GenAI4ELab/papercli-papers huggingface dataset:
Derivative-Informed Neural Operator Acceleration of Geometric MCMC for Infinite-Dimensional Bayesian Inverse Problems
Authors: Lianghao Cao; Thomas O'Leary-Roseberry; Omar Ghattas
Venue: JMLR 2025 (main)

Abstract: We propose an operator learning approach to accelerate geometric Markov chain Monte Carlo (MCMC) for solving infinite-dimensional Bayesian inverse problems (BIPs). While geometric MCMC employs high-quality proposals that adapt to posterior local geometry, it requires repeated computations of gradients and Hessians of the log-likelihood, which becomes prohibitive when the parameter-to-observable (PtO) map is defined through expensive-to-solve parametric partial differential equations (PDEs). We consider a delayed-acceptance geometric MCMC method driven by a neural operator surrogate of the PtO map, where the proposal exploits fast surrogate predictions of the log-likelihood and, simultaneously, its gradient and Hessian. To achieve a substantial speedup, the surrogate must accurately approximate the PtO map and its Jacobian, which often demands a prohibitively large number of PtO map samples via conventional operator learning methods. In this work, we present an extension of derivative-informed operator learning [O'Leary-Roseberry et al., J. Comput. Phys., 496 (2024)] that uses joint samples of the PtO map and its Jacobian. This leads to derivative-informed neural operator (DINO) surrogates that accurately predict the observables and posterior local geometry at a significantly lower training cost than conventional methods. Cost and error analysis for reduced basis DINO surrogates are provided. Numerical studies demonstrate that DINO-driven MCMC generates effective posterior samples 3--9 times faster than geometric MCMC and 60--97 times faster than prior geometry-based MCMC. Furthermore, the training cost of DINO surrogates breaks even compared to geometric MCMC after just 10--25 effective posterior samples.
Dynamic angular synchronization under smoothness constraints
Authors: Ernesto Araya; Mihai Cucuringu; Hemant Tyagi
Venue: JMLR 2025 (main)

Abstract: Given an undirected measurement graph $\mathcal{H} = ([n], \mathcal{E})$, 
the classical angular synchronization problem consists of recovering unknown angles $\theta_1^*,\dots,\theta_n^*$ from a collection of noisy pairwise measurements of the form $(\theta_i^* - \theta_j^*) \mod 2\pi$, for all $\{i,j\} \in \mathcal{E}$. This problem arises in a variety of applications, including computer vision, time synchronization of distributed networks, and ranking from pairwise comparisons. In this paper, we consider a dynamic version of this problem where the angles, and also the measurement graphs evolve over $T$ time points. Assuming a smoothness condition on the evolution of the
latent angles, we derive three algorithms for joint estimation of the angles over all time points. Moreover, for one of the algorithms, we establish non-asymptotic recovery guarantees for the mean-squared error (MSE) under different statistical models. In particular, we show that the MSE converges to zero as $T$ increases under milder conditions than in the static setting. This includes the setting where the measurement graphs are highly sparse and disconnected, and also when the measurement noise is large and can potentially increase with $T$. We complement our theoretical results with experiments on synthetic data.
GraphNeuralNetworks.jl: Deep Learning on Graphs with Julia
Authors: Carlo Lucibello; Aurora Rossi
Venue: JMLR 2025 (main)

Abstract: GraphNeuralNetworks.jl is an open-source framework for deep learning on graphs, written in the Julia programming language. It supports multiple GPU backends, generic sparse or dense graph representations, and offers convenient interfaces for manipulating standard, heterogeneous, and temporal graphs with attributes at the node, edge, and graph levels. The framework allows users to define custom graph convolutional layers using gather/scatter message-passing primitives or optimized fused operations. It also includes several popular layers, enabling efficient experimentation with complex deep architectures. The package is available on GitHub: https://github.com/JuliaGraphs/GraphNeuralNetworks.jl.
Towards Optimal Branching of Linear and Semidefinite Relaxations for Neural Network Robustness Certification
Authors: Brendon G. Anderson; Ziye Ma; Jingqi Li; Somayeh Sojoudi
Venue: JMLR 2025 (main)

Abstract: In this paper, we study certifying the robustness of ReLU neural networks against adversarial input perturbations. To diminish the relaxation error suffered by the popular linear programming (LP) and semidefinite programming (SDP) certification methods, we take a branch-and-bound approach to propose partitioning the input uncertainty set and solving the relaxations on each part separately. We show that this approach reduces relaxation error, and that the error is eliminated entirely upon performing an LP relaxation with a partition intelligently designed to exploit the nature of the ReLU activations. To scale this approach to large networks, we consider using a coarser partition whereby the number of parts in the partition is reduced. We prove that computing such a coarse partition that directly minimizes the LP relaxation error is NP-hard. By instead minimizing the worst-case LP relaxation error, we develop a closed-form branching scheme in the single-hidden layer case. We extend the analysis to the SDP, where the feasible set geometry is exploited to design a branching scheme that minimizes the worst-case SDP relaxation error. Experiments on MNIST, CIFAR-10, and Wisconsin breast cancer diagnosis classifiers demonstrate significant increases in the percentages of test samples certified. By independently increasing the input size and the number of layers, we empirically illustrate under which regimes the branched LP and branched SDP are best applied. Finally, we extend our LP branching method into a multi-layer branching heuristic, which attains comparable performance to prior state-of-the-art heuristics on large-scale, deep neural network certification benchmarks.
Implicit vs Unfolded Graph Neural Networks
Authors: Yongyi Yang; Tang Liu; Yangkun Wang; Zengfeng Huang; David Wipf
Venue: JMLR 2025 (main)

Abstract: It has been observed that message-passing graph neural networks (GNN) sometimes struggle to maintain a healthy balance between the efficient / scalable modeling of long-range dependencies across nodes while avoiding unintended consequences such oversmoothed node representations, sensitivity to spurious edges, or inadequate model interpretability.  To address these and other issues, two separate strategies have recently been proposed, namely implicit and unfolded GNNs (that we abbreviate to IGNN and UGNN respectively).  The former treats node representations as the fixed points of a deep equilibrium model that can efficiently facilitate arbitrary implicit propagation across the graph with a fixed memory footprint.  In contrast, the latter involves treating graph propagation as unfolded descent iterations as applied to some graph-regularized energy function.  While motivated differently, in this paper we carefully quantify explicit situations where the solutions they produce are equivalent and others where their properties sharply diverge.  This includes the analysis of convergence, representational capacity, and interpretability.  In support of this analysis, we also provide empirical head-to-head comparisons across multiple synthetic and public real-world node classification benchmarks.  These results indicate that while IGNN is substantially more memory-efficient, UGNN models support unique, integrated graph attention mechanisms and propagation rules that can achieve strong node classification accuracy across disparate regimes such as adversarially-perturbed graphs, graphs with heterophily, and graphs involving long-range dependencies.
Causal Abstraction: A Theoretical Foundation for Mechanistic Interpretability
Authors: Atticus Geiger; Duligur Ibeling; Amir Zur; Maheep Chaudhary; Sonakshi Chauhan; Jing Huang; Aryaman Arora; Zhengxuan Wu; Noah Goodman; Christopher Potts; Thomas Icard
Venue: JMLR 2025 (main)

Abstract: Causal abstraction provides a theoretical foundation for mechanistic interpretability, the field concerned with providing intelligible algorithms that are faithful simplifications of the known, but opaque low-level details of black box AI models. Our contributions are (1) generalizing the theory of causal abstraction from mechanism replacement (i.e., hard and soft interventions) to arbitrary mechanism transformation (i.e., functionals from old mechanisms to new mechanisms), (2) providing a flexible, yet precise formalization for the core concepts of polysemantic neurons, the linear representation hypothesis, modular features, and graded faithfulness, and (3) unifying a variety of mechanistic interpretability methods in the common language of causal abstraction, namely, activation and path patching, causal mediation analysis, causal scrubbing, causal tracing, circuit analysis, concept erasure, sparse autoencoders, differential binary masking, distributed alignment search, and steering.
Random Pruning Over-parameterized Neural Networks Can Improve Generalization: A Training Dynamics Analysis
Authors: Hongru Yang; Yingbin Liang; Xiaojie Guo; Lingfei Wu; Zhangyang Wang
Venue: JMLR 2025 (main)

Abstract: It has been observed that applying pruning-at-initialization methods and training the sparse networks can sometimes yield slightly better test performance than training the original dense network. Such experimental observations are yet to be understood theoretically. This work makes the first attempt to study this phenomenon. Specifically, we identify a theoretical minimal setting and study a classification task with a one-hidden-layer neural network, which is randomly pruned according to different rates at the initialization. We show that as long as the pruning rate is below a certain threshold, the network provably exhibits good generalization performance after training.More surprisingly, the generalization bound gets better as the pruning rate mildly gets larger. To complement this positive result, we also show a negative result: there exists a large pruning rate such that while gradient descent is still able to drive the training loss toward zero, the generalization performance is no better than random guessing. This further suggests that pruning can change the feature learning process, which leads to the performance drop of the pruned neural network. To our knowledge, this is the first theory work studying how different pruning rates affect neural networks' performance, suggesting that an appropriate pruning rate might improve the neural network's generalization.
On Inference for the Support Vector Machine
Authors: Jakub Rybak; Heather Battey; Wen-Xin Zhou
Venue: JMLR 2025 (main)

Abstract: The linear support vector machine has a parametrised decision boundary. The paper considers inference for the corresponding parameters, which indicate the effects of individual variables on the decision boundary. The proposed inference is via a convolution-smoothed version of the SVM loss function, this having several inferential advantages over the original SVM, whose associated loss function is not everywhere differentiable. Notably, convolution-smoothing comes with non-asymptotic theoretical guarantees, including a distributional approximation to the parameter estimator that scales more favourably with the dimension of the feature vector. The differentiability of the loss function produces other advantages in some settings; for instance, by facilitating the inclusion of penalties or the synthesis of information from a large number of small samples. The paper closes by relating the linear SVM parameters to those of some probability models for binary outcomes.
Integral Probability Metrics Meet Neural Networks: The Radon-Kolmogorov-Smirnov Test
Authors: Seunghoon Paik; Michael Celentano; Alden Green; Ryan J. Tibshirani
Venue: JMLR 2025 (main)

Abstract: Integral probability metrics (IPMs) constitute a general class of nonparametric two-sample tests that are based on maximizing the mean difference between samples from one distribution $P$ versus another $Q$, over all choices of data transformations $f$ living in some function space $\mathcal{F}$. Inspired by recent work that connects what are known as functions of Radon bounded variation (RBV) and neural networks (Parhi and Nowak, 2021, 2023), we study the IPM defined by taking $\mathcal{F}$ to be the unit ball in the RBV space of a given smoothness degree $k \geq 0$. This test, which we refer to as the Radon-Kolmogorov-Smirnov (RKS) test, can be viewed as a generalization of the well-known and classical Kolmogorov-Smirnov (KS) test to multiple dimensions and higher orders of smoothness. It is also intimately connected to neural networks: we prove that the witness in the RKS testâthe function $f$ achieving the maximum mean differenceâis always a ridge spline of degree $k$, i.e., a single neuron in a neural network. We can thus leverage the power of modern neural network optimization toolkits to (approximately) maximize the criterion that underlies the RKS test. We prove that the RKS test has asymptotically full power at distinguishing any distinct pair $P \not= Q$ of distributions, derive its asymptotic null distribution, and carry out experiments to elucidate the strengths and weaknesses of the RKS test versus the more traditional kernel MMD test.
How good is your Laplace approximation of the Bayesian posterior? Finite-sample computable error bounds for a variety of useful divergences
Authors: Mikolaj J. Kasprzak; Ryan Giordano; Tamara Broderick
Venue: JMLR 2025 (main)

Abstract: The Laplace approximation is a popular method for constructing a Gaussian approximation to the Bayesian posterior and thereby approximating the posterior mean and variance. But approximation quality is a concern. One might consider using rate-of-convergence bounds from certain versions of the Bayesian Central Limit Theorem (BCLT) to provide quality guarantees. But existing bounds require assumptions that are unrealistic even for relatively simple real-life Bayesian analyses; more specifically, existing bounds either (1) require knowing the true data-generating parameter, (2) are asymptotic in the number of samples, (3) do not control the Bayesian posterior mean, or (4) require strongly log concave models to compute. In this work, we provide the first computable bounds on quality that simultaneously (1) do not require knowing the true parameter, (2) apply to finite samples, (3) control posterior means and variances, and (4) apply generally to models that satisfy the conditions of the asymptotic BCLT. Moreover, we substantially improve the dimension dependence of existing bounds; in fact, we achieve the lowest-order dimension dependence possible in the general case. We compute exact constants in our bounds for a variety of standard models, including logistic regression, and numerically demonstrate their utility. We provide a framework for analysis of more complex models.
Feature Learning in Finite-Width Bayesian Deep Linear Networks with Multiple Outputs and Convolutional Layers
Authors: Federico Bassetti; Marco Gherardi; Alessandro Ingrosso; Mauro Pastore; Pietro Rotondo
Venue: JMLR 2025 (main)

Abstract: Deep linear networks have been extensively studied, as they provide simplified models of deep learning. However, little is known in the case of finite-width architectures with multiple outputs and convolutional layers. In this manuscript, we provide rigorous results for the statistics of functions implemented by the aforementioned class of networks, thus moving closer to a complete characterization of feature learning in the Bayesian setting.  Our results include: (i) an exact and elementary non-asymptotic integral representation for the joint prior distribution over the outputs, given in terms of a mixture of Gaussians; (ii) an analytical formula for the posterior distribution in the case of squared error loss function (Gaussian likelihood); (iii) a quantitative description of the feature learning infinite-width regime, using large deviation theory. From a physical perspective, deep architectures with multiple outputs or convolutional layers represent different manifestations of kernel shape renormalization, and our work provides a dictionary that translates this physics intuition and terminology into rigorous Bayesian statistics.
High-Dimensional L2-Boosting: Rate of Convergence
Authors: Ye Luo; Martin Spindler; Jannis Kueck
Venue: JMLR 2025 (main)

Abstract: Boosting is one of the most significant developments in machine learning. This paper studies the rate of convergence of L2-Boosting in a high-dimensional setting under early stopping. We close a gap in the literature and provide the rate of convergence of L2-Boosting in a high-dimensional setting under approximate sparsity and without beta-min condition. We also show that the rate of convergence of the classical L2-Boosting depends on the design matrix described by a sparse eigenvalue condition. To show the latter results, we derive new, improved approximation results for the pure greedy algorithm, based on analyzing the revisiting behavior of L2-Boosting. These results might be of independent interest. Moreover, we introduce so-called  "restricted" L2-Boosting. The restricted L2-Boosting algorithm sticks to the set of the previously chosen variables, exploits the information contained in these variables first and then only occasionally allows to add new variables to this set. We derive the rate of convergence for restricted L2-Boosting under early stopping which is close to the convergence rate of Lasso in an approximate sparse, high-dimensional setting without beta-min condition. We also introduce feasible rules for early stopping, which can be easily implemented and used in applied work. Finally, we present simulation studies to illustrate the relevance of our theoretical results and to provide insights into the practical aspects of boosting. In these simulation studies, L2-Boosting clearly outperforms Lasso. An empirical illustration and the proofs are contained in the Appendix.
Uplift Model Evaluation with Ordinal Dominance Graphs
Authors: Brecht Verbeken; Marie-Anne Guerry; Wouter Verbeke; Sam Verboven
Venue: JMLR 2025 (main)

Abstract: Uplift modelling is a subfield of causal learning that focuses on ranking entities by individual treatment effects. Uplift models are typically evaluated using Qini curves or Qini scores. While intuitive, the theoretical grounding for Qini in the literature is limited, and the mathematical connection to the well-understood Receiver Operating Characteristic (ROC) curve is unclear. In this paper, we introduce pROCini, a novel uplift evaluation metric that improves upon Qini in two important ways. First, it explicitly incorporates more information by taking into account negative outcomes. Second, it leverages this additional information within the Ordinal Dominance Graph framework, which is the basis behind the well known ROC curve, resulting in a mathematically well-behaved metric that facilitates theoretical analysis. We derive confidence bounds for pROCini, exploiting its theoretical properties. Finally, we empirically validate the improved discriminative power of ROCini and pROCini in a simulation study as well as via experiments on real data.
Causal Effect of Functional Treatment
Authors: Ruoxu Tan; Wei Huang; Zheng Zhang; Guosheng Yin
Venue: JMLR 2025 (main)

Abstract: We study the causal effect with a functional treatment variable, where practical applications often arise in neuroscience, biomedical sciences, etc. Previous research concerning the effect of a functional variable on an outcome is typically restricted to exploring correlation rather than causality. The generalized propensity score, which is often used to calibrate the selection bias, is not directly applicable to a functional treatment variable due to a lack of definition of probability density function for functional data. We propose three estimators for the average dose-response functional based on the functional linear model, namely, the functional stabilized weight estimator, the outcome regression estimator and the doubly robust estimator, each of which has its own merits. We study their theoretical properties, which are corroborated through extensive numerical experiments. A real data application on electroencephalography data and disease severity demonstrates the practical value of our methods.
Affine Rank Minimization via Asymptotic Log-Det Iteratively Reweighted Least Squares
Authors: Sebastian KrÃ¤mer
Venue: JMLR 2025 (main)

Abstract: The affine rank minimization problem is a well-known approach to matrix recovery. While there are various surrogates to this NP-hard problem, we prove that the asymptotic minimization of log-det objective functions indeed always reveals the desired, lowest-rank matrices---whereas such may or may not recover a sought-after ground truth. Concerning commonly applied methods such as iteratively reweighted least squares, one thus remains with two difficult to distinguish concerns: how problematic are local minima inherent to the approach truly; and opposingly, how influential instead is the numerical realization. We first show that comparable solution statements do not hold true for Schatten-$p$ functions, including the nuclear norm, and discuss the role of divergent minimizers. Subsequently, we outline corresponding implications for general optimization approaches as well as the more specific IRLS-$0$ algorithm, emphasizing through examples that the transition of the involved smoothing parameter to zero is frequently a more substantial issue than non-convexity. Lastly, we analyze several presented aspects empirically in a series of numerical experiments. In particular, allowing for instance sufficiently many iterations, one may even observe a phase transition for generic recoverability at the absolute theoretical minimum.
Outlier Robust and Sparse Estimation of Linear Regression Coefficients
Authors: Takeyuki Sasai; Hironori Fujisawa
Venue: JMLR 2025 (main)

Abstract: We consider outlier-robust and sparse estimation of linear regression coefficients, when the covariates and the noises are contaminated by adversarial outliers and noises are sampled from a heavy-tailed distribution. Our results present sharper error bounds under weaker assumptions than prior studies that share similar interests with this study. Our analysis relies on some sharp concentration inequalities resulting from generic chaining.
Posterior Concentrations of Fully-Connected Bayesian Neural Networks with General Priors on the Weights
Authors: Insung Kong; Yongdai Kim
Venue: JMLR 2025 (main)

Abstract: Bayesian approaches for training deep neural networks (BNNs) have received significant interest and have been effectively utilized in a wide range of applications. Several studies have examined the properties of posterior concentrations in BNNs. However, most of these studies focus solely on BNN models with sparse or heavy-tailed priors. Surprisingly, there are currently no theoretical results for BNNs using Gaussian priors, which are the most commonly used in practice. The lack of theory arises from the absence of approximation results of Deep Neural Networks (DNNs) that are non-sparse and have bounded parameters. In this paper, we present a new approximation theory for non-sparse DNNs with bounded parameters. Additionally, based on the approximation theory,  we show that BNNs with non-sparse general priors can achieve near-minimax optimal posterior concentration rates around the true model.