GenAI4ELab/papercli-papers huggingface dataset:
Modelling Populations of Interaction Networks via Distance Metrics
Authors: George Bolt; SimÃ³n LunagÃ³mez; Christopher Nemeth
Venue: JMLR 2025 (main)

Abstract: Network data arises through the observation of relational information between a collection of entities, for example, friendships (relations) amongst a sample of people (entities). Traditionally, statistical models of such data have been developed to analyse a single network, that is, a single collection of entities and relations. More recently, attention has shifted to analysing samples of networks. A driving force has been the analysis of connectome data, arising in neuroscience applications, where a single network is observed for each patient in a study. These models typically assume, within each network, the entities are the units of observation, that is, more data equates to including more entities. However, an alternative paradigm considers relationsâsuch as edges or pathsâas the observational units, exemplified by email exchanges or user navigations across a website. This interaction network framework has generally been applied to single networks, without extending to the case where multiple such networks are observed, for instance, analysing navigation patterns from many users. Motivated by this gap, we propose a new Bayesian modelling framework to analyse such data. Our approach is based on practitioner-specified distance metrics between networks, allowing us to parameterise models analogous to Gaussian distributions in network space, using location and scale parameters. We address the key challenge of defining meaningful distances between interaction networks, proposing two new metrics with theoretical guarantees and practical computation strategies. To enable efficient Bayesian inference, we develop specialised Markov chain Monte Carlo (MCMC) algorithms within the involutive MCMC (iMCMC) framework, tailored to the doubly-intractable and discrete nature of the induced posteriors. Through simulation studies, we demonstrate the robustness and efficiency of our approach, and we showcase its applicability with a case study on a location-based social network (LSBN) dataset.
Actor-Critic learning  for mean-field control in continuous time
Authors: Noufel FRIKHA; Maximilien GERMAIN; Mathieu LAURIERE; Huyen PHAM; Xuanye SONG
Venue: JMLR 2025 (main)

Abstract: We study policy gradient for mean-field control in continuous time in a  reinforcement learning setting. By considering randomised policies with entropy regularisation, we derive a gradient expectation representation of the value function, which is amenable to actor-critic type  algorithms, where the value functions and the policies are learnt alternately based on observation samples of the state  and model-free estimation of the population state distribution, either by offline or online learning. In the linear-quadratic mean-field framework, we obtain an exact parametrisation of the actor and critic functions defined on the Wasserstein space. Finally, we illustrate the results of our algorithms with some numerical experiments on  concrete examples.
Optimal Sample Selection Through Uncertainty Estimation and Its Application in Deep Learning
Authors: Yong Lin; Chen Liu; Chenlu Ye; Qing Lian; Yuan Yao; Tong Zhang
Venue: JMLR 2025 (main)

Abstract: Modern deep learning heavily relies on large labeled datasets, which often comse with high costs in terms of both manual labeling and computational resources. To mitigate these challenges, researchers have explored the use of informative subset selection techniques. In this study, we present a theoretically optimal solution for addressing both sampling with and without labels within the context of linear softmax regression. Our proposed method, COPS (unCertainty based OPtimal Sub-sampling), is designed to minimize the expected loss of a model trained on subsampled data. Unlike existing approaches that rely on explicit calculations of the inverse covariance matrix, which are not easily applicable to deep learning scenarios, COPS leverages the model's logits to estimate the sampling ratio. This sampling ratio is closely associated with model uncertainty and can be effectively applied to deep learning tasks. Furthermore, we address the challenge of model sensitivity to misspecification by incorporating a down-weighting approach for low-density samples, drawing inspiration from previous works. To assess the effectiveness of our proposed method, we conducted extensive empirical experiments using deep neural networks on benchmark datasets. The results consistently showcase the superior performance of COPS compared to baseline methods, reaffirming its efficacy.
Transformers from Diffusion: A Unified Framework for Neural Message Passing
Authors: Qitian Wu; David Wipf; Junchi Yan
Venue: JMLR 2025 (main)

Abstract: Learning representations for structured data with certain geometries (e.g., observed or unobserved) is a fundamental challenge, wherein message passing neural networks (MPNNs) have become a de facto class of model solutions. In this paper, inspired by physical systems, we propose an energy-constrained diffusion model, which integrates the inductive bias of diffusion on manifolds with layer-wise constraints of energy minimization. We identify that the diffusion operators have a one-to-one correspondence with the energy functions implicitly descended by the diffusion process, and the finite-difference iteration for solving the energy-constrained diffusion system induces the propagation layers of various types of MPNNs operating on observed or latent structures. This leads to a unified mathematical framework for common neural architectures whose computational flows can be cast as message passing (or its special case), including MLPs, GNNs, and Transformers. Building on these insights, we devise a new class of neural message passing models, dubbed diffusion-inspired Transformers (DIFFormer), whose global attention layers are derived from the principled energy-constrained diffusion framework. Across diverse datasets ranging from real-world networks to images, texts, and physical particles, we demonstrate that the new model achieves promising performance in scenarios where the data structures are observed (as a graph), partially observed, or entirely unobserved.
Categorical Semantics of Compositional Reinforcement Learning
Authors: Georgios Bakirtzis; Michail Savvas; Ufuk Topcu
Venue: JMLR 2025 (main)

Abstract: Compositional knowledge representations in reinforcement learning (RL) facilitate modular, interpretable, and safe task specifications. However, generating compositional models requires the characterization of minimal assumptions for the robustness of the compositionality feature, especially in the case of functional decompositions. Using a categorical point of view, we develop a knowledge representation framework for a compositional theory of RL. Our approach relies on the theoretical study of the category $\mathsf{MDP}$, whose objects are Markov decision processes (MDPs) acting as models of tasks. The categorical semantics models the compositionality of tasks through the application of pushout operations akin to combining puzzle pieces. As a practical application of these pushout operations, we introduce zig-zag diagrams that rely on the compositional guarantees engendered by the category $\mathsf{MDP}$. We further prove that properties of the category $\mathsf{MDP}$ unify concepts, such as enforcing safety requirements and exploiting symmetries, generalizing previous abstraction theories for RL.
On the O(sqrt(d)/T^(1/4)) Convergence Rate of RMSProp and Its Momentum Extension Measured by l_1 Norm
Authors: Huan Li; Yiming Dong; Zhouchen Lin
Venue: JMLR 2025 (main)

Abstract: Although adaptive gradient methods have been extensively used in deep learning, their convergence rates proved in the literature are all slower than that of SGD, particularly with respect to their dependence on the dimension. This paper considers the classical RMSProp and its momentum extension and establishes the convergence rate of $\frac{1}{T}\sum_{k=1}^TE\left[||\nabla f(\mathbf{x}^k)||_1\right]\leq O(\frac{\sqrt{d}C}{T^{1/4}})$ measured by $\ell_1$ norm without the bounded gradient assumption, where $d$ is the dimension of the optimization variable, $T$ is the iteration number, and $C$ is a constant identical to that appeared in the optimal convergence rate of SGD. Our convergence rate matches the lower bound with respect to all the coefficients except the dimension $d$. Since $||\mathbf{x}||_2\ll ||\mathbf{x}||_1\leq\sqrt{d}||\mathbf{x}||_2$ for problems with extremely large $d$, our convergence rate can be considered to be analogous to the $\frac{1}{T}\sum_{k=1}^TE\left[||\nabla f(\mathbf{x}^k)||_2\right]\leq O(\frac{C}{T^{1/4}})$ rate of SGD in the ideal case of $||\nabla f(\mathbf{x})||_1=\varTheta(\sqrt{d})||\nabla f(\mathbf{x})||_2$.
Score-Aware Policy-Gradient and Performance Guarantees using Local Lyapunov Stability
Authors: CÃ©line Comte; Matthieu Jonckheere; Jaron Sanders; Albert Senen-Cerda
Venue: JMLR 2025 (main)

Abstract: In this paper, we introduce a policy-gradient method for model-based reinforcement learning (RL) that exploits a type of stationary distributions commonly obtained from Markov decision processes (MDPs) in stochastic networks, queueing systems, and statistical mechanics. Specifically, when the stationary distribution of the MDP belongs to an exponential family that is parametrized by policy parameters, we can improve existing policy gradient methods for average-reward RL. Our key identification is a family of gradient estimators, called score-aware gradient estimators (SAGEs), that enable policy gradient estimation without relying on value-function estimation in the aforementioned setting. We show that SAGE-based policy-gradient locally converges, and we obtain its regret. This includes cases when the state space of the MDP is countable and unstable policies can exist. Under appropriate assumptions such as starting sufficiently close to a maximizer and the existence of a local Lyapunov function, the policy under SAGE-based stochastic gradient ascent has an overwhelming probability of converging to the associated optimal policy. Furthermore, we conduct a numerical comparison between a SAGE-based policy-gradient method and an actor-critic method on several examples inspired from stochastic networks, queueing systems, and models derived from statistical physics. Our results demonstrate that a SAGE-based method finds close-to-optimal policies faster than an actor-critic method.
PREMAP: A Unifying PREiMage APproximation Framework for Neural Networks
Authors: Xiyue Zhang; Benjie Wang; Marta Kwiatkowska; Huan Zhang
Venue: JMLR 2025 (main)

Abstract: Most methods for neural network verification focus on bounding the image, i.e., set of outputs for a given input set. This can be used to, for example, check the robustness of neural network predictions to bounded perturbations of an input. However, verifying properties concerning the preimage, i.e., the set of inputs satisfying an output property, requires abstractions in the input space. We present a general framework for preimage abstraction that produces under- and over-approximations of any polyhedral output set. Our framework employs cheap parameterised linear relaxations of the neural network, together with an anytime refinement procedure that iteratively partitions the input region by splitting on input features and neurons. The effectiveness of our approach relies on carefully designed heuristics and optimisation objectives to achieve rapid improvements in the approximation volume. We evaluate our method on a range of tasks, demonstrating significant improvement in efficiency and scalability to high-input-dimensional image classification tasks compared to state-of-the-art techniques. Further, we showcase the application to quantitative verification and robustness analysis, presenting a sound and complete algorithm for the former and providing sound quantitative results for the latter.
Characterizing Dynamical Stability of Stochastic Gradient Descent in Overparameterized Learning
Authors: Dennis Chemnitz; Maximilian Engel
Venue: JMLR 2025 (main)

Abstract: For overparameterized optimization tasks, such as those found in modern machine learning, global minima are generally not unique. In order to understand generalization in these settings, it is vital to study to which minimum an optimization algorithm converges. The possibility of having minima that are unstable under the dynamics imposed by the optimization algorithm limits the potential minima that the algorithm can find. In this paper, we characterize the global minima that are dynamically stable/unstable for both deterministic and stochastic gradient descent (SGD). In particular, we introduce a characteristic Lyapunov exponent that depends on the local dynamics around a global minimum and rigorously prove that the sign of this Lyapunov exponent determines whether SGD can accumulate at the respective global minimum.
Optimal and Efficient Algorithms for Decentralized Online Convex Optimization
Authors: Yuanyu Wan; Tong Wei; Bo Xue; Mingli Song; Lijun Zhang
Venue: JMLR 2025 (main)

Abstract: We investigate decentralized online convex optimization (D-OCO), in which a set of local learners are required to minimize a sequence of global loss functions using only local computations and communications. Previous studies have established $O(n^{5/4}\rho^{-1/2}\sqrt{T})$ and ${O}(n^{3/2}\rho^{-1}\log T)$ regret bounds for convex and strongly convex functions respectively, where $n$ is the number of local learners, $\rho<1$ is the spectral gap of the communication matrix, and $T$ is the time horizon. However, there exist large gaps from the existing lower bounds, i.e., $\Omega(n\sqrt{T})$ for convex functions and $\Omega(n)$ for strongly convex functions. To fill these gaps, in this paper, we first develop a novel D-OCO algorithm that can respectively reduce the regret bounds for convex and strongly convex functions to $\tilde{O}(n\rho^{-1/4}\sqrt{T})$ and $\tilde{O}(n\rho^{-1/2}\log T)$. The primary technique is to design an online accelerated gossip strategy that enjoys a faster average consensus among local learners. Furthermore, by carefully exploiting spectral properties of a specific network topology, we enhance the lower bounds for convex and strongly convex functions to $\Omega(n\rho^{-1/4}\sqrt{T})$ and $\Omega(n\rho^{-1/2}\log T)$, respectively. These results suggest that the regret of our algorithm is nearly optimal in terms of $T$, $n$, and $\rho$ for both convex and strongly convex functions. Finally, we propose a projection-free variant of our algorithm to efficiently handle practical applications with complex constraints. Our analysis reveals that the projection-free variant can achieve ${O}(nT^{3/4})$ and ${O}(nT^{2/3}(\log T)^{1/3})$ regret bounds for convex and strongly convex functions with nearly optimal $\tilde{O}(\rho^{-1/2}\sqrt{T})$ and $\tilde{O}(\rho^{-1/2}T^{1/3}(\log T)^{2/3})$ communication rounds, respectively.
Minimax Optimal Deep Neural Network Classifiers Under Smooth Decision Boundary
Authors: Tianyang Hu; Ruiqi Liu; Zuofeng Shang; Guang Cheng
Venue: JMLR 2025 (main)

Abstract: Deep learning has gained huge empirical successes in large-scale classification problems. In contrast, there is a lack of statistical understanding about deep learning methods, particularly in the minimax optimality perspective. For instance, in the classical smooth decision boundary setting, existing deep neural network (DNN) approaches are rate-suboptimal, and it remains elusive how to construct minimax optimal DNN classifiers. Moreover, it is interesting to explore whether DNN classifiers can circumvent the "curse of dimensionality" in handling high-dimensional data. The contributions of this paper are two-fold. First, based on a localized margin framework, we discover the source of suboptimality of existing DNN approaches. Motivated by this, we propose a new deep learning classifier using a divide-and-conquer technique: DNN classifiers are constructed on each local region and then aggregated to a global one. We further propose a localized version of the classical Tsybakovâs noise condition, under which statistical optimality of our new classifier is established. Second, we show that DNN classifiers can adapt to low-dimensional data structures and circumvent the âcurse of dimensionalityâ in the sense that the minimax rate only depends on the effective dimension, potentially much smaller than the actual data dimension. Numerical experiments are conducted on simulated data to corroborate our theoretical results.
Randomly Projected Convex Clustering Model: Motivation, Realization, and Cluster Recovery Guarantees
Authors: Ziwen Wang; Yancheng Yuan; Jiaming Ma; Tieyong Zeng; Defeng Sun
Venue: JMLR 2025 (main)

Abstract: In this paper, we propose a randomly projected convex clustering model for clustering a collection of $n$ high dimensional data points in $\mathbb{R}^d$ with $K$ hidden clusters. Compared to the convex clustering model for clustering original data with dimension $d$, we prove that, under some mild conditions, the perfect recovery of the cluster membership assignments of the convex clustering model, if exists, can be preserved by the randomly projected convex clustering model with embedding dimension $m = O(\epsilon^{-2}\log(n))$, where $\epsilon > 0$ is some given parameter. We further prove that the embedding dimension can be improved to be $O(\epsilon^{-2}\log(K))$, which is independent of the number of data points. We also establish the recovery guarantees of our proposed model with uniform weights for clustering a mixture of spherical Gaussians. Extensive numerical results demonstrate the robustness and superior performance of the randomly projected convex clustering model. The numerical results will also demonstrate that the randomly projected convex clustering model can outperform other popular clustering models on the dimension-reduced data, including the randomly projected K-means model.
Finite Expression Method for Solving High-Dimensional Partial Differential Equations
Authors: Senwei Liang; Haizhao Yang
Venue: JMLR 2025 (main)

Abstract: Designing efficient and accurate numerical solvers for high-dimensional partial differential equations (PDEs) remains a challenging and important topic in computational science and engineering, mainly due to the "curse of dimensionality" in designing numerical schemes that scale in dimension. This paper introduces a new methodology that seeks an approximate PDE solution in the space of functions with finitely many analytic expressions and, hence, this methodology is named the finite expression method (FEX). It is proved in approximation theory that FEX can avoid the curse of dimensionality. As a proof of concept, a deep reinforcement learning method is proposed to implement FEX for various high-dimensional PDEs in different dimensions, achieving high and even machine accuracy with a memory complexity polynomial in dimension and an amenable time complexity. An approximate solution with finite analytic expressions also provides interpretable insights into the ground truth PDE solution, which can further help to advance the understanding of physical systems and design postprocessing techniques for a refined solution.
Diffeomorphism-based feature learning using PoincarÃ© inequalities on augmented input space
Authors: Romain VerdiÃ¨re; ClÃ©mentine Prieur; Olivier Zahm
Venue: JMLR 2025 (main)

Abstract: We propose a gradient-enhanced algorithm for high-dimensional function approximation.
The algorithm proceeds in two steps: firstly, we reduce the input dimension by learning the relevant input features from gradient evaluations, and secondly, we regress the function output against the pre-learned features. To ensure theoretical guarantees, we construct the feature map as the first components of a diffeomorphism, which we learn by minimizing an error bound obtained using PoincarÃ© Inequality applied either in the input space or in the feature space. This leads to two different strategies, which we compare both theoretically and numerically and relate to existing methods in the literature.
In addition, we propose a dimension augmentation trick to increase the approximation power of feature detection.
A generalization to vector-valued functions demonstrate that our methodology directly applies to learning autoencoders. Here, we approximate the identity function over a given dataset by a composition of feature map (encoder) with the regression function (decoder). In practice, we construct the diffeomorphism using coupling flows, a particular class of invertible neural networks.
Numerical experiments on various high-dimensional functions show that the proposed algorithm outperforms state-of-the-art competitors, especially with small datasets.
Deep Variational Multivariate Information Bottleneck - A Framework for Variational Losses
Authors: Eslam Abdelaleem; Ilya Nemenman; K. Michael Martini
Venue: JMLR 2025 (main)

Abstract: Variational dimensionality reduction methods are widely used for their accuracy, generative capabilities, and robustness. We introduce a unifying framework that generalizes both such as traditional and state-of-the-art methods. The framework is based on an interpretation of the multivariate information bottleneck, trading off the information preserved in an encoder graph (defining what to compress) against that in a decoder graph (defining a generative model for data). Using this approach, we rederive existing methods, including the deep variational information bottleneck, variational autoencoders, and deep multiview information bottleneck. We naturally extend the deep variational CCA (DVCCA) family to beta-DVCCA and introduce a new method, the deep variational symmetric information bottleneck (DVSIB). DSIB, the deterministic limit of DVSIB, connects to modern contrastive learning approaches such as Barlow Twins, among others. We evaluate these methods on Noisy MNIST and Noisy CIFAR-100, showing that algorithms better matched to the structure of the problem like DVSIB and beta-DVCCA produce better latent spaces as measured by classification accuracy, dimensionality of the latent variables, sample efficiency, and consistently outperform other approaches under comparable conditions. Additionally, we benchmark against state-of-the-art models, achieving superior or competitive accuracy. Our results demonstrate that this framework can seamlessly incorporate diverse multi-view representation learning algorithms, providing a foundation for designing novel, problem-specific loss functions.
Conditional Wasserstein Distances with Applications in Bayesian OT Flow Matching
Authors: Jannis Chemseddine; Paul Hagemann; Gabriele Steidl; Christian Wald
Venue: JMLR 2025 (main)

Abstract: In inverse problems, many conditional generative models approximate the posterior measure by minimizing a distance between the joint measure and its learned approximation. While this approach also controls the distance between the posterior measures in the case of the KullbackâLeibler divergence, the same in general does not hold true for the Wasserstein distance. In this paper, we introduce a conditional Wasserstein distance via a set of restricted couplings that equals the expected Wasserstein distance of the posteriors. Interestingly, the dual formulation of the conditional Wasserstein-1 distance resembles losses in the conditional Wasserstein GAN literature in a quite natural way. We derive theoretical properties of the conditional Wasserstein distance, characterize the corresponding geodesics and velocity fields as well as the flow ODEs. Subsequently, we propose to approximate the velocity fields by relaxing the conditional Wasserstein distance. Based on this, we propose an extension of OT Flow Matching for solving Bayesian inverse problems and demonstrate its numerical advantages on an inverse problem and class-conditional image generation.