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.
By Khoat Than, Dat Phan
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:2311. 02960v5 Announce Type: replace Abstract: Over the past decade, deep learning has proven to be a highly effective tool for learning meaningful features from raw data.
By Peng Wang, Xiao Li, Can Yaras, Zhihui Zhu, Laura Balzano, Wei Hu, Qing Qu
arXiv:2505.09716v4 Announce Type: replace
Abstract: Out-of-distribution (OOD) generalisation through composition requires a system to discover invariant properties from input-output associations and...
By George Dimitriadis, Spyridon Samothrakis
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.
By Shaojie Li, Yunbei Xu
The paper introduces Neural Low-Degree Filtering (Neural LoFi), a stylized limit of gradient-based training that turns hierarchical feature learning into an explicit iterative spectral procedure. In this framework, each layer independently selects directions with maximal low-degree correlation to the label, providing a tractable surrogate for deep learning and a kernel-space interpretation. Experiments on fully connected and convolutional networks show that Neural LoFi outperforms lazy random-feature baselines, recovers meaningful structured filters, and aligns with early gradient-descent feature discovery on real datasets.
By Yatin Dandi, Matteo Vilucchio, Luca Arnaboldi, Hugo Tabanelli, Florent Krzakala