arXiv Machine Learning

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.

arXiv AI
Jun 29

Derivation of effective gradient flow equations and dynamical truncation of training data in 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.

By Thomas Chen
arXiv Machine Learning
Jul 20

From Diffusion to Reaction-Diffusion: A Dynamical-Systems View of Oversmoothing in Hypergraph Neural Networks

arXiv:2607. 15773v1 Announce Type: new Abstract: Higher-order couplings enhance the expressive power of hypergraph neural networks (HGNNs), but they also intensify representation collapse in deep propagation due to strong multi-way feature mixing.

By Zhiheng Zhou, Mengyao Zhou, Yancheng Chen, Dengyi Zhao, Xingqin Qi, Guiying Yan
arXiv Machine Learning
Jul 1

Revisiting the Volume Hypothesis

arXiv:2606. 31282v1 Announce Type: new Abstract: Modern deep neural networks often contain far more parameters than needed to fit their training data, yet they achieve impressive generalization.

By Ari Pakman, Lior Kreimer, Yakir Berchenko