arXiv:2606. 08308v1 Announce Type: new Abstract: Predicting the generalization performance of deep neural networks without relying on hold-out validation data is a fundamental challenge in machine learning.
arXiv:2510.05606v2 Announce Type: replace Abstract: Fundamental limits to predictability are central to our understanding of many physical and computational systems. In deep learning, training outcom...
arXiv:2206. 04359v3 Announce Type: replace Abstract: One of the fundamental challenges in the deep learning community is to theoretically understand how well a deep neural network generalizes to unseen data.
arXiv:2505. 11766v4 Announce Type: replace Abstract: Neural Operators (NOs) are powerful architectures for learning mappings between function spaces.
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:2606. 06772v2 Announce Type: replace-cross Abstract: Characterizing the optimization dynamics and statistical performance of over-parameterized deep neural networks (DNNs) remains a central challenge in understanding the remarkable success of deep learning.
arXiv:2606. 06772v1 Announce Type: cross Abstract: Understanding the generalization performance of over-parameterized neural networks has become a central topic in deep learning theory.
arXiv:2605. 27991v2 Announce Type: replace-cross Abstract: Gradient-flow optimization is usually viewed as an algorithmic procedure for minimizing empirical loss, with training duration selected by validation or heuristic early-stopping rules.
Tsallis statistics generalizes Boltzmann-Gibbs statistical mechanics through a single real parameter $q$ that controls the weight assigned to rare and frequent events. Originally proposed to describe physical systems with long-range correlations, multifractal geometry, and heavy-tailed fluctuations, the framework has become a recurring ingredient in modern artificial intelligence (AI): it underlies sparse attention mechanisms (\textsc{sparsemax} and $α$-\textsc{entmax}), maximum-entropy reinforcement learning with controllable exploration, robust and heavy-tailed probabilistic models, and a family of generalized loss functions and regularizers.
arXiv:2505. 13196v3 Announce Type: replace-cross Abstract: We introduce Velocity-Regularized Adam (VRAdam), a physics-inspired optimizer for training deep neural networks that draws on ideas from quartic terms for kinetic energy with its stabilizing effects on various system dynamics.
arXiv:2606. 13818v1 Announce Type: new Abstract: This thesis investigates how Bayesian principles can deepen our understanding of modern deep learning systems.
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:2606. 16575v1 Announce Type: new Abstract: Deep neural networks (DNNs) have achieved remarkable success in scientific computing, yet they often suffer from spectral bias in capturing oscillatory and multiscale behaviors.