arXiv:2607. 01010v1 Announce Type: cross Abstract: The success of deep learning models in classification and regression is widely attributed to the low-dimensional structure that real-world data tend to exhibit, despite their high-dimensional representation.
arXiv:2606. 30822v1 Announce Type: cross Abstract: In this paper, we attempt to enhance the theoretical understanding of convolutional neural networks (CNNs) as feature extractors in classification tasks by analyzing them through the lens of Cover's function-counting theory.
The paper investigates how many data samples per domain are needed for effective learning across multiple domains. It derives criteria from learning bounds that reveal an inverse linear relationship between the number of training domains and the required samples per domain, offering theoretical guidance for dataset adequacy and construction. The study also establishes a close link between in-domain learning and out-of-domain generalization through new generalization bounds.
arXiv:2606. 31110v1 Announce Type: new Abstract: Artificial neural networks (NNs) and machine learning (ML) algorithms are poorly understood from a theoretical perspective, which makes it difficult to fully realize their potential and overcome their weaknesses.
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.
arXiv:2608.24007v1 Announce Type: new Abstract: Understanding how neural networks learn and organize features is central to understanding their behavior. Much existing theory of feature learning has...
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:2506. 16704v3 Announce Type: replace Abstract: We study a fundamental question of domain generalization: given a family of domains (i.
arXiv:2606. 07007v1 Announce Type: cross Abstract: We propose a unified mathematical framework for a geometric understanding of concept learning and neuron interpretation in sparse autoencoders (SAEs).
arXiv:2609.39512v1 Announce Type: new Abstract: The small-sample learning problem remains a fundamental challenge in machine learning because limited training data lead to unstable model estimation a...
arXiv:2608. 01357v1 Announce Type: new Abstract: Traditional approximation theory measures convergence rates in terms of the number of parameters or degrees of freedom.
arXiv:2603.25579v2 Announce Type: replace-cross Abstract: A key capability of modern neural networks is their capacity to simultaneously learn underlying rules and memorize specific facts or exceptio...
arXiv:2606. 29043v1 Announce Type: new Abstract: Sharpness and complexity are two central factors in the generalization analysis of deep neural networks.