arXiv Machine Learning
Jun 3
Generating Rectifiable Measures through Neural Networks
arXiv:2412. 05109v2 Announce Type: replace Abstract: We derive universal approximation results for the class of (countably) $m$-rectifiable measures.
Fast approximation and learning of binary classification tasks in o-minimal structures using ReLU neural networks
arXiv:2607. 01266v1 Announce Type: cross Abstract: We study binary classification problems whose decision sets are given by definable sets in o-minimal expansions of the real field.
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arXiv Machine Learning
Aug 4
Do Neural Networks Really Beat the Curse of Dimensionality? A Bit-Complexity View
arXiv:2608. 01357v1 Announce Type: new Abstract: Traditional approximation theory measures convergence rates in terms of the number of parameters or degrees of freedom.
arXiv Machine Learning
Jul 14
Approximation of Analytic Functions by ReLU Neural Networks with Adjustable Depth and Width
arXiv:2607. 10589v1 Announce Type: cross Abstract: In contrast to most studies on neural network approximation theory that characterize results through a single parameter, such as the total number of network parameters, \cite{shen2020deep} pioneered the characterization of approximation rates as a joint function of the width parameter $N$ and the depth parameter $L$, thereby granting greater architectural flexibility.
arXiv Machine Learning
Jun 16
Online Realizable Regression and Applications for ReLU Networks
arXiv:2602. 19172v2 Announce Type: replace Abstract: Realizable online regression can behave very differently from online classification.
arXiv Machine Learning
Jul 24
New Complexity-Theoretic Frontiers of Tractability for Neural Network Training
arXiv:2607. 20811v1 Announce Type: new Abstract: In spite of the fundamental role of neural networks in contemporary machine learning research, our understanding of the computational complexity of optimally training neural networks remains incomplete even when dealing with the simplest kinds of activation functions.
arXiv Machine Learning
Jul 27
Approximation and learning of anisotropic and mixed smooth functions by deep ReLU neural networks
arXiv:2605. 31152v2 Announce Type: replace-cross Abstract: This paper studies how efficiently deep ReLU neural networks can approximate and learn smooth functions.
Hugging Face Trending Papers
Jul 23
New Complexity-Theoretic Frontiers of Tractability for Neural Network Training
In spite of the fundamental role of neural networks in contemporary machine learning research, our understanding of the computational complexity of optimally training neural networks remains incomplete even when dealing with the simplest kinds of activation functions. Indeed, while there has been a number of very recent results that establish ever-tighter lower bounds for the problem under linear and ReLU activation functions, less progress has been made towards the identification of novel polynomial-time tractable network architectures.
arXiv Machine Learning
Jun 30
Replica Symmetry Breaking and Algorithmic Thresholds in Empirical Risk Minimization under Multi-Index Model
arXiv:2606. 28573v1 Announce Type: new Abstract: Modern machine learning models are trained by optimizing high-dimensional non-convex empirical risk functions.
arXiv Machine Learning
Aug 7
Worst-Case Distance-Aware Error Bounds for Neural Networks
arXiv:2510. 22021v3 Announce Type: replace Abstract: Safety-critical applications of machine learning require uncertainty estimates that support reliable worst-case analysis.
arXiv Machine Learning
Jun 3
Optimal Rates for Generalization of Gradient Descent for Deep ReLU Classification
arXiv:2510. 02779v4 Announce Type: replace Abstract: Recent advances have significantly improved our understanding of the generalization performance of gradient descent (GD) methods in deep neural networks.
arXiv Machine Learning
Aug 13
Linear-Core Surrogates: Smooth Loss Functions with Linear Rates for Classification and Structured Prediction
arXiv:2604. 27742v2 Announce Type: replace Abstract: A fundamental dichotomy in the theory of classification sets smoothness against statistical efficiency: smooth surrogate losses such as the logistic loss enable fast $O(1/T)$ optimization but yield slow square-root $H$-consistency bounds, while piecewise-linear losses like the Hinge loss achieve optimal linear $H$-consistency rates but are non-differentiable.
arXiv Machine Learning
Jul 8
Width-Robust Learnability in Mean-Field Bayesian Neural Networks
arXiv:2607. 05735v1 Announce Type: cross Abstract: Infinite-width limits are a standard way to reason about neural networks, but it is not automatic that the limiting learner has the same complexity-theoretic inductive bias as large finite networks.