arXiv:2501. 18530v3 Announce Type: replace-cross Abstract: We consider a teacher-student model of supervised learning with a fully-trained two-layer neural network whose width $k$ and input dimension $d$ are large and proportional.
arXiv:2505. 24849v2 Announce Type: replace-cross Abstract: For three decades statistical mechanics has been providing a framework to analyse neural networks.
arXiv:2510. 24616v4 Announce Type: replace-cross Abstract: For four decades statistical physics has been providing a framework to analyse neural networks.
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.
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.
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."
arXiv:2505. 22578v2 Announce Type: replace Abstract: The optimization of neural networks under weight decay remains poorly understood from a theoretical standpoint.
arXiv:2609.07755v1 Announce Type: new Abstract: Understanding generalization remains a central challenge in machine learning because it requires jointly considering data, architecture, and training d...
arXiv:2605.12597v3 Announce Type: replace-cross Abstract: Computational sampling has been central to the sciences since the mid-20th century. While machine-learning-based approaches have recently ena...
arXiv:2606. 00340v1 Announce Type: new Abstract: We study optimal learning-rate selection in two-layer and three-layer linear neural networks trained to learn linear target functions.
arXiv:2607. 27000v1 Announce Type: cross Abstract: Optimization in non-convex neural network models is strongly influenced by the geometry of the solution space: sparse, isolated, point-like clusters are typically algorithmically inaccessible, whereas wide and flat regions can be found efficiently despite being relatively rare.
arXiv:2610.00420v1 Announce Type: new Abstract: A weight space network (or metanetwork) takes the weights of another neural network as input and predicts properties of it. Most prior work trains such...
arXiv:2512. 22088v3 Announce Type: replace-cross Abstract: The scaling law, a cornerstone of Large Language Model (LLM) development, predicts improvements in model performance with increasing computational resources.