Sparse Super-Regular Networks

It has been argued by Thom and Palm that sparsely-connected neural networks (SCNs) show improved performance over fully-connected networks (FCNs). Super-regular networks (SRNs) are neural networks composed of a set of stacked sparse layers of (epsilon, delta)-super-regular pairs, and randomly permuted node order. Using the Blow-up Lemma, we prove that as a result of the individual super-regularity of each pair of layers, SRNs guarantee a number of properties that make them suitable replacements for FCNs for many tasks. These guarantees include edge uniformity across all large-enough subsets, minimum node in- and out-degree, input-output sensitivity, and the ability to embed pre-trained constructs. Indeed, SRNs have the capacity to act like FCNs, and eliminate the need for costly regularization schemes like Dropout. We show that SRNs perform similarly to X-Nets via readily reproducible experiments, and offer far greater guarantees and control over network structure.