions – there are always many ways to model this question, and the “correct” model often depends on the exact application. However, we believe that our primary insights are robust to the exact modeling choices, and that our choices are reasonable. First, in response to the reviews, we include additional arXiv experiments in the response PDF. - Figures 1 and 2 relax the symmetric utility assumption in the same setting as Figure 2 from the original paper, using exposure (and different levels of correlation) for item utility. The figures show that the diversity phenomenon is robust to this assumption, and that under different item utility models item fairness constraints still do not empirically increase the price of mis-estimation. - Figure 3 shows that the diversity phenomenon is robust to different definitions of fairness by modifying the experiments of Figure 2 in the original paper to use Nash welfare [43] to define fairness. We also see the same phenomenon when we use the sum of the $k$ minimum participant utilities (which is a smoother extension of max-min fairness), with $k = 3$. We will update our manuscript to include these experiments, showing that our results do not exactly depend on our theoretical choices. Moreover, we believe that our restriction to symmetric utilities and minimized fairness for our theoretical analysis are reasonable choices for the theoretical analysis. Symmetric utility. Our model assumes that users and items share a common utility $w_{ij}$ for recommending paper $j$ to user $i$. 1. Extended model: We would like to draw attention to line 1092 in Appendix E, where we provide an extension of our model in which user and item utilities are only assumed to be proportional to some shared value (that is, when item $j$ is recommended to user $i$, $i$ and $j$'s utilities are $\alpha_i w_{ij}$ and $\beta_j w_{ij}$ respectively for some $\alpha_i, \beta_j > 0$). Our theoretical results hold in this extended setting. 2. Prior work: Fixing a particular model of item utility is consistent with related work, as this is typically necessary for theoretical analysis. We use $w_{ij}^I = w_{ij}^U$, which resembles the "market share" utility model in [11]. Exposure ($w_{ij}^I = 1$ for all $i,j$) is also a popular choice [10,32] for this model, as we do in the new empirical analyses. 3. Simple models: As pointed out by the reviewers, neither model can fully capture the nuances of producer preferences. However, we believe that the symmetric utility model reflects a basic structure behind producer preferences in many cases ("items prefer to be recommended to users who like them, as that predicts consumption/purchase"), and that our theoretical findings should extend to settings with more or less this structure. 4. Symmetry vs exposure: We argue in Appendix E that having user and item preferences depend on a common value such as a purchase probability or click-through rate to be a more realistic representation of producer preferences than exposure in many cases. For example in an online marketplace a producer prefers their item to be recommended to users who are likely to buy their product, and in the paper recommendation setting an author prefers their paper to be recommended to a reader who is likely to engage with their work. This type of preference is not captured by exposure but is captured by the symmetric model. We will update the writing to discuss these points, as well as alternative approaches. Minimized fairness. Our model defines fairness as the normalized utility of the minimum user. 1. Min utility is a common notion of individual fairness in algorithmic fairness (called Rawlsian or egalitarian fairness); other reasonable choices include Nash welfare, which we now include in our empirical analysis ($\sum_i \log U_i(\rho)$, $\sum_j \log I_j(\rho)$ for users and items respectively; see pdf). We agree with reviewers that generalizing to other definitions is interesting and leave a theoretical extension for future work. 2. We expect the results to extend beyond this choice. One intuition for our diversity result is to consider the most user-diverse population: a population where every ranking of items is equally represented (and there is a consistent mapping from rankings to utilities). The user-optimal solution of giving every user their favorite item is also optimally item-fair for any reasonable* definition of individual item fairness, so there is no tradeoff. This intuition (and others) is independent of the definition of fairness, so we expect our results to generalize (and indeed they appear to do so in the new experiments in Figure 3). *since it assigns all items the same utility and maximizes the total item utility. Note: In this and the individual responses, we use the numbered references in our paper to refer to related work. For our experiments using different definitions of fairness, we add the following citation. [43] Ioannis Caragiannis, David Kurokawa, Hervé Moulin, Ariel D. Procaccia, Nisarg Shah, and Junxing Wang. 2019. The Unreasonable Fairness of Maximum Nash Welfare. ACM Trans. Econ. Comput. 7, 3, Article 12 (August 2019), 32 pages. Pdf: /pdf/edeecccafa6308e00bb740caa180ba6d95d173d9.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Zero-shot Generalizable Incremental Learning for Vision-Language Object Detection	Accept (poster)	Summary: This paper presents Incremental Vision-Language Object Detection (IVLOD), a novel learning task designed to incrementally adapt pre-trained Vision-Language Object Detection Models (VLODMs) to various specialized domains, while simultaneously preserving their zero-shot generalization capabilities for the generalized domain. To this end, Zero-interference Reparameterizable Adaptation (ZiRa) is proposed to tackle IVLOD without incurring a significant increase in memory usage. Experiments on COCO and ODinW-13 datasets demonstrate that ZiRa effectively safeguards the zero-shot generalization ability of VLODMs while continuously adapting to new tasks. Strengths: 1. The paper is well-written and easy to follow. 2. The authors propose RDB and ZiL to generalize the VLODMs to specific domains without losing their general zero-shot capability. 3. A novel learning task is designed to incrementally adapt pre-trained Vision-Language Object Detection Models (VLODMs) to various specialized domains. Weaknesses: 1. The key contribution of this paper is RDB and ZiL. However, RDB has been proposed by [1]. Therefore, I would owe the novelty to the differentiated learning rate and ZiL (basically L1 norm). From this point of view, the novelty is somewhat incremental. Importantly, the authors should cite [1] and highlight the distinction. 2. The paper only evaluates the general zero-shot performance after incremental learning. Is zero-shot specific-domain inference possible after learning on few examples in this specific domain? 3. It's suggested to include more comprehensive incremental object detection literature, including but not limited to [2-3]. [1] Zhang, Chang-Bin, et al. "Representation compensation networks for continual semantic segmentation." Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2022. [2] Qiao, Limeng, et al. "Defrcn: Decoupled faster r-cnn for few-shot object detection." Proceedings of the IEEE/CVF International Conference on Computer Vision. 2021. [3] Yang, Ze, et al. "Efficient few-shot object detection via knowledge inheritance." IEEE Transactions on Image Processing 32 (2022): 321-334. Minors: L178 between stability and plasticity L342 typo VOLDM Technical Quality: 3 Clarity: 3 Questions for Authors: 1. Is TFA also pre-trained on Objects365 [30], GoldG [17], and Cap4M? I have some doubts about the TFA ZCOCO performance in Table 1 if it's pretrained on COCO. To my best knowledge, TFA only finetunes the last classifier layer for the incremental steps and has demonstrated strong performance on the base classes. 2. How is general IOD (e.g. TFA) tested on Zero-shot COCO? General IOD generally does not support zero-shot inference. Is there any adaptation to achieve it? 3. What learning rate is applied to w/ Rep+ (the first line of Table 2)? Is it the high or low one? Confidence: 5 Soundness: 3 Presentation: 3 Contribution: 3 Limitations: No negative societal impact is expected. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: ## Weekness 1 Reviewer Concern: The key contribution of this paper is RDB and ZiL. However, RDB has been proposed by [1]. Therefore, I would owe the novelty to the differentiated learning rate and ZiL (basically L1 norm). From this point of view, the novelty is somewhat incremental. Importantly, the authors should cite [1] and highlight the distinction. Response: Thank you for your insightful feedback. We acknowledge the prior work on Reparameterizable Dual Branch (RDB) and the need to clearly distinguish our contributions. We will ensure that [1] is appropriately cited in our manuscript. The primary novelty of our work lies in the differentiated learning rate and the introduction of Zero-interference Loss (ZiL), which are key enhancements over the existing RDB framework. These innovations address the specific challenges of Incremental Vision-Language Object Detection (IVLOD) by balancing incremental learning performance and zero-shot capabilities more effectively. Revised Explanation in Manuscript: "Our work builds upon the Reparameterizable Dual Branch (RDB) concept initially proposed by [1]. The key innovations introduced in our approach include the use of differentiated learning rates for the High Learning Rate Branch (HLRB) and Low Learning Rate Branch (LLRB), and the implementation of Zero-interference Loss (ZiL). These enhancements allow for a more effective balance between learning new tasks and preserving previously acquired knowledge, distinguishing our method from prior work." ## Weekness 2 Reviewer Concern: The paper only evaluates the general zero-shot performance after incremental learning. Is zero-shot specific-domain inference possible after learning on few examples in this specific domain? Response: Thank you for your question. In our approach, we do not directly evaluate zero-shot inference in specific domains after learning on a few examples from those domains. Instead, our methodology involves tuning a pre-trained model on the ODinW dataset, which comprises 13 datasets, and then immediately evaluating the model on COCO to assess its zero-shot performance. This evaluation is conducted without exposing the model to any images from COCO during the incremental training phase. ## Weekness 3 Reviewer Concern: It's suggested to include more comprehensive incremental object detection literature, including but not limited to [2-3]. Response: Thank you for your valuable suggestion. We acknowledge the importance of providing a comprehensive review of the literature on incremental object detection. In the revised manuscript, we will include a detailed survey of relevant work, including but not limited to the references [2-3] you mentioned. ## Question1 Reviewer Concern: Is TFA also pre-trained on Objects365 [30], GoldG [17], and Cap4M? I have some doubts about the TFA ZCOCO performance in Table 1 if it's pretrained on COCO. To my best knowledge, TFA only finetunes the last classifier layer for the incremental steps and has demonstrated strong performance on the base classes. Response: For consistency and fair comparison, all methods, including TFA, were re-implemented and evaluated using the same pre-training datasets (Objects365, GoldG, and Cap4M) and the same pre-trained Grounding DINO model. ## Question 2 Reviewer Concern: How is general IOD (e.g. TFA) tested on Zero-shot COCO? General IOD generally does not support zero-shot inference. Is there any adaptation to achieve it? Response: Thank you for your question. We acknowledge that general Incremental Object Detection (IOD) methods, such as TFA, do not inherently support zero-shot inference. To address this, we re-implemented these general IOD methods based on the Grounding DINO framework. By leveraging Grounding DINO, which supports zero-shot inference, we adapted these methods to enable zero-shot capabilities. Since all the compared baselines support a DETR-like architecture, re-implementing them based on Grounding DINO was feasible and straightforward. This approach ensures that all methods can be evaluated consistently within the same experimental setup. ## Qusetion 3 Reviewer Concern: What learning rate is applied to w/ Rep+ (the first line of Table 2)? Is it the high or low one? Response: Thank you for your question. We used a high learning rate applied to w/ Rep+ (the first line of Table 2). We also tested using a low learning rate and found that the results were similar to those obtained with the high learning rate. We infer that the absolute value of the learning rate does not significantly impact the performance of the RDB. Instead, the differential learning rates play a crucial role, allowing the High Learning Rate Branch (HLRB) and Low Learning Rate Branch (LLRB) to share different learning burdens effectively. Here is the performance (w/ Rep+) using the low learning rate: \| ZCOCO \| Avg \| hAP \| Ae \| Aq \| Co \| Eg \| Mu \| Pa \| Pv \| Pi \| Po \| Ra \| Sh \| Th \| Ve \| \|-------\|------\|------\|------\|------\|------\|------\|------\|------\|------\|------\|------\|------\|------\|------\|------\| \| 40.11 \| 58.20\| 47.49\| 31.23\| 46.85\| 69.40\| 66.32\| 56.94\| 58.35\| 64.12\| 68.98\| 48.12\| 63.77\| 41.51\| 77.02\| 64.05\| --- Rebuttal Comment 1.1: Comment: The authors' rebuttal has addressed my concerns. I believe this work should be credited for introducing a new and practical task, i.e., incremental vision-language object detection (IVLOD), where the goal is to continuously adapt VLODMs to various unforeseen downstream tasks while not sacrificing the general zero-shot capability. Plus, the proposed differentiated learning rates and zero-interference loss (ZiL) are well-tailored for this specific task. One small suggestion is to also include continual learning literature, for instance, but not limited to [1-3] (continual object detection to be added as well), since the proposed task is related to the continual learning concept. Overall, I finalize my rating to 7 Accept. [1] Cermelli, Fabio, et al. "Modeling the background for incremental learning in semantic segmentation." Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2020. [2] Zhang, Chang-Bin, et al. "Representation compensation networks for continual semantic segmentation." Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. [3] Yang, Ze, et al. "Label-guided knowledge distillation for continual semantic segmentation on 2d images and 3d point clouds." Proceedings of the IEEE/CVF International Conference on Computer Vision. 2023. --- Reply to Comment 1.1.1: Comment: Thank you for your thorough review and positive feedback. We are pleased that our work on Incremental Vision-Language Object Detection (IVLOD) and the proposed differentiated learning rates and Zero-interference Loss (ZiL) have been well-received. We appreciate your suggestion to include literature on continual learning. We will ensure that these references are included in the revised manuscript to provide a more comprehensive background and context for our work.	Summary: In order to extend the application of VLODM in a broader domain, the authors propose to combine incremental learning and zero-shot generalization to solve the problem. However, the widespread catastrophic forgetting and maintaining zero-shot generalization capability in incremental learning are two important issues to be considered. To address the challenges in incremental learning, the authors propose to construct a Zero-interference Reparameterizable Adaptation using Reparameterizable Dual Branch. Strengths: 1. The authors have innovatively proposed a parameterizable double-branching structure. 2. The writing logic is clear and the article is well structured. Weaknesses: 1. The authors do not highlight the need for this work and its similarities and differences with other work in the introduction and related work. 2. Although the authors have designed an innovative Reparameterizable Dual Branch structure, it is not very interpretable for the problem to be solved. 3. Although the authors give very rich experimental results in Table 1, the description of the metrics. is not clear enough. What is " the zero-shot performance on COCO as “ZCOCO" "? Is it mAP on the base class or the novel class, or all classes? Is it mAP or AP50, or AP75? Technical Quality: 2 Clarity: 2 Questions for Authors: 1. The authors introduce the names VLOD and VLODMs in the introduction and cite the literature [11, 17, 20, 24, 39] as the source for the derivation of these names. In these works, tasks such as open vocabulary/open set object detection, grounding, etc. using Vision-Language Model are included. Is the VLOD proposed by the authors consistent with or similar to the task setting of open vocabulary/open set object detection? If it is consistent, why use the term VLOD? If it is similar, the difference between them should be highlighted in the introduction. 2. In GLIP, the authors give the statement, i.e., " without seeing any images in COCO during pre-training". However, in this work, the authors do not discuss or clarify this. Considering the task setting of zero-shot generalization, how do the authors ensure that the images/objects in the test set has not appeared in the pre-training phase? 3. Based on question 1, where the author claims "Our work distinguishes itself by performing incremental learning on VLODMs, which are more favorable for open-world problems. " in related work, is the author's work incremental or zero-shot learning, or a combination of both? What are the similarities and differences between that work and the open-world object detection? 4. How should the scaling factor “s” be determined in Equation 1? The Reparameterizable Dual Branch structure process contains both HLRB and LLRB, does the size of the scaling factor imply which weight is dominant? If HLRB is dominant, how to ensure that no knowledge forgetting occurs? If LLRB is dominant, how can generalization ability be ensured? Table 7 does not allow a reasonable interpretation of this question. 5. The authors give Figure 4 and analyze it to prove the validity of ZiL, but how to define " small-norm " and why do the authors claim " the model’s performance is not significantly affected by the addition of small-norm random noise to the input " when “The average AP on COCO” drops more than 30%? 6. The authors use the model structure of the Grounding DINO work, in which text representation is an important part of the work. The text template used by the authors is quite different from the one used in Grounding DINO and the authors have not analyzed or explained it, why? Confidence: 5 Soundness: 2 Presentation: 2 Contribution: 2 Limitations: See Waeknesses and Questions. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: ### Weakness 1 Response: Thank you for this valuable feedback. We acknowledge the importance of clearly stating the need for this work and situating it within the context of existing research. In the revised manuscript, we will enhance the introduction and related work sections to better articulate the motivation for our study and to delineate the similarities and differences between our approach and previous methods. ### Weakness 2 Response: Thank you for your feedback. We understand the importance of interpretability in demonstrating the effectiveness of our proposed approach. The core of our solution lies in constraining the Reparameterizable Dual Branch (RDB) with Zero-interference Loss (ZiL). ZiL serves as a regularization mechanism that minimizes interference from newly learned tasks on previously acquired tasks, ensuring that the model maintains its zero-shot capabilities while adapting to new data. ### Weakness 3 Response: Thank you for highlighting the need for clearer descriptions of the metrics used in our experiments. The "ZCOCO" metric refers to the mean Average Precision (mAP) on all classes in the COCO dataset. Specifically, it represents the mAP@0.5:0.95 (the average of mAP at IoU thresholds from 0.5 to 0.95). This measure provides a comprehensive evaluation of the model's zero-shot performance across all classes on the COCO dataset. In the revised manuscript, we will update the description of the metrics in Table 1 to explicitly state that "ZCOCO" refers to the mAP on all classes in the COCO dataset, measured at IoU thresholds from 0.5 to 0.95. This clarification will ensure that readers have a precise understanding of the evaluation criteria used in our experiments. ### Questions 1 Response: Thank you for pointing out this important aspect. We recognize the need to clarify the relationship between Vision-Language Object Detection (VLOD) and open vocabulary/open set object detection. The VLOD task is indeed consistent with the principles of open vocabulary and open set object detection. VLOD aims to extend the capabilities of Vision-Language Models (VLMs) to detect objects from both known and unknown categories using natural language prompts. The primary reason for using the term VLOD is to emphasize the integration of vision and language in object detection tasks and to highlight the incremental learning aspect, which is a key focus of our work. ### Questions 2 Response: Thank you for pointing out the need for clarification regarding zero-shot generalization and the handling of pre-training data. We acknowledge the importance of ensuring that the test set remains unseen during the pre-training phase to validate the zero-shot capabilities of our model. To address this, we will clarify that we use the pre-trained weights of Grounding DINO, which are trained on O365, GoldG, and Cap4M datasets. These pre-training datasets are the same as those used for GLIP-T. This ensures that our model has not seen any images from the COCO dataset during pre-training, maintaining the integrity of the zero-shot generalization task. ### Questions 3 Response: Thank you for your insightful question. Our work combines both incremental learning and zero-shot learning to address the challenges of open-world object detection (OWOD). Both OWOD and IVLOD need to detect seen and unseen objects. However, in IVLOD, models are pre-trained to detect unknown objects before the incremental learning process begins. In contrast, existing OWOD methods train the model's ability to detect unknown objects concurrently with incremental learning. In addition, OWOD does not further classify unknown objects. In contrast, IVLOD leverages VLODMs to classify unknown objects through language prompts, allowing for more precise identification and categorization of previously unseen objects. Given the superior zero-shot generalization capabilities provided by current vision-language models, we believe that starting with a pre-trained vision-language model for open-world detection represents a more effective approach compared to the traditional OWOD paradigm (which involves incrementally learning new objects while simultaneously learning open-set detection). ### Questions 4 Response: We simultaneously insert RDB in both the vision and language components for learning. We believe that the parameters of RDB in different modalities require different update speeds. Therefore, we introduce a learnable scaling factor "s" to adjust the parameter update speeds for different modalities. In fact, rather than adjusting the scaling factor directly, we ensure HLRB is dominant by adjusting the learning rates of HLRB and LLRB. We use ZiL to constrain HLRB, mitigating the occurrence of forgetting. ### Questions 5 Response: When we refer to "small-norm" random noise, we define it based on the standard deviation of the noise added to the input. Specifically, our experiments show that when the norm of the random noise is small (with a standard deviation (std) within 2), the model’s zero-shot AP on COCO remains above 45. Therefore, we claim that the model’s performance is not significantly affected by the addition of small-norm random noise because, within this range, the decrease in performance is minimal and the model retains a high level of accuracy. The observed drop in average AP by more than 30% occurs when the norm of the random noise exceeds this small-norm arrange. The ZiL can ensure that the RDB's output is within the small-norm arrange, therefore protects the the model’s zero-shot AP on COCO. In the revised manuscript, we will ensure that this definition and explanation are clearly stated to avoid any confusion. ### Questions 6 Response: We use the same text template as Grounding DINO. --- Rebuttal Comment 1.1: Title: Official Comment by Reviewer 8RRL Comment: The authors' rebuttal has addressed my concerns. I raise the score to 6.	Summary: This paper proposes the new problem of incremental visual-language object detection (IVLOD), which aims to preserve zero-shot generalization performance of VLMs, while also adapting to new concepts over time. Authors address IVLOD by proposing the zero-interference reparameterizable adaptation (ZiRa), a light weight branch added to the text and image encoders of VLMs to address this task. Authors demonstrate that their proposed approach outperforms prior work by a considerable margin. Strengths: Problem Motivation. The proposed problem is of significant interest for practical applications, particularly because many vision-language models (e.g. CLIP) are pre-trained on private datasets, making incremental learning with VLMs challenging. Interesting Insight. Authors highlight that VLMs are robust to noise (cf. Fig 4 and 5), and propose an incremental learning strategy that updates VLMs weights by ensuring that the updated parameters have low L1 norm. It would be interesting to also plot the zero-shot accuracy on COCO for both modes trained with and without ZiL in Fig 5 as the number of learned downstream tasks increases. Simple and Scalable Approach. The proposed approach adds a small number of tunable parameters to GroundingDINO. Notably, the proposed approach maintains a relatively constant runtime and number of parameters even when adapting to an increasing number of tasks. Weaknesses: Differences in Baseline Pre-Training. Although authors benchmark their approach against relevant prior work, many of these methods are not trained on the same scale of pre-training data as GroundingDINO. Given that prior works typically operate in a closed-world, and are pre-trained on much smaller datasets, it is unclear how to make an "apples-to-apples" comparison between methods. One strategy might be to reimplement prior works (e.g. TFA and iDETR) using GroundingDINO. Demonstrate ZiRa with Other Architectures. Although authors claim that their proposed approach can work with any DETR based architecture, they only showcase its performance with GroundingDINO. Given that this work establishes a new problem, it would be useful to extensively evaluate different architectures to provide a "lay of the land". Technical Quality: 3 Clarity: 2 Questions for Authors: Impact of Pre-Training Data on IVLOD Performance. The performance of VLMs is significantly impacted by the data used for pre-training. How might the specific pre-training data used impact the effectiveness of incremental learning? Adapting to a Large Number of Tasks. As shown in Figure 5, the L1 norm steadily increases as the number of downstream tasks increases. Does this suggests that the proposed approach does not scale well to a large number of tasks? Adapting to More Than One Class at a Time. Although each class is considered a new "task", one may want to adapt to multiple classes at once. How would the proposed approach perform when learning more than one class at a time? Runtime and Memory Usage. A key benefit of the proposed approach is that adapting to a new task only marginally increases runtime and memory usage. It would be useful to quantify this such that future works can benchmark on this axis as well. Writing Quality. Although the approach is clear, the grammar and writing quality hinders comprehension. For example "inputted" is not a word, and "input end" is a confusing phrase. I would encourage authors to further polish the manuscript. In addition, authors should include more descriptive captions in their tables. Notably, I don't believe the full class names in Table 1, 2 (e.g. Ae, Aq, Co) are provided. Confidence: 4 Soundness: 3 Presentation: 2 Contribution: 3 Limitations: Yes, authors highlight that the current implementation is based on the DETR architecture, which may not work for all VLODMs. In addition, authors state that ZiRa is designed for IVLOD, and should be evaluated in the context of other incremental learning tasks. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: ### Rebuttal for Weaknesses #### 1. Differences in Baseline Pre-Training Response: Thank you for this important observation. We want to clarify that all compared methods, including TFA and iDETR, were indeed reimplemented using the pre-trained GroundingDINO model. This approach ensures a fair "apples-to-apples" comparison, as all methods were evaluated on the same scale of pre-training data. We will revise the manuscript to more clearly convey this setup and ensure there is no confusion regarding the comparability of the methods. #### 2. Demonstrate ZiRa with Other Architectures Response: We appreciate the suggestion to evaluate ZiRa with additional architectures. To address this, we have demonstrated ZiRa with OV-DINO [1]. All the method are implemented with the same OV-DINO (swin-T) pre-trained on O365, GoldG, and Cap1M datasets. The results are as follows: ### Table: Performance of Various Methods based on OV-DINO \| Shots \| Methods \| ZCOCO \| Avg \| HAP \| Ae \| Aq \| Co \| Eg \| Mu \| Pa \| Pv \| Pi \| Po \| Ra \| Sh \| Th \| Ve \| \|-------\|----------------\|-------\|-------\|-------\|-------\|-------\|-------\|-------\|-------\|-------\|-------\|-------\|-------\|-------\|-------\|-------\|-------\| \| Zero \| Original Model \| 50.22 \| 26.64 \| 34.81 \| 15.69 \| 19.37 \| 11.79 \| 40.67 \| 1.23 \| 59.26 \| 50.78 \| 12.19 \| 2.44 \| 33.81 \| 8.50 \| 43.68 \| 46.86 \| \| Full \| iDETR \| 37.71 \| 46.91 \| 41.81 \| 24.09 \| 30.56 \| 49.16 \| 68.49 \| 26.05 \| 67.45 \| 61.85 \| 30.75 \| 29.50 \| 66.83 \| 27.11 \| 71.27 \| 56.69 \| \| Full \| CL-DETR \| 34.52 \| 45.28 \| 39.18 \| 23.07 \| 27.90 \| 46.81 \| 67.72 \| 25.39 \| 66.56 \| 59.12 \| 28.04 \| 29.48 \| 64.71 \| 25.58 \| 68.28 \| 56.05 \| \| Full \| AT \| 36.80 \| 44.33 \| 40.21 \| 22.46 \| 27.42 \| 45.78 \| 67.10 \| 24.10 \| 65.08 \| 58.17 \| 26.65 \| 28.88 \| 64.46 \| 24.60 \| 67.30 \| 54.27 \| \| Full \| ZiRa \| 49.07 \| 50.21 \| 49.63 \| 23.37 \| 40.43 \| 69.02 \| 66.21 \| 20.74 \| 58.51 \| 67.74 \| 46.71 \| 34.13 \| 64.62 \| 39.44 \| 58.01 \| 63.81 \| This evaluation demonstrates that ZiRa performs effectively across different DETR-based architectures, validating its versatility. By incorporating ZiRa with OV-DINO, we show that our approach is not limited to GroundingDINO and can be broadly applied to other models. [1] OV-DINO: Unified Open-Vocabulary Detection with Language-Aware Selective Fusion. Hao Wang, Pengzhen Ren, Zequn Jie, Xiao Dong, Chengjian Feng, Yinlong Qian, Lin Ma, Dongmei Jiang, Yaowei Wang, Xiangyuan Lan, Xiaodan Liang. arXiv, 2024. ### Rebuttal for Questions #### 3. Impact of Pre-Training Data on IVLOD Performance Response: The specific pre-training data used can significantly impact the effectiveness of incremental learning in Vision-Language Models (VLMs). Models pre-trained on diverse and extensive datasets tend to have better generalization capabilities, which can facilitate more effective incremental learning. Conversely, models pre-trained on limited or less diverse datasets might struggle with generalization, leading to more pronounced performance degradation when learning new tasks incrementally. We will include an analysis in the revised manuscript discussing the potential impacts of different pre-training datasets on the effectiveness of incremental learning, reinforcing the importance of diverse and comprehensive pre-training data for robust IVLOD performance. #### 4. Adapting to a Large Number of Tasks Response: Thank you for this insightful question. Upon examining the evolution curves in Figure 5 more closely, we observe that in the initial stages, ZiL plays a relatively minor role in curbing the growth of the RDB's output norm. However, as the process of accumulating new knowledge progresses, the influence of ZiL becomes more significant, leading to stronger constraint effects. This increase in ZiL's impact leads to a dynamic balance: the interference caused by integrating new knowledge is counteracted by the interference reduction achieved by ZiL. As a result, while the L1 norm of the RDB's output does increase with the number of tasks, it does not rise unboundedly but rather stabilizes after learning a certain number of tasks. Therefore, our proposed approach does manage to scale to a large number of tasks to a certain extent, achieving a balance between the accumulation of new knowledge and the mitigation of interference. #### 5. Adapting to More Than One Class at a Time Response: In our experimental setup, each "task" corresponds to learning an entire dataset, each of which contains more than one class. Thus, our proposed approach inherently handles the learning of multiple classes simultaneously. Our results demonstrate that the proposed method can effectively manage the incremental learning of multiple classes within each dataset, preserving zero-shot generalization capabilities while adapting to new tasks. We will clarify this aspect in the revised manuscript to ensure that it is clear that our approach supports learning multiple classes at a time. #### 6. Runtime and Memory Usage Response: Thank you for highlighting this crucial aspect. We agree that quantifying the marginal increase in runtime and memory usage when adapting to new tasks would provide valuable insights for future benchmarks. We will conduct additional experiments to measure and report the runtime and memory usage associated with our approach. These results will be included in the revised manuscript, providing clear benchmarks that can be used for comparison in future work. #### 7. Writing Quality Response: Thank you for your feedback regarding the writing quality. We apologize for any confusion caused by grammatical errors and unclear phrases. We will thoroughly review and polish the manuscript to improve clarity and readability. Additionally, all dataset names (not class names) (e.g., Ae, Aq, Co) in Tables 1 and 2 are fully provided in the Subsection " Datasets" of Section "Experiments Setup". --- Rebuttal Comment 1.1: Comment: Authors have sufficiently addressed my questions. I recommend this paper should be accepted. Although other reviewers point out that there is limited novelty in the method, I think that this paper should get credit for proposing a new problem and establishing extensive baselines. I would encourage authors to add relevant background information suggested by other reviewers. --- Reply to Comment 1.1.1: Comment: Thank you for your positive feedback and recommendation for acceptance. We appreciate your recognition of our efforts in proposing a new problem and establishing extensive baselines. Additionally, we will carefully consider the suggestions made by other reviewers and incorporate the relevant background information to further strengthen the manuscript. --- Reply to Comment 1.1.2: Comment: Thank you very much for your positive feedback and recommendation for acceptance. We appreciate your recognition of the contributions of our work, particularly the introduction of the new task of Incremental Vision-Language Object Detection (IVLOD) and the establishment of extensive baselines. We also noticed that while you have recommended our paper for acceptance, the final score was not mentioned. We would be grateful if you could kindly update your review to reflect this. We have taken into account all the suggestions from you and other reviewers and incorporated the relevant background information in the revised manuscript (ref. response to Reviewer NuJX). Thank you once again for your thoughtful review and support.	Summary: This paper deals with the object detection problem in a zero-shot and incremental learning setting. Specifically, Incremental Vision-Language Object Detection (IVLOD) task is proposed to incrementally adapt the pre-trained Vision-Language Object Detection Models (VLODMs) to various specialized domain. The technical design is Zero-interferences Reparametrizable Adaptation (ZiRA), which includes low learning rate and high learning rate adaptation branches for both vision and language encoder. In addition, an L1-norm is applied on top of the adaptation branch outputs. Experiments are conducted on the Zero-shot COCO (ZCOCO) and ODinW-13 benchmarks. A series of baselines such as TFA, OW-DETR, CL-DETR, Adapting-tuning (AT), and iDETR were compared. Ablation study on modules, vision or language finetuning were also conducted. Strengths: ### 1. The overall framework for incremental object detection is reasonable and complete. - 1.1 This paper designs a Reparameterizable Dual Branch module for feature adaptation, and specifically devises low learning rate and high learning rate branches to address the learning-forgetting balance. An additional mechanism to gradually merge high learning rate branch into low learning rate branch is also proposed. The idea makes sense and is verified to be effective in both zero-shot COCO and average performance. - 1.2 The L1-norm is reasonable in zero-shot generalizability and seems to be effective according to Fig. 4-5. ### 2. Experimental results verify the effectiveness of the model design - On both the zero-shot and the Avg setting, the proposed method outperforms baseline methods. - Ablation studies were conducted w.r.t module designs, vision/language adaptation, branches, etc. Weaknesses: ### 1. The new task of IVLOD is not well desribed and compared with existing one - Incremental Vision-Language Object Detection (IVLOD) is claimed to be a new task. However, it is unclear what are the differences between this new task and existing works such as CL-DETR, Ground DINO, iDETR etc. - How is the language specially used in IVLOD compared with existing method? - Claimed as the first contribution, but no separate detailed description/subsection to compare IVLOD with existing task setting, either verbally or visually. Fig. 1 only compares with the final performance, which is less intuitive. ### 2. The main contribution is the different learning rates - For the Reparameterizable Dual Branch (RDB), although the name is special, the module design is no much different with existing approaches such as LoRA, Adapter, [6], etc. - The structure design is not quite novel, but leveraging different learning rates can be a novel point. - It is encoraged to have a better survey of relevant adaptation-based methods for incremental learning. ### 3. Experimental section have flaws - ODinW was adopted, but only 13 datasets were selected. How are those 13 datasets selected? Other methods used much more datasets for evaluation, e.g. 35. - In Table 1, AT was not used for Full evaluation. CL-DETR/OW-DETR were not used for lower shots evaluation. What is the reason? - The prompt in Fig. 6 looks strange. How is the prompt leveraged by the proposed model? - In Table 3, why the model performance on zero-shot COCO underperforms Vanilla one by 1.31%? - There are many hyper-parameters such as $\lambda$ for loss, $\eta$ for learning rate, scaling $s$. How are those parameters selected and tuned? It seems in Table 5 and 6 that the hyper-parameters matters. - In Table 8, how about no norm is adopted? ### 4. Other minors - 1st not 1-th in Fig. 1 - Incorrect usage of double quotes in this paper, e.g. “Locality Injection" - Line 209 lacks a period Technical Quality: 2 Clarity: 2 Questions for Authors: Please refer to the above Weaknesses for questions. Confidence: 4 Soundness: 2 Presentation: 2 Contribution: 2 Limitations: N/A Flag For Ethics Review: ['No ethics review needed.'] Rating: 5 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: ### 1. The new task of IVLOD is not well described and compared with existing ones Response: Thank you for your insightful feedback. We recognize the need to clearly define and differentiate Incremental Vision-Language Object Detection (IVLOD) from existing methods. IVLOD is distinct in that it combines the incremental learning of new tasks with the preservation of zero-shot generalization capabilities. Unlike traditional incremental object detection methods such as CL-DETR and iDETR, which focus on learning new tasks incrementally without maintaining zero-shot abilities, IVLOD ensures that models can continue to generalize to unseen categories even after adaptation. Furthermore, while Grounding DINO utilizes natural language prompts for object detection, it does not address incremental task adaptation. In IVLOD, language is used as prompts for the objects to be detected, the same as how it is utilized in Grounding DINO. To enhance clarity, we will include a dedicated subsection comparing IVLOD with these existing methods both verbally (with Descriptive Subsection) and visually (with enhanced Figure 1), thereby providing a comprehensive understanding of its unique contributions. ### 2. The main contribution is the different learning rates Response: We acknowledge the importance of clearly presenting the novel aspects of our work and distinguishing it from existing methods. The key innovation in our approach lies in the use of Zero-interference Loss (ZiL) to constrain the Reparameterizable Dual Branch (RDB), which effectively balances incremental learning performance and zero-shot performance of the VLODM. While methods like LoRA and Adapter introduce additional parameters for efficient fine-tuning, they do not employ a mechanism like ZiL. Our approach uniquely combines RDB with ZiL, addressing the specific challenges of incremental vision-language object detection. We will expand our literature review to include a comprehensive survey of adaptation-based methods for incremental learning, highlighting how our approach builds upon and differentiates itself from these methods. ### 3. Experimental section has flaws Response: 1. The selection of the 13 datasets from the ODinW benchmark was based on the same subset used in the GLIP evaluation, ensuring consistency with prior work. We acknowledge that the full ODinW benchmark comprises 35 datasets. Due to computational resource constraints, we limited our evaluation to 13 datasets. However, we plan to extend our evaluation to include all 35 datasets in future work to provide a more comprehensive assessment. 2. CL-DETR and OW-DETR are not specifically designed for lower shot scenarios and do not perform well under low shot settings. These methods are more suited for settings where there is a larger amount of training data available. Comparing them with lower shots evaluation would not provide meaningful insights due to their design and intended use cases. We will provide the results of AT under full evaluation. The results are as follows: \| Shots \| Methods \| ZCOCO \| Avg \| Ae \| Aq \| Co \| Eg \| Mu \| Pa \| Pv \| Pi \| Po \| Ra \| Sh \| Th \| Ve \| \|-------\|---------\|-------\|------\|------\|------\|------\|------\|------\|------\|------\|------\|------\|------\|------\|------\|------\| \| Full \| AT \| 42.30 \| 51.14\| 23.62\| 39.90\| 72.32\| 65.51\| 31.47\| 50.48\| 60.51\| 66.07\| 39.09\| 53.50\| 34.04\| 68.07\| 60.23\| 3. Grounding DINO requires all the prompts to be combined into a single sentence, with periods separating each prompt. For instance, if the prompts are "dog," "cat," and "car," the combined prompt fed into the model would be "dog. cat. car." 4. When adapting to new tasks, the zero-shot performance of the original Vision-Language Object Detection Model (VLODM) typically degrades. This is a common issue in incremental learning scenarios and is the primary motivation for proposing the Incremental Vision-Language Object Detection (IVLOD) task. While our method shows a 1.31% decrease in zero-shot COCO performance compared to the Vanilla model, this reduction is significantly less than that observed with other methods. Our approach effectively minimizes the decline in zero-shot capability, demonstrating its efficacy. 5. Thank you for highlighting the importance of hyper-parameters in our method. We acknowledge that the presence of multiple hyper-parameters is a limitation of our approach. However, this does not detract from the main contributions of our paper. 6. We need to incorporate a norm into the final loss function to ensure effective training and optimization. Without a norm, it would be difficult to train and optimize the model properly. ### 4. Other minors Response: Thank you for pointing out these minor issues. We will make the necessary revisions to address them. --- Rebuttal Comment 1.1: Comment: The rebuttal addresses some of my concerns regarding a new task and contribution, part of the experimental questions are addressed. I would like to encourage the authors to add the new task discussion in the revision. After taking into account the rebuttal and considering other reviewers's comments, I would like to increase my score. --- Reply to Comment 1.1.1: Comment: Thank you for increasing your score. We appreciate the opportunity to clarify the differences between Incremental Vision-Language Object Detection (IVLOD) and other related tasks, including open vocabulary/open set object detection and open-world object detection (OWOD). 1. IVLOD vs. Open Vocabulary/Open Set Object Detection: - Open Vocabulary/Open Set Object Detection focuses on detecting both seen and unseen objects by leveraging pre-trained models, typically without the need for incremental learning. These models are designed to recognize and localize objects that were not explicitly included in the training data but can be identified through language prompts or other contextual information. - In contrast, IVLOD not only aims to detect unseen objects but also involves the incremental adaptation of Vision-Language Object Detection Models (VLODMs) to new tasks or domains while preserving their zero-shot generalization capability. Unlike open vocabulary detection, which does not involve updating the model after the initial training phase, IVLOD requires the model to continuously adapt to new tasks without forgetting previously learned knowledge. 2. IVLOD vs. Open-World Object Detection (OWOD): - OWOD also aims to detect both seen and unseen objects, but it involves the simultaneous learning of new objects and the detection of unknown objects during the incremental learning process. This means that as new tasks are introduced, the model is trained to detect new objects and maintain its ability to recognize unknown objects in real time. - IVLOD, on the other hand, pre-trains models to detect unknown objects before the incremental learning process begins. The focus during incremental learning is on maintaining the model’s ability to detect these pre-trained unknown objects while adapting to new tasks. Additionally, while OWOD does not further classify unknown objects beyond detection, IVLOD leverages VLODMs to classify unknown objects using language prompts, enabling more precise identification and categorization of previously unseen objects. - Given the superior zero-shot generalization capabilities of current vision-language models, we believe that starting with a pre-trained vision-language model for IVLOD represents a more effective approach compared to the traditional OWOD paradigm, which involves incrementally learning new objects while simultaneously learning open-set detection. In summary, while there are similarities between IVLOD and both open vocabulary/open set object detection and OWOD, IVLOD introduces the unique challenge of incrementally adapting models to new tasks while preserving their zero-shot capabilities, distinguishing it from these related tasks. We will ensure that these distinctions are clearly articulated in the revised manuscript to provide a comprehensive understanding of our contributions.	null	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null
Compositional PAC-Bayes: Generalization of GNNs with persistence and beyond	Accept (poster)	Summary: This paper derives novel generalization bounds for a special class of GNNs augmented with persistent homology descriptors, specifically PersLay. They empirically test the bound and use the bound to propose a regularization, which works well in practice. Strengths: 1. The paper provides a clear background introduction to persistence homology and its integration with GNNs. 2. The derived bound has positive correlation with the empirical generalization gap of GNNs. 3. The paper is well positioned within related works on perturbation based generalization bounds of MLPs and GNNs. Weaknesses: 1. It is hard to parse the significance of this work as the bound applies only to a restricted family of models augmented with PersLay. This issue could be mitigated by demonstrating that a model derived from this analysis is comparable with more advanced GNN models (not necessarily with PH), which the paper fails to do. 2. The paper would benefit from listing all assumptions used in the derivation. 3. The experiments could be strengthened by considering different GNN models augmented by different PersLay variants. Technical Quality: 3 Clarity: 3 Questions for Authors: How does the bound for GNNs with PH compare with their counterparts without PH? Does the result provide any insights into why PH is beneficial for enhancing GNN performance? Confidence: 3 Soundness: 3 Presentation: 3 Contribution: 2 Limitations: Please refer to the weaknesses section. Flag For Ethics Review: ['No ethics review needed.'] Rating: 4 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thanks for your feedback. We reply to your comments/questions below. > It is hard to parse the significance of this work as the bound applies only to a restricted family of models augmented with PersLay. This issue could be mitigated by demonstrating that a model derived from this analysis is comparable with more advanced GNN models (not necessarily with PH), which the paper fails to do. Thank you for the opportunity to clarify important aspects of our work. The main result (Lemma 2) and the Corollaries about model compositionality apply to a broad class of models and are not restricted to models augmented with PersLay. We used GNNs combined with PersLay to showcase our developed recipe since, despite their increasing popularity [1,2,3,4], their generalization behavior is heavily underexplored. Moreover, our analysis can be extended to other GNN architectures, such as GraphSAGE. Indeed, given the similarity between GraphSAGE and GCN, our analysis already subsumes GraphSAGE, as we can upper-bound GraphSAGE by leveraging full neighborhoods. We have included additional experiments with different PH-augmented GNNs (GCN, GraphSAGE, and GIN) in Table 2 of the rebuttal PDF. The results show the benefits of our bound used as a regularizer — the regularized variants achieve smaller generalization gaps and lower errors in most experiments. > The paper would benefit from listing all assumptions used in the derivation. Thank you for this comment. While our main result (Lemma 2) does not make any assumptions beyond data being iid, we agree that the perturbation analysis requires certain assumptions. We will gladly include all assumptions in the Appendix and overview them in the main text. The following list provides the assumptions: - Data (i.e. tuples) are i.i.d samples from some unknown distribution $\mathcal{D}$. - the width of all layers is bounded by $h$ (stated in Lemma 2). - For MLP: all inputs are contained in the $\ell_2$-ball of radius $B$. - For GCNs and MPGNNs: graphs are simple with maximum degree of $d$ and node features are contained in $\ell_2$-ball of radius $B$. (listed in the caption for Table 2 in the main paper) - For PersLay: the norm of the elements of persistence diagrams are contained in a $\ell_2$-ball with a radius $B$ and all of the considered point transformations and weight functions are Lipschitz continuous with respect to the parameters. > The experiments could be strengthened by considering different GNN models augmented by different PersLay variants. Thanks for your suggestion. We have run additional experiments using regularized versions of GraphSAGE, GIN, and GCN combined with PersLay (see Table 2 in the rebuttal PDF). Overall, our results show that the regularized methods achieve smaller generalization gaps and slightly lower classification errors. We will add these experiments to the revised manuscript. > How does the bound for GNNs with PH compare with their counterparts without PH? Does the result provide any insights into why PH is beneficial for enhancing GNN performance? From Informal Lemma 4 (two models in parallel), $C_{norm}$ and $C_{pert}$ (as well as $T$) of the combined bound scale as the maximum of the corresponding parameters of the GNN and PersLay bounds. Since GNNs usually have more parameters than PH in practice, the bound for the combined network would scale with the GNN bound, so PH does not introduce a lot of overhead in the generalization performance. We also note that combining PH with GNNs indeed improves the latter's expressivity [3,5] --- for instance, persistence diagrams contain information about the number of components and cycles that 1-WL (Weisfeiler-Leman) GNNs can not decide. However, while the expressivity of PH-augmented GNNs has been explored [5,6], their generalization capabilities remain largely uncharted, which is the motivation for our work. [1] PersLay. AISTATS 2020. [2] Topological neural networks go persistent, equivariant, and continuous. ICML, 2024. [3] Topological graph neural networks. ICLR 2022. [4] Position: Topological Deep Learning is the New Frontier for Relational Learning. ICML, 2024. [5] Going beyond persistent homology using persistent homology. NeurIPS 2023. [6] On the Expressivity of Persistent Homology in Graph Learning. arXiv, 2023 --- We're grateful for your feedback. We hope our answers have addressed your concerns and improved your assessment of this work. --- Rebuttal Comment 1.1: Comment: Dear reviewer, Thank you again for your constructive feedback. As detailed above, we've acted on all your comments and suggestions (including clarifying how our main result applied broadly significantly beyond PersLay, listing all assumptions, and providing results of additional experiments that demonstrate improved generalization with regularized PH-augmented GraphSAGE, GCN, GIN). We will include all these in the updated version. Please also see our global response, where we summarize the key steps taken to address the concerns of all the reviewers. We believe acting on your feedback has helped us consolidate our contributions, and reinforced the strengths of this work. Since only a few hours are left until the end of the discussion period, we would greatly appreciate if you could update your score to reflect the same. Many thanks! Best regards.	Summary: The paper introduces a novel Compositional PAC-Bayes framework that addresses challenges related to the heterogeneity of Graph Neural Network (GNN) layers and persistent vectorization components. It provides data-dependent generalization bounds for PH vectorization schemes and persistence-augmented GNNs, offering insights into improved classifier design and generalization performance predictions. Strengths: 1. The introduction of the Compositional PAC-Bayes framework is a significant contribution to the field, especially in handling heterogeneous GNN layers. 2. The provision of data-dependent generalization bounds adds a valuable dimension to the analysis of GNNs and persistence-augmented models. 3. The empirical evaluations on real-world datasets demonstrate the practical applicability and effectiveness of the proposed framework. Weaknesses: Clarity: Some sections of the paper may require further clarification to enhance readability and understanding for a broader audience. From experiments, we can observe that there exists a considerable gap between the theoretical results and empirical results. Technical Quality: 3 Clarity: 3 Questions for Authors: 1. This paper mentioned the expressivity of PH and GNNs for many times. Does the expressivity have anything to do with the generalization? 2. What is the influence of using different filtration functions in the proposed framework? 3. Does the proposed framework have any concrete applications? Can you provide a case study? 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: Thank you for your feedback. We hope our answers below satisfactorily address your concerns. Otherwise, we will be happy to engage further. > Clarity: Some sections of the paper may require further clarification to enhance readability and understanding for a broader audience. Thanks for your comment. To further improve the clarity of our manuscript, we will: - include a list with the assumptions related to PAC-Bayes and the perturbation analysis adopted in the paper; - add a discussion about the main takeaways of our analysis, especially regarding how we can use it to choose better hyperparameters (see last answer to reviewer toK8). Should the reviewer provide additional suggestions for improvements, we would be happy to incorporate them. > From experiments, we can observe that there exists a considerable gap between the theoretical results and empirical results. Thanks for your comment. Overall, we note that our theoretical bounds strongly correlate with empirical generalization gaps for most datasets and models. This is what one would expect, given that theoretical generalization bounds are often loose. To complement our analysis, we have included additional experiments with different PH-augmented GNNs (GCN, GraphSAGE, and GIN) in Table 2 of the rebuttal PDF. The results reinforce that the regularized variants achieve smaller generalization gaps. We also report empirical vs. theoretical generalization plots for GraphSAGE — the results again confirm the practical relevance of our work. > This paper mentioned the expressivity of PH and GNNs for many times. Does the expressivity have anything to do with the generalization? Thank you for the opportunity to clarify this. In fact, expressivity and generalization can be at odds with each other, and finding a good tradeoff holds the key to success of machine learning models [1]. Indeed, enhancing expressivity typically comes at the expense of generalization. [2] established such a result for Graph Neural Networks, showing that the VC-dimension of GNNs with $L$ layers is lower bounded by the maximal number of graphs that can be distinguished by 1-WL (Weisfeiler-Leman test for isomorphism). High VC-dimension directly translates to poor generalization, whereas by definition greater the number of graphs that can be distinguished greater the expressivity. Thus, [2] showed the tension between expressivity and generalization in the context of message passing GNNs that are at most as expressive as the 1-WL test. Expressivity of machine learning models is certainly important [3]; however, it does not guarantee that powerful models that do well on training data would generalize, i.e., predict well on unseen data as well. Moreover, most of the generalization bounds in the literature share a common structure: population risk is bounded by empirical risk + complexity of the model class ($\approx$ expressivity). This fact also suggests the intricate connection between generalization and expressivity. > What is the influence of using different filtration functions in the proposed framework? Our work considers fixed filtration functions, and the exact choice of filtration function does not affect the bound. This happens because the considered filtration functions are parameter-free --- this part of the model does not impact the output change due to parameter perturbations. However, the choice of the filtration function affects the risk, not the bound on the difference. Also please see the global response for the discussion about learnable filtration functions. > Does the proposed framework have any concrete applications? Can you provide a case study? As a general result, Lemma 2 and the Corollaries about model compositionality of heterogeneous layers apply to a broad class of models. Indeed, in the paper, we show specific case studies where we can recover existing bounds (for MLPs, GCNs, and MPNNs) from our framework. In addition, we use our framework to derive new bounds for PH-augmented GNNs and PersLay --- as case studies. From an empirical standpoint, we leverage our results to derive integrated regularization procedures for different methods, including PersLay and PH-augmented GNNs. Our results show that the regularized variants can achieve better (test) classification performance and smaller empirical generalization gaps. In the rebuttal PDF (see Table 2), we provide additional results for different GNN architectures to further support our claims. [1] Generalization and Representational Limits of Graph Neural Networks. ICML, 2020 [2] WL meet VC. arXiv, 2023 [3] A Survey on The Expressive Power of Graph Neural Networks. arXiv , 2020 Many thanks again for your thoughtful comments, which have helped us reinforce the strengths of this work. --- Rebuttal Comment 1.1: Comment: Thanks for all the authors' efforts to address my other concerns. I have no further questions. I am positive to an acceptance. --- Reply to Comment 1.1.1: Comment: We are glad that our answers addressed your concerns and that you are positive about acceptance. Thank you again for your review and for acknowledging our rebuttal.	Summary: This paper introduces a novel compositional PAC-Bayes framework for analyzing the generalization of heterogeneous machine learning models, with a particular focus on graph neural networks (GNNs) augmented with persistent homology (PH) features. The work develops a general PAC-Bayes lemma for heterogeneous models that not only recovers existing bounds for neural networks and GNNs but also extends them to more complex architectures. Notably, it provides the first data-dependent generalization bounds for PH-based models. The key innovation lies in the compositional approach, presenting lemmas that allow for combining bounds from different model components. This enables the analysis of complex architectures like GNNs augmented with PH features, bridging an important gap in the theoretical understanding of topology-based graph representation learning methods. The framework's versatility is demonstrated by recovering existing bounds for various models and deriving new bounds for PersLay and its variants. The empirical evaluations across multiple datasets validate the theoretical results, showing correlation between the derived bounds and observed generalization performance. Strengths: - Novel theoretical contributions that advance the state-of-the-art in generalization analysis for GNNs and PH-based methods. - Flexible framework that recovers existing bounds and enables analysis of new model compositions Weaknesses: - Empirical evaluation focuses mostly on graph classification tasks; additional experiments on node classification or link prediction could strengthen the results Technical Quality: 3 Clarity: 4 Questions for Authors: - The theoretical analysis assumes fixed filtration functions for PH. How limiting is this in practice, and could the framework be extended to learnable filtrations? Confidence: 2 Soundness: 3 Presentation: 4 Contribution: 3 Limitations: - While the experiments cover several datasets, they focus primarily on graph classification tasks. The paper could benefit from a broader range of experiments, including node classification or link prediction tasks, to demonstrate the generality of the approach. - While the paper derives a regularization scheme from the bounds, it doesn't fully explore how the theoretical results could guide the design of better GNN+PH architectures in general. Some discussion on how the bounds suggest optimal ways to combine GNNs and PersLay could enhance the practical impact of the work. These points did not diminish the overall contribution of the paper but addressing them could significantly strengthen its impact and applicability. Flag For Ethics Review: ['No ethics review needed.'] Rating: 7 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Thank you for the feedback and for appreciating our work. We hope that the answers below sufficiently address your concerns. Otherwise, we would be happy to engage further. > Empirical evaluation focuses mostly on graph classification tasks; additional experiments on node classification or link prediction could strengthen the results Thanks for your comment. While we agree that developing bounds (and running experiments) for different tasks would be valuable, our work focuses on graph-level prediction tasks. Extending it to node-level tasks, for instance, would require adapting the theoretical framework — the i.i.d. assumption (basic assumption in PAC-Bayes) may not hold. Since our experiments aim to validate and demonstrate the practical relevance of our analysis, we abide by the settings we consider in Sections 3 and 4. We also note that PH-augmented GNNs for node classification tasks often apply local topological descriptors [e.g., 1], which fundamentally differ from what we discuss elsewhere in the paper. > The theoretical analysis assumes fixed filtration functions for PH. How limiting is this in practice, and could the framework be extended to learnable filtrations? Thanks for your question. For an in-depth discussion about learnable filtrations, we kindly refer to the global response. > While the paper derives a regularization scheme from the bounds, it doesn't fully explore how the theoretical results could guide the design of better GNN+PH architectures in general. Some discussion on how the bounds suggest optimal ways to combine GNNs and PersLay could enhance the practical impact of the work. Indeed, this would strengthen our work; thank you for pointing this out! From our theoretical findings, we can say: - since the $C_{pert}$ constant for PersLay depends on the square root of its dimension, one should choose it significantly smaller than the dimension of the GNN to avoid an $O(h\sqrt{\ln h})$ dependency of the total generalization bound on $h$ instead of $O(\sqrt{h \ln h})$; - compared to the “k-Max” and “Mean” functions, the “Sum” aggregation function introduces a $\max\limits_{G\in\mathcal{G}} card(G)$ term to the bound, which in practice can be rather large. So, we recommend using “Mean” instead of “Sum”. Moreover, using our analysis, we can compare different PersLay variants (see Table 3 in the paper). Let us consider the constant weighting function for simplicity. Then, $C_{pert} = 2C_{norm}$, and as a result, we can rank different PersLay variants (e.g., k-landscapes, images, and silhouettes) by simply comparing their associated constants $C_{pert}$. For landscapes, $C_{pert} = 2\cdot 3\cdot B\sqrt{h}$; for images, we have $2 \cdot card \cdot \max \\{\sqrt{h}, \frac{1}{\tau e^{1/2}}\\}$; for silhouettes we have $2 \cdot card \max \\{B \sqrt{h}, \frac{1}{\tau e^{1/2}} \\}$. If the last two options use ‘sum’ as an aggregating function, then our generalization analysis suggests that k-landscapes would have stronger guarantees. If the last two options use ‘mean’ as an aggregating function, then $C_{pert}$ for k-landscapes would be at most $C_{pert}$ for silhouettes, and the result of comparison of k-landscapes and images could be in favor of both landscapes and images depending on chosen parameters $\tau$ and $B$. We will add this discussion to the revised manuscript. [1] Persistence Enhanced Graph Neural Network. AISTATS, 2020. We are grateful for your constructive feedback. Many thanks! --- Rebuttal Comment 1.1: Comment: Thank you for the feedback and clarification. I will keep my score.	Summary: This paper presents a compositional PAC learning framework for bounding the generalization gap in deep graph networks that are augmented by PersLay-vectorization of persistent homology features. Topological features can be complementary to deep features. Empirically, this combination can boost the empirical test performance. This paper investigates whether this observation reflects to the theory, and concludes that it does, up to some assumptions, for example in filtrations. Strengths: - To the best of my knowledge, this is the first generalization bound of its kind, presenting bounds for a heterogeneous network composed of PH vectorization and GNNs. - I really like the presentation and exposition in this paper, that makes it informative and easy to follow. - The idea of using a compositional pac-bayes framework for bounding generalization in PH-augmented GNNs really makes sense to me. - Although I have not been able to thoroughly check all the proofs, the theoretical parts I investigated made sense. - Given the nicheness of the topic, the models (GNN + PersLay) are intuitive for integrating topological features in deep graph learning. I have seen such architectures a few times. Weaknesses: - One obvious drawback is that the architectures of concern in this paper are rather limited and not the ones used in practice. While this limits the applicability, the paper's theoretical contributions make it less of a concern. According to me, speaking of generalization for PH-augmented GNNs through the lens of compositional pac-bayes is interesting in its own right. - Most importantly, does the proposed bound, similar to the KL-terms in Neyshabur's bound, depend on the number of parameters in the network? (I was suspecting this due to the use of the norm.) If so, it is definitely worth discussing, as the recent theory of deep learning states that the intrinsic dimension matters rather than the ambient dimension. And if not, please clarify. - I'm curious about the limitations of the compositional framework. Can we leverage the nature of PH and the integration to do something more specific to tighten the bound? The compositional framework seems to adapt a rather late fusion. - Ln. 81: The generalization error is defined to be the population risk and not as the difference between them. I believe some sort of a difference between test/train would be more appropriate. Why is this chosen? Is this common convention? - I see PH as a hand-crafted way of extracting topological features, which goes a bit orthogonal to the current trends. Can the same analysis be extended to hybrid classical & topological deep learning (like the ones presented in [,]) which also operates on complexes? If so, do the authors see a straightforward way? - There are multiple ways to combine PH(-vectorization) and GNNs. A two-branch architecture + PersLay is definitely a good way. Yet, I would expect that the paper investigates other forms of combination. For example, what about learning a filtration? - I'm noticing that only a single family of GNNs is used in the paper. Is it possible to show results with more modern architectures at least like GraphSage? - There is also a rather recent literature of leveraging PH to bound generalization [*] (other way around), which this paper does not seem to discuss. It would be good to have both sides of this picture to stress on the impact of PH in the generalization theory. [] Hajij, Mustafa et al. "Topological deep learning: Going beyond graph data." arXiv preprint arXiv:2206.00606 (2022). [] Papamarkou, Theodore, Tolga Birdal, Michael M. Bronstein, Gunnar E. Carlsson, Justin Curry, Yue Gao, Mustafa Hajij et al. "Position: Topological Deep Learning is the New Frontier for Relational Learning." In Forty-first International Conference on Machine Learning. 2024. [*] Birdal, Tolga, Aaron Lou, Leonidas J. Guibas, and Umut Simsekli. "Intrinsic dimension, persistent homology and generalization in neural networks." Advances in Neural Information Processing Systems 34 (2021): 6776-6789. Technical Quality: 3 Clarity: 4 Questions for Authors: I have appended my questions after each relevant weakness. I would be happy if the authors could address them. In addition: - Why would the bounds worsen with the increase number of epochs (where I believe training gets better)? - There is also growth in the width disproportionately to the empirical gap. Why would this happen? In general, some more light on the empirical findings would be useful. Confidence: 3 Soundness: 3 Presentation: 4 Contribution: 3 Limitations: The paper appropriately discusses the limitations and remains to be largely theoretical in a very niche domain of machine learning. As such, I don't see any issues with broader impact. Flag For Ethics Review: ['No ethics review needed.'] Rating: 6 Code Of Conduct: Yes	Rebuttal 1: Rebuttal: Many thanks for your thoughtful, constructive, and insightful review. We hope that the answers below sufficiently address your concerns. > the architectures of concern in this paper are rather limited and not the ones used in practice. Despite the generality of our framework, we focused on PH and PH-augmented GNNs due to the lack of generalization bounds for these classes of models and their increasing popularity in the graph learning community. In this regard, a prominent way to combine persistence diagrams (PDs) with GNNs consists of leveraging PDs as global topological descriptors, which are then concatenated (in parallel) with graph-level GNN embeddings (see [1]). We followed this approach in our work. Importantly, our work paves the way for the generalization analysis of different classes of topological neural networks and their integration with PH [2,3]. For instance, compositional PAC-Bayes may be an asset in analyzing models that exploit 0-dim PD as node-level information that can be combined with node embeddings at each GNN layer (see [4]). > does the proposed bound [...] depend on the number of parameters in the network? Like Neyshabur’s bound, our results implicitly depend on the number of model parameters via model hyper-parameters (e.g., number of layers) and parameter values (e.g., spectral norms). We show in Table 1 of the rebuttal PDF the dependence of our bounds on model parameters and hyperparameters separately. While we initially found PAC-Bayes particularly suitable to develop a general recipe for composing bounds for heterogeneous layers, we agree that applying our ideas to other generalization frameworks (e.g., in terms of intrinsic dimension) can provide further insights into generalization in DL. We believe this is a fascinating research direction for future work. > Can we leverage the nature of PH and the integration to do something more specific to tighten the bound? In this work, we focused more on deriving a flexible recipe that can accommodate a broad class of models and less on tightening bounds. However, extending our ideas regarding the compositionality of heterogeneous layers to other generalization paradigms (e.g., PH-dim [6]) is a very interesting direction, and it seems a promising approach to get tighter bounds. > The generalization error is defined to be the population risk and not as the difference between them. Indeed, it is possible to define it as a difference, but we wanted to be consistent with some reference works in the PAC-Bayesian literature, such as [7,8,9]. > Can the same analysis be extended to hybrid classical & topological DL … which also operates on complexes? Indeed, we believe that Lemma 2 can be used to derive bounds for higher-order TNNs [2, 5] and their combination with the classical PH approach. Intuitively, we would expect T (a relevant component in Lemma 2) to depend on the norms of the weights associated with the different neighborhood structures. We note that the technical details to ensure that the conditions in Lemma 2 are satisfied need to be figured out. We believe this is an interesting future work. > What about learning a filtration? For a discussion about learnable filtration functions, please see the global response. > Is it possible to show results with more modern architectures at least like GraphSage? We have run additional experiments using GraphSage (see Tab 2 in the rebuttal PDF). Although our bound is not particularly tailored to GraphSAGE, due to its similarity to GCNs (GraphSAGE samples neighbors at every iteration instead of counting on all neighbors), our regularization scheme also benefits GraphSAGE. Table 2 also contains additional results regarding regularized versions of GCN and GIN combined with PersLay. Overall, the regularized methods achieve smaller generalization gaps and lower errors in most experiments. From a theoretical perspective, we can upper-bound GraphSAGE by leveraging full neighborhoods — obtaining GCNs. In some sense, our analysis already subsumes GraphSAGE. In fact, our additional experiments using GraphSAGE show that the empirical generalization gap strongly correlates with our bound (see Fig 2 in the rebuttal PDF). However, achieving tighter bounds would require deriving a specific perturbation analysis for GraphSAGE. > There is also a rather recent literature of leveraging PH to bound generalization [..] which this paper does not seem to discuss. We agree that using PH to bound generalization is an important line of work. Indeed, Appendix G of our paper discusses it. We will also appropriately position these influential works in the main text in the revised manuscript. > Why would the bounds worsen with the increase number of epochs? The bounds worsen because the spectral norms increase during training to fit the training data. To validate this, we now report the average spectral norms for GNN and MLP layers in Fig 1 of rebuttal PDF. > There is also growth in the width disproportionately to the empirical gap. Why would this happen? We suspect that some dependencies in our bounds could be improved, which may explain the discrepancy you noted. [1] Going beyond persistent homology using persistent homology. NeurIPS 2023. [2] Topological deep learning: Going beyond graph data. Arxiv, 2022. [3] Topological neural networks go persistent, equivariant, and continuous. ICML, 2024. [4] Topological graph neural networks. ICLR 2022. [5] Weisfeiler and Lehman Go Cellular: CW Networks. NeurIPS 2021. [6] Intrinsic Dimension, Persistent Homology and Generalization in Neural Networks, NeurIPS 2021. [7] A PAC-Bayesian Approach To Spectrally-Normalized Margin Bounds for Neural Networks. ICLR 2018 [8] Simplified PAC-Bayesian Margin Bounds. Learning Theory and Kernel Machines, Lecture Notes in Computer Science, 2003 [9] A PAC-Bayesian Approach to Generalization Bounds for Graph Neural Networks. ICLR 2021 We're grateful for your constructive feedback. Many thanks! --- Rebuttal Comment 1.1: Comment: I thank the authors for the good work and their explanations. I will maintain my recommendation of acceptance. Note that, in the newly provided plots, the gap between the empirical error and the proposed bound grows with epochs. This might be seen as a little concerning and stresses the importance of tightening the bounds in future works, for example through some of the directions I suggested.	Rebuttal 1: Rebuttal: We are grateful to all the reviewers for their time and insightful comments, as well as to the (senior) area, program, and general chairs for their service to the community. We are pleased to note that reviewers appreciate the novelty (zp7n, toK8, Hv3h, ynbU) and the presentation (zp7n, toK8) of our work. Also reviewers found that our work provides a flexible framework (toK8) and empirical evaluations on real-world datasets that demonstrate the practical applicability and effectiveness (Hv3h). To the best of our efforts, we have tried to address all the specific comments that have been raised by each reviewer. Below, we provide some of the main revisions: 1. Reviewer zp7n asked about the dependency of our bounds on the number of model parameters. We used this opportunity to clarify how PAC-Bayesian bounds depend on parameter values and hyper-parameters. Table 1 in the rebuttal PDF outlines these dependencies. 2. Reviewers zp7n and ynbU asked about other GNN architectures, such as GraphSAGE (zp7n). We have run additional experiments considering GCN, GraphSAGE, and GIN combined with PersLay to assess the effectiveness of our theoretical bounds as a regularization scheme (see Table 2 of the rebuttal PDF). We considered 3 datasets (NCI1, NCI109, and PROTEINS) and reported test classification errors and empirical generalization gaps. Our results show that the regularized versions achieve competitive classification errors and significantly smaller generalization gaps. In addition, in Figure 2 (attached PDF), we show that our theoretical bound strongly correlates with the empirical gap for GraphSAGE. 3. Reviewer zp7n asked why the generalization bound increases with the number of epochs. To explain that, we report in Figure 1 (attached PDF) the average spectral norms over training. Interestingly, we observe that MLP layers dominate GNN ones — i.e., the average norm of MLPs is higher than that of GNNs. 4. Reviewer ynbU asked for clarification regarding the assumptions of our analysis. To summarize, our main results (Lemma 2 and corollaries about compositionality) assume i.i.d data, while the remaining (model specific) results make typical assumptions related to perturbation analysis (e.g., inputs lie in a $\ell_2$-norm ball, graphs have bounded degree). In the revised manuscript, we will list the assumptions for every result in the Appendix and overview them in the main text. 5. Reviewer toK8 suggested providing a discussion on takeaways from our theoretical analysis. We will add the discussion about the choices of PersLay hyperparameters one can make informed by our theoretical bound. 6. Reviewers asked about analyzing learnable filtration functions. Below, we summarize the reasons behind our modeling choice as well as insights into how to extend results for the learnable filtration case: - Fixed filtration functions dominate the PH/ML literature. The widespread use of learnable functions is a relatively recent phenomenon in PH-based ML, and usually runs orders of magnitude slower compared to non-learnable ones. Arguably, applying non-learnable functions still represents the mainstream approach in TDA. - Some works have explicitly advocated for fixed filtration functions (with learnable vectorizations) over learnable filtrations. Filtration functions can come in different flavors; for instance, they can rely on node degree [1], cliques [2], or node attributes [3]. Some of the popular options are parameter-free. Also, while some works showed gains using learnable filtrations [4], others have reported no benefits and adopted fixed functions instead [5,6]. There is still no consensus about the significance of the gains associated with learnable filtration in many applications. - Perslay [5] uses fixed filtration functions. Despite the generality of our results, we provide specific bounds for PersLay, which employs fixed filtration functions. - Our work lays a strong foundation for analyzing learnable filtrations. One way to analyze PH with learnable filtration schemes could be to get upper bounds on perturbation of outputs in terms of the filtration function parameters. This would additionally require an analysis of Wasserstein distances between persistence diagrams obtained with different parameters. We believe that for a specific class of graphs we can get modified upper bounds for perturbation with respect to filtration function parameters that would depend on Wasserstein distance of the same order. This additional analysis could be readily integrated into our framework to get generalization bounds for learnable filtrations. [1] Deep learning with topological signatures. NeurIPS 2017. [2] Networks and cycles: A persistent homology approach to complex networks. ECCS 2013. [3] Going beyond persistent homology using persistent homology. NeurIPS 2023. [4] Topological GNNs. ICLR 2022. [5] PersLay. AISTATS 2020. [6] Improving Self-supervised Molecular Representation Learning using Persistent Homology. NeurIPS 2023. --- We thank reviewers again for their very constructive comments. Pdf: /pdf/e7d6e6515986f6d725f8ca6eefb82317b3076ebf.pdf	NeurIPS_2024_submissions_huggingface	2,024	null	null	null	null	null	null	null	null

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