arXiv:2607. 01311v1 Announce Type: new Abstract: Deep learning has outgrown any single mathematical explanation.
arXiv:2501. 02436v5 Announce Type: replace Abstract: Advancements in artificial intelligence call for a deeper understanding of the fundamental mechanisms underlying deep learning.
arXiv:2501. 07400v2 Announce Type: replace-cross Abstract: We derive explicit equations governing the cumulative biases and weights in Deep Learning with ReLU activation function, based on gradient descent for the Euclidean loss in the input layer, and under the assumption that the weights are, in a precise sense, adapted to the coordinate system distinguished by the activations.
arXiv:2606. 06624v1 Announce Type: new Abstract: In the current era of deep learning and especially generative models, there is significant investment in training very large generative models.
arXiv:2607. 16329v1 Announce Type: cross Abstract: Lipschitz continuity is a fundamental property of neural networks that characterizes their sensitivity to input perturbations.
arXiv:2602. 04078v2 Announce Type: replace-cross Abstract: Deep learning has achieved remarkable success across a wide range of domains, significantly expanding the frontiers of what is achievable in artificial intelligence.
arXiv:2606. 20299v1 Announce Type: cross Abstract: Deep learning has managed to evade numerous intuitions from classical statistics to achieve unprecedented performance on a number of real-world tasks.
arXiv:2607. 07884v1 Announce Type: new Abstract: In this short note we consider the gradient descent dynamics of deep scalar linear networks, $f(x) = \prod_{l=1}^L w_l x$, which enjoy exact time-course solutions for any integer depth.
arXiv:2606. 01302v1 Announce Type: new Abstract: Modern large-scale deep learning exhibits two striking empirical phenomena: behavioural scaling laws (predictable performance gains with increasing scale) and emergent mechanisms (structured internal representations and circuits in deep neural networks).
arXiv:2606. 13818v1 Announce Type: new Abstract: This thesis investigates how Bayesian principles can deepen our understanding of modern deep learning systems.
arXiv:2607. 23397v1 Announce Type: new Abstract: Hierarchical neural networks are widely used in artificial intelligence, yet their mathematical properties remain incompletely understood.
arXiv:2608. 04442v1 Announce Type: new Abstract: Robustness to natural corruptions remains a fundamental challenge for deep neural networks.
arXiv:2509. 18025v2 Announce Type: replace-cross Abstract: One can see deep-learning models as compositions of functions within the so-called tame geometry.