arXiv:2505. 24849v2 Announce Type: replace-cross Abstract: For three decades statistical mechanics has been providing a framework to analyse neural networks.
By Jean Barbier, Francesco Camilli, Minh-Toan Nguyen, Mauro Pastore, Rudy Skerk
arXiv:2510. 24616v4 Announce Type: replace-cross Abstract: For four decades statistical physics has been providing a framework to analyse neural networks.
By Jean Barbier, Francesco Camilli, Minh-Toan Nguyen, Mauro Pastore, Rudy Skerk
arXiv:2606. 28242v1 Announce Type: cross Abstract: Understanding how performance scales jointly with model size and data is a central problem in modern machine learning.
By Julius Girardin, Emanuele Troiani, Yizhou Xu, Vittorio Erba, Florent Krzakala, Lenka Zdeborov\'a
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
The paper investigates how the geometry of teacher neural networks affects the learnability of student networks in teacher‑student setups. By formalizing learnability as the success rate of reaching the global minimum, the authors identify two teacher distributions—one maximizing node dissimilarity (easy) and one minimizing it (hard)—that lead to markedly different success rates across various settings and activation functions. They analyze the loss landscape of small networks, revealing two types of suboptimal local minima (out‑of‑bounds and interior) whose attraction regions depend on teacher structure, and demonstrate that adjusting learning rates for the readout layer and inner biases can improve success rates.
whyItMatters:"The study highlights that teacher geometry, often overlooked, plays a crucial role in determining how effectively a student network can learn, offering guidance for designing more realistic teacher‑student experiments."
By Kai J. Sandbrink, Flavio Martinelli, Alexander van Meegen, Wulfram Gerstner, Johanni Brea
arXiv:2505. 22578v2 Announce Type: replace Abstract: The optimization of neural networks under weight decay remains poorly understood from a theoretical standpoint.
By Etienne Boursier, Matthew Bowditch, Matthias Englert, Ranko Lazic