arXiv AI
Understanding Deep Learning via Entropy Space Theory
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Geometric and Information Compression of Representations in Deep Learning
arXiv:2606. 21593v2 Announce Type: replace Abstract: Deep neural networks transform input data into latent representations that support a wide range of downstream tasks.
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From Approximation to Emergence: A Theory of Deep Learning
arXiv:2607. 01311v1 Announce Type: new Abstract: Deep learning has outgrown any single mathematical explanation.
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Informational Frustration in Neural Manifolds: Shannon Bottlenecks and the Limits of Learnability
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.
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On the Entropy Formula for Real, Complex, and Quaternionic Deep Linear Networks
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 $\mathbb{H}$.
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Jun 9
Bulk-boundary decomposition of neural networks
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.
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Do Neural Networks Really Beat the Curse of Dimensionality? A Bit-Complexity View
arXiv:2608. 01357v1 Announce Type: new Abstract: Traditional approximation theory measures convergence rates in terms of the number of parameters or degrees of freedom.