Volkan Cevher

Grigorios G Chrysos, Bohan Wang, Jiankang Deng et al.

Deep Neural Networks (DNNs) have obtained impressive performance across tasks, however they still remain as black boxes, e.g., hard to theoretically analyze. At the same time, Polynomial Networks (PNs) have emerged as an alternative method with a promising performance and improved interpretability but have yet to reach the performance of the powerful DNN baselines. In this work, we aim to close this performance gap. We introduce a class of PNs, which are able to reach the performance of ResNet across a range of six benchmarks. We demonstrate that strong regularization is critical and conduct an extensive study of the exact regularization schemes required to match performance. To further motivate the regularization schemes, we introduce D-PolyNets that achieve a higher-degree of expansion than previously proposed polynomial networks. D-PolyNets are more parameter-efficient while achieving a similar performance as other polynomial networks. We expect that our new models can lead to an understanding of the role of elementwise activation functions (which are no longer required for training PNs). The source code is available at https://github.com/grigorisg9gr/regularized_polynomials.

Amazon AGI, Aaron Langford, Aayush Shah et al. · amazon-science

We present Amazon Nova, a new generation of state-of-the-art foundation models that deliver frontier intelligence and industry-leading price performance. Amazon Nova Pro is a highly-capable multimodal model with the best combination of accuracy, speed, and cost for a wide range of tasks. Amazon Nova Lite is a low-cost multimodal model that is lightning fast for processing images, video, documents and text. Amazon Nova Micro is a text-only model that delivers our lowest-latency responses at very low cost. Amazon Nova Canvas is an image generation model that creates professional grade images with rich customization controls. Amazon Nova Reel is a video generation model offering high-quality outputs, customization, and motion control. Our models were built responsibly and with a commitment to customer trust, security, and reliability. We report benchmarking results for core capabilities, agentic performance, long context, functional adaptation, runtime performance, and human evaluation.

Elias Abad Rocamora, Mehmet Fatih Sahin, Fanghui Liu et al.

Polynomial Networks (PNs) have demonstrated promising performance on face and image recognition recently. However, robustness of PNs is unclear and thus obtaining certificates becomes imperative for enabling their adoption in real-world applications. Existing verification algorithms on ReLU neural networks (NNs) based on classical branch and bound (BaB) techniques cannot be trivially applied to PN verification. In this work, we devise a new bounding method, equipped with BaB for global convergence guarantees, called Verification of Polynomial Networks or VPN for short. One key insight is that we obtain much tighter bounds than the interval bound propagation (IBP) and DeepT-Fast [Bonaert et al., 2021] baselines. This enables sound and complete PN verification with empirical validation on MNIST, CIFAR10 and STL10 datasets. We believe our method has its own interest to NN verification. The source code is publicly available at https://github.com/megaelius/PNVerification.

Clement Vignac, Igor Krawczuk, Antoine Siraudin et al.

This work introduces DiGress, a discrete denoising diffusion model for generating graphs with categorical node and edge attributes. Our model utilizes a discrete diffusion process that progressively edits graphs with noise, through the process of adding or removing edges and changing the categories. A graph transformer network is trained to revert this process, simplifying the problem of distribution learning over graphs into a sequence of node and edge classification tasks. We further improve sample quality by introducing a Markovian noise model that preserves the marginal distribution of node and edge types during diffusion, and by incorporating auxiliary graph-theoretic features. A procedure for conditioning the generation on graph-level features is also proposed. DiGress achieves state-of-the-art performance on molecular and non-molecular datasets, with up to 3x validity improvement on a planar graph dataset. It is also the first model to scale to the large GuacaMol dataset containing 1.3M drug-like molecules without the use of molecule-specific representations.

Wanyun Xie, Fabian Latorre, Kimon Antonakopoulos et al.

This paper rethinks Sharpness-Aware Minimization (SAM), which is originally formulated as a zero-sum game where the weights of a network and a bounded perturbation try to minimize/maximize, respectively, the same differentiable loss. To fundamentally improve this design, we argue that SAM should instead be reformulated using the 0-1 loss. As a continuous relaxation, we follow the simple conventional approach where the minimizing (maximizing) player uses an upper bound (lower bound) surrogate to the 0-1 loss. This leads to a novel formulation of SAM as a bilevel optimization problem, dubbed as BiSAM. BiSAM with newly designed lower-bound surrogate loss indeed constructs stronger perturbation. Through numerical evidence, we show that BiSAM consistently results in improved performance when compared to the original SAM and variants, while enjoying similar computational complexity. Our code is available at https://github.com/LIONS-EPFL/BiSAM.

Paul Rolland, Volkan Cevher, Matthäus Kleindessner et al.

This paper demonstrates how to recover causal graphs from the score of the data distribution in non-linear additive (Gaussian) noise models. Using score matching algorithms as a building block, we show how to design a new generation of scalable causal discovery methods. To showcase our approach, we also propose a new efficient method for approximating the score's Jacobian, enabling to recover the causal graph. Empirically, we find that the new algorithm, called SCORE, is competitive with state-of-the-art causal discovery methods while being significantly faster.

Joel A. Tropp, Alp Yurtsever, Madeleine Udell et al.

This paper argues that randomized linear sketching is a natural tool for on-the-fly compression of data matrices that arise from large-scale scientific simulations and data collection. The technical contribution consists in a new algorithm for constructing an accurate low-rank approximation of a matrix from streaming data. This method is accompanied by an a priori analysis that allows the user to set algorithm parameters with confidence and an a posteriori error estimator that allows the user to validate the quality of the reconstructed matrix. In comparison to previous techniques, the new method achieves smaller relative approximation errors and is less sensitive to parameter choices. As concrete applications, the paper outlines how the algorithm can be used to compress a Navier--Stokes simulation and a sea surface temperature dataset.

Anastasios Kyrillidis, Volkan Cevher

In this paper, we present and analyze a new set of low-rank recovery algorithms for linear inverse problems within the class of hard thresholding methods. We provide strategies on how to set up these algorithms via basic ingredients for different configurations to achieve complexity vs. accuracy tradeoffs. Moreover, we study acceleration schemes via memory-based techniques and randomized, $ε$-approximate matrix projections to decrease the computational costs in the recovery process. For most of the configurations, we present theoretical analysis that guarantees convergence under mild problem conditions. Simulation results demonstrate notable performance improvements as compared to state-of-the-art algorithms both in terms of reconstruction accuracy and computational complexity.

Thomas Pethick, Puya Latafat, Panagiotis Patrinos et al.

This paper introduces a new extragradient-type algorithm for a class of nonconvex-nonconcave minimax problems. It is well-known that finding a local solution for general minimax problems is computationally intractable. This observation has recently motivated the study of structures sufficient for convergence of first order methods in the more general setting of variational inequalities when the so-called weak Minty variational inequality (MVI) holds. This problem class captures non-trivial structures as we demonstrate with examples, for which a large family of existing algorithms provably converge to limit cycles. Our results require a less restrictive parameter range in the weak MVI compared to what is previously known, thus extending the applicability of our scheme. The proposed algorithm is applicable to constrained and regularized problems, and involves an adaptive stepsize allowing for potentially larger stepsizes. Our scheme also converges globally even in settings where the underlying operator exhibits limit cycles.

Ali Kavis, Kfir Yehuda Levy, Volkan Cevher

In this paper, we propose a new, simplified high probability analysis of AdaGrad for smooth, non-convex problems. More specifically, we focus on a particular accelerated gradient (AGD) template (Lan, 2020), through which we recover the original AdaGrad and its variant with averaging, and prove a convergence rate of $\mathcal O (1/ \sqrt{T})$ with high probability without the knowledge of smoothness and variance. We use a particular version of Freedman's concentration bound for martingale difference sequences (Kakade & Tewari, 2008) which enables us to achieve the best-known dependence of $\log (1 / δ)$ on the probability margin $δ$. We present our analysis in a modular way and obtain a complementary $\mathcal O (1 / T)$ convergence rate in the deterministic setting. To the best of our knowledge, this is the first high probability result for AdaGrad with a truly adaptive scheme, i.e., completely oblivious to the knowledge of smoothness and uniform variance bound, which simultaneously has best-known dependence of $\log( 1/ δ)$. We further prove noise adaptation property of AdaGrad under additional noise assumptions.

Panayotis Mertikopoulos, Ya-Ping Hsieh, Volkan Cevher

We develop a flexible stochastic approximation framework for analyzing the long-run behavior of learning in games (both continuous and finite). The proposed analysis template incorporates a wide array of popular learning algorithms, including gradient-based methods, the exponential/multiplicative weights algorithm for learning in finite games, optimistic and bandit variants of the above, etc. In addition to providing an integrated view of these algorithms, our framework further allows us to obtain several new convergence results, both asymptotic and in finite time, in both continuous and finite games. Specifically, we provide a range of criteria for identifying classes of Nash equilibria and sets of action profiles that are attracting with high probability, and we also introduce the notion of coherence, a game-theoretic property that includes strict and sharp equilibria, and which leads to convergence in finite time. Importantly, our analysis applies to both oracle-based and bandit, payoff-based methods - that is, when players only observe their realized payoffs.

Beatriz Borges, Negar Foroutan, Deniz Bayazit et al.

AI assistants are being increasingly used by students enrolled in higher education institutions. While these tools provide opportunities for improved teaching and education, they also pose significant challenges for assessment and learning outcomes. We conceptualize these challenges through the lens of vulnerability, the potential for university assessments and learning outcomes to be impacted by student use of generative AI. We investigate the potential scale of this vulnerability by measuring the degree to which AI assistants can complete assessment questions in standard university-level STEM courses. Specifically, we compile a novel dataset of textual assessment questions from 50 courses at EPFL and evaluate whether two AI assistants, GPT-3.5 and GPT-4 can adequately answer these questions. We use eight prompting strategies to produce responses and find that GPT-4 answers an average of 65.8% of questions correctly, and can even produce the correct answer across at least one prompting strategy for 85.1% of questions. When grouping courses in our dataset by degree program, these systems already pass non-project assessments of large numbers of core courses in various degree programs, posing risks to higher education accreditation that will be amplified as these models improve. Our results call for revising program-level assessment design in higher education in light of advances in generative AI.

Yu-Guan Hsieh, Kimon Antonakopoulos, Volkan Cevher et al.

We examine the problem of regret minimization when the learner is involved in a continuous game with other optimizing agents: in this case, if all players follow a no-regret algorithm, it is possible to achieve significantly lower regret relative to fully adversarial environments. We study this problem in the context of variationally stable games (a class of continuous games which includes all convex-concave and monotone games), and when the players only have access to noisy estimates of their individual payoff gradients. If the noise is additive, the game-theoretic and purely adversarial settings enjoy similar regret guarantees; however, if the noise is multiplicative, we show that the learners can, in fact, achieve constant regret. We achieve this faster rate via an optimistic gradient scheme with learning rate separation -- that is, the method's extrapolation and update steps are tuned to different schedules, depending on the noise profile. Subsequently, to eliminate the need for delicate hyperparameter tuning, we propose a fully adaptive method that attains nearly the same guarantees as its non-adapted counterpart, while operating without knowledge of either the game or of the noise profile.

Thomas Pethick, Olivier Fercoq, Puya Latafat et al.

This paper introduces a family of stochastic extragradient-type algorithms for a class of nonconvex-nonconcave problems characterized by the weak Minty variational inequality (MVI). Unlike existing results on extragradient methods in the monotone setting, employing diminishing stepsizes is no longer possible in the weak MVI setting. This has led to approaches such as increasing batch sizes per iteration which can however be prohibitively expensive. In contrast, our proposed methods involves two stepsizes and only requires one additional oracle evaluation per iteration. We show that it is possible to keep one fixed stepsize while it is only the second stepsize that is taken to be diminishing, making it interesting even in the monotone setting. Almost sure convergence is established and we provide a unified analysis for this family of schemes which contains a nonlinear generalization of the celebrated primal dual hybrid gradient algorithm.

Fanghui Liu, Luca Viano, Volkan Cevher

This paper provides a theoretical study of deep neural function approximation in reinforcement learning (RL) with the $ε$-greedy exploration under the online setting. This problem setting is motivated by the successful deep Q-networks (DQN) framework that falls in this regime. In this work, we provide an initial attempt on theoretical understanding deep RL from the perspective of function class and neural networks architectures (e.g., width and depth) beyond the ``linear'' regime. To be specific, we focus on the value based algorithm with the $ε$-greedy exploration via deep (and two-layer) neural networks endowed by Besov (and Barron) function spaces, respectively, which aims at approximating an $α$-smooth Q-function in a $d$-dimensional feature space. We prove that, with $T$ episodes, scaling the width $m = \widetilde{\mathcal{O}}(T^{\frac{d}{2α+ d}})$ and the depth $L=\mathcal{O}(\log T)$ of the neural network for deep RL is sufficient for learning with sublinear regret in Besov spaces. Moreover, for a two layer neural network endowed by the Barron space, scaling the width $Ω(\sqrt{T})$ is sufficient. To achieve this, the key issue in our analysis is how to estimate the temporal difference error under deep neural function approximation as the $ε$-greedy exploration is not enough to ensure ``optimism''. Our analysis reformulates the temporal difference error in an $L^2(\mathrm{d}μ)$-integrable space over a certain averaged measure $μ$, and transforms it to a generalization problem under the non-iid setting. This might have its own interest in RL theory for better understanding $ε$-greedy exploration in deep RL.

Stephen Becker, Volkan Cevher, Anastasios Kyrillidis

Affine rank minimization algorithms typically rely on calculating the gradient of a data error followed by a singular value decomposition at every iteration. Because these two steps are expensive, heuristic approximations are often used to reduce computational burden. To this end, we propose a recovery scheme that merges the two steps with randomized approximations, and as a result, operates on space proportional to the degrees of freedom in the problem. We theoretically establish the estimation guarantees of the algorithm as a function of approximation tolerance. While the theoretical approximation requirements are overly pessimistic, we demonstrate that in practice the algorithm performs well on the quantum tomography recovery problem.

Zhenyu Zhu, Fanghui Liu, Grigorios G Chrysos et al.

We study the average robustness notion in deep neural networks in (selected) wide and narrow, deep and shallow, as well as lazy and non-lazy training settings. We prove that in the under-parameterized setting, width has a negative effect while it improves robustness in the over-parameterized setting. The effect of depth closely depends on the initialization and the training mode. In particular, when initialized with LeCun initialization, depth helps robustness with the lazy training regime. In contrast, when initialized with Neural Tangent Kernel (NTK) and He-initialization, depth hurts the robustness. Moreover, under the non-lazy training regime, we demonstrate how the width of a two-layer ReLU network benefits robustness. Our theoretical developments improve the results by [Huang et al. NeurIPS21; Wu et al. NeurIPS21] and are consistent with [Bubeck and Sellke NeurIPS21; Bubeck et al. COLT21].

Luca Viano, Angeliki Kamoutsi, Gergely Neu et al.

This work develops new algorithms with rigorous efficiency guarantees for infinite horizon imitation learning (IL) with linear function approximation without restrictive coherence assumptions. We begin with the minimax formulation of the problem and then outline how to leverage classical tools from optimization, in particular, the proximal-point method (PPM) and dual smoothing, for online and offline IL, respectively. Thanks to PPM, we avoid nested policy evaluation and cost updates for online IL appearing in the prior literature. In particular, we do away with the conventional alternating updates by the optimization of a single convex and smooth objective over both cost and Q-functions. When solved inexactly, we relate the optimization errors to the suboptimality of the recovered policy. As an added bonus, by re-interpreting PPM as dual smoothing with the expert policy as a center point, we also obtain an offline IL algorithm enjoying theoretical guarantees in terms of required expert trajectories. Finally, we achieve convincing empirical performance for both linear and neural network function approximation.

Zhenyu Zhu, Fanghui Liu, Grigorios G Chrysos et al.

Neural Architecture Search (NAS) has fostered the automatic discovery of state-of-the-art neural architectures. Despite the progress achieved with NAS, so far there is little attention to theoretical guarantees on NAS. In this work, we study the generalization properties of NAS under a unifying framework enabling (deep) layer skip connection search and activation function search. To this end, we derive the lower (and upper) bounds of the minimum eigenvalue of the Neural Tangent Kernel (NTK) under the (in)finite-width regime using a certain search space including mixed activation functions, fully connected, and residual neural networks. We use the minimum eigenvalue to establish generalization error bounds of NAS in the stochastic gradient descent training. Importantly, we theoretically and experimentally show how the derived results can guide NAS to select the top-performing architectures, even in the case without training, leading to a train-free algorithm based on our theory. Accordingly, our numerical validation shed light on the design of computationally efficient methods for NAS. Our analysis is non-trivial due to the coupling of various architectures and activation functions under the unifying framework and has its own interest in providing the lower bound of the minimum eigenvalue of NTK in deep learning theory.

Zhenyu Zhu, Francesco Locatello, Volkan Cevher

This paper provides statistical sample complexity bounds for score-matching and its applications in causal discovery. We demonstrate that accurate estimation of the score function is achievable by training a standard deep ReLU neural network using stochastic gradient descent. We establish bounds on the error rate of recovering causal relationships using the score-matching-based causal discovery method of Rolland et al. [2022], assuming a sufficiently good estimation of the score function. Finally, we analyze the upper bound of score-matching estimation within the score-based generative modeling, which has been applied for causal discovery but is also of independent interest within the domain of generative models.

Ali Kavis, Stratis Skoulakis, Kimon Antonakopoulos et al.

We propose an adaptive variance-reduction method, called AdaSpider, for minimization of $L$-smooth, non-convex functions with a finite-sum structure. In essence, AdaSpider combines an AdaGrad-inspired [Duchi et al., 2011, McMahan & Streeter, 2010], but a fairly distinct, adaptive step-size schedule with the recursive stochastic path integrated estimator proposed in [Fang et al., 2018]. To our knowledge, Adaspider is the first parameter-free non-convex variance-reduction method in the sense that it does not require the knowledge of problem-dependent parameters, such as smoothness constant $L$, target accuracy $ε$ or any bound on gradient norms. In doing so, we are able to compute an $ε$-stationary point with $\tilde{O}\left(n + \sqrt{n}/ε^2\right)$ oracle-calls, which matches the respective lower bound up to logarithmic factors.

Paul Rolland, Luca Viano, Norman Schuerhoff et al.

While Reinforcement Learning (RL) aims to train an agent from a reward function in a given environment, Inverse Reinforcement Learning (IRL) seeks to recover the reward function from observing an expert's behavior. It is well known that, in general, various reward functions can lead to the same optimal policy, and hence, IRL is ill-defined. However, (Cao et al., 2021) showed that, if we observe two or more experts with different discount factors or acting in different environments, the reward function can under certain conditions be identified up to a constant. This work starts by showing an equivalent identifiability statement from multiple experts in tabular MDPs based on a rank condition, which is easily verifiable and is shown to be also necessary. We then extend our result to various different scenarios, i.e., we characterize reward identifiability in the case where the reward function can be represented as a linear combination of given features, making it more interpretable, or when we have access to approximate transition matrices. Even when the reward is not identifiable, we provide conditions characterizing when data on multiple experts in a given environment allows to generalize and train an optimal agent in a new environment. Our theoretical results on reward identifiability and generalizability are validated in various numerical experiments.

Jiayuan Ye, Zhenyu Zhu, Fanghui Liu et al.

We analytically investigate how over-parameterization of models in randomized machine learning algorithms impacts the information leakage about their training data. Specifically, we prove a privacy bound for the KL divergence between model distributions on worst-case neighboring datasets, and explore its dependence on the initialization, width, and depth of fully connected neural networks. We find that this KL privacy bound is largely determined by the expected squared gradient norm relative to model parameters during training. Notably, for the special setting of linearized network, our analysis indicates that the squared gradient norm (and therefore the escalation of privacy loss) is tied directly to the per-layer variance of the initialization distribution. By using this analysis, we demonstrate that privacy bound improves with increasing depth under certain initializations (LeCun and Xavier), while degrades with increasing depth under other initializations (He and NTK). Our work reveals a complex interplay between privacy and depth that depends on the chosen initialization distribution. We further prove excess empirical risk bounds under a fixed KL privacy budget, and show that the interplay between privacy utility trade-off and depth is similarly affected by the initialization.

Junaid Ali, Matthaeus Kleindessner, Florian Wenzel et al.

We propose a novel taxonomy for bias evaluation of discriminative foundation models, such as Contrastive Language-Pretraining (CLIP), that are used for labeling tasks. We then systematically evaluate existing methods for mitigating bias in these models with respect to our taxonomy. Specifically, we evaluate OpenAI's CLIP and OpenCLIP models for key applications, such as zero-shot classification, image retrieval and image captioning. We categorize desired behaviors based around three axes: (i) if the task concerns humans; (ii) how subjective the task is (i.e., how likely it is that people from a diverse range of backgrounds would agree on a labeling); and (iii) the intended purpose of the task and if fairness is better served by impartiality (i.e., making decisions independent of the protected attributes) or representation (i.e., making decisions to maximize diversity). Finally, we provide quantitative fairness evaluations for both binary-valued and multi-valued protected attributes over ten diverse datasets. We find that fair PCA, a post-processing method for fair representations, works very well for debiasing in most of the aforementioned tasks while incurring only minor loss of performance. However, different debiasing approaches vary in their effectiveness depending on the task. Hence, one should choose the debiasing approach depending on the specific use case.

Youngsuk Park, Kailash Budhathoki, Liangfu Chen et al.

Powerful foundation models, including large language models (LLMs), with Transformer architectures have ushered in a new era of Generative AI across various industries. Industry and research community have witnessed a large number of new applications, based on those foundation models. Such applications include question and answer, customer services, image and video generation, and code completions, among others. However, as the number of model parameters reaches to hundreds of billions, their deployment incurs prohibitive inference costs and high latency in real-world scenarios. As a result, the demand for cost-effective and fast inference using AI accelerators is ever more higher. To this end, our tutorial offers a comprehensive discussion on complementary inference optimization techniques using AI accelerators. Beginning with an overview of basic Transformer architectures and deep learning system frameworks, we deep dive into system optimization techniques for fast and memory-efficient attention computations and discuss how they can be implemented efficiently on AI accelerators. Next, we describe architectural elements that are key for fast transformer inference. Finally, we examine various model compression and fast decoding strategies in the same context.

Alexander Robey, Fabian Latorre, George J. Pappas et al.

One prominent approach toward resolving the adversarial vulnerability of deep neural networks is the two-player zero-sum paradigm of adversarial training, in which predictors are trained against adversarially chosen perturbations of data. Despite the promise of this approach, algorithms based on this paradigm have not engendered sufficient levels of robustness and suffer from pathological behavior like robust overfitting. To understand this shortcoming, we first show that the commonly used surrogate-based relaxation used in adversarial training algorithms voids all guarantees on the robustness of trained classifiers. The identification of this pitfall informs a novel non-zero-sum bilevel formulation of adversarial training, wherein each player optimizes a different objective function. Our formulation yields a simple algorithmic framework that matches and in some cases outperforms state-of-the-art attacks, attains comparable levels of robustness to standard adversarial training algorithms, and does not suffer from robust overfitting.

Yongtao Wu, Zhenyu Zhu, Fanghui Liu et al.

Neural tangent kernel (NTK) is a powerful tool to analyze training dynamics of neural networks and their generalization bounds. The study on NTK has been devoted to typical neural network architectures, but it is incomplete for neural networks with Hadamard products (NNs-Hp), e.g., StyleGAN and polynomial neural networks (PNNs). In this work, we derive the finite-width NTK formulation for a special class of NNs-Hp, i.e., polynomial neural networks. We prove their equivalence to the kernel regression predictor with the associated NTK, which expands the application scope of NTK. Based on our results, we elucidate the separation of PNNs over standard neural networks with respect to extrapolation and spectral bias. Our two key insights are that when compared to standard neural networks, PNNs can fit more complicated functions in the extrapolation regime and admit a slower eigenvalue decay of the respective NTK, leading to a faster learning towards high-frequency functions. Besides, our theoretical results can be extended to other types of NNs-Hp, which expand the scope of our work. Our empirical results validate the separations in broader classes of NNs-Hp, which provide a good justification for a deeper understanding of neural architectures.

Yongtao Wu, Fanghui Liu, Grigorios G Chrysos et al.

In this paper, we aim to build the global convergence theory of encoder-only shallow Transformers under a realistic setting from the perspective of architectures, initialization, and scaling under a finite width regime. The difficulty lies in how to tackle the softmax in self-attention mechanism, the core ingredient of Transformer. In particular, we diagnose the scaling scheme, carefully tackle the input/output of softmax, and prove that quadratic overparameterization is sufficient for global convergence of our shallow Transformers under commonly-used He/LeCun initialization in practice. Besides, neural tangent kernel (NTK) based analysis is also given, which facilitates a comprehensive comparison. Our theory demonstrates the separation on the importance of different scaling schemes and initialization. We believe our results can pave the way for a better understanding of modern Transformers, particularly on training dynamics.

Kimon Antonakopoulos, Ali Kavis, Volkan Cevher

This work proposes a universal and adaptive second-order method for minimizing second-order smooth, convex functions. Our algorithm achieves $O(σ/ \sqrt{T})$ convergence when the oracle feedback is stochastic with variance $σ^2$, and improves its convergence to $O( 1 / T^3)$ with deterministic oracles, where $T$ is the number of iterations. Our method also interpolates these rates without knowing the nature of the oracle apriori, which is enabled by a parameter-free adaptive step-size that is oblivious to the knowledge of smoothness modulus, variance bounds and the diameter of the constrained set. To our knowledge, this is the first universal algorithm with such global guarantees within the second-order optimization literature.

Ali Ramezani-Kebrya, Fanghui Liu, Thomas Pethick et al.

This paper addresses intra-client and inter-client covariate shifts in federated learning (FL) with a focus on the overall generalization performance. To handle covariate shifts, we formulate a new global model training paradigm and propose Federated Importance-Weighted Empirical Risk Minimization (FTW-ERM) along with improving density ratio matching methods without requiring perfect knowledge of the supremum over true ratios. We also propose the communication-efficient variant FITW-ERM with the same level of privacy guarantees as those of classical ERM in FL. We theoretically show that FTW-ERM achieves smaller generalization error than classical ERM under certain settings. Experimental results demonstrate the superiority of FTW-ERM over existing FL baselines in challenging imbalanced federated settings in terms of data distribution shifts across clients.

Lorenzo Brusca, Lars C. P. M. Quaedvlieg, Stratis Skoulakis et al.

This work presents a graph neural network (GNN) framework for solving the maximum independent set (MIS) problem, inspired by dynamic programming (DP). Specifically, given a graph, we propose a DP-like recursive algorithm based on GNNs that firstly constructs two smaller sub-graphs, predicts the one with the larger MIS, and then uses it in the next recursive call. To train our algorithm, we require annotated comparisons of different graphs concerning their MIS size. Annotating the comparisons with the output of our algorithm leads to a self-training process that results in more accurate self-annotation of the comparisons and vice versa. We provide numerical evidence showing the superiority of our method vs prior methods in multiple synthetic and real-world datasets.

Soumajyoti Sarkar, Leonard Lausen, Volkan Cevher et al.

Sparse Mixture of Expert (SMoE) models have emerged as a scalable alternative to dense models in language modeling. These models use conditionally activated feedforward subnetworks in transformer blocks, allowing for a separation between total model parameters and per-example computation. However, large token-routed SMoE models face a significant challenge: during inference, the entire model must be used for a sequence or a batch, resulting in high latencies in a distributed setting that offsets the advantages of per-token sparse activation. Our research explores task-specific model pruning to inform decisions about designing SMoE architectures, mainly modulating the choice of expert counts in pretraining. We investigate whether such pruned models offer advantages over smaller SMoE models trained from scratch, when evaluating and comparing them individually on tasks. To that end, we introduce an adaptive task-aware pruning technique UNCURL to reduce the number of experts per MoE layer in an offline manner post-training. Our findings reveal a threshold pruning factor for the reduction that depends on the number of experts used in pretraining, above which, the reduction starts to degrade model performance. These insights contribute to our understanding of model design choices when pretraining with SMoE architectures, particularly useful when considering task-specific inference optimization for later stages.

Thomas Pethick, Wanyun Xie, Volkan Cevher

This paper presents a theoretical analysis of linear interpolation as a principled method for stabilizing (large-scale) neural network training. We argue that instabilities in the optimization process are often caused by the nonmonotonicity of the loss landscape and show how linear interpolation can help by leveraging the theory of nonexpansive operators. We construct a new optimization scheme called relaxed approximate proximal point (RAPP), which is the first explicit method without anchoring to achieve last iterate convergence rates for $ρ$-comonotone problems while only requiring $ρ> -\tfrac{1}{2L}$. The construction extends to constrained and regularized settings. By replacing the inner optimizer in RAPP we rediscover the family of Lookahead algorithms for which we establish convergence in cohypomonotone problems even when the base optimizer is taken to be gradient descent ascent. The range of cohypomonotone problems in which Lookahead converges is further expanded by exploiting that Lookahead inherits the properties of the base optimizer. We corroborate the results with experiments on generative adversarial networks which demonstrates the benefits of the linear interpolation present in both RAPP and Lookahead.

Thomas Pethick, Grigorios G. Chrysos, Volkan Cevher

Despite progress in adversarial training (AT), there is a substantial gap between the top-performing and worst-performing classes in many datasets. For example, on CIFAR10, the accuracies for the best and worst classes are 74% and 23%, respectively. We argue that this gap can be reduced by explicitly optimizing for the worst-performing class, resulting in a min-max-max optimization formulation. Our method, called class focused online learning (CFOL), includes high probability convergence guarantees for the worst class loss and can be easily integrated into existing training setups with minimal computational overhead. We demonstrate an improvement to 32% in the worst class accuracy on CIFAR10, and we observe consistent behavior across CIFAR100 and STL10. Our study highlights the importance of moving beyond average accuracy, which is particularly important in safety-critical applications.

Volkan Cevher, Georgios Piliouras, Ryann Sim et al.

In this paper we present a first-order method that admits near-optimal convergence rates for convex/concave min-max problems while requiring a simple and intuitive analysis. Similarly to the seminal work of Nemirovski and the recent approach of Piliouras et al. in normal form games, our work is based on the fact that the update rule of the Proximal Point method (PP) can be approximated up to accuracy $ε$ with only $O(\log 1/ε)$ additional gradient-calls through the iterations of a contraction map. Then combining the analysis of (PP) method with an error-propagation analysis we establish that the resulting first order method, called Clairvoyant Extra Gradient, admits near-optimal time-average convergence for general domains and last-iterate convergence in the unconstrained case.

Fanghui Liu, Luca Viano, Volkan Cevher

In online reinforcement learning (RL), instead of employing standard structural assumptions on Markov decision processes (MDPs), using a certain coverage condition (original from offline RL) is enough to ensure sample-efficient guarantees (Xie et al. 2023). In this work, we focus on this new direction by digging more possible and general coverage conditions, and study the potential and the utility of them in efficient online RL. We identify more concepts, including the $L^p$ variant of concentrability, the density ratio realizability, and trade-off on the partial/rest coverage condition, that can be also beneficial to sample-efficient online RL, achieving improved regret bound. Furthermore, if exploratory offline data are used, under our coverage conditions, both statistically and computationally efficient guarantees can be achieved for online RL. Besides, even though the MDP structure is given, e.g., linear MDP, we elucidate that, good coverage conditions are still beneficial to obtain faster regret bound beyond $\widetilde{O}(\sqrt{T})$ and even a logarithmic order regret. These results provide a good justification for the usage of general coverage conditions in efficient online RL.

Aram Davtyan, Leello Tadesse Dadi, Volkan Cevher et al.

Conditional Flow Matching (CFM), a simulation-free method for training continuous normalizing flows, provides an efficient alternative to diffusion models for key tasks like image and video generation. The performance of CFM in solving these tasks depends on the way data is coupled with noise. A recent approach uses minibatch optimal transport (OT) to reassign noise-data pairs in each training step to streamline sampling trajectories and thus accelerate inference. However, its optimization is restricted to individual minibatches, limiting its effectiveness on large datasets. To address this shortcoming, we introduce LOOM-CFM (Looking Out Of Minibatch-CFM), a novel method to extend the scope of minibatch OT by preserving and optimizing these assignments across minibatches over training time. Our approach demonstrates consistent improvements in the sampling speed-quality trade-off across multiple datasets. LOOM-CFM also enhances distillation initialization and supports high-resolution synthesis in latent space training.

Ali Ramezani-Kebrya, Kimon Antonakopoulos, Igor Krawczuk et al.

We consider monotone variational inequality (VI) problems in multi-GPU settings where multiple processors/workers/clients have access to local stochastic dual vectors. This setting includes a broad range of important problems from distributed convex minimization to min-max and games. Extra-gradient, which is a de facto algorithm for monotone VI problems, has not been designed to be communication-efficient. To this end, we propose a quantized generalized extra-gradient (Q-GenX), which is an unbiased and adaptive compression method tailored to solve VIs. We provide an adaptive step-size rule, which adapts to the respective noise profiles at hand and achieve a fast rate of ${\mathcal O}(1/T)$ under relative noise, and an order-optimal ${\mathcal O}(1/\sqrt{T})$ under absolute noise and show distributed training accelerates convergence. Finally, we validate our theoretical results by providing real-world experiments and training generative adversarial networks on multiple GPUs.

Yongtao Wu, Grigorios G Chrysos, Volkan Cevher

Time-frequency (TF) representations in audio synthesis have been increasingly modeled with real-valued networks. However, overlooking the complex-valued nature of TF representations can result in suboptimal performance and require additional modules (e.g., for modeling the phase). To this end, we introduce complex-valued polynomial networks, called APOLLO, that integrate such complex-valued representations in a natural way. Concretely, APOLLO captures high-order correlations of the input elements using high-order tensors as scaling parameters. By leveraging standard tensor decompositions, we derive different architectures and enable modeling richer correlations. We outline such architectures and showcase their performance in audio generation across four benchmarks. As a highlight, APOLLO results in $17.5\%$ improvement over adversarial methods and $8.2\%$ over the state-of-the-art diffusion models on SC09 dataset in audio generation. Our models can encourage the systematic design of other efficient architectures on the complex field.

Luca Viano, Till Freihaut, Emanuele Nevali et al.

In this work, we present the first theoretical analysis of multi-agent imitation learning (MAIL) in linear Markov games where both the transition dynamics and each agent's reward function are linear in some given features. We demonstrate that by leveraging this structure, it is possible to replace the state-action level "all policy deviation concentrability coefficient" (Freihaut et al., arXiv:2510.09325) with a concentrability coefficient defined at the feature level which can be much smaller than the state-action analog when the features are informative about states' similarity. Furthermore, to circumvent the need for any concentrability coefficient, we turn to the interactive setting. We provide the first, computationally efficient, interactive MAIL algorithm for linear Markov games and show that its sample complexity depends only on the dimension of the feature map $d$. Building on these theoretical findings, we propose a deep MAIL interactive algorithm which clearly outperforms BC on games such as Tic-Tac-Toe and Connect4.

Rustem Islamov, Roman Machacek, Aurelien Lucchi et al.

We study the role of batch size in stochastic conditional gradient methods under a $μ$-Kurdyka-Łojasiewicz ($μ$-KL) condition. Focusing on momentum-based stochastic conditional gradient algorithms (e.g., Scion), we derive a new analysis that explicitly captures the interaction between stepsize, batch size, and stochastic noise. Our study reveals a regime-dependent behavior: increasing the batch size initially improves optimization accuracy but, beyond a critical threshold, the benefits saturate and can eventually degrade performance under a fixed token budget. Notably, the theory predicts the magnitude of the optimal stepsize and aligns well with empirical practices observed in large-scale training. Leveraging these insights, we derive principled guidelines for selecting the batch size and stepsize, and propose an adaptive strategy that increases batch size and sequence length during training while preserving convergence guarantees. Experiments on NanoGPT are consistent with the theoretical predictions and illustrate the emergence of the predicted scaling regimes. Overall, our results provide a theoretical framework for understanding batch size scaling in stochastic conditional gradient methods and offer guidance for designing efficient training schedules in large-scale optimization.

Antoine Bergerault, Volkan Cevher, Negar Mehr

Multi-agent imitation learning (MA-IL) aims to learn optimal policies from expert demonstrations of interactions in multi-agent interactive domains. Despite existing guarantees on the performance of the resulting learned policies, characterizations of how far the learned polices are from a Nash equilibrium are missing for offline MA-IL. In this paper, we demonstrate impossibility and hardness results of learning low-exploitable policies in general $n$-player Markov Games. We do so by providing examples where even exact measure matching fails, and demonstrating a new hardness result on characterizing the Nash gap given a fixed measure matching error. We then show how these challenges can be overcome using strategic dominance assumptions on the expert equilibrium. Specifically, for the case of dominant strategy expert equilibria, assuming Behavioral Cloning error $ε_{\text{BC}}$, this provides a Nash imitation gap of $\mathcal{O}\left(nε_{\text{BC}}/(1-γ)^2\right)$ for a discount factor $γ$. We generalize this result with a new notion of best-response continuity, and argue that this is implicitly encouraged by standard regularization techniques.

Roy Rinberg, Pol Puigdemont, Martin Pawelczyk et al.

Evaluating machine unlearning methods remains technically challenging, with recent benchmarks requiring complex setups and significant engineering overhead. We introduce a unified and extensible benchmarking suite that simplifies the evaluation of unlearning algorithms using the KLoM (KL divergence of Margins) metric. Our framework provides precomputed model ensembles, oracle outputs, and streamlined infrastructure for running evaluations out of the box. By standardizing setup and metrics, it enables reproducible, scalable, and fair comparison across unlearning methods. We aim for this benchmark to serve as a practical foundation for accelerating research and promoting best practices in machine unlearning. Our code and data are publicly available.

Adam Barla, Emanuele Nevali, Luca Viano et al.

We introduce PEPO (Pessimistic Ensemble based Preference Optimization), a single-step Direct Preference Optimization (DPO)-like algorithm to mitigate the well-known over-optimization issue in preference learning without requiring the knowledge of the data-generating distribution or learning an explicit reward model. PEPO achieves pessimism via an ensemble of preference-optimized policies trained on disjoint data subsets and then aggregates them through a worst case construction that favors the agreement across models. In the tabular setting, PEPO achieves sample complexity guarantees depending only on a single-policy concentrability coefficient, thus avoiding the all-policy concentrability which affects the guarantees of algorithms prone to over-optimization, such as DPO. The theoretical findings are corroborated by a convincing practical performance, while retaining the simplicity and the practicality of DPO-style training.

Thomas Pethick, Kimon Antonakopoulos, Antonio Silveti-Falls et al.

This article reviews modern optimization methods for training neural networks with an emphasis on efficiency and scale. We present state-of-the-art optimization algorithms under a unified algorithmic template that highlights the importance of adapting to the structures in the problem. We then cover how to make these algorithms agnostic to the scale of the problem. Our exposition is intended as an introduction for both practitioners and researchers who wish to be involved in these exciting new developments.

Thomas Pethick, Wanyun Xie, Kimon Antonakopoulos et al.

In this work, we study optimization methods that leverage the linear minimization oracle (LMO) over a norm-ball. We propose a new stochastic family of algorithms that uses the LMO to adapt to the geometry of the problem and, perhaps surprisingly, show that they can be applied to unconstrained problems. The resulting update rule unifies several existing optimization methods under a single framework. Furthermore, we propose an explicit choice of norm for deep architectures, which, as a side benefit, leads to the transferability of hyperparameters across model sizes. Experimentally, we demonstrate significant speedups on nanoGPT training using our algorithm, Scion, without any reliance on Adam. The proposed method is memory-efficient, requiring only one set of model weights and one set of gradients, which can be stored in half-precision. The code is available at https://github.com/LIONS-EPFL/scion .

Zhan Li, Yongtao Wu, Yihang Chen et al.

Large vision-language models (VLLMs) exhibit promising capabilities for processing multi-modal tasks across various application scenarios. However, their emergence also raises significant data security concerns, given the potential inclusion of sensitive information, such as private photos and medical records, in their training datasets. Detecting inappropriately used data in VLLMs remains a critical and unresolved issue, mainly due to the lack of standardized datasets and suitable methodologies. In this study, we introduce the first membership inference attack (MIA) benchmark tailored for various VLLMs to facilitate training data detection. Then, we propose a novel MIA pipeline specifically designed for token-level image detection. Lastly, we present a new metric called MaxRényi-K%, which is based on the confidence of the model output and applies to both text and image data. We believe that our work can deepen the understanding and methodology of MIAs in the context of VLLMs. Our code and datasets are available at https://github.com/LIONS-EPFL/VL-MIA.

Diganta Misra, Antonio Orvieto, Rediet Abebe et al.

Large language models are increasingly deployed as automated judges to evaluate the strength of arguments. As this role expands, their legitimacy depends on consistency, transparency, and the ability to separate argumentative structure from rhetorical appeal. However, we show that holistic judging - a common LLM-as-a-Judge practice where a model provides a global verdict on a debate - suffers from substantial inter-model disagreement. We argue that this instability arises from collapsing a debate's complex interaction structure into a single opaque score. To address this, we propose GRASP (Gradual Ranking with Attacks and Support Propagation), a deterministic framework that aggregates stable local interaction judgments into a global ranking via a convergent attack--defense propagation operator. We show that local interaction judgments are more reproducible than holistic rankings in LLM-as-a-Judge evaluations, allowing GRASP to produce more consistent global rankings. We further show that GRASP scores do not correlate with human "convincingness" labels, highlighting a vital sociotechnical distinction: GRASP does not measure persuasion, factuality, or rhetorical appeal, but structural sufficiency - a defense-aware notion of argument robustness over the explicit interaction graph. Overall, GRASP offers a transparent and auditable alternative to holistic LLM judging.

Thomas Pethick, Wanyun Xie, Mete Erdogan et al.

This work introduces a hybrid non-Euclidean optimization method which generalizes gradient norm clipping by combining steepest descent and conditional gradient approaches. The method achieves the best of both worlds by establishing a descent property under a generalized notion of ($L_0$,$L_1$)-smoothness. Weight decay is incorporated in a principled manner by identifying a connection to the Frank-Wolfe short step. In the stochastic case, we show an order optimal $O(n^{-1/4})$ convergence rate by leveraging a momentum based gradient estimator. We discuss how to instantiate the algorithms for deep learning, which we dub Clipped Scion, and demonstrate their properties on image classification and language modeling. The code is available at https://github.com/LIONS-EPFL/ClippedScion.

Leyla Naz Candogan, Yongtao Wu, Elias Abad Rocamora et al.

Defending aligned Large Language Models (LLMs) against jailbreaking attacks is a challenging problem, with existing approaches requiring multiple requests or even queries to auxiliary LLMs, making them computationally heavy. Instead, we focus on detecting jailbreaking input in a single forward pass. Our method, called Single Pass Detection SPD, leverages the information carried by the logits to predict whether the output sentence will be harmful. This allows us to defend in just one forward pass. SPD can not only detect attacks effectively on open-source models, but also minimizes the misclassification of harmless inputs. Furthermore, we show that SPD remains effective even without complete logit access in GPT-3.5 and GPT-4. We believe that our proposed method offers a promising approach to efficiently safeguard LLMs against adversarial attacks.