GenAI4ELab/papercli-papers huggingface dataset:
High-Rank Irreducible Cartesian Tensor Decomposition and Bases of Equivariant Spaces
Authors: Shihao Shao; Yikang Li; Zhouchen Lin; Qinghua Cui
Venue: JMLR 2025 (main)

Abstract: Irreducible Cartesian tensors (ICTs) play a crucial role in the design of equivariant graph neural networks, as well as in theoretical chemistry and chemical physics. Meanwhile, the design space of available linear operations on tensors that preserve symmetry presents a significant challenge. The ICT decomposition and a basis of this equivariant space are difficult to obtain for high-rank tensors. After decades of research, Bonvicini (2024) has recently achieved an explicit ICT decomposition for $n=5$ with factorial time/space complexity. In this work we, for the first time, obtain decomposition matrices for ICTs up to rank $n=9$ with reduced and affordable complexity, by constructing what we call path matrices. The path matrices are obtained via performing chain-like contractions with Clebsch-Gordan matrices following the parentage scheme. We prove and leverage that the concatenation of path matrices is an orthonormal change-of-basis matrix between the Cartesian tensor product space and the spherical direct sum spaces. Furthermore, we identify a complete orthogonal basis for the equivariant space, rather than a spanning set (Pearce-Crump, 2023b), through this path matrices technique. Our method avoids the RREF algorithm and maintains a fully analytical derivation of each ICT decomposition matrix, thereby significantly improving the algorithmâs speed to obtain arbitrary rank orthogonal ICT decomposition matrices and orthogonal equivariant bases. We further extend our result to the arbitrary tensor product and direct sum spaces, enabling free design between different spaces while keeping symmetry. The Python code is available at https://github.com/ShihaoShao-GH/ICT-decomposition-and-equivariant-bases, where the $n=6,\dots,9$ ICT decomposition matrices are obtained in 1s, 3s, 11s, and 4m32s on 28-core Intel Xeon Gold 6330 CPU @ 2.00GHz, respectively.
Fast Algorithm for Constrained Linear Inverse Problems
Authors: Mohammed Rayyan Sheriff; Floor Fenne Redel; Peyman Mohajerin Esfahani
Venue: JMLR 2025 (main)

Abstract: We consider the constrained Linear Inverse Problem (LIP), where a certain atomic norm (like the $\ell_1 $ norm) is minimized subject to a quadratic constraint. Typically, such cost functions are non-differentiable, which makes them not amenable to the fast optimization methods existing in practice. We propose two equivalent reformulations of the constrained LIP with improved convex regularity: (i) a smooth convex minimization problem, and (ii) a strongly convex min-max problem. These problems could be solved by applying existing acceleration-based convex optimization methods which provide better $ O \left( \frac{1}{k^2} \right)$ theoretical convergence guarantee, improving upon the current best rate of $O \left( \frac{1}{k} \right)$. We also provide a novel algorithm named the Fast Linear Inverse Problem Solver (FLIPS), which is tailored to maximally exploit the structure of the reformulations. We demonstrate the performance of FLIPS on the classical problems of Binary Selection, Compressed Sensing, and Image Denoising. We also provide open source \texttt{MATLAB} and \texttt{PYTHON} packages for these three examples, which can be easily adapted to other LIPs.
Four Axiomatic Characterizations of the Integrated Gradients Attribution Method
Authors: Daniel Lundstrom; Meisam Razaviyayn
Venue: JMLR 2025 (main)

Abstract: Deep neural networks have produced significant progress among machine learning models in terms of accuracy and functionality, but their inner workings are still largely unknown. Attribution  methods seek to shine  a light on these "black box" models by indicating how much each input contributed to a model's outputs. The Integrated Gradients (IG) method is a state of the art baseline attribution method in the axiomatic vein, meaning it is designed to conform to particular principles of attributions. We present four axiomatic characterizations of IG, establishing IG as the unique method satisfying four different sets of axioms.
Bagged Regularized k-Distances for Anomaly Detection
Authors: Yuchao Cai; Hanfang Yang; Yuheng Ma; Hanyuan Hang
Venue: JMLR 2025 (main)

Abstract: We consider the paradigm of unsupervised anomaly detection, which involves the identification of anomalies within a dataset in the absence of labeled examples. Though distance-based methods are top-performing for unsupervised anomaly detection, they suffer heavily from the sensitivity to the choice of the number of the nearest neighbors. In this paper, we propose a new distance-based algorithm called bagged regularized $k$-distances for anomaly detection (BRDAD), converting the unsupervised anomaly detection problem into a convex optimization problem. Our BRDAD algorithm selects the weights by minimizing the surrogate risk, i.e., the finite sample bound of the empirical risk of the bagged weighted $k$-distances for density estimation (BWDDE). This approach enables us to successfully address the sensitivity challenge of the hyperparameter choice in distance-based algorithms. Moreover, when dealing with large-scale datasets, the efficiency issues can be addressed by the incorporated bagging technique in our BRDAD algorithm. On the theoretical side, we establish fast convergence rates of the AUC regret of our algorithm and demonstrate that the bagging technique significantly reduces the computational complexity. On the practical side, we conduct numerical experiments to illustrate the insensitivity of the parameter selection of our algorithm compared with other state-of-the-art distance-based methods. Furthermore, our method achieves superior performance on real-world datasets with the introduced bagging technique compared to other approaches.
Assumption-lean and data-adaptive post-prediction inference
Authors: Jiacheng Miao; Xinran Miao; Yixuan Wu; Jiwei Zhao; Qiongshi Lu
Venue: JMLR 2025 (main)

Abstract: A primary challenge facing modern scientific research is the limited availability of gold-standard data, which can be costly, labor-intensive, or invasive to obtain. With the rapid development of machine learning (ML), scientists can now employ ML algorithms to predict gold-standard outcomes using variables that are easier to obtain. However, these predicted outcomes are often used directly in subsequent statistical analyses, ignoring imprecision and heterogeneity introduced by the prediction procedure. This will likely result in false positive findings and invalid scientific conclusions. In this work, we introduce PoSt-Prediction Adaptive inference (PSPA) that allows valid and powerful inference based on ML-predicted data. Its âassumption-leanâ property guarantees reliable statistical inference without assumptions on the ML prediction. Its âdata-adaptiveâ feature guarantees an efficiency gain over existing methods, regardless of the accuracy of ML prediction. We demonstrate the statistical superiority and broad applicability of our method through simulations and real-data applications.
"What is Different Between These Datasets?" A Framework for Explaining Data Distribution Shifts
Authors: Varun Babbar*; Zhicheng Guo*; Cynthia Rudin
Venue: JMLR 2025 (main)

Abstract: The performance of machine learning models relies heavily on the quality of input data, yet real-world applications often face significant data-related challenges. A common issue arises when curating training data or deploying models: two datasets from the same domain may exhibit differing distributions. While many techniques exist for detecting such distribution shifts, there is a lack of comprehensive methods to explain these differences in a human-understandable way beyond opaque quantitative metrics. To bridge this gap, we propose a versatile framework of interpretable methods for comparing datasets. Using a variety of case studies, we demonstrate the effectiveness of our approach across diverse data modalitiesâincluding tabular data, text data, images, time-series signals â in both low and high-dimensional settings. These methods complement existing techniques by providing actionable and interpretable insights to better understand and address distribution shifts.
Generative Adversarial Networks: Dynamics
Authors: Matias G. Delgadino; Bruno B. Suassuna; Rene Cabrera
Venue: JMLR 2025 (main)

Abstract: We study quantitatively the overparametrization limit of the original Wasserstein-GAN algorithm. Effectively, we show that the algorithm is a stochastic discretization of a system of continuity equations for the parameter distributions of the generator and discriminator. We show that parameter clipping to satisfy the Lipschitz condition in the algorithm induces a discontinuous vector field in the mean field dynamics, which gives rise to blow-up in finite time of the mean field dynamics. We look into a specific toy example that shows that all solutions to the mean field equations converge in the long time limit to time periodic solutions, this helps explain the failure to converge of the algorithm.
Hierarchical Decision Making Based on Structural Information Principles
Authors: Xianghua Zeng; Hao Peng; Dingli Su; Angsheng Li
Venue: JMLR 2025 (main)

Abstract: Hierarchical Reinforcement Learning (HRL) is a promising approach for managing task complexity across multiple levels of abstraction and accelerating long-horizon agent exploration. However, the effectiveness of hierarchical policies heavily depends on prior knowledge and manual assumptions about skill definitions and task decomposition. In this paper, we propose a novel Structural Information principles-based framework, namely SIDM, for hierarchical Decision Making in both single-agent and multi-agent scenarios. Central to our work is the utilization of structural information embedded in the decision-making process to adaptively and dynamically discover and learn hierarchical policies through environmental abstractions. Specifically, we present an abstraction mechanism that processes historical state-action trajectories to construct abstract representations of states and actions. We define and optimize directed structural entropyâa metric quantifying the uncertainty in transition dynamics between abstract statesâto discover skills that capture key transition patterns in RL environments. Building on these findings, we develop a skill-based learning method for single-agent scenarios and a role-based collaboration method for multi-agent scenarios, both of which can flexibly integrate various underlying algorithms for enhanced performance. Extensive evaluations on challenging benchmarks demonstrate that our framework significantly and consistently outperforms state-of-the-art baselines, improving the effectiveness, efficiency, and stability of policy learning by up to 32.70%, 64.86%, and 88.26%, respectively, as measured by average rewards, convergence timesteps, and standard deviations.
Early Alignment in Two-Layer Networks Training is a Two-Edged Sword
Authors: Etienne Boursier; Nicolas Flammarion
Venue: JMLR 2025 (main)

Abstract: Training neural networks with first order optimisation methods is at the core of the empirical success of deep learning. The scale of initialisation is a crucial factor, as small initialisations are generally associated to a feature learning regime, for which gradient descent is implicitly biased towards simple solutions. This work provides a general and quantitative description of the early alignment phase, originally introduced by Maennel et al. (2018). For small initialisation and one hidden ReLU layer networks, the early stage of the training dynamics leads to an alignment of the neurons towards key directions. This alignment induces a sparse representation of the network, which is directly related to the implicit bias of gradient flow  at convergence. This sparsity inducing alignment however comes at the expense of difficulties in minimising the training objective: we also provide a simple data example for which overparameterised networks fail to converge towards global minima and only converge to a spurious stationary point instead.
Imprecise Multi-Armed Bandits: Representing Irreducible Uncertainty as a Zero-Sum Game
Authors: Vanessa Kosoy
Venue: JMLR 2025 (main)

Abstract: We introduce a novel multi-armed bandit framework, where each arm is associated with a fixed unknown credal set over the space of outcomes (which can be richer than just the reward). The arm-to-credal-set correspondence comes from a known class of hypotheses. We then define a notion of regret corresponding to the lower prevision defined by these credal sets. Equivalently, the setting can be regarded as a two-player zero-sum game, where, on each round, the agent chooses an arm and the adversary chooses the distribution over outcomes from a set of options associated with this arm. The regret is defined with respect to the value of game. For certain natural hypothesis classes, loosely analogous to stochastic linear bandits (which are a special case of the resulting setting), we propose an algorithm and prove a corresponding upper bound on regret.
Optimizing Return Distributions with Distributional Dynamic Programming
Authors: Bernardo Ãvila Pires; Mark Rowland; Diana Borsa; Zhaohan Daniel Guo; Khimya Khetarpal; AndrÃ© Barreto; David Abel; RÃ©mi Munos; Will Dabney
Venue: JMLR 2025 (main)

Abstract: We introduce distributional dynamic programming (DP) methods for optimizing statistical functionals of the return distribution, with standard reinforcement learning as a special case. Previous distributional DP methods could optimize the same class of expected utilities as classic DP. To go beyond, we combine distributional DP with stock augmentation, a technique previously introduced for classic DP in the context of risk-sensitive RL, where the MDP state is augmented with a statistic of the rewards obtained since the first time step. We find that a number of recently studied problems can be formulated as stock-augmented return distribution optimization, and we show that we can use distributional DP to solve them. We analyze distributional value and policy iteration, with bounds and a study of what objectives these distributional DP methods can or cannot optimize. We describe a number of applications outlining how to use distributional DP to solve different stock-augmented return distribution optimization problems, for example maximizing conditional value-at-risk, and homeostatic regulation. To highlight the practical potential of stock-augmented return distribution optimization and distributional DP, we introduce an agent that combines DQN and the core ideas of distributional DP, and empirically evaluate it for solving instances of the applications discussed.
Exponential Family Graphical Models: Correlated Replicates and Unmeasured Confounders, with Applications to fMRI Data
Authors: Yanxin Jin; Yang Ning; Kean Ming Tan
Venue: JMLR 2025 (main)

Abstract: Graphical models have been used extensively for modeling brain connectivity networks. However, unmeasured confounders and correlations among measurements are often overlooked during model fitting, which may lead to spurious scientific discoveries. Motivated by functional magnetic resonance imaging (fMRI) studies, we propose a novel method for constructing brain connectivity networks with correlated replicates and latent effects. In a typical fMRI study, each participant is scanned and fMRI measurements are collected across a period of time. In many cases, subjects may have different states of mind that cannot be measured during the brain scan: for instance, some subjects may be awake during the first half of the brain scan, and may fall asleep during the second half of the brain scan. To model the correlation among replicates and latent effects induced by the different states of mind, we assume that the correlated replicates within each independent subject follow a one-lag vector autoregressive model, and that the latent effects induced by the unmeasured confounders are piecewise constant. Theoretical guarantees are established for parameter estimation. We demonstrate via extensive numerical studies that our method is able to estimate latent variable graphical models with correlated replicates more accurately than existing methods.
Learning from Similar Linear Representations: Adaptivity, Minimaxity, and Robustness
Authors: Ye Tian; Yuqi Gu; Yang Feng
Venue: JMLR 2025 (main)

Abstract: Representation multi-task learning (MTL) has achieved tremendous success in practice. However, the theoretical understanding of these methods is still lacking. Most existing theoretical works focus on cases where all tasks share the same representation, and claim that MTL almost always improves performance. Nevertheless, as the number of tasks grows, assuming all tasks share the same representation is unrealistic. Furthermore, empirical findings often indicate that a shared representation does not necessarily improve single-task learning performance. In this paper, we aim to understand how to learn from tasks with similar but not exactly the same linear representations, while dealing with outlier tasks. Assuming a known intrinsic dimension, we propose a penalized empirical risk minimization method and a spectral method that are adaptive to the similarity structure and robust to outlier tasks. Both algorithms outperform single-task learning when representations across tasks are sufficiently similar and the proportion of outlier tasks is small. Moreover, they always perform at least as well as single-task learning, even when the representations are dissimilar. We provide information-theoretic lower bounds to demonstrate that both methods are nearly minimax optimal in a large regime, with the spectral method being optimal in the absence of outlier tasks. Additionally, we introduce a thresholding algorithm to adapt to an unknown intrinsic dimension. We conduct extensive numerical experiments to validate our theoretical findings.
Multiple Instance Verification
Authors: Xin Xu; Eibe Frank; Geoffrey Holmes
Venue: JMLR 2025 (main)

Abstract: We explore multiple instance verification, a problem setting in which a query instance is verified against a bag of target instances with heterogeneous, unknown relevancy. We show that naive adaptations of attention-based multiple instance learning (MIL) methods and standard verification methods like Siamese neural networks are unsuitable for this setting: directly combining state-of-the-art (SOTA) MIL methods and Siamese networks is shown to be no better, and sometimes significantly worse, than a simple baseline model. Postulating that this may be caused by the failure of the representation of the target bag to incorporate the query instance, we introduce a new pooling approach named âcross-attention poolingâ (CAP). Under the CAP framework, we propose two novel attention functions to address the challenge of distinguishing between highly similar instances in a target bag. Through empirical studies on three different verification tasks, we demonstrate that CAP outperforms adaptations of SOTA MIL methods and the baseline by substantial margins, in terms of both classification accuracy and the ability to detect key instances. The superior ability to identify key instances is attributed to the new attention functions by ablation studies.
EF21 with Bells & Whistles: Six Algorithmic Extensions of Modern Error Feedback
Authors: Ilyas Fatkhullin; Igor Sokolov; Eduard Gorbunov; Zhize Li; Peter RichtÃ¡rik
Venue: JMLR 2025 (main)

Abstract: First proposed by Seide (2014) as a heuristic, error feedback (EF) is a very popular mechanism for enforcing convergence of distributed gradient-based optimization methods enhanced with communication compression strategies based on the application of contractive compression operators. However, existing theory of EF relies on very strong assumptions (e.g., bounded gradients), and provides pessimistic convergence rates (e.g., while the best known rate for EF in the smooth nonconvex regime, and when full gradients are compressed, is $O(1/T^{2/3})$, the rate of gradient descent in the same regime is $O(1/T)$). Recently, RichtÃ rik et al. (2021) proposed a new error feedback mechanism, EF21, based on the construction of a Markov compressor induced by a contractive compressor. EF21 removes the aforementioned theoretical deficiencies of EF and at the same time works better in practice. In this work we propose six practical extensions of EF21, all supported by strong convergence theory: partial participation, stochastic approximation, variance reduction, proximal setting, momentum, and bidirectional compression. To the best of our knowledge, several of these techniques have not been previously analyzed in combination with EF, and in cases where prior analysis exists---such as for bidirectional compression---our theoretical convergence guarantees significantly improve upon existing results.
Model-free Change-Point Detection Using AUC of a Classifier
Authors: Rohit Kanrar; Feiyu Jiang; Zhanrui Cai
Venue: JMLR 2025 (main)

Abstract: In contemporary data analysis, it is increasingly common to work with non-stationary complex data sets. These data sets typically extend beyond the classical low-dimensional Euclidean space, making it challenging to detect shifts in their distribution without relying on strong structural assumptions. This paper proposes a novel offline change-point detection method that leverages classifiers developed in the statistics and machine learning community.  With suitable data splitting, the test statistic is constructed through sequential computation of the Area Under the Curve (AUC) of a classifier, which is trained on data segments on both ends of the sequence. It is shown that the resulting AUC process attains its maxima at the true change-point location, which facilitates the change-point estimation. The proposed method is characterized by its complete nonparametric nature, high versatility, considerable flexibility, and absence of stringent assumptions on the underlying data or any distributional shifts. Theoretically, we derive the limiting pivotal distribution of the proposed test statistic under null, as well as the asymptotic behaviors under both local and fixed alternatives. The localization rate of the change-point estimator is also provided. Extensive simulation studies and the analysis of two real-world data sets illustrate the superior performance of our approach compared to existing model-free change-point detection methods.
A New Random Reshuffling Method for Nonsmooth Nonconvex Finite-sum Optimization
Authors: Junwen Qiu; Xiao Li; Andre Milzarek
Venue: JMLR 2025 (main)

Abstract: Random reshuffling techniques are prevalent in large-scale applications, such as training neural networks. While the convergence and acceleration effects of random reshuffling-type methods are fairly well understood in the smooth setting, much less studies seem available in the nonsmooth case. In this work, we design a new normal map-based proximal random reshuffling (norm-PRR) method for nonsmooth nonconvex finite-sum problems. We show that norm-PRR achieves the iteration complexity ${\cal O}(n^{-1/3}T^{-2/3})$ where $n$ denotes the number of component functions $f(\cdot,i)$ and $T$ counts the total number of iterations. This improves the currently known complexity bounds for this class of problems by a factor of $n^{-1/3}$ in terms of the number of gradient evaluations.  Additionally, we prove that norm-PRR converges linearly under the (global) Polyak-Åojasiewicz condition and in the interpolation setting. We further complement these non-asymptotic results and provide an in-depth analysis of the asymptotic properties of norm-PRR. Specifically, under the (local) Kurdyka-Åojasiewicz  inequality, the whole sequence of iterates generated by norm-PRR is shown to converge to a single stationary point. Moreover, we derive last-iterate convergence rates that can match those in the smooth, strongly convex setting. Finally, numerical experiments are performed on nonconvex classification tasks to illustrate the efficiency of the proposed approach.