Grassmannian Packings in Neural Networks: Learning with Maximal Subspace Packings for Diversity and Anti-Sparsity

Abstract

Kernel sparsity ("dying ReLUs") and lack of diversity are commonly observed in CNN kernels, which decreases model capacity. Drawing inspiration from information theory and wireless communications, we demonstrate the intersection of coding theory and deep learning through the Grassmannian subspace packing problem in CNNs. We propose Grassmannian packings for initial kernel layers to be initialized maximally far apart based on chordal or Fubini-Study distance. Convolutional kernels initialized with Grassmannian packings exhibit diverse features and obtain diverse representations. We show that Grassmannian packings, especially in the initial layers, address kernel sparsity and encourage diversity, while improving classification accuracy across shallow and deep CNNs with better convergence rates.