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2% Transport 3 NA NA 0% Transport Collab. 3 NA NA 0% Overcooked 2 102.267 26 80% Overcooked 3 194.794 28 40% Rover 1 21.360 39 59% Rover 2 87.305 38 11% Rover 3 120.732 49 2% Rover 4 NA NA 0% Satellite 1 0.036 12 100% Satellite 2 1.600 21 78% Satellite 3 6.915 25 44% Satellite 4 NA NA 0% Table 3: Plan Difficulty of Tra... | https://arxiv.org/abs/2505.22597v1 |
RL policy restricts its applicability to problems involving similar ob- jects. In many cases, when only dynamic predicates are used for observations, the RL policy is confined to a fixed static condition. Changes like varying agent numbers, adding/re- moving objects, or altering static conditions require a dif- ferent ... | https://arxiv.org/abs/2505.22597v1 |
on Artificial Intelligence Planning Sys- tems (AIPS) . Favier, A.; Verma, P.; La, N.; and Shah, J. A. 2025. Lever- aging LLMs for Collaborative Human-AI Decision Making. InProceedings of the AAAI 2025 Spring Symposium on Cur- rent and Future Varieties of Human-AI Collaboration . Fine-Morris, M.; Hsiao, V .; Smith, L. N... | https://arxiv.org/abs/2505.22597v1 |
and Reinforcement Learning (PRL) . Taitler, A.; Gimelfarb, M.; Jeong, J.; Gopalakrishnan, S.; Mladenov, M.; Liu, X.; and Sanner, S. 2023. pyRDDLGym: From RDDL to Gym Environments. In ICAPS 2023 Work- shop on Bridging the Gap Between AI Planning and Rein- forcement Learning (PRL) . Verma, P.; Marpally, S. R.; and Srivas... | https://arxiv.org/abs/2505.22597v1 |
On the performance of machine-learning assisted Monte Carlo in sampling from simple statistical physics models Luca Maria Del Bono,1, 2Federico Ricci-Tersenghi,1, 2, 3and Francesco Zamponi1 1Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 5, Rome 00185, Italy 2CNR-Nanotec, Rome unit, Piazzale Al... | https://arxiv.org/abs/2505.22598v1 |
starting from Mequilibrated configurations, a new series of configurations is generated using a neural network at a slightly lower temperature. The new configurations are equilibrated at the lower temperature and the neural network is then retrained using the new equilibrated configurations, as the starting point for t... | https://arxiv.org/abs/2505.22598v1 |
with vanilla Metropolis Monte Carlo (IVC). Finally, in Sec. V we draw our conclusions and highlight some possible future developments. II. BACKGROUND A. The Curie-Weiss model In this paper, we consider the simplest model of ferromagnetic phase transitions, the Curie-Weiss (CW) model. In the CW model, the state of the s... | https://arxiv.org/abs/2505.22598v1 |
order to satisfy detailed balance: Acc[σ→σ′] = min 1,PGB(σ′)×PNN(σ) PGB(σ)×PNN(σ′) , (4) where PNN(σ)is the probability that the NN generates the configuration σ. Note that in this case the whole configuration is updated in a single operation, which then corresponds roughly to a Monte Carlo Sweep. While this strategy... | https://arxiv.org/abs/2505.22598v1 |
a generative NN. In this paper, we consider a shallow MADE, as described in the next section. 1For instance, in the CW model below Tc, LMMC can remain stuck in the state with positive (negative) magnetization. Escaping the state and reaching the state with negative (positive) magnetization requires a time growing expon... | https://arxiv.org/abs/2505.22598v1 |
coupling Jℓyields: X {σ}PGB(σ)M<ℓσℓ=X {σ}PGB(σ)M<ℓtanh( JℓM<ℓ). (8) In the CW model, the sum over the 2Nspin configurations can be reduced to a polynomial sum by rewriting the Gibbs-Boltzmann distribution PGBin Eq. (1) with the CW Hamiltonian in Eq. (2) via a Hubbard-Stratonovich transformation as: PGB(σ) =1 ˆZ(β)Z dh ... | https://arxiv.org/abs/2505.22598v1 |
as: J(t+1) ℓ=J(t) ℓ−ηℓ∇ℓSc(J(t)), (16) 7 0.04 0.02 0.00 0.02 0.04 J 1.0 0.5 0.00.51.0J =2 =8 =12 =15 =20 FIG. 3. Comparison between the gradients obtained by linearizing around the optimal solution J∗ ℓ(full lines) and the gradients computed using pytorch backpropagation on a large dataset (data points) as a function o... | https://arxiv.org/abs/2505.22598v1 |
ˆτℓ=τℓ ηℓ=N 1+(ℓ−2)cN. These predictions are verified in Fig. 5. Notice that Eq. (24) requires to specify the learning rate ηℓfor weight ℓ. From a discretization of the gradient flow Eq. (24), noticing that in GD one performs a single discrete step at each time so that the minimum increment in tis one, it follows that ... | https://arxiv.org/abs/2505.22598v1 |
(intensive) magnetizations, which can be described in terms of a simple one-dimensional Markov chain. Then, we consider the time required by the chain to first reach a magnetization equal or greater (in modulus) than a target magnetization. At fixed β, we take as the target magnetization the equilibrium magnetization, ... | https://arxiv.org/abs/2505.22598v1 |
∆E=−21 N−σm . (31) Ifm= 0,∆E <0and the move is always accepted. When |m|>0and one selects a spin at random, the probability of it having a sign opposite to mis1−|m| 2(and that of having the same sign is1+|m| 2). Using this and equations (30) and (31), we can write the transition probability of the Markov chain, keepi... | https://arxiv.org/abs/2505.22598v1 |
βc= 1(we recall that these weights are non-zero at finite N). We then evaluate the times required to reach the absolute equilibrium magnetization |m∗|given by Eq. (3) at inverse temperature β≥βc(i.e. below the critical temperature) starting from zero magnetization, and we consider the ratio R=2τM+L τM, (36) where τMand... | https://arxiv.org/abs/2505.22598v1 |
compute the average first passage times as in the previous section. Following the discussion in Sec. IIIA3, we fix the learning rate η=N−3 2. We plot Rat fixed b= 0.5as a function of the training time in Fig. 8a. From Fig. 7b, for b= 0.5we expect R∞∼1.6 at infinite training time, which is confirmed by Fig. 8a. We see t... | https://arxiv.org/abs/2505.22598v1 |
= exp Ab2 , hence it remains finite with the chosen scaling of ∆β=b/√ N. When instead β−βc=O(1), the LMMC needs a time scaling exponentially in N, and the gain from using the MADE becomes even more visible. V. CONCLUSIONS In this work, we were able to fully describe a generative autoregressive architecture, the shall... | https://arxiv.org/abs/2505.22598v1 |
Ricci-Tersenghi, Gabriele Sicuro, Francesco Zamponi, and Marc Mezard. Spin glass theory and far beyond: replica symmetry breaking after 40 years . World Scientific, 2023. [4] Koji Hukushima and Koji Nemoto. Exchange monte carlo method and application to spin glass simulations. Journal of the Physical Society of Japan ,... | https://arxiv.org/abs/2505.22598v1 |
diffusion model with inverse renormalization group flows. arXiv preprint arXiv:2501.09064 , 2025. [24] Leonardo Galliano, Riccardo Rende, and Daniele Coslovich. Policy-guided monte carlo on general state spaces: Application to glass-forming mixtures. The Journal of Chemical Physics , 161(6), 2024. 16 [25] Daria Pugache... | https://arxiv.org/abs/2505.22598v1 |
arXiv:2505.22601v1 [cs.LG] 28 May 2025Machine Unlearning under Overparameterization Jacob L. Block∗Aryan Mokhtari∗Sanjay Shakkottai∗ Abstract Machine unlearning algorithms aim to remove the influence of specific training samples, ideally recovering the model that would have resulted from training on the remaining data ... | https://arxiv.org/abs/2505.22601v1 |
model class contains many interpolating solutions. Crucially, the training loss no longer admits a unique minimizer, and defining the unlearning solution by loss optimality alone no longer suffices: the original model θ∗ minimizes the loss over both DandDr, andθ∗clearly encodes information about Df, the data to be remo... | https://arxiv.org/abs/2505.22601v1 |
theory traces back to influence functions [Ham74], a classic statistical tool for estimating the effect of down-weighting a sample on a learned function [BNLGG22]. Extensions have explored approximate unlearning via differential privacy [SAKS21; GGHV20]. Previous works have considered different unlearning paradigms. [S... | https://arxiv.org/abs/2505.22601v1 |
where Jis defined as the average of the sample-wise loss L: A(D) =θ∗∈argmin θJ(θ;D) = argmin θ1 nX (x,y)∈DL(θ;x,y). (1) For our theoretical discussion, we consider sample-wise loss functions L(θ;x,y)which are minimized when f(θ,x) =y, meaning that sample interpolation implies loss minimization. For example, this is the... | https://arxiv.org/abs/2505.22601v1 |
associated with optimal generalization performance [HMRT22]. Then given the training algorithm AR, side information about the retain set Ir, a minimizer to the original training loss A(D), and the forget set Df, an unlearning algorithm M(AR,Ir,A(D),Df) attempts to recover AR(Dr), the least complex loss minimizer over D... | https://arxiv.org/abs/2505.22601v1 |
constraint relaxation the resulting optimization problem would be: min ∆R(θ∗+∆) s.t. ∇f(θ∗,xi)⊤∆= 0∀(xi,yi)∈ D r, (6) where for notational convenience, we define the drift variable as ∆=θ−θ∗. While this relaxation is sensible, it presents a clear limitation: approximating a general function with its linearization is on... | https://arxiv.org/abs/2505.22601v1 |
the effective linear predictor: R(θ) = A⊤ 1···A⊤ L−1c 2=∥w(θ)∥2. Given θ∗= c∗; vec(A∗ 1) ;. . .; vec(A∗ L−1) such that w(θ∗)⊤xi=yi for all ( xi, yi)∈ D, we aim to solve (4)for this choice of R. In this case the mapping fis non-linear with respect to θ. As a result, the first-order approximation for the constraints is... | https://arxiv.org/abs/2505.22601v1 |
the total number of neurons and ϕ:R→Ris some activation function. We abuse notation and write ϕ(Ax) to denote the element-wise application of ϕtoAx. We analyze the case where Rmeasures the number of active neurons, i.e., the width of the network. Formally, we denote a⊤ ias the ith row ofA, and we set R(θ) =Ph i=11{|ci|... | https://arxiv.org/abs/2505.22601v1 |
a worst-case interpolation width of at most nr, thereby improving the general bound of nr+ 1 implied by [RSSZ07] for minimum width interpolation. The drift regularizer ˆRonly allows perturbations to c∗, so the solution to (7)reduces width via sparsity in the updated last layer c∗+˜∆c, while leaving the first layer A∗un... | https://arxiv.org/abs/2505.22601v1 |
cost of gradient descent when npert<√nB, where nB=|B|is the batch size. Moreover, we often set λt=∞for many epochs in practice, skipping this cost entirely. 5.1 Experiments We test our algorithm against the following existing methods. GD [NRS21] runs gradient descent on J(θ;Dr), while Noisy GD (NGD) [CS23] adds gradien... | https://arxiv.org/abs/2505.22601v1 |
become more consistent as the number of unlearning epochs increases. We observe in general that the methods which mainly descend the loss on Dr(GD, NGD, Ridge) struggle to escape from the initial solution which fits the poisoned samples, while the methods which include ascent (NGP, GA) diverge from the sine curve in re... | https://arxiv.org/abs/2505.22601v1 |
on gray-colored test samples, and forget quality by the mean squared error between the predicted gray probability and the ideal value of 1 across all colored inputs. Figure 2 shows the Pareto frontier for each method. Each point is a median over 5 trials for one hyperparameter setting, with shaded uncertainty as half t... | https://arxiv.org/abs/2505.22601v1 |
R. B. Grosse. “If influence functions are the answer, then what is the question?” Advances in Neural Information Processing Systems 35 (2022), pp. 17953–17967 (pages 2, 3, 5, 6). [BCCJTZLP21] L. Bourtoule, V. Chandrasekaran, C. A. Choquette-Choo, H. Jia, A. Travers, B. Zhang, D. Lie, and N. Papernot. “Machine Unlearnin... | https://arxiv.org/abs/2505.22601v1 |
on Applications of Computer Vision . 2024, pp. 4819–4828 (page 3). 14 [JBVRCCH25] X. Jin, Z. Bu, B. Vinzamuri, A. Ramakrishna, K. -W. Chang, V. Cevher, and M. Hong. “Unlearning as multi-task optimization: A normalized gradient difference approach with an adaptive learning rate”. In: Proceedings of the 2025 Conference o... | https://arxiv.org/abs/2505.22601v1 |
8). [ZLBM24] R. Zhang, L. Lin, Y. Bai, and S. Mei. “Negative Preference Optimization: From Catastrophic Collapse to Effective Unlearning”. In: First Conference on Language Modeling . 2024 (pages 3, 11, 27). 16 Appendix A Minimum Norm Solutions to Linear Regression Here we prove various properties of minimum norm soluti... | https://arxiv.org/abs/2505.22601v1 |
Does not Protect Against Data Leakage The following example concretely demonstrates how certain minimizers of the retain set loss do not align with the intended goals of unlearning. Recall the unlearning problem for linear regression discussed in Section 4.1. In this case, we use the linear model f(θ,x) =θ⊤xparameteriz... | https://arxiv.org/abs/2505.22601v1 |
y)∈ D, and we want to recover θ∗ r, the minimum ℓ2norm solution over just a subset Dr⊆ D: θ∗ r= argmin θ∥θ∥2s.t.θ⊤x=y∀(x, y)∈ D r (16) Consider solving the relaxed unlearning problem (7) for ˜R(θ) =∥θ∥2: ˜∆= argmin ∆∥θ∗+∆∥2s.t.∆⊥x∀(x,y)∈ D r 19 Define Sr= span {x|(x, y)∈ D r}and write the equivalent problem: ˜∆= argmin... | https://arxiv.org/abs/2505.22601v1 |
non-zero only in the entries corresponding to A1, applying Rand ˜R yields the same value: R(θ∗+˜∆) =˜R(θ∗+˜∆) and R(θ∗+∆∗) =˜R(θ∗+∆∗) 21 Thus, R(θ∗+∆∗) =R(θ∗+˜∆), soθ∗+∆∗achieves the optimal objective value of (4). Since we established feasibility and optimality, θ∗+∆∗must solve (4). C.4.1 Necessity of Additional Regul... | https://arxiv.org/abs/2505.22601v1 |
the rank-1 matrix A∗ 1Pw∗rmust preserve optimality of any solution that contains A∗ 1. Write A∗ 1Pw∗r=λ1v1w∗⊤ rfor some λ1∈R,v1∈Rhℓwith∥v1∥2= 1. We can apply an analogous argument with the matrix Pv1, which projects its input onto span(v1), to show that any solution that contains A∗ 2must remain optimal with A∗ 2replac... | https://arxiv.org/abs/2505.22601v1 |
theorem. Proof of Lemma 6 : Let the columns of some P∈Rh×(h−s)form a basis for G⊥so that im(P) =G⊥. Consider the reduced column echelon form of Pdenoted rcef(P) =˜P. By definition, im(˜P) =im(P) =G⊥, so rank(˜P) =h−sand thus each of the h−scolumns of ˜Phas a leading one. Let ˜pibe the ith column of ˜Pand let jidenote t... | https://arxiv.org/abs/2505.22601v1 |
decay rate TProj MinNorm-OG Projection period npert MinNorm-OG Subsample size to compute gradient space E.1 Implementations We now define the exact implementation of each method. Consider a batch of retain samples Br and forget samples Bf, along with loss function J. For each method, we use the AdamW [LH19] optimizer w... | https://arxiv.org/abs/2505.22601v1 |
current parameter vector, θnewis the updated vector, and mod denotes the modulo operation. iftmod TProj̸= 0 or t≥T−TGD θnew=θ0 else ˜∆= argmin ∆∈G′⊥r∥θ0+∆∥2 2+λ∥∆∥2 2 θnew=θ0+˜∆ λ←λ+ 1 γreg−1 Gradients for Classification. We make a special note of how we compute the gradient subspace G′ r for classification tasks. At t... | https://arxiv.org/abs/2505.22601v1 |
the unlearning algorithms over a sweep of hyperpa- rameters and evaluate the output θof each unlearning method by measuring the deviation from the retain set trend, given by supx∈X|f(θ,x)−sin(x)|. We fix the number of epochs for each algorithm and allow full data access, so each method has access to all of Drduring unl... | https://arxiv.org/abs/2505.22601v1 |
when given 1000 unlearning epochs for the Data Poisoning experiment, where the forget points distort the retain set trend y= sin( x). 31 E.3 Multi-Class Label Erasure We use the MNIST and CIFAR-10 [LCB10; Kri09] datasets, creating red, green, and gray copies of each image in the training sets. We construct the retain s... | https://arxiv.org/abs/2505.22601v1 |
the Pareto frontier for each method, where the optimal point is at (1 ,0) which indicates perfect retain accuracy and zero gray prediction error. Each point in the frontier for a given method represents the median results over 5 trials of a single hyperparameter combination, with the shaded uncertainty shown as half th... | https://arxiv.org/abs/2505.22601v1 |
the results in Figure 8 running the Multi-Label Class Erasure experiment on MNIST with pretain =.05 and T= 2. Hyperparameter Sweep Values η {10−4,3×10−4,5×10−4,10−3} λGA {10−3,10−2,10−1,1.0} λreg {0.1,0.3,0.5,1.0,3.0} σ {0.1,0.5} TGD {0,1} γreg {0.3,0.6,0.9} TProj {1,2} npert {20,40} 34 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Reta... | https://arxiv.org/abs/2505.22601v1 |
0.4 0.5 0.6 0.7 0.8 Retain Quality (Higher ↑)0.00.10.20.30.40.50.60.70.8Forget Quality (Lower ↓) GTGD GA NGD NGP NPO Scrub Ridge MinNorm-OG GT Figure 13: Pareto frontiers for each method across hyperparameter settings in the Multi-Class Label Erasure task on CIFAR-10 with pretain =.01 and T= 10. E.4 Representation Coll... | https://arxiv.org/abs/2505.22601v1 |
accessible, which we denote pretain∈[0,1]. Just as in the Multi-Class Label Erasure experiment, during each unlearning epoch the algorithms iterate over batches from the forget set and sample a corresponding batch of the same size from the available retained data. The epoch ends once all forget set batches have been pr... | https://arxiv.org/abs/2505.22601v1 |
One Rank at a Time: Cascading Error Dynamics in Sequential Learning Mahtab Alizadeh Vandchali∗Fangshuo (Jasper) Liao† Anastasios Kyrillidis Department of Computer Science Rice University ma202@rice.edu, fl15@rice.edu, anastasios@rice.edu Abstract Sequential learning –where complex tasks are broken down into simpler, hi... | https://arxiv.org/abs/2505.22602v1 |
learning could be structured as a series of stages or levels [ 7,8,9,10,11,12]. Sequential learning is especially relevant when the notion of “skills” is orthogonal or correlated to each other, or even layered hierarchically [ 13,14]. For instance, in a multitask learning environment [ 15,16,17,18], basic skills might ... | https://arxiv.org/abs/2505.22602v1 |
large language models, while maintaining performance. But even beyond AI, recommendation systems [ 32] require real-time updates, and sequential low-rank modi- fications offer a computationally efficient way to incorporate new user-item interactions. This validates the hypothesis that complex transformations can be app... | https://arxiv.org/abs/2505.22602v1 |
not fall into the sequential scenario we focus on. Learning rank-1 subspaces sequentially. Our aim is to study routines like the ones de- scribed in (1)and (2). I.e., we are interested in the sequential, rank-1-updated linear regression setting, and our focus will be on the theoretical understanding of how errors in ca... | https://arxiv.org/abs/2505.22602v1 |
Y⋆ kin Algorithm 1, as well as depends on approximate current estimates bka⊤ kX, and not b⋆ ka⋆⊤ kXas in the exact case. To study the influence of the numerical errors produced by (5), we introduce the following definition: Definition 1 (Numerical Error) .Let(ak,bk)represents the exact rank-1 solution that approxi- mat... | https://arxiv.org/abs/2505.22602v1 |
of how errors propagate when using lower ranks remains unexplored. Recent works consider a collection of LoRAs via merging, such as [84, 85, 86, 87, 88, 89]. 3 Error propagation during training Recall that Lemma 1 guarantees that the rank-1 components given by the exact Algorithm 1 recovers the top- rsingular vector/va... | https://arxiv.org/abs/2505.22602v1 |
a slower decay of singular values —corresponding to a smaller eigengap—error propagation is amplified, making approximation steps more susceptible to the accumulation of individual errors δk, and vice versa. This dependency on the singular spectrum necessitates more precision in each step for data matrices with dense s... | https://arxiv.org/abs/2505.22602v1 |
to the overall generalization ability. Generalization under noisy labels. In the previous section, we studied the generalization ability of Algorithm 2 under a noiseless scenario with Y=W⋆X, where the algorithmic choice of choosing r=rank(Y)can be shown to be optimal. However, this argument may not hold when the labels... | https://arxiv.org/abs/2505.22602v1 |
allocated to the earlier components and more to later ones. Our analysis dictates that errors in early components propagate to later components, suggest- ing that allocating more iterations to earlier components leads to better overall performance. Figure 1 shows the reconstruction and training errors, respectively, fo... | https://arxiv.org/abs/2505.22602v1 |
weight change during fine-tuning as a low-rank decomposition: ∆W=BA⊤∈Rm×n, where A∈Rn×rand B∈Rm×rwith r≪min(m, n). In these experiments and w.l.o.g., r= 3. In our approach, instead of optimizing all rcomponents simultaneously, we optimize one rank-1 component at a time, using the residual error from previous components... | https://arxiv.org/abs/2505.22602v1 |
one needs to consider different rvalues from scratch before making the final decision. Figure 4: αβγdenotes sequential training with α, β andγepochs for each component. Not all combinations are shown.Sequential training paths. Figure 4 illustrates the effec- tiveness of different sequen- tial training paths for the c... | https://arxiv.org/abs/2505.22602v1 |
Arian Hosseini, Friederike Niedtner, and Nicolas Le Roux. Joint prompt optimization of stacked llms using variational inference. Advances in Neural Information Processing Systems , 36, 2024. [6]Lucas Page-Caccia, Edoardo Maria Ponti, Zhan Su, Matheus Pereira, Nicolas Le Roux, and Alessandro Sordoni. Multi-head adapter ... | https://arxiv.org/abs/2505.22602v1 |
Ma. Rethinking bias- variance trade-off for generalization of neural networks. In International Conference on Machine Learning , pages 10767–10777. PMLR, 2020. [27] Xianbing Zhao, Lizhen Qu, Tao Feng, Jianfei Cai, and Buzhou Tang. Learning in order! a sequential strategy to learn invariant features for multimodal senti... | https://arxiv.org/abs/2505.22602v1 |
pages 27585–27610. PMLR, 2023. [48] Edward J Hu, Phillip Wallis, Zeyuan Allen-Zhu, Yuanzhi Li, Shean Wang, Lu Wang, Weizhu Chen, et al. LoRA: Low-rank adaptation of large language models. In Interna- tional Conference on Learning Representations , 2021. [49] Kiryung Lee and Yoram Bresler. Guaranteed minimum rank approx... | https://arxiv.org/abs/2505.22602v1 |
Anastasios Kyrillidis, and Sujay Sanghavi. Dropping convexity for faster semi-definite optimization. In Conference on Learning Theory , pages 530–582, 2016. [67] Srinadh Bhojanapalli, Behnam Neyshabur, and Nati Srebro. Global optimality of local search for low rank matrix recovery. In Advances in Neural Information Pro... | https://arxiv.org/abs/2505.22602v1 |
preprint arXiv:2303.10512 , 2023. [84] Ziyu Zhao, Tao Shen, Didi Zhu, Zexi Li, Jing Su, Xuwu Wang, Kun Kuang, and Fei Wu. Merging LoRAs like playing LEGO: Pushing the modularity of LoRA to extremes through rank-wise clustering. arXiv preprint arXiv:2409.16167 , 2024. 16 [85] Nikolaos Dimitriadis, Pascal Frossard, and F... | https://arxiv.org/abs/2505.22602v1 |
k. By the triangle inequality: Y−rX k=1bka⊤ kX F≤pX k=r+1σ⋆ k+ rX k=1b⋆ ka⋆⊤ kX−rX k=1bka⊤ kX F+rX k=1∥δkX∥F ≤pX k=r+1σ⋆ k+rX k=1 b⋆ ka⋆⊤ kX−bka⊤ kX F+rX k=1∥δkX∥F.(16) Therefore, our analysis will primarily focus on upper-bounding b⋆ ka⋆⊤ kX−bka⊤ kX F. Intuitively, this depends on the difference between YkandY⋆ k. As ... | https://arxiv.org/abs/2505.22602v1 |
∥σ⋆ k∥F· ∥u⋆ kv⋆⊤ k−u1kv⊤ 1k∥F+∥σ⋆ k−σ1k∥F· ∥u1k∥2|{z} =1·∥v⊤ 1k∥2|{z} =1 ≤ |σ⋆ k| · ∥u⋆ kv⋆⊤ k−u1kv⊤ 1k∥F+|σ⋆ k−σ1k|. Therefore, ∥b⋆ ka⋆⊤ kX−bka⊤ kX∥F≤σ⋆ k· ∥u⋆ kv⋆⊤ k−u1kv⊤ 1k∥F+|σ⋆ k−σ1k|. (20) Now, we express the term ∥u⋆ kv⋆⊤ k−u1kv⊤ 1k∥Fas follows: ∥u⋆ kv⋆⊤ k−u1kv⊤ 1k∥F=∥u⋆ k(v⋆⊤ k−v⊤ 1k) + (u⋆ k−u1k)v⊤ 1k∥F ≤ ∥u... | https://arxiv.org/abs/2505.22602v1 |
k . Define error bound E(k)as: E(k) :=σmax(X)k−1X k′=0∥δk′∥Fk−1Y j=k′+1 6σ⋆ j T⋆ j+ 2! 21 If∥δk∥F’s are small enough such that E(k)<1 2minj>k|σ⋆ k−σ⋆ j|, then for any r≤r′≤r⋆, the output of Algorithm 2 satisfies: Y(r′)−rX k=1bka⊤ kX F≤r′X k=r+1σ⋆ k+σmax(X)rX k=1kX k′=0∥δk′∥FkY j=k′+1 2 +6σ⋆ j T⋆ k (26) Notice that Th... | https://arxiv.org/abs/2505.22602v1 |
.ˆbm. Then, we can write Y⋆as: Y=W⋆X+ˆBˆB⊤E+ˆB⊥ˆB⊥⊤E=ˆB(ΣˆA⊤X+E1) +ˆB⊥E2, where E1∈Rr⋆×nandE2∈R(m−r⋆)×nare noise matrices with I.I.D. Gaussian entries. Therefore, based on the above decomposition, E1can be seen as the unavoidable noise, which will adds up to the training error, and E2is the error that can be avoided if... | https://arxiv.org/abs/2505.22602v1 |
T⋆ minˆmX k=1 E⊤u⋆ k 2 2+∥Ev⋆ k∥2 2 =4 T⋆ min E⊤U⋆ ˆm 2 F+∥EV⋆ ˆm∥2 F Since E∈Rm×ncontains I.I.D. Gaussian entries from N(0, ε2), we must have that U⋆ kE∈ Rˆm×nandEV⋆ k∈Rm׈mcontains I.I.D. Gaussian entries from N(0, ε2). By Lemma 6, we have that with probability at least 1−δ, it holds that U⋆⊤ ˆmE 2 F+∥EV⋆ ˆm∥2 F≤... | https://arxiv.org/abs/2505.22602v1 |
and Σis a diagonal matrix with singular values σ1≥σ2≥ ··· ≥ σmin(m,n)≥0. For any integer k≤min(m, n), let Ak=UkΣkV⊤ kbe the best rank- kapproximation of A, where UkandVkconsist of the first k columns of UandV, andΣkis the diagonal matrix of the largest ksingular values. ThenAkminimizes the approximation error in both t... | https://arxiv.org/abs/2505.22602v1 |
value profile. We study whether the singular value profile of W⋆has impact on error propagation through the term T⋆ k= min {minj>k|σ⋆ k−σ⋆ j|, σ⋆ k}in our error bound. Figure 5 shows the singular value decay patterns of both W⋆and the resulting Y under different spectral profiles. Figure 6 illustrates the training and ... | https://arxiv.org/abs/2505.22602v1 |
decay, with its large leading singular values and wider gaps, allows early components to capture most of 30 (a)κ= 0.05 (b)κ= 0.1 (c)κ= 0.5 (d)κ= 1 Figure 9: Effect of singular value profiles under noise. Power-law decay consistently achieves lower reconstruction error, followed by exponential and then uniform profiles,... | https://arxiv.org/abs/2505.22602v1 |
path represents a sequence of component training durations. For example, path “1 →3→5” indicates a rank-3 LoRA where the first component received 1 epoch of training, the second component 3 epochs, and the third component 5 epochs. In all cases, it is evident that good first component implies (almost all the times) a b... | https://arxiv.org/abs/2505.22602v1 |
arXiv:2505.22608v1 [cs.SD] 28 May 2025Effective and Efficient One-pass Compression of Speech Foundation Models Using Sparsity-aware Self-pinching Gates Haoning Xu1, Zhaoqing Li1, Youjun Chen1, Huimeng Wang1, Guinan Li1, Mengzhe Geng2, Chengxi Deng1, Xunying Liu1 1The Chinese University of Hong Kong, Hong Kong SAR, Chin... | https://arxiv.org/abs/2505.22608v1 |
time inevitably arises from post-pruning refinement stages, including knowledge distillation [29], fine- tuning [21], and iterative pruning [24, 27, 32–34], which not only prolong development cycles but also complicate experi- mental workflows due to multi-stage requirements. 4) Exces- sive pruning-required parameter o... | https://arxiv.org/abs/2505.22608v1 |
[22, 29], ii)the number of candidates [10, 25] or iii)the layer size [35]. 2. wav2vec2.0 and HuBERT Models Speech SSL models such as wav2vec2.0 [1], HuBERT [2], and WavLM [3] share similar Transformer backbones. For example, HuBERT consists of a CNN encoder, a Transformer encoder, a projection layer and a code embeddin... | https://arxiv.org/abs/2505.22608v1 |
While NAS-based techniques ensure consistency between model pruning and parameter update, they introduce consider- able computational and parameter overhead. Furthermore, their effectiveness is highly dependent on the design of candidates. 4. Sparsity-aware Self-pinching Gates The core concept of Sparsity-aware Self-pi... | https://arxiv.org/abs/2505.22608v1 |
HuBERT- large systems are obtained by fine-tuning 30 and 10 epochs from the baselines of wav2vec2.0- base and HuBERT- large , respectively. The threshold tin each layer is initialized to 1e-5. Tandτare cosine-annealed from 0.5 to 0.01. All experiments are conducted on a single NVIDIA A40 (48 GB). 5.2. Main results To f... | https://arxiv.org/abs/2505.22608v1 |
50% and 40% (Fig. 2 (3)-(4)). We conjecture that the inferior performance of UMP is par- tially caused by the inconsistency that decouples pruning from parameter optimization. To verify this, we implement a decou- pled version of our method, which involves pruning the param- eters with relatively small magnitude from t... | https://arxiv.org/abs/2505.22608v1 |
2 (1)-(4). Regarding the addi- tional components, NAS-CP requires 7 architecture-dependent parameters per layer (e.g., 1008 total for HuBERT- large of Sys. 23 in Tab. 1) in our configurations (Sec. 3.2). In contrast, our method maintains only one threshold per layer (e.g., 144 total for HuBERT- large of Sys. 11 in Tab.... | https://arxiv.org/abs/2505.22608v1 |
et al. , “Lossless 4-bit quantization of architecture compressed conformer asr systems on the 300-hr switchboard corpus,” in Interspeech , 2023. [11] H. Wang and W.-Q. Zhang, “Unstructured pruning and low rank factorisation of self-supervised pre-trained speech models,” IEEE Journal of Selected Topics in Signal Process... | https://arxiv.org/abs/2505.22608v1 |
, “DPHuBERT: Joint dis- tillation and pruning of self-supervised speech models,” in Inter- speech , 2023. [30] L. Zampierin, G. B. Hacene, B. Nguyen et al. , “Skill: Similarity- aware knowledge distillation for speech self-supervised learning,” in2024 IEEE International Conference on Acoustics, Speech, and Signal Proce... | https://arxiv.org/abs/2505.22608v1 |
RICO: Improving Accuracy and Completeness in Image Recaptioning via Visual Reconstruction Yuchi Wang1, Yishuo Cai2, Shuhuai Ren1, Sihan Yang3, Linli Yao1, Yuanxin Liu1, Yuanxing Zhang4, Pengfei Wan4, Xu Sun1 1National Key Laboratory for Multimedia Information Processing, Peking University 2Central South University3Xi’a... | https://arxiv.org/abs/2505.22613v1 |
sky with white clouds and a bright area on the right side . Some greenery is also visible in the distance. The overall scene suggests a bus depot or a parking area for buses.Original Caption (Generated byQwen2 -VL) GPT-4oRecaptioning RICO (Ours) Human RecaptioningWrong orAmbiguous Information Other Added DetailsCorrect... | https://arxiv.org/abs/2505.22613v1 |
ted. These issues cannot be fully resolved even with the integration of additional models or hu- man editing. For example, as illustrated in Fig. 1, the caption generated by Qwen2-VL (Wang et al., 2024b) contains ambiguous or incorrect informa- tion that cannot be fully corrected even with GPT- 4o (OpenAI et al., 2024)... | https://arxiv.org/abs/2505.22613v1 |
comprehensiveness. For instance, it consis- tently achieves improvements of over 10 points on CapsBench (Liu et al., 2024a). Moreover, RICO- Flash outperforms all recaptioning baselines. From the reverse perspective of text-to-image generation, we find that models trained on captions refined by RICO-Flash exhibit a str... | https://arxiv.org/abs/2505.22613v1 |
introduced the idea of replacing low-quality or overly simplistic captions with synthetic alterna- tives. Since then, numerous approaches have lever- aged image recaptioning to improve multimodal large language models (MLLMs) (Chen et al., 2023), text-to-image generation models (Betker et al., 2023), and CLIP-style vis... | https://arxiv.org/abs/2505.22613v1 |
foliage… oriented toward the right side of the frame… …… …Original Image / Image 0(𝒗𝟎) Image 1(𝒗𝟏) Image 2(𝒗𝟐)① ② ③ ④ ⑤Missing information Extracted information Initial Captioning Reconstruction 𝑻 Refinement 𝑹 Caption 1(𝒄𝟏) a dairy cow … dense layer of flowers … background features dense foliage… oriented tow... | https://arxiv.org/abs/2505.22613v1 |
andincompleteness . For inaccuracy, the model is instructed to identify and correct errors based on discrepancies between the original and reconstructed images, and to revise any ambigu- ous descriptions in the previous caption that may have caused inaccurate reconstruction. For incom- pleteness, the model is encourage... | https://arxiv.org/abs/2505.22613v1 |
represent object coverage, pixel coverage, attribute score, and relation score, respectively. Over. in Amber refers to overall performance (see § B.2 for details). Green text indicates improvements. RICO demonstrates significant gains over the original captions, while RICO-Flash achieves performance close to that of RI... | https://arxiv.org/abs/2505.22613v1 |
et al., 2024b) as the initial caption- ing models to produce baseline captions, which are then refined by RICO. As shown in Tab. 1, even with just two refinement iterations, the captions generated by RICO exhibit substantial improve- ments across all benchmarks and metrics. Notably, the improvement in the overall score... | https://arxiv.org/abs/2505.22613v1 |
on a classical downstream task: text-to-image generation. We collect an image dataset from Hug- gingface1and use RICO to perform recaptioning. Specifically, for each image v, we obtain both the initial caption c0and the refined caption cN, forming two datasets: Dinitial ={(v(i), c(i) 0)}and Drefined ={(v(i), c(i) N)}. ... | https://arxiv.org/abs/2505.22613v1 |
(+12.4) 56.0 / 60.3 (+4.3) Qwen2-VL (Prompt 1) 42.0 / 59.0 (+17.0) 55.9 / 61.4 (+5.5) Qwen2-VL (Prompt 2) 46.0 / 57.6 (+11.6) 57.2 / 60.6 (+3.4) Qwen2-VL (Prompt 3) 41.9 / 54.9 (+13.0) 56.9 / 60.9 (+4.0) Table 6: Ablation studies. MethodCapsBench Acc. Color Rel. Pos. Shape RICO 59.02 67.14 59.51 53.68 RICO-Flash 55.32 ... | https://arxiv.org/abs/2505.22613v1 |
survey. Preprint , arXiv:2404.18930. James Betker, Gabriel Goh, Li Jing, Tim Brooks, Jian- feng Wang, Linjie Li, Long Ouyang, Juntang Zhuang, Joyce Lee, Yufei Guo, Wesam Manassra, Prafulla Dhariwal, Casey Chu, Yunxin Jiao, and Aditya Ramesh. 2023. Improving image generation with better captions. Lin Chen, Jinsong Li, X... | https://arxiv.org/abs/2505.22613v1 |
Lai, Haotian Zhang, Bowen Zhang, Wen- tao Wu, Haoping Bai, Aleksei Timofeev, Xianzhi Du, Zhe Gan, Jiulong Shan, Chen-Nee Chuah, Yin- fei Yang, and Meng Cao. 2024. Veclip: Improving clip training via visual-enriched captions. Preprint , arXiv:2310.07699. Junnan Li, Dongxu Li, Silvio Savarese, and Steven Hoi. 2023a. Blip... | https://arxiv.org/abs/2505.22613v1 |
ral Information Processing Systems , 36. Colin Raffel, Noam Shazeer, Adam Roberts, Katherine Lee, Sharan Narang, Michael Matena, Yanqi Zhou, Wei Li, and Peter J. Liu. 2023. Exploring the limits of transfer learning with a unified text-to-text trans- former. Preprint , arXiv:1910.10683. Shuhuai Ren, Linli Yao, Shicheng ... | https://arxiv.org/abs/2505.22613v1 |
Image captioning via re-aligning alt-text. Preprint , arXiv:2410.17251. Le Xue, Manli Shu, Anas Awadalla, Jun Wang, An Yan, Senthil Purushwalkam, Honglu Zhou, Viraj Prabhu, Yutong Dai, Michael S Ryoo, Shrikant Kendre, Jieyu Zhang, Can Qin, Shu Zhang, Chia-Chih Chen, Ning Yu, Juntao Tan, Tulika Manoj Awalgaonkar, Shelby... | https://arxiv.org/abs/2505.22613v1 |
al., 2023) for gen- erating refined captions. In our implementation, we follow the same procedure to obtain enhancedTable 7: Instructions provided to human annotators in the caption editing experiment. ==INSTRUCTION TO ANNOTATORS == We are working on an image captioning task. The following caption was generated by an A... | https://arxiv.org/abs/2505.22613v1 |
blanket, along with two boxes filled with food. In the pond, a group of people enjoying the serenity of the sunset in a rowboat. Some people stand on a small island in the lake on the left side of the frame . In the distance, a two-story Japanese tower is perched on the lake. surrounded by numerous cherry blossom trees... | https://arxiv.org/abs/2505.22613v1 |
ModelDPG-BenchVQAScore Entity Relation Attribute Global Overall FLUX w/ Init. Cap. 85.110 89.950 80.080 72.414 78.502 0.841 FLUX w/ RICO-DPO 86.850 90.551 82.831 75.172 80.336 0.852 design a self-looping caption improvement pipeline guided by this metric. In detail, the method de- tects objects in the image, generates ... | https://arxiv.org/abs/2505.22613v1 |
ice's surface. The overall composition is balanced, with the skater and the ice slice drawing the viewer's eye towards the horizon. The image is taken from a low angle, emphasizing the vastness of the landscape and the skater's actionThe main differences between the original and reconstructed images lie in the foregrou... | https://arxiv.org/abs/2505.22613v1 |
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