论文检索

Deep Learning · Self-Supervised Learning

Zhiyuan Li, Rongzhen Zhao, Wenyan Yang, Wenshuai Zhao, Pekka Marttinen, Joni Pajarinen

The de facto approach in video object-centric learning maintains temporal consistency through learned dynamics modules that predict future object representations, called slots. We demonstrate that these predictors function as expensive approximations of discrete correspondence problems. Modern self-supervised vision backbones already encode instance-discriminative features that distinguish objects reliably. Exploiting these features eliminates the need for learned temporal prediction. We introduce Grounded Correspondence, a framework that replaces learned transition functions with deterministic bipartite matching. Slots initialize from salient regions in frozen backbone features. Frame-to-frame identity is maintained through Hungarian matching on slot representations. The approach requires zero learnable parameters for temporal modeling yet achieves competitive performance on MOVi-D, MOVi-E, and YouTube-VIS. Project page: https://magenta-sherbet-85b101.netlify.app/

General Machine Learning · Scalable Algorithms

Alessandro Manenti, Kumar Avinava Dubey, Arijit Sehanobish, Cesare Alippi, Krzysztof Choromanski

We propose SWING: Space Walks for Implicit Network Graphs, a new class of algorithms for computations involving Graph Random Features on graphs given by implicit representations (i-graphs), where edge-weights are defined as bi-variate functions of feature vectors in the corresponding nodes. Those classes of graphs include several prominent examples, such as: *$\epsilon$-neighborhood* graphs, used on regular basis in machine learning. Rather than conducting walks on graphs' nodes, those methods rely on walks in continuous spaces, in which those graphs are embedded. To accurately and efficiently approximate original combinatorial calculations, SWING applies customized Gumbel-softmax sampling mechanism with linearized kernels, obtained via random features coupled with importance sampling techniques. This mechanism is of its own interest. SWING relies on the deep connection between implicitly defined graphs and Fourier analysis, presented in this paper. SWING is accelerator-friendly and does not require input graph materialization. We provide detailed analysis of SWING and complement it with thorough experiments on different classes of i-graphs.

Deep Learning · Generative Models and Autoencoders

Feiyang Fu, Hehe Fan

Discrete flow matching (DFM) provides a principled framework for generative modeling on discrete state spaces via continuous-time Markov chain dynamics. In practice, sampling for DFM commonly employs discretizations such as $\tau$-leaping, yet efficient sampling methods under a limited number of function evaluations (NFE) remain less studied. To address this gap, we propose the Time-Reparameterized Cumulative Intensity Extrapolation (TR-CIE) sampler, which aims to improve sampling quality when function evaluations are restricted. TR-CIE consists of two components. First, a schedule-based time reparameterization rescales the time grid according to the noise schedule. Under standard factorized DFM rate parameterizations, this transformation of variables absorbs the schedule-dependent growth term and mitigates stiffness near the terminal sampling stage. Second, we introduce a cumulative-intensity extrapolation updating rule. By reusing cached model outputs from the previous step as a history term, this improves the approximation of stepwise cumulative intensities on the resulting non-uniform time grid. We provide a theoretical analysis that bounds the local approximation error of cumulative intensities and establishes convergence results. The resulting sampler requires one NFE per step and introduces no additional model evaluations compared to the standard $\tau$-leaping sampler. Extensive experiments on synthetic tasks, text generation, and text-to-image benchmarks demonstrate that our method improves sampling quality under limited NFE.

Social Aspects · Accountability, Transparency, and Interpretability

Maxime Méloux, François Portet, Maxime Peyrard

Mechanistic Interpretability (MI) aims to reverse-engineer model behaviors by identifying functional sub-networks. Yet, the scientific validity of these findings depends on their stability. In this work, we argue that circuit discovery is not a standalone task but a statistical estimation problem built upon causal mediation analysis (CMA). We uncover a fundamental instability at this base layer: exact, single-input CMA scores exhibit high intrinsic variance, implying that the causal effect of a component is a volatile random variable rather than a fixed property. We then demonstrate that circuit discovery pipelines inherit this variance and further amplify it. Fast approximation methods, such as Edge Attribution Patching and its successors, introduce additional estimation noise, while aggregating these noisy scores over datasets leads to fragile structural estimates. Consequently, small perturbations in input data or hyperparameters yield vastly different circuits. We systematically decompose these sources of variance and advocate for more rigorous MI practices, prioritizing statistical robustness and routine reporting of stability metrics.

General Machine Learning · Scalable Algorithms

Haike Xu, Sandeep Silwal, Piotr Indyk

We propose a new ``bi-metric'' framework for designing nearest neighbor data structures. Our framework assumes two dissimilarity functions: a ground-truth metric that is accurate but expensive to compute, and a proxy metric that is cheaper but less accurate. In both theory and practice, we show how to construct data structures using only the proxy metric such that the query procedure achieves the accuracy of the expensive metric, while only using a limited number of calls to both metrics. Our theoretical results instantiate this framework for two popular nearest neighbor search algorithms: DiskANN and Cover Tree. In both cases we show that, as long as the proxy metric used to construct the data structure approximates the ground-truth metric up to a bounded factor, our data structure achieves arbitrarily good approximation guarantees with respect to the ground-truth metric. On the empirical side, we apply the framework to the text retrieval problem with two dissimilarity functions evaluated by ML models with vastly different computational costs. We observe that for almost all the large data sets in the BEIR benchmark, our approach achieves a considerably better accuracy-efficiency tradeoff than the alternatives, such as retrieve-then-rerank.

Deep Learning · Large Language Models

Yepeng Liu, Yu Huang, Yu-Xiang Wang, Yingbin LIANG, Yuheng Bu

Convexity recognition plays a central role in many optimization, control, and learning problems. However, the ability of Large Language Models (LLMs) to identify this property in symbolic expressions remains unexamined. We introduce \cb, a scalable and mechanically verifiable benchmark for testing whether LLMs can determine the convexity of a symbolic objective under deep functional composition. Experiments on frontier LLMs reveal a sharp \textit{compositional reasoning gap}: performance degrades rapidly with increasing depth, dropping from an F1-score of $1.0$ at depth $2$ to approximately $0.2$ at depth $100$. Inspection of models' reasoning traces indicates two failure modes: \textit{parsing failure} and \textit{lazy reasoning}. To address these limitations, we propose an agentic divide-and-conquer framework that (i) offloads parsing to an external tool to construct an abstract syntax tree (AST) and (ii) enforces recursive reasoning over each intermediate sub-expression with focused context. This framework reliably mitigates deep-composition failures, achieving substantial performance improvement at large depths (e.g., F1-Score $= 1.0$ at depth $100$).

Theory · Reinforcement Learning and Planning

Ruiquan Huang, Donghao Li, Yingbin LIANG, Jing Yang

Reinforcement learning (RL) is a fundamental framework for sequential decision-making, in which an agent learns an optimal policy through interactions with an unknown environment. In settings with function approximation, many existing RL algorithms achieve favorable sample complexity, but often rely on computationally intractable oracles. In this paper, we use supervised learning as a computational proxy to establish a clear hierarchy of commonly adopted RL oracles under low-rank Markov Decision Processes (MDPs). This hierarchy shows that policy evaluation is the most computationally efficient oracle, provided that supervised learning can be efficiently solved. Motivated by this observation, we propose a novel optimistic actor–critic algorithm that relies solely on the policy evaluation oracle. We prove that our algorithm outperforms the existing sample complexity guarantees for low-rank MDPs while avoiding computationally expensive planning or optimization oracles commonly assumed in prior works. We further extend our theoretical results to approximately low-rank MDPs and demonstrate that this setting captures a broad class of real-world environments. Finally, we validate our theoretical results with experiments on several standard Gym benchmarks.

Theory · Reinforcement Learning and Planning

Haoxing Tian, Zaiwei Chen, Ioannis Paschalidis, Alex Olshevsky

The analysis of Temporal Difference (TD) learning in the average-reward setting faces notable theoretical difficulties because the Bellman operator is not contractive with respect to any norm. This complicates standard analyses of stochastic updates that are effective in discounted settings. Although a considerable body of literature addresses these challenges, existing theoretical approaches come with limitations. We introduce a novel algorithm designed explicitly for policy evaluation in the average-reward setting, utilizing sampling from two Markovian trajectories. Our proposed method overcomes previous limitations by guaranteeing convergence to the unique solution of a properly defined projected Bellman equation. Notably, and in contrast to earlier work, our convergence analysis is uniformly applicable to both linear function approximation and tabular settings and does not involve explicit dimension-dependent terms in its convergence bounds. These results align with what is known to hold in the discounted setting. Furthermore, our algorithm achieves improved dependence on the problem's condition number, reducing the sample complexity from quartic, as in prior literature, to quadratic scaling, and thus matching the efficiency seen in the discounted setting.

Deep Learning · Theory

Yijin Zhou, Yutang Ge, Wenyuan XIE, Linqian Zeng, Xiaowen Dong, Yuguang Wang

Transformers excel in natural language processing and computer vision tasks. However, they still face challenges in generalizing to Out-of-Distribution (OOD) datasets, i.e. data whose distribution differs from that seen during training. OOD detection aims to distinguish outliers while preserving in-distribution (ID) data performance. This paper introduces the OOD detection Probably Approximately Correct (PAC) Theory for transformers, which establishes the conditions for data distribution and model configurations for the OOD detection learnability of transformers. It shows that outliers can be accurately represented and distinguished with sufficient data under conditions. The theoretical implications highlight the trade-off between theoretical principles and practical training paradigms. By examining this trade-off, we naturally derived the rationale for leveraging auxiliary outliers to enhance OOD detection. Our theory suggests that by penalizing the misclassification of outliers within the loss function and strategically generating soft synthetic outliers, one can robustly bolster the reliability of transformer networks. This approach yields a novel algorithm that ensures learnability and refines the decision boundaries between inliers and outliers. In practice, the algorithm consistently achieves state-of-the-art (SOTA) performance across various data formats.

Theory · Learning Theory

Kedar Karhadkar, Alexander Sietsema, Deanna Needell, Guido Montufar

Motivated by recent work on benign overfitting in overparameterized machine learning, we study the generalization behavior of functions in Sobolev spaces $W^{k, p}(\mathbb{R}^d)$ that perfectly fit a noisy training data set. Under assumptions of label noise and sufficient regularity in the data distribution, we show that approximately norm-minimizing interpolators, which are canonical solutions selected by smoothness bias, exhibit harmful overfitting: even as the training sample size $n \to \infty$, the generalization error remains bounded below by a positive constant with high probability. Our results hold for arbitrary values of $p \in [1, \infty)$, in contrast to prior results studying the Hilbert space case ($p = 2$) using kernel methods. Our proof uses a geometric argument which identifies harmful neighborhoods of the training data using Sobolev inequalities.

General Machine Learning · Methodology

CHAO WANG, Luca Nepote, Giulio Franzese, Pietro Michiardi

Trajectory Inference (TI) seeks to reconstruct latent dynamical processes from snapshot data, which consist of independent samples from time-indexed marginals of an underlying stochastic system. In applications such as single-cell genomics, destructive measurements preclude direct observation of trajectories, making the induced distribution over paths fundamentally ill-posed given finitely many marginals. However, despite extensive work on modeling approaches, little attention has been paid to evaluating the inferred object itself, namely, a probability measure over trajectories. Since path-space laws are not identifiable from snapshot data, evaluation protocols based on predictive accuracy at held-out marginals provide only limited information and fail to constrain trajectory-level behavior. We introduce a general framework for estimating the Kullback–Leibler divergence (KL) between probability measures on function space: we obtain a tractable estimator that can be approximated from data, is practical, and scales to realistic problem sizes (number and size of snapshot data). We apply this framework to a systematic empirical study of trajectory inference methods on synthetic and real datasets. We show that current evaluation metrics yield inconsistent assessments, whereas path-space KL provides a coherent comparison that reveals discrepancies in inferred dynamics, particularly in regions with sparse or missing data. These results support the use of functional KL as a principled criterion for evaluating TI methods under partial observability.

Theory · Reinforcement Learning and Planning

Orin Levy, Yishay Mansour

We present the first high-probability optimal regret bound for a policy optimization technique applied to the problem of stochastic contextual multi-armed bandit (CMAB) with general offline function approximation. Our algorithm is both efficient and achieves an optimal regret bound of $\widetilde{O}(\sqrt{ K|\mathcal{A}|\log|\mathcal{F}|})$, where $K$ is the number of rounds, $\mathcal{A}$ is the set of arms, and $\mathcal{F}$ is the function class used to approximate the losses. Our results bridge the gap between theory and practice, demonstrating that the widely used policy optimization methods for the contextual bandit problem can achieve a rigorously-proved optimal regret bound. We support our theoretical results with an empirical evaluation of our algorithm.

Deep Learning · Generative Models and Autoencoders

Jerry Huang, Justin Lin, Sheel Shah, Kartik Nair, Nicholas Boffi

In generative modeling, we often wish to produce samples that satisfy a user-specified reward such as measurement consistency, aesthetic quality, or alignment with human intent, a problem known as inference-time guidance. While flow-based models enable high-quality generation, existing guidance methods either require expensive multi-particle, many-step schemes to sample from a reward-tilted distribution or rely on heuristic approximations. To design efficient algorithms, we instead reformulate guidance as a deterministic optimal control problem, rather than the stochastic control problem from which the reward tilt emerges. We find that the flow map arises naturally in the optimal solution, and that many existing flow-based guidance methods are best understood as coarse approximations that replace it with a single Euler step. Rather than relying on these approximations, we propose Flow Map Trajectory Guidance (FMTG): a principled framework that uses the flow map to both integrate and guide, enabling training-free alignment in just a few network evaluations. We demonstrate FMTG at text-to-image scale using a FLUX.1-distilled flow map, showing that it achieves comparable performance to baselines across inverse problems and image editing tasks with up to 10 times fewer function evaluations.

Deep Learning · Algorithms

Shenghao Yang, Zhichao Wang, Oleg Balabanov, N. Benjamin Erichson, Michael Mahoney

Matrix functions such as square root, inverse roots, and orthogonalization play a central role in preconditioned gradient methods for neural network training. This has motivated the development of iterative algorithms that avoid explicit eigendecompositions and rely primarily on matrix multiplications, making them well suited for modern GPU accelerators. We present PRISM (Polynomial-fitting and Randomized Iterative Sketching for Matrix functions computation), a general framework for accelerating iterative algorithms for computing matrix functions. PRISM combines adaptive polynomial approximation with randomized sketching: at each iteration, it fits a polynomial surrogate to the current spectrum via a sketched least-squares problem, adapting to the instance at hand with minimal overhead. We apply PRISM to accelerate Newton–Schulz-like iterations for matrix square roots and orthogonalization, which are core primitives in machine learning. Unlike prior methods, PRISM requires no explicit spectral bounds or singular value estimates; it adapts automatically to the evolving spectrum. Empirically, PRISM accelerates training when integrated into Shampoo and Muon optimizers.

Probabilistic Methods · Monte Carlo and Sampling Methods

James Cuin, Davide Carbone, Yanbo Tang, O. Akyildiz

The problem of optimising functions with intractable gradients frequently arise in machine learning and statistics, ranging from maximum marginal likelihood estimation procedures to fine-tuning of generative models. Stochastic approximation methods for this class of problems typically require inner sampling loops to obtain (biased) stochastic gradient estimates, which rapidly becomes computationally expensive. In this work, we develop sequential Monte Carlo (SMC) samplers for optimisation of functions with intractable gradients. Our approach replaces expensive inner sampling methods with efficient SMC approximations, which can result in significant computational gains. We establish convergence results for the basic recursions defined by our methodology which SMC samplers approximate. We demonstrate the effectiveness of our approach on the reward-tuning of energy-based models within various settings.

Theory · Learning Theory

Xin He, Yuling Jiao, Xiliang Lu, Jerry Yang

We explore the expressive power of Transformers by establishing precise approximation error upper and lower bounds for Hölder class. Specifically, a new approximation upper bound is derived for the standard Transformer architecture equipped with Softmax operators, ReLU activation functions, and residual connections. We prove that a Transformer network composed of at most $\mathcal{O}(\varepsilon^{-{d_{0}}/{\alpha}})$ blocks can approximate any bounded Hölder function with $d_{0}$-dimensional input and smoothness $\alpha\in(0,1]$ under any accuracy $\varepsilon>0$. In the case of approximation lower bounds, leveraging the VC-dimension upper bound, we are the first to rigorously prove that Transformers demand for at least $\mathcal{O}(\varepsilon^{-{d_{0}}/({4\alpha})})$ blocks to achieve the $\varepsilon$ approximation accuracy. As a final step, we extend the derived results for standard Transformers to a general regression task and establish the corresponding excess risk rates demonstrating Transformers' empirical effectiveness in real-world settings.

Optimization · Everything Else

Artem Artemev, Rui Xia, Benjamin M. Boyd, Youjing Yu, Felix Dangel, Guillaume Hennequin, Alberto Bernacchia

Many machine learning techniques rely on approximating a loss function's curvature, but this is notoriously hard to do at the scale of modern deep networks. Surprisingly, no previous work has exploited the curvature constraints that arise from well known weight-space symmetries in loss landscapes. By analytically averaging over group actions that leave the loss invariant, we construct structured Hessian approximations from single gradients that can be tractably estimated, stored, and inverted. The choice of user-specified symmetry group directly governs the trade-off between approximation accuracy and computational cost. Moreover, our framework provides a unifying theoretical lens for viewing existing methods; in particular, a specific choice of symmetry group recovers Shampoo/Muon-like curvature estimates. We validate our method on a range of network architectures, and deploy it to second-order optimization benchmarks, including a small language model. Our curvature estimation framework might find applications in other machine learning problems such as uncertainty estimation, continual learning, compression/pruning, training data attribution, and more.

Maosen Tang, Alex Townsend

We study neural networks with trainable low-degree rational activation functions and show that they are more expressive and parameter-efficient than modern piecewise-linear and smooth activations such as ELU, LeakyReLU, LogSigmoid, PReLU, ReLU, SELU, CELU, Sigmoid, SiLU, Mish, Softplus, Tanh, Softmin, Softmax, and LogSoftmax. For an error target of $\varepsilon>0$, we establish approximation-theoretic separations: Any network built from standard fixed activations can be uniformly approximated on compact domains by a rational-activation network with only $\mathrm{poly}(\log\log(1/\varepsilon))$ overhead in size, while the converse provably requires $\Omega(\log(1/\varepsilon))$ parameters in the worst case. This exponential gap persists at the level of full networks and extends to gated activations and transformer-style nonlinearities. In practice, rational activations integrate seamlessly into standard architectures and training pipelines, allowing rationals to match or outperform fixed activations under identical architectures and optimizers.

Deep Learning · Large Language Models

Yilang Zhang, Xiaodong Yang, Yiwei Cai, Georgios B. Giannakis

As large language models (LLMs) continue to scale in size, the computational overhead has become a major bottleneck for task-specific fine-tuning. While low-rank adaptation (LoRA) effectively curtails this cost by confining the weight updates to a low-dimensional subspace, such a restriction can hinder effectiveness and slow convergence. This contribution deals with these limitations by accumulating progressively a high-rank weight update from consecutive low-rank increments. Specifically, the per update optimal low-rank matrix is identified to minimize the loss function and closely approximate full fine-tuning. To endow efficient and seamless optimization without restarting, this optimal choice is formed by appropriately scaling the columns of the original low-rank matrix. Rigorous performance guarantees reveal that the optimal scaling can be found analytically. Extensive numerical tests with popular LLMs scaling up to 12 billion parameters demonstrate a consistent performance gain and fast convergence relative to state-of-the-art LoRA variants on diverse tasks including natural language understanding, commonsense reasoning, and mathematical problem solving.

Reinforcement Learning · Everything Else

Aneri Muni, Vincent Taboga, Esther Derman, Pierre-Luc Bacon, Erick Delage

Tail-end risk measures such as static conditional value-at-risk (CVaR) are used in safety-critical applications to prevent rare, yet catastrophic events. Unlike risk-neutral objectives, the static CVaR of the return depends on entire trajectories without admitting a recursive Bellman decomposition in the underlying Markov decision process. A classical resolution relies on state augmentation with a continuous variable. However, unless restricted to a specialized class of admissible value functions, this formulation induces sparse rewards and degenerate fixed points. In this work, we propose a novel formulation of the static CVaR objective based on augmentation. Our alternative approach leads to a Bellman operator with: (1) dense per-step rewards; (2) contracting properties on the full space of bounded value functions. Building on this theoretical foundation, we develop risk-averse value iteration and model-free Q-learning algorithms that rely on discretized augmented states. We further provide convergence guarantees and approximation error bounds due to discretization. Empirical results demonstrate that our algorithms successfully learn CVaR-sensitive policies and achieve effective performance-safety trade-offs.