arXiv Machine Learning By Yuki Kurumadani

Upper Bounds for Local Learning Coefficients of Three-Layer Neural Networks

Read the original on arXiv Machine Learning →

arXiv:2603. 12785v2 Announce Type: replace Abstract: Three-layer neural networks are known to form singular learning models, and their Bayesian asymptotic behavior is governed by the learning coefficient, or real log canonical threshold.

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arXiv Machine Learning
Aug 21

Exact Algebraic Computation of Learning Coefficients for Two-Dimensional Singular Models

arXiv:2608. 20183v1 Announce Type: new Abstract: Classical information criteria such as the Bayesian Information Criterion (BIC) rely on regularity assumptions that break down for singular models, leading to incorrect model selection in settings such as deep learning.

By Gr\'egoire Sergeant-Perthuis (CQSB, Sorbonne Universit\'e), Elias Tsigaridas (Ouragan Team, INRIA), Jules Tsukahara (Ouragan Team, INRIA)
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.

By Yanming Lai, Defeng Sun, Yang Wang
arXiv AI
Sep 24

Path Regularization: A Near-Complete and Optimal Nonasymptotic Generalization Theory for Multilayer Neural Networks and Double Descent Phenomenon

The paper presents a near-complete, nonasymptotic generalization theory for multilayer neural networks using path regularization, applicable to broad Lipschitz loss functions without requiring bounded loss or extreme network hyperparameters. It provides an explicit upper bound that addresses approximation rates in generalized Barron spaces and demonstrates the double descent phenomenon for ReLU networks. The authors claim near-minimax optimality for regression problems and plan to establish matching lower bounds in future work.

By Hao Yu