arXiv:2606. 21593v2 Announce Type: replace Abstract: Deep neural networks transform input data into latent representations that support a wide range of downstream tasks.
arXiv:2607. 01311v1 Announce Type: new Abstract: Deep learning has outgrown any single mathematical explanation.
arXiv:2606. 30512v1 Announce Type: cross Abstract: Why overparameterised deep networks generalise so remarkably well remains one of the most stubborn open questions in machine learning theory.
arXiv:2606. 16579v1 Announce Type: new Abstract: We extend the entropy formula of Menon and Yu for the real Deep Linear Network (DLN) to its complex and quaternionic analogues, obtaining a unified formula for DLNs over $\mathbb{R}$, $\mathbb{C}$, and $\mathbb{H}$.
arXiv:2511. 02003v2 Announce Type: replace Abstract: We present the bulk--boundary decomposition as a new framework for understanding the training dynamics of deep neural networks.
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:2610. 21820v1 Announce Type: new Abstract: How depth and width of neural networks shape learned representations is usually studied only after training.
arXiv:2501. 02436v5 Announce Type: replace Abstract: Advancements in artificial intelligence call for a deeper understanding of the fundamental mechanisms underlying deep learning.
arXiv:2509. 23544v2 Announce Type: replace-cross Abstract: Many modern applications involve predicting structured, non-Euclidean outputs such as probability distributions, networks, and symmetric positive-definite matrices.
arXiv:2607. 21366v1 Announce Type: cross Abstract: Deep neural networks encode complex representations, but deconstructing this internal knowledge remains a challenge.
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:2505. 23869v4 Announce Type: replace-cross Abstract: A proposition that connects randomness and compression is put forward via Gibbs entropy over set of measurement vectors associated with a compression process.