Spectral Analysis of Information Flow and Local Contraction in Deep Neural Networks

This preprint presents a rigorous study of information flow in deep neural networks (DNNs) using spectral analysis of layer-wise Markov channels. We quantify layer-wise information compression and preservation through the local contraction coefficient α_loc derived from normalized mutual information (NMI) with Jensen-Shannon divergence. Experiments on multiple fully-connected architectures trained on MNIST demonstrate a consistent pattern: the second singular value s₂(M) of symmetrized channel matrices increases with layer depth, suggesting a two-stage information processing strategy—early-layer compression and late-layer preservation. Detailed methodology, results, discussion, and appendices are included.