Sparse Super-Regular Networks

• URL: http://arxiv.org/abs/2201.01363v1
• Date: Tue, 4 Jan 2022 22:07:55 GMT
• Title: Sparse Super-Regular Networks
• Authors: Andrew W.E. McDonald and Ali Shokoufandeh
• Abstract summary: It has been argued 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. We show that SRNs perform similarly to X-Nets via readily reproducible experiments, and offer far greater guarantees and control over network structure.
• Score: 0.44689528869908496
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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