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.
arXiv:2509. 24882v2 Announce Type: replace Abstract: Neural scaling laws underlie many of the recent advances in deep learning, yet their theoretical understanding remains largely confined to linear models.
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: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.
The paper introduces a pointwise generalization theory for fully connected deep neural networks, using a pointwise Riemannian Dimension derived from eigenvalues of learned feature representations across layers. This framework provides hypothesis-dependent, representation-aware generalization bounds that are significantly tighter than traditional size- or norm-based approaches, both theoretically and experimentally. The authors analytically identify structural properties that explain deep networks’ tractability and empirically show that the pointwise Riemannian Dimension captures feature compression, over‑parameterization effects, and optimizer bias.
arXiv:2607. 16720v1 Announce Type: new Abstract: Understanding deep neural networks remains a central challenge in machine learning.
arXiv:2502. 11152v4 Announce Type: replace-cross Abstract: The optimization foundations of deep linear networks have recently received significant attention.
arXiv:2505. 22578v2 Announce Type: replace Abstract: The optimization of neural networks under weight decay remains poorly understood from a theoretical standpoint.
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.
arXiv:2504.16450v4 Announce Type: replace Abstract: We derive a differential equation that governs the evolution of the generalization gap when a model is trained by gradient descent-based methods. T...
arXiv:2505. 21423v3 Announce Type: replace Abstract: The remarkable generalization properties of overparameterized networks are often attributed to implicit biases, such as norm minimization at small learning rates and low sharpness in the Edge-of-Stability regime.
arXiv:2602. 10545v2 Announce Type: replace-cross Abstract: Modern large-scale neural networks are often trained and released in multiple sizes to accommodate diverse inference budgets.
arXiv:2503. 07325v2 Announce Type: replace Abstract: Understanding and certifying the behavior of modern deep neural networks remains a fundamental challenge in reliable machine learning.