Weakly-correlated synapses promote dimension reduction in deep neural networks

TL;DR

This paper presents a theoretical model showing that weakly-correlated synapses facilitate dimension reduction in deep neural networks, influencing neural decorrelation and network efficiency.

Contribution

It introduces a simplified, self-consistent model linking synaptic correlations to dimension reduction, supported by theoretical analysis and numerical simulations.

Findings

Weakly-correlated synapses promote dimension reduction.

Synapses slow down decorrelation along network depth.

Theoretical predictions match numerical simulations.

Abstract

By controlling synaptic and neural correlations, deep learning has achieved empirical successes in improving classification performances. How synaptic correlations affect neural correlations to produce disentangled hidden representations remains elusive. Here we propose a simplified model of dimension reduction, taking into account pairwise correlations among synapses, to reveal the mechanism underlying how the synaptic correlations affect dimension reduction. Our theory determines the synaptic-correlation scaling form requiring only mathematical self-consistency, for both binary and continuous synapses. The theory also predicts that weakly-correlated synapses encourage dimension reduction compared to their orthogonal counterparts. In addition, these synapses slow down the decorrelation process along the network depth. These two computational roles are explained by the proposed mean-field equation. The theoretical predictions are in excellent agreement with numerical simulations, and the key features are also captured by a deep learning with Hebbian rules.