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.
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: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:2608. 01357v1 Announce Type: new Abstract: Traditional approximation theory measures convergence rates in terms of the number of parameters or degrees of freedom.
arXiv:2606. 29043v1 Announce Type: new Abstract: Sharpness and complexity are two central factors in the generalization analysis of deep neural networks.
arXiv:2511. 02496v2 Announce Type: replace Abstract: We study latent geometry as an explicit component of representation quality in data-scarce learning.
arXiv:2607. 05546v1 Announce Type: cross Abstract: We develop a unified function space theory of deep fully connected neural networks.
arXiv:2603. 22962v3 Announce Type: replace Abstract: We study the theoretical behavior of denoising score matching--the learning task associated to diffusion models--when the data distribution is supported on a low-dimensional manifold and the score is parameterized using a random feature neural network.
arXiv:2512. 21315v2 Announce Type: replace Abstract: The data processing inequality is an information-theoretic principle stating that the information content of a signal cannot be increased by processing the observations.
arXiv:2501. 10538v3 Announce Type: replace Abstract: The practical success of deep learning has led to the discovery of several surprising phenomena.